Finite Group Databasebeta

← #29699729

Subgroups — #29699729

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454615C211yesmaximal, characteristic
2#21454483C211yesmaximal, characteristic, complemented
3#21454481C211yesmaximal, characteristic, complemented
4#21446709C211yesmaximal, characteristic
5#21446706C211yesmaximal, characteristic
6#21446469C211yesmaximal, characteristic, complemented
7#21446468C211yesmaximal, characteristic, complemented
8#21446466C211yesmaximal, characteristic, complemented
9#21445992C211yesmaximal, characteristic, complemented
10#21445838C211yesmaximal, characteristic, complemented
11#21445837C211yesmaximal, characteristic, complemented
12#21445702C211yesmaximal, characteristic, complemented
13#21445699C211yesmaximal, characteristic, complemented
14#21445692C211yesmaximal, characteristic, complemented
15C61×#1929C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17#41×Dic61C2211yescharacteristic
18#16840230C2211yescharacteristic
19#16839871C411yescharacteristic, complemented
20#16839871C411yescharacteristic, complemented
21#16839866C411yescharacteristic, complemented
22#16839866C411yescharacteristic, complemented
23#16839865C411yescharacteristic, complemented
24#16839865C411yescharacteristic, complemented
25#16839859C411yescharacteristic, complemented
26#16839859C411yescharacteristic, complemented
27#16839824—21no—
28#16839821—21no—
29#16839820—21no—
30#16839820—21no—
31#16839817—21no—
32#16839816—21no—
33#16839813—21no—
34#16839812—21no—
35C2×#14519713C2211yescharacteristic
36C2×#14519712C2211yescharacteristic
37C2×#14519712C2211yescharacteristic
38#16839798C2211yescharacteristic
39#16839785C2211yescharacteristic
40#16839785C2211yescharacteristic
41C2×#14519706C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519704C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839730C2211yescharacteristic
47#16839729C2211yescharacteristic
48#16839728C2211yescharacteristic
49#16839720C2211yescharacteristic
50#16839718C2211yescharacteristic
51#16839717C2211yescharacteristic
52C2×#14519688C2211yescharacteristic
53C2×#14519687C2211yescharacteristic
54C2×C8×Dic61C2211yescharacteristic
55C4×#11758196C2211yescharacteristic
56#16839523C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839521C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#108×C61C2211yescharacteristic
61C2×#104×C61C2211yescharacteristic
62C61×#416C2211yescharacteristic
63C61×#408C2211yescharacteristic
64C61×#405C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519797—22no—
69#14519797—22no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78Q8×Dic61C2×C411yescharacteristic
79Q8×Dic61C2×C411yescharacteristic
80#14519742C2×C411yescharacteristic
81#14519742C2×C411yescharacteristic
82D4×Dic61—21no—
83D4×Dic61—21no—
84D4×Dic61C2×C411yescharacteristic
85D4×Dic61C2×C411yescharacteristic
86#14519739C2×C411yescharacteristic
87#14519739C2×C411yescharacteristic
88#14519737—21no—
89#14519737—21no—
90#14519736—21no—
91#14519736C2311yescharacteristic
92#14519734—21no—
93C2×#11758196—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2311yescharacteristic
96C2×C4×Dic61C2311yescharacteristic
97C42×D61—21no—
98#14519713—41no—
99#14519712—22no—
100#14519712—22no—
101#14519710C2×C411yescharacteristic
102#14519710C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104#14519708C2×C411yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706D411yescharacteristic
110#14519706D411yescharacteristic
111#14519706D411yescharacteristic
112#14519706D411yescharacteristic
113#14519705—41no—
114#14519704—41no—
115#14519703—41no—
116#14519702C2×C411yescharacteristic
117#14519702C2×C411yescharacteristic
118#14519699C2×C411yescharacteristic
119#14519699C2×C411yescharacteristic
120C22⋊#92418—21no—
121C22⋊#92418—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125#14519689—21no—
126#14519688—21no—
127#14519688—22no—
128#14519687—21no—
129#14519687—21no—
130#14519687C2×C411yescharacteristic
131#14519687C2×C411yescharacteristic
132#14519687C2×C411yescharacteristic
133#14519687C2×C411yescharacteristic
134C4×#92418—21no—
135C8×Dic61—21no—
136C8×Dic61—21no—
137C8×Dic61—22no—
138#14519684—21no—
139C2×#41×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C2×M16×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144#117×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146#108×C61—41no—
147#104×C61—41no—
148#103×C61C2×C411yescharacteristic
149#103×C61C2×C411yescharacteristic
150#102×C61C2×C411yescharacteristic
151#102×C61C2×C411yescharacteristic
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154#97×C61—21no—
155C4×C8×C61—21no—
156#41×C61—21no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160C2×Q8×C61C22×C411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61C22×C411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61#4111yescharacteristic
171C22×Dic61#4111yescharacteristic
172#11758222—21no—
173#11758222—21no—
174#11758222—21no—
175#11758222—21no—
176C2×D244C22×C411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C4⋊C4×C61C22×C411yescharacteristic
197C22⋊C4×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C22⋊Dic61—21no—
202C22⋊Dic61—21no—
203C22⋊Dic61—21no—
204#11758202—22no—
205#11758201—22no—
206#11758200—22no—
207#11758199—22no—
208#11758198—21no—
209#11758198—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22×C411yescharacteristic
213C4⋊Dic61C22×C411yescharacteristic
214#11758196—21no—
215#11758196—21no—
216#11758196—42no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C22×C411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C22×C411yescharacteristic
237C2×#92418C22×C411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239C2×#92418C2×D411yescharacteristic
240C2×#92418#4112yes—
241C2×#92418#4112yes—
242C23×C61—21no—
243C23×C61C2×#4111yescharacteristic
244C22×D61—21no—
245Q8×C61—21no—
246Q8×C61—21no—
247D4×C61—21no—
248D4×C61—21no—
249D4×C61—41no—
250D4×C61—41no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C22⋊D61—41no—
266C22⋊D61—41no—
267C2×Dic61—22no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—42no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—81no—
277C2×Dic61C4×D411yescharacteristic
278C2×Dic61C4×D411yescharacteristic
279C2×Dic61C4×D411yescharacteristic
280C2×Dic61C4×D411yescharacteristic
281D244—21no—
282D244—21no—
283C4×D61—42no—
284C4×D61—41no—
285C4×D61—41no—
286C4×D61—81no—
287Dic122—21no—
288Dic122—21no—
289C8×C61—21no—
290C8×C61—21no—
291C8×C61—21no—
292C8×C61—21no—
293C8×C61—41no—
294C8×C61—41no—
295#92418—21no—
296#92418—21no—
297#92418—41no—
298#92418—41no—
299#92418#11712yes—
300#92418#11712yes—
301#22804—611nomaximal, Sylow
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—41no—
307C22×C61C2×C4×D411yescharacteristic
308C22×C61#55511yescharacteristic
309C22×C61#55611yescharacteristic
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—81no—
317C4×C61C2×#11711yescharacteristic
318C4×C61#52011yescharacteristic
319C4×C61#54711yescharacteristic
320C4×C61#55011yescharacteristic
321Dic61—21no—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—42no—
326Dic61—41no—
327Dic61—41no—
328Dic61—41no—
329#2943—611no—
330#2925—611no—
331#2925—611no—
332#1975—611no—
333#1974—611no—
334#1929—611no—
335#1929—611no—
336#1929—611no—
337#1929D6111yescharacteristic, complemented
338#1849—611no—
339#1806—611no—
340#1806—611no—
341#1773—611no—
342#1772—611no—
343#1771—611no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61—81no—
347C2×C61#235411yescharacteristic
348C2×C61#295511yescharacteristic
349C2×C61#295611yescharacteristic
350D61—81no—
351C2×#135—611no—
352C4×#41—611no—
353C4×#41—611no—
354#442—611no—
355#442—611no—
356#441—611no—
357#441—611no—
358#440—611no—
359#440—611no—
360#440—611no—
361#440—611no—
362#433—1221no—
363#433—1221no—
364#433—1221no—
365#433—1221no—
366#432—1221no—
367#432—1221no—
368#431—1221no—
369#431—1221no—
370C2×#108—611no—
371C2×#108—611no—
372C2×#108—611no—
373C2×#108C2×D6111yescharacteristic
374#427—611no—
375#423—611no—
376#423—611no—
377C2×C4⋊C8—611no—
378C2×#104—611no—
379C2×#104—611no—
380C2×#104—611no—
381C2×#104C2×D6111yescharacteristic
382#416—611no—
383#416C2×D6111yescharacteristic
384#408—611no—
385#408—611no—
386#408—611no—
387#408C2×D6111yescharacteristic
388#405—611no—
389#405—611no—
390#405—611no—
391#405C2×D6111yescharacteristic
392C2×#97—611no—
393C2×#97—611no—
394C2×C4×C8—611no—
395C4×C4⋊C4—611no—
396#339—611no—
397#339—611no—
398#339—611no—
399#339C2×D6111yescharacteristic
400#336—611no—
401#336C2×D6111yescharacteristic
402C61#2280411yescharacteristic, complemented, Sylow
403C2×#41—611no—
404C2×#41C22×D6111yescharacteristic
405#135—1222no—
406#135—1222no—
407C2×Q16—611no—
408C2×SD16—611no—
409C2×SD16—611no—
410C2×D8—611no—
411C2×M16—611no—
412C2×M16—611no—
413C2×M16C22×D6111yescharacteristic
414C2×M16C22×D6111yescharacteristic
415C22×C8—611no—
416C22×C8—611no—
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419C4×Q8—611no—
420C4×Q8—611no—
421C4×Q8—611no—
422C4×Q8—611no—
423C4×D4—611no—
424C4×D4—611no—
425C4×D4—611no—
426C4×D4—611no—
427C4×D4—1221no—
428C4×D4—1221no—
429C4×D4—1221no—
430C4×D4—1221no—
431#117—611no—
432#117—1221no—
433#117—1221no—
434#117C22×D6111yescharacteristic
435C2×C4⋊C4—1221no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441#108—41no—
442#108—1222no—
443#108—1222no—
444#108—2441no—
445#107—611no—
446#107—611no—
447#106—611no—
448#106—611no—
449C4⋊C8—611no—
450C4⋊C8—611no—
451C4⋊C8—611no—
452C4⋊C8—611no—
453C4⋊C8—1221no—
454C4⋊C8—1221no—
455C4⋊C8—1221no—
456C4⋊C8—1221no—
457#104—41no—
458#104—2441no—
459#104—2441no—
460#104—2441no—
461#103—611no—
462#103—611no—
463#103C4×D6111yescharacteristic
464#103C4×D6111yescharacteristic
465#102—611no—
466#102—611no—
467#102C4×D6111yescharacteristic
468#102C4×D6111yescharacteristic
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—1221no—
472C22⋊C8—1221no—
473C22⋊C8—1221no—
474C22⋊C8—1221no—
475C22⋊C8—1221no—
476C22⋊C8—1221no—
477#97—21no—
478#97—611no—
479#97—611no—
480#97—611no—
481#97—611no—
482#97—1222no—
483#97—1221no—
484#97—1221no—
485#97—1221no—
486C4×C8—21no—
487C4×C8—1221no—
488C4×C8—1222no—
489C4×C8—1221no—
490C4×C8—1221no—
491#95—1221no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—1221no—
497#41—1221no—
498#41—1221no—
499#41—1221no—
500C2×Q8—611no—
501C2×Q8C2×C4×D6111yescharacteristic
502C2×D4—21no—
503C2×D4—611no—
504C2×D4—1221no—
505C2×D4C2×C4×D6111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4C23×D6111yescharacteristic
517Q16—1222no—
518SD16—1222no—
519SD16—1222no—
520D8—1222no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16—1221no—
526M16—1221no—
527M16—1221no—
528M16—1221no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—611no—
536C2×C8—611no—
537C2×C8—612no—
538C2×C8—612no—
539C2×C8—611no—
540C2×C8—611no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8C2×C4×D6111yescharacteristic
546C2×C8C2×C4×D6111yescharacteristic
547C2×C8D4×D6111yescharacteristic
548C2×C8D4×D6111yescharacteristic
549C4⋊C4—611no—
550C4⋊C4—611no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—2442no—
556C4⋊C4C2×C4×D6111yescharacteristic
557C4⋊C4C2×C4×D6111yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—1221no—
560C22⋊C4—1221no—
561C22⋊C4—1221no—
562C22⋊C4—1221no—
563C22⋊C4—1221no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—611no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C23—21no—
579C23—1221no—
580C23#41×D6111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—1221no—
584Q8—1221no—
585D4—21no—
586D4—21no—
587D4—41no—
588D4—41no—
589D4—1221no—
590D4—1221no—
591D4—2441no—
592D4—2441no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—1222no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—4881no—
610C2×C4—4881no—
611C2×C4—2442no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2442no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4C22×C4×D6111yescharacteristic
620C2×C4C2×D4×D6111yescharacteristic
621C2×C4#41×D6111yescharacteristic
622C2×C4#41×D6111yescharacteristic
623C2×C4#1451982211yescharacteristic
624C2×C4#1451982411yescharacteristic
625C8—21no—
626C8—21no—
627C8—21no—
628C8—21no—
629C8—41no—
630C8—41no—
631C8—612no—
632C8—612no—
633C8—1221no—
634C8—1221no—
635C8—2441no—
636C8—2441no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22C4×D4×D6111yescharacteristic
646C22#1684047411yescharacteristic
647C22#1684047911yescharacteristic
648C4—41no—
649C4—41no—
650C4—41no—
651C4—81no—
652C4—1221no—
653C4—1221no—
654C4—1221no—
655C4—1221no—
656C4—2442no—
657C4—2441no—
658C4—2441no—
659C4—2441no—
660C4#117×D6111yescharacteristic
661C4#1684024111yescharacteristic
662C4#1684041011yescharacteristic
663C4#1684043011yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—4881no—
668C2#2144876511yescharacteristic
669C2#2145471711yescharacteristic
670C2#2145472711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1929C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1929D61
hypocenterC61#22804
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. #21454483C2semidirect
3. #21454481C2semidirect
6. #21446469C2semidirect
7. #21446468C2semidirect
8. #21446466C2semidirect
9. #21445992C2semidirect
10. #21445838C2semidirect
11. #21445837C2semidirect
12. #21445702C2semidirect
13. #21445699C2semidirect
14. #21445692C2semidirect
15. C61×#1929C2semidirect
19. #16839871C4semidirect
20. #16839871C4semidirect
21. #16839866C4semidirect
22. #16839866C4semidirect
23. #16839865C4semidirect
24. #16839865C4semidirect
25. #16839859C4semidirect
26. #16839859C4semidirect
337. #1929D61semidirect
402. C61#22804semidirect

Maximal subgroups

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

subgroupindex
#214546152
#214544832
#214544812
#214467092
#214467062
#214464692
#214464682
#214464662
#214459922
#214458382
#214458372
#214457022
#214456992
#214456922
C61×#19292
#2280461