Finite Group Databasebeta

← #11873309

Subgroups — #11873309

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595349C211yesmaximal, characteristic
2#10595347C211yesmaximal, characteristic
3#10592883C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic
7#10591581C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10591574C211yesmaximal, characteristic, complemented
10#10591558C211yesmaximal, characteristic
11#10591547C211yesmaximal, characteristic, complemented
12#10590815C211yesmaximal, characteristic, complemented
13#10590791C211yesmaximal, characteristic, complemented
14#10590711C211yesmaximal, characteristic
15#10590699C211yesmaximal, characteristic
16#80461—31nomaximal
17#80177—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27#63870—21no—
28#63869C2211yescharacteristic
29#63862—21no—
30#63861—21no—
31#63856C2211yescharacteristic
32#63855—21no—
33#63855C2211yescharacteristic
34#63845—21no—
35#63843—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63644C2211yescharacteristic
46#63642C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5812—31no—
62#5731—31no—
63#5625—31no—
64#5572—31no—
65C3×#462—31no—
66C3×#451—31no—
67#5228—31no—
68#5186—31no—
69#5186D311yescharacteristic
70#5184—31no—
71#5184—31no—
72#5184—61no—
73#5182—31no—
74#5182D311yescharacteristic, complemented
75Dic3×Q16—31no—
76Dic3×Q16—31no—
77#5090—31no—
78#5045—31no—
79#5022—31no—
80#4840—31no—
81#4829—31no—
82#4815—31no—
83#4814—31no—
84#4799—31no—
85#4796—31no—
86#4790—31no—
87#4790—31no—
88#4789—31no—
89#4789—31no—
90#4723—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103C4⋊(C3⋊Dic3)—21no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×#216—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3718—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C2×C3×Q16C2×D311yescharacteristic
148C2×C3×Q16C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C22⋊Q8—31no—
151C3×C4×Q8—31no—
152#946—31no—
153#946C2×D311yescharacteristic
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—61no—
162Q8×Dic3—61no—
163Q8×Dic3—61no—
164Q8×Dic3—61no—
165Q8×Dic3C2×D311yescharacteristic
166#944C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216C2×D311yescharacteristic
170C2×#216C2×D311yescharacteristic
171#926—31no—
172#926—31no—
173#926—61no—
174#926—61no—
175#924—31no—
176#898—61no—
177#898—61no—
178#892—31no—
179#892—61no—
180#890—31no—
181#890—61no—
182#889—61no—
183#889—61no—
184#889—61no—
185#887—31no—
186#887—31no—
187#887—61no—
188#879—61no—
189#879—61no—
190#872—31no—
191#872—61no—
192#870—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#835—61no—
209#835C2×D311yescharacteristic
210#835C2×D311yescharacteristic
211#830—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818—31no—
215#818—31no—
216#817—31no—
217#817—31no—
218#817—61no—
219#816—31no—
220#816—31no—
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#815—31no—
224#815—31no—
225#815—61no—
226Dic3⋊C8—31no—
227Dic3⋊C8C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
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
254C3×C4×D3—24no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—24no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C3⋊(C3⋊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—31no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C22×D311yescharacteristic
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294D3×Q8—22no—
295D3×Q8—22no—
296C2×C4×D3—21no—
297C2×C4×D3C22×D311yescharacteristic
298C2×Dic6—21no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—24no—
302C3×Q16—22no—
303C3×Q16—22no—
304C3×Q16—62no—
305C3×Q16—62no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C42—31no—
319C3×C42—61no—
320#217—31no—
321#217—31no—
322#217—61no—
323#217—61no—
324#216—22no—
325#216—22no—
326#216—62no—
327#216—62no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333C4⋊Dic3—21no—
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—61no—
350C4⋊Dic3—121no—
351C4⋊Dic3—121no—
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367C4×Dic3—21no—
368C4×Dic3—31no—
369C4×Dic3—31no—
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—61no—
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—21no—
404C3×Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—91no—
414C2×Q16D3211yescharacteristic
415C4⋊Q8—31no—
416#126—181no—
417#126—181no—
418#125—91no—
419#125—181no—
420#125—181no—
421C22⋊Q8—31no—
422C22⋊Q8—91no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—181no—
430C4×Q8—181no—
431#117—91no—
432#117—91no—
433#117—181no—
434#117—181no—
435#107—91no—
436#107—91no—
437#106—91no—
438#106—91no—
439C4⋊C8—31no—
440C4⋊C8—91no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449C22⋊C8—31no—
450C22⋊C8—91no—
451#97—91no—
452C4×C8—91no—
453C23×C3—31no—
454C22×D3D3×D411yescharacteristic
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—22no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—22no—
463C3×Q8—32no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—64no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—61no—
470C3×Q8#23712yes—
471C3×Q8#23712yes—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—64no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4C23×D311yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509C2×Dic3D3×D411yescharacteristic
510C4×D3—24no—
511C4×D3—21no—
512C4×D3—21no—
513Dic6—24no—
514Dic6—21no—
515Dic6—21no—
516Dic6—21no—
517Dic6#23712yes—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—61no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8C2×D3211yescharacteristic
538C2×Q8C2×D3211yescharacteristic
539C22×C4—31no—
540C22×C4—61no—
541Q16—22no—
542Q16—62no—
543Q16—62no—
544Q16—182no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8—91no—
548C2×C8C2×D3211yescharacteristic
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C22⋊C4—61no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—91no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42—181no—
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—22no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—62no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23711yescharacteristic
606C3×C4C2×#23711yescharacteristic
607C3×C4C2×#23711yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—22no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—61no—
617Dic3—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3—241no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—32no—
634Q8—64no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8#380512yes—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—64no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—61no—
658C8—61no—
659C8—181no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#558611yescharacteristic
665C2×C3#560611yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#576611yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22D32×D411yescharacteristic
675C4—22no—
676C4—41no—
677C4—61no—
678C4—62no—
679C4—61no—
680C4—61no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—181no—
685C4—181no—
686C4—361no—
687C4—361no—
688C4D3×#23711yescharacteristic
689C4C2×#380511yescharacteristic
690C3—21no—
691C3#8017711yescharacteristic, complemented
692C3#8046111yescharacteristic, complemented
693C2—121no—
694C2#1059476611yescharacteristic
695C2#1059476611yescharacteristic
696C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10592883C2semidirect
5. C3×#5182C2semidirect
7. #10591581C2semidirect
8. #10591581C2semidirect
9. #10591574C2semidirect
11. #10591547C2semidirect
12. #10590815C2semidirect
13. #10590791C2semidirect
74. #5182D3semidirect
628. C32#3127semidirect
691. C3#80177semidirect
692. C3#80461semidirect

Maximal subgroups

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

subgroupindex
#105953492
#105953472
#105928832
C3×#51862
C3×#51822
#105915942
#105915812
#105915742
#105915582
#105915472
#105908152
#105907912
#105907112
#105906992
#804613
#801773