Finite Group Databasebeta

← #11895679

Subgroups — #11895679

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593963C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590872C212yesmaximal, complemented
7#10590813C212yesmaximal, complemented
8#10590769C212yesmaximal, complemented
9#10590758C212yesmaximal, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic
12#81041—31nomaximal
13#79935—31nomaximal
14C2×#3744C2212yes—
15#64083C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63897—22no—
21#63894—21no—
22#63894C2212yes—
23#63873—21no—
24#63869C2212yes—
25#63864—21no—
26#63864C2212yes—
27#63847—22no—
28#63844C2212yes—
29#63843—21no—
30C2×#3719C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33C3×#817C2212yes—
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63564C2212yes—
42#63564C2212yes—
43#5721—31no—
44#5585—31no—
45#5585—31no—
46#5567—31no—
47C3×#475—31no—
48C3×C8×Q8—31no—
49#5088—31no—
50C4×#216—31no—
51#4871—32no—
52#4852—32no—
53#4851D311yescharacteristic, complemented
54#4848—31no—
55#4848—31no—
56#4848—61no—
57#4847—32no—
58#4845—32no—
59#4830D311yescharacteristic, complemented
60#4800—32no—
61#4798—32no—
62C4×Dic12—31no—
63#4697—32no—
64#4694—31no—
65C4×#204—32no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×Dic6—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×#624—22no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78C4×C3⋊Dic3—21no—
79#3744—24no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic3C2312yes—
83C3×C4⋊Dic3C2311yescharacteristic
84C3×Dic3⋊C4—21no—
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3—21no—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95#3722—22no—
96Dic32—22no—
97#3719—22no—
98#3365—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4×Q8—31no—
101C3×C4×Q8—31no—
102#947—32no—
103#947—61no—
104Q8×Dic3—61no—
105#944—61no—
106#944—61no—
107C2×#216—31no—
108C2×Dic12—31no—
109C2×#204—32no—
110C2×#204—32no—
111C2×#204—62no—
112#894—62no—
113#894—62no—
114#893—32no—
115#893—61no—
116#890—32no—
117#889—62no—
118#889—62no—
119#887—32no—
120#887—61no—
121#875—32no—
122#875—61no—
123#874—31no—
124#874—31no—
125#874—61no—
126C4×D12—32no—
127C4×D12—61no—
128#870—32no—
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—32no—
137C3×C4⋊C8—21no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8C2×D311yescharacteristic
140C3×C4⋊C8C2×D311yescharacteristic
141C3×#103—32no—
142C3×C4×C8—32no—
143C3×C4×C8—31no—
144#835—31no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—62no—
150#818—31no—
151#817C2×D312yes—
152#816—31no—
153#816—31no—
154#816C2×D312yes—
155Dic3⋊C8C2×D312yes—
156C8×Dic3C2×D312yes—
157#810—31no—
158#809—32no—
159#809—32no—
160#807—31no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—22no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—22no—
170C4⋊(C3⋊D3)—42no—
171C4⋊(C3⋊D3)—81no—
172#634—21no—
173#634#4112yes—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—22no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—42no—
183#624—82no—
184C32×C8—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—91no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—31no—
193#464—92no—
194#460—91no—
195C8×Q8—31no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—121no—
209C2×D12—121no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×Dic6—21no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6D1211yescharacteristic
217C2×Dic6C22×D311yescharacteristic
218C2×C3×C8—22no—
219C2×C3×C8—31no—
220C2×C3×C8—31no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C22×D312yes—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C42—21no—
230C3×C42—32no—
231C3×C42—61no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#216—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—62no—
246C4⋊Dic3D1211yescharacteristic
247C4⋊Dic3C22×D311yescharacteristic
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—21no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—61no—
254Dic3⋊C4—61no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—121no—
258Dic3⋊C4D1212yes—
259C4×Dic3—21no—
260C4×Dic3—62no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—62no—
264C4×Dic3—121no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268Dic12—62no—
269#204—64no—
270#204—64no—
271#204—124no—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C32×C4—21no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C2×Q16—91no—
288C2×SD16—92no—
289C4⋊Q8—31no—
290C4⋊Q8—181no—
291#127—91no—
292#125—92no—
293#125—182no—
294#124—92no—
295#124—181no—
296#123—182no—
297C4×Q8—31no—
298C4×Q8—31no—
299C4×Q8—92no—
300C4×Q8—91no—
301C4×Q8—181no—
302C4×D4—92no—
303C4×D4—181no—
304#107—91no—
305#106—32no—
306C4⋊C8—32no—
307C4⋊C8D3211yescharacteristic
308#103—32no—
309#103—91no—
310#103—91no—
311#102—92no—
312#102—92no—
313#102—92no—
314C4×C8—32no—
315C4×C8—31no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C3×Q8—62no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×Q8—122no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—62no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3C2×D1212yes—
347C2×Dic3C2×D1212yes—
348D12—62no—
349D12—62no—
350D12—62no—
351D12—62no—
352D12—122no—
353D12—122no—
354D12—122no—
355D12—122no—
356D12—242no—
357D12—241no—
358D12—241no—
359D12—242no—
360C4×D3—242no—
361C4×D3—242no—
362Dic6—22no—
363Dic6—21no—
364Dic6—21no—
365Dic6—32no—
366Dic6—32no—
367Dic6—42no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371Dic6—121no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3×C8—61no—
376C3×C8—61no—
377C3⋊C8—21no—
378C3⋊C8—21no—
379C2×C32#54811yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C2×C32#57711yescharacteristic
382C3⋊D3—82no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×Q8—61no—
386C2×Q8—91no—
387C2×D4—92no—
388C2×D4—181no—
389C2×D4—181no—
390C22×C4—182no—
391Q16—182no—
392SD16—184no—
393C2×C8—31no—
394C2×C8—31no—
395C2×C8C2×D3212yes—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—91no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—181no—
407C22⋊C4—182no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C42—32no—
411C42—61no—
412C42—182no—
413C42—181no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3C22×D1211yescharacteristic
417C22×C3C2×D3×D411yescharacteristic
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—122no—
436C3×C4—121no—
437C3×C4—121no—
438C3×C4#90412yes—
439C3×C4#91612yes—
440C3×C4#100711yescharacteristic
441C3×C4#100711yescharacteristic
442C3×C4D3×#4111yescharacteristic
443C3×C4D3×#4111yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—41no—
447Dic3—42no—
448Dic3—41no—
449Dic3—62no—
450Dic3—62no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—241no—
455C32#336511yescharacteristic, complemented, Sylow
456C23—182no—
457Q8—62no—
458Q8—61no—
459Q8—61no—
460Q8—92no—
461Q8—122no—
462Q8—181no—
463D4—182no—
464D4—182no—
465D4—362no—
466D4—721no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—722no—
475C2×C4D3×D1211yescharacteristic
476C2×C4D3×D1211yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—22no—
479C8—61no—
480C8—61no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3#557611yescharacteristic
485C2×C3#563311yescharacteristic
486C2×C3C2×#90411yescharacteristic
487C2×C3#575111yescharacteristic
488C2×C3C2×#91611yescharacteristic
489C2×C3#577811yescharacteristic
490D3—242no—
491D3—242no—
492D3—482no—
493C22—362no—
494C22—362no—
495C22—362no—
496C22C2×D3×D1211yescharacteristic
497C4—21no—
498C4—62no—
499C4—62no—
500C4—121no—
501C4—122no—
502C4—121no—
503C4—182no—
504C4—361no—
505C4#6380612yes—
506C4#6431211yescharacteristic
507C4#6431611yescharacteristic
508C3—21no—
509C3#7993511yescharacteristic, complemented
510C3#8104111yescharacteristic, complemented
511C2—722no—
512C2#1059432911yescharacteristic
513C2C2×#6380611yescharacteristic
514C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#3365
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
4. C3×#4851C2semidirect
5. C3×#4830C2semidirect
6. #10590872C2semidirect
7. #10590813C2semidirect
8. #10590769C2semidirect
9. #10590758C2semidirect
10. C4×#3719C2semidirect
53. #4851D3semidirect
59. #4830D3semidirect
455. C32#3365semidirect
509. C3#79935semidirect
510. C3#81041semidirect

Maximal subgroups

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

subgroupindex
#105939632
#105938642
#105925472
C3×#48512
C3×#48302
#105908722
#105908132
#105907692
#105907582
C4×#37192
#105902812
#810413
#799353