Finite Group Databasebeta

← #29695341

Subgroups — #29695341

Order 15616.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840404C211yesmaximal, characteristic
2C2×#16839735C211yesmaximal, characteristic, complemented
3C2×#99×D61C211yesmaximal, characteristic, complemented
4#21448669C211yesmaximal, characteristic, complemented
5#21448661C211yesmaximal, characteristic, complemented
6#21446653C211yesmaximal, characteristic, complemented
7#21446653C211yesmaximal, characteristic, complemented
8#21446278C211yesmaximal, characteristic, complemented
9#21446271C211yesmaximal, characteristic, complemented
10#21446271C211yesmaximal, characteristic, complemented
11#21445806C211yesmaximal, characteristic, complemented
12#21445736C211yesmaximal, characteristic, complemented
13#21445732C211yesmaximal, characteristic, complemented
14#21445606C211yesmaximal, characteristic, complemented
15C61×#1899C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18#16840404—21no—
19#16840404—21no—
20#16840404—21no—
21#16840404—21no—
22#16840404—21no—
23#16840404—21no—
24#16840404—21no—
25#16840404—21no—
26C2×#14519763C411yescharacteristic, complemented
27C2×#14519762C411yescharacteristic, complemented
28C2×#14519755C411yescharacteristic, complemented
29C2×#14519752C411yescharacteristic, complemented
30C2×#14519750C411yescharacteristic, complemented
31C2×#14519749C2211yescharacteristic
32C2×#14519747C411yescharacteristic, complemented
33C2×#14519747C2211yescharacteristic
34C2×#14519739C411yescharacteristic, complemented
35C2×#14519737C2211yescharacteristic
36C2×#14519736C2211yescharacteristic, complemented
37C22×#11758198C2211yescharacteristic
38C2×C22⋊C4×D61C411yescharacteristic, complemented
39C2×C22⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61C2211yescharacteristic
41#16839735—24no—
42C2×#14519692C2211yescharacteristic
43C2×#14519692C2211yescharacteristic
44C2×#14519691C2211yescharacteristic
45C2×#14519691C2211yescharacteristic
46C2×#14519691C2211yescharacteristic
47C2×#14519691C2211yescharacteristic
48C2×#14519691C2211yescharacteristic, complemented
49C2×#14519691C2211yescharacteristic, complemented
50C2×#14519691C2211yescharacteristic, complemented
51C2×#14519691C2211yescharacteristic, complemented
52#99×D61—24no—
53#16839654—21no—
54#16839653—21no—
55#16839652—21no—
56#16839651—21no—
57#16839636—21no—
58#16839633—21no—
59#16839625C2211yescharacteristic, complemented
60#16839620C2211yescharacteristic, complemented
61#16839620C2211yescharacteristic, complemented
62#16839617C2211yescharacteristic
63#16839617C2211yescharacteristic
64C22⋊C4×Dic61C2211yescharacteristic, complemented
65C22⋊C4×Dic61C2211yescharacteristic, complemented
66C4×#11758198—21no—
67#16839609—21no—
68#16839529C2211yescharacteristic, complemented
69#16839529C2211yescharacteristic, complemented
70C2×#123×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic, complemented
72C2×#99×C61C2211yescharacteristic
73C2×#99×C61C2211yescharacteristic
74C61×#381C2211yescharacteristic, complemented
75C61×#342C2211yescharacteristic, complemented
76C61×#342C2211yescharacteristic, complemented
77C24×D61C2×C411yescharacteristic
78C24×D61C2311yescharacteristic
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—21no—
82C2×#11758222—21no—
83C2×#11758222—22no—
84C2×#11758222—22no—
85C2×#11758222—41no—
86C2×#11758222—41no—
87C22×Dic122C2×C411yescharacteristic, complemented
88C22×D244C2×C411yescharacteristic
89C22×D244C2×C411yescharacteristic
90C22×D244C2×C411yescharacteristic
91C22×D244C2×C411yescharacteristic, complemented
92C22×C22⋊D61C2×C411yescharacteristic
93C22×C22⋊D61C2×C411yescharacteristic, complemented
94C22×C22⋊D61C2311yescharacteristic
95C22×C22⋊D61C2311yescharacteristic
96C2×D4×D61—21no—
97C2×D4×D61—21no—
98C2×D4×D61—21no—
99C2×D4×D61—21no—
100C2×D4×D61—22no—
101C2×D4×D61—22no—
102C2×D4×D61—41no—
103C2×D4×D61—41no—
104C23×Dic61C2311yescharacteristic
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61C2×C411yescharacteristic
108C22×C4×D61C2×C411yescharacteristic, complemented
109C22×C4×D61C2×C411yescharacteristic, complemented
110C22×C4×D61C2×C411yescharacteristic, complemented
111#14519763—21no—
112#14519763—21no—
113#14519763—21no—
114#14519763—21no—
115#14519762—21no—
116#14519762—21no—
117#14519762—21no—
118#14519762—21no—
119#14519755—21no—
120#14519755—21no—
121#14519755—21no—
122#14519755—21no—
123#14519752—21no—
124#14519752—21no—
125#14519752—21no—
126#14519752—21no—
127#14519750—21no—
128#14519750—21no—
129#14519750—21no—
130#14519750—21no—
131#14519749—21no—
132#14519749—21no—
133#14519749—21no—
134#14519749—21no—
135#14519747—21no—
136#14519747—21no—
137#14519747—21no—
138#14519747—21no—
139#14519747—21no—
140#14519747—21no—
141#14519747—21no—
142#14519747—21no—
143#14519739—21no—
144#14519739—21no—
145#14519739—21no—
146#14519739—21no—
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519736—22no—
152#14519736—41no—
153C2×C4⋊Dic61—21no—
154C2×#11758196—21no—
155C2×#11758196—21no—
156C2×#11758196C2×C411yescharacteristic, complemented
157C2×#11758196C2×C411yescharacteristic, complemented
158C2×C22⋊Dic61C2×C411yescharacteristic, complemented
159C2×C22⋊Dic61C2311yescharacteristic
160C2×C22⋊Dic61C2311yescharacteristic
161C2×C22⋊Dic61C2311yescharacteristic
162C2×C22⋊Dic61C2311yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198C2×C411yescharacteristic
170C2×#11758198C2×C411yescharacteristic
171C2×#11758198C2×C411yescharacteristic
172C2×#11758198C2×C411yescharacteristic
173C2×#11758198C2×C411yescharacteristic
174C2×#11758198C2×C411yescharacteristic
175C2×#11758198C2×C411yescharacteristic, complemented
176C2×#11758198C2×C411yescharacteristic, complemented
177C2×#11758198D411yescharacteristic
178C2×#11758198D411yescharacteristic
179C2×#11758198D411yescharacteristic
180C2×#11758198D411yescharacteristic
181C2×#11758198D411yescharacteristic
182C2×#11758198D411yescharacteristic
183C2×#11758198D411yescharacteristic
184C2×#11758198D411yescharacteristic
185C22⋊C4×D61—21no—
186C22⋊C4×D61—21no—
187C22⋊C4×D61—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61—22no—
190C22⋊C4×D61—22no—
191C22⋊C4×D61—41no—
192C22⋊C4×D61—41no—
193C2×C4×Dic61—21no—
194C2×C4×Dic61—21no—
195C2×C4×Dic61—21no—
196C2×C4×Dic61C2×C411yescharacteristic, complemented
197#14519692—22no—
198#14519692—41no—
199#14519691—22no—
200#14519691—22no—
201#14519691—22no—
202#14519691—22no—
203#14519691—22no—
204#14519691—41no—
205#14519691—41no—
206#14519691D414yescomplemented
207#14519684—21no—
208#14519684—21no—
209#14519684—21no—
210#14519684—21no—
211#14519684—21no—
212#14519684—21no—
213C22×D4×C61C2311yescharacteristic
214C23×C4×C61C2311yescharacteristic
215#123×C61—21no—
216#123×C61—21no—
217#123×C61—21no—
218#123×C61—21no—
219#117×C61—22no—
220#117×C61—41no—
221C2×C4⋊C4×C61—21no—
222C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
223C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
224C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
225C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
226C2×C22⋊C4×C61C2311yescharacteristic
227C2×C22⋊C4×C61C2311yescharacteristic
228C2×C22⋊C4×C61C2311yescharacteristic
229C2×C22⋊C4×C61C2311yescharacteristic
230C2×C22⋊C4×C61C2311yescharacteristic
231C2×C42×C61—21no—
232#99×C61—22no—
233#99×C61—41no—
234#95×C61—21no—
235#95×C61—21no—
236C24×C61C22×C411yescharacteristic
237C24×C61C2411yescharacteristic
238C23×D61—21no—
239C23×D61—21no—
240C23×D61—21no—
241C23×D61—21no—
242C23×D61—21no—
243C23×D61—21no—
244C23×D61—22no—
245C23×D61—42no—
246C23×D61—41no—
247C23×D61—42no—
248C23×D61—81no—
249C23×D61—81no—
250C23×D61C22×C411yescharacteristic
251C23×D61C22×C411yescharacteristic
252C23×D61C22×C411yescharacteristic
253C23×D61C22×C411yescharacteristic
254C23×D61C2×D411yescharacteristic
255C23×D61C2×D411yescharacteristic
256C23×D61C2×D411yescharacteristic
257C23×D61C2×D411yescharacteristic
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61C22×C411yescharacteristic
273C22×C4×C61C22×C411yescharacteristic
274C22×C4×C61C22×C411yescharacteristic
275C22×C4×C61C22×C411yescharacteristic
276C22×C4×C61C22×C411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2×D411yescharacteristic
281C2×C22⋊D61—21no—
282C2×C22⋊D61—21no—
283C2×C22⋊D61—21no—
284C2×C22⋊D61—21no—
285C2×C22⋊D61—21no—
286C2×C22⋊D61—21no—
287C2×C22⋊D61—21no—
288C2×C22⋊D61—21no—
289C2×C22⋊D61—21no—
290C2×C22⋊D61—21no—
291C2×C22⋊D61—21no—
292C2×C22⋊D61—21no—
293C2×C22⋊D61—21no—
294C2×C22⋊D61—21no—
295C2×C22⋊D61—22no—
296C2×C22⋊D61—41no—
297C2×C22⋊D61—81no—
298C2×C22⋊D61C2×D412yes—
299C2×C22⋊D61#4112yes—
300C22×Dic61—21no—
301C22×Dic61—21no—
302C22×Dic61—21no—
303C22×Dic61—21no—
304C22×Dic61—81no—
305C22×Dic61C22×C411yescharacteristic
306C22×Dic61C22×C411yescharacteristic
307C22×Dic61C22×C411yescharacteristic
308C22×Dic61C22×C411yescharacteristic
309C22×Dic61C2×D411yescharacteristic
310C22×Dic61C2×D411yescharacteristic
311C22×Dic61C2×D411yescharacteristic
312C22×Dic61C2×D411yescharacteristic
313D4×D61—42no—
314D4×D61—42no—
315D4×D61—42no—
316D4×D61—42no—
317D4×D61—42no—
318D4×D61—42no—
319D4×D61—42no—
320D4×D61—42no—
321#11758222—42no—
322#11758222—42no—
323#11758222—42no—
324#11758222—42no—
325#11758222—42no—
326#11758222—42no—
327#11758222—42no—
328#11758222—42no—
329C2×D244—21no—
330C2×D244—21no—
331C2×D244—21no—
332C2×D244—21no—
333C2×D244—22no—
334C2×D244—22no—
335C2×D244—21no—
336C2×D244—21no—
337C2×D244—21no—
338C2×D244—21no—
339C2×D244—41no—
340C2×D244—41no—
341C2×D244—42no—
342C2×D244—81no—
343C2×C4×D61—21no—
344C2×C4×D61—21no—
345C2×C4×D61—22no—
346C2×C4×D61—21no—
347C2×C4×D61—21no—
348C2×C4×D61—21no—
349C2×C4×D61—21no—
350C2×C4×D61—22no—
351C2×C4×D61—22no—
352C2×C4×D61—21no—
353C2×C4×D61—21no—
354C2×C4×D61—41no—
355C2×C4×D61—41no—
356C2×C4×D61—41no—
357C2×C4×D61—42no—
358C2×C4×D61—42no—
359C2×C4×D61—42no—
360C2×C4×D61—42no—
361C2×C4×D61—81no—
362C2×C4×D61—81no—
363C2×C4×D61—81no—
364C2×Dic122—21no—
365C2×Dic122—21no—
366C2×Dic122—22no—
367C2×Dic122—41no—
368C4⋊C4×C61—21no—
369C4⋊C4×C61—21no—
370C4⋊C4×C61—21no—
371C4⋊C4×C61—21no—
372C4⋊C4×C61—42no—
373C22⋊C4×C61—21no—
374C22⋊C4×C61—21no—
375C22⋊C4×C61—21no—
376C22⋊C4×C61—21no—
377C22⋊C4×C61—21no—
378C22⋊C4×C61—21no—
379C22⋊C4×C61—21no—
380C22⋊C4×C61—21no—
381C22⋊C4×C61—21no—
382C22⋊C4×C61—21no—
383C22⋊C4×C61—21no—
384C22⋊C4×C61—21no—
385C22⋊C4×C61—21no—
386C22⋊C4×C61C2×D412yes—
387C42×C61—42no—
388C22⋊Dic61—21no—
389C22⋊Dic61—21no—
390C22⋊Dic61—21no—
391C22⋊Dic61—21no—
392C22⋊Dic61—21no—
393C22⋊Dic61—21no—
394C22⋊Dic61—21no—
395C22⋊Dic61—21no—
396C22⋊Dic61—21no—
397C22⋊Dic61C2×D412yes—
398#11758198—21no—
399#11758198—21no—
400#11758198—21no—
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198—21no—
405#11758198—21no—
406#11758198—42no—
407#11758198—42no—
408#11758198—42no—
409#11758198—42no—
410#11758198—81no—
411#11758198—81no—
412#11758198C22⋊C411yescharacteristic
413#11758198C22⋊C411yescharacteristic
414#11758198C22⋊C411yescharacteristic
415#11758198C22⋊C411yescharacteristic
416#11758198C22⋊C411yescharacteristic
417#11758198C22⋊C411yescharacteristic
418#11758198C22⋊C411yescharacteristic
419#11758198C22⋊C411yescharacteristic
420#11758198C22⋊C411yescharacteristic
421#11758198C22⋊C411yescharacteristic
422#11758198C22⋊C411yescharacteristic
423#11758198C22⋊C411yescharacteristic
424#11758198C22⋊C411yescharacteristic
425#11758198C22⋊C411yescharacteristic
426#11758198C22⋊C411yescharacteristic
427#11758198C22⋊C411yescharacteristic
428C4⋊Dic61—42no—
429#11758196—21no—
430#11758196—21no—
431#11758196—21no—
432#11758196—21no—
433#11758196—81no—
434#11758196—81no—
435C4×Dic61—21no—
436C4×Dic61—21no—
437C4×Dic61—42no—
438C4×Dic61—81no—
439C4×Dic61—81no—
440C23×C61—21no—
441C23×C61—21no—
442C23×C61—21no—
443C23×C61—41no—
444C23×C61—41no—
445C23×C61—41no—
446C23×C61—41no—
447C23×C61C23×C411yescharacteristic
448C23×C61C22×D411yescharacteristic
449C23×C61C22×D411yescharacteristic
450C23×C61C22×D411yescharacteristic
451C23×C61C2×#4111yescharacteristic
452C23×C61H(5,𝔽2)11yescharacteristic
453C23×C61H(5,𝔽2)11yescharacteristic
454C22×D61—21no—
455C22×D61—21no—
456C22×D61—21no—
457C22×D61—21no—
458C22×D61—21no—
459C22×D61—21no—
460C22×D61—21no—
461C22×D61—21no—
462C22×D61—21no—
463C22×D61—21no—
464C22×D61—21no—
465C22×D61—21no—
466C22×D61—21no—
467C22×D61—21no—
468C22×D61—22no—
469C22×D61—22no—
470C22×D61—22no—
471C22×D61—21no—
472C22×D61—21no—
473C22×D61—21no—
474C22×D61—41no—
475C22×D61—41no—
476C22×D61—41no—
477C22×D61—41no—
478C22×D61—41no—
479C22×D61—41no—
480C22×D61—41no—
481C22×D61—41no—
482C22×D61—41no—
483C22×D61—42no—
484C22×D61—42no—
485C22×D61—42no—
486C22×D61—41no—
487C22×D61—41no—
488C22×D61—42no—
489C22×D61—41no—
490C22×D61—41no—
491C22×D61—81no—
492C22×D61—81no—
493C22×D61—82no—
494C22×D61—82no—
495C22×D61—82no—
496C22×D61—82no—
497C22×D61—84no—
498C22×D61—84no—
499C22×D61C2×C22⋊C411yescharacteristic
500C22×D61C2×C22⋊C411yescharacteristic
501C22×D61C2×C22⋊C411yescharacteristic
502C22×D61C2×C22⋊C411yescharacteristic
503C22×D61C4×D412yes—
504D4×C61—41no—
505D4×C61—41no—
506D4×C61—41no—
507D4×C61—41no—
508C2×C4×C61—21no—
509C2×C4×C61—21no—
510C2×C4×C61—21no—
511C2×C4×C61—21no—
512C2×C4×C61—21no—
513C2×C4×C61—21no—
514C2×C4×C61—21no—
515C2×C4×C61—21no—
516C2×C4×C61—21no—
517C2×C4×C61—21no—
518C2×C4×C61—21no—
519C2×C4×C61—21no—
520C2×C4×C61—21no—
521C2×C4×C61—21no—
522C2×C4×C61—21no—
523C2×C4×C61—21no—
524C2×C4×C61—21no—
525C2×C4×C61—22no—
526C2×C4×C61—41no—
527C2×C4×C61—41no—
528C2×C4×C61—41no—
529C2×C4×C61—41no—
530C2×C4×C61—41no—
531C2×C4×C61—41no—
532C2×C4×C61—41no—
533C2×C4×C61—41no—
534C2×C4×C61—41no—
535C2×C4×C61—41no—
536C2×C4×C61—41no—
537C2×C4×C61—41no—
538C2×C4×C61—41no—
539C2×C4×C61C2×C22⋊C411yescharacteristic
540C2×C4×C61C2×C22⋊C411yescharacteristic
541C2×C4×C61C2×C22⋊C411yescharacteristic
542C2×C4×C61C2×C22⋊C411yescharacteristic
543C22⋊D61—22no—
544C22⋊D61—22no—
545C22⋊D61—22no—
546C22⋊D61—22no—
547C22⋊D61—42no—
548C22⋊D61—42no—
549C22⋊D61—41no—
550C22⋊D61—41no—
551C22⋊D61—41no—
552C22⋊D61—41no—
553C22⋊D61—81no—
554C22⋊D61—81no—
555C2×Dic61—21no—
556C2×Dic61—21no—
557C2×Dic61—21no—
558C2×Dic61—21no—
559C2×Dic61—21no—
560C2×Dic61—22no—
561C2×Dic61—41no—
562C2×Dic61—41no—
563C2×Dic61—41no—
564C2×Dic61—41no—
565C2×Dic61—41no—
566C2×Dic61—41no—
567C2×Dic61—41no—
568C2×Dic61—41no—
569C2×Dic61—41no—
570C2×Dic61—41no—
571C2×Dic61—41no—
572C2×Dic61—41no—
573C2×Dic61—41no—
574C2×Dic61—41no—
575C2×Dic61—41no—
576C2×Dic61—41no—
577C2×Dic61—41no—
578C2×Dic61C2×C22⋊C411yescharacteristic
579C2×Dic61C2×C22⋊C411yescharacteristic
580C2×Dic61C2×C22⋊C411yescharacteristic
581C2×Dic61C2×C22⋊C411yescharacteristic
582C2×Dic61C4×D412yes—
583D244—42no—
584D244—42no—
585D244—42no—
586D244—42no—
587D244—42no—
588D244—42no—
589D244—81no—
590D244—81no—
591C4×D61—42no—
592C4×D61—42no—
593C4×D61—42no—
594C4×D61—42no—
595C4×D61—42no—
596C4×D61—42no—
597C4×D61—81no—
598C4×D61—81no—
599C4×D61—84no—
600C4×D61—84no—
601Dic122—42no—
602Dic122—42no—
603#22405—611nomaximal, Sylow
604C22×C61—21no—
605C22×C61—21no—
606C22×C61—21no—
607C22×C61—21no—
608C22×C61—21no—
609C22×C61—21no—
610C22×C61—41no—
611C22×C61—41no—
612C22×C61—41no—
613C22×C61—41no—
614C22×C61—41no—
615C22×C61—41no—
616C22×C61—41no—
617C22×C61—81no—
618C22×C61—81no—
619C22×C61C22×C22⋊C411yescharacteristic
620C22×C61C2×C4×D411yescharacteristic
621C22×C61#51811yescharacteristic
622C22×C61D4211yescharacteristic
623C22×C61D4211yescharacteristic
624C22×C61#54611yescharacteristic
625C22×C61#54611yescharacteristic
626C2×D61—21no—
627C2×D61—21no—
628C2×D61—22no—
629C2×D61—21no—
630C2×D61—21no—
631C2×D61—21no—
632C2×D61—21no—
633C2×D61—21no—
634C2×D61—21no—
635C2×D61—21no—
636C2×D61—21no—
637C2×D61—21no—
638C2×D61—42no—
639C2×D61—42no—
640C2×D61—42no—
641C2×D61—42no—
642C2×D61—42no—
643C2×D61—42no—
644C2×D61—42no—
645C2×D61—41no—
646C2×D61—41no—
647C2×D61—42no—
648C2×D61—41no—
649C2×D61—41no—
650C2×D61—41no—
651C2×D61—84no—
652C2×D61—81no—
653C2×D61—81no—
654C2×D61—81no—
655C2×D61—81no—
656C2×D61—81no—
657C2×D61—81no—
658C2×D61—84no—
659C2×D61—81no—
660C2×D61—81no—
661C2×D61#41012yescomplemented
662C4×C61—21no—
663C4×C61—21no—
664C4×C61—21no—
665C4×C61—21no—
666C4×C61—42no—
667C4×C61—41no—
668C4×C61—41no—
669C4×C61—41no—
670C4×C61—81no—
671C4×C61—81no—
672C4×C61—81no—
673Dic61—22no—
674Dic61—21no—
675Dic61—21no—
676Dic61—21no—
677Dic61—21no—
678Dic61—42no—
679Dic61—41no—
680Dic61—81no—
681Dic61—81no—
682Dic61—81no—
683C2×#546—611no—
684C2×#410—611no—
685C22×#99—611no—
686#2342—611no—
687#2342—611no—
688#1964—611no—
689#1964—611no—
690#1899—611no—
691#1899D6111yescharacteristic, complemented
692#1898—611no—
693#1898—611no—
694#1799—611no—
695#1782—611no—
696#1781—611no—
697C4×#99—611no—
698C2×C61—21no—
699C2×C61—21no—
700C2×C61—21no—
701C2×C61—21no—
702C2×C61—21no—
703C2×C61—21no—
704C2×C61—81no—
705C2×C61D4×C22⋊C411yescharacteristic
706C2×C61C2×#41011yescharacteristic
707C2×C61#288311yescharacteristic
708D61—22no—
709D61—41no—
710D61—41no—
711D61—41no—
712D61—42no—
713D61—81no—
714C22×#41—611no—
715C23×D4—611no—
716#546—1221no—
717#546—1221no—
718#546—1221no—
719#546—1221no—
720#546—1221no—
721#546—1221no—
722#546—1221no—
723#546—1221no—
724C2×#124—611no—
725C2×#123—611no—
726C2×#123C2×D6111yescharacteristic
727C2×C22⋊Q8—611no—
728C2×#121—611no—
729C2×#121—611no—
730C2×#121—611no—
731C2×#120—611no—
732C2×#120—611no—
733C2×C4×D4—611no—
734C2×C4×D4—611no—
735C2×#117—611no—
736C2×#117C2×D6111yescharacteristic, complemented
737C22×C22⋊C4—611no—
738C22×C22⋊C4—611no—
739C22×C22⋊C4—611no—
740C22×C22⋊C4—611no—
741#410—1224no—
742C2×#99—611no—
743C2×#99—611no—
744C2×#99—611no—
745C2×#99—611no—
746C2×#99—611no—
747C2×#99—611no—
748C2×#99—611no—
749C2×#99—611no—
750C2×#99—611no—
751C2×#99—611no—
752C2×#99—1224no—
753C2×#99C2×D6111yescharacteristic
754C2×#99C2×D6111yescharacteristic
755#388—1221no—
756#388—1221no—
757#388—1221no—
758#388—1221no—
759#385—1221no—
760#385—1221no—
761#381—611no—
762#381C2×D6111yescharacteristic, complemented
763#380—611no—
764#380—611no—
765#379—611no—
766#379—611no—
767C4×C22⋊C4—611no—
768C4×C22⋊C4—611no—
769C4×C22⋊C4—1221no—
770C4×C22⋊C4—1221no—
771#342—611no—
772#342—611no—
773#342C2×D6111yescharacteristic, complemented
774#342C2×D6111yescharacteristic, complemented
775C61#2240511yescharacteristic, complemented, Sylow
776C25—611no—
777C25—611no—
778C2×#41—1222no—
779C2×#41—1222no—
780C2×#41—1221no—
781C2×#41—1221no—
782C2×#41—1221no—
783C2×#41—1221no—
784C2×#41—2441no—
785C2×#41—2441no—
786C22×Q8—611no—
787C22×D4—611no—
788C22×D4—611no—
789C22×D4—611no—
790C22×D4—611no—
791C22×D4—611no—
792C22×D4—611no—
793C22×D4—611no—
794C22×D4—611no—
795C22×D4—1222no—
796C22×D4—1222no—
797C22×D4—1221no—
798C22×D4—1221no—
799C22×D4—1221no—
800C22×D4—1221no—
801C22×D4—2441no—
802C22×D4—2441no—
803C22×D4C22×D6111yescharacteristic
804C23×C4—611no—
805C23×C4—611no—
806C23×C4—611no—
807C23×C4—611no—
808C23×C4—611no—
809C23×C4—1221no—
810C23×C4—1221no—
811C23×C4C22×D6111yescharacteristic
812#124—1221no—
813#124—1221no—
814#124—1221no—
815#124—1221no—
816#123—21no—
817#123—21no—
818#123—21no—
819#123—21no—
820#123—1221no—
821#123—1221no—
822#123—1221no—
823#123—1221no—
824C22⋊Q8—1221no—
825C22⋊Q8—1221no—
826C22⋊Q8—1221no—
827C22⋊Q8—1221no—
828#121—1221no—
829#121—1221no—
830#121—1221no—
831#121—1221no—
832#121—1221no—
833#121—1221no—
834#121—1221no—
835#121—1221no—
836#121—1221no—
837#121—1221no—
838#121—1221no—
839#121—1221no—
840#120—1221no—
841#120—1221no—
842#120—1221no—
843#120—1221no—
844#120—1221no—
845#120—1221no—
846#120—1221no—
847#120—1221no—
848C4×D4—1221no—
849C4×D4—1221no—
850C4×D4—1221no—
851C4×D4—1221no—
852C4×D4—1221no—
853C4×D4—1221no—
854C4×D4—1221no—
855C4×D4—1221no—
856#117—22no—
857#117—41no—
858#117—1222no—
859#117—2441no—
860C2×C4⋊C4—21no—
861C2×C4⋊C4—611no—
862C2×C4⋊C4—611no—
863C2×C4⋊C4—1221no—
864C2×C4⋊C4—1221no—
865C2×C4⋊C4—1221no—
866C2×C4⋊C4C4×D6111yescharacteristic, complemented
867C2×C4⋊C4C4×D6111yescharacteristic, complemented
868C2×C22⋊C4—611no—
869C2×C22⋊C4—611no—
870C2×C22⋊C4—611no—
871C2×C22⋊C4—611no—
872C2×C22⋊C4—611no—
873C2×C22⋊C4—611no—
874C2×C22⋊C4—611no—
875C2×C22⋊C4—611no—
876C2×C22⋊C4—611no—
877C2×C22⋊C4—611no—
878C2×C22⋊C4—611no—
879C2×C22⋊C4—611no—
880C2×C22⋊C4—611no—
881C2×C22⋊C4—611no—
882C2×C22⋊C4—611no—
883C2×C22⋊C4—611no—
884C2×C22⋊C4—611no—
885C2×C22⋊C4—611no—
886C2×C22⋊C4—611no—
887C2×C22⋊C4—611no—
888C2×C22⋊C4—611no—
889C2×C22⋊C4—1221no—
890C2×C22⋊C4—1221no—
891C2×C22⋊C4—1221no—
892C2×C22⋊C4—1221no—
893C2×C22⋊C4—1222no—
894C2×C22⋊C4—1222no—
895C2×C22⋊C4—1221no—
896C2×C22⋊C4—1221no—
897C2×C22⋊C4—1221no—
898C2×C22⋊C4—1221no—
899C2×C22⋊C4—1221no—
900C2×C22⋊C4—1221no—
901C2×C22⋊C4—2441no—
902C2×C22⋊C4—2441no—
903C2×C22⋊C4C4×D6111yescharacteristic, complemented
904C2×C22⋊C4C4×D6111yescharacteristic, complemented
905C2×C22⋊C4C22×D6111yescharacteristic
906C2×C22⋊C4C22×D6111yescharacteristic
907C2×C22⋊C4C22×D6111yescharacteristic
908C2×C22⋊C4C22×D6111yescharacteristic
909C2×C22⋊C4C22×D6111yescharacteristic
910C2×C42—21no—
911C2×C42—611no—
912C2×C42—1221no—
913C2×C42—1221no—
914C2×C42—1221no—
915#99—22no—
916#99—41no—
917#99—614no—
918#99—1222no—
919#99—1222no—
920#99—1222no—
921#99—1222no—
922#99—1222no—
923#99—1222no—
924#99—2441no—
925#99—2441no—
926#99—2441no—
927#95—21no—
928#95—21no—
929#95—1221no—
930#95—1221no—
931#95—1221no—
932#95—1221no—
933#95—1221no—
934#95—1221no—
935C24—611no—
936C24—611no—
937C24—611no—
938C24—611no—
939C24—611no—
940C24—611no—
941C24—611no—
942C24—611no—
943C24—1222no—
944C24—1221no—
945C24—1221no—
946C24—1221no—
947C24—1221no—
948C24—1221no—
949C24—1221no—
950C24—4881no—
951C24—4881no—
952C24—2441no—
953C24—2442no—
954C24—2442no—
955C24C2×C4×D6111yescharacteristic
956C24C23×D6111yescharacteristic
957#41—2442no—
958#41—2442no—
959#41—2442no—
960#41—2442no—
961#41—2442no—
962#41—2442no—
963#41—2442no—
964#41—2442no—
965C2×Q8—1222no—
966C2×Q8—1221no—
967C2×Q8—1221no—
968C2×Q8—2441no—
969C2×D4—21no—
970C2×D4—21no—
971C2×D4—21no—
972C2×D4—21no—
973C2×D4—21no—
974C2×D4—21no—
975C2×D4—612no—
976C2×D4—612no—
977C2×D4—1221no—
978C2×D4—1221no—
979C2×D4—1221no—
980C2×D4—1221no—
981C2×D4—1221no—
982C2×D4—1221no—
983C2×D4—1222no—
984C2×D4—1222no—
985C2×D4—1221no—
986C2×D4—1221no—
987C2×D4—1222no—
988C2×D4—1221no—
989C2×D4—1221no—
990C2×D4—1221no—
991C2×D4—1221no—
992C2×D4—1221no—
993C2×D4—1221no—
994C2×D4—1221no—
995C2×D4—1221no—
996C2×D4—1221no—
997C2×D4—1221no—
998C2×D4—1221no—
999C2×D4—1221no—
1000C2×D4—1221no—
1001C2×D4—1221no—
1002C2×D4—4881no—
1003C2×D4—4881no—
1004C2×D4—2441no—
1005C2×D4—2441no—
1006C2×D4—2442no—
1007C2×D4—2441no—
1008C2×D4—2442no—
1009C2×D4—2442no—
1010C2×D4—2442no—
1011C2×D4—2442no—
1012C2×D4—2442no—
1013C2×D4—2442no—
1014C2×D4—2442no—
1015C2×D4—2442no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—611no—
1025C22×C4—611no—
1026C22×C4—611no—
1027C22×C4—611no—
1028C22×C4—611no—
1029C22×C4—611no—
1030C22×C4—611no—
1031C22×C4—611no—
1032C22×C4—1221no—
1033C22×C4—1221no—
1034C22×C4—1222no—
1035C22×C4—1222no—
1036C22×C4—1221no—
1037C22×C4—1221no—
1038C22×C4—1222no—
1039C22×C4—1221no—
1040C22×C4—1221no—
1041C22×C4—1221no—
1042C22×C4—1221no—
1043C22×C4—1221no—
1044C22×C4—1221no—
1045C22×C4—1221no—
1046C22×C4—1221no—
1047C22×C4—4881no—
1048C22×C4—4881no—
1049C22×C4—4881no—
1050C22×C4—4881no—
1051C22×C4—2441no—
1052C22×C4—2441no—
1053C22×C4—2441no—
1054C22×C4—2442no—
1055C22×C4—2442no—
1056C22×C4—2442no—
1057C22×C4—2442no—
1058C22×C4C2×C4×D6111yescharacteristic
1059C22×C4C2×C4×D6111yescharacteristic
1060C22×C4C2×C4×D6111yescharacteristic
1061C22×C4C2×C4×D6111yescharacteristic
1062C22×C4C2×C4×D6111yescharacteristic
1063C22×C4D4×D6111yescharacteristic
1064C22×C4D4×D6111yescharacteristic
1065C22×C4D4×D6111yescharacteristic
1066C22×C4D4×D6111yescharacteristic
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—42no—
1072C4⋊C4—1221no—
1073C4⋊C4—1221no—
1074C4⋊C4—1221no—
1075C4⋊C4—1221no—
1076C4⋊C4—4881no—
1077C4⋊C4—4881no—
1078C4⋊C4—2442no—
1079C22⋊C4—21no—
1080C22⋊C4—21no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—21no—
1085C22⋊C4—21no—
1086C22⋊C4—21no—
1087C22⋊C4—21no—
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—611no—
1093C22⋊C4—611no—
1094C22⋊C4—611no—
1095C22⋊C4—611no—
1096C22⋊C4—611no—
1097C22⋊C4—611no—
1098C22⋊C4—611no—
1099C22⋊C4—611no—
1100C22⋊C4—611no—
1101C22⋊C4—611no—
1102C22⋊C4—611no—
1103C22⋊C4—611no—
1104C22⋊C4—611no—
1105C22⋊C4—611no—
1106C22⋊C4—611no—
1107C22⋊C4—611no—
1108C22⋊C4—612no—
1109C22⋊C4—1221no—
1110C22⋊C4—1221no—
1111C22⋊C4—1221no—
1112C22⋊C4—1221no—
1113C22⋊C4—1221no—
1114C22⋊C4—1221no—
1115C22⋊C4—1221no—
1116C22⋊C4—1221no—
1117C22⋊C4—1221no—
1118C22⋊C4—1221no—
1119C22⋊C4—1221no—
1120C22⋊C4—1221no—
1121C22⋊C4—1221no—
1122C22⋊C4—1221no—
1123C22⋊C4—1221no—
1124C22⋊C4—1221no—
1125C22⋊C4—1221no—
1126C22⋊C4—4881no—
1127C22⋊C4—4881no—
1128C22⋊C4—2442no—
1129C22⋊C4—2442no—
1130C22⋊C4—2442no—
1131C22⋊C4—2442no—
1132C22⋊C4D4×D6112yes—
1133C42—42no—
1134C42—1221no—
1135C42—1221no—
1136C42—4881no—
1137C42—4881no—
1138C42—2442no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—611no—
1147C23—611no—
1148C23—611no—
1149C23—611no—
1150C23—612no—
1151C23—1222no—
1152C23—1222no—
1153C23—1222no—
1154C23—1221no—
1155C23—1221no—
1156C23—1221no—
1157C23—1221no—
1158C23—1221no—
1159C23—1221no—
1160C23—1221no—
1161C23—1221no—
1162C23—1221no—
1163C23—1221no—
1164C23—1221no—
1165C23—1221no—
1166C23—1221no—
1167C23—1221no—
1168C23—1221no—
1169C23—1221no—
1170C23—1221no—
1171C23—4881no—
1172C23—4881no—
1173C23—4882no—
1174C23—4882no—
1175C23—4882no—
1176C23—4882no—
1177C23—4884no—
1178C23—4884no—
1179C23—2441no—
1180C23—2441no—
1181C23—2441no—
1182C23—2441no—
1183C23—2441no—
1184C23—2441no—
1185C23—2441no—
1186C23—2441no—
1187C23—2441no—
1188C23—2441no—
1189C23—2441no—
1190C23—2441no—
1191C23—2441no—
1192C23—2442no—
1193C23—2442no—
1194C23—2442no—
1195C23—2442no—
1196C23C22×C4×D6111yescharacteristic
1197C23C2×D4×D6111yescharacteristic
1198C23C2×D4×D6111yescharacteristic
1199C23C2×D4×D6111yescharacteristic
1200C23#41×D6111yescharacteristic
1201C23#1451982211yescharacteristic
1202C23#1451982311yescharacteristic
1203Q8—2442no—
1204Q8—2442no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—1222no—
1210D4—1222no—
1211D4—1222no—
1212D4—1222no—
1213D4—4881no—
1214D4—4881no—
1215D4—4881no—
1216D4—4881no—
1217D4—2442no—
1218D4—2442no—
1219D4—2442no—
1220D4—2442no—
1221D4—2442no—
1222D4—2442no—
1223D4—2442no—
1224D4—2442no—
1225D4—2441no—
1226D4—2441no—
1227D4—2441no—
1228D4—2441no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—611no—
1261C2×C4—611no—
1262C2×C4—611no—
1263C2×C4—611no—
1264C2×C4—612no—
1265C2×C4—1221no—
1266C2×C4—1221no—
1267C2×C4—1221no—
1268C2×C4—1221no—
1269C2×C4—1221no—
1270C2×C4—1222no—
1271C2×C4—4881no—
1272C2×C4—4881no—
1273C2×C4—4884no—
1274C2×C4—4884no—
1275C2×C4—2442no—
1276C2×C4—2442no—
1277C2×C4—2442no—
1278C2×C4—2442no—
1279C2×C4—2442no—
1280C2×C4—2442no—
1281C2×C4—2441no—
1282C2×C4—2441no—
1283C2×C4—2441no—
1284C2×C4—2441no—
1285C2×C4—2441no—
1286C2×C4—2441no—
1287C2×C4—2441no—
1288C2×C4—2441no—
1289C2×C4—2441no—
1290C2×C4—2441no—
1291C2×C4—2441no—
1292C2×C4—2441no—
1293C2×C4—2441no—
1294C2×C4—2441no—
1295C2×C4—2441no—
1296C2×C4—2441no—
1297C2×C4—2441no—
1298C2×C4C22⋊C4×D6111yescharacteristic
1299C2×C4C22⋊C4×D6111yescharacteristic
1300C2×C4C22⋊C4×D6111yescharacteristic
1301C2×C4C22⋊C4×D6111yescharacteristic
1302C22—21no—
1303C22—21no—
1304C22—21no—
1305C22—21no—
1306C22—21no—
1307C22—21no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—81no—
1316C22—81no—
1317C22—612no—
1318C22—1221no—
1319C22—1221no—
1320C22—1222no—
1321C22—1221no—
1322C22—1221no—
1323C22—1221no—
1324C22—1221no—
1325C22—1221no—
1326C22—1221no—
1327C22—1221no—
1328C22—1221no—
1329C22—1221no—
1330C22—4881no—
1331C22—4881no—
1332C22—4881no—
1333C22—4881no—
1334C22—4881no—
1335C22—4881no—
1336C22—4881no—
1337C22—4881no—
1338C22—4884no—
1339C22—4884no—
1340C22—2442no—
1341C22—2442no—
1342C22—2442no—
1343C22—2442no—
1344C22—2442no—
1345C22—2442no—
1346C22—2442no—
1347C22—2442no—
1348C22—2441no—
1349C22—2441no—
1350C22—2441no—
1351C22—2441no—
1352C22—2441no—
1353C22C2×C22⋊C4×D6111yescharacteristic
1354C22C4×D4×D6111yescharacteristic
1355C22#1684023411yescharacteristic
1356C22#1684039411yescharacteristic
1357C22#1684039611yescharacteristic
1358C22#1684040111yescharacteristic
1359C22#1684040411yescharacteristic
1360C4—21no—
1361C4—21no—
1362C4—21no—
1363C4—21no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—1222no—
1372C4—1221no—
1373C4—1221no—
1374C4—1221no—
1375C4—1221no—
1376C4—4881no—
1377C4—4881no—
1378C4—4881no—
1379C4—2442no—
1380C4—2441no—
1381C2—21no—
1382C2—21no—
1383C2—21no—
1384C2—21no—
1385C2—21no—
1386C2—21no—
1387C2—81no—
1388C2—1222no—
1389C2—4881no—
1390C2—2441no—
1391C2—2441no—
1392C2—2441no—
1393C2—2442no—
1394C2#2144863711yescharacteristic
1395C2#410×D6111yescharacteristic
1396C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1899C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840404C2
cosocleC24×C61C24
hypercenter#1899D61
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839735C2semidirect
3. C2×#99×D61C2semidirect
4. #21448669C2semidirect
5. #21448661C2semidirect
6. #21446653C2semidirect
7. #21446653C2semidirect
8. #21446278C2semidirect
9. #21446271C2semidirect
10. #21446271C2semidirect
11. #21445806C2semidirect
12. #21445736C2semidirect
13. #21445732C2semidirect
14. #21445606C2semidirect
15. C61×#1899C2semidirect
26. C2×#14519763C4semidirect
27. C2×#14519762C4semidirect
28. C2×#14519755C4semidirect
29. C2×#14519752C4semidirect
30. C2×#14519750C4semidirect
32. C2×#14519747C4semidirect
34. C2×#14519739C4semidirect
36. C2×#14519736C22semidirect
38. C2×C22⋊C4×D61C4semidirect
48. C2×#14519691C22semidirect
49. C2×#14519691C22semidirect
50. C2×#14519691C22semidirect
51. C2×#14519691C22semidirect
59. #16839625C22semidirect
60. #16839620C22semidirect
61. #16839620C22semidirect
64. C22⋊C4×Dic61C22semidirect
65. C22⋊C4×Dic61C22semidirect
68. #16839529C22semidirect
69. #16839529C22semidirect
71. C2×#117×C61C22semidirect
74. C61×#381C22semidirect
75. C61×#342C22semidirect
76. C61×#342C22semidirect
87. C22×Dic122C2×C4semidirect
91. C22×D244C2×C4semidirect
93. C22×C22⋊D61C2×C4semidirect
108. C22×C4×D61C2×C4semidirect
109. C22×C4×D61C2×C4semidirect
110. C22×C4×D61C2×C4semidirect
156. C2×#11758196C2×C4semidirect
157. C2×#11758196C2×C4semidirect
158. C2×C22⋊Dic61C2×C4semidirect
175. C2×#11758198C2×C4semidirect
176. C2×#11758198C2×C4semidirect
196. C2×C4×Dic61C2×C4semidirect
206. #14519691D4semidirect
222. C2×C4⋊C4×C61C2×C4semidirect
223. C2×C4⋊C4×C61C2×C4semidirect
224. C2×C22⋊C4×C61C2×C4semidirect
225. C2×C22⋊C4×C61C2×C4semidirect
661. C2×D61#410semidirect
691. #1899D61semidirect
736. C2×#117C2×D61semidirect
762. #381C2×D61semidirect
773. #342C2×D61semidirect
774. #342C2×D61semidirect
775. C61#22405semidirect
866. C2×C4⋊C4C4×D61semidirect
867. C2×C4⋊C4C4×D61semidirect
903. C2×C22⋊C4C4×D61semidirect
904. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404042
C2×#168397352
C2×#99×D612
#214486692
#214486612
#214466532
#214462782
#214462712
#214458062
#214457362
#214457322
#214456062
C61×#18992
#2240561