Finite Group Databasebeta

← #11774506

Subgroups — #11774506

Order 1152.

565 conjugacy classes of subgroups.

The subgroup lattice has 505 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593968C211yesmaximal, characteristic
2C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589325C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#69853—31nomaximal
9#68171—31nomaximal
10C2×#3798—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C4×D12C2211yescharacteristic
14C3×C42×D3C2211yescharacteristic
15#63918C411yescharacteristic
16#63911C411yescharacteristic
17#63909C411yescharacteristic
18#63908C411yescharacteristic
19#63906—21no—
20C4×#626—21no—
21#63852—21no—
22C32×C4×C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#815—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27(C2×D3)⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29#5548—31no—
30#5477—31no—
31C3×C4×M16—31no—
32#4925—31no—
33#4833—31no—
34C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4483—31no—
38#4459—31no—
39#4459—31no—
40#4459—31no—
41#4459—31no—
42#4459—61no—
43#4459D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3C2×C411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×#627—21no—
52C2×#626—21no—
53C2×#626—21no—
54C2×#626—21no—
55C2×#625—21no—
56#3798—42no—
57#3798—42no—
58C2×C32×C8—21no—
59C32×C42C2311yescharacteristic
60#3752—21no—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×C4×Dic3C2×C411yescharacteristic
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C3×ΓL(1,𝔽25)—24no—
71Dic3⋊Dic3—21no—
72#3722—21no—
73(C2×D3)⋊Dic3—21no—
74#1484—91noSylow
75C2×#235—61no—
76C2×#235—61no—
77C2×C3×M16—61no—
78C3×C4×D4—31no—
79C2×C3×C42—31no—
80#940—31no—
81#938—31no—
82#930—31no—
83#930—31no—
84#930—61no—
85C4×#67—61no—
86C2×ΓL(1,𝔽25)—21no—
87#895—31no—
88#888—31no—
89#885—61no—
90#884—61no—
91#875—61no—
92#874—31no—
93C4×D12—31no—
94C4×D12—31no—
95C4×D12—61no—
96C4×D12—61no—
97C4×D12C2×D311yescharacteristic
98C42×D3C2×D311yescharacteristic
99#869—31no—
100C3×C4⋊C8—31no—
101C3×#97—61no—
102C3×C4×C8—21no—
103C3×C4×C8—31no—
104C3×C4×C8C2×D311yescharacteristic
105C3×C4×C8C2×D311yescharacteristic
106#830—61no—
107(C2×D3)⋊C8—61no—
108#815—21no—
109C8×Dic3—61no—
110C4⋊(C3⋊C8)—31no—
111C4⋊(C3⋊C8)—31no—
112C4⋊(C3⋊C8)—61no—
113C4⋊(C3⋊C8)C2×D311yescharacteristic
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—21no—
123C4⋊(C3⋊D3)—21no—
124C4⋊(C3⋊D3)—21no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C2×C3×Dic3C22⋊C411yescharacteristic
131C3×D12—21no—
132C3×D12—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—22no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140#627—42no—
141#626—42no—
142#626—42no—
143#626—42no—
144#625—42no—
145C32×C8—22no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149#532—91no—
150#431—91no—
151C4×M16—31no—
152D4⋊C8—31no—
153D4⋊C8—91no—
154D4⋊C8—91no—
155D4⋊C8—91no—
156C2×C3×D4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—61no—
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—61no—
166#235—122no—
167#235—122no—
168#235—122no—
169#235—122no—
170C2×D12—31no—
171C2×D12—31no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12C4×D311yescharacteristic
177C2×C4×D3—21no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—121no—
181C2×C4×D3C4×D311yescharacteristic
182C2×C4×D3D1211yescharacteristic
183C2×C4×D3#6711yescharacteristic
184C2×Dic6—61no—
185C2×Dic6—61no—
186C3×M16—64no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—41no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—31no—
193C3×C22⋊C4—61no—
194C3×C42—21no—
195C3×C42—31no—
196C3×C42—31no—
197C3×C42—31no—
198C3×C42C22×D311yescharacteristic
199C3×C42C22×D311yescharacteristic
200#217—61no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—121no—
208C4⋊Dic3—31no—
209C4⋊Dic3—31no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3C4×D311yescharacteristic
213Dic3⋊C4—61no—
214C4×Dic3C4×D311yescharacteristic
215C4×Dic3D1211yescharacteristic
216C4×Dic3#6711yescharacteristic
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222ΓL(1,𝔽25)—24no—
223C22×C32C2×C22⋊C411yescharacteristic
224C2×C3⋊D3—41no—
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3×D3—21no—
228C2×C3×D3—21no—
229C2×C3×D3—21no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4#13111yescharacteristic
235C32×C4#13111yescharacteristic
236C32×C4AGL(1,ℤ/8)11yescharacteristic
237C32×C4AGL(1,ℤ/8)11yescharacteristic
238C3⋊Dic3—41no—
239C3×Dic3—21no—
240C3×Dic3—21no—
241C3×Dic3—41no—
242C3×Dic3#10412yes—
243C2×#41—181no—
244C2×M16—61no—
245C4⋊Q8—91no—
246#127—91no—
247#124—181no—
248#121—91no—
249#121—91no—
250#121—181no—
251C4×D4—31no—
252C4×D4—91no—
253C4×D4—181no—
254C2×C42—31no—
255C4⋊C8—31no—
256C4⋊C8—91no—
257C22⋊C8—181no—
258#97—61no—
259C4×C8—31no—
260C4×C8—181no—
261C4×C8D3211yescharacteristic
262C23×C3—31no—
263C23×C3—61no—
264C22×D3—21no—
265C22×D3—61no—
266C22×D3—61no—
267C22×D3—121no—
268C22×D3(C2×D3)⋊C411yescharacteristic
269C3×D4—61no—
270C3×D4—61no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—62no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291#67—122no—
292#67—122no—
293#67—122no—
294#67—122no—
295#67—122no—
296C2×Dic3—21no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—121no—
300C2×Dic3(C2×D3)⋊C411yescharacteristic
301C2×Dic3(C2×D3)⋊C411yescharacteristic
302C2×Dic3(C2×D3)⋊C411yescharacteristic
303D12—21no—
304D12—21no—
305D12—62no—
306D12—61no—
307D12—61no—
308D12—61no—
309D12—61no—
310D12—121no—
311D12—122no—
312D12—122no—
313D12—122no—
314C4×D3—21no—
315C4×D3—21no—
316C4×D3—21no—
317C4×D3—21no—
318C4×D3—22no—
319C4×D3—41no—
320C4×D3—41no—
321C4×D3—121no—
322C4×D3—121no—
323C4×D3—121no—
324C4×D3—121no—
325C4×D3—241no—
326C4×D3—241no—
327Dic6—122no—
328Dic6—122no—
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—42no—
332C3×C8—62no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8—121no—
337C3⋊C8—121no—
338C3⋊C8—241no—
339C2×C32#40811yescharacteristic
340C2×C32#41811yescharacteristic
341C2×C32C2×#10411yescharacteristic
342C3⋊D3—81no—
343C3×D3—41no—
344C3×D3—81no—
345#41—362no—
346#41—362no—
347C2×Q8—181no—
348C2×D4—31no—
349C2×D4—91no—
350C2×D4—181no—
351C2×D4—181no—
352C2×D4—181no—
353C2×D4—181no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—61no—
358C22×C4—181no—
359M16—64no—
360C2×C8—21no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—181no—
364C4⋊C4—31no—
365C4⋊C4—91no—
366C4⋊C4—181no—
367C22⋊C4—61no—
368C22⋊C4—181no—
369C22⋊C4—181no—
370C22⋊C4—181no—
371C42—31no—
372C42—31no—
373C42—31no—
374C42C2×D3211yescharacteristic
375C22×C3—21no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3—121no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3D3×C22⋊C411yescharacteristic
383C22×C3C2×(C2×D3)⋊C411yescharacteristic
384C2×D3—21no—
385C2×D3—21no—
386C2×D3—21no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—122no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—121no—
395C2×D3—121no—
396C2×D3—121no—
397C2×D3—241no—
398C2×D3—241no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—32no—
406C3×C4—41no—
407C3×C4—61no—
408C3×C4—61no—
409C3×C4—121no—
410C3×C4#90111yescharacteristic
411C3×C4#90711yescharacteristic
412C3×C4#90711yescharacteristic
413C3×C4#90711yescharacteristic
414C3×C4#90811yescharacteristic
415C3×C4#90811yescharacteristic
416C3×C4#91111yescharacteristic
417C3×C4#91411yescharacteristic
418Dic3—21no—
419Dic3—21no—
420Dic3—41no—
421Dic3—121no—
422Dic3—121no—
423Dic3—241no—
424Dic3#80512yes—
425C32#148411yescharacteristic, complemented, Sylow
426C23—31no—
427C23—61no—
428C23—181no—
429Q8—362no—
430D4—61no—
431D4—61no—
432D4—181no—
433D4—181no—
434D4—362no—
435D4—362no—
436D4—362no—
437D4—362no—
438C2×C4—31no—
439C2×C4—31no—
440C2×C4—31no—
441C2×C4—62no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—121no—
448C2×C4—121no—
449C2×C4—181no—
450C2×C4—361no—
451C2×C4—361no—
452C2×C4C4×D3211yescharacteristic
453C2×C4D3×D1211yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C8—22no—
456C8—62no—
457C8—121no—
458C8—361no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—121no—
463C2×C3—241no—
464C2×C3#472711yescharacteristic
465C2×C3#477011yescharacteristic
466C2×C3D3×#10411yescharacteristic
467C2×C3C2×#80511yescharacteristic
468C2×C3#512911yescharacteristic
469C2×C3#513111yescharacteristic
470D3—41no—
471D3—81no—
472D3—242no—
473D3—241no—
474D3—241no—
475C22—61no—
476C22—61no—
477C22—61no—
478C22—121no—
479C22—121no—
480C22—121no—
481C22—361no—
482C22—361no—
483C22—361no—
484C22D3×(C2×D3)⋊C411yescharacteristic
485C4—21no—
486C4—32no—
487C4—61no—
488C4—61no—
489C4—121no—
490C4—361no—
491C4#6379411yescharacteristic
492C4#6379511yescharacteristic
493C4#6380411yescharacteristic
494C4#6380511yescharacteristic
495C3—21no—
496C3#6817111yescharacteristic, complemented
497C3#6985311yescharacteristic, complemented
498C2—121no—
499C2—241no—
500C2—721no—
501C2D3×#80511yescharacteristic
502C2#1059093911yescharacteristic
503C2#1059095511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radical#10593968C2
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1484
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. C3×C4×ΓL(1,𝔽25)C2semidirect
3. #10590248C2semidirect
4. #10589325C2semidirect
5. C3×#4459C2semidirect
6. #10589082C2semidirect
7. #10589081C2semidirect
34. C4×ΓL(1,𝔽25)D3semidirect
43. #4459D3semidirect
425. C32#1484semidirect
496. C3#68171semidirect
497. C3#69853semidirect

Maximal subgroups

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

subgroupindex
#105939682
C3×C4×ΓL(1,𝔽25)2
#105902482
#105893252
C3×#44592
#105890822
#105890812
#698533
#681713