Finite Group Databasebeta

← #29695704

Subgroups — #29695704

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459302C211yesmaximal, characteristic
2#21454551C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4C22×#14519705C211yesmaximal, characteristic, complemented
5#21448262C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446649C211yesmaximal, characteristic, complemented
8#21446266C211yesmaximal, characteristic, complemented
9#21446122C211yesmaximal, characteristic, complemented
10#21446120C211yesmaximal, characteristic, complemented
11#21445838C211yesmaximal, characteristic, complemented
12#21445762C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445628C211yesmaximal, characteristic, complemented
15C61×#1896C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C2×M16×D61C2211yescharacteristic, complemented
20#16840430C411yescharacteristic, complemented
21#16840425C411yescharacteristic, complemented
22#16840422C411yescharacteristic, complemented
23#16840418C411yescharacteristic, complemented
24#16840414C411yescharacteristic, complemented
25#16840410—21no—
26#16840409C411yescharacteristic, complemented
27#16840404—21no—
28#16840403C411yescharacteristic, complemented
29#16840399—21no—
30#16840396C411yescharacteristic, complemented
31#16840394—21no—
32#16840309—21no—
33#16840308C2211yescharacteristic
34#16840274C2211yescharacteristic
35#16840271—21no—
36#16840271—21no—
37#16840230C2211yescharacteristic
38C2×C4×C22⋊D61C2211yescharacteristic
39C4×D4×D61—21no—
40C2×#14519734C2211yescharacteristic, complemented
41#16839837—21no—
42#16839836—21no—
43#16839830—21no—
44#16839825—21no—
45#16839785C2211yescharacteristic, complemented
46#16839777—24no—
47C2×#14519705—24no—
48C2×#14519705C2211yescharacteristic
49C2×#14519705C2211yescharacteristic
50C2×#14519705C2211yescharacteristic, complemented
51C2×#14519705C2211yescharacteristic, complemented
52C2×#14519704C2211yescharacteristic, complemented
53C2×#14519704C2211yescharacteristic, complemented
54C2×#14519703C2211yescharacteristic
55C2×#14519703C2211yescharacteristic
56C2×#14519703C2211yescharacteristic, complemented
57C2×#14519703C2211yescharacteristic, complemented
58#16839725C2211yescharacteristic, complemented
59M16×Dic61C2211yescharacteristic, complemented
60#16839653—21no—
61#16839646—21no—
62#16839641—21no—
63#16839635—21no—
64C4×#11758196C2211yescharacteristic, complemented
65C4×#11758198C2211yescharacteristic, complemented
66C4×C22⋊Dic61C2211yescharacteristic, complemented
67#16839608C2211yescharacteristic, complemented
68#16839521C2211yescharacteristic, complemented
69#16839521C2211yescharacteristic, complemented
70C61×#525C2211yescharacteristic
71C22×C42×C61C2211yescharacteristic, complemented
72C2×#104×C61C2211yescharacteristic, complemented
73C2×#104×C61C2211yescharacteristic, complemented
74C61×#407C2211yescharacteristic, complemented
75C61×#339C2211yescharacteristic, complemented
76C61×#339C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic, complemented
78C2×#11758222—21no—
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—22no—
82C2×#11758222—22no—
83C2×#11758222—41no—
84C2×#11758222—41no—
85C2×#11758222C2×C411yescharacteristic
86C2×#11758222C2×C411yescharacteristic
87C2×#11758222C2311yescharacteristic
88C2×#11758222C2311yescharacteristic
89C2×#11758224—21no—
90C2×#11758224C2×C411yescharacteristic, complemented
91#41×D61—22no—
92#41×D61—22no—
93#41×D61—41no—
94#41×D61—41no—
95C22×Dic122C2×C411yescharacteristic
96C2×Q8×D61C2×C411yescharacteristic, complemented
97C22×D244C2×C411yescharacteristic
98C22×C22⋊D61—21no—
99C22×C22⋊D61D411yescharacteristic
100C2×D4×D61—21no—
101C2×D4×D61—21no—
102C2×D4×D61C2×C411yescharacteristic, complemented
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C2×#11758194—21no—
107C2×#11758194—22no—
108C2×#11758194—41no—
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758189—21no—
112M16×D61—22no—
113M16×D61—41no—
114C22×#92418—21no—
115C2×C8×D61—21no—
116#14519776—21no—
117#14519775C2×C411yescharacteristic, complemented
118#14519773—21no—
119#14519773C2×C411yescharacteristic, complemented
120#14519766C2×C411yescharacteristic, complemented
121#14519764C2×C411yescharacteristic, complemented
122#14519763—21no—
123#14519763—21no—
124#14519762—21no—
125#14519762—21no—
126#14519761—21no—
127#14519759—21no—
128#14519759—21no—
129#14519757C2×C411yescharacteristic, complemented
130#14519757C2×C411yescharacteristic, complemented
131#14519755—21no—
132#14519755—21no—
133#14519754—21no—
134#14519754—21no—
135#14519752—21no—
136#14519752C2×C411yescharacteristic, complemented
137#14519752C2×C411yescharacteristic, complemented
138#14519750—21no—
139#14519750—21no—
140#14519750—21no—
141#14519750—21no—
142#14519749—21no—
143#14519749—21no—
144#14519749—21no—
145#14519749—21no—
146#14519748—21no—
147#14519747—21no—
148#14519747—21no—
149#14519747—21no—
150#14519745—21no—
151#14519745—21no—
152#14519742C2×C411yescharacteristic, complemented
153#14519742C2×C411yescharacteristic, complemented
154C4×D244—21no—
155C4×D244—21no—
156D4×Dic61—21no—
157#14519739—21no—
158#14519739C2×C411yescharacteristic, complemented
159#14519739C2×C411yescharacteristic, complemented
160C4×C22⋊D61—21no—
161C4×C22⋊D61—21no—
162C4×C22⋊D61C2×C411yescharacteristic
163C4×C22⋊D61C2×C411yescharacteristic
164C4×C22⋊D61C2×C411yescharacteristic
165C4×C22⋊D61C2×C411yescharacteristic
166C4×C22⋊D61D411yescharacteristic
167C4×C22⋊D61D411yescharacteristic
168C4×C22⋊D61D411yescharacteristic
169C4×C22⋊D61D411yescharacteristic
170#14519737—21no—
171#14519737—21no—
172#14519737—21no—
173#14519737—21no—
174#14519734—22no—
175#14519734—21no—
176#14519734—41no—
177C2×#11758196—21no—
178C2×#11758196—21no—
179C2×#11758196D411yescharacteristic
180C4⋊C4×D61—21no—
181C2×C22⋊Dic61—21no—
182C2×C22⋊Dic61D411yescharacteristic
183C2×#11758198—21no—
184C2×#11758198—21no—
185C2×#11758198D411yescharacteristic
186C22⋊C4×D61—21no—
187C22⋊C4×D61—21no—
188C2×C4×Dic61C2311yescharacteristic
189C2×C4×Dic61C2311yescharacteristic
190C2×C4×Dic61C2311yescharacteristic
191C42×D61—21no—
192#14519706—21no—
193#14519706—21no—
194#14519705—22no—
195#14519705—22no—
196#14519705—22no—
197#14519705D414yescomplemented
198#14519704—22no—
199#14519704—41no—
200#14519703—22no—
201#14519703—22no—
202#14519703—41no—
203#14519703—41no—
204#14519689—21no—
205#14519689—21no—
206#14519687—21no—
207C8×Dic61—21no—
208#14519684—21no—
209#14519684—21no—
210#14519684—21no—
211#14519684—21no—
212#14519684—21no—
213C2×#41×C61C2311yescharacteristic
214C23×C4×C61—21no—
215C23×C4×C61C2311yescharacteristic
216C2×M16×C61C2311yescharacteristic
217C2×M16×C61C2311yescharacteristic
218#123×C61—21no—
219C22⋊Q8×C61C2×C411yescharacteristic
220C22⋊Q8×C61C2×C411yescharacteristic
221#121×C61C2×C411yescharacteristic
222#121×C61C2×C411yescharacteristic
223#120×C61—21no—
224C4×D4×C61—21no—
225C4×D4×C61—21no—
226#117×C61C2311yescharacteristic
227C2×C42×C61—22no—
228C2×C42×C61—21no—
229C2×C42×C61—41no—
230C2×C42×C61C2311yescharacteristic
231C2×C42×C61C2311yescharacteristic
232#104×C61—22no—
233#104×C61—41no—
234C22⋊C8×C61—21no—
235C22⋊C8×C61—21no—
236C24×C61C2×D411yescharacteristic
237C23×D61—21no—
238C23×D61—21no—
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—21no—
243#41×C61—21no—
244C2×Q8×C61C22×C411yescharacteristic
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61C22×C411yescharacteristic
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—42no—
257C22×C4×C61—42no—
258C22×C4×C61—42no—
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2411yescharacteristic
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61—21no—
270C2×C22⋊D61—21no—
271C2×C22⋊D61—21no—
272C2×C22⋊D61—21no—
273C2×C22⋊D61—42no—
274C2×C22⋊D61—42no—
275C2×C22⋊D61—42no—
276C2×C22⋊D61C22⋊C411yescharacteristic
277C2×C22⋊D61C22⋊C411yescharacteristic
278C2×C22⋊D61C22⋊C411yescharacteristic
279C2×C22⋊D61C22⋊C411yescharacteristic
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D411yescharacteristic
286C22×Dic61C2×D411yescharacteristic
287#11758226—22no—
288#11758226—41no—
289Q8×D61—22no—
290Q8×D61—41no—
291#11758224—22no—
292#11758224—41no—
293#11758224—42no—
294#11758224—42no—
295D4×D61—22no—
296D4×D61—41no—
297D4×D61—42no—
298D4×D61—42no—
299D4×D61—44no—
300#11758222—21no—
301#11758222—21no—
302#11758222—21no—
303#11758222—21no—
304#11758222—21no—
305#11758222—21no—
306#11758222—22no—
307#11758222—22no—
308#11758222—41no—
309#11758222—41no—
310#11758222—42no—
311#11758222—42no—
312#11758222—42no—
313#11758222—42no—
314#11758222—42no—
315#11758222—42no—
316#11758222C2×D412yes—
317#11758222#4112yes—
318C2×D244—22no—
319C2×D244—21no—
320C2×D244—21no—
321C2×D244—21no—
322C2×D244—21no—
323C2×D244—41no—
324C2×D244C22×C411yescharacteristic
325C2×D244C22×C411yescharacteristic
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61—42no—
341C2×C4×D61—42no—
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×Dic122—22no—
347C2×Dic122—21no—
348C2×Dic122—21no—
349C2×Dic122—41no—
350C2×Dic122C22×C411yescharacteristic
351C2×Dic122C22×C411yescharacteristic
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61—21no—
356C2×C8×C61—21no—
357C2×C8×C61—21no—
358C4⋊C4×C61—21no—
359C4⋊C4×C61—21no—
360C4⋊C4×C61C22×C411yescharacteristic
361C4⋊C4×C61C22×C411yescharacteristic
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C22⋊C4×C61—21no—
365C22⋊C4×C61—21no—
366C22⋊C4×C61—21no—
367C42×C61—21no—
368C42×C61—21no—
369C42×C61—21no—
370C42×C61—21no—
371C42×C61—42no—
372C42×C61C2×D412yescomplemented
373C22⋊Dic61—21no—
374C22⋊Dic61—21no—
375C22⋊Dic61—42no—
376C22⋊Dic61C22⋊C411yescharacteristic
377C22⋊Dic61C22⋊C411yescharacteristic
378C22⋊Dic61C22⋊C411yescharacteristic
379C22⋊Dic61C22⋊C411yescharacteristic
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—21no—
387#11758198—21no—
388#11758198—42no—
389#11758198—42no—
390#11758198C22⋊C411yescharacteristic
391#11758198C22⋊C411yescharacteristic
392#11758198C22⋊C411yescharacteristic
393#11758198C22⋊C411yescharacteristic
394C4⋊Dic61—21no—
395C4⋊Dic61—21no—
396#11758196—21no—
397#11758196—21no—
398#11758196—21no—
399#11758196—21no—
400#11758196—42no—
401#11758196—42no—
402#11758196C22⋊C411yescharacteristic
403#11758196C22⋊C411yescharacteristic
404#11758196C22⋊C411yescharacteristic
405#11758196C22⋊C411yescharacteristic
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—21no—
411C4×Dic61—21no—
412C4×Dic61C22×C411yescharacteristic
413C4×Dic61C22×C411yescharacteristic
414C4×Dic61C2×D411yescharacteristic
415C4×Dic61C2×D411yescharacteristic
416#11758194—21no—
417#11758194—21no—
418#11758194—21no—
419#11758194—42no—
420#11758194C2×D412yescomplemented
421C2×#92418—21no—
422C2×#92418—21no—
423C2×#92418—42no—
424#11758189—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61—22no—
429C23×C61—21no—
430C23×C61—41no—
431C23×C61C2×C22⋊C411yescharacteristic
432C23×C61C2×C22⋊C411yescharacteristic
433C23×C61C22×D411yescharacteristic
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61—41no—
439C22×D61—41no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—42no—
443C22×D61—42no—
444C22×D61—81no—
445C22×D61—81no—
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450D4×C61—21no—
451D4×C61—21no—
452D4×C61—41no—
453D4×C61—41no—
454D4×C61—42no—
455D4×C61—81no—
456C2×C4×C61—21no—
457C2×C4×C61—21no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—22no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—22no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—48no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61—41no—
478C2×C4×C61C2×C22⋊C411yescharacteristic
479C2×C4×C61C2×C22⋊C411yescharacteristic
480C2×C4×C61C23×C411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C22×D411yescharacteristic
483C2×C4×C61C2×#4111yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C2×C4×C61H(5,𝔽2)11yescharacteristic
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—22no—
489C22⋊D61—22no—
490C22⋊D61—41no—
491C22⋊D61—41no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—42no—
495C22⋊D61—42no—
496C22⋊D61—42no—
497C22⋊D61—41no—
498C22⋊D61—41no—
499C22⋊D61—81no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—41no—
505C2×Dic61—41no—
506C2×Dic61—42no—
507C2×Dic61—42no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61—41no—
512C2×Dic61—41no—
513C2×Dic61—41no—
514C2×Dic61C2×C22⋊C411yescharacteristic
515C2×Dic61C2×C22⋊C411yescharacteristic
516C2×Dic61C2×C22⋊C411yescharacteristic
517C2×Dic61C2×C22⋊C411yescharacteristic
518C2×Dic61C2×C22⋊C411yescharacteristic
519C2×Dic61C2×C22⋊C411yescharacteristic
520D244—21no—
521D244—21no—
522D244—21no—
523D244—42no—
524D244—42no—
525D244—42no—
526D244—81no—
527D244C4×D412yes—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—22no—
535C4×D61—21no—
536C4×D61—21no—
537C4×D61—22no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—42no—
542C4×D61—42no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—81no—
546Dic122—21no—
547Dic122—21no—
548Dic122—21no—
549Dic122—42no—
550Dic122—42no—
551Dic122C4×D412yes—
552C8×C61—41no—
553C8×C61—41no—
554#92418—22no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—42no—
565C22×C61—42no—
566C22×C61—41no—
567C22×C61—41no—
568C22×C61—41no—
569C22×C61#42112yescomplemented
570C22×C61C22×C22⋊C411yescharacteristic
571C22×C61D4211yescharacteristic
572C22×C61#54611yescharacteristic
573C2×D61—21no—
574C2×D61—21no—
575C2×D61—22no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—81no—
586C2×D61—81no—
587C2×D61—84no—
588C2×D61—84no—
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—42no—
592C4×C61—42no—
593C4×C61—41no—
594C4×C61—41no—
595C4×C61—41no—
596C4×C61C2×C4×D411yescharacteristic
597C4×C61#51811yescharacteristic
598C4×C61D4211yescharacteristic
599C4×C61#54611yescharacteristic
600Dic61—22no—
601Dic61—21no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—21no—
607Dic61—41no—
608Dic61—81no—
609Dic61—81no—
610D4×#41—611no—
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963—611no—
617#1897—611no—
618#1896D6111yescharacteristic, complemented
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—22no—
628C2×C61—41no—
629C2×C61—81no—
630C2×C61D4×C22⋊C411yescharacteristic
631C2×C61C2×#42111yescharacteristic
632C2×C61#290111yescharacteristic
633D61—41no—
634D61—41no—
635D61—42no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—611no—
649#546—1221no—
650#546—1221no—
651D42—611no—
652D42—1221no—
653#532—611no—
654#532—1221no—
655#525—611no—
656#525—1221no—
657#525—1221no—
658#525C2×D6111yescharacteristic
659C4×#41—611no—
660C2×C4×D4—611no—
661C2×C4×D4—1221no—
662C2×#117—611no—
663C22×C42C2×D6111yescharacteristic, complemented
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423—611no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—611no—
679C2×#104—611no—
680C2×#104—1224no—
681C2×#104C2×D6111yescharacteristic, complemented
682C2×#104C2×D6111yescharacteristic, complemented
683#407—611no—
684#407C2×D6111yescharacteristic, complemented
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376—611no—
694#339—611no—
695#339—611no—
696#339C2×D6111yescharacteristic, complemented
697#339C2×D6111yescharacteristic, complemented
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—611no—
705C2×#41—1221no—
706C2×#41—1222no—
707C2×#41—1222no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1221no—
711C2×#41—1222no—
712C2×#41—1222no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41—2441no—
717C2×#41C22×D6111yescharacteristic
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4—1221no—
726C23×C4—21no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4C22×D6111yescharacteristic
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—1221no—
734C2×M16—1221no—
735C2×M16—1222no—
736C2×M16—1222no—
737C2×M16—2441no—
738C2×M16—2441no—
739C2×M16C22×D6111yescharacteristic
740C2×M16C22×D6111yescharacteristic
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—611no—
744C4⋊Q8—1221no—
745#127—611no—
746#127—1221no—
747#124—611no—
748#124—611no—
749#124—1221no—
750#124—1221no—
751#123—21no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8C4×D6111yescharacteristic
764C22⋊Q8C4×D6111yescharacteristic
765#121—611no—
766#121—611no—
767#121—1221no—
768#121—1221no—
769#121—1221no—
770#121—1221no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121C4×D6111yescharacteristic
778#121C4×D6111yescharacteristic
779#120—21no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8—611no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—611no—
796C4×D4—611no—
797C4×D4—611no—
798C4×D4—611no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807C4×D4—1221no—
808C4×D4—1221no—
809#117—1221no—
810#117—1222no—
811#117—2441no—
812#117C22×D6111yescharacteristic
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—22no—
825C2×C42—21no—
826C2×C42—41no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—611no—
830C2×C42—1221no—
831C2×C42C22×D6111yescharacteristic
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—22no—
836#104—41no—
837#104—614no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—2441no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—21no—
848C22⋊C8—21no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—1221no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—611no—
859C24—1221no—
860C24—1221no—
861C24D4×D6111yescharacteristic
862#41—21no—
863#41—21no—
864#41—21no—
865#41—21no—
866#41—612no—
867#41—612no—
868#41—1222no—
869#41—1222no—
870#41—1221no—
871#41—1221no—
872#41—1222no—
873#41—1222no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—1221no—
878#41—2442no—
879#41—2442no—
880#41—2441no—
881#41—2441no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2442no—
886#41—2441no—
887#41—2442no—
888#41—2442no—
889#41—2441no—
890C2×Q8—611no—
891C2×Q8—611no—
892C2×Q8—1221no—
893C2×Q8—1222no—
894C2×Q8—1221no—
895C2×Q8—1222no—
896C2×Q8—2441no—
897C2×Q8—2441no—
898C2×Q8C2×C4×D6111yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—1222no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1222no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—2441no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2444no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4—2442no—
930C2×D4C2×C4×D6111yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—611no—
946C22×C4—611no—
947C22×C4—611no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—2442no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4C2×C4×D6111yescharacteristic
969C22×C4C2×C4×D6111yescharacteristic
970C22×C4D4×D6111yescharacteristic
971C22×C4D4×D6111yescharacteristic
972C22×C4D4×D6111yescharacteristic
973C22×C4C23×D6111yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—612no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—611no—
993C4⋊C4—611no—
994C4⋊C4—611no—
995C4⋊C4—611no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—2442no—
1003C4⋊C4—2442no—
1004C4⋊C4C2×C4×D6111yescharacteristic
1005C4⋊C4C2×C4×D6111yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—611no—
1018C22⋊C4—611no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—1221no—
1028C22⋊C4—1221no—
1029C22⋊C4—2442no—
1030C22⋊C4—2442no—
1031C22⋊C4—2442no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—42no—
1037C42—611no—
1038C42—611no—
1039C42—611no—
1040C42—611no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—1221no—
1047C42D4×D6112yescomplemented
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—41no—
1053C23—611no—
1054C23—611no—
1055C23—1221no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—4881no—
1060C23—4881no—
1061C23—2441no—
1062C23—2441no—
1063C23—2442no—
1064C23—2442no—
1065C23—2442no—
1066C23—2442no—
1067C23C22⋊C4×D6111yescharacteristic
1068C23C22⋊C4×D6111yescharacteristic
1069C23C2×D4×D6111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—612no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—21no—
1079D4—21no—
1080D4—42no—
1081D4—41no—
1082D4—41no—
1083D4—81no—
1084D4—612no—
1085D4—1222no—
1086D4—1222no—
1087D4—1222no—
1088D4—1222no—
1089D4—1221no—
1090D4—1221no—
1091D4—1221no—
1092D4—4881no—
1093D4—4881no—
1094D4—2442no—
1095D4—2442no—
1096D4—2442no—
1097D4—2441no—
1098D4—2441no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2442no—
1103D4—2442no—
1104D4—2441no—
1105D4—2441no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—48no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—611no—
1129C2×C4—611no—
1130C2×C4—611no—
1131C2×C4—611no—
1132C2×C4—611no—
1133C2×C4—611no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1222no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1222no—
1147C2×C4—1221no—
1148C2×C4—4881no—
1149C2×C4—2442no—
1150C2×C4—2442no—
1151C2×C4—2442no—
1152C2×C4—2442no—
1153C2×C4—2442no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2442no—
1157C2×C4—2442no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4C22⋊C4×D6111yescharacteristic
1167C2×C4C22⋊C4×D6111yescharacteristic
1168C2×C4C22×C4×D6111yescharacteristic
1169C2×C4C2×D4×D6111yescharacteristic
1170C2×C4C2×D4×D6111yescharacteristic
1171C2×C4#41×D6111yescharacteristic
1172C2×C4#1451982211yescharacteristic
1173C2×C4#1451982311yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—1222no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—42no—
1186C22—42no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1222no—
1197C22—4884no—
1198C22—4881no—
1199C22—4881no—
1200C22—4884no—
1201C22—2441no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22#1683977712yescomplemented
1207C22C2×C22⋊C4×D6111yescharacteristic
1208C22#1684039411yescharacteristic
1209C22#1684040411yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—42no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—1221no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—1221no—
1223C4—1222no—
1224C4—4881no—
1225C4—4881no—
1226C4—2441no—
1227C4C4×D4×D6111yescharacteristic
1228C4#1684023411yescharacteristic
1229C4#1684039611yescharacteristic
1230C4#1684040111yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—81no—
1236C2—4881no—
1237C2—2441no—
1238C2—2441no—
1239C2—2442no—
1240C2#2144863711yescharacteristic
1241C2C2×#1683977711yescharacteristic
1242C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1896C2
socleC22×C61C22×C22⋊C4
prime radical#21459302C2
cosocleC22×C4×C61C24
hypercenter#1896D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. #21454551C2semidirect
3. C2×#16839777C2semidirect
4. C22×#14519705C2semidirect
5. #21448262C2semidirect
6. #21446736C2semidirect
7. #21446649C2semidirect
8. #21446266C2semidirect
9. #21446122C2semidirect
10. #21446120C2semidirect
11. #21445838C2semidirect
12. #21445762C2semidirect
13. #21445761C2semidirect
14. #21445628C2semidirect
15. C61×#1896C2semidirect
18. C22×#11758194C22semidirect
19. C2×M16×D61C22semidirect
20. #16840430C4semidirect
21. #16840425C4semidirect
22. #16840422C4semidirect
23. #16840418C4semidirect
24. #16840414C4semidirect
26. #16840409C4semidirect
28. #16840403C4semidirect
30. #16840396C4semidirect
40. C2×#14519734C22semidirect
45. #16839785C22semidirect
50. C2×#14519705C22semidirect
51. C2×#14519705C22semidirect
52. C2×#14519704C22semidirect
53. C2×#14519704C22semidirect
56. C2×#14519703C22semidirect
57. C2×#14519703C22semidirect
58. #16839725C22semidirect
59. M16×Dic61C22semidirect
64. C4×#11758196C22semidirect
65. C4×#11758198C22semidirect
66. C4×C22⋊Dic61C22semidirect
67. #16839608C22semidirect
68. #16839521C22semidirect
69. #16839521C22semidirect
71. C22×C42×C61C22semidirect
72. C2×#104×C61C22semidirect
73. C2×#104×C61C22semidirect
74. C61×#407C22semidirect
75. C61×#339C22semidirect
76. C61×#339C22semidirect
77. C2×#11758226C2×C4semidirect
90. C2×#11758224C2×C4semidirect
96. C2×Q8×D61C2×C4semidirect
102. C2×D4×D61C2×C4semidirect
117. #14519775C2×C4semidirect
119. #14519773C2×C4semidirect
120. #14519766C2×C4semidirect
121. #14519764C2×C4semidirect
129. #14519757C2×C4semidirect
130. #14519757C2×C4semidirect
136. #14519752C2×C4semidirect
137. #14519752C2×C4semidirect
152. #14519742C2×C4semidirect
153. #14519742C2×C4semidirect
158. #14519739C2×C4semidirect
159. #14519739C2×C4semidirect
197. #14519705D4semidirect
372. C42×C61C2×D4semidirect
420. #11758194C2×D4semidirect
569. C22×C61#421semidirect
618. #1896D61semidirect
663. C22×C42C2×D61semidirect
681. C2×#104C2×D61semidirect
682. C2×#104C2×D61semidirect
684. #407C2×D61semidirect
696. #339C2×D61semidirect
697. #339C2×D61semidirect
698. C61#22434semidirect
1047. C42D4×D61semidirect
1206. C22#16839777semidirect

Maximal subgroups

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

subgroupindex
#214593022
#214545512
C2×#168397772
C22×#145197052
#214482622
#214467362
#214466492
#214462662
#214461222
#214461202
#214458382
#214457622
#214457612
#214456282
C61×#18962
#2243461