Finite Group Databasebeta

← #11873326

Subgroups — #11873326

Order 1152.

770 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
1#10593885C211yesmaximal, characteristic
2#10593881C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic, complemented
4C3×#4840C211yesmaximal, characteristic
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590952C211yesmaximal, characteristic
7#10590952C211yesmaximal, characteristic
8#10590810C211yesmaximal, characteristic, complemented
9#10590807C211yesmaximal, characteristic, complemented
10#10590794C211yesmaximal, characteristic, complemented
11#10590793C211yesmaximal, characteristic, complemented
12#10590709C211yesmaximal, characteristic
13#10590708C211yesmaximal, characteristic
14#10590385C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#81211—31nomaximal
17#79396—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×#3746C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21#64078C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#872C2211yescharacteristic
24C3×#870C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63878—21no—
27#63877—21no—
28#63861—21no—
29#63861—21no—
30#63857C2211yescharacteristic
31#63857C2211yescharacteristic
32#63845—21no—
33#63845—21no—
34#63844C2211yescharacteristic
35#63844C2211yescharacteristic
36#63844C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63841C2211yescharacteristic
39#63838—21no—
40#63837—21no—
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63567C2211yescharacteristic
61#5698—31no—
62#5572—31no—
63#5518—31no—
64#5516—31no—
65C3×#479—31no—
66C3×#433—31no—
67#5063—31no—
68#5031—31no—
69#4888—31no—
70#4873—31no—
71#4868—31no—
72#4853—31no—
73#4849—31no—
74#4849—31no—
75#4849—31no—
76#4849—61no—
77#4840D311yescharacteristic
78#4829—31no—
79#4829D311yescharacteristic, complemented
80#4809—31no—
81#4809—31no—
82#4790—31no—
83#4789—31no—
84#4739—31no—
85#4739—31no—
86#4723—31no—
87#4723—31no—
88#4716—31no—
89#4716—31no—
90C4×Dic12—31no—
91C4×Dic12—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109#3746—22no—
110#3746—22no—
111C3×(C2×D3)⋊C4D411yescharacteristic
112C3×(C2×D3)⋊C4D411yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4D411yescharacteristic
120C3×Dic3⋊C4D411yescharacteristic
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3719—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C3×#117—31no—
147Q8×Dic3—31no—
148C2×#216—31no—
149C2×#216—31no—
150#926—31no—
151#924—31no—
152#924—31no—
153C2×Dic12—31no—
154C2×Dic12—31no—
155C2×Dic12—31no—
156C2×Dic12—31no—
157C2×Dic12—31no—
158C2×Dic12—31no—
159C2×Dic12—61no—
160C2×Dic12—61no—
161#898—61no—
162#898—61no—
163#897—31no—
164#897—31no—
165#892—31no—
166#892—61no—
167#890—61no—
168#890—61no—
169#889—61no—
170#889—61no—
171#887—31no—
172#887—31no—
173#887—31no—
174#887—61no—
175#887—61no—
176#887—61no—
177#879—61no—
178#879—61no—
179#877—61no—
180#877—61no—
181#872—61no—
182#872C2×D311yescharacteristic
183#870C2×D311yescharacteristic
184#869—31no—
185#869—31no—
186#869—61no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C4×Dic6C2×D311yescharacteristic
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C2×D311yescharacteristic
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207C3×C4×C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209(C2×D3)⋊C8C2×D311yescharacteristic
210#818—31no—
211#818C2×D311yescharacteristic
212#817—31no—
213#817C2×D311yescharacteristic
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—61no—
223#816—61no—
224#816C2×D311yescharacteristic
225#816C2×D311yescharacteristic
226#815C2×D311yescharacteristic
227C8×Dic3C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243#634—21no—
244#634—21no—
245#634—21no—
246#634—21no—
247#634—21no—
248#634#4112yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—24no—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—31no—
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—31no—
281C2×C3×Q8—31no—
282C22×C3×C4—31no—
283C22×Dic3—61no—
284D3×Q8—62no—
285D3×Q8—62no—
286C2×C4×D3—61no—
287C2×C4×D3C22×D311yescharacteristic
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—62no—
301C2×Dic6C22×D311yescharacteristic
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C22⋊C4—31no—
319C3×C22⋊C4—31no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42C22×D311yescharacteristic
324C3×C42C22×D311yescharacteristic
325#217—61no—
326#217—61no—
327#217—61no—
328#216—62no—
329#216—62no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4D1211yescharacteristic
334(C2×D3)⋊C4D1211yescharacteristic
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—121no—
346C4⋊Dic3—121no—
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—121no—
365Dic3⋊C4D1211yescharacteristic
366Dic3⋊C4D1211yescharacteristic
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—121no—
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384Dic12—62no—
385Dic12—62no—
386Dic12—62no—
387Dic12—62no—
388Dic12—62no—
389Dic12—62no—
390Dic12—122no—
391Dic12—122no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4C2×#4111yescharacteristic
399C32×C4C2×#4111yescharacteristic
400C3⋊Dic3—22no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3⋊Dic3—41no—
404C3×Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C22×Q8—91no—
412C2×Q16—91no—
413C2×Q16—91no—
414C2×Q16—91no—
415C2×Q16—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#125—31no—
420#125—181no—
421#125—181no—
422C22⋊Q8—91no—
423C22⋊Q8—91no—
424C4×Q8—31no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—181no—
431C4×Q8—181no—
432#117—31no—
433#117—91no—
434#117—181no—
435#117—181no—
436#107—31no—
437#107—91no—
438#106—31no—
439#106—91no—
440C4⋊C8—31no—
441C4⋊C8D3211yescharacteristic
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103—91no—
450C22⋊C8—31no—
451C22⋊C8—31no—
452#97—31no—
453C4×C8—31no—
454C23×C3—31no—
455C22×D3C2×D1211yescharacteristic
456C3×Q8—32no—
457C3×Q8—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4C2×D1211yescharacteristic
471C2×C3×C4C2×D1211yescharacteristic
472C2×C3×C4D3×D411yescharacteristic
473C2×C3×C4D3×D411yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—64no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3C2×D1211yescharacteristic
494C2×Dic3C2×D1211yescharacteristic
495C2×Dic3C2×D1211yescharacteristic
496C4×D3—21no—
497C4×D3—21no—
498C4×D3—64no—
499Dic6—21no—
500Dic6—32no—
501Dic6—32no—
502Dic6—62no—
503Dic6—64no—
504Dic6—64no—
505Dic6—61no—
506Dic6—61no—
507Dic6—61no—
508Dic6—61no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—121no—
517Dic6—121no—
518Dic6—121no—
519Dic6—121no—
520Dic6#23912yes—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—21no—
525C3×C8—41no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C2×C32#52511yescharacteristic
532C2×C32#57811yescharacteristic
533C2×C32#57811yescharacteristic
534C3×D3—41no—
535C2×Q8—31no—
536C2×Q8—91no—
537C2×Q8—91no—
538C2×Q8—91no—
539C2×Q8—181no—
540C2×Q8—182no—
541C2×Q8—182no—
542C22×C4—31no—
543C22×C4—181no—
544Q16—182no—
545Q16—182no—
546Q16—182no—
547Q16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8C2×D3211yescharacteristic
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C42—31no—
576C42—61no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42—181no—
581C42—181no—
582C42—181no—
583C42C2×D3211yescharacteristic
584C22×C3—21no—
585C22×C3—61no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3C22×D1211yescharacteristic
589C22×C3C2×D3×D411yescharacteristic
590C2×D3—21no—
591C2×D3—21no—
592C2×D3—21no—
593C3×C4—22no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—41no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—62no—
604C3×C4—61no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×#23911yescharacteristic
609C3×C4D3×#4111yescharacteristic
610C3×C4D3×#4111yescharacteristic
611C3×C4D3×#4111yescharacteristic
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—22no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—62no—
620Dic3—62no—
621Dic3—122no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629Dic3—241no—
630Dic3—241no—
631C32#312711yescharacteristic, complemented, Sylow
632C23—31no—
633Q8—32no—
634Q8—61no—
635Q8—92no—
636Q8—184no—
637Q8—181no—
638Q8—181no—
639Q8—181no—
640Q8—181no—
641Q8—181no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—184no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4D3×D1211yescharacteristic
657C2×C4D3×D1211yescharacteristic
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—21no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—121no—
667C2×C3#552411yescharacteristic
668C2×C3#562711yescharacteristic
669C2×C3#575311yescharacteristic
670C2×C3#575311yescharacteristic
671C2×C3#577111yescharacteristic
672C2×C3#577911yescharacteristic
673D3—41no—
674C22—61no—
675C22—61no—
676C22—61no—
677C22C2×D3×D1211yescharacteristic
678C4—21no—
679C4—21no—
680C4—61no—
681C4—62no—
682C4—61no—
683C4—61no—
684C4—121no—
685C4—121no—
686C4—121no—
687C4—182no—
688C4—361no—
689C4—361no—
690C4—361no—
691C4#6431211yescharacteristic
692C4D3×#23911yescharacteristic
693C3—21no—
694C3#7939611yescharacteristic, complemented
695C3#8121111yescharacteristic, complemented
696C2—121no—
697C2#1059462711yescharacteristic
698C2#1059469211yescharacteristic
699C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592548C2semidirect
5. C3×#4829C2semidirect
8. #10590810C2semidirect
9. #10590807C2semidirect
10. #10590794C2semidirect
11. #10590793C2semidirect
14. #10590385C2semidirect
15. #10590292C2semidirect
79. #4829D3semidirect
631. C32#3127semidirect
694. C3#79396semidirect
695. C3#81211semidirect

Maximal subgroups

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

subgroupindex
#105938852
#105938812
#105925482
C3×#48402
C3×#48292
#105909522
#105908102
#105908072
#105907942
#105907932
#105907092
#105907082
#105903852
#105902922
#812113
#793963