Finite Group Databasebeta

← #29695708

Subgroups — #29695708

Order 15616.

1472 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459302C211yesmaximal, characteristic
2#21454551C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21448278C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446645C211yesmaximal, 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#21445623C211yesmaximal, characteristic, complemented
15C61×#1897C211yesmaximal, 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#16839780—24no—
47#16839777—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#16839662—21no—
61#16839657—21no—
62#16839656—21no—
63#16839652—21no—
64C4×#11758196C2211yescharacteristic, complemented
65C4×#11758198C2211yescharacteristic, complemented
66C4×C22⋊Dic61C2211yescharacteristic, complemented
67C42×Dic61C2211yescharacteristic, complemented
68#16839521C2211yescharacteristic, complemented
69#16839521C2211yescharacteristic, complemented
70C61×#525C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic, complemented
72C2×#104×C61C2211yescharacteristic, complemented
73C2×#104×C61C2211yescharacteristic, complemented
74C61×#407C2211yescharacteristic, complemented
75C61×#339C2211yescharacteristic, complemented
76C61×#339C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic
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
91#41×D61—22no—
92#41×D61—22no—
93#41×D61—41no—
94#41×D61—41no—
95C22×Dic122C2×C411yescharacteristic
96C2×Q8×D61C2×C411yescharacteristic
97C22×D244C2×C411yescharacteristic
98C22×C22⋊D61—21no—
99C22×C22⋊D61D411yescharacteristic
100C2×D4×D61—21no—
101C2×D4×D61—21no—
102C2×D4×D61C2×C411yescharacteristic
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
118#14519773—21no—
119#14519773C2×C411yescharacteristic
120#14519766C2×C411yescharacteristic
121#14519764C2×C411yescharacteristic
122#14519763—21no—
123#14519763—21no—
124#14519762—21no—
125#14519762—21no—
126#14519761—21no—
127#14519759—21no—
128#14519759—21no—
129#14519757C2×C411yescharacteristic
130#14519757C2×C411yescharacteristic
131#14519755—21no—
132#14519755—21no—
133#14519754—21no—
134#14519754—21no—
135#14519752—21no—
136#14519752C2×C411yescharacteristic
137#14519752C2×C411yescharacteristic
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
153#14519742C2×C411yescharacteristic
154C4×D244—21no—
155C4×D244—21no—
156D4×Dic61—21no—
157#14519739—21no—
158#14519739C2×C411yescharacteristic
159#14519739C2×C411yescharacteristic
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×Dic61—21no—
189C2×C4×Dic61—21no—
190C2×C4×Dic61C2311yescharacteristic
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194#14519706—21no—
195#14519706—21no—
196#14519705—22no—
197#14519705—22no—
198#14519705—22no—
199#14519705D414yescomplemented
200#14519704—22no—
201#14519704—41no—
202#14519703—22no—
203#14519703—22no—
204#14519703—41no—
205#14519703—41no—
206#14519689—21no—
207#14519689—21no—
208#14519687—21no—
209C8×Dic61—21no—
210#14519684—21no—
211#14519684—21no—
212#14519684—21no—
213C2×#41×C61C2311yescharacteristic
214C23×C4×C61C2311yescharacteristic
215C2×M16×C61C2311yescharacteristic
216C2×M16×C61C2311yescharacteristic
217#123×C61—21no—
218C22⋊Q8×C61C2×C411yescharacteristic
219C22⋊Q8×C61C2×C411yescharacteristic
220#121×C61C2×C411yescharacteristic
221#121×C61C2×C411yescharacteristic
222#120×C61—21no—
223C4×D4×C61—21no—
224C4×D4×C61—21no—
225#117×C61—22no—
226#117×C61—41no—
227#117×C61C2311yescharacteristic
228C2×C4⋊C4×C61—21no—
229C2×C22⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2411yescharacteristic
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61—21no—
270C2×C22⋊D61—42no—
271C2×C22⋊D61—42no—
272C2×C22⋊D61—42no—
273C2×C22⋊D61C22⋊C411yescharacteristic
274C2×C22⋊D61C22⋊C411yescharacteristic
275C2×C22⋊D61C22⋊C411yescharacteristic
276C2×C22⋊D61C22⋊C411yescharacteristic
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61C2×D411yescharacteristic
282C22×Dic61C2×D411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284#11758226—22no—
285#11758226—41no—
286Q8×D61—22no—
287Q8×D61—41no—
288#11758224—22no—
289#11758224—41no—
290#11758224—42no—
291#11758224—42no—
292D4×D61—22no—
293D4×D61—41no—
294D4×D61—42no—
295D4×D61—42no—
296D4×D61—44no—
297#11758222—21no—
298#11758222—21no—
299#11758222—21no—
300#11758222—21no—
301#11758222—21no—
302#11758222—21no—
303#11758222—22no—
304#11758222—22no—
305#11758222—41no—
306#11758222—41no—
307#11758222—42no—
308#11758222—42no—
309#11758222—42no—
310#11758222—42no—
311#11758222—42no—
312#11758222—42no—
313#11758222C2×D412yes—
314#11758222#4112yes—
315C2×D244—22no—
316C2×D244—21no—
317C2×D244—21no—
318C2×D244—21no—
319C2×D244—21no—
320C2×D244—41no—
321C2×D244C22×C411yescharacteristic
322C2×D244C22×C411yescharacteristic
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
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—42no—
336C2×C4×D61—42no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61C22×C411yescharacteristic
340C2×C4×D61C22×C411yescharacteristic
341C2×C4×D61C2×D411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×Dic122—22no—
344C2×Dic122—21no—
345C2×Dic122—21no—
346C2×Dic122—41no—
347C2×Dic122C22×C411yescharacteristic
348C2×Dic122C22×C411yescharacteristic
349M16×C61—21no—
350M16×C61—21no—
351M16×C61—21no—
352M16×C61—21no—
353C2×C8×C61—21no—
354C2×C8×C61—21no—
355C4⋊C4×C61—21no—
356C4⋊C4×C61—21no—
357C4⋊C4×C61—42no—
358C4⋊C4×C61C22×C411yescharacteristic
359C4⋊C4×C61C22×C411yescharacteristic
360C22⋊C4×C61—21no—
361C22⋊C4×C61—21no—
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C22⋊C4×C61—21no—
365C22⋊C4×C61—42no—
366C42×C61—21no—
367C42×C61—21no—
368C42×C61—21no—
369C42×C61—21no—
370C42×C61C2×D412yescomplemented
371C22⋊Dic61—21no—
372C22⋊Dic61—21no—
373C22⋊Dic61—42no—
374C22⋊Dic61C22⋊C411yescharacteristic
375C22⋊Dic61C22⋊C411yescharacteristic
376C22⋊Dic61C22⋊C411yescharacteristic
377C22⋊Dic61C22⋊C411yescharacteristic
378#11758198—21no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383#11758198—21no—
384#11758198—21no—
385#11758198—21no—
386#11758198—42no—
387#11758198—42no—
388#11758198C22⋊C411yescharacteristic
389#11758198C22⋊C411yescharacteristic
390#11758198C22⋊C411yescharacteristic
391#11758198C22⋊C411yescharacteristic
392C4⋊Dic61—21no—
393C4⋊Dic61—21no—
394#11758196—21no—
395#11758196—21no—
396#11758196—21no—
397#11758196—21no—
398#11758196—42no—
399#11758196—42no—
400#11758196C22⋊C411yescharacteristic
401#11758196C22⋊C411yescharacteristic
402#11758196C22⋊C411yescharacteristic
403#11758196C22⋊C411yescharacteristic
404C4×Dic61—21no—
405C4×Dic61—21no—
406C4×Dic61—21no—
407C4×Dic61—21no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—42no—
411C4×Dic61—42no—
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—21no—
429C23×C61—41no—
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—42no—
453D4×C61—41no—
454D4×C61—41no—
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—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—22no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61—41no—
477C2×C4×C61C2×C22⋊C411yescharacteristic
478C2×C4×C61C2×C22⋊C411yescharacteristic
479C2×C4×C61C23×C411yescharacteristic
480C2×C4×C61C22×D411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C2×#4111yescharacteristic
483C2×C4×C61H(5,𝔽2)11yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C22⋊D61—22no—
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—22no—
489C22⋊D61—41no—
490C22⋊D61—41no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—42no—
495C22⋊D61—41no—
496C22⋊D61—41no—
497C22⋊D61—42no—
498C22⋊D61—81no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—21no—
502C2×Dic61—22no—
503C2×Dic61—22no—
504C2×Dic61—21no—
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×Dic61C2×C22⋊C411yescharacteristic
514C2×Dic61C2×C22⋊C411yescharacteristic
515C2×Dic61C2×C22⋊C411yescharacteristic
516C2×Dic61C2×C22⋊C411yescharacteristic
517C2×Dic61C2×C22⋊C411yescharacteristic
518C2×Dic61C2×C22⋊C411yescharacteristic
519D244—21no—
520D244—21no—
521D244—21no—
522D244—42no—
523D244—42no—
524D244—42no—
525D244—81no—
526D244C4×D412yes—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—22no—
534C4×D61—21no—
535C4×D61—21no—
536C4×D61—22no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—41no—
542C4×D61—41no—
543C4×D61—42no—
544C4×D61—81no—
545Dic122—21no—
546Dic122—21no—
547Dic122—21no—
548Dic122—42no—
549Dic122—42no—
550Dic122C4×D412yes—
551C8×C61—41no—
552C8×C61—41no—
553#92418—22no—
554#92418—41no—
555#22435—611nomaximal, Sylow
556C22×C61—21no—
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—41no—
565C22×C61—41no—
566C22×C61—41no—
567C22×C61—81no—
568C22×C61—81no—
569C22×C61C22×C22⋊C411yescharacteristic
570C22×C61D4211yescharacteristic
571C22×C61#54611yescharacteristic
572C2×D61—21no—
573C2×D61—21no—
574C2×D61—22no—
575C2×D61—21no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—41no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—81no—
585C2×D61—81no—
586C2×D61—84no—
587C2×D61—84no—
588C4×C61—21no—
589C4×C61—21no—
590C4×C61—42no—
591C4×C61—41no—
592C4×C61—41no—
593C4×C61—41no—
594C4×C61—81no—
595C4×C61C2×C4×D411yescharacteristic
596C4×C61#51811yescharacteristic
597C4×C61D4211yescharacteristic
598C4×C61#54611yescharacteristic
599Dic61—22no—
600Dic61—21no—
601Dic61—21no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—42no—
606Dic61—41no—
607Dic61—81no—
608Dic61#42112yescomplemented
609D4×#41—611no—
610D4×M16—611no—
611C2×#421—611no—
612C2×#421—611no—
613#2293—611no—
614#1980—611no—
615#1962—611no—
616#1897—611no—
617#1897D6111yescharacteristic, complemented
618#1871—611no—
619#1871—611no—
620#1806—611no—
621#1789—611no—
622#1789—611no—
623C4×#104—611no—
624C2×C61—21no—
625C2×C61—21no—
626C2×C61—41no—
627C2×C61—41no—
628C2×C61—81no—
629C2×C61D4×C22⋊C411yescharacteristic
630C2×C61C2×#42111yescharacteristic
631C2×C61#290111yescharacteristic
632D61—41no—
633D61—41no—
634D61—42no—
635D61—81no—
636C22×#41—611no—
637C22×#41—611no—
638C22×M16—611no—
639C22×M16—611no—
640#550—611no—
641D4×Q8—611no—
642#548—611no—
643#548—611no—
644#547—611no—
645#547—1221no—
646#546—611no—
647#546—611no—
648#546—1221no—
649#546—1221no—
650D42—611no—
651D42—1221no—
652#532—611no—
653#532—1221no—
654#525—611no—
655#525—1221no—
656#525—1221no—
657#525C2×D6111yescharacteristic
658C4×#41—611no—
659C2×C4×D4—611no—
660C2×C4×D4—1221no—
661C2×#117—611no—
662C2×#117C2×D6111yescharacteristic, complemented
663#436—1221no—
664#435—1221no—
665#435—1221no—
666C8×D4—1221no—
667#423—611no—
668#421—1224no—
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×#104C2×D6111yescharacteristic, complemented
681C2×#104C2×D6111yescharacteristic, complemented
682#407—611no—
683#407C2×D6111yescharacteristic, complemented
684C4×M16—611no—
685#390—1221no—
686#389—1221no—
687#388—1221no—
688#388—1221no—
689C4×C4⋊C4—611no—
690C4×C22⋊C4—611no—
691C4×C22⋊C4—611no—
692C43—611no—
693#339—611no—
694#339—611no—
695#339C2×D6111yescharacteristic, complemented
696#339C2×D6111yescharacteristic, complemented
697C61#2243511yescharacteristic, complemented, Sylow
698C2×#41—611no—
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—1221no—
705C2×#41—1222no—
706C2×#41—1222no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—2441no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41C22×D6111yescharacteristic
717C22×Q8—611no—
718C22×Q8—611no—
719C22×D4—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—1221no—
723C22×D4—1221no—
724C22×D4—1221no—
725C23×C4—611no—
726C23×C4—1221no—
727C23×C4—1221no—
728C23×C4C22×D6111yescharacteristic
729C2×M16—611no—
730C2×M16—611no—
731C2×M16—1221no—
732C2×M16—1221no—
733C2×M16—1222no—
734C2×M16—1222no—
735C2×M16—2441no—
736C2×M16—2441no—
737C2×M16C22×D6111yescharacteristic
738C2×M16C22×D6111yescharacteristic
739C22×C8—1221no—
740C22×C8—1221no—
741C4⋊Q8—611no—
742C4⋊Q8—1221no—
743#127—611no—
744#127—1221no—
745#124—611no—
746#124—611no—
747#124—1221no—
748#124—1221no—
749#123—21no—
750#123—1221no—
751#123—1221no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755C22⋊Q8—611no—
756C22⋊Q8—611no—
757C22⋊Q8—1221no—
758C22⋊Q8—1221no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8C4×D6111yescharacteristic
762C22⋊Q8C4×D6111yescharacteristic
763#121—611no—
764#121—611no—
765#121—1221no—
766#121—1221no—
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#121C4×D6111yescharacteristic
776#121C4×D6111yescharacteristic
777#120—21no—
778#120—1221no—
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783C4×Q8—611no—
784C4×Q8—611no—
785C4×D4—21no—
786C4×D4—21no—
787C4×D4—611no—
788C4×D4—611no—
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—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807#117—22no—
808#117—41no—
809#117—1221no—
810#117—1222no—
811#117—2441no—
812#117C22×D6111yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—611no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C4⋊C4—1221no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—611no—
820C2×C22⋊C4—611no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C22⋊C4—1221no—
825C2×C22⋊C4—1221no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—1221no—
830C2×C42—1221no—
831C2×C42—1221no—
832C2×C42C22×D6111yescharacteristic
833C2×C42C22×D6111yescharacteristic
834C4⋊C8—1221no—
835C4⋊C8—1221no—
836#104—22no—
837#104—41no—
838#104—614no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—1222no—
845#104—2441no—
846#104—2441no—
847#104—2441no—
848C22⋊C8—21no—
849C22⋊C8—21no—
850C22⋊C8—1221no—
851C22⋊C8—1221no—
852#97—1221no—
853C4×C8—1221no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857C24—611no—
858C24—1221no—
859C24—1221no—
860C24D4×D6111yescharacteristic
861#41—21no—
862#41—21no—
863#41—21no—
864#41—21no—
865#41—612no—
866#41—612no—
867#41—1222no—
868#41—1222no—
869#41—1221no—
870#41—1221no—
871#41—1222no—
872#41—1222no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—2442no—
878#41—2442no—
879#41—2441no—
880#41—2441no—
881#41—2442no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2441no—
886#41—2442no—
887#41—2442no—
888#41—2441no—
889C2×Q8—611no—
890C2×Q8—611no—
891C2×Q8—1221no—
892C2×Q8—1222no—
893C2×Q8—1221no—
894C2×Q8—1222no—
895C2×Q8—2441no—
896C2×Q8—2441no—
897C2×Q8C2×C4×D6111yescharacteristic
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—1222no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1222no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—2441no—
922C2×D4—2441no—
923C2×D4—2442no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2444no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4C2×C4×D6111yescharacteristic
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—611no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
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—2442no—
961C22×C4—2442no—
962C22×C4—2442no—
963C22×C4—2442no—
964C22×C4C2×C4×D6111yescharacteristic
965C22×C4C2×C4×D6111yescharacteristic
966C22×C4D4×D6111yescharacteristic
967C22×C4D4×D6111yescharacteristic
968C22×C4D4×D6111yescharacteristic
969C22×C4C23×D6111yescharacteristic
970M16—21no—
971M16—21no—
972M16—21no—
973M16—21no—
974M16—612no—
975M16—1221no—
976M16—1221no—
977M16—1221no—
978M16—2442no—
979M16—2442no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—1221no—
983C2×C8—1221no—
984C2×C8—2442no—
985C2×C8—2442no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—42no—
989C4⋊C4—611no—
990C4⋊C4—611no—
991C4⋊C4—611no—
992C4⋊C4—611no—
993C4⋊C4—1221no—
994C4⋊C4—1221no—
995C4⋊C4—1221no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—2442no—
1000C4⋊C4—2442no—
1001C4⋊C4C2×C4×D6111yescharacteristic
1002C4⋊C4C2×C4×D6111yescharacteristic
1003C22⋊C4—21no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—42no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—1221no—
1018C22⋊C4—1221no—
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—2442no—
1028C22⋊C4—2442no—
1029C22⋊C4—2442no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—611no—
1035C42—611no—
1036C42—611no—
1037C42—611no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—2442no—
1045C42—2442no—
1046C42D4×D6112yescomplemented
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—41no—
1051C23—41no—
1052C23—611no—
1053C23—611no—
1054C23—1221no—
1055C23—1221no—
1056C23—1221no—
1057C23—1221no—
1058C23—4881no—
1059C23—4881no—
1060C23—2441no—
1061C23—2441no—
1062C23—2442no—
1063C23—2442no—
1064C23—2442no—
1065C23—2442no—
1066C23C22⋊C4×D6111yescharacteristic
1067C23C22⋊C4×D6111yescharacteristic
1068C23C2×D4×D6111yescharacteristic
1069Q8—21no—
1070Q8—21no—
1071Q8—612no—
1072Q8—1221no—
1073Q8—1221no—
1074Q8—1221no—
1075Q8—2442no—
1076Q8—2442no—
1077D4—21no—
1078D4—21no—
1079D4—42no—
1080D4—41no—
1081D4—41no—
1082D4—81no—
1083D4—612no—
1084D4—1222no—
1085D4—1222no—
1086D4—1222no—
1087D4—1222no—
1088D4—1221no—
1089D4—1221no—
1090D4—1221no—
1091D4—4881no—
1092D4—4881no—
1093D4—2442no—
1094D4—2442no—
1095D4—2442no—
1096D4—2442no—
1097D4—2441no—
1098D4—2441no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2442no—
1103D4—2441no—
1104D4—2441no—
1105C2×C4—21no—
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—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—611no—
1127C2×C4—611no—
1128C2×C4—611no—
1129C2×C4—611no—
1130C2×C4—611no—
1131C2×C4—611no—
1132C2×C4—1222no—
1133C2×C4—1221no—
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—1222no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1222no—
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—2442no—
1156C2×C4—2442no—
1157C2×C4—2441no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4C22⋊C4×D6111yescharacteristic
1165C2×C4C22⋊C4×D6111yescharacteristic
1166C2×C4C22×C4×D6111yescharacteristic
1167C2×C4C2×D4×D6111yescharacteristic
1168C2×C4C2×D4×D6111yescharacteristic
1169C2×C4#41×D6111yescharacteristic
1170C2×C4#1451982211yescharacteristic
1171C2×C4#1451982311yescharacteristic
1172C8—41no—
1173C8—41no—
1174C8—1222no—
1175C8—2441no—
1176C22—21no—
1177C22—21no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—81no—
1188C22—81no—
1189C22—1221no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1222no—
1196C22—4881no—
1197C22—4881no—
1198C22—4884no—
1199C22—4884no—
1200C22—2441no—
1201C22—2441no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22C2×C22⋊C4×D6111yescharacteristic
1206C22#1684039411yescharacteristic
1207C22#1684040411yescharacteristic
1208C4—21no—
1209C4—21no—
1210C4—42no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—81no—
1215C4—612no—
1216C4—1221no—
1217C4—1221no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1222no—
1222C4—4881no—
1223C4—2442no—
1224C4—2441no—
1225C4C4×D4×D6111yescharacteristic
1226C4#1684023411yescharacteristic
1227C4#1684039611yescharacteristic
1228C4#1684040111yescharacteristic
1229C2—21no—
1230C2—21no—
1231C2—41no—
1232C2—41no—
1233C2—81no—
1234C2—4881no—
1235C2—2441no—
1236C2—2441no—
1237C2—2442no—
1238C2#2144863711yescharacteristic
1239C2#421×D6111yescharacteristic
1240C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1897C2
socleC22×C61C22×C22⋊C4
prime radical#21459302C2
cosocleC22×C4×C61C24
hypercenter#1897D61
hypocenterC61#22435
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #21454551C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839777C2semidirect
5. #21448278C2semidirect
6. #21446736C2semidirect
7. #21446645C2semidirect
8. #21446266C2semidirect
9. #21446122C2semidirect
10. #21446120C2semidirect
11. #21445838C2semidirect
12. #21445762C2semidirect
13. #21445761C2semidirect
14. #21445623C2semidirect
15. C61×#1897C2semidirect
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. C42×Dic61C22semidirect
68. #16839521C22semidirect
69. #16839521C22semidirect
71. C2×#117×C61C22semidirect
72. C2×#104×C61C22semidirect
73. C2×#104×C61C22semidirect
74. C61×#407C22semidirect
75. C61×#339C22semidirect
76. C61×#339C22semidirect
199. #14519705D4semidirect
370. C42×C61C2×D4semidirect
420. #11758194C2×D4semidirect
608. Dic61#421semidirect
617. #1897D61semidirect
662. C2×#117C2×D61semidirect
680. C2×#104C2×D61semidirect
681. C2×#104C2×D61semidirect
683. #407C2×D61semidirect
695. #339C2×D61semidirect
696. #339C2×D61semidirect
697. C61#22435semidirect
1046. C42D4×D61semidirect

Maximal subgroups

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

subgroupindex
#214593022
#214545512
C2×#168397802
C2×#168397772
#214482782
#214467362
#214466452
#214462662
#214461222
#214461202
#214458382
#214457622
#214457612
#214456232
C61×#18972
#2243561