Finite Group Databasebeta

← #44487706

Subgroups — #44487706

Order 30592.

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×#21439932C211yesmaximal, characteristic
2#29504675C211yesmaximal, characteristic, complemented
3#29504672C211yesmaximal, characteristic, complemented
4#29504661C211yesmaximal, characteristic, complemented
5#29504660C211yesmaximal, characteristic, complemented
6#29504659C211yesmaximal, characteristic, complemented
7#29504654C211yesmaximal, characteristic, complemented
8#29504651C211yesmaximal, characteristic, complemented
9#29504648C211yesmaximal, characteristic, complemented
10#29504648C211yesmaximal, characteristic, complemented
11#29504646C211yesmaximal, characteristic, complemented
12#29504645C211yesmaximal, characteristic, complemented
13#29504633C211yesmaximal, characteristic, complemented
14#29504630C211yesmaximal, characteristic, complemented
15#386×C239C211yesmaximal, characteristic, complemented
16C22×C22⋊D239C2211yescharacteristic
17C22×C22⋊D239C2211yescharacteristic
18C23×Dic239C2211yescharacteristic
19C22×C4×D239C2211yescharacteristic
20#21439932C418yescomplemented
21C2×C4⋊Dic239C2211yescharacteristic
22C2×Dic239⋊C4C2211yescharacteristic
23C2×Dic239⋊C4C2211yescharacteristic
24C2×Dic239⋊C4C2211yescharacteristic
25C2×Dic239⋊C4C2211yescharacteristic
26C2×C22⋊Dic239C2211yescharacteristic
27C2×C22⋊Dic239C2211yescharacteristic
28C2×C22⋊Dic239C2211yescharacteristic
29C2×C22⋊Dic239C2211yescharacteristic
30C2×C22⋊Dic239C2211yescharacteristic
31C2×(C2×D239)⋊C4C2211yescharacteristic
32C2×(C2×D239)⋊C4C2211yescharacteristic
33C2×(C2×D239)⋊C4C2211yescharacteristic
34C2×(C2×D239)⋊C4C2211yescharacteristic
35C2×C4×Dic239C2211yescharacteristic
36C2×C4×Dic239C2211yescharacteristic
37C239⋊#95C2211yescharacteristic
38C239⋊#95C2211yescharacteristic
39C239⋊#95C2211yescharacteristic
40C239⋊#95C2211yescharacteristic
41C239⋊#95C2211yescharacteristic
42C239⋊#95C2211yescharacteristic
43C239⋊#95C2211yescharacteristic
44C239⋊#95C2211yescharacteristic
45C22×D4×C239C2211yescharacteristic
46C23×C4×C239C2211yescharacteristic
47C2×C22⋊C4×C239C2211yescharacteristic
48C2×C22⋊C4×C239C2211yescharacteristic
49C2×C22⋊C4×C239C2211yescharacteristic
50#95×C239C2211yescharacteristic
51#95×C239C2211yescharacteristic
52C23×D239C2311yescharacteristic
53C2×C22⋊D239—41no—
54C2×C22⋊D239—41no—
55C2×C22⋊D239—41no—
56C2×C22⋊D239—41no—
57C2×C22⋊D239C2×C414yes—
58C2×C22⋊D239C2×C414yescomplemented
59C22×Dic239—41no—
60C22×Dic239—41no—
61C22×Dic239C2×C414yescomplemented
62C22×Dic239C2311yescharacteristic
63C22×Dic239C2311yescharacteristic
64C22×Dic239C2311yescharacteristic
65C22×Dic239C2311yescharacteristic
66C22×Dic239C2311yescharacteristic
67C22×Dic239C2311yescharacteristic
68C22×Dic239C2311yescharacteristic
69C2×C4×D239—41no—
70C2×C4×D239—41no—
71C2×C4×D239—41no—
72C4⋊Dic239—41no—
73Dic239⋊C4—41no—
74Dic239⋊C4—41no—
75Dic239⋊C4—41no—
76Dic239⋊C4C2×C414yescomplemented
77C22⋊Dic239—41no—
78C22⋊Dic239—41no—
79C22⋊Dic239—41no—
80C22⋊Dic239—41no—
81C22⋊Dic239C2×C414yescomplemented
82(C2×D239)⋊C4—41no—
83(C2×D239)⋊C4—41no—
84(C2×D239)⋊C4—41no—
85(C2×D239)⋊C4C2×C414yescomplemented
86C4×Dic239—41no—
87C4×Dic239—41no—
88C24×C239C2311yescharacteristic
89C24×C239C2311yescharacteristic
90C2×D4×C239—41no—
91C2×D4×C239—41no—
92C2×D4×C239C2×C414yescomplemented
93C22×C4×C239—41no—
94C22×C4×C239—41no—
95C22×C4×C239—41no—
96C22×C4×C239C2311yescharacteristic
97C22×C4×C239C2311yescharacteristic
98C22×C4×C239C2311yescharacteristic
99C22×C4×C239C2311yescharacteristic
100C22×C4×C239C2311yescharacteristic
101C22⋊C4×C239—41no—
102C22⋊C4×C239—41no—
103C22⋊C4×C239—41no—
104C22×D239—21no—
105C22×D239—21no—
106C22×D239—21no—
107C22×D239—21no—
108C22×D239—21no—
109C22×D239—21no—
110C22×D239C22×C412yes—
111C22⋊D239—44no—
112C22⋊D239—44no—
113C2×Dic239—21no—
114C2×Dic239—21no—
115C2×Dic239—21no—
116C2×Dic239—21no—
117C2×Dic239—21no—
118C2×Dic239—21no—
119C2×Dic239—21no—
120C2×Dic239—21no—
121C2×Dic239—21no—
122C2×Dic239—21no—
123C2×Dic239—21no—
124C2×Dic239—21no—
125C2×Dic239—21no—
126C2×Dic239—21no—
127C2×Dic239—21no—
128C2×Dic239—21no—
129C2×Dic239—21no—
130C2×Dic239—21no—
131C2×Dic239—44no—
132C2×Dic239C22×C412yes—
133C2×Dic239C22×C412yes—
134C2×Dic239C22×C412yes—
135C4×D239—44no—
136C23×C239—21no—
137C23×C239—21no—
138C23×C239—21no—
139C23×C239—21no—
140C23×C239—21no—
141C23×C239—21no—
142C23×C239—21no—
143C23×C239—21no—
144C23×C239—21no—
145C23×C239—21no—
146C23×C239—21no—
147C23×C239—21no—
148C23×C239C22×C412yes—
149C23×C239C22×C412yes—
150C23×C239C2411yescharacteristic
151D4×C239—44no—
152C2×C4×C239—21no—
153C2×C4×C239—21no—
154C2×C4×C239—21no—
155C2×C4×C239—21no—
156C2×C4×C239—21no—
157C2×C4×C239—21no—
158C2×C4×C239—21no—
159C2×C4×C239—21no—
160C2×C4×C239—21no—
161C2×C4×C239—21no—
162C2×C4×C239—21no—
163C2×C4×C239—21no—
164C2×C4×C239—21no—
165C2×C4×C239—21no—
166C2×C4×C239—44no—
167C2×C4×C239C22×C412yes—
168C22×C239—22no—
169C22×C239—22no—
170C22×C239—22no—
171C22×C239—22no—
172C22×C239—22no—
173C22×C239—22no—
174C22×C239—41no—
175C22×C239—41no—
176C22×C239—41no—
177C22×C239—41no—
178C22×C239—41no—
179C22×C239—41no—
180C22×C239—41no—
181C22×C239—41no—
182C22×C239C23×C411yescharacteristic
183C22×C239H(5,𝔽2)11yescharacteristic
184C22×C239H(5,𝔽2)11yescharacteristic
185C22×C239H(5,𝔽2)11yescharacteristic
186C22×C239H(5,𝔽2)11yescharacteristic
187C22×C239H(5,𝔽2)11yescharacteristic
188C22×C2392−1+411yescharacteristic
189C2×D239—22no—
190C2×D239—22no—
191C2×D239—22no—
192C2×D239—41no—
193C2×D239—41no—
194C2×D239—41no—
195C2×D239—41no—
196C4×C239—22no—
197C4×C239—41no—
198C4×C239—41no—
199C4×C239—41no—
200C4×C239—41no—
201Dic239—22no—
202Dic239—22no—
203Dic239—22no—
204Dic239—41no—
205Dic239—41no—
206Dic239—41no—
207Dic239—41no—
208C2×C239—42no—
209C2×C239—42no—
210C2×C239#51811yescharacteristic
211C2×C239#51811yescharacteristic
212C2×C239#52011yescharacteristic
213C2×C239#56011yescharacteristic
214C2×C239#56011yescharacteristic
215C2×C239#56211yescharacteristic
216C2×C239#56211yescharacteristic
217D239—42no—
218C239#237711yescharacteristic, complemented, Sylow
219#2377—2391nomaximal, Sylow
220C2×#121—2391no—
221#390—2391no—
222#390—2391no—
223#388—2391no—
224#388—2391no—
225#387—2391no—
226#387—2391no—
227#386—2391no—
228#386—2391no—
229#386—2391no—
230#386D23911yescharacteristic, complemented
231#385—2391no—
232#385—2391no—
233#381—2391no—
234#380—2391no—
235C22×D4—2391no—
236C22×D4—2391no—
237C22×D4C2×D23911yescharacteristic
238C23×C4—2391no—
239C23×C4—2391no—
240C23×C4C2×D23911yescharacteristic
241#121—2398no—
242C2×C4⋊C4—2391no—
243C2×C4⋊C4—2391no—
244C2×C4⋊C4—2391no—
245C2×C4⋊C4—2391no—
246C2×C4⋊C4—2391no—
247C2×C22⋊C4—2391no—
248C2×C22⋊C4—2391no—
249C2×C22⋊C4—2391no—
250C2×C22⋊C4—2391no—
251C2×C22⋊C4—2391no—
252C2×C22⋊C4—2391no—
253C2×C22⋊C4—2391no—
254C2×C22⋊C4—2391no—
255C2×C22⋊C4—2391no—
256C2×C22⋊C4C2×D23911yescharacteristic
257C2×C22⋊C4C2×D23911yescharacteristic
258C2×C22⋊C4C2×D23911yescharacteristic
259C2×C42—2391no—
260C2×C42—2391no—
261#95—2391no—
262#95—2391no—
263#95—2391no—
264#95—2391no—
265#95—2391no—
266#95—2391no—
267#95—2391no—
268#95—2391no—
269#95C2×D23911yescharacteristic
270#95C2×D23911yescharacteristic
271C24—2391no—
272C24C22×D23911yescharacteristic
273C24C22×D23911yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—9561no—
277C2×D4—9561no—
278C2×D4—9561no—
279C2×D4—9561no—
280C2×D4—2394no—
281C2×D4—2394no—
282C2×D4C4×D23914yescomplemented
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—9561no—
287C22×C4—9561no—
288C22×C4—9561no—
289C22×C4—9561no—
290C22×C4—9561no—
291C22×C4—2394no—
292C22×C4—2391no—
293C22×C4—2391no—
294C22×C4—2391no—
295C22×C4—2391no—
296C22×C4—2391no—
297C22×C4—2391no—
298C22×C4—2391no—
299C22×C4C22×D23911yescharacteristic
300C22×C4C22×D23911yescharacteristic
301C22×C4C22×D23911yescharacteristic
302C22×C4C22×D23911yescharacteristic
303C22×C4C22×D23911yescharacteristic
304C4⋊C4—9561no—
305C4⋊C4—9561no—
306C4⋊C4—9561no—
307C4⋊C4—9561no—
308C4⋊C4—2394no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—9561no—
313C22⋊C4—9561no—
314C22⋊C4—9561no—
315C22⋊C4—9561no—
316C22⋊C4—9561no—
317C22⋊C4—9561no—
318C22⋊C4—9561no—
319C22⋊C4—2394no—
320C22⋊C4—2394no—
321C42—9561no—
322C42—9561no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—4781no—
336C23—4781no—
337C23—4781no—
338C23—4781no—
339C23—4781no—
340C23—4781no—
341C23—2392no—
342C23C2×C4×D23912yes—
343C23C2×C4×D23912yes—
344C23C23×D23911yescharacteristic
345D4—44no—
346D4—9564no—
347D4—9564no—
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—44no—
363C2×C4—9564no—
364C2×C4—9564no—
365C2×C4—4781no—
366C2×C4—4781no—
367C2×C4—4781no—
368C2×C4—4781no—
369C2×C4—4781no—
370C2×C4—4781no—
371C2×C4—4781no—
372C2×C4—4781no—
373C2×C4—4781no—
374C2×C4—4781no—
375C2×C4—4781no—
376C2×C4—4781no—
377C2×C4—4781no—
378C2×C4—4781no—
379C2×C4—4781no—
380C2×C4—4781no—
381C2×C4—4781no—
382C2×C4—4781no—
383C2×C4—2392no—
384C2×C4—2392no—
385C2×C4—2392no—
386C2×C4C2×C4×D23912yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—9561no—
402C22—9561no—
403C22—9561no—
404C22—9561no—
405C22—4782no—
406C22—4782no—
407C22—4782no—
408C22C22×C4×D23911yescharacteristic
409C22#2144000511yescharacteristic
410C22#2144000511yescharacteristic
411C22#2144000511yescharacteristic
412C22#2144000511yescharacteristic
413C22#2144000611yescharacteristic
414C22#2144000711yescharacteristic
415C4—22no—
416C4—41no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—9561no—
421C4—9561no—
422C4—9561no—
423C4—9561no—
424C4—4782no—
425C4—4782no—
426C4—4782no—
427C2—42no—
428C2—42no—
429C2—9562no—
430C2#2950524411yescharacteristic
431C2#2950524511yescharacteristic
432C2#2950525111yescharacteristic
433C2#2950551011yescharacteristic
434C2#2950551111yescharacteristic
435C2#2950551711yescharacteristic
436C2#2950551911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#386×C239C2
socle, cosocleC23×C239C24
prime radicalC2×#21439932C2
hypercenter#386D239
hypocenterC239#2377
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. #29504675C2semidirect
3. #29504672C2semidirect
4. #29504661C2semidirect
5. #29504660C2semidirect
6. #29504659C2semidirect
7. #29504654C2semidirect
8. #29504651C2semidirect
9. #29504648C2semidirect
10. #29504648C2semidirect
11. #29504646C2semidirect
12. #29504645C2semidirect
13. #29504633C2semidirect
14. #29504630C2semidirect
15. #386×C239C2semidirect
20. #21439932C4semidirect
58. C2×C22⋊D239C2×C4semidirect
61. C22×Dic239C2×C4semidirect
76. Dic239⋊C4C2×C4semidirect
81. C22⋊Dic239C2×C4semidirect
85. (C2×D239)⋊C4C2×C4semidirect
92. C2×D4×C239C2×C4semidirect
218. C239#2377semidirect
230. #386D239semidirect
282. C2×D4C4×D239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399322
#295046752
#295046722
#295046612
#295046602
#295046592
#295046542
#295046512
#295046482
#295046462
#295046452
#295046332
#295046302
#386×C2392
#2377239