Finite Group Databasebeta

← #11898306

Subgroups — #11898306

Order 1152.

908 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic
3C3×#5027C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591620C212yesmaximal, complemented
6#10591569C212yesmaximal, complemented
7#10590553C212yesmaximal, complemented
8#10590460C212yesmaximal, complemented
9#10590369C211yesmaximal, characteristic, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80378—31nomaximal
13#79637—31nomaximal
14C2×#3795—21no—
15C32×C4×Q8C2211yescharacteristic
16#64153C2212yes—
17#64098—22no—
18#64096C2212yes—
19#64079—21no—
20#64078C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#215C2212yes—
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27#63914C2212yes—
28#63908—21no—
29#63898C2212yes—
30#63885—22no—
31C2×#3716C2212yes—
32C2×#3716C2212yes—
33C2×#3716C2212yes—
34C3×#835C2211yescharacteristic
35C3×#809C2211yescharacteristic
36C3×#809C2212yes—
37C3×#808C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40#63572C2212yes—
41#63567C2212yes—
42#63553C2212yes—
43#5718—31no—
44#5567—31no—
45#5567—31no—
46#5567—61no—
47#5553—31no—
48C3×#460—31no—
49C3×C4×SD16—31no—
50#5175—32no—
51#5175—32no—
52#5162—32no—
53#5076—31no—
54#5027D311yescharacteristic, complemented
55C4×#215D311yescharacteristic, complemented
56#5019—31no—
57#4852—32no—
58#4841—31no—
59#4830—31no—
60#4818—32no—
61#4762—32no—
62#4762—32no—
63#4758—32no—
64#4693—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634D411yescharacteristic
68C2×#634C2312yes—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)D411yescharacteristic
85#3750—22no—
86#3750—22no—
87#3750—22no—
88#3750D412yes—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C3×#215—22no—
92C3×#215—42no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99#3716—24no—
100#3716—42no—
101#3716—42no—
102#3392—91noSylow
103C2×#237—61no—
104C2×#235—61no—
105C2×C3×SD16—31no—
106C2×C3×SD16—32no—
107C3×#127—31no—
108C3×C4×Q8—21no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×D4—31no—
112#944—32no—
113#944—32no—
114#944—62no—
115C2×#215C2×D311yescharacteristic
116C2×#215C2×D312yes—
117#940—32no—
118#940—32no—
119#939—62no—
120#938—61no—
121D4×Dic3—32no—
122C2×#214—32no—
123C2×#214—32no—
124C2×#214—32no—
125#930—61no—
126C2×#204—32no—
127C2×#204—32no—
128C2×#204—32no—
129#893—32no—
130#889—62no—
131#889—62no—
132#889—64no—
133#887—32no—
134#887—32no—
135#887—62no—
136#884—62no—
137#874C2×D311yescharacteristic
138C4×D12C2×D311yescharacteristic
139#870—61no—
140#870—61no—
141#870—62no—
142#869—31no—
143#869—31no—
144#869—61no—
145C4×Dic6—31no—
146C4×Dic6—31no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C4×Dic6—61no—
150C4×Dic6—62no—
151C3×#106—31no—
152C3×C4⋊C8—31no—
153C3×#103—31no—
154C3×#102—32no—
155C3×#102—31no—
156C3×C4×C8—31no—
157#835C2×D311yescharacteristic
158#816—32no—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161C8×Dic3—32no—
162C8×Dic3—32no—
163#810—32no—
164#809C2×D311yescharacteristic
165#809C2×D312yes—
166#808C2×D311yescharacteristic
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C32×Q8—21no—
172C32×Q8—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3C2×D412yes—
180C2×C3⋊Dic3C2×D412yes—
181#634—22no—
182#634—22no—
183#634SD1614yescomplemented
184C2×C3×Dic3—21no—
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—42no—
190C3×D12—81no—
191C3×C4×D3—42no—
192#625—44no—
193#625—82no—
194D3×Dic3—44no—
195C3×C3⋊C8—21no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8#4112yescomplemented
198#557—91no—
199#550—91no—
200#492—91no—
201#492—92no—
202#461—92no—
203#461—91no—
204#460—31no—
205#460—92no—
206C8×Q8—91no—
207C4×SD16—31no—
208C4×SD16—92no—
209C2×C3×Q8—21no—
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×Q8C22×D311yescharacteristic
212C2×C3×D4—32no—
213C2×C3×D4—31no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C22×C3×C4—61no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C22×Dic3—62no—
222#237—124no—
223#235—124no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12C22×D311yescharacteristic
227C2×D12C22×D312yes—
228C2×C4×D3—21no—
229C2×C4×D3—62no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—61no—
235C2×Dic6—62no—
236C3×SD16—62no—
237C3×SD16—122no—
238C2×C3×C8—31no—
239C2×C3×C8—32no—
240C2×C3×C8—31no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C22⋊C4—61no—
249C3×C42—22no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#217—62no—
256#215—22no—
257#215—42no—
258#214—64no—
259#214—122no—
260#214—122no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—32no—
274Dic3⋊C4—32no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285C4×Dic3—32no—
286C4×Dic3—32no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3—64no—
291C2×C3⋊C8C22×D311yescharacteristic
292C2×C3⋊C8C22×D312yes—
293C2×C3⋊C8C22×D311yescharacteristic
294#204—64no—
295#204—122no—
296#204—122no—
297C22×C32C22×D411yescharacteristic
298C2×C3×D3—41no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C2×C3×D3—42no—
304C32×C4—21no—
305C32×C4—41no—
306C32×C4—41no—
307C32×C4C2×SD1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4H(5,𝔽2)11yescharacteristic
310C3⋊Dic3—22no—
311C3⋊Dic3—42no—
312C3⋊Dic3C2×SD1614yes—
313C3×Dic3—41no—
314C2×#41—181no—
315C2×SD16—31no—
316C2×SD16—32no—
317C2×SD16—92no—
318C2×SD16—92no—
319C2×SD16—92no—
320C4⋊Q8—92no—
321C4⋊Q8—91no—
322#127—31no—
323#127—92no—
324#125—181no—
325#125—182no—
326#121—182no—
327#121—181no—
328C4×Q8—91no—
329C4×Q8—92no—
330C4×Q8—181no—
331C4×Q8D3211yescharacteristic
332C4×D4—31no—
333C4×D4—92no—
334#106—31no—
335C4⋊C8—31no—
336C4⋊C8—92no—
337#103—31no—
338#103—92no—
339#102—31no—
340#102—32no—
341C4×C8—31no—
342C4×C8—92no—
343C23×C3—62no—
344C23×C3—61no—
345C22×D3—21no—
346C22×D3—22no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—21no—
351C3×Q8—41no—
352C3×Q8—41no—
353C3×D4—62no—
354C3×D4—61no—
355C3×D4—61no—
356C3×D4—62no—
357C3×D4—122no—
358C3×D4—241no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—61no—
369C2×C3×C4—122no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—124no—
377#67—124no—
378#67—242no—
379#67—242no—
380C2×Dic3—21no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—124no—
391D12—21no—
392D12—22no—
393D12—22no—
394D12—21no—
395D12—42no—
396D12—81no—
397C4×D3—42no—
398C4×D3—124no—
399Dic6—34no—
400Dic6—34no—
401Dic6—64no—
402Dic6—62no—
403Dic6—62no—
404Dic6—62no—
405Dic6—62no—
406Dic6—122no—
407Dic6—122no—
408C3×C8—32no—
409C3×C8—61no—
410C3×C8—62no—
411C3⋊C8—22no—
412C3⋊C8—21no—
413C3⋊C8#23512yescomplemented
414C2×C32#55011yescharacteristic
415C2×C32C22×SD1611yescharacteristic
416C2×C32#57711yescharacteristic
417C3×D3—81no—
418C3×D3—82no—
419#41—364no—
420C2×Q8—91no—
421C2×Q8—92no—
422C2×Q8C2×D3211yescharacteristic
423C2×D4—31no—
424C2×D4—32no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—182no—
428C2×D4—182no—
429C22×C4—61no—
430C22×C4—182no—
431SD16—62no—
432SD16—122no—
433SD16—184no—
434SD16—362no—
435SD16—362no—
436C2×C8—31no—
437C2×C8—31no—
438C2×C8—32no—
439C4⋊C4—21no—
440C4⋊C4—31no—
441C4⋊C4—92no—
442C4⋊C4—91no—
443C4⋊C4—182no—
444C4⋊C4—182no—
445C4⋊C4—182no—
446C4⋊C4—181no—
447C4⋊C4—181no—
448C4⋊C4C2×D3211yescharacteristic
449C22⋊C4—61no—
450C22⋊C4—182no—
451C42—21no—
452C42—92no—
453C42—182no—
454C42C2×D3211yescharacteristic
455C22×C3—21no—
456C22×C3—122no—
457C22×C3—121no—
458C22×C3—122no—
459C22×C3—121no—
460C22×C3—122no—
461C22×C3—121no—
462C22×C3C2×D3×D411yescharacteristic
463C22×C3C2×D3×D411yescharacteristic
464C2×D3—41no—
465C2×D3—42no—
466C2×D3—41no—
467C2×D3—42no—
468C2×D3—41no—
469C2×D3—42no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—42no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—121no—
483C3×C4D3×SD1612yes—
484C3×C4D3×SD1612yes—
485C3×C4C2×#23511yescharacteristic
486C3×C4#100411yescharacteristic
487C3×C4D3×#4111yescharacteristic
488C3×C4#100911yescharacteristic
489Dic3—34no—
490Dic3—34no—
491Dic3—41no—
492Dic3—64no—
493Dic3—62no—
494Dic3—62no—
495Dic3—122no—
496Dic3—124no—
497Dic3—122no—
498Dic3—122no—
499C32#339211yescharacteristic, complemented, Sylow
500C23—61no—
501C23—62no—
502Q8—21no—
503Q8—21no—
504Q8—94no—
505Q8—182no—
506Q8—182no—
507D4—61no—
508D4—62no—
509D4—62no—
510D4—61no—
511D4—122no—
512D4—241no—
513D4—364no—
514D4—722no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—61no—
518C2×C4—92no—
519C2×C4—92no—
520C2×C4—122no—
521C2×C4—182no—
522C2×C4—364no—
523C2×C4#381111yescharacteristic
524C2×C4#381111yescharacteristic
525C2×C4C22×D3211yescharacteristic
526C8—32no—
527C8—62no—
528C8—61no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—242no—
533C2×C3—241no—
534C2×C3#555311yescharacteristic
535C2×C3#559911yescharacteristic
536C2×C3C2×D3×SD1611yescharacteristic
537C2×C3C2×D3×SD1611yescharacteristic
538C2×C3#577011yescharacteristic
539C2×C3#577511yescharacteristic
540D3—81no—
541D3—82no—
542C22—121no—
543C22—122no—
544C22—122no—
545C22—121no—
546C22—121no—
547C22—122no—
548C22C2×#381111yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—94no—
553C4—121no—
554C4—182no—
555C4—362no—
556C4#6394012yes—
557C4D3×#23511yescharacteristic
558C4#6430711yescharacteristic
559C3—21no—
560C3#7963711yescharacteristic, complemented
561C3#8037811yescharacteristic, complemented
562C2—242no—
563C2—241no—
564C2#1059491911yescharacteristic
565C2C2×#6394011yescharacteristic
566C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4×Q8D32
hypocenterC32#3392
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. #10596038C2semidirect
3. C3×#5027C2semidirect
4. C3×C4×#215C2semidirect
5. #10591620C2semidirect
6. #10591569C2semidirect
7. #10590553C2semidirect
8. #10590460C2semidirect
9. #10590369C2semidirect
10. #10590365C2semidirect
11. #10590254C2semidirect
54. #5027D3semidirect
55. C4×#215D3semidirect
183. #634SD16semidirect
197. C3×C3⋊C8#41semidirect
413. C3⋊C8#235semidirect
499. C32#3392semidirect
560. C3#79637semidirect
561. C3#80378semidirect

Maximal subgroups

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

subgroupindex
#105960382
#105939062
C3×#50272
C3×C4×#2152
#105916202
#105915692
#105905532
#105904602
#105903692
#105903652
#105902542
#803783
#796373