Finite Group Databasebeta

← #15684950

Subgroups — #15684950

Order 2944.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625122C211yesmaximal, characteristic, complemented
2C2×#10625083C211yesmaximal, characteristic, complemented
3#13093073C211yesmaximal, characteristic, complemented
4#13093066C211yesmaximal, characteristic, complemented
5#13092808C211yesmaximal, characteristic, complemented
6#13092661C211yesmaximal, characteristic, complemented
7#13092657C211yesmaximal, characteristic, complemented
8#13092630C211yesmaximal, characteristic, complemented
9#13092626C211yesmaximal, characteristic, complemented
10#13092580C211yesmaximal, characteristic, complemented
11#13092576C211yesmaximal, characteristic, complemented
12#13092575C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092491C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67290C2211yescharacteristic
19C22×Dic46C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic
22C23×#121C2211yescharacteristic
23#10625122—24no—
24#10625117C2211yescharacteristic
25#10625115C2211yescharacteristic
26C2×#67275C2211yescharacteristic
27C2×#67275C2211yescharacteristic
28#10625110—21no—
29#10625110—21no—
30#10625107C2211yescharacteristic
31#10625106—21no—
32D4×Dic23—21no—
33D4×Dic23C2211yescharacteristic
34C2×#67273C2211yescharacteristic
35C2×#67273C2211yescharacteristic
36C2×#67273C2211yescharacteristic
37#10625100—21no—
38C4×C22⋊D23C2211yescharacteristic
39#10625095C2211yescharacteristic
40C2×Dic23⋊C4—21no—
41C2×#67267C2211yescharacteristic
42#10625083—24no—
43C2×Dic92C2211yescharacteristic
44C2×Dic92C2211yescharacteristic
45C2×C8×D23C2211yescharacteristic
46#10625068C2211yescharacteristic
47#10625058C2211yescharacteristic
48#10625056—21no—
49#10625049—21no—
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic
53#10625014C2211yescharacteristic
54(C2×D23)⋊C8C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624997C2211yescharacteristic
58Dic23⋊C8C2211yescharacteristic
59#10624992C2211yescharacteristic
60#10624989C2211yescharacteristic
61#41×C23—22no—
62#41×C23—41no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—21no—
65C2×D4×C23—21no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23—21no—
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23D411yescharacteristic
73C22×Dic23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23—21no—
77#67290—22no—
78#67290—22no—
79#67290—41no—
80#67290—41no—
81C2×C4×D23C2311yescharacteristic
82C2×Dic46—22no—
83C2×Dic46—21no—
84C2×Dic46—41no—
85C2×Dic46C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88SD16×C23—41no—
89D8×C23—22no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23C2311yescharacteristic
93C22⋊C4×C23—21no—
94C22⋊Dic23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23—21no—
98C22⋊Dic23D411yescharacteristic
99#67275—22no—
100#67275—22no—
101#67273—22no—
102#67273—22no—
103#67273D414yescomplemented
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4D411yescharacteristic
107C4⋊Dic23—21no—
108C4⋊Dic23C2311yescharacteristic
109Dic23⋊C4—21no—
110Dic23⋊C4—21no—
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117#67267—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120Dic92—22no—
121Dic92—41no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23C2×D411yescharacteristic
126C22×D23C2×D411yescharacteristic
127Q8×C23—21no—
128Q8×C23—21no—
129D4×C23—21no—
130D4×C23—21no—
131D4×C23—21no—
132D4×C23—42no—
133D4×C23—42no—
134D4×C23C2×D412yes—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—42no—
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—41no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—42no—
150C2×Dic23—42no—
151C2×Dic23—42no—
152C2×Dic23—42no—
153C2×Dic23C2×D411yescharacteristic
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156C4×D23—21no—
157C4×D23—21no—
158Dic46—21no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—42no—
164Dic46C2×D412yes—
165C8×C23—21no—
166C8×C23—21no—
167C23⋊C8—21no—
168C23⋊C8C2×D412yes—
169#3269—231nomaximal, Sylow
170C22×C23—21no—
171C22×C23—22no—
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23C22×D411yescharacteristic
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—21no—
183C4×C23—21no—
184C4×C23—41no—
185C4×C23—41no—
186C4×C23C22×D411yescharacteristic
187C4×C23H(5,𝔽2)11yescharacteristic
188Dic23—22no—
189Dic23—21no—
190Dic23—21no—
191Dic23—21no—
192Dic23—41no—
193Dic23—41no—
194Dic23—41no—
195C2×#137—231no—
196C2×#135—231no—
197#548—231no—
198#547—231no—
199#497—231no—
200#468—231no—
201#467—231no—
202#463—231no—
203#462—231no—
204#452—231no—
205#452—231no—
206#451—231no—
207#449D2311yescharacteristic, complemented
208#440—231no—
209#435—231no—
210C2×C23—41no—
211C2×C23—42no—
212C2×C23—81no—
213C2×C23D4211yescharacteristic
214C2×C23#57511yescharacteristic
215C2×C23#57811yescharacteristic
216D23—41no—
217C2×#41—231no—
218C2×#41—231no—
219C2×#41C2×D2311yescharacteristic
220C22×Q8—231no—
221#137—464no—
222#135—464no—
223C2×Q16—231no—
224C2×Q16—231no—
225C2×Q16—231no—
226C2×Q16—231no—
227C2×SD16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16C2×D2311yescharacteristic
231C2×D8C2×D2311yescharacteristic
232C2×M16—231no—
233C22×C8—231no—
234C4⋊Q8—231no—
235#124—231no—
236#124—461no—
237#123—461no—
238#123—461no—
239C22⋊Q8—231no—
240C22⋊Q8—231no—
241C22⋊Q8—231no—
242C22⋊Q8—461no—
243#121—461no—
244#121—461no—
245#121C2×D2311yescharacteristic
246C4×Q8—231no—
247C4×D4—231no—
248C4×D4—231no—
249C4×D4—461no—
250C2×C4⋊C4—461no—
251#107—231no—
252C4⋊C8—231no—
253#103—231no—
254#103—231no—
255#103—231no—
256#103C2×D2311yescharacteristic
257#102—231no—
258#102C2×D2311yescharacteristic
259C22⋊C8—231no—
260C22⋊C8C2×D2311yescharacteristic
261#97—231no—
262C23#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—41no—
265#41—462no—
266#41—462no—
267#41—921no—
268#41—921no—
269C2×Q8—231no—
270C2×Q8—231no—
271C2×Q8—231no—
272C2×Q8—462no—
273C2×Q8—461no—
274C2×Q8—921no—
275C2×Q8C22×D2311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—231no—
279C2×D4—461no—
280C2×D4—461no—
281C2×D4C22×D2311yescharacteristic
282C2×D4C22×D2311yescharacteristic
283C22×C4—21no—
284C22×C4—231no—
285C22×C4—461no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4C22×D2311yescharacteristic
290Q16—462no—
291Q16—462no—
292Q16—462no—
293Q16—921no—
294SD16—41no—
295SD16—234no—
296SD16—462no—
297SD16—462no—
298D8—22no—
299M16—462no—
300C2×C8—231no—
301C2×C8—231no—
302C2×C8—462no—
303C2×C8C22×D2311yescharacteristic
304C2×C8C22×D2311yescharacteristic
305C4⋊C4—231no—
306C4⋊C4—231no—
307C4⋊C4—461no—
308C4⋊C4—461no—
309C4⋊C4—461no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4C22×D2311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—231no—
316C22⋊C4—231no—
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C42—231no—
324C42—461no—
325C23—21no—
326C23—21no—
327C23—231no—
328C23D4×D2311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—232no—
332Q8—461no—
333Q8—461no—
334Q8—461no—
335Q8—461no—
336Q8—461no—
337Q8—922no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—921no—
344D4—922no—
345D4—922no—
346D4D4×D2312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—231no—
353C2×C4—231no—
354C2×C4—231no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—922no—
362C2×C4—922no—
363C2×C4—922no—
364C2×C4—922no—
365C2×C4D4×D2311yescharacteristic
366C2×C4C23×D2311yescharacteristic
367C8—21no—
368C8—21no—
369C8—232no—
370C8—461no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—461no—
381C22—461no—
382C22—461no—
383C22C2×D4×D2311yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—461no—
388C4—461no—
389C4—461no—
390C4—462no—
391C4—921no—
392C4—921no—
393C4—921no—
394C4C2×D4×D2311yescharacteristic
395C4#1062515511yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—921no—
400C2#1309304911yescharacteristic
401C2#1309321311yescharacteristic
402C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3269
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C2×#10625083C2semidirect
3. #13093073C2semidirect
4. #13093066C2semidirect
5. #13092808C2semidirect
6. #13092661C2semidirect
7. #13092657C2semidirect
8. #13092630C2semidirect
9. #13092626C2semidirect
10. #13092580C2semidirect
11. #13092576C2semidirect
12. #13092575C2semidirect
13. #13092514C2semidirect
14. #13092491C2semidirect
15. C23×#449C2semidirect
103. #67273D4semidirect
207. #449D23semidirect
262. C23#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
C2×#106250832
#130930732
#130930662
#130928082
#130926612
#130926572
#130926302
#130926262
#130925802
#130925762
#130925752
#130925142
#130924912
C23×#4492
#326923