Finite Group Databasebeta

← #11887674

Subgroups — #11887674

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2#10593960C211yesmaximal, characteristic
3#10592778C211yesmaximal, characteristic, complemented
4C3×#5090C211yesmaximal, characteristic, complemented
5#10591635C212yesmaximal, complemented
6#10591594C212yesmaximal, complemented
7#10591551C212yesmaximal, complemented
8D3×#835C212yesmaximal, complemented
9C4×#3718C211yesmaximal, characteristic, complemented
10#10590329C211yesmaximal, characteristic
11#10590283C211yesmaximal, characteristic, complemented
12#83551—31nomaximal
13#80491—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#946C2212yes—
18C2×C3×#216C2212yes—
19C3×#896—22no—
20C3×#893—21no—
21C3×#888—21no—
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63896—22no—
26Dic3×D12—21no—
27D3×C4⋊Dic3C2212yes—
28#63869—21no—
29#63856C2212yes—
30C2×#3718C2211yescharacteristic
31C2×D3×C3⋊C8C2212yes—
32#63662C2212yes—
33#63662C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#835C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38#63575C2212yes—
39#63566C2212yes—
40#63565C2211yescharacteristic
41#63565C2211yescharacteristic
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×D4×Q8—31no—
44#5727D311yescharacteristic
45#5579—31no—
46#5543—31no—
47C3×#462—31no—
48#5228—32no—
49C2×#835—32no—
50#5188—32no—
51#5186—32no—
52#5090D311yescharacteristic, complemented
53#5079—31no—
54#5079—31no—
55#5079—61no—
56#5051—32no—
57#5044—32no—
58C4×#216—31no—
59C4×#216—31no—
60#5021—31no—
61D4×C3⋊C8—31no—
62#4850—31no—
63#4834—31no—
64#4811—32no—
65D3×#103—32no—
66C2×C32×Q8C2312yes—
67C2×#634—21no—
68C3×D3×Q8—24no—
69C3×D3×Q8—42no—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—22no—
74C2×C3×Dic6C2311yescharacteristic
75C2×C3×Dic6C2311yescharacteristic
76C2×D3×Dic3—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C42C2311yescharacteristic
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#216—42no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4D412yes—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#3718—22no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C2×D312yes—
104C2×C3×Q16—32no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—61no—
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4⋊Q8C2×D311yescharacteristic
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—62no—
111C3×C4×Q8—31no—
112C3×C4×Q8—31no—
113C3×C4×D4—31no—
114C3×C4×D4—61no—
115#946—32no—
116#946C2×D312yes—
117C2×#216—31no—
118C2×#216—31no—
119C2×#216C2×D312yes—
120D4×Dic3—61no—
121C2×C4⋊Dic3—32no—
122#924—32no—
123C22×C3⋊C8—32no—
124C2×D3×C8—32no—
125#896—22no—
126#896—62no—
127#893—21no—
128D3×C4⋊C4—32no—
129#890—61no—
130#888—21no—
131#878—62no—
132C4×D12—61no—
133C4×D12C2×D311yescharacteristic
134#870—61no—
135#869—31no—
136#869—31no—
137#869—61no—
138C4×Dic6C2×D311yescharacteristic
139C4×Dic6C2×D311yescharacteristic
140C3×C4⋊C8—31no—
141C3×#103—32no—
142#835—32no—
143#835—32no—
144#835—32no—
145#835—32no—
146#835—31no—
147#835—31no—
148#835—32no—
149#835—62no—
150#835—62no—
151#835C2×D312yes—
152#830—32no—
153(C2×D3)⋊C8—32no—
154#818—32no—
155#816—32no—
156#810—31no—
157#810—31no—
158#807—31no—
159#807—31no—
160#807—32no—
161C4⋊(C3⋊C8)C2×D311yescharacteristic
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
165C22×C3×D3C2×D412yes—
166C32×Q8—22no—
167C32×Q8—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C3×D12Q1614yescomplemented
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3—44no—
183C3×Dic6—21no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C3×Dic6—44no—
187C3×Dic6#4112yes—
188D3×Dic3—82no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
191C3×C3⋊C8—22no—
192#554—91no—
193D4×Q8—31no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—31no—
199#451—92no—
200C4×Q16—91no—
201C8×D4—91no—
202C2×#103—92no—
203C2×C3×Q8—22no—
204C2×C3×Q8—31no—
205C2×C3×Q8—31no—
206C2×C3×Q8—62no—
207C2×C3×Q8—64no—
208C2×C3×Q8—122no—
209C2×C3×Q8C22×D312yes—
210C2×C3×Q8C22×D312yes—
211C2×C3×D4—31no—
212C22×C3×C4—32no—
213C22×C3×C4—62no—
214C22×Dic3—62no—
215D3×Q8—24no—
216D3×Q8—42no—
217C2×D12#6711yescharacteristic
218C2×C4×D3—22no—
219C2×C4×D3—62no—
220C2×C4×D3C22×D312yes—
221C2×Dic6—22no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—121no—
225C2×Dic6C22×D311yescharacteristic
226C2×Dic6C22×D311yescharacteristic
227C3×Q16—122no—
228C2×C3×C8—32no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—41no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C22⋊C4—32no—
242C3×C22⋊C4—62no—
243C3×C42—21no—
244C3×C42—61no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#216—42no—
250#216—62no—
251#216—62no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4#6712yes—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—121no—
262C4⋊Dic3#6711yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—21no—
267Dic3⋊C4—22no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271C4×Dic3—21no—
272C4×Dic3—21no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8C22×D312yes—
281D3×C8—122no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3C2×Q1614yes—
286C32×C4—21no—
287C32×C4—42no—
288C32×C4C2×Q1612yes—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—32no—
298C2×Q16—32no—
299C2×Q16—91no—
300C22×C8—92no—
301C4⋊Q8—61no—
302C4⋊Q8—91no—
303C4⋊Q8D3211yescharacteristic
304#125—181no—
305C22⋊Q8—32no—
306C22⋊Q8—62no—
307C22⋊Q8—92no—
308C22⋊Q8—182no—
309C4×Q8—31no—
310C4×Q8—31no—
311C4×D4—31no—
312C4×D4—61no—
313C4×D4—181no—
314C2×C4⋊C4—92no—
315#107—91no—
316#107—92no—
317C4⋊C8—31no—
318#103—32no—
319#103—91no—
320#103—91no—
321#103—92no—
322#103—92no—
323#103—92no—
324C22⋊C8—92no—
325C4×C8—91no—
326C23×C3—32no—
327C22×D3C2×#6712yes—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—32no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—61no—
336C3×Q8—61no—
337C3×Q8—61no—
338C3×Q8—124no—
339C3×D4—34no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—42no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—124no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—242no—
368C2×Dic3C2×#6712yes—
369D12#21614yescomplemented
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—44no—
373C4×D3—242no—
374Dic6—21no—
375Dic6—21no—
376Dic6—21no—
377Dic6—44no—
378Dic6—241no—
379Dic6—241no—
380Dic6—242no—
381Dic6#23712yes—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—121no—
389C3⋊C8—121no—
390C2×C32#54611yescharacteristic
391C2×C32C22×Q1611yescharacteristic
392C2×C32#57711yescharacteristic
393C3×D3—24no—
394C2×Q8—31no—
395C2×Q8—31no—
396C2×Q8—62no—
397C2×Q8—64no—
398C2×Q8—122no—
399C2×Q8—181no—
400C2×Q8C2×D3212yes—
401C2×D4—31no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—182no—
405Q16—122no—
406Q16—182no—
407C2×C8—32no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—362no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—31no—
414C4⋊C4—31no—
415C4⋊C4—31no—
416C4⋊C4—62no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—92no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C22⋊C4—32no—
424C22⋊C4—62no—
425C22⋊C4—182no—
426C42—61no—
427C42—61no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—62no—
432C22×C3—62no—
433C22×C3C2×D3×D411yescharacteristic
434C22×C3C22×#6711yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3C2×#21614yes—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—82no—
449C3×C4—121no—
450C3×C4—121no—
451C3×C4—121no—
452C3×C4D3×Q1612yes—
453C3×C4C2×#21612yes—
454C3×C4C2×#23711yescharacteristic
455C3×C4#100411yescharacteristic
456C3×C4#100411yescharacteristic
457C3×C4D3×#4111yescharacteristic
458Dic3—22no—
459Dic3—22no—
460Dic3—41no—
461Dic3—41no—
462Dic3—41no—
463Dic3—122no—
464Dic3—122no—
465Dic3—242no—
466C32#329911yescharacteristic, complemented, Sylow
467C23—32no—
468Q8—22no—
469Q8—22no—
470Q8—32no—
471Q8—61no—
472Q8—61no—
473Q8—61no—
474Q8—124no—
475Q8—721no—
476D4—34no—
477C2×C4—22no—
478C2×C4—32no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—124no—
486C2×C4—182no—
487C2×C4—722no—
488C2×C4D3×#6711yescharacteristic
489C2×C4D3×#6711yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—62no—
492C8—181no—
493C8—181no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—64no—
498C2×C3#561211yescharacteristic
499C2×C3C2×D3×Q1611yescharacteristic
500C2×C3#577811yescharacteristic
501C2×C3#580611yescharacteristic
502C2×C3C22×#21611yescharacteristic
503C2×C3#583711yescharacteristic
504D3—24no—
505C22—34no—
506C22—62no—
507C22—62no—
508C22C2×D3×#6711yescharacteristic
509C4—21no—
510C4—42no—
511C4—62no—
512C4—62no—
513C4—121no—
514C4—121no—
515C4—121no—
516C4—362no—
517C4D3×#21612yes—
518C4D3×#23711yescharacteristic
519C4#6431311yescharacteristic
520C3—21no—
521C3#8049111yescharacteristic, complemented
522C3#8355111yescharacteristic, complemented
523C2—64no—
524C2#1059522811yescharacteristic
525C2#1059531911yescharacteristic
526C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#3299
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
3. #10592778C2semidirect
4. C3×#5090C2semidirect
5. #10591635C2semidirect
6. #10591594C2semidirect
7. #10591551C2semidirect
8. D3×#835C2semidirect
9. C4×#3718C2semidirect
11. #10590283C2semidirect
52. #5090D3semidirect
179. C3×D12Q16semidirect
369. D12#216semidirect
466. C32#3299semidirect
521. C3#80491semidirect
522. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105939602
#105927782
C3×#50902
#105916352
#105915942
#105915512
D3×#8352
C4×#37182
#105903292
#105902832
#835513
#804913