Finite Group Databasebeta

← #15682850

Subgroups — #15682850

Order 2944.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625075C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13092963C211yesmaximal, characteristic, complemented
4#13092885C211yesmaximal, characteristic, complemented
5#13092642C211yesmaximal, characteristic, complemented
6#13092638C211yesmaximal, characteristic, complemented
7#13092635C211yesmaximal, characteristic, complemented
8#13092631C211yesmaximal, characteristic, complemented
9#13092626C211yesmaximal, characteristic, complemented
10#13092621C211yesmaximal, characteristic, complemented
11#13092616C211yesmaximal, characteristic, complemented
12#13092611C211yesmaximal, characteristic, complemented
13C2×Dic23⋊C8C211yesmaximal, characteristic, complemented
14#13092411C211yesmaximal, characteristic, complemented
15C23×#416C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C23×#117C2211yescharacteristic
21#10625121—24no—
22#10625118C2211yescharacteristic
23#10625115C2211yescharacteristic
24C2×#67275C2211yescharacteristic
25C2×#67274C2211yescharacteristic
26#10625111C2211yescharacteristic
27#10625110—21no—
28#10625110—21no—
29#10625107C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32C4×C22⋊D23—21no—
33C4×C22⋊D23—21no—
34C2×C4×Dic23C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C2×Dic92C2211yescharacteristic
37#10625075—24no—
38C2×D184C2211yescharacteristic
39C2×#67263C2211yescharacteristic
40C2×#67263C2211yescharacteristic
41#10625064C2211yescharacteristic
42#10625064C2211yescharacteristic
43#10625058C2211yescharacteristic
44#10625058C2211yescharacteristic
45(C22⋊D23)⋊C4—21no—
46(C22⋊D23)⋊C4—21no—
47#10625043—21no—
48C42×D23—21no—
49C23×#103C2211yescharacteristic
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×#102C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56Dic23⋊C8C2211yescharacteristic
57#10624992C2211yescharacteristic
58#10624992C2211yescharacteristic
59#10624991C2211yescharacteristic
60#10624991C2211yescharacteristic
61#41×C23—22no—
62#41×C23—22no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C22×Dic23D411yescharacteristic
73C22×Dic23D411yescharacteristic
74#67288—22no—
75#67288—22no—
76#67288—22no—
77#67288D414yescomplemented
78C2×D92C2311yescharacteristic
79C2×D92C2311yescharacteristic
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23—21no—
84C2×Dic46C2311yescharacteristic
85C2×Dic46C2311yescharacteristic
86C2×C8×C23—22no—
87C2×C8×C23C2311yescharacteristic
88C2×C8×C23C2311yescharacteristic
89C4⋊C4×C23C2311yescharacteristic
90C4⋊C4×C23C2311yescharacteristic
91C22⋊C4×C23—21no—
92C42×C23—21no—
93C22⋊Dic23—21no—
94C22⋊Dic23—21no—
95#67275—22no—
96#67274—22no—
97#67273—22no—
98#67272—22no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106Dic23⋊C4—21no—
107C4×Dic23—21no—
108C4×Dic23—21no—
109C4×Dic23D411yescharacteristic
110C4×Dic23D411yescharacteristic
111C4×Dic23C2311yescharacteristic
112C4×Dic23C2311yescharacteristic
113C2×C23⋊C8—22no—
114C2×C23⋊C8C2311yescharacteristic
115C2×C23⋊C8C2311yescharacteristic
116Dic92—22no—
117D184—22no—
118#67263—22no—
119#67263—22no—
120C23×C23—21no—
121C23×C23C2×D411yescharacteristic
122C22×D23—21no—
123C22×D23—21no—
124Q8×C23—21no—
125Q8×C23—21no—
126D4×C23—21no—
127D4×C23—21no—
128D4×C23—42no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—42no—
133C2×C4×C23C2×D412yes—
134C2×C4×C23C2×D411yescharacteristic
135C2×C4×C23#4112yes—
136C2×C4×C23C2411yescharacteristic
137C22⋊D23—24no—
138C22⋊D23—42no—
139C22⋊D23—42no—
140C22⋊D23—42no—
141C2×Dic23—21no—
142C2×Dic23—22no—
143C2×Dic23—21no—
144C2×Dic23—41no—
145C2×Dic23C2×D411yescharacteristic
146C2×Dic23C2×D411yescharacteristic
147C2×Dic23C2×D411yescharacteristic
148C2×Dic23C2×D411yescharacteristic
149D92—21no—
150D92—21no—
151D92—21no—
152D92C2×D412yes—
153C4×D23—24no—
154C4×D23—42no—
155C4×D23—42no—
156C4×D23—42no—
157Dic46—21no—
158Dic46—21no—
159Dic46—21no—
160Dic46C2×D412yes—
161C8×C23—21no—
162C8×C23—21no—
163C23⋊C8—21no—
164C23⋊C8—21no—
165#3035—231nomaximal, Sylow
166C22×C23—21no—
167C22×C23—21no—
168C22×C23—41no—
169C22×C23—41no—
170C22×C23—41no—
171C22×C23#12112yes—
172C22×C23C22×D411yescharacteristic
173C2×D23—22no—
174C2×D23—41no—
175C2×D23—41no—
176C2×D23—41no—
177C2×D23—41no—
178C2×D23—41no—
179C4×C23—41no—
180C4×C23—41no—
181C4×C23—41no—
182C4×C23#12112yes—
183C4×C23C22×D411yescharacteristic
184C4×C23C2×#4111yescharacteristic
185Dic23—22no—
186Dic23—21no—
187Dic23—21no—
188Dic23—21no—
189Dic23—41no—
190Dic23#13512yescomplemented
191C2×#135—231no—
192C2×#135—231no—
193#532—231no—
194C4×#41—231no—
195#464—231no—
196#464—231no—
197#463—231no—
198#463—231no—
199#462—231no—
200#461—231no—
201#460—231no—
202#459—231no—
203C2×C4⋊C8—231no—
204#416—231no—
205#416D2311yescharacteristic, complemented
206C2×C23—22no—
207C2×C23—81no—
208C2×C23C2×#12111yescharacteristic
209C2×C23C2×#13511yescharacteristic
210C2×C23#57511yescharacteristic
211D23—42no—
212D23—81no—
213C2×#41—231no—
214C2×#41—231no—
215C2×#41C2×D2311yescharacteristic
216#135—464no—
217#135—464no—
218C2×Q16—231no—
219C2×Q16—231no—
220C2×SD16—231no—
221C2×SD16—231no—
222C2×SD16—231no—
223C2×SD16—231no—
224C2×D8—231no—
225C2×D8—231no—
226C22×C8—231no—
227C22×C8C2×D2311yescharacteristic
228C4⋊Q8—231no—
229#127—231no—
230#124—231no—
231#124—231no—
232#121—461no—
233#121—461no—
234C4×Q8—231no—
235C4×Q8—231no—
236C4×D4—231no—
237C4×D4—231no—
238C4×D4—461no—
239C4×D4—461no—
240C4×D4—461no—
241C4×D4—461no—
242#117—461no—
243#117C2×D2311yescharacteristic
244C2×C42—231no—
245C2×C42—461no—
246C4⋊C8—231no—
247C4⋊C8—231no—
248C4⋊C8—231no—
249C4⋊C8—231no—
250#103—231no—
251#103—231no—
252#103C2×D2311yescharacteristic
253#103C2×D2311yescharacteristic
254#102—231no—
255#102—231no—
256#102C2×D2311yescharacteristic
257#102C2×D2311yescharacteristic
258C23#303511yescharacteristic, complemented, Sylow
259#41—22no—
260#41—22no—
261#41—234no—
262#41—462no—
263#41—462no—
264#41—462no—
265C2×Q8—231no—
266C2×Q8—231no—
267C2×Q8C22×D2311yescharacteristic
268C2×D4—21no—
269C2×D4—231no—
270C2×D4—231no—
271C2×D4—461no—
272C2×D4—461no—
273C2×D4—461no—
274C2×D4—461no—
275C2×D4C22×D2311yescharacteristic
276C22×C4—21no—
277C22×C4—231no—
278C22×C4—231no—
279C22×C4—461no—
280C22×C4—461no—
281C22×C4—461no—
282C22×C4—461no—
283C22×C4C22×D2311yescharacteristic
284Q16—462no—
285Q16—462no—
286SD16—462no—
287SD16—462no—
288SD16—462no—
289SD16—462no—
290D8—462no—
291D8—462no—
292C2×C8—22no—
293C2×C8—231no—
294C2×C8—231no—
295C2×C8—462no—
296C2×C8C22×D2311yescharacteristic
297C2×C8C22×D2311yescharacteristic
298C4⋊C4—461no—
299C4⋊C4—461no—
300C4⋊C4—461no—
301C4⋊C4—461no—
302C4⋊C4C22×D2311yescharacteristic
303C4⋊C4C22×D2311yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—461no—
306C22⋊C4—461no—
307C22⋊C4—461no—
308C22⋊C4—461no—
309C22⋊C4—461no—
310C22⋊C4—461no—
311C42—21no—
312C42—231no—
313C42—231no—
314C42—231no—
315C42—231no—
316C42—461no—
317C42—461no—
318C23—21no—
319C23—461no—
320C23—461no—
321C23D4×D2311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—232no—
325Q8—461no—
326Q8—461no—
327Q8—461no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—232no—
332D4—464no—
333D4—461no—
334D4—461no—
335D4—461no—
336D4—922no—
337D4—922no—
338D4—922no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—231no—
344C2×C4—231no—
345C2×C4—231no—
346C2×C4—231no—
347C2×C4—462no—
348C2×C4—461no—
349C2×C4—464no—
350C2×C4—461no—
351C2×C4—922no—
352C2×C4—922no—
353C2×C4—921no—
354C2×C4—922no—
355C2×C4#6728812yes—
356C2×C4D4×D2312yes—
357C2×C4D4×D2311yescharacteristic
358C2×C4C23×D2311yescharacteristic
359C8—21no—
360C8—21no—
361C8—461no—
362C8—461no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—462no—
369C22—921no—
370C22—921no—
371C22—921no—
372C22—921no—
373C22—921no—
374C22#1062505512yes—
375C22C2×D4×D2311yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—232no—
380C4—462no—
381C4—461no—
382C4—461no—
383C4—461no—
384C4—921no—
385C4#1062505512yes—
386C4C2×#6728811yescharacteristic
387C4C2×D4×D2311yescharacteristic
388C2—22no—
389C2—81no—
390C2—922no—
391C2—1841no—
392C2C2×#1062505511yescharacteristic
393C2#135×D2311yescharacteristic
394C2#1309321411yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
hypercenter#416D23
hypocenterC23#3035
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#10625075C2semidirect
2. C2×#10625121C2semidirect
3. #13092963C2semidirect
4. #13092885C2semidirect
5. #13092642C2semidirect
6. #13092638C2semidirect
7. #13092635C2semidirect
8. #13092631C2semidirect
9. #13092626C2semidirect
10. #13092621C2semidirect
11. #13092616C2semidirect
12. #13092611C2semidirect
13. C2×Dic23⋊C8C2semidirect
14. #13092411C2semidirect
15. C23×#416C2semidirect
77. #67288D4semidirect
190. Dic23#135semidirect
205. #416D23semidirect
258. C23#3035semidirect

Maximal subgroups

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

subgroupindex
C2×#106250752
C2×#106251212
#130929632
#130928852
#130926422
#130926382
#130926352
#130926312
#130926262
#130926212
#130926162
#130926112
C2×Dic23⋊C82
#130924112
C23×#4162
#303523