Finite Group Databasebeta

← #11774777

Subgroups — #11774777

Order 1152.

499 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593873C211yesmaximal, characteristic
2C3×C4×D3×C8C211yesmaximal, characteristic
3#10590336C211yesmaximal, characteristic
4#10589322C211yesmaximal, characteristic, complemented
5C3×#4456C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#69738—31nomaximal
9#68240—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×D3×C8—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—
22C2×#3711—21no—
23C32×C4×C8C2211yescharacteristic
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C3×C8×Dic3—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28Dic3⋊(C3⋊C8)—21no—
29#5578—31no—
30#5470—31no—
31C2×C3×C4×C8—31no—
32#4924—31no—
33#4837—31no—
34C4×D3×C8D311yescharacteristic
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×D3×C8—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#3711—42no—
73#1493—91noSylow
74C22×C3×C8—61no—
75C3×C4×Q8—31no—
76C2×C3×C42—31no—
77#946—31no—
78#944—31no—
79#926—61no—
80#924—31no—
81#924—31no—
82#924—61no—
83C2×#208—61no—
84C2×ΓL(1,𝔽25)—61no—
85C2×D3×C8—21no—
86#897—31no—
87#896—61no—
88#889—61no—
89#888—31no—
90#872—61no—
91C42×D3C2×D311yescharacteristic
92#870—61no—
93#869—31no—
94#869—31no—
95C4×Dic6—31no—
96C4×Dic6—31no—
97C4×Dic6—61no—
98C4×Dic6—61no—
99C4×Dic6—61no—
100C4×Dic6C2×D311yescharacteristic
101C3×C4⋊C8—31no—
102C3×C4×C8—21no—
103C3×C4×C8—31no—
104C3×C4×C8—61no—
105C3×C4×C8C2×D311yescharacteristic
106C3×C4×C8C2×D311yescharacteristic
107Dic3⋊C8—61no—
108C8×Dic3—21no—
109C4⋊(C3⋊C8)—31no—
110C4⋊(C3⋊C8)—31no—
111C4⋊(C3⋊C8)—61no—
112C4⋊(C3⋊C8)—61no—
113C4⋊(C3⋊C8)C2×D311yescharacteristic
114C4×C3⋊C8C2×D311yescharacteristic
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×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—22no—
131C3×C4×D3SD1612yes—
132C3×C4×D3Q1612yes—
133C3×Dic6—21no—
134C3×Dic6—21no—
135#627—42no—
136C32×C8—22no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140#533—91no—
141#423—91no—
142C2×C4×C8—31no—
143Q8⋊C8—31no—
144Q8⋊C8—91no—
145Q8⋊C8—91no—
146Q8⋊C8—91no—
147C2×C3×Q8—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C2×C4×D3C4×D311yescharacteristic
152C2×C4×D3D1211yescharacteristic
153C2×C4×D3#6711yescharacteristic
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×Dic6C4×D311yescharacteristic
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—64no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C42—21no—
169C3×C42—31no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—61no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#217—61no—
176#217—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3C4×D311yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—121no—
197C4×Dic3—21no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—121no—
201C4×Dic3C4×D311yescharacteristic
202C4×Dic3D1211yescharacteristic
203C4×Dic3#6711yescharacteristic
204#208—122no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210ΓL(1,𝔽25)—122no—
211D3×C8—24no—
212C22×C32C2×C22⋊C411yescharacteristic
213C2×C3×D3—21no—
214C2×C3×D3—21no—
215C2×C3×D3#10312yes—
216C32×C4—21no—
217C32×C4#13111yescharacteristic
218C32×C4#13111yescharacteristic
219C32×C4C2×SD1611yescharacteristic
220C32×C4C2×Q1611yescharacteristic
221C3⋊Dic3—41no—
222C3⋊Dic3—41no—
223C3×Dic3—21no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3#10312yes—
227C3×Dic3#10412yes—
228C2×M16—181no—
229C22×C8—61no—
230C4⋊Q8—91no—
231C4⋊Q8—91no—
232#125—181no—
233C22⋊Q8—91no—
234C22⋊Q8—91no—
235C22⋊Q8—181no—
236C4×Q8—31no—
237C4×Q8—91no—
238C4×Q8—181no—
239#117—181no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—91no—
243C4⋊C8—181no—
244C4×C8—31no—
245C4×C8—61no—
246C4×C8D3211yescharacteristic
247C23×C3—31no—
248C22×D3(C2×D3)⋊C411yescharacteristic
249C3×Q8—61no—
250C3×Q8—61no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—32no—
257C2×C3×C4—32no—
258C2×C3×C4—31no—
259C2×C3×C4—62no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278C2×Dic3(C2×D3)⋊C411yescharacteristic
279C2×Dic3(C2×D3)⋊C411yescharacteristic
280C2×Dic3(C2×D3)⋊C411yescharacteristic
281C4×D3—21no—
282C4×D3—21no—
283C4×D3—22no—
284C4×D3#20412yes—
285C4×D3Dic1212yes—
286Dic6—21no—
287Dic6—21no—
288Dic6—62no—
289Dic6—61no—
290Dic6—61no—
291Dic6—61no—
292Dic6—61no—
293Dic6—121no—
294Dic6—122no—
295Dic6—122no—
296C3×C8—22no—
297C3×C8—22no—
298C3×C8—42no—
299C3×C8—62no—
300C3×C8—121no—
301C3⋊C8—22no—
302C3⋊C8—41no—
303C3⋊C8—121no—
304C3⋊C8—121no—
305C3⋊C8—241no—
306C2×C32#40811yescharacteristic
307C2×C32C2×#10311yescharacteristic
308C2×C32C2×#10411yescharacteristic
309C3×D3—22no—
310C2×Q8—31no—
311C2×Q8—91no—
312C2×Q8—181no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—31no—
316M16—362no—
317C2×C8—21no—
318C2×C8—64no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—91no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C42—31no—
334C42—31no—
335C42—31no—
336C42—61no—
337C42—181no—
338C42C2×D3211yescharacteristic
339C22×C3—21no—
340C22×C3—32no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3D3×C22⋊C411yescharacteristic
344C22×C3C2×(C2×D3)⋊C411yescharacteristic
345C2×D3—21no—
346C2×D3—21no—
347C2×D3#81612yes—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—32no—
355C3×C4—32no—
356C3×C4—41no—
357C3×C4—61no—
358C3×C4—121no—
359C3×C4—121no—
360C3×C4#90111yescharacteristic
361C3×C4#90111yescharacteristic
362C3×C4#90111yescharacteristic
363C3×C4C2×#20411yescharacteristic
364C3×C4C2×Dic1211yescharacteristic
365C3×C4#90711yescharacteristic
366C3×C4D3×SD1611yescharacteristic
367C3×C4D3×Q1611yescharacteristic
368Dic3—21no—
369Dic3—41no—
370Dic3—41no—
371Dic3—122no—
372Dic3—121no—
373Dic3—121no—
374Dic3—121no—
375Dic3—121no—
376Dic3—241no—
377Dic3#80512yes—
378Dic3#81612yes—
379C32#149311yescharacteristic, complemented, Sylow
380C23—31no—
381Q8—61no—
382Q8—61no—
383Q8—181no—
384Q8—181no—
385Q8—362no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—31no—
391C2×C4—62no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—181no—
397C2×C4—181no—
398C2×C4C4×D3211yescharacteristic
399C2×C4D3×D1211yescharacteristic
400C2×C4D3×#6711yescharacteristic
401C8—22no—
402C8—62no—
403C8—121no—
404C8—361no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—62no—
409C2×C3#472711yescharacteristic
410C2×C3D3×#10311yescharacteristic
411C2×C3D3×#10411yescharacteristic
412C2×C3C2×#80511yescharacteristic
413C2×C3C2×#81611yescharacteristic
414C2×C3#511011yescharacteristic
415D3—22no—
416C22—32no—
417C22—61no—
418C22—61no—
419C22D3×(C2×D3)⋊C411yescharacteristic
420C4—21no—
421C4—32no—
422C4—32no—
423C4—61no—
424C4—121no—
425C4—121no—
426C4—361no—
427C4—361no—
428C4D3×#20411yescharacteristic
429C4D3×Dic1211yescharacteristic
430C4#6380311yescharacteristic
431C4#6380411yescharacteristic
432C3—21no—
433C3#6824011yescharacteristic, complemented
434C3#6973811yescharacteristic, complemented
435C2—62no—
436C2D3×#80511yescharacteristic
437C2D3×#81611yescharacteristic
438C2#1059095311yescharacteristic
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#1493
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
379. C32#1493semidirect
433. C3#68240semidirect
434. C3#69738semidirect

Maximal subgroups

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

subgroupindex
#105938732
C3×C4×D3×C82
#105903362
#105893222
C3×#44562
#105890852
#105890842
#697383
#682403