Finite Group Databasebeta

← #15685150

Subgroups — #15685150

Order 2944.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625087C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13093086C211yesmaximal, characteristic, complemented
4#13093085C211yesmaximal, characteristic, complemented
5#13092792C211yesmaximal, characteristic, complemented
6#13092652C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092616C211yesmaximal, characteristic, complemented
9#13092615C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092564C211yesmaximal, characteristic, complemented
12#13092559C211yesmaximal, characteristic, complemented
13#13092509C211yesmaximal, characteristic, complemented
14(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×#67290C2211yescharacteristic
19C2×#67288C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic
22C23×#121C2211yescharacteristic
23#10625121—24no—
24Q8×Dic23C2211yescharacteristic
25C2×#67275C2211yescharacteristic
26C2×#67274C2211yescharacteristic
27#10625111—21no—
28#10625111—21no—
29#10625111C2211yescharacteristic
30#10625111C2211yescharacteristic
31#10625110—21no—
32#10625109—21no—
33#10625109C2211yescharacteristic
34C2×#67273C2211yescharacteristic
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37#10625101—21no—
38#10625101C2211yescharacteristic
39C4×C22⋊D23—21no—
40C4×C22⋊D23C2211yescharacteristic
41C22×C23⋊C8C2211yescharacteristic
42#10625087—24no—
43C2×D184C2211yescharacteristic
44C2×#67263C2211yescharacteristic
45C2×C8×D23C2211yescharacteristic
46#10625066C2211yescharacteristic
47#10625058C2211yescharacteristic
48#10625055—21no—
49(C22⋊D23)⋊C4—21no—
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic
56#10624998C2211yescharacteristic
57Dic23⋊C8C2211yescharacteristic
58C8×Dic23C2211yescharacteristic
59#10624991C2211yescharacteristic
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⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23—21no—
78C2×C22⋊D23D411yescharacteristic
79C22×Dic23—21no—
80#67292—22no—
81#67292—41no—
82#67290—22no—
83#67290—41no—
84#67288—22no—
85#67288—41no—
86C2×D92—21no—
87C2×D92—21no—
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93C2×Dic46C2311yescharacteristic
94SD16×C23—22no—
95D8×C23—41no—
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23D411yescharacteristic
102#67275D414yescomplemented
103#67274—22no—
104#67273—22no—
105#67272—22no—
106#67272—22no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4D411yescharacteristic
110C4⋊Dic23—21no—
111C4⋊Dic23C2311yescharacteristic
112Dic23⋊C4—21no—
113Dic23⋊C4D411yescharacteristic
114C4×Dic23—21no—
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—41no—
121#67263—22no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23C2×D411yescharacteristic
129Q8×C23—21no—
130Q8×C23C2×D412yes—
131D4×C23—21no—
132D4×C23—21no—
133D4×C23—21no—
134D4×C23—21no—
135D4×C23—42no—
136D4×C23—81no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—42no—
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2411yescharacteristic
144C22⋊D23—22no—
145C22⋊D23—42no—
146C22⋊D23—42no—
147C22⋊D23—42no—
148C22⋊D23—42no—
149C22⋊D23—81no—
150C22⋊D23—81no—
151C22⋊D23—81no—
152C22⋊D23—81no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—42no—
156C2×Dic23C2×D411yescharacteristic
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—21no—
160D92—21no—
161D92—21no—
162D92—21no—
163D92—42no—
164D92—81no—
165C4×D23—21no—
166C4×D23—21no—
167C4×D23—42no—
168C4×D23—42no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
175#3287—231nomaximal, Sylow
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—21no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C4×C23—21no—
196C4×C23—22no—
197C4×C23—41no—
198C4×C23C22×D411yescharacteristic
199C4×C23H(5,𝔽2)11yescharacteristic
200Dic23—22no—
201Dic23—21no—
202Dic23—21no—
203Dic23—41no—
204Dic23#13512yescomplemented
205C2×#135—231no—
206C2×#135—231no—
207#550—231no—
208#550—231no—
209#493—231no—
210#466—231no—
211#466—231no—
212#460—231no—
213#460—231no—
214#449—231no—
215#449—231no—
216#449—231no—
217#449D2311yescharacteristic, complemented
218C4×Q16—231no—
219C8×D4—231no—
220C2×C23—41no—
221C2×C23—81no—
222C2×C23—81no—
223C2×C23D4211yescharacteristic
224C2×C23C2×#13511yescharacteristic
225C2×C23#57611yescharacteristic
226D23—41no—
227D23—81no—
228D23—81no—
229C2×#41—231no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41C2×D2311yescharacteristic
233#135—464no—
234#135—464no—
235C2×Q16—231no—
236C2×SD16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16C2×D2311yescharacteristic
240C2×D8—231no—
241C2×D8—231no—
242C2×D8—231no—
243C2×D8C2×D2311yescharacteristic
244C22×C8—231no—
245C22×C8—231no—
246#127—231no—
247#127—231no—
248#127—461no—
249#127—461no—
250#121—231no—
251#121—231no—
252#121—231no—
253#121—461no—
254#121—461no—
255#121—461no—
256#121—461no—
257#121C2×D2311yescharacteristic
258C4×Q8—231no—
259C4×Q8—231no—
260C4×D4—231no—
261C4×D4—461no—
262C4×D4—461no—
263#107—231no—
264C4⋊C8—231no—
265#103—231no—
266#103C2×D2311yescharacteristic
267#102—231no—
268#102—231no—
269#102—231no—
270#102C2×D2311yescharacteristic
271C22⋊C8—231no—
272C22⋊C8C2×D2311yescharacteristic
273C4×C8—231no—
274C23#328711yescharacteristic, complemented, Sylow
275#41—22no—
276#41—41no—
277#41—462no—
278#41—462no—
279#41—462no—
280#41—921no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8C22×D2311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—231no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4C22×D2311yescharacteristic
301C2×D4C22×D2311yescharacteristic
302C22×C4—21no—
303C22×C4—231no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4—461no—
307C22×C4C22×D2311yescharacteristic
308Q16—234no—
309SD16—22no—
310SD16—462no—
311SD16—462no—
312SD16—462no—
313D8—41no—
314D8—462no—
315D8—462no—
316D8—921no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8—462no—
321C2×C8C22×D2311yescharacteristic
322C2×C8C22×D2311yescharacteristic
323C4⋊C4—231no—
324C4⋊C4—231no—
325C4⋊C4—461no—
326C4⋊C4—461no—
327C4⋊C4C22×D2311yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—231no—
330C22⋊C4—231no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C42—231no—
335C42—461no—
336C42—461no—
337C23—21no—
338C23—21no—
339C23—231no—
340C23—461no—
341C23—461no—
342C23D4×D2311yescharacteristic
343Q8—21no—
344Q8—232no—
345Q8—461no—
346Q8D4×D2312yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—462no—
354D4—461no—
355D4—461no—
356D4—461no—
357D4—461no—
358D4—922no—
359D4—922no—
360D4—922no—
361D4—922no—
362D4—922no—
363D4—1841no—
364D4—1841no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—231no—
374C2×C4—231no—
375C2×C4—231no—
376C2×C4—461no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—922no—
381C2×C4—922no—
382C2×C4—922no—
383C2×C4D4×D2311yescharacteristic
384C2×C4C23×D2311yescharacteristic
385C8—21no—
386C8—21no—
387C8—232no—
388C8—461no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—461no—
399C22—461no—
400C22—461no—
401C22—921no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22C2×D4×D2311yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—232no—
412C4—461no—
413C4—461no—
414C4—462no—
415C4—921no—
416C4C2×D4×D2311yescharacteristic
417C4#1062515511yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—921no—
422C2—1841no—
423C2—1841no—
424C2#1309304911yescharacteristic
425C2#135×D2311yescharacteristic
426C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3287
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×#10625087C2semidirect
2. C2×#10625121C2semidirect
3. #13093086C2semidirect
4. #13093085C2semidirect
5. #13092792C2semidirect
6. #13092652C2semidirect
7. #13092651C2semidirect
8. #13092616C2semidirect
9. #13092615C2semidirect
10. #13092565C2semidirect
11. #13092564C2semidirect
12. #13092559C2semidirect
13. #13092509C2semidirect
14. (C22⋊D23)⋊C8C2semidirect
15. C23×#449C2semidirect
102. #67275D4semidirect
204. Dic23#135semidirect
217. #449D23semidirect
274. C23#3287semidirect

Maximal subgroups

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

subgroupindex
C2×#106250872
C2×#106251212
#130930862
#130930852
#130927922
#130926522
#130926512
#130926162
#130926152
#130925652
#130925642
#130925592
#130925092
(C22⋊D23)⋊C82
C23×#4492
#328723