Finite Group Databasebeta

← #11775813

Subgroups — #11775813

Order 1152.

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

normal subgroups only

This group has 454 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
1D3×#870C211yesmaximal, characteristic
2C3×#4707C211yesmaximal, characteristic
3#10590262C211yesmaximal, characteristic
4#10589331C211yesmaximal, characteristic, complemented
5C3×#4465C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#69863—31nomaximal
9#68363—31nomaximal
10#64079C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C42×D3C2211yescharacteristic
13C3×#870C2211yescharacteristic
14D3×C4⋊Dic3C411yescharacteristic
15D3×C4⋊Dic3C411yescharacteristic
16D3×Dic3⋊C4—21no—
17D3×Dic3⋊C4—21no—
18#63869C411yescharacteristic
19#63869C411yescharacteristic
20#63867—21no—
21#63867—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×C8×Dic3—21no—
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29D3×#125—31no—
30C2×#870—31no—
31C3×C4×M16—31no—
32#4926—31no—
33#4707D311yescharacteristic
34#4705—31no—
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×D3×Dic3—21no—
48C2×D3×Dic3—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—
66#3724—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70Dic3⋊Dic3—21no—
71Dic3⋊Dic3—21no—
72#1528—91noSylow
73C2×C3×M16—61no—
74C3×#125—31no—
75C2×C3×C42—31no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×Dic3⋊C4—61no—
79C2×Dic3⋊C4—61no—
80C2×ΓL(1,𝔽25)—21no—
81D3×C4⋊C4—31no—
82D3×C4⋊C4—31no—
83D3×C4⋊C4—61no—
84D3×C4⋊C4—61no—
85#890—31no—
86#890—31no—
87#889—61no—
88#889—61no—
89C42×D3C2×D311yescharacteristic
90#870—31no—
91#870—31no—
92#870—31no—
93#870—31no—
94#870—61no—
95#870—61no—
96#870—61no—
97#870C2×D311yescharacteristic
98C3×#97—21no—
99C3×#97—31no—
100C3×#97—31no—
101C3×#97C2×D311yescharacteristic
102C3×#97C2×D311yescharacteristic
103C3×C4×C8—61no—
104#830—61no—
105(C2×D3)⋊C8—61no—
106Dic3⋊C8—61no—
107C8×Dic3—21no—
108C4⋊(C3⋊C8)—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113#803C2×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—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3C22⋊C411yescharacteristic
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—41no—
128D3×Dic3—42no—
129D3×Dic3—42no—
130C32×C8—22no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134C2×#125—91no—
135#432—91no—
136C4×M16—31no—
137#330—31no—
138#330—91no—
139#330—91no—
140#330—91no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3C4×D311yescharacteristic
149C2×C4×D3D1211yescharacteristic
150C2×C4×D3#6711yescharacteristic
151C3×M16—64no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—41no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42—31no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3C4×D311yescharacteristic
178C4⋊Dic3C4×D311yescharacteristic
179Dic3⋊C4—21no—
180Dic3⋊C4—21no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—121no—
194Dic3⋊C4—121no—
195C4×Dic3C4×D311yescharacteristic
196C4×Dic3D1211yescharacteristic
197C4×Dic3#6711yescharacteristic
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—121no—
203ΓL(1,𝔽25)—24no—
204C22×C32C2×C22⋊C411yescharacteristic
205C2×C3×D3—21no—
206C2×C3×D3—21no—
207C2×C3×D3#10412yes—
208C32×C4—21no—
209C32×C4—21no—
210C32×C4—21no—
211C3⋊Dic3—41no—
212C3⋊Dic3—41no—
213C3×Dic3—21no—
214C3×Dic3—21no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3#10112yes—
218C2×M16—61no—
219#125—31no—
220#125—91no—
221#125—91no—
222#125—91no—
223#125—181no—
224#125—181no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—181no—
228C2×C4⋊C4—181no—
229C2×C42—31no—
230C4⋊C8—181no—
231C22⋊C8—181no—
232#97—31no—
233#97—31no—
234#97—91no—
235#97D3211yescharacteristic
236C4×C8—61no—
237C23×C3—31no—
238C22×D3(C2×D3)⋊C411yescharacteristic
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—31no—
243C2×C3×C4—31no—
244C2×C3×C4—31no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—121no—
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×C4×D311yescharacteristic
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264C2×Dic3—122no—
265C2×Dic3—122no—
266C2×Dic3(C2×D3)⋊C411yescharacteristic
267C2×Dic3(C2×D3)⋊C411yescharacteristic
268C2×Dic3(C2×D3)⋊C411yescharacteristic
269C4×D3—22no—
270C4×D3—22no—
271C4×D3—41no—
272C4×D3—122no—
273C4×D3—122no—
274C3×C8—22no—
275C3×C8—22no—
276C3×C8—42no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—41no—
281C3⋊C8—121no—
282C3⋊C8—121no—
283C3⋊C8—122no—
284C2×C32C2×#10111yescharacteristic
285C2×C32C2×#10411yescharacteristic
286C2×C32#42111yescharacteristic
287C3×D3—22no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—31no—
291C22×C4—181no—
292C22×C4—181no—
293M16—64no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—61no—
297C2×C8—181no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—91no—
303C4⋊C4—91no—
304C4⋊C4—181no—
305C4⋊C4—181no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C42—31no—
313C42—31no—
314C42—31no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3D3×C22⋊C411yescharacteristic
321C22×C3C2×(C2×D3)⋊C411yescharacteristic
322C2×D3—21no—
323C2×D3—21no—
324C2×D3#80512yes—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—32no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—41no—
335C3×C4—61no—
336C3×C4—61no—
337C3×C4—121no—
338C3×C4—121no—
339Dic3—21no—
340Dic3—21no—
341Dic3—41no—
342Dic3—41no—
343Dic3—121no—
344Dic3—121no—
345Dic3—121no—
346Dic3—121no—
347Dic3—241no—
348Dic3—241no—
349Dic3#82412yes—
350C32#152811yescharacteristic, complemented, Sylow
351C23—31no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—121no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4—362no—
363C2×C4—362no—
364C2×C4C4×D3211yescharacteristic
365C2×C4D3×D1211yescharacteristic
366C2×C4D3×#6711yescharacteristic
367C8—22no—
368C8—62no—
369C8—121no—
370C8—361no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—62no—
375C2×C3D3×#10111yescharacteristic
376C2×C3D3×#10411yescharacteristic
377C2×C3#482111yescharacteristic
378C2×C3C2×#80511yescharacteristic
379C2×C3C2×#82411yescharacteristic
380C2×C3#513911yescharacteristic
381D3—22no—
382C22—32no—
383C22—61no—
384C22—61no—
385C22D3×(C2×D3)⋊C411yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—32no—
390C4—61no—
391C4—61no—
392C4—121no—
393C4—121no—
394C4—361no—
395C4—361no—
396C3—21no—
397C3#6836311yescharacteristic, complemented
398C3#6986311yescharacteristic, complemented
399C2—62no—
400C2D3×#80511yescharacteristic
401C2D3×#82411yescharacteristic
402C2#1059100511yescharacteristic
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#1528
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
350. C32#1528semidirect
397. C3#68363semidirect
398. C3#69863semidirect

Maximal subgroups

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

subgroupindex
D3×#8702
C3×#47072
#105902622
#105893312
C3×#44652
#105890892
#105890882
#698633
#683633