Finite Group Databasebeta

← #11774618

Subgroups — #11774618

Order 1152.

547 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3796C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×#4484C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#68237—31nomaximal
9#68173—31nomaximal
10C2×#3796C411yescharacteristic
11C42×C3⋊D3C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C4×#626—21no—
15#63898C411yescharacteristic
16#63881—21no—
17#63878—21no—
18C4×D3×Dic3—21no—
19#63849C411yescharacteristic
20#63843C411yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22#63647—21no—
23#63642—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#63572—21no—
28#63557—21no—
29C4×#239—31no—
30C4×#237—31no—
31#4835—31no—
32#4835—31no—
33#4835—61no—
34#4685—31no—
35#4685—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484D311yescharacteristic, complemented
41#4483D311yescharacteristic, complemented
42#4459—31no—
43#4456—31no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3796—22no—
54#3796—22no—
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72Dic32—21no—
73#1488—91noSylow
74C2×#239—31no—
75C2×#237—31no—
76C3×C4×Q8—31no—
77C3×C4×D4—31no—
78Q8×Dic3—31no—
79D4×Dic3—31no—
80C4×#67—61no—
81C2×C4×Dic3—61no—
82#893—31no—
83#893—61no—
84#892—31no—
85#892—31no—
86#892—61no—
87#887—31no—
88#67⋊C4—61no—
89#877—61no—
90C4×D12—61no—
91C4×D12C2×D311yescharacteristic
92C42×D3—31no—
93C42×D3—31no—
94C42×D3—61no—
95C42×D3—61no—
96C4×Dic6C2×D311yescharacteristic
97C3×C4⋊C8—21no—
98C3×C4⋊C8C2×D311yescharacteristic
99C3×C4⋊C8C2×D311yescharacteristic
100C3×C4×C8—31no—
101C3×C4×C8—31no—
102(C2×D3)⋊C8—61no—
103(C2×D3)⋊C8—61no—
104(C2×D3)⋊C8—61no—
105(C2×D3)⋊C8—61no—
106(C2×D3)⋊C8—62no—
107#815—61no—
108#815—61no—
109#815—62no—
110Dic3⋊C8—61no—
111Dic3⋊C8—61no—
112C4⋊(C3⋊C8)—31no—
113C4⋊(C3⋊C8)—31no—
114C4⋊(C3⋊C8)—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C4×C3⋊C8C2×D311yescharacteristic
117C22×C3⋊D3C22⋊C411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C3×D12—21no—
134C3×D12M1612yes—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137C3×Dic6—21no—
138C3×Dic6M1612yes—
139#626—24no—
140D3×Dic3—24no—
141D3×Dic3—42no—
142C32×C8—41no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146C4×#41—91no—
147#432—91no—
148#431—91no—
149Q8⋊C8—31no—
150Q8⋊C8—91no—
151D4⋊C8—31no—
152D4⋊C8—91no—
153C2×C3×Q8—31no—
154C2×C3×D4—31no—
155C22×C3×C4—61no—
156C2×#67—61no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159#239—62no—
160#239—62no—
161#237—62no—
162#237—62no—
163C2×D12—61no—
164C2×D12C4×D311yescharacteristic
165C2×C4×D3—21no—
166C2×C4×D3—31no—
167C2×C4×D3—31no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—31no—
172C2×C4×D3—61no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×Dic6C4×D311yescharacteristic
178C2×C3×C8—22no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—21no—
188C3×C42—61no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#217—61no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3C4×D311yescharacteristic
198C4⋊Dic3C4×D311yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—61no—
201C4×Dic3—21no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—62no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C22×C32C2×C22⋊C411yescharacteristic
221C2×C3⋊D3—21no—
222C2×C3⋊D3—21no—
223C2×C3⋊D3—21no—
224C2×C3×D3—22no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C32×C4—21no—
228C32×C4C2×M1611yescharacteristic
229C32×C4C2×M1611yescharacteristic
230C32×C4#13511yescharacteristic
231C32×C4#13511yescharacteristic
232C3⋊Dic3—21no—
233C3⋊Dic3—21no—
234C3⋊Dic3—21no—
235C3×Dic3—22no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C2×#41—91no—
239C4×Q8—31no—
240C4×Q8—91no—
241C4×D4—31no—
242C4×D4—91no—
243C4×D4—181no—
244C4×D4—181no—
245#117—91no—
246#117—181no—
247C2×C42—91no—
248C2×C42—181no—
249C4⋊C8—91no—
250C4⋊C8—181no—
251C4⋊C8D3211yescharacteristic
252C22⋊C8—181no—
253C22⋊C8—181no—
254#97—181no—
255C4×C8—31no—
256C4×C8—31no—
257C23×C3—61no—
258C22×D3—21no—
259C22×D3—31no—
260C22×D3—31no—
261C22×D3—61no—
262C3×Q8—32no—
263C3×Q8—61no—
264C3×D4—32no—
265C3×D4—61no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×C4×D311yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280#67—64no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—31no—
285C2×Dic3—31no—
286C2×Dic3—31no—
287C2×Dic3—31no—
288C2×Dic3—31no—
289C2×Dic3—31no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—64no—
294C2×Dic3—122no—
295D12—21no—
296D12—64no—
297D12ΓL(1,𝔽25)12yes—
298C4×D3—41no—
299C4×D3—41no—
300C4×D3—64no—
301C4×D3—61no—
302C4×D3—61no—
303C4×D3—61no—
304C4×D3—61no—
305C4×D3—61no—
306C4×D3—61no—
307C4×D3—61no—
308C4×D3—61no—
309C4×D3—121no—
310C4×D3—121no—
311C4×D3—121no—
312C4×D3—121no—
313C4×D3—121no—
314C4×D3—121no—
315C4×D3—122no—
316C4×D3—122no—
317Dic6—21no—
318Dic6ΓL(1,𝔽25)12yes—
319C3×C8—42no—
320C3×C8—41no—
321C3×C8—41no—
322C3×C8—121no—
323C3×C8—121no—
324C3⋊C8—41no—
325C3⋊C8—41no—
326C3⋊C8—122no—
327C3⋊C8—121no—
328C3⋊C8—121no—
329C2×C32#40711yescharacteristic
330C2×C32#41611yescharacteristic
331C2×C32#42111yescharacteristic
332C3⋊D3—41no—
333C3×D3—42no—
334#41—182no—
335#41—182no—
336C2×Q8—31no—
337C2×D4—31no—
338C2×D4—181no—
339C22×C4—61no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—181no—
344C22×C4—181no—
345C2×C8—21no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—181no—
349C4⋊C4—31no—
350C4⋊C4—31no—
351C4⋊C4—61no—
352C4⋊C4—181no—
353C22⋊C4—61no—
354C22⋊C4—181no—
355C22⋊C4—181no—
356C42—61no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42—181no—
361C42—181no—
362C42C2×D3211yescharacteristic
363C22×C3—21no—
364C22×C3—62no—
365C22×C3—121no—
366C22×C3—121no—
367C22×C3D3×C22⋊C411yescharacteristic
368C22×C3D3×C22⋊C411yescharacteristic
369C2×D3—22no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—62no—
373C2×D3—61no—
374C2×D3—61no—
375C2×D3—61no—
376C2×D3—61no—
377C2×D3—61no—
378C2×D3—61no—
379C2×D3—121no—
380C2×D3—121no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—41no—
388C3×C4—62no—
389C3×C4—121no—
390C3×C4—121no—
391C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
392C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
393C3×C4D3×M1611yescharacteristic
394C3×C4D3×M1611yescharacteristic
395C3×C4#91211yescharacteristic
396C3×C4#91611yescharacteristic
397C3×C4#91611yescharacteristic
398C3×C4#91911yescharacteristic
399Dic3—22no—
400Dic3—41no—
401Dic3—41no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—61no—
407Dic3—61no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411C32#148811yescharacteristic, complemented, Sylow
412C23—61no—
413C23—91no—
414Q8—32no—
415Q8—61no—
416D4—32no—
417D4—61no—
418D4—184no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—184no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—361no—
433C2×C4—362no—
434C2×C4C4×D3211yescharacteristic
435C2×C4#380211yescharacteristic
436C2×C4#381111yescharacteristic
437C8—41no—
438C8—121no—
439C8—121no—
440C8—361no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—122no—
445C2×C3#472611yescharacteristic
446C2×C3#472611yescharacteristic
447C2×C3#477211yescharacteristic
448C2×C3#480411yescharacteristic
449C2×C3#482111yescharacteristic
450C2×C3#482111yescharacteristic
451D3—42no—
452D3—122no—
453D3—121no—
454D3—121no—
455C22—62no—
456C22—121no—
457C22—121no—
458C22—181no—
459C22—181no—
460C22—181no—
461C22#6392111yescharacteristic
462C4—21no—
463C4—62no—
464C4—121no—
465C4—121no—
466C4—181no—
467C4—181no—
468C4—181no—
469C4D3×ΓL(1,𝔽25)11yescharacteristic
470C4D3×ΓL(1,𝔽25)11yescharacteristic
471C4#6393611yescharacteristic
472C4#6395011yescharacteristic
473C3—21no—
474C3#6817311yescharacteristic, complemented
475C3#6823711yescharacteristic, complemented
476C2—122no—
477C2—361no—
478C2#1059061111yescharacteristic
479C2#1059093711yescharacteristic
480C2#1059100911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3796C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592534C2semidirect
3. #10590297C2semidirect
4. C3×#4484C2semidirect
5. C3×#4483C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
40. #4484D3semidirect
41. #4483D3semidirect
411. C32#1488semidirect
474. C3#68173semidirect
475. C3#68237semidirect

Maximal subgroups

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

subgroupindex
C4×#37962
#105925342
#105902972
C3×#44842
C3×#44832
#105890842
#105890812
#682373
#681733