Finite Group Databasebeta

← #11887676

Subgroups — #11887676

Order 1152.

830 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591596C212yesmaximal, complemented
6#10591595C212yesmaximal, complemented
7#10591551C212yesmaximal, complemented
8D3×#835C212yesmaximal, complemented
9C4×#3719C211yesmaximal, characteristic, complemented
10C3⋊C8×D12C211yesmaximal, characteristic
11#10590310C211yesmaximal, characteristic, complemented
12#83551—31nomaximal
13#81613—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3756C2212yes—
17C4×#634C2211yescharacteristic
18C3×#946C2212yes—
19C3×#896—22no—
20C3×#893—21no—
21C3×#888—21no—
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63898—21no—
26D3×C4⋊Dic3C2212yes—
27#63887—22no—
28#63872—21no—
29#63857C2212yes—
30C2×#3719C2211yescharacteristic
31C2×D3×C3⋊C8C2212yes—
32#63662C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63576C2212yes—
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2211yescharacteristic
41#63565C2212yes—
42(C2×D3)⋊(C3⋊C8)C2212yes—
43C3×D4×Q8—31no—
44#5730—31no—
45#5727D311yescharacteristic
46#5543—31no—
47C3×#487—31no—
48#5228—32no—
49C2×#835—32no—
50#5091—31no—
51#5090—31no—
52#5090—31no—
53#5090—61no—
54#5079D311yescharacteristic, complemented
55#5051—32no—
56#5044—32no—
57C4×#216—31no—
58#5021—31no—
59D4×C3⋊C8—31no—
60#4813—32no—
61#4811—32no—
62#4809—32no—
63D3×#103—32no—
64C4×Dic12—31no—
65C8×D12—31no—
66C2×C32×Q8C2312yes—
67C2×#634C2311yescharacteristic
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×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×D3×Dic3—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C42C2311yescharacteristic
80#3756—42no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4D412yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—21no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#3719—22no—
100D3×C3⋊C8—42no—
101#3299—91noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C2×D312yes—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
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×D4—31no—
113C3×C4×D4—61no—
114#946—62no—
115#946C2×D312yes—
116C2×#216—32no—
117C2×#216—32no—
118C2×#216—31no—
119C2×#216—62no—
120D4×Dic3—61no—
121C2×C4⋊Dic3—32no—
122#924—32no—
123C22×C3⋊C8—32no—
124C2×Dic12—31no—
125C2×D3×C8—32no—
126#897—32no—
127#896—22no—
128#893—21no—
129#893—61no—
130D3×C4⋊C4—32no—
131#890—61no—
132#890—61no—
133#888—21no—
134#878—62no—
135C4×D12C2×D311yescharacteristic
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#103—32no—
142C3×#103—32no—
143C3×C4×C8—31no—
144#835—32no—
145#835—32no—
146#835—32no—
147#835—31no—
148#835—62no—
149#835C2×D312yes—
150#835C2×D312yes—
151#830—32no—
152(C2×D3)⋊C8—32no—
153#818—31no—
154#816—31no—
155#816—31no—
156#810—32no—
157#810—31no—
158#807—32no—
159#807—32no—
160#807—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8C2×D311yescharacteristic
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—21no—
173C2×C3⋊Dic3—21no—
174#634—21no—
175#634—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C2×D412yes—
180C3×D12Q1614yescomplemented
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×C4×D3—44no—
184C3×Dic6—21no—
185C3×Dic6—44no—
186C3×Dic6—81no—
187C3×Dic6#4112yes—
188D3×Dic3—82no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#554—91no—
193D4×Q8—31no—
194#487—31no—
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—22no—
204C2×C3×Q8—31no—
205C2×C3×Q8—62no—
206C2×C3×Q8—61no—
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—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—61no—
226C2×Dic6C22×D311yescharacteristic
227C2×C3×C8—31no—
228C2×C3×C8—31no—
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—32no—
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×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—62no—
248#216—62no—
249#216—122no—
250#216—122no—
251#216—124no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4#6712yes—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—21no—
265Dic3⋊C4—22no—
266Dic3⋊C4—62no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—62no—
270Dic3⋊C4—121no—
271C4×Dic3—21no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—121no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281Dic12—62no—
282D3×C8—122no—
283C22×C32C22×D411yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3C2×Q1614yes—
287C32×C4—21no—
288C32×C4—42no—
289C32×C4C2×Q1612yes—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C22×Q8—32no—
299C2×Q16—91no—
300C2×Q16—92no—
301C22×C8—92no—
302C4⋊Q8—31no—
303C4⋊Q8—61no—
304C4⋊Q8D3211yescharacteristic
305#125—181no—
306C22⋊Q8—32no—
307C22⋊Q8—62no—
308C22⋊Q8—92no—
309C22⋊Q8—182no—
310C4×Q8—31no—
311C4×Q8—91no—
312C4×D4—31no—
313C4×D4—61no—
314C4×D4—181no—
315C2×C4⋊C4—92no—
316#107—92no—
317#107—91no—
318C4⋊C8—91no—
319#103—32no—
320#103—32no—
321#103—91no—
322#103—92no—
323#103—91no—
324#103—92no—
325C22⋊C8—92no—
326C4×C8—31no—
327C23×C3—32no—
328C22×D3C2×#6712yes—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—22no—
333C3×Q8—32no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—61no—
337C3×Q8—124no—
338C3×Q8—241no—
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—62no—
352C2×C3×C4—124no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—242no—
369C2×Dic3C2×#6712yes—
370D12#21614yescomplemented
371C4×D3—22no—
372C4×D3—22no—
373C4×D3—44no—
374C4×D3—242no—
375Dic6—21no—
376Dic6—44no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—81no—
383Dic6—121no—
384Dic6#23712yes—
385C3×C8—61no—
386C3×C8—61no—
387C3⋊C8—21no—
388C3⋊C8—21no—
389C3⋊C8—62no—
390C3⋊C8—62no—
391C3⋊C8—122no—
392C2×C32#54611yescharacteristic
393C2×C32C22×Q1611yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—24no—
396C2×Q8—31no—
397C2×Q8—62no—
398C2×Q8—61no—
399C2×Q8—64no—
400C2×Q8—91no—
401C2×Q8—122no—
402C2×Q8C2×D3212yes—
403C2×D4—31no—
404C22×C4—32no—
405C22×C4—62no—
406C22×C4—182no—
407Q16—182no—
408Q16—362no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—92no—
412C2×C8—362no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—62no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C4⋊C4—91no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C22⋊C4—32no—
426C22⋊C4—62no—
427C22⋊C4—182no—
428C42—61no—
429C42—181no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—34no—
433C22×C3—62no—
434C22×C3—62no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—22no—
438C2×D3—22no—
439C2×D3C2×#21614yes—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—41no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—82no—
451C3×C4—121no—
452C3×C4—122no—
453C3×C4D3×Q1612yes—
454C3×C4C2×#21612yes—
455C3×C4C2×#23711yescharacteristic
456C3×C4#100411yescharacteristic
457C3×C4D3×#4111yescharacteristic
458C3×C4#100911yescharacteristic
459Dic3—22no—
460Dic3—22no—
461Dic3—42no—
462Dic3—41no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466Dic3—121no—
467Dic3—121no—
468Dic3—241no—
469C32#329911yescharacteristic, complemented, Sylow
470C23—32no—
471Q8—22no—
472Q8—22no—
473Q8—32no—
474Q8—61no—
475Q8—124no—
476Q8—181no—
477Q8—181no—
478Q8—241no—
479D4—34no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—62no—
487C2×C4—124no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—722no—
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—61no—
495C8—61no—
496C8—182no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—64no—
501C2×C3#567611yescharacteristic
502C2×C3#576211yescharacteristic
503C2×C3C2×D3×Q1611yescharacteristic
504C2×C3#580611yescharacteristic
505C2×C3C22×#21611yescharacteristic
506C2×C3#583711yescharacteristic
507D3—24no—
508C22—34no—
509C22—62no—
510C22—62no—
511C22C2×D3×#6711yescharacteristic
512C4—21no—
513C4—42no—
514C4—62no—
515C4—62no—
516C4—122no—
517C4—121no—
518C4—361no—
519C4—361no—
520C4D3×#21612yes—
521C4D3×#23711yescharacteristic
522C4#6431411yescharacteristic
523C3—21no—
524C3#8161311yescharacteristic, complemented
525C3#8355111yescharacteristic, complemented
526C2—64no—
527C2#1059522911yescharacteristic
528C2#1059531811yescharacteristic
529C2C2×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. #10592789C2semidirect
4. C3×#5079C2semidirect
5. #10591596C2semidirect
6. #10591595C2semidirect
7. #10591551C2semidirect
8. D3×#835C2semidirect
9. C4×#3719C2semidirect
11. #10590310C2semidirect
54. #5079D3semidirect
180. C3×D12Q16semidirect
370. D12#216semidirect
469. C32#3299semidirect
524. C3#81613semidirect
525. C3#83551semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105939562
#105927892
C3×#50792
#105915962
#105915952
#105915512
D3×#8352
C4×#37192
C3⋊C8×D122
#105903102
#835513
#816133