Finite Group Databasebeta

← #11895163

Subgroups — #11895163

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593904C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4841C211yesmaximal, characteristic
6#10590901C212yesmaximal, complemented
7#10590816C212yesmaximal, complemented
8#10590775C212yesmaximal
9#10590748C212yesmaximal
10C4×#3715C211yesmaximal, characteristic
11#10590290C211yesmaximal, characteristic, complemented
12#81037—31nomaximal
13#80414—31nomaximal
14C2×D3×Dic6—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2212yes—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63919C2212yes—
22#63899—22no—
23#63898C2212yes—
24#63873C2212yes—
25#63869—21no—
26#63856—21no—
27#63847—22no—
28#63844—21no—
29#63843C2212yes—
30C2×#3715C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#817C2212yes—
36C3×#816C2212yes—
37C3×#816C2212yes—
38#63574C2211yescharacteristic
39#63565C2212yes—
40#63565C2212yes—
41#63565C2211yescharacteristic
42#63562C2211yescharacteristic
43#5727—31no—
44#5721—31no—
45#5567—31no—
46D4×Dic6—31no—
47C3×#475—31no—
48C3×#461—31no—
49#5162—32no—
50Dic3×SD16—32no—
51#5093—31no—
52#5079—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4854—32no—
56#4852—32no—
57#4851D311yescharacteristic, complemented
58#4841D311yescharacteristic
59#4830—31no—
60#4830—31no—
61#4830—61no—
62#4818—32no—
63#4792—32no—
64#4792—32no—
65#4791—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C2×C32×C8C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)D411yescharacteristic
78#3750D412yes—
79C4×C3⋊Dic3C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C3×#204—24no—
92#3724—22no—
93#3724—22no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3715—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—31no—
105C3×C4×Q8—31no—
106C3×C4×D4—31no—
107#946—61no—
108Q8×Dic3—32no—
109#944—32no—
110#944—32no—
111C2×#215—31no—
112D4×Dic3—32no—
113C2×#214—31no—
114#924—61no—
115C2×#204C2×D312yes—
116#896—62no—
117#893—32no—
118#890—61no—
119#889—62no—
120#889—62no—
121#888—32no—
122#888—32no—
123#887—32no—
124#887—61no—
125#878—62no—
126C4×D12C2×D311yescharacteristic
127#870—61no—
128#869C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—61no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×#106—32no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#103—32no—
140C3×#103—32no—
141#835—32no—
142#835—32no—
143#835—31no—
144#832—31no—
145#817C2×D312yes—
146#816C2×D312yes—
147#816C2×D312yes—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—62no—
151C8×Dic3—32no—
152C8×Dic3—32no—
153C8×Dic3—62no—
154#810—31no—
155#810—32no—
156#810—32no—
157#809—31no—
158#808—31no—
159#808—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169#634SD1614yescomplemented
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12#4112yes—
177C3×C4×D3—42no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—22no—
182C3×Dic6—42no—
183#627—44no—
184D3×Dic3—44no—
185C32×C8—22no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188#557—91no—
189D4×Q8—91no—
190#487—92no—
191#487—91no—
192#475—31no—
193#475—92no—
194#461—31no—
195#461—92no—
196C8×Q8—91no—
197C4×SD16—92no—
198C4×SD16—91no—
199C2×C3×Q8—32no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C22×Dic3—62no—
205D3×Q8—124no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—62no—
209C2×Dic6—21no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—61no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—124no—
216C2×Dic6C22×D312yes—
217C2×Dic6C22×D311yescharacteristic
218C3×SD16—64no—
219C2×C3×C8—22no—
220C2×C3×C8C22×D312yes—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—61no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#215—62no—
236#214—62no—
237(C2×D3)⋊C4—21no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—62no—
246C4⋊Dic3C22×D311yescharacteristic
247C4⋊Dic3C22×D311yescharacteristic
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—21no—
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260C4×Dic3—21no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272#204—24no—
273C22×C32C22×D411yescharacteristic
274C2×C3×D3—22no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C32×C4—21no—
278C32×C4C2×SD1612yes—
279C32×C4C2×#4111yescharacteristic
280C32×C42−1+411yescharacteristic
281C3⋊Dic3—22no—
282C3⋊Dic3C2×SD1614yes—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C22×Q8—181no—
289C2×SD16—32no—
290C2×SD16—91no—
291C4⋊Q8—31no—
292C4⋊Q8—31no—
293C4⋊Q8—92no—
294C4⋊Q8—92no—
295#125—181no—
296#125—182no—
297C22⋊Q8—182no—
298C22⋊Q8—181no—
299C4×Q8—31no—
300C4×Q8—91no—
301C4×Q8—92no—
302C4×Q8—181no—
303C4×D4—31no—
304C4×D4—92no—
305#106—32no—
306#106—91no—
307C4⋊C8—92no—
308C4⋊C8D3211yescharacteristic
309#103—32no—
310#103—32no—
311#103—91no—
312#103—92no—
313#103—92no—
314#102—91no—
315C4×C8—92no—
316C4×C8—91no—
317C23×C3—61no—
318C22×D3—21no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—61no—
323C3×Q8—122no—
324C3×D4—32no—
325C3×D4—61no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—61no—
330C2×C3×C4—62no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—122no—
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—124no—
353D12—21no—
354D12#23712yes—
355C4×D3—42no—
356C4×D3—124no—
357Dic6—22no—
358Dic6—21no—
359Dic6—21no—
360Dic6—22no—
361Dic6—34no—
362Dic6—34no—
363Dic6—42no—
364Dic6—64no—
365Dic6—124no—
366Dic6—124no—
367C3×C8—22no—
368C3×C8—22no—
369C3×C8—42no—
370C3⋊C8—62no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
376C2×C32#54811yescharacteristic
377C2×C32C22×SD1611yescharacteristic
378C2×C32#57811yescharacteristic
379C3×D3—42no—
380C2×Q8—31no—
381C2×Q8—32no—
382C2×Q8—61no—
383C2×Q8—91no—
384C2×Q8—182no—
385C2×Q8—364no—
386C2×D4—31no—
387C22×C4—61no—
388C22×C4—182no—
389SD16—64no—
390SD16—182no—
391C2×C8—91no—
392C2×C8—91no—
393C2×C8C2×D3212yes—
394C4⋊C4—31no—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—61no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—92no—
402C4⋊C4—91no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C22⋊C4—61no—
408C22⋊C4—182no—
409C42—61no—
410C42—92no—
411C42—182no—
412C42C2×D3211yescharacteristic
413C22×C3—21no—
414C22×C3—62no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3C2×D3×D411yescharacteristic
418C22×C3C2×D3×D411yescharacteristic
419C2×D3—22no—
420C2×D3—41no—
421C2×D3—41no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—41no—
428C3×C4—122no—
429C3×C4—121no—
430C3×C4—122no—
431C3×C4—121no—
432C3×C4—121no—
433C3×C4D3×SD1612yes—
434C3×C4D3×SD1612yes—
435C3×C4C2×#23711yescharacteristic
436C3×C4#100711yescharacteristic
437C3×C4D3×#4111yescharacteristic
438C3×C4#101011yescharacteristic
439Dic3—34no—
440Dic3—34no—
441Dic3—41no—
442Dic3—42no—
443Dic3—41no—
444Dic3—41no—
445Dic3—42no—
446Dic3—64no—
447Dic3—62no—
448Dic3—62no—
449Dic3—122no—
450C32#335911yescharacteristic, complemented, Sylow
451C23—61no—
452Q8—62no—
453Q8—61no—
454Q8—61no—
455Q8—62no—
456Q8—94no—
457Q8—122no—
458Q8—364no—
459D4—32no—
460D4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—62no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—92no—
467C2×C4—92no—
468C2×C4—122no—
469C2×C4—364no—
470C2×C4#380211yescharacteristic
471C2×C4#380211yescharacteristic
472C2×C4C22×D3211yescharacteristic
473C8—22no—
474C8—181no—
475C8—181no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—122no—
480C2×C3#559811yescharacteristic
481C2×C3#563311yescharacteristic
482C2×C3C2×D3×SD1611yescharacteristic
483C2×C3C2×D3×SD1611yescharacteristic
484C2×C3#577911yescharacteristic
485C2×C3#577911yescharacteristic
486D3—42no—
487C22—62no—
488C22—121no—
489C22—121no—
490C22C2×#380211yescharacteristic
491C4—21no—
492C4—94no—
493C4—121no—
494C4—122no—
495C4—121no—
496C4—121no—
497C4—122no—
498C4—182no—
499C4#6379612yes—
500C4D3×#23711yescharacteristic
501C4#6431511yescharacteristic
502C3—21no—
503C3#8041411yescharacteristic, complemented
504C3#8103711yescharacteristic, complemented
505C2—122no—
506C2#1059452511yescharacteristic
507C2C2×#6379611yescharacteristic
508C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3359
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. #10593864C2semidirect
3. #10592529C2semidirect
4. C3×#4851C2semidirect
6. #10590901C2semidirect
7. #10590816C2semidirect
11. #10590290C2semidirect
57. #4851D3semidirect
169. #634SD16semidirect
450. C32#3359semidirect
503. C3#80414semidirect
504. C3#81037semidirect

Maximal subgroups

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

subgroupindex
#105939042
#105938642
#105925292
C3×#48512
C3×#48412
#105909012
#105908162
#105907752
#105907482
C4×#37152
#105902902
#810373
#804143