Finite Group Databasebeta

← #11896068

Subgroups — #11896068

Order 1152.

782 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590388C211yesmaximal, characteristic, complemented
5#10590383C212yesmaximal, complemented
6#10590378C212yesmaximal
7C4×#3716C211yesmaximal, characteristic
8#10590301C212yesmaximal, complemented
9#10590287C211yesmaximal, characteristic, complemented
10#10590276C212yesmaximal
11#10590268C211yesmaximal, characteristic
12#83677—31nomaximal
13#79981—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15Q8×C3⋊Dic3—21no—
16#64097—21no—
17#64097—22no—
18#64078C2211yescharacteristic
19#64078C2212yes—
20C4×#634C2211yescharacteristic
21C4×#634C2212yes—
22C3×#946—21no—
23C3×#898—22no—
24C3×#892—21no—
25C3×#875C2212yes—
26C3×C4×D12C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3719C2212yes—
30C2×#3716C2211yescharacteristic
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×#803C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63573C2212yes—
36#63573C2211yescharacteristic
37#63567C2211yescharacteristic
38#63566C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63563C2211yescharacteristic
43C3×#556—31no—
44#5584D311yescharacteristic
45Q8×Dic6—31no—
46Q8×Dic6—31no—
47Q8×Dic6—61no—
48C3×#446—31no—
49#5090—31no—
50#5079—31no—
51#5055—32no—
52#5054—32no—
53#5030—32no—
54#5024D311yescharacteristic, complemented
55#5020—32no—
56C4×#214—31no—
57#5008—31no—
58#4851—32no—
59#4849—31no—
60#4845—32no—
61#4842—31no—
62#4716—32no—
63#4714—32no—
64C4×#204—31no—
65#4681—31no—
66C2×C32×Q8D411yescharacteristic
67C2×#634—22no—
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2312yes—
73C32×C4⋊C4D411yescharacteristic
74C32×C4⋊C4D412yes—
75C32×C42C2311yescharacteristic
76C32×C42C2312yes—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—22no—
82#3750—21no—
83C4×C3⋊Dic3—22no—
84C4×C3⋊Dic3—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96#3719—24no—
97#3716—22no—
98#3369—91noSylow
99C3×C4⋊Q8—31no—
100C3×#126—62no—
101C3×#124—32no—
102C3×C22⋊Q8—61no—
103C3×C4×Q8—21no—
104C3×C4×Q8—32no—
105C3×C4×Q8C2×D311yescharacteristic
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×D4—31no—
108C3×#117—61no—
109#946—21no—
110Q8×Dic3—62no—
111Q8×Dic3—61no—
112Q8×Dic3—61no—
113C2×#216—32no—
114C2×#214—31no—
115C2×Dic12—32no—
116C2×#204—31no—
117#898—22no—
118#892—21no—
119#888—62no—
120#888—64no—
121#888—61no—
122#888—62no—
123#888—61no—
124#888—62no—
125#875C2×D312yes—
126C4×D12C2×D311yescharacteristic
127#869—31no—
128#869—32no—
129#869—31no—
130#869—32no—
131#869—62no—
132#869—61no—
133#869C2×D311yescharacteristic
134C4×Dic6—31no—
135C4×Dic6—32no—
136C4×Dic6—31no—
137C4×Dic6—32no—
138C4×Dic6—61no—
139C4×Dic6—62no—
140C4×Dic6C2×D312yes—
141C3×C4⋊C8—31no—
142C3×C4⋊C8—32no—
143C3×#97—32no—
144C3×C4×C8—31no—
145#835—32no—
146#835—32no—
147#835—32no—
148#832—32no—
149#832—31no—
150#821—31no—
151#821—32no—
152#817—31no—
153#817—32no—
154#816—32no—
155#816—32no—
156#816—32no—
157#816—31no—
158#810—31no—
159#808—32no—
160#808—31no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4⋊(C3⋊C8)C2×D312yes—
163#803C2×D312yes—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3—21no—
166C32×Q8—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—21no—
175#634—21no—
176#634—82no—
177#634—81no—
178#634#4112yes—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189Q82—91no—
190#556—31no—
191#489—92no—
192#487—91no—
193#476—91no—
194#475—92no—
195#464—92no—
196#462—91no—
197#446—31no—
198#441—92no—
199C4×SD16—91no—
200C2×C3×Q8—21no—
201C2×C3×Q8—32no—
202C2×C3×Q8D1211yescharacteristic
203C2×C3×Q8#6711yescharacteristic
204C2×C3×D4—31no—
205C22×C3×C4—61no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
211C2×Dic6—64no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—62no—
216C2×Dic6—61no—
217C2×Dic6C22×D312yes—
218C2×C3×C8—31no—
219C2×C3×C8—31no—
220C2×C3×C8—32no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4D1211yescharacteristic
228C3×C4⋊C4D1212yes—
229C3×C4⋊C4#6711yescharacteristic
230C3×C4⋊C4#6712yes—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—62no—
234C3×C42—21no—
235C3×C42—22no—
236C3×C42—62no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D312yes—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D312yes—
241#216—64no—
242#214—62no—
243(C2×D3)⋊C4—21no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—32no—
249C4⋊Dic3—31no—
250C4⋊Dic3—32no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—64no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3C22×D311yescharacteristic
261Dic3⋊C4—22no—
262Dic3⋊C4—64no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—61no—
266Dic3⋊C4—62no—
267Dic3⋊C4—61no—
268C4×Dic3—22no—
269C4×Dic3—64no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—61no—
273C4×Dic3—62no—
274C4×Dic3—61no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D312yes—
278Dic12—64no—
279#204—62no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C32×C4—22no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4#13712yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3⋊Dic3—42no—
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×Q16—92no—
296C2×SD16—91no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#126—62no—
303#124—32no—
304C22⋊Q8—61no—
305C4×Q8—32no—
306C4×Q8—91no—
307C4×Q8—92no—
308C4×Q8—181no—
309C4×Q8D3211yescharacteristic
310C4×D4—31no—
311#117—61no—
312#106—91no—
313#106—92no—
314C4⋊C8—31no—
315C4⋊C8—32no—
316#103—91no—
317#103—92no—
318#103—92no—
319#103—92no—
320#102—91no—
321#102—92no—
322#97—32no—
323C4×C8—31no—
324C23×C3—61no—
325C22×D3—21no—
326C3×Q8—24no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×D4—61no—
332C3×D4—61no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—122no—
341C2×C3×C4C2×D1212yes—
342C2×C3×C4C2×D1212yes—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4C2×#6712yes—
346C2×C3×C4C2×#6712yes—
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—64no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—62no—
361C2×Dic3—61no—
362D12—21no—
363D12—21no—
364C4×D3—42no—
365Dic6—22no—
366Dic6—22no—
367Dic6—32no—
368Dic6—32no—
369Dic6—62no—
370Dic6—62no—
371Dic6—61no—
372Dic6—61no—
373Dic6—242no—
374Dic6—241no—
375Dic6—242no—
376Dic6—241no—
377Dic6—244no—
378Dic6—242no—
379C3×C8—61no—
380C3×C8—62no—
381C3×C8—61no—
382C3⋊C8—21no—
383C3⋊C8—21no—
384C3⋊C8—22no—
385C2×C32#54811yescharacteristic
386C2×C32C2×#13711yescharacteristic
387C2×C32#57711yescharacteristic
388C3×D3—81no—
389C2×Q8—32no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×Q8—181no—
393C2×Q8#62611yescharacteristic
394C2×D4—31no—
395C22×C4—61no—
396Q16—184no—
397SD16—182no—
398C2×C8—31no—
399C2×C8—31no—
400C2×C8—32no—
401C4⋊C4—31no—
402C4⋊C4—61no—
403C4⋊C4—62no—
404C4⋊C4—61no—
405C4⋊C4—91no—
406C4⋊C4—92no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4#62611yescharacteristic
412C4⋊C4#62612yes—
413C22⋊C4—62no—
414C22⋊C4—61no—
415C22⋊C4—62no—
416C42—62no—
417C42—182no—
418C42—181no—
419C42C2×D3211yescharacteristic
420C42C2×D3212yes—
421C22×C3—21no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3C22×D1211yescharacteristic
426C22×C3C22×#6711yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—24no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—121no—
443C3×C4—122no—
444C3×C4#90912yes—
445C3×C4#95112yes—
446C3×C4#100711yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4D3×#4111yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—41no—
451Dic3—42no—
452Dic3—64no—
453Dic3—62no—
454Dic3—62no—
455Dic3—124no—
456Dic3—122no—
457Dic3—121no—
458Dic3—122no—
459Dic3—121no—
460Dic3—122no—
461C32#336911yescharacteristic, complemented, Sylow
462C23—61no—
463Q8—22no—
464Q8—62no—
465Q8—62no—
466Q8—92no—
467Q8—181no—
468Q8—722no—
469Q8—721no—
470D4—61no—
471D4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—122no—
475C2×C4—181no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4C2×#62612yes—
479C2×C4C2×#62612yes—
480C2×C4C2×#62611yescharacteristic
481C2×C4C2×#62611yescharacteristic
482C2×C4C22×D3211yescharacteristic
483C8—61no—
484C8—61no—
485C8—62no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—241no—
490C2×C3#557611yescharacteristic
491C2×C3C2×#90911yescharacteristic
492C2×C3#575111yescharacteristic
493C2×C3C2×#95111yescharacteristic
494C2×C3#583111yescharacteristic
495C2×C3#583711yescharacteristic
496D3—81no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22C22×#62611yescharacteristic
501C4—22no—
502C4—21no—
503C4—22no—
504C4—122no—
505C4—121no—
506C4—182no—
507C4—362no—
508C4—361no—
509C4#6383112yes—
510C4#6431511yescharacteristic
511C4#6431911yescharacteristic
512C3—21no—
513C3#7998111yescharacteristic, complemented
514C3#8367711yescharacteristic, complemented
515C2—241no—
516C2C2×#6383111yescharacteristic
517C2#1059541411yescharacteristic
518C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
3. C3×#5024C2semidirect
4. #10590388C2semidirect
5. #10590383C2semidirect
8. #10590301C2semidirect
9. #10590287C2semidirect
54. #5024D3semidirect
461. C32#3369semidirect
513. C3#79981semidirect
514. C3#83677semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55842
C3×#50242
#105903882
#105903832
#105903782
C4×#37162
#105903012
#105902872
#105902762
#105902682
#836773
#799813