Finite Group Databasebeta

← #11774534

Subgroups — #11774534

Order 1152.

471 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593873C211yesmaximal, characteristic
2C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589322C211yesmaximal, characteristic, complemented
5C3×#4456C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#69856—31nomaximal
9#68235—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C42×D3C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63918C411yescharacteristic
15C4×#627—21no—
16#63867—21no—
17#63866C411yescharacteristic
18#63857C411yescharacteristic
19#63856C411yescharacteristic
20#63855—21no—
21#63851—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#5578—31no—
30#5470—31no—
31C3×C4×M16—31no—
32#4925—31no—
33#4833—31no—
34C4×ΓL(1,𝔽25)D311yescharacteristic
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484—31no—
38#4456—31no—
39#4456—31no—
40#4456—31no—
41#4456—31no—
42#4456—61no—
43#4456D311yescharacteristic, complemented
44C2×#634C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6C2×C411yescharacteristic
49C2×#627—21no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C3×ΓL(1,𝔽25)—24no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72#1485—91noSylow
73C2×C3×M16—61no—
74C3×C4×Q8—31no—
75C2×C3×C42—31no—
76#946—31no—
77#944—31no—
78#926—61no—
79#924—31no—
80#924—31no—
81#924—61no—
82C2×ΓL(1,𝔽25)—21no—
83#897—31no—
84#896—61no—
85#889—61no—
86#888—31no—
87#872—61no—
88C42×D3C2×D311yescharacteristic
89#870—61no—
90#869—31no—
91#869—31no—
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—61no—
95C4×Dic6—61no—
96C4×Dic6—61no—
97C4×Dic6C2×D311yescharacteristic
98C3×C4⋊C8—31no—
99C3×#97—61no—
100C3×C4×C8—21no—
101C3×C4×C8—31no—
102C3×C4×C8C2×D311yescharacteristic
103C3×C4×C8C2×D311yescharacteristic
104#830—61no—
105(C2×D3)⋊C8—61no—
106#815—21no—
107C8×Dic3—61no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—31no—
110C4⋊(C3⋊C8)—61no—
111C4⋊(C3⋊C8)C2×D311yescharacteristic
112C4×C3⋊C8—61no—
113C4×C3⋊C8C2×D311yescharacteristic
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120#634—21no—
121#634—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×C4×D3—21no—
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—22no—
132C3×Dic6—21no—
133C3×Dic6—21no—
134#627—42no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—41no—
139#533—91no—
140#431—91no—
141C4×M16—31no—
142Q8⋊C8—31no—
143Q8⋊C8—91no—
144Q8⋊C8—91no—
145Q8⋊C8—91no—
146C2×C3×Q8—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C2×C4×D3C4×D311yescharacteristic
151C2×C4×D3D1211yescharacteristic
152C2×C4×D3#6711yescharacteristic
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6C4×D311yescharacteristic
159C3×M16—64no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—61no—
167C3×C42—21no—
168C3×C42—31no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—61no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#217—61no—
175#217—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3C4×D311yescharacteristic
186Dic3⋊C4—21no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—121no—
196C4×Dic3—21no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—121no—
200C4×Dic3C4×D311yescharacteristic
201C4×Dic3D1211yescharacteristic
202C4×Dic3#6711yescharacteristic
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208ΓL(1,𝔽25)—24no—
209C22×C32C2×C22⋊C411yescharacteristic
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C32×C4—21no—
214C32×C4#13111yescharacteristic
215C32×C4#13111yescharacteristic
216C32×C4#13711yescharacteristic
217C32×C4#13711yescharacteristic
218C3⋊Dic3—41no—
219C3⋊Dic3—41no—
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3#10412yes—
225C2×M16—61no—
226C4⋊Q8—91no—
227C4⋊Q8—91no—
228#125—181no—
229C22⋊Q8—91no—
230C22⋊Q8—91no—
231C22⋊Q8—181no—
232C4×Q8—31no—
233C4×Q8—91no—
234C4×Q8—181no—
235#117—181no—
236C2×C42—31no—
237C4⋊C8—31no—
238C4⋊C8—91no—
239C22⋊C8—181no—
240#97—61no—
241C4×C8—31no—
242C4×C8—181no—
243C4×C8D3211yescharacteristic
244C23×C3—31no—
245C22×D3(C2×D3)⋊C411yescharacteristic
246C3×Q8—61no—
247C3×Q8—61no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—62no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—121no—
274C2×Dic3—121no—
275C2×Dic3(C2×D3)⋊C411yescharacteristic
276C2×Dic3(C2×D3)⋊C411yescharacteristic
277C2×Dic3(C2×D3)⋊C411yescharacteristic
278C4×D3—21no—
279C4×D3—21no—
280C4×D3—21no—
281C4×D3—21no—
282C4×D3—22no—
283Dic6—21no—
284Dic6—21no—
285Dic6—62no—
286Dic6—61no—
287Dic6—61no—
288Dic6—61no—
289Dic6—61no—
290Dic6—121no—
291Dic6—122no—
292Dic6—122no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—42no—
296C3×C8—62no—
297C3×C8—121no—
298C3⋊C8—22no—
299C3⋊C8—41no—
300C3⋊C8—121no—
301C3⋊C8—121no—
302C3⋊C8—241no—
303C2×C32#40811yescharacteristic
304C2×C32#41911yescharacteristic
305C2×C32C2×#10411yescharacteristic
306C3×D3—41no—
307C2×Q8—31no—
308C2×Q8—91no—
309C2×Q8—181no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313M16—64no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—61no—
320C4⋊C4—91no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C42—31no—
330C42—31no—
331C42—31no—
332C42—61no—
333C42—181no—
334C42C2×D3211yescharacteristic
335C22×C3—21no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3D3×C22⋊C411yescharacteristic
340C22×C3C2×(C2×D3)⋊C411yescharacteristic
341C2×D3—21no—
342C2×D3—21no—
343C2×D3—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—32no—
351C3×C4—41no—
352C3×C4—61no—
353C3×C4—61no—
354C3×C4—121no—
355C3×C4—121no—
356C3×C4#90111yescharacteristic
357C3×C4#90711yescharacteristic
358C3×C4#90711yescharacteristic
359C3×C4#90711yescharacteristic
360C3×C4#90911yescharacteristic
361C3×C4#90911yescharacteristic
362C3×C4#91511yescharacteristic
363C3×C4#91811yescharacteristic
364Dic3—21no—
365Dic3—21no—
366Dic3—41no—
367Dic3—41no—
368Dic3—122no—
369Dic3—121no—
370Dic3—121no—
371Dic3—121no—
372Dic3—121no—
373Dic3—241no—
374Dic3#80512yes—
375C32#148511yescharacteristic, complemented, Sylow
376C23—31no—
377Q8—61no—
378Q8—61no—
379Q8—181no—
380Q8—181no—
381Q8—362no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—31no—
385C2×C4—62no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—181no—
393C2×C4—181no—
394C2×C4C4×D3211yescharacteristic
395C2×C4D3×D1211yescharacteristic
396C2×C4D3×#6711yescharacteristic
397C8—22no—
398C8—62no—
399C8—121no—
400C8—361no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—121no—
405C2×C3#472711yescharacteristic
406C2×C3#480211yescharacteristic
407C2×C3D3×#10411yescharacteristic
408C2×C3C2×#80511yescharacteristic
409C2×C3#512011yescharacteristic
410C2×C3#512911yescharacteristic
411D3—41no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22D3×(C2×D3)⋊C411yescharacteristic
416C4—21no—
417C4—32no—
418C4—61no—
419C4—61no—
420C4—121no—
421C4—121no—
422C4—361no—
423C4—361no—
424C4#6380011yescharacteristic
425C4#6380111yescharacteristic
426C4#6380411yescharacteristic
427C4#6380511yescharacteristic
428C3—21no—
429C3#6823511yescharacteristic, complemented
430C3#6985611yescharacteristic, complemented
431C2—121no—
432C2D3×#80511yescharacteristic
433C2#1059094811yescharacteristic
434C2#1059095511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1485
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
4. #10589322C2semidirect
5. C3×#4456C2semidirect
6. #10589085C2semidirect
7. #10589084C2semidirect
43. #4456D3semidirect
375. C32#1485semidirect
429. C3#68235semidirect
430. C3#69856semidirect

Maximal subgroups

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

subgroupindex
#105938732
C3×C4×ΓL(1,𝔽25)2
#105902482
#105893222
C3×#44562
#105890852
#105890842
#698563
#682353