Finite Group Databasebeta

← #11775762

Subgroups — #11775762

Order 1152.

482 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 102 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#10593874C211yesmaximal, characteristic
2C3×#4707C211yesmaximal, characteristic
3#10590334C211yesmaximal, characteristic
4#10589331C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#69862—31nomaximal
9#68362—31nomaximal
10#64079C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C42×D3C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63918C411yescharacteristic
15#63918C411yescharacteristic
16#63851—21no—
17#63851—21no—
18#63841C411yescharacteristic
19#63841C411yescharacteristic
20#63837—21no—
21#63837—21no—
22C2×#3711—21no—
23C32×#97C2211yescharacteristic
24#63630C2211yescharacteristic
25C3×C8×Dic3—21no—
26C3×#803C2211yescharacteristic
27C3×#803C2211yescharacteristic
28Dic3×C3⋊C8—21no—
29#5688—31no—
30#5470—31no—
31C3×C4×M16—31no—
32C4×#208—31no—
33#4707—31no—
34#4707D311yescharacteristic
35C3×#330—31no—
36#4543—31no—
37#4465—31no—
38#4465—31no—
39#4465—31no—
40#4465—31no—
41#4465—31no—
42#4465—61no—
43#4465D311yescharacteristic, complemented
44C2×C3×C4×D3C2×C411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×#627—21no—
48C2×#627—21no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54#3750—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×C4⋊Dic3C2×C411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊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—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71Dic32—21no—
72#3711—24no—
73#1526—91noSylow
74C2×C3×M16—61no—
75C3×#125—31no—
76C2×C3×C42—31no—
77#926—31no—
78#926—31no—
79#924—61no—
80#924—61no—
81C2×#208—61no—
82C2×ΓL(1,𝔽25)—21no—
83C2×ΓL(1,𝔽25)—61no—
84#896—61no—
85#896—61no—
86#892—31no—
87#892—31no—
88#888—31no—
89#888—31no—
90#887—61no—
91#887—61no—
92C42×D3C2×D311yescharacteristic
93#870—31no—
94#870—31no—
95#870—61no—
96#870C2×D311yescharacteristic
97#869—31no—
98#869—31no—
99C4×Dic6—61no—
100C4×Dic6—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97—31no—
104C3×#97C2×D311yescharacteristic
105C3×#97C2×D311yescharacteristic
106C3×C4×C8—61no—
107C8×Dic3—21no—
108C8×Dic3—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113#803C2×D311yescharacteristic
114C4×C3⋊C8—61no—
115C22×C3×D3C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
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×C4×D3—22no—
127C3×C4×D3—22no—
128C3×C4×D3—22no—
129#627—42no—
130#627—42no—
131C32×C8—22no—
132C3⋊(C3⋊C8)—22no—
133C3×C3⋊C8—22no—
134C3×C3⋊C8—22no—
135#533—91no—
136C4×M16—31no—
137C4×M16—91no—
138#330—31no—
139#330—91no—
140#330—91no—
141#330—91no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C2×C4×D3C4×D311yescharacteristic
146C2×C4×D3D1211yescharacteristic
147C2×C4×D3#6711yescharacteristic
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C3×M16—64no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8—61no—
157C2×C3×C8—61no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C42—21no—
163C3×C42—31no—
164C3×C42—31no—
165C3×C42—31no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—61no—
169#217—61no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—61no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3C4×D311yescharacteristic
181C4⋊Dic3C4×D311yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—21no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—121no—
191Dic3⋊C4—121no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C4×Dic3C4×D311yescharacteristic
197C4×Dic3D1211yescharacteristic
198C4×Dic3#6711yescharacteristic
199#208—64no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—121no—
205ΓL(1,𝔽25)—24no—
206ΓL(1,𝔽25)—64no—
207C22×C32C2×C22⋊C411yescharacteristic
208C2×C3×D3—21no—
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C32×C4—21no—
212C32×C4—21no—
213C32×C4—21no—
214C3⋊Dic3—41no—
215C3⋊Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3#10112yes—
219C3×Dic3#10412yes—
220C3×Dic3#10412yes—
221C2×M16—61no—
222C2×M16—181no—
223C4⋊Q8—91no—
224C4⋊Q8—91no—
225#125—31no—
226#125—91no—
227C22⋊Q8—181no—
228C22⋊Q8—181no—
229C4×Q8—181no—
230C4×Q8—181no—
231#117—91no—
232#117—91no—
233C2×C42—31no—
234#97—31no—
235#97—31no—
236#97—91no—
237#97D3211yescharacteristic
238C4×C8—61no—
239C4×C8—181no—
240C23×C3—31no—
241C22×D3(C2×D3)⋊C411yescharacteristic
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—62no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267C2×Dic3(C2×D3)⋊C411yescharacteristic
268C2×Dic3(C2×D3)⋊C411yescharacteristic
269C2×Dic3(C2×D3)⋊C411yescharacteristic
270C4×D3—22no—
271C4×D3—22no—
272C4×D3—22no—
273Dic6—122no—
274Dic6—122no—
275Dic6—122no—
276Dic6—122no—
277C3×C8—22no—
278C3×C8—22no—
279C3×C8—42no—
280C3×C8—62no—
281C3×C8—62no—
282C3⋊C8—22no—
283C3⋊C8—22no—
284C3⋊C8—62no—
285C3⋊C8—62no—
286C3⋊C8—122no—
287C2×C32C2×#10111yescharacteristic
288C2×C32C2×#10411yescharacteristic
289C2×C32C2×#10411yescharacteristic
290C3×D3—41no—
291C2×Q8—181no—
292C2×Q8—181no—
293C22×C4—31no—
294C22×C4—31no—
295C22×C4—31no—
296M16—64no—
297M16—184no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—181no—
302C4⋊C4—31no—
303C4⋊C4—31no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—91no—
307C4⋊C4—91no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C22⋊C4—181no—
313C22⋊C4—181no—
314C42—31no—
315C42—31no—
316C42—31no—
317C42—181no—
318C42—181no—
319C42C2×D3211yescharacteristic
320C22×C3—21no—
321C22×C3—61no—
322C22×C3—61no—
323C22×C3—61no—
324C22×C3D3×C22⋊C411yescharacteristic
325C22×C3C2×(C2×D3)⋊C411yescharacteristic
326C2×D3—21no—
327C2×D3—21no—
328C2×D3—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—32no—
336C3×C4—32no—
337C3×C4—32no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—121no—
342C3×C4—121no—
343Dic3—41no—
344Dic3—41no—
345Dic3—121no—
346Dic3—121no—
347Dic3—121no—
348Dic3—121no—
349Dic3—241no—
350Dic3—241no—
351Dic3#80512yes—
352Dic3#82412yes—
353Dic3#82512yes—
354C32#152611yescharacteristic, complemented, Sylow
355C23—31no—
356Q8—362no—
357Q8—362no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—181no—
367C2×C4—181no—
368C2×C4C4×D3211yescharacteristic
369C2×C4D3×D1211yescharacteristic
370C2×C4D3×#6711yescharacteristic
371C8—22no—
372C8—62no—
373C8—62no—
374C8—182no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—121no—
379C2×C3D3×#10111yescharacteristic
380C2×C3D3×#10411yescharacteristic
381C2×C3D3×#10411yescharacteristic
382C2×C3C2×#80511yescharacteristic
383C2×C3C2×#82411yescharacteristic
384C2×C3C2×#82511yescharacteristic
385D3—41no—
386C22—61no—
387C22—61no—
388C22—61no—
389C22D3×(C2×D3)⋊C411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—32no—
394C4—32no—
395C4—32no—
396C4—121no—
397C4—121no—
398C4—361no—
399C4—361no—
400C3—21no—
401C3#6836211yescharacteristic, complemented
402C3#6986211yescharacteristic, complemented
403C2—121no—
404C2D3×#80511yescharacteristic
405C2D3×#82411yescharacteristic
406C2D3×#82511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenter#97D32
hypocenterC32#1526
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
4. #10589331C2semidirect
5. C3×#4465C2semidirect
6. #10589089C2semidirect
7. #10589088C2semidirect
43. #4465D3semidirect
354. C32#1526semidirect
401. C3#68362semidirect
402. C3#69862semidirect

Maximal subgroups

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

subgroupindex
#105938742
C3×#47072
#105903342
#105893312
C3×#44652
#105890892
#105890882
#698623
#683623