Finite Group Databasebeta

← #11860621

Subgroups — #11860621

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#10595975C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C3×#4964C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic
7#10591059C211yesmaximal, characteristic, complemented
8#10590485C212yesmaximal, complemented
9#10590484C212yesmaximal, complemented
10#10590483C212yesmaximal, complemented
11#10590482C212yesmaximal, complemented
12#79202—31nomaximal
13#78774—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C4×#638—22no—
18#64135C2211yescharacteristic
19#64102C2212yes—
20#64101—21no—
21C4⋊C4×C3⋊D3—21no—
22#64096C2212yes—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63955—22no—
27#63843C2212yes—
28#63843C2212yes—
29Dic3×Dic6—21no—
30Dic3×Dic6—21no—
31C2×#3719C2212yes—
32#63833C418yescomplemented
33C2×#3717C2212yes—
34C3×#810C2212yes—
35C3×#810C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38#63567C2211yescharacteristic
39#63567C2211yescharacteristic
40#63564C2211yescharacteristic
41#63564C2211yescharacteristic
42#63555C2212yes—
43#63553C2212yes—
44#5812—31no—
45C2×#942—31no—
46C2×#909—31no—
47#5516—31no—
48#5504—31no—
49#5504—31no—
50#5504—61no—
51C3×#428—31no—
52C2×C3×#103—31no—
53#5122—31no—
54#5113—31no—
55#5101—31no—
56#5002—31no—
57C2×#810D311yescharacteristic, complemented
58#4964D311yescharacteristic, complemented
59#4889—32no—
60#4873—32no—
61#4853—32no—
62#4852—32no—
63#4817—32no—
64#4790—32no—
65#4789—32no—
66#4788—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—22no—
71#3828C2×C414yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C22×C3×Dic3—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yescomplemented
80C2×C3×Dic6C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83#3757D412yes—
84#3752—22no—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C4⋊(C3⋊Dic3)D411yescharacteristic
87#3750—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4×Dic3—21no—
94C3×#208C2×C414yescomplemented
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C418yescomplemented
104#3717C2×C418yescomplemented
105#2947—91noSylow
106C22×C3×Q8—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C22×Dic6C2×D311yescharacteristic
111C2×C3×M16—31no—
112C22×C3×C8—31no—
113C3×#117—31no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117Q8×Dic3—32no—
118Q8×Dic3—32no—
119Q8×Dic3—61no—
120Q8×Dic3—61no—
121C2×#216—32no—
122#942—38no—
123C2×#215—32no—
124C4×#67—62no—
125C4×#67—62no—
126C4×#67—64no—
127#926—31no—
128#926—31no—
129#926—61no—
130#926—62no—
131#926C2×D311yescharacteristic
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8C2×D311yescharacteristic
134#909—38no—
135C2×Dic12—32no—
136C2×#204—32no—
137#893—32no—
138#893—32no—
139#893—62no—
140#892—61no—
141#892—61no—
142#892—62no—
143D3×C4⋊C4—61no—
144D3×C4⋊C4—61no—
145D3×C4⋊C4—62no—
146#887—32no—
147#887—32no—
148#887—32no—
149#887—32no—
150#887—62no—
151#877—62no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×#107—32no—
155C3×#106—32no—
156C3×#103—32no—
157C3×#103—32no—
158#821—31no—
159#821—31no—
160#816—31no—
161#816—31no—
162#815—32no—
163#815—32no—
164C8×Dic3—32no—
165C8×Dic3—32no—
166#810—31no—
167#810—31no—
168#810C2×D312yes—
169#810C2×D312yes—
170#809—31no—
171#809—31no—
172#808C2×D312yes—
173#807C2×D312yes—
174C23×C32C2×D411yescharacteristic
175C22×C3⋊D3—21no—
176C2×C32×C4—22no—
177C2×C32×C4—81no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3C2×D412yes—
185C2×C3⋊Dic3C2×D412yes—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)C22×C412yes—
188C4×C3⋊D3—24no—
189C4×C3⋊D3—82no—
190#634—21no—
191#634C22×C412yes—
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—91no—
203#520—91no—
204#519—91no—
205#441—92no—
206#440—92no—
207C4×Q16—92no—
208C4×SD16—92no—
209#428—31no—
210#416—91no—
211C2×#103—31no—
212#405—91no—
213C2×C3×Q8—34no—
214C2×C3×Q8—32no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—62no—
225C2×#67—61no—
226C2×#67—61no—
227C22×Dic3—21no—
228#235—34no—
229#235—34no—
230#235—64no—
231#235—64no—
232#235—62no—
233#235—62no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—61no—
237C2×C4×D3—62no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—64no—
243C2×Dic6—21no—
244C2×Dic6—22no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C2×Dic6—61no—
248C2×Dic6C4×D314yescomplemented
249C2×Dic6C22×D312yes—
250C3×M16—34no—
251C2×C3×C8—32no—
252C2×C3×C8—31no—
253C2×C3×C8—31no—
254C2×C3×C8—62no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4C22×D312yes—
262C3×C4⋊C4C22×D312yes—
263C3×C22⋊C4—61no—
264C3×C42—61no—
265#217—21no—
266#217—32no—
267#217—32no—
268#217—62no—
269#216—38no—
270#215—38no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—64no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3C22×D311yescharacteristic
283C4⋊Dic3C22×D311yescharacteristic
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—64no—
289C4×Dic3—21no—
290C4×Dic3—32no—
291C4×Dic3—32no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—64no—
300#208C4×D314yescomplemented
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D312yes—
305Dic12—38no—
306#204—38no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C4×D412yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C32×C4—42no—
315C32×C4C4×D412yes—
316C32×C4C23×C411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—22no—
319C3⋊Dic3—22no—
320C3⋊Dic3—22no—
321C3×Dic3—24no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C2×#41—91no—
325C22×Q8—31no—
326#137—98no—
327C2×Q16—92no—
328C2×SD16—92no—
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—181no—
343C2×C4⋊C4D3211yescharacteristic
344#107—32no—
345#106—32no—
346#103—32no—
347#103—32no—
348#103—91no—
349#103—91no—
350#102—91no—
351#102—91no—
352#97—92no—
353C4×C8—92no—
354C23×C3—21no—
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D411yescharacteristic
357C22×D3—62no—
358C22×D3—61no—
359C22×D3—61no—
360C3×Q8—34no—
361C3×Q8—64no—
362C3×Q8—62no—
363C2×C3×C4—24no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—21no—
370C2×C3×C4—64no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—81no—
375C2×C3×C4—81no—
376C2×C3×C4—82no—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4C2×C4×D312yes—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4#23712yes—
382C2×C3×C4#23912yes—
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—68no—
386#67—64no—
387#67—64no—
388C2×Dic3—24no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—32no—
393C2×Dic3—32no—
394C2×Dic3—32no—
395C2×Dic3—32no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401D12—32no—
402D12—32no—
403D12—62no—
404D12—62no—
405D12—61no—
406D12—61no—
407C4×D3—68no—
408C4×D3—64no—
409C4×D3—64no—
410C4×D3—242no—
411C4×D3—242no—
412C4×D3—244no—
413Dic6—24no—
414Dic6—22no—
415Dic6—32no—
416Dic6—32no—
417Dic6—62no—
418Dic6—62no—
419Dic6—61no—
420Dic6—61no—
421Dic6C2×C4×D314yes—
422C3×C8—34no—
423C3×C8—61no—
424C3×C8—61no—
425C3⋊C8—21no—
426C3⋊C8—21no—
427C3⋊C8C2×C4×D314yes—
428C2×C32—22no—
429C2×C32C2×C4×D411yescharacteristic
430C2×C32#57711yescharacteristic
431C2×C32#57811yescharacteristic
432C3⋊D3—42no—
433#41—94no—
434#41—182no—
435C2×Q8—32no—
436C2×Q8—34no—
437C2×Q8—62no—
438C2×Q8—61no—
439C2×Q8—91no—
440C2×D4—91no—
441C2×D4—181no—
442C22×C4—21no—
443C22×C4—61no—
444C22×C4—182no—
445C22×C4—181no—
446C22×C4C2×D3211yescharacteristic
447Q16—98no—
448SD16—98no—
449M16—34no—
450C2×C8—32no—
451C2×C8—31no—
452C2×C8—31no—
453C2×C8—62no—
454C4⋊C4—21no—
455C4⋊C4—31no—
456C4⋊C4—31no—
457C4⋊C4—91no—
458C4⋊C4—91no—
459C4⋊C4—182no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C4⋊C4C2×D3212yes—
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—21no—
476C22×C3—22no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3#67⋊C412yes—
480C22×C3#89312yes—
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C2×D3—64no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—121no—
491C2×D3—121no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—44no—
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—64no—
499C3×C4—121no—
500C3×C4—121no—
501C3×C4#67⋊C412yes—
502C3×C4#89312yes—
503C3×C4C22×C4×D311yescharacteristic
504C3×C4C22×C4×D311yescharacteristic
505C3×C4C2×#23711yescharacteristic
506C3×C4C2×#23911yescharacteristic
507Dic3—24no—
508Dic3—41no—
509Dic3—41no—
510Dic3—64no—
511Dic3—62no—
512Dic3—62no—
513Dic3—62no—
514Dic3—62no—
515Dic3—62no—
516Dic3—62no—
517Dic3—122no—
518Dic3—122no—
519C32#294711yescharacteristic, complemented, Sylow
520C23—181no—
521C23#381111yescharacteristic
522Q8—34no—
523Q8—62no—
524Q8—64no—
525Q8—92no—
526Q8—181no—
527D4—92no—
528D4—184no—
529D4—181no—
530C2×C4—22no—
531C2×C4—62no—
532C2×C4—64no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—81no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—181no—
539C2×C4—184no—
540C2×C4—722no—
541C2×C4#379612yes—
542C2×C4C4×D3212yes—
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×C3C2×#67⋊C411yescharacteristic
555C2×C3C2×#89311yescharacteristic
556C2×C3#576211yescharacteristic
557C2×C3#576611yescharacteristic
558C2×C3#577511yescharacteristic
559C2×C3#577911yescharacteristic
560D3—124no—
561D3—122no—
562D3—122no—
563C22—21no—
564C22—21no—
565C22—182no—
566C22—361no—
567C22—361no—
568C22#6388112yes—
569C22C2×#381111yescharacteristic
570C4—42no—
571C4—64no—
572C4—121no—
573C4—121no—
574C4—182no—
575C4—182no—
576C4—182no—
577C4#6388112yes—
578C4C2×#379611yescharacteristic
579C4C2×C4×D3211yescharacteristic
580C3—21no—
581C3#7877411yescharacteristic, complemented
582C3#7920211yescharacteristic, complemented
583C2—22no—
584C2—362no—
585C2C2×#6388111yescharacteristic
586C2#1059511511yescharacteristic
587C2#1059533711yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
4. C2×C3×#810C2semidirect
5. C3×#4964C2semidirect
7. #10591059C2semidirect
8. #10590485C2semidirect
9. #10590484C2semidirect
10. #10590483C2semidirect
11. #10590482C2semidirect
32. #63833C4semidirect
57. C2×#810D3semidirect
58. #4964D3semidirect
79. C2×C3×Dic6C2×C4semidirect
94. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
248. C2×Dic6C4×D3semidirect
300. #208C4×D3semidirect
519. C32#2947semidirect
581. C3#78774semidirect
582. C3#79202semidirect

Maximal subgroups

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

subgroupindex
#105959752
#105948182
C2×#638332
C2×C3×#8102
C3×#49642
#105911052
#105910592
#105904852
#105904842
#105904832
#105904822
#792023
#787743