Finite Group Databasebeta

← #11873334

Subgroups — #11873334

Order 1152.

764 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5516C211yesmaximal, characteristic
2#10594824C211yesmaximal, characteristic
3#10592695C211yesmaximal, characteristic
4C3×#4996C211yesmaximal, characteristic
5#10591186C211yesmaximal, characteristic
6#10591185C211yesmaximal, characteristic
7#10591056C211yesmaximal, characteristic
8#10590561C211yesmaximal, characteristic, complemented
9#10590561C211yesmaximal, characteristic, complemented
10#10590544C211yesmaximal, characteristic, complemented
11#10590543C211yesmaximal, characteristic, complemented
12#10590481C211yesmaximal, characteristic, complemented
13#10590480C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#82555—31nomaximal
17#81499—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64133C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#877—21no—
28C3×#877—21no—
29C3×C4×Dic6—21no—
30C3×C4×Dic6—21no—
31#63956—21no—
32#63956—21no—
33#63869C2211yescharacteristic
34#63866C2211yescharacteristic
35#63847—21no—
36#63846—21no—
37#63844C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43#63657C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46#63635C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#519—31no—
62#5625—31no—
63#5518—31no—
64#5516D311yescharacteristic
65C3×#485—31no—
66#5228—31no—
67#5228—31no—
68#5050—31no—
69#5031—31no—
70#5031—31no—
71#5030—31no—
72#5030—31no—
73C4×#216—31no—
74C4×#216—31no—
75#5022—31no—
76#5022—31no—
77#5000—31no—
78#4996—31no—
79#4996—31no—
80#4996—61no—
81#4996D311yescharacteristic
82#4877—31no—
83#4873—31no—
84#4857—31no—
85#4853—31no—
86#4795—31no—
87#4795—31no—
88#4790—31no—
89#4789—31no—
90#4739—31no—
91#4720—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C22×C3×Dic3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—22no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×C4⋊C4C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104C32×C42—21no—
105#3757—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#217—21no—
111C3×#217D411yescharacteristic
112C3×#217D411yescharacteristic
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3719—22no—
138#3719—22no—
139#3718—22no—
140#3718—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C22×Dic6C2×D311yescharacteristic
144C3×C22⋊Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—61no—
150C3×C4×Q8—61no—
151C3×#117—21no—
152C3×#117—31no—
153C3×#117—61no—
154C3×#117—61no—
155C3×#117C2×D311yescharacteristic
156C3×#117C2×D311yescharacteristic
157Q8×Dic3—31no—
158#944—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165#926C2×D311yescharacteristic
166#924—31no—
167#924—31no—
168#924—61no—
169#924C2×D311yescharacteristic
170C2×Dic12—31no—
171C2×Dic12—31no—
172#890—31no—
173#890—61no—
174#889—61no—
175#889—61no—
176#889—61no—
177#887—31no—
178#887C2×D311yescharacteristic
179#887C2×D311yescharacteristic
180#887C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#879—61no—
183#879—61no—
184#879—61no—
185#879—61no—
186#877—21no—
187#877—21no—
188#870—31no—
189#869—31no—
190C4×Dic6—21no—
191C4×Dic6—21no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830C2×D311yescharacteristic
207#816—31no—
208#816—31no—
209#815—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—61no—
220#810—61no—
221#810C2×D311yescharacteristic
222#810C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—61no—
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244#634—21no—
245#634—21no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6#4112yes—
261C3×Dic6#4112yes—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—31no—
268#485—31no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C2×C3×Q8—61no—
287C22×C3×C4—21no—
288C22×C3×C4—61no—
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×Dic3—21no—
292C2×Dic6—21no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C22⋊C4—21no—
318C3×C22⋊C4—21no—
319C3×C22⋊C4—31no—
320C3×C22⋊C4—31no—
321C3×C22⋊C4—41no—
322C3×C22⋊C4—61no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—41no—
328C3×C42—61no—
329C3×C42—61no—
330C3×C42—61no—
331C3×C42—61no—
332#217—21no—
333#217—61no—
334#217—61no—
335#217—121no—
336#217#6711yescharacteristic
337#217#6711yescharacteristic
338#216—62no—
339#216—62no—
340#216—62no—
341#216—62no—
342#216—62no—
343#216—62no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3#6711yescharacteristic
352C4⋊Dic3#6711yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—121no—
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—21no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3C22×D311yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8—61no—
386C2×C3⋊C8C22×D311yescharacteristic
387C2×C3⋊C8C22×D311yescharacteristic
388Dic12—62no—
389Dic12—62no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32C22×D411yescharacteristic
394C32×C4—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—31no—
410C2×Q16—91no—
411C2×Q16—91no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—91no—
415#126—181no—
416#126—181no—
417#125—91no—
418#125—181no—
419#125—181no—
420C22⋊Q8—31no—
421C22⋊Q8—91no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—61no—
427C4×Q8—61no—
428C4×Q8—91no—
429C4×Q8—91no—
430#117—31no—
431#117—61no—
432#117—61no—
433#117D3211yescharacteristic
434#107—31no—
435#107—91no—
436#106—31no—
437#106—91no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22⋊C8—31no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—91no—
452C23×C3—21no—
453C23×C3D3×D411yescharacteristic
454C23×C3C2×#6711yescharacteristic
455C3×Q8—32no—
456C3×Q8—32no—
457C3×Q8—64no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—61no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—64no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4D3×D411yescharacteristic
486C2×C3×C4C2×#6711yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×Dic3—24no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3C2×#6711yescharacteristic
501C2×Dic3C2×#6711yescharacteristic
502C2×Dic3C2×#6711yescharacteristic
503C2×Dic3C2×#6711yescharacteristic
504Dic6—24no—
505Dic6—21no—
506Dic6—21no—
507Dic6—21no—
508Dic6—21no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6—121no—
515Dic6#23512yes—
516Dic6#23512yes—
517C3×C8—61no—
518C3×C8—61no—
519C3⋊C8—21no—
520C3⋊C8—21no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C3⋊C8—121no—
527C2×C32—41no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—61no—
537C2×Q8—91no—
538C22×C4—61no—
539C22×C4C2×D3211yescharacteristic
540Q16—182no—
541Q16—182no—
542Q16—182no—
543Q16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8—91no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4C2×D3211yescharacteristic
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C42—21no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42—61no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C22×#6711yescharacteristic
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—81no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4C2×#23511yescharacteristic
612C3×C4C2×#23511yescharacteristic
613C3×C4D3×#4111yescharacteristic
614C3×C4D3×#4111yescharacteristic
615Dic3—22no—
616Dic3—22no—
617Dic3—21no—
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—41no—
622Dic3—41no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629C32#312711yescharacteristic, complemented, Sylow
630C23D3×#6711yescharacteristic
631Q8—32no—
632Q8—32no—
633Q8—64no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8—181no—
639Q8—181no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—64no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4D3×#6711yescharacteristic
656C2×C4C22×D3211yescharacteristic
657C8—61no—
658C8—61no—
659C8—181no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—81no—
667C2×C3#565611yescharacteristic
668C2×C3#577111yescharacteristic
669C2×C3#577911yescharacteristic
670C2×C3#579111yescharacteristic
671C2×C3#583811yescharacteristic
672C2×C3#583811yescharacteristic
673C22—21no—
674C22—21no—
675C22—21no—
676C22C2×D3×#6711yescharacteristic
677C4—21no—
678C4—41no—
679C4—41no—
680C4—62no—
681C4—62no—
682C4—61no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—121no—
687C4—121no—
688C4—361no—
689C4—361no—
690C4D3×#23511yescharacteristic
691C4D3×#23511yescharacteristic
692C3—21no—
693C3#8149911yescharacteristic, complemented
694C3#8255511yescharacteristic, complemented
695C2—41no—
696C2#1059489611yescharacteristic
697C2#1059546511yescharacteristic
698C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#117D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
8. #10590561C2semidirect
9. #10590561C2semidirect
10. #10590544C2semidirect
11. #10590543C2semidirect
12. #10590481C2semidirect
13. #10590480C2semidirect
14. #10590477C2semidirect
15. #10590476C2semidirect
629. C32#3127semidirect
693. C3#81499semidirect
694. C3#82555semidirect

Maximal subgroups

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

subgroupindex
C3×#55162
#105948242
#105926952
C3×#49962
#105911862
#105911852
#105910562
#105905612
#105905442
#105905432
#105904812
#105904802
#105904772
#105904762
#825553
#814993