Finite Group Databasebeta

← #11775724

Subgroups — #11775724

Order 1152.

498 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593921C211yesmaximal, characteristic
2C3×#4707C211yesmaximal, characteristic, complemented
3D3×#803C211yesmaximal, characteristic, complemented
4#10589331C211yesmaximal, characteristic, complemented
5C3×#4464C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#69858—31nomaximal
9#68341—31nomaximal
10#64079C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×#875C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14#63908C411yescharacteristic
15#63905—21no—
16Dic3×D12C411yescharacteristic
17#63879—21no—
18#63877—21no—
19#63859—21no—
20#63856C411yescharacteristic
21Dic3×Dic6C411yescharacteristic
22C2×D3×C3⋊C8—21no—
23C32×#97C2211yescharacteristic
24#63630C2211yescharacteristic
25C3×C8×Dic3—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28#63554—21no—
29#5680—31no—
30#5479—31no—
31C3×C4×M16—31no—
32C2×#803—31no—
33#4707D311yescharacteristic, complemented
34D3×#97—31no—
35C3×#329—31no—
36#4540—31no—
37#4465—31no—
38#4465—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6C2×C411yescharacteristic
49C2×#625—21no—
50C2×D3×Dic3—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C3×ΓL(1,𝔽25)—24no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72D3×C3⋊C8—24no—
73#1524—91noSylow
74C2×C3×M16—61no—
75C3×#124—31no—
76C2×C3×C42—31no—
77#946—31no—
78Q8×Dic3—31no—
79#938—31no—
80D4×Dic3—31no—
81#930—31no—
82#929—61no—
83C4×#67—61no—
84#924—31no—
85C22×C3⋊C8—61no—
86C2×ΓL(1,𝔽25)—21no—
87C2×D3×C8—61no—
88#883—61no—
89#67⋊C4—61no—
90#879—61no—
91#877—61no—
92#876—61no—
93#875C2×D311yescharacteristic
94C4×D12—31no—
95#872—61no—
96C42×D3C2×D311yescharacteristic
97#870—31no—
98#870—31no—
99#870—61no—
100C4×Dic6—31no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97—31no—
104C3×#97C2×D311yescharacteristic
105C3×#97C2×D311yescharacteristic
106C3×C4×C8—61no—
107#815—61no—
108C8×Dic3—21no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C3×D12—41no—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129C3×C4×D3—41no—
130C3×Dic6—41no—
131#625—42no—
132D3×Dic3—42no—
133C32×C8—22no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—22no—
136C3×C3⋊C8—22no—
137#529—91no—
138C4×M16—31no—
139C2×#97—91no—
140#330—91no—
141#330—91no—
142#329—31no—
143#329—91no—
144C2×C3×Q8—31no—
145C2×C3×D4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C2×#67—61no—
150C2×#67—61no—
151C22×Dic3—61no—
152C2×D12C4×D311yescharacteristic
153C2×C4×D3—61no—
154C2×C4×D3C4×D311yescharacteristic
155C2×C4×D3D1211yescharacteristic
156C2×C4×D3#6711yescharacteristic
157C2×Dic6C4×D311yescharacteristic
158C3×M16—64no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C22⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—31no—
168C3×C42—31no—
169C3×C42—31no—
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172#217—61no—
173#217—61no—
174#217—61no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—121no—
195Dic3⋊C4—121no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3C4×D311yescharacteristic
199C4×Dic3D1211yescharacteristic
200C4×Dic3#6711yescharacteristic
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—121no—
207ΓL(1,𝔽25)—24no—
208D3×C8—64no—
209C22×C32C2×C22⋊C411yescharacteristic
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3#10412yes—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—21no—
219C3⋊Dic3—41no—
220C3⋊Dic3—41no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—41no—
224C3×Dic3#10412yes—
225C2×M16—61no—
226C22×C8—181no—
227#126—181no—
228#125—91no—
229#124—31no—
230#123—181no—
231C22⋊Q8—91no—
232#121—91no—
233C4×Q8—91no—
234C4×D4—91no—
235C4×D4—181no—
236#117—181no—
237C2×C42—31no—
238#97—31no—
239#97—31no—
240#97—91no—
241#97—181no—
242#97D3211yescharacteristic
243C4×C8—61no—
244C23×C3—31no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3(C2×D3)⋊C411yescharacteristic
248C3×Q8—121no—
249C3×D4—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—62no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—122no—
267#67—122no—
268C2×Dic3—21no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—61no—
273C2×Dic3—121no—
274C2×Dic3—121no—
275C2×Dic3—122no—
276C2×Dic3(C2×D3)⋊C411yescharacteristic
277C2×Dic3(C2×D3)⋊C411yescharacteristic
278C2×Dic3(C2×D3)⋊C411yescharacteristic
279D12—41no—
280C4×D3—22no—
281C4×D3—22no—
282C4×D3—41no—
283C4×D3—122no—
284Dic6—41no—
285C3×C8—22no—
286C3×C8—22no—
287C3×C8—42no—
288C3×C8—62no—
289C3×C8—62no—
290C3⋊C8—22no—
291C3⋊C8—22no—
292C3⋊C8—62no—
293C3⋊C8—62no—
294C3⋊C8—122no—
295C2×C32#41311yescharacteristic
296C2×C32C2×#10411yescharacteristic
297C2×C32C2×#10411yescharacteristic
298C3×D3—22no—
299C3×D3—81no—
300C2×Q8—31no—
301C2×D4—31no—
302C2×D4—181no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—181no—
307M16—64no—
308C2×C8—21no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—184no—
312C2×C8—181no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C22⋊C4—61no—
320C22⋊C4—61no—
321C22⋊C4—181no—
322C22⋊C4—181no—
323C22⋊C4—181no—
324C42—31no—
325C42—31no—
326C42—31no—
327C42—181no—
328C42C2×D3211yescharacteristic
329C22×C3—21no—
330C22×C3—32no—
331C22×C3—61no—
332C22×C3—61no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3D3×C22⋊C411yescharacteristic
337C22×C3C2×(C2×D3)⋊C411yescharacteristic
338C2×D3—21no—
339C2×D3—21no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3#80512yes—
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—41no—
353C3×C4—41no—
354C3×C4—61no—
355C3×C4—61no—
356C3×C4—121no—
357Dic3—21no—
358Dic3—21no—
359Dic3—41no—
360Dic3—121no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—241no—
365Dic3—241no—
366Dic3#82512yes—
367C32#152411yescharacteristic, complemented, Sylow
368C23—31no—
369C23—61no—
370Q8—121no—
371D4—121no—
372D4—362no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—31no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—61no—
379C2×C4—121no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—362no—
383C2×C4C4×D3211yescharacteristic
384C2×C4D3×D1211yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C8—22no—
387C8—62no—
388C8—62no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—62no—
394C2×C3—241no—
395C2×C3#474511yescharacteristic
396C2×C3D3×#10411yescharacteristic
397C2×C3D3×#10411yescharacteristic
398C2×C3C2×#80511yescharacteristic
399C2×C3#513211yescharacteristic
400C2×C3C2×#82511yescharacteristic
401D3—22no—
402D3—81no—
403C22—32no—
404C22—61no—
405C22—61no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22D3×(C2×D3)⋊C411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—32no—
414C4—61no—
415C4—61no—
416C4—121no—
417C4—361no—
418C4—361no—
419C3—21no—
420C3#6834111yescharacteristic, complemented
421C3#6985811yescharacteristic, complemented
422C2—62no—
423C2—241no—
424C2D3×#80511yescharacteristic
425C2D3×#82511yescharacteristic
426C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radical#63908C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#4707C2semidirect
3. D3×#803C2semidirect
4. #10589331C2semidirect
5. C3×#4464C2semidirect
6. #10589089C2semidirect
7. #10589086C2semidirect
33. #4707D3semidirect
43. #4464D3semidirect
367. C32#1524semidirect
420. C3#68341semidirect
421. C3#69858semidirect

Maximal subgroups

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

subgroupindex
#105939212
C3×#47072
D3×#8032
#105893312
C3×#44642
#105890892
#105890862
#698583
#683413