Finite Group Databasebeta

← #11896083

Subgroups — #11896083

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593879C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592548C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590895C212yesmaximal
7#10590861C212yesmaximal
8#10590810C212yesmaximal, complemented
9#10590802C212yesmaximal, complemented
10C4×#3716C211yesmaximal, characteristic
11#10590288C211yesmaximal, characteristic, complemented
12#81091—31nomaximal
13#79981—31nomaximal
14C2×#3746C2212yes—
15#64078C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63919—21no—
21#63918C2212yes—
22#63861—22no—
23#63860C2212yes—
24#63856—21no—
25#63844C2212yes—
26#63844C2212yes—
27#63843—21no—
28#63841—21no—
29#63839—22no—
30C2×#3716C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#817C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63567C2211yescharacteristic
42#63563C2211yescharacteristic
43#5722—31no—
44#5584—31no—
45Q8×Dic6—31no—
46#5542—31no—
47C3×#476—31no—
48C3×#446—31no—
49#5093—31no—
50C4×#214—31no—
51#4854—32no—
52#4853—32no—
53#4851—32no—
54#4849—31no—
55#4849—31no—
56#4849—61no—
57#4845—32no—
58#4842D311yescharacteristic
59#4831D311yescharacteristic, complemented
60#4767—32no—
61#4765—32no—
62#4716—32no—
63#4714—32no—
64C4×#204—31no—
65#4681—31no—
66C2×#634C2312yes—
67C2×#634C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×#627—22no—
73C2×C32×C8C2312yes—
74C32×C42C2311yescharacteristic
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79C4×C3⋊Dic3—21no—
80#3746—24no—
81C3×(C2×D3)⋊C4—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96Dic32—22no—
97#3716—22no—
98#3369—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×D4—31no—
102#946—61no—
103Q8×Dic3—61no—
104#944—62no—
105#936—32no—
106C2×#214—31no—
107#926—61no—
108#924—61no—
109C2×Dic12—32no—
110C2×Dic12—32no—
111C2×Dic12—62no—
112C2×#204—31no—
113#898—62no—
114#892—61no—
115#888—32no—
116#888—61no—
117#888—62no—
118#888—61no—
119#887—32no—
120#887—32no—
121#887—61no—
122#879—62no—
123#875—32no—
124C4×D12C2×D311yescharacteristic
125#869—32no—
126#869—31no—
127#869—31no—
128#869—61no—
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—32no—
133C4×Dic6—32no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D311yescharacteristic
141C3×#102—32no—
142C3×#97—32no—
143C3×C4×C8—31no—
144#832—31no—
145#821—31no—
146#821C2×D312yes—
147#817—31no—
148#817C2×D312yes—
149#816—32no—
150#816—32no—
151#816—32no—
152#816—32no—
153#816—31no—
154#816—62no—
155#815C2×D312yes—
156Dic3⋊C8C2×D312yes—
157#810—31no—
158#810—32no—
159#810—32no—
160#808—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—21no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169#634—21no—
170#634—22no—
171#634—22no—
172#634#4112yes—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—81no—
182#627—82no—
183C32×C8—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—91no—
187#556—91no—
188#489—92no—
189#487—91no—
190#476—31no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—31no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×D4—31no—
200C22×C3×C4—61no—
201C2×D12C22×D311yescharacteristic
202C2×C4×D3—21no—
203C2×Dic6—21no—
204C2×Dic6—31no—
205C2×Dic6—31no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6D1211yescharacteristic
213C2×C3×C8—22no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C2×C3×C8C22×D312yes—
217C2×C3×C8C22×D312yes—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C42—21no—
225C3×C42—32no—
226C3×C42C22×D311yescharacteristic
227C3×C42C22×D311yescharacteristic
228#217—62no—
229#217—62no—
230#214—62no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234C4⋊Dic3—21no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—61no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4⋊Dic3—121no—
245C4⋊Dic3D1211yescharacteristic
246C4⋊Dic3C22×D312yes—
247C4⋊Dic3C22×D311yescharacteristic
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—121no—
256Dic3⋊C4D1212yes—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—121no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12—64no—
268Dic12—64no—
269Dic12—124no—
270#204—62no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—21no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—22no—
280C3⋊Dic3—42no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C2×Q16—92no—
287C2×SD16—91no—
288C4⋊Q8—31no—
289C4⋊Q8—92no—
290C4⋊Q8—91no—
291C4⋊Q8—181no—
292C4⋊Q8—182no—
293#126—182no—
294#124—92no—
295C22⋊Q8—181no—
296C4×Q8—31no—
297C4×Q8—92no—
298C4×Q8—92no—
299C4×Q8—91no—
300C4×Q8—181no—
301C4×D4—31no—
302#117—181no—
303#106—32no—
304#106—91no—
305C4⋊C8—32no—
306C4⋊C8D3211yescharacteristic
307#103—91no—
308#103—92no—
309#103—92no—
310#103—92no—
311#102—32no—
312#102—91no—
313#97—32no—
314C4×C8—31no—
315C23×C3—61no—
316C22×D3—21no—
317C3×Q8—62no—
318C3×Q8—241no—
319C3×D4—61no—
320C3×D4—61no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—122no—
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—21no—
336C2×Dic3—22no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—62no—
341C2×Dic3—61no—
342C2×Dic3—62no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—122no—
346C2×Dic3C2×D1212yes—
347C2×Dic3C2×D1212yes—
348D12—21no—
349D12—21no—
350C4×D3—42no—
351Dic6—22no—
352Dic6—32no—
353Dic6—32no—
354Dic6—62no—
355Dic6—61no—
356Dic6—61no—
357Dic6—62no—
358Dic6—62no—
359Dic6—62no—
360Dic6—62no—
361Dic6—81no—
362Dic6—121no—
363Dic6—122no—
364Dic6—122no—
365Dic6—242no—
366Dic6—242no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3×C8—61no—
371C3×C8—61no—
372C3⋊C8—21no—
373C3⋊C8—21no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C3×D3—81no—
378C2×Q8—31no—
379C2×Q8—61no—
380C2×Q8—91no—
381C2×Q8—92no—
382C2×Q8—182no—
383C2×D4—31no—
384C22×C4—61no—
385Q16—184no—
386SD16—182no—
387C2×C8—31no—
388C2×C8—31no—
389C2×C8C2×D3212yes—
390C4⋊C4—31no—
391C4⋊C4—32no—
392C4⋊C4—32no—
393C4⋊C4—31no—
394C4⋊C4—61no—
395C4⋊C4—91no—
396C4⋊C4—182no—
397C4⋊C4—182no—
398C4⋊C4—182no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4—181no—
402C22⋊C4—61no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C42—32no—
406C42—182no—
407C42—182no—
408C42—181no—
409C42C2×D3211yescharacteristic
410C22×C3—21no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3C22×D1211yescharacteristic
415C22×C3C2×D3×D411yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—41no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—121no—
428C3×C4—122no—
429C3×C4#90912yes—
430C3×C4#91512yes—
431C3×C4#100711yescharacteristic
432C3×C4#100711yescharacteristic
433C3×C4D3×#4111yescharacteristic
434C3×C4D3×#4111yescharacteristic
435Dic3—22no—
436Dic3—22no—
437Dic3—41no—
438Dic3—42no—
439Dic3—62no—
440Dic3—62no—
441Dic3—122no—
442Dic3—122no—
443Dic3—121no—
444Dic3—121no—
445Dic3—122no—
446Dic3—242no—
447Dic3—241no—
448C32#336911yescharacteristic, complemented, Sylow
449C23—61no—
450Q8—62no—
451Q8—92no—
452Q8—181no—
453Q8—182no—
454Q8—182no—
455Q8—241no—
456Q8—722no—
457D4—61no—
458D4—61no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—122no—
464C2×C4—181no—
465C2×C4—182no—
466C2×C4—181no—
467C2×C4D3×D1211yescharacteristic
468C2×C4D3×D1211yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—22no—
471C8—61no—
472C8—61no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—241no—
477C2×C3#557611yescharacteristic
478C2×C3#563311yescharacteristic
479C2×C3C2×#90911yescharacteristic
480C2×C3#575111yescharacteristic
481C2×C3C2×#91511yescharacteristic
482C2×C3#577511yescharacteristic
483D3—81no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22C2×D3×D1211yescharacteristic
488C4—21no—
489C4—62no—
490C4—62no—
491C4—121no—
492C4—122no—
493C4—182no—
494C4—362no—
495C4—361no—
496C4#6380012yes—
497C4#6431211yescharacteristic
498C4#6431611yescharacteristic
499C3—21no—
500C3#7998111yescharacteristic, complemented
501C3#8109111yescharacteristic, complemented
502C2—241no—
503C2#1059432911yescharacteristic
504C2C2×#6380011yescharacteristic
505C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3369
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. #10593856C2semidirect
3. #10592548C2semidirect
5. C3×#4831C2semidirect
8. #10590810C2semidirect
9. #10590802C2semidirect
11. #10590288C2semidirect
59. #4831D3semidirect
448. C32#3369semidirect
500. C3#79981semidirect
501. C3#81091semidirect

Maximal subgroups

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

subgroupindex
#105938792
#105938562
#105925482
C3×#48422
C3×#48312
#105908952
#105908612
#105908102
#105908022
C4×#37162
#105902882
#810913
#799813