Finite Group Databasebeta

← #11895983

Subgroups — #11895983

Order 1152.

818 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590882C212yesmaximal, complemented
7#10590799C212yesmaximal, complemented
8#10590767C212yesmaximal, complemented
9#10590766C212yesmaximal, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#80371—31nomaximal
13#79980—31nomaximal
14C2×#3796—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×#874C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63916—21no—
22#63911C2212yes—
23Dic3×D12C2212yes—
24#63886—22no—
25#63869C2212yes—
26#63866—21no—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3717C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33#63645C2212yes—
34C3×#821C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63563C2212yes—
42#63563C2212yes—
43#5718—31no—
44#5577—31no—
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48C3×#446—31no—
49#5164—32no—
50#5163—32no—
51#5070—31no—
52C4×#215—31no—
53#4848—32no—
54#4848D311yescharacteristic, complemented
55#4847—32no—
56#4846—31no—
57#4846—31no—
58#4846—61no—
59#4831D311yescharacteristic, complemented
60#4766—32no—
61#4764—32no—
62#4713—32no—
63#4710—32no—
64#4694—31no—
65C4×#204—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80#3752—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3—21no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×#204—24no—
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3717—22no—
99#3368—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C2×C3×SD16—32no—
103C3×#127—31no—
104C3×C4×Q8—31no—
105C3×C4×Q8—31no—
106Q8×Dic3—32no—
107#944—61no—
108C2×#215—31no—
109#940—32no—
110#939—62no—
111#938—61no—
112D4×Dic3—32no—
113C2×#204—31no—
114C2×#204C2×D312yes—
115#895—62no—
116#895—61no—
117#890—32no—
118#890—62no—
119#889—62no—
120#887—61no—
121#874—32no—
122#874C2×D311yescharacteristic
123C4×D12—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—61no—
127#870—32no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—21no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8C2×D311yescharacteristic
139C3×C4⋊C8C2×D311yescharacteristic
140C3×#102—32no—
141C3×#97—32no—
142C3×C4×C8—31no—
143#835—31no—
144#832—32no—
145#832—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—31no—
151#821—62no—
152#821C2×D312yes—
153#818—32no—
154#818—32no—
155#818—62no—
156#817—31no—
157#816—31no—
158#815C2×D312yes—
159Dic3⋊C8C2×D312yes—
160#809—31no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)—21no—
172C4×C3⋊D3—42no—
173#634—42no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—22no—
179C3×D12—22no—
180C3×D12—42no—
181C3×D12—81no—
182C3×Dic6—22no—
183C3×Dic6—21no—
184C3×Dic6#4112yescomplemented
185#626—44no—
186#626—82no—
187D3×Dic3—44no—
188C32×C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192#550—91no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—91no—
197#460—31no—
198#460—92no—
199#446—31no—
200#440—92no—
201C4×SD16—91no—
202C2×C3×Q8—31no—
203C2×C3×Q8—31no—
204C2×C3×D4—32no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×#67—62no—
208C2×#67—62no—
209C22×Dic3—62no—
210#239—124no—
211#237—124no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12C22×D312yes—
220C2×C4×D3—62no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—121no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6D1211yescharacteristic
228C2×Dic6C22×D311yescharacteristic
229C3×SD16—64no—
230C2×C3×C8—22no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8C22×D312yes—
234C2×C3×C8C22×D312yes—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—61no—
239C3×C42—21no—
240C3×C42—32no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#215—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—121no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—61no—
255C4⋊Dic3—62no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—121no—
261C4⋊Dic3D1211yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—21no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4D1212yes—
269C4×Dic3—21no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8C22×D311yescharacteristic
274C2×C3⋊C8C22×D311yescharacteristic
275#204—24no—
276#204—62no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C32×C4—21no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C2×#41—181no—
295C2×SD16—32no—
296C2×SD16—91no—
297C4⋊Q8—91no—
298C4⋊Q8—181no—
299#127—31no—
300#127—92no—
301#125—92no—
302#125—182no—
303#121—181no—
304#121—182no—
305C4×Q8—31no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—181no—
309C4×D4—92no—
310C4×D4—91no—
311#107—92no—
312#106—91no—
313C4⋊C8—32no—
314C4⋊C8D3211yescharacteristic
315#103—91no—
316#102—32no—
317#102—91no—
318#102—92no—
319#102—92no—
320#102—92no—
321#97—32no—
322C4×C8—31no—
323C23×C3—62no—
324C22×D3—22no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—121no—
328C3×Q8—32no—
329C3×Q8—62no—
330C3×Q8—61no—
331C3×D4—62no—
332C3×D4—62no—
333C3×D4—122no—
334C3×D4—241no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—124no—
349#67—242no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—62no—
353C2×Dic3—61no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—122no—
357C2×Dic3—121no—
358C2×Dic3—124no—
359C2×Dic3C2×D1212yes—
360C2×Dic3C2×D1212yes—
361D12—22no—
362D12—22no—
363D12—42no—
364D12—62no—
365D12—61no—
366D12—61no—
367D12—61no—
368D12—61no—
369D12—81no—
370D12—121no—
371D12—124no—
372D12—242no—
373C4×D3—124no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3—242no—
377Dic6—22no—
378Dic6—21no—
379Dic6—122no—
380Dic6—122no—
381Dic6—242no—
382Dic6#23712yescomplemented
383C3×C8—22no—
384C3×C8—22no—
385C3×C8—42no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—21no—
390C2×C32#54811yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—81no—
394C3×D3—82no—
395#41—364no—
396C2×Q8—31no—
397C2×Q8—31no—
398C2×Q8—181no—
399C2×D4—32no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—182no—
405C22×C4—182no—
406C22×C4—181no—
407SD16—64no—
408SD16—182no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8C2×D3212yes—
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—31no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C22⋊C4—182no—
423C22⋊C4—181no—
424C42—32no—
425C42—61no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3C22×D1211yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—122no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—241no—
445C2×D3—241no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—121no—
456C3×C4#90812yes—
457C3×C4#91412yes—
458C3×C4C2×#23711yescharacteristic
459C3×C4#100711yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4#101011yescharacteristic
462Dic3—22no—
463Dic3—22no—
464Dic3—22no—
465Dic3—41no—
466Dic3—122no—
467Dic3—121no—
468Dic3—122no—
469Dic3—121no—
470Dic3—242no—
471Dic3—241no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—62no—
474C23—181no—
475Q8—32no—
476Q8—62no—
477Q8—61no—
478Q8—362no—
479D4—62no—
480D4—62no—
481D4—122no—
482D4—181no—
483D4—181no—
484D4—241no—
485D4—364no—
486D4—722no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—182no—
492C2×C4—181no—
493C2×C4—364no—
494C2×C4—362no—
495C2×C4D3×D1211yescharacteristic
496C2×C4D3×D1211yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—22no—
499C8—61no—
500C8—61no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—242no—
505C2×C3#557611yescharacteristic
506C2×C3#559811yescharacteristic
507C2×C3C2×#90811yescharacteristic
508C2×C3#575111yescharacteristic
509C2×C3C2×#91411yescharacteristic
510C2×C3#577511yescharacteristic
511D3—82no—
512D3—242no—
513D3—241no—
514D3—241no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22C2×D3×D1211yescharacteristic
522C4—21no—
523C4—62no—
524C4—62no—
525C4—62no—
526C4—121no—
527C4—361no—
528C4—362no—
529C4#6379412yes—
530C4D3×#23711yescharacteristic
531C4#6431511yescharacteristic
532C3—21no—
533C3#7998011yescharacteristic, complemented
534C3#8037111yescharacteristic, complemented
535C2—242no—
536C2—721no—
537C2#1059438211yescharacteristic
538C2C2×#6379411yescharacteristic
539C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4⋊C8D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
3. #10592545C2semidirect
4. C3×#4848C2semidirect
5. C3×#4831C2semidirect
6. #10590882C2semidirect
7. #10590799C2semidirect
8. #10590767C2semidirect
9. #10590766C2semidirect
10. C4×#3717C2semidirect
11. #10590273C2semidirect
54. #4848D3semidirect
59. #4831D3semidirect
184. C3×Dic6#41semidirect
382. Dic6#237semidirect
472. C32#3368semidirect
533. C3#79980semidirect
534. C3#80371semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105938602
#105925452
C3×#48482
C3×#48312
#105908822
#105907992
#105907672
#105907662
C4×#37172
#105902732
#803713
#799803