Finite Group Databasebeta

← #11774841

Subgroups — #11774841

Order 1152.

467 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593974C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70499—31nomaximal
9#68178—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C4×D12C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14#63908C411yescharacteristic
15#63905—21no—
16C4×#625—21no—
17#63869C411yescharacteristic
18#63860C411yescharacteristic
19#63859—21no—
20#63857C411yescharacteristic
21#63855—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×Dic3⋊C8—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29#5557—31no—
30#5479—31no—
31C3×#423—31no—
32#4925—31no—
33#4837D311yescharacteristic, complemented
34#4685—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42#4483D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C3×ΓL(1,𝔽25)—42no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72#1495—91noSylow
73C2×C3×M16—61no—
74C3×C4×D4—31no—
75C2×C3×C42—31no—
76#938—31no—
77#936—31no—
78#930—31no—
79#929—61no—
80C4×#67—61no—
81C4×#67—61no—
82#926—61no—
83#924—31no—
84C2×ΓL(1,𝔽25)—21no—
85#897—31no—
86#890—31no—
87#883—61no—
88#879—61no—
89#876—61no—
90#875—31no—
91C4×D12C2×D311yescharacteristic
92#872—61no—
93C42×D3C2×D311yescharacteristic
94#870—31no—
95C4×Dic6—31no—
96C4×Dic6—31no—
97C4×Dic6—61no—
98C3×C4⋊C8—21no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—61no—
101C3×C4⋊C8C2×D311yescharacteristic
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4×C8—31no—
104#830—61no—
105(C2×D3)⋊C8—61no—
106Dic3⋊C8—21no—
107Dic3⋊C8—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8—31no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—61no—
113C4×C3⋊C8C2×D311yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121#634—21no—
122#634—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×D12—21no—
128C3×D12—21no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136#625—42no—
137C32×C8—41no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141#529—91no—
142#431—91no—
143#423—31no—
144Q8⋊C8—91no—
145Q8⋊C8—91no—
146D4⋊C8—31no—
147D4⋊C8—91no—
148C2×C3×D4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—61no—
153C2×#67—61no—
154C2×#67—61no—
155C2×D12C4×D311yescharacteristic
156C2×C4×D3—21no—
157C2×C4×D3C4×D311yescharacteristic
158C2×C4×D3D1211yescharacteristic
159C2×C4×D3#6711yescharacteristic
160C2×Dic6—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C3×M16—122no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—31no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—61no—
178#217—61no—
179#217—61no—
180#217—61no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3C4×D311yescharacteristic
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—121no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—121no—
202C4×Dic3C4×D311yescharacteristic
203C4×Dic3D1211yescharacteristic
204C4×Dic3#6711yescharacteristic
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210ΓL(1,𝔽25)—42no—
211C22×C32C2×C22⋊C411yescharacteristic
212C2×C3×D3—21no—
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4#13111yescharacteristic
220C32×C4#13111yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C32×C4#13711yescharacteristic
223C3⋊Dic3—41no—
224C3⋊Dic3—41no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C2×M16—61no—
230#126—181no—
231#125—91no—
232#124—91no—
233#123—181no—
234C22⋊Q8—91no—
235#121—91no—
236C4×Q8—91no—
237C4×D4—31no—
238C4×D4—181no—
239#117—181no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—61no—
243C4⋊C8—181no—
244C4⋊C8D3211yescharacteristic
245C22⋊C8—181no—
246C4×C8—31no—
247C4×C8—91no—
248C23×C3—31no—
249C23×C3—61no—
250C22×D3—21no—
251C22×D3(C2×D3)⋊C411yescharacteristic
252C3×D4—61no—
253C3×D4—61no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274#67—122no—
275#67—122no—
276C2×Dic3—21no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3(C2×D3)⋊C411yescharacteristic
284C2×Dic3(C2×D3)⋊C411yescharacteristic
285C2×Dic3(C2×D3)⋊C411yescharacteristic
286D12—21no—
287D12—21no—
288C4×D3—21no—
289C4×D3—21no—
290C4×D3—21no—
291C4×D3—21no—
292C4×D3—41no—
293C4×D3—41no—
294C4×D3—41no—
295Dic6—62no—
296Dic6—61no—
297Dic6—61no—
298Dic6—61no—
299Dic6—61no—
300Dic6—121no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—81no—
304C3×C8—121no—
305C3×C8—121no—
306C3⋊C8—41no—
307C3⋊C8—41no—
308C3⋊C8—121no—
309C3⋊C8—121no—
310C3⋊C8—122no—
311C2×C32#40811yescharacteristic
312C2×C32#41711yescharacteristic
313C2×C32#42111yescharacteristic
314C3×D3—41no—
315C3×D3—81no—
316C2×Q8—91no—
317C2×D4—31no—
318C2×D4—181no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323M16—122no—
324C2×C8—21no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—31no—
329C4⋊C4—91no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C22⋊C4—61no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C42—31no—
340C42—31no—
341C42—31no—
342C42—181no—
343C42C2×D3211yescharacteristic
344C22×C3—21no—
345C22×C3—61no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3D3×C22⋊C411yescharacteristic
352C22×C3C2×(C2×D3)⋊C411yescharacteristic
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—21no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—41no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—61no—
367C3×C4—61no—
368C3×C4—61no—
369C3×C4—121no—
370C3×C4#90111yescharacteristic
371C3×C4#90711yescharacteristic
372C3×C4#90711yescharacteristic
373C3×C4#90711yescharacteristic
374C3×C4#91111yescharacteristic
375C3×C4#91511yescharacteristic
376C3×C4#93211yescharacteristic
377C3×C4#94211yescharacteristic
378Dic3—21no—
379Dic3—21no—
380Dic3—21no—
381Dic3—41no—
382Dic3—122no—
383Dic3—121no—
384Dic3—121no—
385Dic3—121no—
386Dic3—121no—
387Dic3—241no—
388C32#149511yescharacteristic, complemented, Sylow
389C23—31no—
390C23—61no—
391Q8—181no—
392Q8—181no—
393D4—61no—
394D4—61no—
395D4—362no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4C4×D3211yescharacteristic
410C2×C4D3×D1211yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—41no—
413C8—121no—
414C8—121no—
415C8—361no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—121no—
420C2×C3—241no—
421C2×C3#472711yescharacteristic
422C2×C3#477111yescharacteristic
423C2×C3#482111yescharacteristic
424C2×C3#496611yescharacteristic
425C2×C3#512911yescharacteristic
426C2×C3#513911yescharacteristic
427D3—41no—
428D3—81no—
429C22—61no—
430C22—61no—
431C22—61no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22D3×(C2×D3)⋊C411yescharacteristic
436C4—21no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—121no—
441C4—361no—
442C4—361no—
443C4#6380411yescharacteristic
444C4#6380511yescharacteristic
445C4#6393211yescharacteristic
446C4#6394611yescharacteristic
447C3—21no—
448C3#6817811yescharacteristic, complemented
449C3#7049911yescharacteristic, complemented
450C2—121no—
451C2—241no—
452C2#1059060711yescharacteristic
453C2#1059095511yescharacteristic
454C2#1059100511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#63908C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1495
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×#4837C2semidirect
3. #10590261C2semidirect
4. #10589350C2semidirect
5. C3×#4483C2semidirect
6. #10589085C2semidirect
7. #10589080C2semidirect
33. #4837D3semidirect
42. #4483D3semidirect
388. C32#1495semidirect
448. C3#68178semidirect
449. C3#70499semidirect

Maximal subgroups

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

subgroupindex
#105939742
C3×#48372
#105902612
#105893502
C3×#44832
#105890852
#105890802
#704993
#681783