Finite Group Databasebeta

← #11887646

Subgroups — #11887646

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4#10591188C212yesmaximal, complemented
5#10591185C212yesmaximal, complemented
6#10591132C212yesmaximal, complemented
7C2×#63565C212yesmaximal, complemented
8#10590384C211yesmaximal, characteristic, complemented
9C4×#3718C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11#10590290C211yesmaximal, characteristic, complemented
12#83640—31nomaximal
13#83551—31nomaximal
14C22×C3×Dic6C2212yes—
15C32×C4×D4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2212yes—
17C3×D4×Dic3—21no—
18C3×D4×Dic3—21no—
19C2×C3×C4⋊Dic3C2212yes—
20C3×#924C2212yes—
21C3×#924C2212yes—
22C3×#890—21no—
23C3×#888—21no—
24C3×#878—22no—
25C3×#878—22no—
26C3×#869C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C2×#3718C2211yescharacteristic
31C2×#3718C2212yes—
32#63657C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63576C2212yes—
36#63576C2211yescharacteristic
37#63565C2212yes—
38#63565C2212yes—
39#63565C2212yes—
40#63565C2211yescharacteristic
41#63565C2212yes—
42#63565C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5543D311yescharacteristic
46D4×Dic6D311yescharacteristic
47#5228—32no—
48C2×#835—32no—
49#5093—31no—
50#5091—31no—
51#5090—31no—
52#5079—31no—
53#5051—32no—
54#5051—32no—
55#5050—32no—
56#5044—32no—
57#5031—31no—
58C4×#216—31no—
59C4×#216—31no—
60#5021—31no—
61D4×C3⋊C8—31no—
62D4×C3⋊C8—31no—
63D4×C3⋊C8—61no—
64#4970—32no—
65C2×#810—32no—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C2×C3×Dic6—24no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—42no—
74C2×C3×Dic6C2311yescharacteristic
75C2×C3×Dic6C2312yes—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4D411yescharacteristic
78C32×C22⋊C4D412yes—
79C32×C42C2311yescharacteristic
80C2×C3⋊(C3⋊C8)—42no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×#217—22no—
85C3×#217—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99#3718—22no—
100#3718—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C22×Dic6C2×D312yes—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8—61no—
107C3×#125—61no—
108C3×C22⋊Q8—32no—
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—62no—
111C3×C22⋊Q8—62no—
112C3×C4×Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×D4—21no—
115C3×C4×D4—61no—
116C3×C4×D4—61no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C2×D311yescharacteristic
119C2×C3×C4⋊C4—32no—
120C2×#216—31no—
121C2×#216—31no—
122C2×#216—32no—
123C2×#216—32no—
124D4×Dic3—21no—
125D4×Dic3—21no—
126C2×C4⋊Dic3C2×D312yes—
127#924C2×D312yes—
128#924C2×D312yes—
129C22×C3⋊C8—32no—
130C22×C3⋊C8—32no—
131C22×C3⋊C8—62no—
132#890—21no—
133#888—21no—
134#878—22no—
135#878—22no—
136#869C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138C4×Dic6C2×D311yescharacteristic
139C4×Dic6C2×D311yescharacteristic
140#835—31no—
141#835—32no—
142#835—32no—
143#835—32no—
144#835—32no—
145#835—31no—
146#830—32no—
147#830—32no—
148#830—62no—
149#810—31no—
150#810—32no—
151#810—32no—
152#810—32no—
153#810—32no—
154#810—31no—
155#807—31no—
156#807—32no—
157#807—32no—
158#807—31no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—61no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—61no—
165C23×C32C2×D412yes—
166C32×D4Q1614yescomplemented
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3—82no—
181C3×Dic6—21no—
182C3×Dic6—21no—
183C3×Dic6—22no—
184C3×Dic6—21no—
185C3×Dic6—22no—
186C3×Dic6—44no—
187C3×Dic6—81no—
188C3×Dic6#4112yes—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—22no—
192#554—31no—
193D4×Q8—31no—
194#487—91no—
195#484—92no—
196#477—91no—
197#467—92no—
198#462—91no—
199#451—92no—
200C4×Q16—91no—
201C8×D4—91no—
202C2×#103—92no—
203C2×C3×Q8—31no—
204C2×C3×Q8—32no—
205C2×C3×Q8—31no—
206C2×C3×Q8—64no—
207C2×C3×Q8—62no—
208C2×C3×Q8—61no—
209C2×C3×Q8—122no—
210C2×C3×D4—21no—
211C2×C3×D4#6711yescharacteristic
212C2×C3×D4#6711yescharacteristic
213C22×C3×C4—22no—
214C22×C3×C4—62no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D312yes—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C2×Dic6—24no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6—42no—
224C2×Dic6C22×D312yes—
225C2×Dic6C22×D311yescharacteristic
226C2×Dic6C22×D311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4#6711yescharacteristic
240C3×C4⋊C4#6711yescharacteristic
241C3×C22⋊C4—22no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244C3×C22⋊C4#6712yes—
245C3×C22⋊C4#6712yes—
246C3×C42—21no—
247C3×C42—61no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—22no—
252#217—22no—
253#216—62no—
254#216—62no—
255#216—122no—
256#216—122no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—22no—
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—21no—
265Dic3⋊C4—21no—
266Dic3⋊C4—22no—
267Dic3⋊C4—22no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8—122no—
281C2×C3⋊C8—124no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32C2×Q1614yes—
285C22×C32C22×D411yescharacteristic
286C32×C4—22no—
287C32×C4—21no—
288C32×C4C2×Q1612yes—
289C32×C4C2×#4111yescharacteristic
290C32×C4H(5,𝔽2)11yescharacteristic
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×Q8—32no—
298C2×Q16—91no—
299C2×Q16—92no—
300C22×C8—92no—
301C4⋊Q8—31no—
302C4⋊Q8—31no—
303C4⋊Q8—61no—
304#125—61no—
305C22⋊Q8—32no—
306C22⋊Q8—32no—
307C22⋊Q8—62no—
308C22⋊Q8—62no—
309C4×Q8—31no—
310C4×Q8—31no—
311C4×D4—61no—
312C4×D4—61no—
313C4×D4D3211yescharacteristic
314C2×C4⋊C4—32no—
315#107—91no—
316#107—92no—
317C4⋊C8—91no—
318#103—91no—
319#103—92no—
320#103—92no—
321#103—92no—
322#103—91no—
323#103—92no—
324C22⋊C8—92no—
325C4×C8—91no—
326C23×C3—22no—
327C23×C3C2×#6712yes—
328C23×C3C2×#6712yes—
329C3×Q8—32no—
330C3×Q8—61no—
331C3×Q8—61no—
332C3×Q8—61no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—124no—
336C3×Q8—241no—
337C3×D4—24no—
338C3×D4#21614yescomplemented
339C3×D4#21614yescomplemented
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—124no—
357C2×C3×C4—242no—
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6712yes—
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—44no—
373C2×Dic3—82no—
374Dic6—21no—
375Dic6—22no—
376Dic6—22no—
377Dic6—21no—
378Dic6—21no—
379Dic6—44no—
380Dic6—81no—
381Dic6#23712yes—
382C3⋊C8—62no—
383C3⋊C8—61no—
384C3⋊C8—61no—
385C3⋊C8—62no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—62no—
389C3⋊C8—121no—
390C3⋊C8—122no—
391C2×C32—24no—
392C2×C32#54611yescharacteristic
393C2×C32C22×Q1611yescharacteristic
394C2×C32#57711yescharacteristic
395C2×Q8—31no—
396C2×Q8—32no—
397C2×Q8—31no—
398C2×Q8—64no—
399C2×Q8—62no—
400C2×Q8—61no—
401C2×Q8—122no—
402C2×D4#62511yescharacteristic
403C22×C4—62no—
404C22×C4—62no—
405C22×C4C2×D3212yes—
406Q16—182no—
407Q16—362no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—92no—
411C2×C8—362no—
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—31no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—61no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4#62511yescharacteristic
424C22⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4#62512yes—
427C42—61no—
428C42—61no—
429C42C2×D3211yescharacteristic
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—24no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3C2×#21614yes—
439C22×C3C2×#21614yes—
440C22×C3C22×#6711yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—62no—
452C3×C4—121no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4C2×#21612yes—
458C3×C4C2×#21612yes—
459C3×C4C2×#23711yescharacteristic
460C3×C4#100411yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4#100911yescharacteristic
463Dic3—22no—
464Dic3—42no—
465Dic3—41no—
466Dic3—42no—
467Dic3—41no—
468Dic3—41no—
469C32#329911yescharacteristic, complemented, Sylow
470C23C2×#62512yes—
471Q8—32no—
472Q8—61no—
473Q8—61no—
474Q8—62no—
475Q8—61no—
476Q8—62no—
477Q8—124no—
478Q8—241no—
479D4#371814yescomplemented
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—124no—
489C2×C4—242no—
490C2×C4C2×#62511yescharacteristic
491C2×C4C2×#62512yes—
492C2×C4C2×#62511yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—181no—
495C8—181no—
496C8—182no—
497C2×C3—24no—
498C2×C3—24no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—44no—
503C2×C3#580611yescharacteristic
504C2×C3C22×#21611yescharacteristic
505C2×C3C22×#21611yescharacteristic
506C2×C3#582911yescharacteristic
507C2×C3#583611yescharacteristic
508C2×C3#583711yescharacteristic
509C22—22no—
510C22—22no—
511C22C2×#371814yes—
512C22C22×#62511yescharacteristic
513C4—21no—
514C4—22no—
515C4—62no—
516C4—121no—
517C4—122no—
518C4—121no—
519C4—122no—
520C4—121no—
521C4C2×#371812yes—
522C4D3×#23711yescharacteristic
523C4#6431411yescharacteristic
524C3—21no—
525C3#8355111yescharacteristic, complemented
526C3#8364011yescharacteristic, complemented
527C2—24no—
528C2C22×#371811yescharacteristic
529C2#1059524411yescharacteristic
530C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10591188C2semidirect
5. #10591185C2semidirect
6. #10591132C2semidirect
7. C2×#63565C2semidirect
8. #10590384C2semidirect
9. C4×#3718C2semidirect
10. #10590310C2semidirect
11. #10590290C2semidirect
166. C32×D4Q16semidirect
338. C3×D4#216semidirect
339. C3×D4#216semidirect
469. C32#3299semidirect
479. D4#3718semidirect
525. C3#83551semidirect
526. C3#83640semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
C3×D4×Dic62
D4×C3⋊(C3⋊C8)2
#105911882
#105911852
#105911322
C2×#635652
#105903842
C4×#37182
#105903102
#105902902
#836403
#835513