Finite Group Databasebeta

← #11895676

Subgroups — #11895676

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic
5#10590539C212yesmaximal, complemented
6#10590538C212yesmaximal, complemented
7#10590474C212yesmaximal, complemented
8#10590460C212yesmaximal, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10#10590377C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#81589—31nomaximal
13#81041—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15Q8×C3⋊Dic3—21no—
16#64153—21no—
17#64099C2212yes—
18#64098—22no—
19#64096C2212yes—
20C4×#634C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#874C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63898C2212yes—
25Dic3×D12—21no—
26#63884—22no—
27#63863C2212yes—
28#63860—21no—
29C2×#3719C2211yescharacteristic
30C2×#3716C2212yes—
31C3×#810C2212yes—
32C3×#809C2212yes—
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38#63572C2212yes—
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63563C2212yes—
42#63553C2212yes—
43#5721—31no—
44#5721—31no—
45#5721—61no—
46#5713—31no—
47#5585—31no—
48C3×#486—31no—
49C3×#475—31no—
50#5094D311yescharacteristic, complemented
51#5088D311yescharacteristic
52#5075—31no—
53C4×#216—31no—
54#4871—32no—
55#4852—32no—
56#4848—31no—
57#4830—31no—
58#4800—32no—
59#4798—32no—
60#4768—32no—
61#4767—32no—
62#4766—32no—
63#4758—32no—
64C4×Dic12—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×#634D411yescharacteristic
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81#3750—22no—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3—21no—
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96#3719—22no—
97#3716—24no—
98#3365—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×#127—31no—
103C3×C4×Q8—31no—
104#947—32no—
105Q8×Dic3—61no—
106Q8×Dic3—61no—
107Q8×Dic3—62no—
108#944—61no—
109#944—61no—
110#944—62no—
111C2×#216—31no—
112#936—32no—
113#936—61no—
114#935—62no—
115D4×Dic3—32no—
116D4×Dic3—61no—
117C2×#214—32no—
118C2×Dic12—31no—
119C2×#204—32no—
120#894—62no—
121#893—32no—
122#890—32no—
123#890—32no—
124#890—62no—
125#889—62no—
126#889—62no—
127#889—64no—
128#887—32no—
129#887—32no—
130#887—62no—
131#875—61no—
132#874C2×D311yescharacteristic
133C4×D12—61no—
134C4×Dic6—31no—
135C4×Dic6—31no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#106—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—31no—
148#832—32no—
149#821—32no—
150#818—31no—
151#816—31no—
152#816—31no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156C8×Dic3—32no—
157#810—31no—
158#810C2×D312yes—
159#809C2×D312yes—
160#809C2×D312yes—
161#808C2×D312yes—
162#807—31no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3—22no—
166C32×Q8—42no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175#634—21no—
176#634—22no—
177#634#4112yes—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186D3×Dic3—82no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—91no—
191#557—91no—
192#488—92no—
193#486—31no—
194#478—92no—
195#475—31no—
196#464—92no—
197#460—91no—
198C8×Q8—91no—
199C4×Q16—91no—
200C4×SD16—92no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×Dic3—62no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×C4×D3—62no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—31no—
221C2×C3×C8—32no—
222C2×C3×C8—31no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C42—21no—
232C3×C42—61no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—62no—
236#217—62no—
237#217—62no—
238#216—62no—
239#214—64no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—64no—
252C4⋊Dic3C22×D311yescharacteristic
253Dic3⋊C4—21no—
254Dic3⋊C4—32no—
255Dic3⋊C4—32no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266C4×Dic3—21no—
267C4×Dic3—32no—
268C4×Dic3—32no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—64no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279Dic12—62no—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—42no—
287C32×C4#13512yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—22no—
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C2×Q16—91no—
297C2×SD16—92no—
298C4⋊Q8—181no—
299C4⋊Q8D3211yescharacteristic
300#127—31no—
301#125—92no—
302#125—182no—
303#124—92no—
304#124—181no—
305#123—182no—
306C4×Q8—31no—
307C4×Q8—91no—
308C4×Q8—92no—
309C4×Q8—91no—
310C4×Q8—181no—
311C4×D4—92no—
312C4×D4—181no—
313#107—91no—
314#106—32no—
315C4⋊C8—31no—
316C4⋊C8—92no—
317#103—32no—
318#103—91no—
319#103—91no—
320#102—32no—
321#102—32no—
322#102—92no—
323C4×C8—31no—
324C4×C8—92no—
325C23×C3—62no—
326C22×D3—22no—
327C3×Q8—44no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×Q8—61no—
331C3×Q8—61no—
332C3×D4—62no—
333C3×D4—62no—
334C3×D4—122no—
335C3×D4—241no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—62no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—242no—
365D12—22no—
366D12—22no—
367D12—42no—
368D12—81no—
369C4×D3—242no—
370Dic6—21no—
371Dic6—21no—
372Dic6—32no—
373Dic6—32no—
374Dic6—62no—
375Dic6—62no—
376Dic6—62no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—122no—
381C3×C8—61no—
382C3×C8—62no—
383C3×C8—61no—
384C3⋊C8—22no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C2×Q8—21no—
392C2×Q8—31no—
393C2×Q8—91no—
394C2×Q8—91no—
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C22×C4—182no—
399Q16—182no—
400SD16—184no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—32no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—61no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—91no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—181no—
414C4⋊C4C2×D3212yes—
415C22⋊C4—182no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C42—61no—
419C42—92no—
420C42—182no—
421C42—181no—
422C42C2×D3211yescharacteristic
423C22×C3—21no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—41no—
438C3×C4—44no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—121no—
442C3×C4—121no—
443C3×C4#91212yes—
444C3×C4#91612yes—
445C3×C4#100711yescharacteristic
446C3×C4D3×#4111yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449Dic3—41no—
450Dic3—41no—
451Dic3—64no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—122no—
459Dic3—122no—
460Dic3—122no—
461Dic3—121no—
462Dic3—121no—
463C32#336511yescharacteristic, complemented, Sylow
464C23—62no—
465Q8—42no—
466Q8—61no—
467Q8—61no—
468Q8—92no—
469Q8—181no—
470Q8—182no—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—22no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—722no—
483C2×C4#381111yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—61no—
487C8—62no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—242no—
493C2×C3#563311yescharacteristic
494C2×C3#567711yescharacteristic
495C2×C3C2×#91211yescharacteristic
496C2×C3C2×#91611yescharacteristic
497C2×C3#576211yescharacteristic
498C2×C3#577811yescharacteristic
499D3—82no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22C2×#381111yescharacteristic
504C4—21no—
505C4—42no—
506C4—121no—
507C4—121no—
508C4—182no—
509C4—182no—
510C4—182no—
511C4—361no—
512C4#6393612yes—
513C4#6431511yescharacteristic
514C4#6431911yescharacteristic
515C3—21no—
516C3#8104111yescharacteristic, complemented
517C3#8158911yescharacteristic, complemented
518C2—242no—
519C2C2×#6393611yescharacteristic
520C2#1059532411yescharacteristic
521C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#3365
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. #10596192C2semidirect
3. C3×#5094C2semidirect
5. #10590539C2semidirect
6. #10590538C2semidirect
7. #10590474C2semidirect
8. #10590460C2semidirect
9. C4×#3719C2semidirect
11. #10590254C2semidirect
50. #5094D3semidirect
463. C32#3365semidirect
516. C3#81041semidirect
517. C3#81589semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105939512
C3×#50942
C3×#50882
#105905392
#105905382
#105904742
#105904602
C4×#37192
#105903772
#105902542
#815893
#810413