Finite Group Databasebeta

← #29698790

Subgroups — #29698790

Order 15616.

796 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×D244C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic
3C2×#16839832C211yesmaximal, characteristic
4#21446595C211yesmaximal, characteristic, complemented
5#21446025C211yesmaximal, characteristic, complemented
6#21446025C211yesmaximal, characteristic, complemented
7#21446022C211yesmaximal, characteristic, complemented
8#21446022C211yesmaximal, characteristic, complemented
9#21445959C211yesmaximal, characteristic, complemented
10#21445858C211yesmaximal, characteristic, complemented
11#21445854C211yesmaximal, characteristic, complemented
12#21445726C211yesmaximal, characteristic, complemented
13#21445544C211yesmaximal, characteristic, complemented
14#341×D61C211yesmaximal, characteristic, complemented
15C61×#1950C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20C2×M16×D61C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839841—21no—
24#16839839—21no—
25#16839835—21no—
26#16839835—21no—
27#16839832—21no—
28#16839832—21no—
29#16839832C412yes—
30#16839832C412yes—
31#16839832C412yes—
32#16839832C412yes—
33C8×D244—21no—
34#16839827—21no—
35C2×#14519713C2211yescharacteristic
36C2×#14519713C2211yescharacteristic
37C2×#14519712C2211yescharacteristic
38C2×#14519712C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839725C2211yescharacteristic
41#16839725C2211yescharacteristic
42#16839725C2211yescharacteristic
43#16839725C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C4×#11758194C2211yescharacteristic
47C2×#14519688C2211yescharacteristic
48#16839527C2211yescharacteristic
49#16839527C2211yescharacteristic
50#16839526C2211yescharacteristic
51#16839526C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56C2×#108×C61C2211yescharacteristic
57C2×#108×C61C2211yescharacteristic
58C61×#423C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic
60C4×M16×C61C2211yescharacteristic
61C61×#341C2211yescharacteristic
62C61×#341C2211yescharacteristic
63C22×D244Q811yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C2×#11758194C2311yescharacteristic
69C2×#11758194C2311yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—41no—
75C2×#11758189—41no—
76C2×#11758189C2×C412yes—
77C2×#11758189C2×C412yes—
78M16×D61—22no—
79M16×D61—22no—
80M16×D61—22no—
81M16×D61—22no—
82M16×D61—41no—
83M16×D61—41no—
84M16×D61—41no—
85M16×D61—41no—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C2×C8×D61—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92C2×C8×D61—41no—
93C2×C8×D61—41no—
94C2×C8×D61C2×C412yes—
95C2×C8×D61C2×C412yes—
96C4×D244C2×C411yescharacteristic
97C4×D244C2×C411yescharacteristic
98C4×D244C2×C411yescharacteristic
99C4×D244C2×C411yescharacteristic
100C4×D244D411yescharacteristic
101C4×D244D411yescharacteristic
102C4×D244D411yescharacteristic
103C4×D244D411yescharacteristic
104C2×C4⋊Dic61Q811yescharacteristic
105C2×#11758198Q811yescharacteristic
106C2×#11758198Q811yescharacteristic
107#14519713—41no—
108#14519713—41no—
109#14519712—22no—
110#14519712—22no—
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689—21no—
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689C2×C412yes—
122#14519689C2×C412yes—
123#14519689C2×C412yes—
124#14519689C2×C412yes—
125#14519688—21no—
126#14519688C2×C412yes—
127#14519688C2×C412yes—
128C4×#92418—21no—
129C2×M16×C61C2311yescharacteristic
130C2×M16×C61C2311yescharacteristic
131C2×M16×C61C2311yescharacteristic
132C2×M16×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#108×C61—41no—
137#108×C61—41no—
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2×C412yes—
141C4⋊C8×C61C2×C412yes—
142#97×C61—21no—
143C4×C8×C61—21no—
144C23×D61C2×Q811yescharacteristic
145C23×D61C2×Q811yescharacteristic
146C22×C4×C61C2×Q811yescharacteristic
147C22×C4×C61C2×Q811yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C22×Dic61C2×Q811yescharacteristic
150C22×Dic61C2×Q811yescharacteristic
151C2×D244—42no—
152C2×D244C4⋊C411yescharacteristic
153C2×D244C4⋊C411yescharacteristic
154C2×D244C4⋊C411yescharacteristic
155C2×D244C4⋊C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×D411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172M16×C61—21no—
173M16×C61—21no—
174M16×C61—21no—
175M16×C61—21no—
176M16×C61—21no—
177M16×C61—21no—
178M16×C61—21no—
179M16×C61#4112yes—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61C22×C412yes—
189C2×C8×C61C22×C412yes—
190C42×C61C22×C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192C42×C61C2×D411yescharacteristic
193C42×C61C2×D411yescharacteristic
194#11758198C4⋊C411yescharacteristic
195#11758198C4⋊C411yescharacteristic
196#11758198C4⋊C411yescharacteristic
197#11758198C4⋊C411yescharacteristic
198#11758198C4⋊C411yescharacteristic
199#11758198C4⋊C411yescharacteristic
200#11758198C4⋊C411yescharacteristic
201#11758198C4⋊C411yescharacteristic
202C4⋊Dic61C4⋊C411yescharacteristic
203C4⋊Dic61C4⋊C411yescharacteristic
204C4⋊Dic61C4⋊C411yescharacteristic
205C4⋊Dic61C4⋊C411yescharacteristic
206#11758194—21no—
207#11758194—21no—
208#11758194—21no—
209#11758194—21no—
210#11758194—21no—
211#11758194—21no—
212#11758194—21no—
213#11758194#4112yes—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C22×C412yes—
223C2×#92418C22×C412yes—
224#11758189—42no—
225#11758189—42no—
226#11758189—42no—
227#11758189—42no—
228#11758189—42no—
229#11758189—42no—
230C8×D61—42no—
231C8×D61—42no—
232C8×D61—42no—
233C8×D61—42no—
234C8×D61—42no—
235C8×D61—42no—
236C23×C61C22×Q811yescharacteristic
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—22no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61C2×C4⋊C411yescharacteristic
246C22×D61C2×C4⋊C411yescharacteristic
247C22×D61C2×C4⋊C411yescharacteristic
248C22×D61C2×C4⋊C411yescharacteristic
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61C2×C4⋊C411yescharacteristic
252C2×C4×C61C2×C4⋊C411yescharacteristic
253C2×C4×C61C2×C4⋊C411yescharacteristic
254C2×C4×C61C2×C4⋊C411yescharacteristic
255C2×C4×C61C23×C411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C61H(5,𝔽2)11yescharacteristic
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61C2×C4⋊C411yescharacteristic
266C2×Dic61C2×C4⋊C411yescharacteristic
267C2×Dic61C2×C4⋊C411yescharacteristic
268C2×Dic61C2×C4⋊C411yescharacteristic
269D244—22no—
270D244—22no—
271D244—41no—
272D244—41no—
273C4×D61—21no—
274C4×D61—21no—
275C4×D61—21no—
276C4×D61—21no—
277C4×D61—21no—
278C4×D61—21no—
279C4×D61—21no—
280C4×D61—21no—
281C4×D61—21no—
282C4×D61—21no—
283C4×D61—21no—
284C4×D61—21no—
285C4×D61—21no—
286C4×D61—21no—
287C4×D61—21no—
288C4×D61—21no—
289C8×C61—22no—
290C8×C61—22no—
291C8×C61—22no—
292C8×C61—41no—
293C8×C61—41no—
294C8×C61—41no—
295#92418—22no—
296#92418—22no—
297#92418—22no—
298#92418—41no—
299#92418—41no—
300#92418—41no—
301#22718—611nomaximal, Sylow
302C22×C61—21no—
303C22×C61—21no—
304C22×C61C22×C4⋊C411yescharacteristic
305C22×C61#55411yescharacteristic
306C22×C61#55411yescharacteristic
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—21no—
312C2×D61—21no—
313C2×D61—21no—
314C2×D61—21no—
315C2×D61—21no—
316C2×D61—21no—
317C2×D61—21no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—81no—
321C2×D61—81no—
322C2×D61#43012yes—
323C4×C61—21no—
324C4×C61—21no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61C4×#4111yescharacteristic
328C4×C61#51811yescharacteristic
329C4×C61#54611yescharacteristic
330C4×C61#54611yescharacteristic
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335D4×M16—611no—
336D4×M16—611no—
337C2×#435—611no—
338#1950—611no—
339#1950D6111yescharacteristic, complemented
340#1855—611no—
341#1855—611no—
342#1855—611no—
343#1855—611no—
344#1838—611no—
345#1811—611no—
346#1810—611no—
347#1778—611no—
348#1738—611no—
349C2×#341—611no—
350C2×C61—21no—
351C2×C61—21no—
352C2×C61#234911yescharacteristic
353C2×C61C2×#43011yescharacteristic
354C2×C61#291611yescharacteristic
355D61—22no—
356D61—41no—
357D61—41no—
358D61—41no—
359C22×M16—611no—
360C22×M16—611no—
361C22×M16—611no—
362C22×M16—611no—
363C22×M16—611no—
364C23×C8—611no—
365C2×C4×D4—611no—
366#436—1221no—
367#436—1221no—
368#435—612no—
369#435—612no—
370#435—612no—
371#435—612no—
372#435—1221no—
373#435—1221no—
374#435—1221no—
375#435—1221no—
376C8×D4—1221no—
377C8×D4—1221no—
378C2×#108—611no—
379C2×#108—611no—
380C2×#108—611no—
381C2×#108—611no—
382C2×#108C2×D6111yescharacteristic
383C2×#108C2×D6111yescharacteristic
384#423—611no—
385#423C2×D6111yescharacteristic
386C2×C4⋊C8C2×D6111yescharacteristic
387#407—611no—
388#407—611no—
389#407—611no—
390#407—611no—
391C2×C22⋊C8—611no—
392C2×C22⋊C8—611no—
393C4×M16—611no—
394C4×M16C2×D6111yescharacteristic
395C2×#97—611no—
396#341—611no—
397#341—611no—
398#341—611no—
399#341—611no—
400#341—611no—
401#341—611no—
402#341—611no—
403#341—611no—
404#341C2×D6111yescharacteristic
405#341C2×D6111yescharacteristic
406C61#2271811yescharacteristic, complemented, Sylow
407C22×D4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C2×M16—612no—
411C2×M16—612no—
412C2×M16—611no—
413C2×M16—611no—
414C2×M16—611no—
415C2×M16—611no—
416C2×M16—1221no—
417C2×M16—1221no—
418C2×M16—1221no—
419C2×M16—1221no—
420C2×M16—1222no—
421C2×M16—1222no—
422C2×M16—1222no—
423C2×M16—1222no—
424C2×M16—2441no—
425C2×M16—2441no—
426C2×M16—2441no—
427C2×M16—2441no—
428C2×M16—2441no—
429C2×M16—2441no—
430C2×M16C22×D6111yescharacteristic
431C2×M16C22×D6111yescharacteristic
432C2×M16C22×D6111yescharacteristic
433C2×M16C22×D6111yescharacteristic
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—612no—
437C22×C8—612no—
438C22×C8—1221no—
439C22×C8—1221no—
440C22×C8—1221no—
441C22×C8—1221no—
442C22×C8—2441no—
443C22×C8—2441no—
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C4×D4—611no—
447C4×D4—611no—
448C4×D4—611no—
449C4×D4—611no—
450C4×D4—611no—
451C4×D4—611no—
452C4×D4—611no—
453C4×D4—611no—
454C2×C4⋊C4—611no—
455C2×C22⋊C4—611no—
456C2×C22⋊C4—611no—
457C2×C42C22×D6111yescharacteristic
458#108—41no—
459#108—41no—
460#108—1222no—
461#108—1222no—
462#108—2441no—
463#108—2441no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8C4×D6112yes—
469C4⋊C8C4×D6112yes—
470C22⋊C8—612no—
471C22⋊C8—612no—
472C22⋊C8—612no—
473C22⋊C8—612no—
474C22⋊C8—1221no—
475C22⋊C8—1221no—
476C22⋊C8—1221no—
477C22⋊C8—1221no—
478C22⋊C8—1221no—
479C22⋊C8—1221no—
480C22⋊C8—1221no—
481C22⋊C8—1221no—
482#97—21no—
483#97—612no—
484#97—612no—
485#97—1221no—
486C4×C8—21no—
487C4×C8—1221no—
488C24—611no—
489C24—611no—
490C2×D4—611no—
491C2×D4—611no—
492C2×D4—611no—
493C2×D4—611no—
494C2×D4—2442no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4Q8×D6111yescharacteristic
514C22×C4Q8×D6111yescharacteristic
515C22×C4C23×D6111yescharacteristic
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—612no—
524M16—1221no—
525M16—1221no—
526M16—1221no—
527M16—1221no—
528M16—1221no—
529M16—1221no—
530M16—1221no—
531M16—2442no—
532M16—2442no—
533M16—2442no—
534M16—2442no—
535M16—2442no—
536M16—2442no—
537M16#1175822612yes—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—612no—
547C2×C8—612no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—2442no—
557C2×C8—2442no—
558C2×C8—2442no—
559C2×C8—2442no—
560C2×C8—2442no—
561C2×C8—2442no—
562C2×C8C2×C4×D6112yes—
563C2×C8C2×C4×D6112yes—
564C4⋊C4—611no—
565C4⋊C4—611no—
566C4⋊C4—611no—
567C4⋊C4—611no—
568C22⋊C4—611no—
569C22⋊C4—611no—
570C22⋊C4—611no—
571C22⋊C4—611no—
572C22⋊C4—611no—
573C22⋊C4—611no—
574C22⋊C4—611no—
575C22⋊C4—611no—
576C42C2×C4×D6111yescharacteristic
577C42C2×C4×D6111yescharacteristic
578C42D4×D6111yescharacteristic
579C42D4×D6111yescharacteristic
580C23—611no—
581C23—611no—
582C23—611no—
583C23—611no—
584C23—1222no—
585C23—1221no—
586C23—1221no—
587C23—1221no—
588C23—1221no—
589C23—2441no—
590C23—2441no—
591C23—2441no—
592C23C2×Q8×D6111yescharacteristic
593D4—1222no—
594D4—1222no—
595D4—2441no—
596D4—2441no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4C4⋊C4×D6111yescharacteristic
624C2×C4C4⋊C4×D6111yescharacteristic
625C2×C4C4⋊C4×D6111yescharacteristic
626C2×C4C4⋊C4×D6111yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4C2×#1175822611yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982311yescharacteristic
633C8—22no—
634C8—22no—
635C8—22no—
636C8—41no—
637C8—41no—
638C8—41no—
639C8—1222no—
640C8—1222no—
641C8—1222no—
642C8—2441no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—612no—
648C22—1221no—
649C22—1221no—
650C22—1221no—
651C22—1221no—
652C22—1221no—
653C22—1221no—
654C22—1221no—
655C22—1221no—
656C22—1221no—
657C22—1221no—
658C22—1221no—
659C22—4881no—
660C22—4881no—
661C22—2442no—
662C22—2442no—
663C22C2×C4⋊C4×D6111yescharacteristic
664C22#1684046811yescharacteristic
665C22#1684047311yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—1221no—
671C4—1221no—
672C4—1221no—
673C4—1221no—
674C4C4×#1175822611yescharacteristic
675C4#1684023411yescharacteristic
676C4#1684040311yescharacteristic
677C4#1684040911yescharacteristic
678C2—21no—
679C2—21no—
680C2—1222no—
681C2—2441no—
682C2—2441no—
683C2—2441no—
684C2#2144872811yescharacteristic
685C2#430×D6111yescharacteristic
686C2#2145442711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1950C2
socleC22×C61C22×C4⋊C4
prime radicalC22×D244Q8
cosocleC22×C4×C61C24
hypercenter#1950D61
hypocenterC61#22718
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
4. #21446595C2semidirect
5. #21446025C2semidirect
6. #21446025C2semidirect
7. #21446022C2semidirect
8. #21446022C2semidirect
9. #21445959C2semidirect
10. #21445858C2semidirect
11. #21445854C2semidirect
12. #21445726C2semidirect
13. #21445544C2semidirect
14. #341×D61C2semidirect
15. C61×#1950C2semidirect
339. #1950D61semidirect
406. C61#22718semidirect

Maximal subgroups

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

subgroupindex
M16×D2442
#214545542
C2×#168398322
#214465952
#214460252
#214460222
#214459592
#214458582
#214458542
#214457262
#214455442
#341×D612
C61×#19502
#2271861