Finite Group Databasebeta

← #28393480

Subgroups — #28393480

Order 14464.

704 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D113C211yesmaximal, characteristic
2C2×#16813582C211yesmaximal, characteristic
3C2×#16813582C211yesmaximal, characteristic
4#20298495C211yesmaximal, characteristic, complemented
5#20298493C211yesmaximal, characteristic, complemented
6#20298473C211yesmaximal, characteristic, complemented
7#20298472C211yesmaximal, characteristic, complemented
8#20298469C211yesmaximal, characteristic, complemented
9#20298462C211yesmaximal, characteristic, complemented
10#20298456C211yesmaximal, characteristic, complemented
11#20298455C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
13C2×#16813529C211yesmaximal, characteristic, complemented
14#95×D113C211yesmaximal, characteristic, complemented
15#385×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21C22×C4×D113C2211yescharacteristic
22C4×C22⋊D113—24no—
23#16813582—24no—
24#16813582C418yescomplemented
25C2×C4⋊Dic113C2211yescharacteristic
26C2×C4⋊Dic113C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×#14268626C2211yescharacteristic
30C2×#14268626C2211yescharacteristic
31C2×#14268626C2211yescharacteristic
32C2×C22⋊Dic113C2211yescharacteristic
33C2×#14268624C2211yescharacteristic
34C2×#14268624C2211yescharacteristic
35C2×#14268624C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C23×C4×C113C2211yescharacteristic
48C2×C4⋊C4×C113C2211yescharacteristic
49C2×C4⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C22⋊C4×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53#95×C113C2211yescharacteristic
54C23×D113C2311yescharacteristic
55C2×C22⋊D113C2×C414yes—
56C2×C22⋊D113D414yes—
57C2×C22⋊D113Q814yes—
58C22×Dic113—22no—
59C22×Dic113—22no—
60C22×Dic113—41no—
61C22×Dic113—41no—
62C22×Dic113—41no—
63C22×Dic113C2×C414yescomplemented
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C22×Dic113C2311yescharacteristic
70C22×Dic113C2311yescharacteristic
71C2×C4×D113—22no—
72C2×C4×D113—22no—
73C2×C4×D113—22no—
74C2×C4×D113—22no—
75C2×C4×D113—41no—
76C2×C4×D113—41no—
77C2×C4×D113—41no—
78C2×C4×D113—41no—
79C2×C4×D113C2×C414yescomplemented
80C4⋊Dic113—22no—
81C4⋊Dic113—41no—
82#14268626—22no—
83#14268626—22no—
84#14268626—41no—
85#14268626—41no—
86#14268626C2×C414yescomplemented
87C22⋊Dic113—22no—
88#14268624—22no—
89#14268624—22no—
90#14268624C2×C414yescomplemented
91C4×Dic113—22no—
92C4×Dic113—22no—
93C4×Dic113C2×C414yescomplemented
94C24×C113C2311yescharacteristic
95C22×C4×C113—22no—
96C22×C4×C113—22no—
97C22×C4×C113—41no—
98C22×C4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102C22×C4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C4⋊C4×C113—22no—
105C4⋊C4×C113—41no—
106C22⋊C4×C113—22no—
107C22⋊C4×C113C2×C414yescomplemented
108C23×C113—21no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—21no—
112C23×C113C22×C412yes—
113C23×C113C2×D412yes—
114C23×C113C2×Q812yes—
115C23×C113C2411yescharacteristic
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—21no—
120C22×D113C22×C412yes—
121C22×D113C2×D412yes—
122C22×D113C2×Q812yes—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—44no—
139C2×C4×C113C22×C412yes—
140C2×C4×C113C22×C412yes—
141C2×C4×C113#4112yes—
142C22⋊D113C4⋊C4116yescomplemented
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—21no—
157C2×Dic113—21no—
158C2×Dic113—44no—
159C2×Dic113—44no—
160C2×Dic113C22×C412yes—
161C2×Dic113C22×C412yes—
162C2×Dic113C22×C412yes—
163C2×Dic113C2×D412yes—
164C2×Dic113C2×Q812yes—
165C2×Dic113#4112yes—
166C4×D113—44no—
167C4×D113—44no—
168C4×D113—44no—
169C22×C113—22no—
170C22×C113—22no—
171C22×C113—22no—
172C22×C113—22no—
173C22×C113—22no—
174C22×C113—22no—
175C22×C113C2×C4⋊C414yes—
176C22×C113C23×C411yescharacteristic
177C22×C113C22×D411yescharacteristic
178C22×C113C22×Q811yescharacteristic
179C22×C113C2×#4111yescharacteristic
180C22×C113C2×#4111yescharacteristic
181C22×C113H(5,𝔽2)11yescharacteristic
182C22×C113H(5,𝔽2)11yescharacteristic
183C2×D113—22no—
184C2×D113—22no—
185C2×D113—22no—
186C2×D113—22no—
187C2×D113—22no—
188C2×D113—22no—
189C2×D113C2×C4⋊C414yes—
190C4×C113—22no—
191C4×C113—22no—
192C4×C113—22no—
193C4×C113—41no—
194C4×C113—41no—
195C4×C113—41no—
196Dic113—22no—
197Dic113—22no—
198Dic113—22no—
199Dic113—41no—
200Dic113—41no—
201Dic113—41no—
202Dic113C2×C4⋊C414yes—
203C2×C113—24no—
204C2×C113C22×C4⋊C411yescharacteristic
205C2×C113C4×#4111yescharacteristic
206C2×C113#51811yescharacteristic
207C2×C113#54611yescharacteristic
208C2×C113#54611yescharacteristic
209C2×C113#55411yescharacteristic
210C2×C113#55411yescharacteristic
211D113—24no—
212#2349—1131nomaximal, Sylow
213C113#234911yescharacteristic, complemented, Sylow
214C2×C4×D4—1131no—
215C2×C4×D4—1131no—
216C2×C4×D4—1131no—
217#389—1131no—
218#389—1131no—
219#385—1131no—
220#385—1131no—
221#385—1131no—
222#385D11311yescharacteristic, complemented
223#382—1131no—
224#380—1131no—
225#380—1131no—
226C4×C4⋊C4—1131no—
227C2×#95—1131no—
228C2×#95—1131no—
229C22×D4—1131no—
230C23×C4—1131no—
231C23×C4—1131no—
232C23×C4—1131no—
233C23×C4—1131no—
234C23×C4—1131no—
235C23×C4C2×D11311yescharacteristic
236C4×D4—1138no—
237C4×D4—2264no—
238C4×D4—2264no—
239C2×C4⋊C4—1131no—
240C2×C4⋊C4—1131no—
241C2×C4⋊C4—1131no—
242C2×C4⋊C4—1131no—
243C2×C4⋊C4—1131no—
244C2×C4⋊C4—1131no—
245C2×C4⋊C4—1131no—
246C2×C4⋊C4C2×D11311yescharacteristic
247C2×C4⋊C4C2×D11311yescharacteristic
248C2×C22⋊C4—1131no—
249C2×C22⋊C4—1131no—
250C2×C22⋊C4—1131no—
251C2×C22⋊C4—1131no—
252C2×C22⋊C4C2×D11311yescharacteristic
253C2×C22⋊C4C2×D11311yescharacteristic
254C2×C42—1131no—
255C2×C42—1131no—
256C2×C42—1131no—
257#95—1131no—
258#95—1131no—
259#95—1131no—
260#95—1131no—
261#95—1131no—
262#95—1131no—
263#95—1131no—
264#95—1131no—
265#95C2×D11311yescharacteristic
266#95C2×D11311yescharacteristic
267C24—1131no—
268C24C22×D11311yescharacteristic
269C2×D4—1134no—
270C2×D4—1134no—
271C2×D4—1134no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—1131no—
276C22×C4—1134no—
277C22×C4—1131no—
278C22×C4—1131no—
279C22×C4—1131no—
280C22×C4—1134no—
281C22×C4—1131no—
282C22×C4—1131no—
283C22×C4—1131no—
284C22×C4—4521no—
285C22×C4—4521no—
286C22×C4—4521no—
287C22×C4—4521no—
288C22×C4—4521no—
289C22×C4—4521no—
290C22×C4—4521no—
291C22×C4—2262no—
292C22×C4—2262no—
293C22×C4—2262no—
294C22×C4—2262no—
295C22×C4—2262no—
296C22×C4—2262no—
297C22×C4C22×D11311yescharacteristic
298C22×C4C22×D11311yescharacteristic
299C22×C4C22×D11311yescharacteristic
300C22×C4C22×D11311yescharacteristic
301C22×C4C22×D11311yescharacteristic
302C22×C4C22×D11311yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—1134no—
306C4⋊C4—4521no—
307C4⋊C4—4521no—
308C4⋊C4—4521no—
309C4⋊C4—2262no—
310C4⋊C4—2262no—
311C4⋊C4—2262no—
312C22⋊C4—22no—
313C22⋊C4—1134no—
314C22⋊C4—2262no—
315C22⋊C4—2262no—
316C22⋊C4—2262no—
317C22⋊C4C4×D11314yescomplemented
318C42—1134no—
319C42—2262no—
320C42—2262no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—1132no—
326C23—1132no—
327C23—1132no—
328C23—2261no—
329C23—2261no—
330C23—2261no—
331C23—2261no—
332C23C2×C4×D11312yes—
333C23D4×D11312yes—
334C23Q8×D11312yes—
335C23C23×D11311yescharacteristic
336D4—11316no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—1132no—
354C2×C4—1132no—
355C2×C4—1132no—
356C2×C4—1132no—
357C2×C4—1132no—
358C2×C4—1132no—
359C2×C4—4524no—
360C2×C4—4524no—
361C2×C4—4524no—
362C2×C4—4524no—
363C2×C4—4524no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4—2261no—
375C2×C4—2261no—
376C2×C4—2261no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4C2×C4×D11312yes—
380C2×C4C2×C4×D11312yes—
381C2×C4#1426864612yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—1134no—
389C22—2262no—
390C22—2262no—
391C22—2262no—
392C22—2262no—
393C22—2262no—
394C22—2262no—
395C22C4⋊C4×D11314yes—
396C22C22×C4×D11311yescharacteristic
397C22C2×D4×D11311yescharacteristic
398C22C2×Q8×D11311yescharacteristic
399C22#41×D11311yescharacteristic
400C22C2×#1426864611yescharacteristic
401C22#1681366711yescharacteristic
402C22#1681366811yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—1134no—
410C4—4521no—
411C4—4521no—
412C4—4521no—
413C4—2262no—
414C4—2262no—
415C4—2262no—
416C2—24no—
417C2—2264no—
418C2C2×C4⋊C4×D11311yescharacteristic
419C2C4×#1426864611yescharacteristic
420C2#2029907011yescharacteristic
421C2#2029923511yescharacteristic
422C2#2029924011yescharacteristic
423C2#2029930211yescharacteristic
424C2#2029930611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#385×C113C2
socle, cosocleC23×C113C24
prime radicalC22×C22⋊D113C22
hypercenter#385D113
hypocenterC113#2349
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #20298495C2semidirect
5. #20298493C2semidirect
6. #20298473C2semidirect
7. #20298472C2semidirect
8. #20298469C2semidirect
9. #20298462C2semidirect
10. #20298456C2semidirect
11. #20298455C2semidirect
12. C4⋊C4×Dic113C2semidirect
13. C2×#16813529C2semidirect
14. #95×D113C2semidirect
15. #385×C113C2semidirect
24. #16813582C4semidirect
63. C22×Dic113C2×C4semidirect
79. C2×C4×D113C2×C4semidirect
86. #14268626C2×C4semidirect
90. #14268624C2×C4semidirect
93. C4×Dic113C2×C4semidirect
107. C22⋊C4×C113C2×C4semidirect
142. C22⋊D113C4⋊C4semidirect
213. C113#2349semidirect
222. #385D113semidirect
317. C22⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1132
C2×#168135822
#202984952
#202984932
#202984732
#202984722
#202984692
#202984622
#202984562
#202984552
C4⋊C4×Dic1132
C2×#168135292
#95×D1132
#385×C1132
#2349113