Finite Group Databasebeta

← #11897644

Subgroups — #11897644

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2#10593941C211yesmaximal, characteristic
3C3×#5026C211yesmaximal, characteristic
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591631C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic
8#10591571C211yesmaximal, characteristic
9#10590546C211yesmaximal, characteristic, complemented
10#10590472C211yesmaximal, characteristic
11#10590471C211yesmaximal, characteristic
12#10590415C211yesmaximal, characteristic, complemented
13#10590306C211yesmaximal, characteristic, complemented
14#10590272C211yesmaximal, characteristic
15#10590255C211yesmaximal, characteristic, complemented
16#81223—31nomaximal
17#79759—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64097—21no—
22#64097—21no—
23#64097C2211yescharacteristic
24#64097C2211yescharacteristic
25#64078—21no—
26#64078C2211yescharacteristic
27C4×#634—21no—
28C4×#634C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic
32#63919C2211yescharacteristic
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic
35#63896—21no—
36#63893—21no—
37D3×Dic3⋊C4—21no—
38#63872C2211yescharacteristic
39#63851—21no—
40C3×#835C2211yescharacteristic
41C3×#835C2211yescharacteristic
42C3×#835C2211yescharacteristic
43C3×#809C2211yescharacteristic
44C3×#808C2211yescharacteristic
45C3×#807C2211yescharacteristic
46C3×#807C2211yescharacteristic
47C3×C4⋊(C3⋊C8)C2211yescharacteristic
48C3×#803C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63572C2211yescharacteristic
56#63572C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5690—31no—
62Q8×Dic6—31no—
63Q8×Dic6—31no—
64Q8×Dic6—61no—
65#5539—31no—
66C3×#479—31no—
67C3×#440—31no—
68#5164—31no—
69Dic3×SD16—31no—
70#5064—31no—
71#5026D311yescharacteristic
72#5022D311yescharacteristic, complemented
73#5007—31no—
74#4890—31no—
75#4876—31no—
76#4874—31no—
77#4874—31no—
78#4870—31no—
79#4856—31no—
80#4846—31no—
81#4828—31no—
82#4817—31no—
83#4799—31no—
84#4796—31no—
85#4793—31no—
86#4793—31no—
87#4788—31no—
88#4761—31no—
89#4759—31no—
90#4702—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634—21no—
95C2×#634—21no—
96C2×#634D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C42—21no—
105C32×C42C2311yescharacteristic
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750D411yescharacteristic
115#3750D411yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C3×#215Q814yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3385—91noSylow
137C2×C3×SD16—31no—
138C3×#125—31no—
139C3×C4×Q8—21no—
140C3×C4×Q8C2×D311yescharacteristic
141C3×C4×Q8C2×D311yescharacteristic
142C3×C4×D4—31no—
143Q8×Dic3—31no—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147Q8×Dic3—61no—
148Q8×Dic3—61no—
149C2×#215C2×D311yescharacteristic
150D4×Dic3—31no—
151D4×Dic3—31no—
152#924—61no—
153C2×Dic3⋊C4—61no—
154#897—61no—
155#896—61no—
156#896—61no—
157#893—31no—
158#893—31no—
159D3×C4⋊C4—61no—
160#890—31no—
161#890—31no—
162#888—31no—
163#888—31no—
164#888—31no—
165#888—31no—
166#888—31no—
167#888—31no—
168#888—61no—
169#888—61no—
170#888—61no—
171#888—61no—
172#888—61no—
173#888—61no—
174#888—62no—
175#888—62no—
176#878—61no—
177#878—61no—
178C4×D12C2×D311yescharacteristic
179#870C2×D311yescharacteristic
180#869—31no—
181#869—31no—
182#869—61no—
183#869—61no—
184#869—61no—
185#869—62no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C4×Dic6—62no—
192C3×#107—31no—
193C3×#107—31no—
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×#97—31no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#832—31no—
206#821—31no—
207#821—31no—
208#818—31no—
209#818—31no—
210#818—31no—
211#818—31no—
212#817—31no—
213#817—31no—
214#815—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808C2×D311yescharacteristic
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic
231#807C2×D311yescharacteristic
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803C2×D311yescharacteristic
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8C2×Q812yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248#634—22no—
249#634—81no—
250#634—81no—
251#634—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C3×D12—21no—
256C3×D12C2×Q812yes—
257C3×C4×D3—81no—
258#627—81no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8C2×Q812yes—
265Q82—91no—
266#554—91no—
267#501—91no—
268#501—91no—
269#500—91no—
270#479—31no—
271#479—91no—
272#477—91no—
273#476—91no—
274#474—91no—
275#474—91no—
276#446—91no—
277#440—31no—
278#440—91no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C2×D12C22×D311yescharacteristic
288C2×C4×D3—21no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—62no—
301C2×Dic6—62no—
302C2×Dic6—62no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C3×SD16—34no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C22⋊C4—61no—
322C3×C42—22no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328#217—61no—
329#217—61no—
330#215Dic614yescomplemented
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—62no—
350C4⋊Dic3—62no—
351C4⋊Dic3—62no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—22no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—22no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4C22×Q811yescharacteristic
400C32×C42−1+411yescharacteristic
401C3⋊Dic3—21no—
402C3⋊Dic3—21no—
403C3⋊Dic3—21no—
404C3⋊Dic3—41no—
405C3⋊Dic3—41no—
406C3⋊Dic3#13712yes—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C2×SD16—31no—
411C4⋊Q8—91no—
412C4⋊Q8—91no—
413C4⋊Q8—91no—
414C4⋊Q8—91no—
415C4⋊Q8—181no—
416C4⋊Q8—181no—
417C4⋊Q8—181no—
418#125—31no—
419#125—91no—
420C22⋊Q8—181no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×Q8D3211yescharacteristic
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C2×C4⋊C4—181no—
432#107—31no—
433#107—31no—
434#107—91no—
435#107—91no—
436#107—91no—
437#107—91no—
438#106—31no—
439#106—91no—
440#106—91no—
441C4⋊C8—31no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444#103—31no—
445#103—31no—
446#103—31no—
447#102—31no—
448#102—91no—
449#102—91no—
450#97—31no—
451#97—91no—
452C4×C8—91no—
453C23×C3—61no—
454C22×D3—21no—
455C3×Q8—22no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—22no—
459C3×Q8C2×Dic612yes—
460C3×Q8D3×Q812yes—
461C3×D4—32no—
462C3×D4—61no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—241no—
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4D3×D411yescharacteristic
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—122no—
504C2×Dic3—241no—
505D12—21no—
506D12C2×Dic612yes—
507C4×D3—81no—
508C4×D3—122no—
509C4×D3—241no—
510Dic6—62no—
511Dic6—62no—
512Dic6—64no—
513Dic6—241no—
514Dic6—241no—
515Dic6—241no—
516Dic6—241no—
517Dic6—241no—
518Dic6—241no—
519Dic6—241no—
520Dic6—241no—
521Dic6—242no—
522Dic6—242no—
523Dic6—242no—
524C3×C8—32no—
525C3×C8—61no—
526C3×C8—61no—
527C3×C8—61no—
528C3⋊C8—21no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C3⋊C8C2×Dic612yes—
532C2×C32D4×Q811yescharacteristic
533C2×C32C2×#13711yescharacteristic
534C2×C32#57611yescharacteristic
535C3×D3—42no—
536C2×Q8—91no—
537C2×Q8—181no—
538C2×Q8—181no—
539C2×Q8—181no—
540C2×Q8—181no—
541C2×Q8C2×D3211yescharacteristic
542C2×D4—31no—
543C22×C4—61no—
544C22×C4—181no—
545C22×C4—181no—
546SD16—34no—
547C2×C8—31no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—31no—
551C4⋊C4—21no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4C2×D3211yescharacteristic
571C22⋊C4—61no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—21no—
575C42—91no—
576C42—91no—
577C42—181no—
578C42—181no—
579C42C2×D3211yescharacteristic
580C22×C3—21no—
581C22×C3—62no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3C2×D3×D411yescharacteristic
585C22×C3C2×D3×D411yescharacteristic
586C2×D3—22no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—22no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—22no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—41no—
600C3×C4—42no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4C22×Dic611yescharacteristic
607C3×C4C2×D3×Q811yescharacteristic
608C3×C4#101011yescharacteristic
609C3×C4#101011yescharacteristic
610Dic3—32no—
611Dic3—32no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—62no—
616Dic3—62no—
617Dic3—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—121no—
624Dic3—121no—
625Dic3—122no—
626Dic3—122no—
627Dic3—121no—
628Dic3—121no—
629Dic3—121no—
630Dic3—121no—
631C32#338511yescharacteristic, complemented, Sylow
632C23—61no—
633Q8—21no—
634Q8—182no—
635Q8—721no—
636Q8—721no—
637Q8—721no—
638Q8—721no—
639Q8D3×Dic612yes—
640D4—32no—
641D4—61no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—241no—
654C2×C4—362no—
655C2×C4—721no—
656C2×C4#381111yescharacteristic
657C2×C4#381111yescharacteristic
658C2×C4C22×D3211yescharacteristic
659C8—32no—
660C8—61no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—122no—
667C2×C3D4×Dic611yescharacteristic
668C2×C3#563211yescharacteristic
669C2×C3#576911yescharacteristic
670C2×C3#577411yescharacteristic
671C2×C3D3×#13711yescharacteristic
672C2×C3D3×#13711yescharacteristic
673D3—42no—
674C22—62no—
675C22—121no—
676C22—121no—
677C22C2×#381111yescharacteristic
678C4—22no—
679C4—21no—
680C4—21no—
681C4—41no—
682C4—92no—
683C4—121no—
684C4—121no—
685C4—121no—
686C4—181no—
687C4—181no—
688C4—181no—
689C4—361no—
690C4—361no—
691C4C2×D3×Dic611yescharacteristic
692C4#6429811yescharacteristic
693C3—21no—
694C3#7975911yescharacteristic, complemented
695C3#8122311yescharacteristic, complemented
696C2—122no—
697C2#1059491511yescharacteristic
698C2#1059532211yescharacteristic
699C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
4. C3×#5022C2semidirect
5. #10591631C2semidirect
6. #10591615C2semidirect
9. #10590546C2semidirect
12. #10590415C2semidirect
13. #10590306C2semidirect
15. #10590255C2semidirect
72. #5022D3semidirect
120. C3×#215Q8semidirect
330. #215Dic6semidirect
631. C32#3385semidirect
694. C3#79759semidirect
695. C3#81223semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
#105939412
C3×#50262
C3×#50222
#105916312
#105916152
#105915722
#105915712
#105905462
#105904722
#105904712
#105904152
#105903062
#105902722
#105902552
#812233
#797593