Finite Group Databasebeta

← #11873328

Subgroups — #11873328

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593885C211yesmaximal, characteristic
2#10593862C211yesmaximal, characteristic
3#10592528C211yesmaximal, characteristic, complemented
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic
6#10590949C211yesmaximal, characteristic
7#10590949C211yesmaximal, characteristic
8#10590812C211yesmaximal, characteristic, complemented
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10#10590794C211yesmaximal, characteristic, complemented
11#10590793C211yesmaximal, characteristic, complemented
12#10590711C211yesmaximal, characteristic
13#10590710C211yesmaximal, characteristic
14#10590388C211yesmaximal, characteristic, complemented
15#10590302C211yesmaximal, characteristic, complemented
16#80461—31nomaximal
17#79396—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64079C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C2×C3×Dic12C2211yescharacteristic
23C3×#872C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63878—21no—
27#63877—21no—
28#63858—21no—
29#63858—21no—
30#63856C2211yescharacteristic
31#63856C2211yescharacteristic
32#63847—21no—
33#63847—21no—
34#63844C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63841C2211yescharacteristic
39#63838—21no—
40#63837—21no—
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44#63645C2211yescharacteristic
45#63644C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5731—31no—
62#5572—31no—
63#5518—31no—
64#5516—31no—
65C3×#462—31no—
66C3×#433—31no—
67#5186—31no—
68#5186—31no—
69#5184—31no—
70Dic3×Q16—31no—
71#5090—31no—
72#5022—31no—
73#4849—31no—
74#4849D311yescharacteristic, complemented
75#4840D311yescharacteristic
76#4829—31no—
77#4829—31no—
78#4829—31no—
79#4829—61no—
80#4815—31no—
81#4814—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×C3×C4×D3C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
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)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C3×(C2×D3)⋊C4D411yescharacteristic
112C3×(C2×D3)⋊C4D411yescharacteristic
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4D411yescharacteristic
118C3×Dic3⋊C4D411yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124C3×Dic12—22no—
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—
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C4⋊Q8—31no—
147C3×C4×Q8—31no—
148C3×#117—31no—
149#946—31no—
150#946—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154C2×#216—31no—
155C2×#216—31no—
156#926—31no—
157#924—31no—
158#924—31no—
159C2×Dic12—31no—
160C2×Dic12—31no—
161C2×Dic12C2×D311yescharacteristic
162C2×Dic12C2×D311yescharacteristic
163#898—61no—
164#898—61no—
165#892—31no—
166#892—61no—
167#889—61no—
168#889—61no—
169#889—61no—
170#889—61no—
171#887—31no—
172#887—61no—
173#887—61no—
174#887—61no—
175#879—61no—
176#879—61no—
177#877—61no—
178#877—61no—
179#872—61no—
180#872C2×D311yescharacteristic
181#870—31no—
182#870—31no—
183#870—61no—
184#869C2×D311yescharacteristic
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6C2×D311yescharacteristic
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8C2×D311yescharacteristic
197C3×C4⋊C8C2×D311yescharacteristic
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209(C2×D3)⋊C8C2×D311yescharacteristic
210#818—31no—
211#818—31no—
212#818—31no—
213#818—61no—
214#817—31no—
215#817—31no—
216#817—31no—
217#817—61no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#816—61no—
228#816C2×D311yescharacteristic
229#816C2×D311yescharacteristic
230#815C2×D311yescharacteristic
231C8×Dic3C2×D311yescharacteristic
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#4112yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—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—91no—
271#479—91no—
272#462—31no—
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—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C22×C3×C4—31no—
285C22×Dic3—61no—
286D3×Q8—62no—
287D3×Q8—62no—
288C2×C4×D3—61no—
289C2×C4×D3C22×D311yescharacteristic
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—61no—
293C2×Dic6—62no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—62no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C3×Q16—62no—
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—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C22⋊C4—31no—
317C3×C22⋊C4—31no—
318C3×C42—21no—
319C3×C42—31no—
320C3×C42—61no—
321C3×C42C22×D311yescharacteristic
322C3×C42C22×D311yescharacteristic
323#217—61no—
324#217—61no—
325#217—61no—
326#216—62no—
327#216—62no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4D1211yescharacteristic
332(C2×D3)⋊C4D1211yescharacteristic
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
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⋊C4—121no—
366Dic3⋊C4—121no—
367Dic3⋊C4D1211yescharacteristic
368Dic3⋊C4D1211yescharacteristic
369C4×Dic3—21no—
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—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386Dic12—22no—
387Dic12—22no—
388Dic12—62no—
389Dic12—62no—
390C22×C32C22×D411yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—22no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—31no—
415#126—181no—
416#126—181no—
417#125—91no—
418#125—181no—
419#125—181no—
420C22⋊Q8—91no—
421C22⋊Q8—91no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—31no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—91no—
435#107—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8D3211yescharacteristic
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—31no—
450#97—31no—
451C4×C8—31no—
452C23×C3—31no—
453C22×D3C2×D1211yescharacteristic
454C3×Q8—32no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4C2×D1211yescharacteristic
473C2×C3×C4C2×D1211yescharacteristic
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—64no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3C2×D1211yescharacteristic
496C2×Dic3C2×D1211yescharacteristic
497C2×Dic3C2×D1211yescharacteristic
498C4×D3—21no—
499C4×D3—21no—
500C4×D3—64no—
501Dic6—21no—
502Dic6—21no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—32no—
507Dic6—32no—
508Dic6—62no—
509Dic6—64no—
510Dic6—64no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6#23712yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C2×C32#52511yescharacteristic
526C2×C32#57811yescharacteristic
527C2×C32#57811yescharacteristic
528C3×D3—41no—
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×Q8—182no—
535C2×Q8—182no—
536C22×C4—31no—
537C22×C4—181no—
538Q16—62no—
539Q16—62no—
540Q16—182no—
541Q16—182no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8C2×D3211yescharacteristic
545C2×C8C2×D3211yescharacteristic
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C22⋊C4—31no—
565C22⋊C4—31no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—61no—
571C42—181no—
572C42—181no—
573C42—181no—
574C42—181no—
575C42—181no—
576C42—181no—
577C42C2×D3211yescharacteristic
578C22×C3—21no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3C22×D1211yescharacteristic
583C22×C3C2×D3×D411yescharacteristic
584C2×D3—21no—
585C2×D3—21no—
586C2×D3—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4C2×#23711yescharacteristic
603C3×C4D3×#4111yescharacteristic
604C3×C4D3×#4111yescharacteristic
605C3×C4D3×#4111yescharacteristic
606Dic3—21no—
607Dic3—21no—
608Dic3—21no—
609Dic3—22no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—62no—
614Dic3—62no—
615Dic3—122no—
616Dic3—121no—
617Dic3—121no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—241no—
623Dic3—241no—
624Dic3—241no—
625C32#312711yescharacteristic, complemented, Sylow
626C23—31no—
627Q8—32no—
628Q8—61no—
629Q8—61no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633Q8—92no—
634Q8—184no—
635Q8—181no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—184no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4D3×D1211yescharacteristic
651C2×C4D3×D1211yescharacteristic
652C2×C4C22×D3211yescharacteristic
653C8—21no—
654C8—21no—
655C8—61no—
656C8—61no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—121no—
661C2×C3#552411yescharacteristic
662C2×C3#560611yescharacteristic
663C2×C3#575311yescharacteristic
664C2×C3#575311yescharacteristic
665C2×C3#576611yescharacteristic
666C2×C3#577911yescharacteristic
667D3—41no—
668C22—61no—
669C22—61no—
670C22—61no—
671C22C2×D3×D1211yescharacteristic
672C4—21no—
673C4—21no—
674C4—61no—
675C4—62no—
676C4—61no—
677C4—61no—
678C4—121no—
679C4—121no—
680C4—121no—
681C4—182no—
682C4—361no—
683C4—361no—
684C4—361no—
685C4D3×#23711yescharacteristic
686C4#6431911yescharacteristic
687C3—21no—
688C3#7939611yescharacteristic, complemented
689C3#8046111yescharacteristic, complemented
690C2—121no—
691C2#1059462611yescharacteristic
692C2#1059469111yescharacteristic
693C2#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. #10592528C2semidirect
4. C3×#4849C2semidirect
8. #10590812C2semidirect
9. Dic3×Dic12C2semidirect
10. #10590794C2semidirect
11. #10590793C2semidirect
14. #10590388C2semidirect
15. #10590302C2semidirect
74. #4849D3semidirect
625. C32#3127semidirect
688. C3#79396semidirect
689. C3#80461semidirect

Maximal subgroups

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

subgroupindex
#105938852
#105938622
#105925282
C3×#48492
C3×#48402
#105909492
#105908122
Dic3×Dic122
#105907942
#105907932
#105907112
#105907102
#105903882
#105903022
#804613
#793963