Finite Group Databasebeta

← #11873329

Subgroups — #11873329

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
1C3×#5698C211yesmaximal, characteristic
2#10593885C211yesmaximal, characteristic
3#10592762C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5#10590604C211yesmaximal, characteristic
6#10590604C211yesmaximal, characteristic
7#10590481C211yesmaximal, characteristic, complemented
8#10590480C211yesmaximal, characteristic, complemented
9#10590477C211yesmaximal, characteristic, complemented
10#10590476C211yesmaximal, characteristic, complemented
11#10590448C211yesmaximal, characteristic
12#10590447C211yesmaximal, characteristic
13#10590388C211yesmaximal, characteristic, complemented
14#10590384C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic
16#83451—31nomaximal
17#81211—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C3×#898—21no—
22C3×#898—21no—
23C3×#897C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×#890—21no—
26C3×#890—21no—
27C3×#887C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C3×#872C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63878—21no—
33#63877—21no—
34#63844C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63841C2211yescharacteristic
37#63838—21no—
38#63837—21no—
39C2×#3719C2211yescharacteristic
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43#63637C2211yescharacteristic
44#63637C2211yescharacteristic
45#63635C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#541—31no—
62#5698D311yescharacteristic
63#5572—31no—
64#5516—31no—
65C3×#479—31no—
66#5090—31no—
67#5090—31no—
68#5063—31no—
69#5063—31no—
70#5063—61no—
71#5063D311yescharacteristic, complemented
72#5050—31no—
73#5050—31no—
74#5045—31no—
75#5045—31no—
76#5031—31no—
77#5030—31no—
78#5030—31no—
79C4×#216—31no—
80C4×#216—31no—
81#5000—31no—
82#4888—31no—
83#4873—31no—
84#4868—31no—
85#4853—31no—
86#4849—31no—
87#4840—31no—
88#4809—31no—
89#4809—31no—
90#4790—31no—
91#4789—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—
101C32×C4⋊C4—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C42C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4D411yescharacteristic
114C3×(C2×D3)⋊C4D411yescharacteristic
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3719—22no—
138#3719—22no—
139#3718—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C3×C4⋊Q8—31no—
145C3×#126—61no—
146C3×#126—61no—
147C3×#125—21no—
148C3×#125—61no—
149C3×#125—61no—
150C3×#125C2×D311yescharacteristic
151C3×#125C2×D311yescharacteristic
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×#117—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165#926—31no—
166C2×Dic12—31no—
167C2×Dic12—31no—
168#898—21no—
169#898—21no—
170#897C2×D311yescharacteristic
171#897C2×D311yescharacteristic
172#892—31no—
173#892—61no—
174#890—21no—
175#890—21no—
176#887—31no—
177#887—61no—
178#887—61no—
179#887—61no—
180#887C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#877—61no—
183#877—61no—
184#872—61no—
185#872C2×D311yescharacteristic
186#869C2×D311yescharacteristic
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6C2×D311yescharacteristic
194C3×#107—31no—
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#830—31no—
204#830—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207#816—31no—
208#816—31no—
209#815—31no—
210C8×Dic3—31no—
211#810—31no—
212#810—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—31no—
217#810—61no—
218#810—61no—
219#810C2×D311yescharacteristic
220#810C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—61no—
224#808C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
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—
262C3⋊(C3⋊C8)—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
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—91no—
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
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—41no—
312C3×C4⋊C4—41no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—31no—
325C3×C22⋊C4—31no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—21no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—61no—
332C3×C42—61no—
333C3×C42C22×D311yescharacteristic
334C3×C42C22×D311yescharacteristic
335#217—61no—
336#216—62no—
337#216—62no—
338#216—62no—
339#216—62no—
340#216—62no—
341#216—62no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—21no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4#6711yescharacteristic
346(C2×D3)⋊C4#6711yescharacteristic
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3C22×D311yescharacteristic
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—121no—
365Dic3⋊C4#6711yescharacteristic
366Dic3⋊C4#6711yescharacteristic
367C4×Dic3—21no—
368C4×Dic3—21no—
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—121no—
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×C32C22×D411yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4C2×#4111yescharacteristic
399C32×C4C2×#4111yescharacteristic
400C3⋊Dic3—22no—
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—91no—
411C2×Q16—91no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—31no—
415#126—61no—
416#126—61no—
417#125—61no—
418#125—61no—
419#125D3211yescharacteristic
420C22⋊Q8—31no—
421C22⋊Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
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—31no—
435#107—91no—
436#106—31no—
437#106—91no—
438C4⋊C8—31no—
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—91no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—91no—
452C23×C3—31no—
453C22×D3C2×#6711yescharacteristic
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—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4D3×D411yescharacteristic
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4C2×#6711yescharacteristic
481C2×C3×C4C2×#6711yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—64no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3C2×#6711yescharacteristic
496C2×Dic3C2×#6711yescharacteristic
497C2×Dic3C2×#6711yescharacteristic
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#23912yes—
515C3×C8—61no—
516C3×C8—61no—
517C3⋊C8—21no—
518C3⋊C8—21no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8—121no—
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—182no—
539Q16—182no—
540Q16—182no—
541Q16—182no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8—91no—
545C2×C8—91no—
546C4⋊C4—21no—
547C4⋊C4—21no—
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—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4C2×D3211yescharacteristic
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—31no—
565C22⋊C4—31no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—181no—
569C42—31no—
570C42—61no—
571C42—61no—
572C42—61no—
573C42—181no—
574C42—181no—
575C42—181no—
576C42—181no—
577C42C2×D3211yescharacteristic
578C22×C3—21no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C22×#6711yescharacteristic
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—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—62no—
602C3×C4—61no—
603C3×C4—81no—
604C3×C4—81no—
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—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—21no—
637C2×C4—21no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—184no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4D3×#6711yescharacteristic
651C2×C4D3×#6711yescharacteristic
652C2×C4C22×D3211yescharacteristic
653C8—61no—
654C8—61no—
655C8—181no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—121no—
661C2×C3#562711yescharacteristic
662C2×C3#577111yescharacteristic
663C2×C3#577911yescharacteristic
664C2×C3#582811yescharacteristic
665C2×C3#583811yescharacteristic
666C2×C3#583811yescharacteristic
667D3—41no—
668C22—61no—
669C22—61no—
670C22—61no—
671C22C2×D3×#6711yescharacteristic
672C4—21no—
673C4—21no—
674C4—41no—
675C4—41no—
676C4—61no—
677C4—62no—
678C4—61no—
679C4—61no—
680C4—121no—
681C4—121no—
682C4—121no—
683C4—182no—
684C4—361no—
685C4D3×#23911yescharacteristic
686C4#6431911yescharacteristic
687C3—21no—
688C3#8121111yescharacteristic, complemented
689C3#8345111yescharacteristic, complemented
690C2—121no—
691C2#1059542411yescharacteristic
692C2#1059546511yescharacteristic
693C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#125D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #10592762C2semidirect
4. C3×#5063C2semidirect
7. #10590481C2semidirect
8. #10590480C2semidirect
9. #10590477C2semidirect
10. #10590476C2semidirect
13. #10590388C2semidirect
14. #10590384C2semidirect
71. #5063D3semidirect
625. C32#3127semidirect
688. C3#81211semidirect
689. C3#83451semidirect

Maximal subgroups

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

subgroupindex
C3×#56982
#105938852
#105927622
C3×#50632
#105906042
#105904812
#105904802
#105904772
#105904762
#105904482
#105904472
#105903882
#105903842
#105902532
#834513
#812113