Finite Group Databasebeta

← #11868803

Subgroups — #11868803

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C4×#3796C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590612C212yesmaximal
6#10590583C212yesmaximal, complemented
7#10590496C212yesmaximal, complemented
8#10590472C212yesmaximal, complemented
9#10590340C211yesmaximal, characteristic, complemented
10#10590301C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#81012—31nomaximal
13#80966—31nomaximal
14C2×Q8×C3⋊D3—21no—
15C2×#3796C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17#64153—21no—
18C4⋊C4×C3⋊D3—21no—
19C4⋊C4×C3⋊D3C2212yes—
20#64097—21no—
21#64097C2212yes—
22C42×C3⋊D3C2211yescharacteristic
23#64078C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26C4×#626—21no—
27#63898C2211yescharacteristic
28#63881—21no—
29#63878—21no—
30C4×D3×Dic3—21no—
31#63849C2211yescharacteristic
32#63843C2211yescharacteristic
33C2×#3712C2212yes—
34C3×#810C2212yes—
35C3×#809C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63573C2212yes—
42#63572C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45D3×C4⋊Q8—31no—
46D3×C4⋊Q8—31no—
47D3×C4⋊Q8—61no—
48C4×#239—31no—
49C4×#237—31no—
50C3×#475—31no—
51C3×#474—31no—
52#5094D311yescharacteristic, complemented
53#5087D311yescharacteristic, complemented
54#5020—31no—
55#5007—31no—
56#4881—32no—
57#4875—32no—
58#4870—32no—
59#4861—32no—
60#4851—31no—
61#4846—31no—
62#4837—31no—
63#4837—31no—
64#4803—32no—
65#4793—32no—
66#4771—32no—
67#4761—32no—
68C2×C32×Q8—21no—
69Q8×C3⋊D3—44no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×#634—21no—
75C2×#634—22no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×Dic6C2311yescharacteristic
79C2×#626—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82#3796—22no—
83#3796Q814yescomplemented
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C32×C42C2311yescharacteristic
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89#3750—22no—
90#3750—22no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—21no—
105Dic32—21no—
106#3712—24no—
107#3079—91noSylow
108C2×#239—31no—
109C2×D3×Q8—61no—
110C2×D3×Q8—61no—
111C2×D3×Q8—62no—
112C2×#237—31no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8C2×D311yescharacteristic
115C3×C4⋊Q8C2×D311yescharacteristic
116C3×C4×Q8—31no—
117C3×C4×D4—31no—
118Q8×Dic3—31no—
119#944—61no—
120#944—61no—
121#944—62no—
122D4×Dic3—31no—
123C4×#67—61no—
124C2×C4×Dic3—61no—
125C2×ΓL(1,𝔽25)—32no—
126C2×ΓL(1,𝔽25)—32no—
127#893—31no—
128#893—61no—
129#892—31no—
130#892—31no—
131#892—61no—
132D3×C4⋊C4—32no—
133D3×C4⋊C4—32no—
134D3×C4⋊C4—62no—
135D3×C4⋊C4—61no—
136D3×C4⋊C4—61no—
137D3×C4⋊C4—62no—
138#888—32no—
139#888—32no—
140#888—62no—
141#888—61no—
142#888—61no—
143#888—62no—
144#887—31no—
145#67⋊C4—61no—
146#877—61no—
147C4×D12—61no—
148C4×D12C2×D311yescharacteristic
149C42×D3—31no—
150C42×D3—31no—
151C42×D3—61no—
152C42×D3—61no—
153#869—31no—
154#869—31no—
155#869—61no—
156C4×Dic6C2×D311yescharacteristic
157C3×#107—32no—
158C3×#106—32no—
159C3×C4⋊C8—31no—
160C3×C4⋊C8—31no—
161C3×#103—32no—
162C3×#102—32no—
163#835—32no—
164#832—32no—
165#821—32no—
166#818—32no—
167#817—32no—
168#816—32no—
169Dic3⋊C8—32no—
170Dic3⋊C8—32no—
171#810C2×D312yes—
172#809C2×D312yes—
173#808—32no—
174#808C2×D312yes—
175#807—32no—
176#807C2×D312yes—
177C4⋊(C3⋊C8)C2×D311yescharacteristic
178C4⋊(C3⋊C8)C2×D311yescharacteristic
179C22×C3⋊D3C2×D411yescharacteristic
180C22×C3×D3—21no—
181C32×Q8—42no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C4×C3⋊D3—22no—
191C4×C3⋊D3—22no—
192C4×C3⋊D3—44no—
193C4×C3⋊D3C2×Q812yes—
194C4×C3⋊D3#4112yes—
195#634—44no—
196#634—42no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C3×D12—21no—
201C3×D12C2×Q812yescomplemented
202C3×C4×D3—42no—
203C3×Dic6—21no—
204C3×Dic6C2×Q812yescomplemented
205#626—24no—
206D3×Dic3—24no—
207D3×Dic3—42no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210C2×C4⋊Q8—91no—
211C4×#41—91no—
212#477—92no—
213#476—92no—
214#475—31no—
215#475—91no—
216#474—31no—
217#474—91no—
218#428—92no—
219#423—91no—
220#417—92no—
221C2×C3×Q8—22no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—31no—
225C2×C3×D4—31no—
226C22×C3×C4—61no—
227C2×#67—61no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230#239—34no—
231#239—62no—
232D3×Q8—128no—
233D3×Q8—124no—
234D3×Q8—124no—
235#237—34no—
236#237—62no—
237C2×D12—61no—
238C2×D12C22×D311yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—31no—
241C2×C4×D3—31no—
242C2×C4×D3—31no—
243C2×C4×D3—31no—
244C2×C4×D3—31no—
245C2×C4×D3—31no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—64no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—62no—
257C2×Dic6—64no—
258C2×Dic6—61no—
259C2×Dic6—61no—
260C2×Dic6C22×D311yescharacteristic
261C2×C3×C8—32no—
262C2×C3×C8—32no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D312yes—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42—61no—
275C3×C42C22×D311yescharacteristic
276C3×C42C22×D311yescharacteristic
277#217—61no—
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—61no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3C22×D311yescharacteristic
290C4⋊Dic3C22×D311yescharacteristic
291Dic3⋊C4—21no—
292Dic3⋊C4—61no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297Dic3⋊C4—64no—
298Dic3⋊C4—64no—
299C4×Dic3—21no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C2×C3⋊C8C22×D312yes—
314C2×C3⋊C8C22×D312yes—
315ΓL(1,𝔽25)—64no—
316ΓL(1,𝔽25)—64no—
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3C22⋊Q812yes—
321C2×C3×D3—22no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C32×C4—21no—
325C32×C4—42no—
326C32×C4AGL(1,ℤ/8)12yes—
327C32×C4C22×Q811yescharacteristic
328C32×C4C2×#4111yescharacteristic
329C3⋊Dic3—21no—
330C3⋊Dic3—42no—
331C3⋊Dic3C22⋊Q812yes—
332C3⋊Dic3#13712yes—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C2×#41—91no—
337C22×Q8—181no—
338C2×M16—92no—
339C4⋊Q8—92no—
340C4⋊Q8—91no—
341C4⋊Q8—181no—
342C4⋊Q8—181no—
343C4⋊Q8D3211yescharacteristic
344C4×Q8—31no—
345C4×Q8—91no—
346C4×D4—31no—
347C4×D4—91no—
348C4×D4—181no—
349C4×D4—181no—
350#117—91no—
351#117—181no—
352C2×C4⋊C4—92no—
353C2×C4⋊C4—181no—
354C2×C42—91no—
355C2×C42—181no—
356#107—32no—
357#107—92no—
358#106—32no—
359#106—92no—
360C4⋊C8—31no—
361C4⋊C8—31no—
362C4⋊C8—92no—
363#103—32no—
364#103—92no—
365#102—32no—
366#102—92no—
367C23×C3—61no—
368C22×D3—21no—
369C22×D3—31no—
370C22×D3—31no—
371C22×D3—61no—
372C3×Q8—32no—
373C3×Q8—44no—
374C3×Q8—42no—
375C3×Q8—42no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—61no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—122no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—64no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—31no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413D12—21no—
414D12—64no—
415D12D3×Q812yescomplemented
416C4×D3—32no—
417C4×D3—32no—
418C4×D3—32no—
419C4×D3—32no—
420C4×D3—42no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—64no—
426C4×D3—64no—
427C4×D3—64no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—122no—
431C4×D3—128no—
432C4×D3—124no—
433C4×D3—124no—
434Dic6—21no—
435Dic6—128no—
436Dic6—124no—
437Dic6—124no—
438Dic6—124no—
439Dic6—122no—
440Dic6—122no—
441Dic6D3×Q812yescomplemented
442C3×C8—62no—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—22no—
446C2×C32C2×C22⋊Q811yescharacteristic
447C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
448C2×C32C2×#13711yescharacteristic
449C3⋊D3—22no—
450C3×D3—42no—
451#41—94no—
452#41—182no—
453C2×Q8—21no—
454C2×Q8—31no—
455C2×Q8—182no—
456C2×Q8—181no—
457C2×Q8—364no—
458C2×D4—31no—
459C2×D4—181no—
460C22×C4—61no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—182no—
465C22×C4—181no—
466C22×C4—181no—
467M16—184no—
468C2×C8—32no—
469C2×C8—32no—
470C4⋊C4—21no—
471C4⋊C4—31no—
472C4⋊C4—31no—
473C4⋊C4—61no—
474C4⋊C4—92no—
475C4⋊C4—182no—
476C4⋊C4—182no—
477C4⋊C4—181no—
478C4⋊C4—181no—
479C4⋊C4C2×D3212yes—
480C22⋊C4—61no—
481C22⋊C4—181no—
482C22⋊C4—181no—
483C42—61no—
484C42—91no—
485C42—91no—
486C42—91no—
487C42—181no—
488C42—181no—
489C42C2×D3211yescharacteristic
490C22×C3—21no—
491C22×C3—62no—
492C22×C3—121no—
493C22×C3—121no—
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—22no—
497C2×D3—32no—
498C2×D3—32no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—61no—
505C2×D3—61no—
506C2×D3—61no—
507C2×D3—61no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—44no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—62no—
518C3×C4—121no—
519C3×C4—121no—
520C3×C4#91112yes—
521C3×C4#91412yes—
522C3×C4C2×D3×Q811yescharacteristic
523C3×C4C2×D3×Q811yescharacteristic
524C3×C4D3×#4111yescharacteristic
525C3×C4D3×#4111yescharacteristic
526Dic3—22no—
527Dic3—32no—
528Dic3—32no—
529Dic3—32no—
530Dic3—32no—
531Dic3—41no—
532Dic3—41no—
533Dic3—62no—
534Dic3—62no—
535Dic3—62no—
536Dic3—61no—
537Dic3—61no—
538Dic3—124no—
539Dic3—122no—
540Dic3—122no—
541C32#307911yescharacteristic, complemented, Sylow
542C23—61no—
543C23—91no—
544Q8—32no—
545Q8—42no—
546Q8—61no—
547Q8—364no—
548Q8—362no—
549D4—32no—
550D4—61no—
551D4—184no—
552C2×C4—22no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—91no—
557C2×C4—91no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—91no—
561C2×C4—122no—
562C2×C4—182no—
563C2×C4—184no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—364no—
567C2×C4—362no—
568C2×C4#381111yescharacteristic
569C2×C4#381111yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—62no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—122no—
577C2×C3D3×C22⋊Q811yescharacteristic
578C2×C3D3×C22⋊Q811yescharacteristic
579C2×C3C2×#91111yescharacteristic
580C2×C3C2×#91411yescharacteristic
581C2×C3D3×#13711yescharacteristic
582C2×C3D3×#13711yescharacteristic
583D3—42no—
584D3—64no—
585D3—62no—
586D3—62no—
587C22—62no—
588C22—92no—
589C22—121no—
590C22—121no—
591C22—181no—
592C22—181no—
593C22C2×#381111yescharacteristic
594C4—21no—
595C4—42no—
596C4—62no—
597C4—92no—
598C4—92no—
599C4—121no—
600C4—121no—
601C4—181no—
602C4—362no—
603C4#6393712yes—
604C4D32×Q811yescharacteristic
605C4#6431911yescharacteristic
606C3—21no—
607C3#8096611yescharacteristic, complemented
608C3#8101211yescharacteristic, complemented
609C2—122no—
610C2—182no—
611C2C2×#6393711yescharacteristic
612C2#1059532211yescharacteristic
613C2#1059542911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
hypercenterC4⋊Q8D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C4⋊Q8C2semidirect
3. C3×#5094C2semidirect
4. C3×#5087C2semidirect
6. #10590583C2semidirect
7. #10590496C2semidirect
8. #10590472C2semidirect
9. #10590340C2semidirect
10. #10590301C2semidirect
11. #10590272C2semidirect
52. #5094D3semidirect
53. #5087D3semidirect
83. #3796Q8semidirect
201. C3×D12C2×Q8semidirect
204. C3×Dic6C2×Q8semidirect
415. D12D3×Q8semidirect
441. Dic6D3×Q8semidirect
541. C32#3079semidirect
607. C3#80966semidirect
608. C3#81012semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C4×#37962
C3×#50942
C3×#50872
#105906122
#105905832
#105904962
#105904722
#105903402
#105903012
#105902722
#810123
#809663