Finite Group Databasebeta

← #11860633

Subgroups — #11860633

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic
5#10591582C212yesmaximal, complemented
6#10591581C212yesmaximal, complemented
7#10591446C212yesmaximal, complemented
8#10591445C212yesmaximal, complemented
9#10591131C211yesmaximal, characteristic, complemented
10C2×#63566C211yesmaximal, characteristic, complemented
11#10591059C211yesmaximal, characteristic, complemented
12#83965—31nomaximal
13#78821—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17D4×C3⋊Dic3—22no—
18D4×C3⋊Dic3C2212yes—
19#64135—21no—
20#64135C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#951C418yescomplemented
24C2×C3×#216C2212yes—
25C2×C3×#214C2212yes—
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63955—22no—
30#63843C2212yes—
31#63843C2212yes—
32Dic3×Dic6—21no—
33Dic3×Dic6—21no—
34C3×#835C2211yescharacteristic
35C3×#835C2211yescharacteristic
36C3×#832C2211yescharacteristic
37C3×#832C2211yescharacteristic
38#63575C2212yes—
39#63573C2212yes—
40#63566C2212yes—
41#63566C2212yes—
42#63555C2212yes—
43#63553C2212yes—
44C2×C3×#137—31no—
45#5827—31no—
46#5827—31no—
47#5827—61no—
48C2×#951D311yescharacteristic
49#5812—31no—
50#5516—31no—
51C3×#416—31no—
52#5233D311yescharacteristic
53C2×#835—31no—
54#5184—32no—
55Dic3×Q16—32no—
56#5164—32no—
57Dic3×SD16—32no—
58#5122—31no—
59#5121—31no—
60C2×#816—31no—
61#5101—31no—
62#4995—31no—
63#4790—32no—
64#4789—32no—
65#4758—32no—
66#4757—32no—
67C32×#41—22no—
68C32×#41C2×C414yes—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—22no—
76C22×C3×Dic3—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yescomplemented
80C2×C3×Dic6C2312yes—
81#3757—22no—
82#3757D412yes—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3C2312yes—
90C3×#217—21no—
91C3×#216C2×C418yescomplemented
92C3×#214C2×C418yescomplemented
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96C3×#208C2×C414yescomplemented
97C2×C3×C3⋊C8—22no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103Dic32—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C22×C3×Q8—31no—
110C22×Dic6C2×D311yescharacteristic
111C3×#137—38no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C2×C3×M16—31no—
115C22×C3×C8—31no—
116C3×#117—31no—
117#951Dic318yescomplemented
118Q8×Dic3—32no—
119Q8×Dic3—32no—
120Q8×Dic3—32no—
121Q8×Dic3—32no—
122Q8×Dic3—62no—
123Q8×Dic3—61no—
124Q8×Dic3—61no—
125C2×#216C2×D312yes—
126D4×Dic3—32no—
127D4×Dic3—32no—
128D4×Dic3—62no—
129D4×Dic3—62no—
130D4×Dic3—62no—
131D4×Dic3—64no—
132C2×#214C2×D312yes—
133#926—31no—
134#926—31no—
135#926—61no—
136#926—61no—
137#926—61no—
138#926—62no—
139#926—62no—
140#926C2×D311yescharacteristic
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3—61no—
145C2×C4⋊Dic3—61no—
146C2×C4⋊Dic3—62no—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8C2×D311yescharacteristic
149#887—32no—
150#887—32no—
151#877—62no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×#103—31no—
155C3×#103—31no—
156C3×#102—31no—
157C3×#102—31no—
158#835—32no—
159#835—32no—
160#835C2×D311yescharacteristic
161#835C2×D311yescharacteristic
162#832C2×D311yescharacteristic
163#832C2×D311yescharacteristic
164#818—32no—
165#817—32no—
166#816—32no—
167#816—32no—
168#815—32no—
169#815—32no—
170C8×Dic3—32no—
171C8×Dic3—32no—
172#808—32no—
173#807—32no—
174C23×C32—21no—
175C23×C32C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8C22×C412yes—
178C32×D4—24no—
179C32×D4—21no—
180C32×D4C22×C412yes—
181C2×C32×C4—21no—
182C2×C32×C4—24no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—82no—
189C2×C3⋊Dic3—81no—
190C2×C3⋊Dic3C2×D412yes—
191C2×C3⋊Dic3C2×D412yes—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6C22×C414yes—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C22×C414yes—
202C2×#137—31no—
203#520—91no—
204#519—91no—
205#441—92no—
206#440—92no—
207C4×Q16—92no—
208C4×SD16—92no—
209#428—91no—
210#416—31no—
211C2×#103—91no—
212#405—91no—
213C3×#41—24no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—24no—
217C3×#41C4×D314yes—
218C3×#41C2×Dic314yes—
219C2×C3×Q8—21no—
220C2×C3×Q8—34no—
221C2×C3×Q8—32no—
222C2×C3×Q8—61no—
223C2×C3×Q8—62no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4C22×D311yescharacteristic
231C2×C3×D4C22×D311yescharacteristic
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×Dic3—21no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—64no—
243C22×Dic3—62no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C2×Dic6—21no—
247C2×Dic6—22no—
248C2×Dic6C2×Dic314yescomplemented
249C2×Dic6C22×D312yes—
250C3×Q16—38no—
251C3×SD16—38no—
252C3×M16—34no—
253C2×C3×C8—32no—
254C2×C3×C8—31no—
255C2×C3×C8—31no—
256C2×C3×C8—62no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C22⋊C4—61no—
260C3×C42—61no—
261#217—21no—
262#217—32no—
263#217—32no—
264#217—62no—
265#217—62no—
266#217—62no—
267#217—64no—
268#216C2×Dic318yescomplemented
269#214C2×Dic318yescomplemented
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—32no—
275C4⋊Dic3—32no—
276C4⋊Dic3—61no—
277C4⋊Dic3—62no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—64no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291C4×Dic3—21no—
292C4×Dic3—32no—
293C4×Dic3—32no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C4×Dic3—62no—
301C4×Dic3—64no—
302#208C2×Dic314yescomplemented
303C2×C3⋊C8—22no—
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D312yes—
307C22×C32—22no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32C4×D412yes—
313C22×C32C22×D411yescharacteristic
314C32×C4—22no—
315C32×C4C4×D412yes—
316C32×C4C23×C411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—22no—
319C3⋊Dic3—22no—
320C3⋊Dic3—42no—
321C3×Dic3—24no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C2×#41D3211yescharacteristic
325C22×Q8—31no—
326#137—38no—
327C2×Q16—32no—
328C2×SD16—32no—
329C2×M16—31no—
330C22×C8—31no—
331C4×Q8—92no—
332C4×Q8—92no—
333C4×Q8—92no—
334C4×Q8—181no—
335C4×Q8—181no—
336C4×D4—92no—
337C4×D4—182no—
338#117—31no—
339#117—91no—
340#117—182no—
341#117—181no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—181no—
344#107—92no—
345#106—92no—
346#103—31no—
347#103—31no—
348#103—92no—
349#103—92no—
350#102—31no—
351#102—31no—
352#97—92no—
353C4×C8—92no—
354C23×C3—22no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3D3×D411yescharacteristic
359C23×C3D3×D411yescharacteristic
360C3×Q8—22no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—22no—
364C3×Q8—34no—
365C3×Q8—64no—
366C3×Q8—62no—
367C3×Q8C2×C4×D312yes—
368C3×Q8C22×Dic312yes—
369C3×D4—28no—
370C3×D4—22no—
371C3×D4—24no—
372C3×D4—24no—
373C3×D4—21no—
374C3×D4—21no—
375C3×D4—22no—
376C3×D4C2×C4×D312yes—
377C3×D4C22×Dic312yes—
378C2×C3×C4—22no—
379C2×C3×C4—28no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—64no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4C2×C4×D312yes—
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4#23712yes—
396C2×C3×C4#23712yes—
397C2×C3×C4C22×Dic312yes—
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×Dic3—24no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—242no—
414C2×Dic3—242no—
415C2×Dic3—241no—
416C2×Dic3—241no—
417C2×Dic3—244no—
418C2×Dic3—242no—
419Dic6—24no—
420Dic6—22no—
421Dic6C22×Dic314yes—
422C3×C8—34no—
423C3×C8—61no—
424C3×C8—61no—
425C3⋊C8—21no—
426C3⋊C8—21no—
427C3⋊C8C22×Dic314yes—
428C2×C32—22no—
429C2×C32—42no—
430C2×C32C2×C4×D411yescharacteristic
431C2×C32#57711yescharacteristic
432C2×C32#57811yescharacteristic
433#41—22no—
434#41D3×Dic314yes—
435C2×Q8—32no—
436C2×Q8—34no—
437C2×Q8—62no—
438C2×Q8—61no—
439C2×Q8C2×D3211yescharacteristic
440C2×D4—21no—
441C2×D4C2×D3211yescharacteristic
442C22×C4—21no—
443C22×C4—61no—
444C22×C4—182no—
445C22×C4—181no—
446C22×C4C2×D3211yescharacteristic
447Q16—38no—
448SD16—38no—
449M16—34no—
450C2×C8—32no—
451C2×C8—31no—
452C2×C8—31no—
453C2×C8—62no—
454C4⋊C4—31no—
455C4⋊C4—31no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—92no—
459C4⋊C4—182no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4—181no—
463C22⋊C4—61no—
464C22⋊C4—92no—
465C22⋊C4—182no—
466C42—61no—
467C42—92no—
468C42—182no—
469C42—182no—
470C42—182no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—24no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3#67⋊C412yes—
489C22×C3D4×Dic312yes—
490C22×C3C2×D3×D411yescharacteristic
491C22×C3C2×D3×D411yescharacteristic
492C3×C4—24no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—22no—
498C3×C4—64no—
499C3×C4—121no—
500C3×C4—121no—
501C3×C4#67⋊C412yes—
502C3×C4D4×Dic312yes—
503C3×C4C22×C4×D311yescharacteristic
504C3×C4C2×#23711yescharacteristic
505C3×C4C2×#23711yescharacteristic
506C3×C4C23×Dic311yescharacteristic
507Dic3—24no—
508Dic3—41no—
509Dic3—41no—
510Dic3—62no—
511Dic3—62no—
512Dic3—62no—
513Dic3—62no—
514Dic3—122no—
515Dic3—122no—
516Dic3—124no—
517Dic3—122no—
518Dic3—122no—
519C32#294711yescharacteristic, complemented, Sylow
520C23—21no—
521C23#381111yescharacteristic
522Q8—21no—
523Q8—34no—
524Q8—62no—
525Q8—64no—
526Q8C2×D3×Dic312yes—
527D4—24no—
528D4—21no—
529D4C2×D3×Dic312yes—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—62no—
533C2×C4—64no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—182no—
539C2×C4—722no—
540C2×C4—721no—
541C2×C4C2×D3×Dic312yes—
542C2×C4#380512yes—
543C2×C4#381111yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—34no—
546C8—61no—
547C8—61no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—44no—
555C2×C3—42no—
556C2×C3—42no—
557C2×C3C2×#67⋊C411yescharacteristic
558C2×C3#577011yescharacteristic
559C2×C3#577111yescharacteristic
560C2×C3#577811yescharacteristic
561C2×C3#577911yescharacteristic
562C2×C3C2×D4×Dic311yescharacteristic
563C22—21no—
564C22—21no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22#67⋊Dic312yes—
569C22C2×#381111yescharacteristic
570C4—22no—
571C4—64no—
572C4—121no—
573C4—121no—
574C4—182no—
575C4—182no—
576C4—362no—
577C4#67⋊Dic312yes—
578C4C22×D3×Dic311yescharacteristic
579C4C2×#380511yescharacteristic
580C3—21no—
581C3#7882111yescharacteristic, complemented
582C3#8396511yescharacteristic, complemented
583C2—22no—
584C2—42no—
585C2#1059547211yescharacteristic
586C2#1059547311yescharacteristic
587C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10594818C2semidirect
5. #10591582C2semidirect
6. #10591581C2semidirect
7. #10591446C2semidirect
8. #10591445C2semidirect
9. #10591131C2semidirect
10. C2×#63566C2semidirect
11. #10591059C2semidirect
23. C3×#951C4semidirect
79. C2×C3×Dic6C2×C4semidirect
91. C3×#216C2×C4semidirect
92. C3×#214C2×C4semidirect
96. C3×#208C2×C4semidirect
117. #951Dic3semidirect
248. C2×Dic6C2×Dic3semidirect
268. #216C2×Dic3semidirect
269. #214C2×Dic3semidirect
302. #208C2×Dic3semidirect
519. C32#2947semidirect
581. C3#78821semidirect
582. C3#83965semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×C3×#9512
#105948182
C3×#52332
#105915822
#105915812
#105914462
#105914452
#105911312
C2×#635662
#105910592
#839653
#788213