Finite Group Databasebeta

← #16848866

Subgroups — #16848866

Order 3968.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758472C211yesmaximal, characteristic
2#14520951C211yesmaximal, characteristic, complemented
3#14520950C211yesmaximal, characteristic, complemented
4#14520940C211yesmaximal, characteristic, complemented
5#14520938C211yesmaximal, characteristic, complemented
6#14520935C211yesmaximal, characteristic, complemented
7#14520927C211yesmaximal, characteristic, complemented
8#14520927C211yesmaximal, characteristic, complemented
9#14520927C211yesmaximal, characteristic, complemented
10#14520927C211yesmaximal, characteristic, complemented
11#14520923C211yesmaximal, characteristic, complemented
12#14520920C211yesmaximal, characteristic, complemented
13#14520911C211yesmaximal, characteristic, complemented
14#14520908C211yesmaximal, characteristic, complemented
15C31×#387C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C22×D124C2211yescharacteristic
19C22×C4×D31C2211yescharacteristic
20C22×C4×D31C2211yescharacteristic
21C22×C4×D31C2211yescharacteristic
22C2×C4⋊C4×C31C2211yescharacteristic
23C2×C4⋊C4×C31C2211yescharacteristic
24C2×C42×C31C2211yescharacteristic
25C2×(C2×D31)⋊C4C2211yescharacteristic
26C2×(C2×D31)⋊C4C2211yescharacteristic
27C2×(C2×D31)⋊C4C2211yescharacteristic
28C2×(C2×D31)⋊C4C2211yescharacteristic
29C2×(C2×D31)⋊C4C2211yescharacteristic
30C2×(C2×D31)⋊C4C2211yescharacteristic
31C2×(C2×D31)⋊C4C2211yescharacteristic
32C2×(C2×D31)⋊C4C2211yescharacteristic
33C2×(C2×D31)⋊C4C2211yescharacteristic
34C2×(C2×D31)⋊C4C2211yescharacteristic
35C2×(C2×D31)⋊C4C2211yescharacteristic
36C2×(C2×D31)⋊C4C2211yescharacteristic
37C2×C4⋊Dic31C2211yescharacteristic
38C2×Dic31⋊C4C2211yescharacteristic
39C2×Dic31⋊C4C2211yescharacteristic
40C2×C4×Dic31C2211yescharacteristic
41#11758472C418yescomplemented
42C31×#95C2211yescharacteristic
43C31×#95C2211yescharacteristic
44C31×#95C2211yescharacteristic
45C31×#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C31⋊#95C2211yescharacteristic
52C23×D31C2311yescharacteristic
53C23×D31C2311yescharacteristic
54C23×D31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×C4×C31C2311yescharacteristic
59C22×C4×C31C2311yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C2×D124—41no—
68C2×D124—41no—
69C2×D124—41no—
70C2×D124—41no—
71C2×D124—41no—
72C2×D124—41no—
73C2×D124C2×C414yes—
74C2×D124C2×C414yescomplemented
75C2×D124C2×C414yescomplemented
76C2×C4×D31—41no—
77C2×C4×D31—41no—
78C2×C4×D31—41no—
79C2×C4×D31—41no—
80C2×C4×D31—41no—
81C2×C4×D31—41no—
82C2×C4×D31—41no—
83C2×C4×D31—41no—
84C2×C4×D31C2×C414yescomplemented
85C4⋊C4×C31—41no—
86C4⋊C4×C31C2×C414yescomplemented
87C42×C31—41no—
88(C2×D31)⋊C4—41no—
89(C2×D31)⋊C4—41no—
90(C2×D31)⋊C4—41no—
91(C2×D31)⋊C4—41no—
92(C2×D31)⋊C4—41no—
93(C2×D31)⋊C4—41no—
94(C2×D31)⋊C4—41no—
95(C2×D31)⋊C4—41no—
96(C2×D31)⋊C4—41no—
97(C2×D31)⋊C4—41no—
98(C2×D31)⋊C4C2×C414yescomplemented
99(C2×D31)⋊C4C2×C414yescomplemented
100C4⋊Dic31—41no—
101Dic31⋊C4—41no—
102Dic31⋊C4—41no—
103C4×Dic31—41no—
104C23×C31C2411yescharacteristic
105C22×D31—21no—
106C22×D31—21no—
107C22×D31—21no—
108C22×D31—21no—
109C22×D31—21no—
110C22×D31—21no—
111C22×D31—21no—
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—21no—
116C22×D31—21no—
117C22×D31—21no—
118C22×D31—21no—
119C22×D31—21no—
120C22×D31—21no—
121C22×D31—21no—
122C22×D31—21no—
123C22×D31C22×C412yes—
124C22×D31C22×C412yes—
125C22×D31C22×C412yes—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—21no—
142C2×C4×C31—21no—
143C2×C4×C31—21no—
144C2×C4×C31C22×C412yes—
145C2×C4×C31C22×C412yes—
146C2×C4×C31C22×C412yes—
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31—21no—
150C2×Dic31—21no—
151C2×Dic31—21no—
152C2×Dic31—21no—
153C2×Dic31—21no—
154C2×Dic31—21no—
155C2×Dic31—21no—
156C2×Dic31—21no—
157C2×Dic31—21no—
158C2×Dic31—21no—
159C2×Dic31—21no—
160C2×Dic31—21no—
161C2×Dic31C22×C412yes—
162D124—44no—
163D124—44no—
164D124—44no—
165C4×D31—44no—
166C4×D31—44no—
167C4×D31—44no—
168#2377—311nomaximal, Sylow
169C22×C31C23×C411yescharacteristic
170C22×C31H(5,𝔽2)11yescharacteristic
171C22×C31H(5,𝔽2)11yescharacteristic
172C22×C31H(5,𝔽2)11yescharacteristic
173C22×C31H(5,𝔽2)11yescharacteristic
174C22×C31H(5,𝔽2)11yescharacteristic
175C22×C312−1+411yescharacteristic
176C2×D31—22no—
177C2×D31—22no—
178C2×D31—22no—
179C2×D31—22no—
180C2×D31—22no—
181C2×D31—22no—
182C2×D31—22no—
183C2×D31—22no—
184C2×D31—22no—
185C2×D31—41no—
186C2×D31—41no—
187C2×D31—41no—
188C2×D31—41no—
189C2×D31—41no—
190C2×D31—41no—
191C2×D31—41no—
192C2×D31—41no—
193C2×D31—41no—
194C2×D31—41no—
195C2×D31—41no—
196C2×D31—41no—
197C4×C31—22no—
198C4×C31—22no—
199C4×C31—22no—
200C4×C31—41no—
201C4×C31—41no—
202C4×C31—41no—
203C4×C31—41no—
204Dic31—22no—
205Dic31—41no—
206Dic31—41no—
207Dic31—41no—
208Dic31—41no—
209C2×#121—311no—
210#390—311no—
211#390—311no—
212#388—311no—
213#388—311no—
214#387—311no—
215#387D3111yescharacteristic, complemented
216#386—311no—
217#386—311no—
218#386—311no—
219#386—311no—
220#385—311no—
221#385—311no—
222#381—311no—
223#380—311no—
224C2×C31#51811yescharacteristic
225C2×C31#51811yescharacteristic
226C2×C31#52011yescharacteristic
227C2×C31#56011yescharacteristic
228C2×C31#56011yescharacteristic
229C2×C31#56211yescharacteristic
230C2×C31#56211yescharacteristic
231D31—42no—
232D31—42no—
233D31—42no—
234C22×D4—311no—
235C22×D4—311no—
236C22×D4—311no—
237C23×C4—311no—
238C23×C4—311no—
239C23×C4—311no—
240#121—318no—
241C2×C4⋊C4—311no—
242C2×C4⋊C4—311no—
243C2×C4⋊C4—311no—
244C2×C4⋊C4C2×D3111yescharacteristic
245C2×C4⋊C4C2×D3111yescharacteristic
246C2×C22⋊C4—311no—
247C2×C22⋊C4—311no—
248C2×C22⋊C4—311no—
249C2×C22⋊C4—311no—
250C2×C22⋊C4—311no—
251C2×C22⋊C4—311no—
252C2×C22⋊C4—311no—
253C2×C22⋊C4—311no—
254C2×C22⋊C4—311no—
255C2×C22⋊C4—311no—
256C2×C22⋊C4—311no—
257C2×C22⋊C4—311no—
258C2×C42—311no—
259C2×C42C2×D3111yescharacteristic
260#95—311no—
261#95—311no—
262#95—311no—
263#95—311no—
264#95—311no—
265#95—311no—
266#95C2×D3111yescharacteristic
267#95C2×D3111yescharacteristic
268#95C2×D3111yescharacteristic
269#95C2×D3111yescharacteristic
270C31#237711yescharacteristic, complemented, Sylow
271C24—311no—
272C24—311no—
273C24—311no—
274C2×D4—314no—
275C2×D4—314no—
276C2×D4—314no—
277C2×D4—1241no—
278C2×D4—1241no—
279C2×D4—1241no—
280C2×D4—1241no—
281C2×D4—1241no—
282C2×D4—1241no—
283C22×C4—311no—
284C22×C4—314no—
285C22×C4—311no—
286C22×C4—311no—
287C22×C4—311no—
288C22×C4—311no—
289C22×C4—1241no—
290C22×C4—1241no—
291C22×C4—1241no—
292C22×C4—1241no—
293C22×C4—1241no—
294C22×C4—1241no—
295C22×C4—1241no—
296C22×C4—1241no—
297C22×C4C22×D3111yescharacteristic
298C22×C4C22×D3111yescharacteristic
299C22×C4C22×D3111yescharacteristic
300C22×C4C22×D3111yescharacteristic
301C22×C4C22×D3111yescharacteristic
302C22×C4C22×D3111yescharacteristic
303C22×C4C22×D3111yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—1241no—
306C4⋊C4—1241no—
307C4⋊C4—1241no—
308C4⋊C4C4×D3114yescomplemented
309C22⋊C4—314no—
310C22⋊C4—314no—
311C22⋊C4—1241no—
312C22⋊C4—1241no—
313C22⋊C4—1241no—
314C22⋊C4—1241no—
315C22⋊C4—1241no—
316C22⋊C4—1241no—
317C22⋊C4—1241no—
318C22⋊C4—1241no—
319C22⋊C4—1241no—
320C22⋊C4—1241no—
321C42—41no—
322C42—1241no—
323C23—312no—
324C23—312no—
325C23—312no—
326C23—621no—
327C23—621no—
328C23—621no—
329C23—621no—
330C23—621no—
331C23—621no—
332C23—621no—
333C23—621no—
334C23—621no—
335C23—621no—
336C23—621no—
337C23—621no—
338C23—621no—
339C23—621no—
340C23—621no—
341C23—621no—
342C23—621no—
343C23—621no—
344C23C23×D3111yescharacteristic
345D4—1244no—
346D4—1244no—
347D4—1244no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—312no—
367C2×C4—621no—
368C2×C4—621no—
369C2×C4—621no—
370C2×C4—621no—
371C2×C4—621no—
372C2×C4—621no—
373C2×C4—621no—
374C2×C4—621no—
375C2×C4—621no—
376C2×C4—621no—
377C2×C4—621no—
378C2×C4—621no—
379C2×C4—621no—
380C2×C4—621no—
381C2×C4—1244no—
382C2×C4—1244no—
383C2×C4—1244no—
384C2×C4C2×C4×D3112yes—
385C2×C4C2×C4×D3112yes—
386C2×C4C2×C4×D3112yes—
387C22—622no—
388C22—622no—
389C22—622no—
390C22—622no—
391C22—622no—
392C22—622no—
393C22—622no—
394C22—622no—
395C22—622no—
396C22—1241no—
397C22—1241no—
398C22—1241no—
399C22—1241no—
400C22—1241no—
401C22—1241no—
402C22—1241no—
403C22—1241no—
404C22—1241no—
405C22—1241no—
406C22—1241no—
407C22—1241no—
408C22C22×C4×D3111yescharacteristic
409C22#1175856111yescharacteristic
410C22#1175856411yescharacteristic
411C22#1175856611yescharacteristic
412C22#1175856611yescharacteristic
413C22#1175856611yescharacteristic
414C22#1175856611yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—622no—
423C4—1241no—
424C4—1241no—
425C4—1241no—
426C4—1241no—
427C2—1242no—
428C2—1242no—
429C2—1242no—
430C2#1452152111yescharacteristic
431C2#1452152311yescharacteristic
432C2#1452153111yescharacteristic
433C2#1452178911yescharacteristic
434C2#1452179011yescharacteristic
435C2#1452179511yescharacteristic
436C2#1452179711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#387C2
socle, cosocleC23×C31C24
prime radicalC2×#11758472C2
hypercenter#387D31
hypocenterC31#2377
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #14520951C2semidirect
3. #14520950C2semidirect
4. #14520940C2semidirect
5. #14520938C2semidirect
6. #14520935C2semidirect
7. #14520927C2semidirect
8. #14520927C2semidirect
9. #14520927C2semidirect
10. #14520927C2semidirect
11. #14520923C2semidirect
12. #14520920C2semidirect
13. #14520911C2semidirect
14. #14520908C2semidirect
15. C31×#387C2semidirect
41. #11758472C4semidirect
74. C2×D124C2×C4semidirect
75. C2×D124C2×C4semidirect
84. C2×C4×D31C2×C4semidirect
86. C4⋊C4×C31C2×C4semidirect
98. (C2×D31)⋊C4C2×C4semidirect
99. (C2×D31)⋊C4C2×C4semidirect
215. #387D31semidirect
270. C31#2377semidirect
308. C4⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584722
#145209512
#145209502
#145209402
#145209382
#145209352
#145209272
#145209232
#145209202
#145209112
#145209082
C31×#3872
#237731