Finite Group Databasebeta

← #15676295

Subgroups — #15676295

Order 2944.

776 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×C4×C22⋊D23C211yesmaximal, characteristic
2C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
3C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
4C22×Dic23⋊C4C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D23C211yesmaximal, characteristic, complemented
6#13092314C211yesmaximal, characteristic, complemented
7#13092312C211yesmaximal, characteristic, complemented
8#13092292C211yesmaximal, characteristic, complemented
9#13092291C211yesmaximal, characteristic, complemented
10#13092288C211yesmaximal, characteristic, complemented
11#13092286C211yesmaximal, characteristic, complemented
12#13092276C211yesmaximal, characteristic, complemented
13#13092275C211yesmaximal, characteristic, complemented
14#13092268C211yesmaximal, characteristic, complemented
15C23×#385C211yesmaximal, characteristic, complemented
16C23×C4×C23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C23×Dic23C2211yescharacteristic
19C23×Dic23C2211yescharacteristic
20C22×C4×D23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C22×C4×D23C2211yescharacteristic
23C2×C4⋊C4×C23C2211yescharacteristic
24C2×C4⋊C4×C23C2211yescharacteristic
25C2×C22⋊C4×C23C2211yescharacteristic
26C2×C22⋊C4×C23C2211yescharacteristic
27C2×C22⋊Dic23C2211yescharacteristic
28C4×C22⋊D23—24no—
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×(C2×D23)⋊C4C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33C2×C4⋊Dic23C2211yescharacteristic
34C2×Dic23⋊C4—24no—
35C2×Dic23⋊C4C2211yescharacteristic
36C2×Dic23⋊C4C2211yescharacteristic
37C2×Dic23⋊C4C2211yescharacteristic
38C2×Dic23⋊C4C2211yescharacteristic
39C2×Dic23⋊C4C2211yescharacteristic
40C2×Dic23⋊C4C2211yescharacteristic
41C2×Dic23⋊C4C2211yescharacteristic
42C2×Dic23⋊C4C2211yescharacteristic
43C2×Dic23⋊C4C2211yescharacteristic
44C2×C4×Dic23C2211yescharacteristic
45C2×C4×Dic23C2211yescharacteristic
46C2×C4×Dic23C2211yescharacteristic
47C4⋊C4×D23—24no—
48(C22⋊D23)⋊C4—24no—
49(C22⋊D23)⋊C4C418yescomplemented
50C23×#95C2211yescharacteristic
51C23×#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C23⋊#95C2211yescharacteristic
55C23⋊#95C2211yescharacteristic
56C24×C23C2311yescharacteristic
57C23×D23C2311yescharacteristic
58C22×C4×C23—22no—
59C22×C4×C23—22no—
60C22×C4×C23—41no—
61C22×C4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23C2×C414yes—
68C2×C22⋊D23D414yes—
69C2×C22⋊D23Q814yes—
70C22×Dic23—22no—
71C22×Dic23—22no—
72C22×Dic23—22no—
73C22×Dic23—22no—
74C22×Dic23—41no—
75C22×Dic23C2×C414yescomplemented
76C22×Dic23C2311yescharacteristic
77C22×Dic23C2311yescharacteristic
78C22×Dic23C2311yescharacteristic
79C22×Dic23C2311yescharacteristic
80C22×Dic23C2311yescharacteristic
81C22×Dic23C2311yescharacteristic
82C22×Dic23C2311yescharacteristic
83C2×C4×D23—22no—
84C2×C4×D23—22no—
85C2×C4×D23—22no—
86C2×C4×D23—22no—
87C2×C4×D23—22no—
88C2×C4×D23—22no—
89C2×C4×D23—41no—
90C2×C4×D23—41no—
91C2×C4×D23C2×C414yescomplemented
92C4⋊C4×C23—22no—
93C4⋊C4×C23—41no—
94C22⋊C4×C23—22no—
95C22⋊C4×C23C2×C414yescomplemented
96C22⋊Dic23—22no—
97(C2×D23)⋊C4—22no—
98(C2×D23)⋊C4—22no—
99(C2×D23)⋊C4C2×C414yescomplemented
100C4⋊Dic23—22no—
101C4⋊Dic23—41no—
102Dic23⋊C4—22no—
103Dic23⋊C4—22no—
104Dic23⋊C4—22no—
105Dic23⋊C4—22no—
106Dic23⋊C4—22no—
107Dic23⋊C4—22no—
108Dic23⋊C4—22no—
109Dic23⋊C4C2×C414yescomplemented
110Dic23⋊C4D414yescomplemented
111C4×Dic23—22no—
112C4×Dic23—22no—
113C4×Dic23C2×C414yescomplemented
114C23×C23—21no—
115C23×C23—21no—
116C23×C23—21no—
117C23×C23—21no—
118C23×C23C22×C412yes—
119C23×C23C2×D412yes—
120C23×C23C2×Q812yes—
121C23×C23C2411yescharacteristic
122C22×D23—21no—
123C22×D23—21no—
124C22×D23—21no—
125C22×D23—21no—
126C22×D23C22×C412yes—
127C22×D23C2×D412yes—
128C22×D23C2×Q812yes—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—44no—
145C2×C4×C23C22×C412yes—
146C2×C4×C23C22×C412yes—
147C2×C4×C23C2×D412yes—
148C22⋊D23C4⋊C4116yescomplemented
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—28no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—44no—
164C2×Dic23C22×C412yes—
165C2×Dic23C22×C412yes—
166C2×Dic23C22×C412yes—
167C2×Dic23C2×D412yes—
168C2×Dic23C2×D412yes—
169C2×Dic23C2×D412yes—
170C2×Dic23C2×Q812yes—
171C2×Dic23#4112yes—
172C4×D23—28no—
173C4×D23—44no—
174C4×D23—44no—
175D4×C4⋊C4—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—22no—
178C22×C23—22no—
179C22×C23—22no—
180C22×C23—22no—
181C22×C23—22no—
182C22×C23C2×C4⋊C414yescomplemented
183C22×C23C23×C411yescharacteristic
184C22×C23C22×D411yescharacteristic
185C22×C23C22×D411yescharacteristic
186C22×C23C22×Q811yescharacteristic
187C22×C23C2×#4111yescharacteristic
188C22×C23H(5,𝔽2)11yescharacteristic
189C22×C232−1+411yescharacteristic
190C2×D23—22no—
191C2×D23—22no—
192C2×D23—22no—
193C2×D23—22no—
194C2×D23—22no—
195C2×D23—22no—
196C2×D23C2×C4⋊C414yescomplemented
197C4×C23—22no—
198C4×C23—22no—
199C4×C23—22no—
200C4×C23—41no—
201C4×C23—41no—
202C4×C23—41no—
203Dic23—22no—
204Dic23—22no—
205Dic23—41no—
206Dic23—41no—
207Dic23—41no—
208Dic23C2×C4⋊C414yescomplemented
209Dic23C4×D414yescomplemented
210C2×C4×D4—231no—
211C2×C4×D4—231no—
212C2×C4×D4—231no—
213C22×C4⋊C4—231no—
214C22×C4⋊C4—231no—
215#389—231no—
216#389—231no—
217#385—231no—
218#385—231no—
219#385—231no—
220#385D2311yescharacteristic, complemented
221#384—231no—
222#380—231no—
223#380—231no—
224C4×C4⋊C4—231no—
225C2×C23—24no—
226C2×C23C22×C4⋊C411yescharacteristic
227C2×C23C2×C4×D411yescharacteristic
228C2×C23#52011yescharacteristic
229C2×C23D4211yescharacteristic
230C2×C23#54711yescharacteristic
231C2×C23D4×Q811yescharacteristic
232C2×C23#55411yescharacteristic
233D23—24no—
234C22×D4—231no—
235C23×C4—231no—
236C23×C4—231no—
237C23×C4—231no—
238C23×C4—231no—
239C23×C4—231no—
240C23×C4C2×D2311yescharacteristic
241C4×D4—238no—
242C4×D4—464no—
243C4×D4—464no—
244C2×C4⋊C4—231no—
245C2×C4⋊C4—231no—
246C2×C4⋊C4—231no—
247C2×C4⋊C4—231no—
248C2×C4⋊C4—231no—
249C2×C4⋊C4—231no—
250C2×C4⋊C4—231no—
251C2×C4⋊C4—231no—
252C2×C4⋊C4—231no—
253C2×C4⋊C4—231no—
254C2×C4⋊C4—231no—
255C2×C4⋊C4—464no—
256C2×C4⋊C4—464no—
257C2×C4⋊C4C2×D2311yescharacteristic
258C2×C4⋊C4C2×D2311yescharacteristic
259C2×C22⋊C4—231no—
260C2×C22⋊C4—231no—
261C2×C22⋊C4—231no—
262C2×C22⋊C4—231no—
263C2×C22⋊C4C2×D2311yescharacteristic
264C2×C22⋊C4C2×D2311yescharacteristic
265C2×C42—231no—
266C2×C42—231no—
267C2×C42—231no—
268#95—231no—
269#95—231no—
270#95—231no—
271#95—231no—
272#95C2×D2311yescharacteristic
273#95C2×D2311yescharacteristic
274C23D4×C4⋊C411yescharacteristic, complemented, Sylow
275C24—231no—
276C24C22×D2311yescharacteristic
277C2×D4—234no—
278C2×D4—234no—
279C2×D4—234no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—231no—
284C22×C4—231no—
285C22×C4—234no—
286C22×C4—231no—
287C22×C4—231no—
288C22×C4—234no—
289C22×C4—231no—
290C22×C4—231no—
291C22×C4—231no—
292C22×C4—462no—
293C22×C4—462no—
294C22×C4—462no—
295C22×C4—462no—
296C22×C4—462no—
297C22×C4—462no—
298C22×C4—462no—
299C22×C4—462no—
300C22×C4—462no—
301C22×C4—462no—
302C22×C4—921no—
303C22×C4—921no—
304C22×C4—921no—
305C22×C4C22×D2311yescharacteristic
306C22×C4C22×D2311yescharacteristic
307C22×C4C22×D2311yescharacteristic
308C22×C4C22×D2311yescharacteristic
309C22×C4C22×D2311yescharacteristic
310C22×C4C22×D2311yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—234no—
314C4⋊C4—234no—
315C4⋊C4—462no—
316C4⋊C4—462no—
317C4⋊C4—462no—
318C4⋊C4—462no—
319C4⋊C4—462no—
320C4⋊C4—462no—
321C4⋊C4—462no—
322C4⋊C4—462no—
323C4⋊C4—921no—
324C22⋊C4—22no—
325C22⋊C4—234no—
326C22⋊C4—462no—
327C22⋊C4—462no—
328C22⋊C4—462no—
329C22⋊C4C4×D2314yescomplemented
330C42—234no—
331C42—462no—
332C42—462no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—232no—
338C23—232no—
339C23—232no—
340C23—461no—
341C23—461no—
342C23—461no—
343C23—461no—
344C23C2×C4×D2312yes—
345C23D4×D2312yes—
346C23Q8×D2312yes—
347C23C23×D2311yescharacteristic
348D4—2316no—
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—44no—
365C2×C4—232no—
366C2×C4—232no—
367C2×C4—232no—
368C2×C4—232no—
369C2×C4—232no—
370C2×C4—232no—
371C2×C4—232no—
372C2×C4—232no—
373C2×C4—468no—
374C2×C4—468no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—461no—
382C2×C4—461no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—924no—
389C2×C4—924no—
390C2×C4—924no—
391C2×C4C2×C4×D2312yes—
392C2×C4C2×C4×D2312yes—
393C2×C4D4×D2312yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—234no—
401C22—462no—
402C22—462no—
403C22—462no—
404C22—462no—
405C22—462no—
406C22—462no—
407C22C4⋊C4×D2314yescomplemented
408C22C22×C4×D2311yescharacteristic
409C22C2×D4×D2311yescharacteristic
410C22C2×D4×D2311yescharacteristic
411C22#1062515511yescharacteristic
412C22C2×Q8×D2311yescharacteristic
413C22#41×D2311yescharacteristic
414C22#1062516111yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—234no—
422C4—234no—
423C4—462no—
424C4—462no—
425C4—921no—
426C4—921no—
427C4—921no—
428C2—24no—
429C2—464no—
430C2C2×C4⋊C4×D2311yescharacteristic
431C2C4×D4×D2311yescharacteristic
432C2#1309289611yescharacteristic
433C2#1309304911yescharacteristic
434C2#1309306511yescharacteristic
435C2#1309308011yescharacteristic
436C2#1309312111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#385C2
socle, cosocleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenter#385D23
hypocenterC23D4×C4⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. C22×Dic23⋊C4C2semidirect
5. C2×C4⋊C4×D23C2semidirect
6. #13092314C2semidirect
7. #13092312C2semidirect
8. #13092292C2semidirect
9. #13092291C2semidirect
10. #13092288C2semidirect
11. #13092286C2semidirect
12. #13092276C2semidirect
13. #13092275C2semidirect
14. #13092268C2semidirect
15. C23×#385C2semidirect
49. (C22⋊D23)⋊C4C4semidirect
75. C22×Dic23C2×C4semidirect
91. C2×C4×D23C2×C4semidirect
95. C22⋊C4×C23C2×C4semidirect
99. (C2×D23)⋊C4C2×C4semidirect
109. Dic23⋊C4C2×C4semidirect
110. Dic23⋊C4D4semidirect
113. C4×Dic23C2×C4semidirect
148. C22⋊D23C4⋊C4semidirect
182. C22×C23C2×C4⋊C4semidirect
196. C2×D23C2×C4⋊C4semidirect
208. Dic23C2×C4⋊C4semidirect
209. Dic23C4×D4semidirect
220. #385D23semidirect
274. C23D4×C4⋊C4semidirect
329. C22⋊C4C4×D23semidirect
407. C22C4⋊C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D232
C2×(C22⋊D23)⋊C42
C22×Dic23⋊C42
C2×C4⋊C4×D232
#130923142
#130923122
#130922922
#130922912
#130922882
#130922862
#130922762
#130922752
#130922682
C23×#3852
D4×C4⋊C423