Finite Group Databasebeta

← #15683661

Subgroups — #15683661

Order 2944.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093038C211yesmaximal, characteristic, complemented
2#13092897C211yesmaximal, characteristic, complemented
3#13092753C211yesmaximal, characteristic, complemented
4#13092731C211yesmaximal, characteristic, complemented
5#13092713C211yesmaximal, characteristic, complemented
6#13092698C211yesmaximal, characteristic, complemented
7#13092640C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092581C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic
11#13092519C211yesmaximal, characteristic, complemented
12#13092519C211yesmaximal, characteristic, complemented
13C4×Dic92C211yesmaximal, characteristic, complemented
14C4×D184C211yesmaximal, characteristic, complemented
15C23×#433C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C23×#117C2211yescharacteristic
18#10625101C2211yescharacteristic
19C2×C4⋊Dic23C2211yescharacteristic
20#10625095C2211yescharacteristic
21C2×Dic92C2211yescharacteristic
22C2×D184C2211yescharacteristic
23C2×#67263C2211yescharacteristic
24C2×#67263C2211yescharacteristic
25#10625069—21no—
26#10625067—21no—
27#10625063—21no—
28C4⋊C4×D23—21no—
29#10625056—21no—
30#10625054—21no—
31(C22⋊D23)⋊C4—21no—
32(C22⋊D23)⋊C4—21no—
33#10625046C2211yescharacteristic
34C4×D92C2211yescharacteristic
35C4×D92C2211yescharacteristic
36C4×D92C2211yescharacteristic
37#10625040C2211yescharacteristic
38C4×Dic46C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41C23×C4⋊C8C2211yescharacteristic
42C23×C4⋊C8C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45C23×#97C2211yescharacteristic
46C4×C8×C23C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625000C2211yescharacteristic
52#10625000C2211yescharacteristic
53#10625000C2211yescharacteristic
54#10625000C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624998C2211yescharacteristic
58#10624998C2211yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C2×C22⋊D23—21no—
61C2×C22⋊D23—21no—
62C22×Dic23—21no—
63#67288—22no—
64#67288—22no—
65C2×D92C2311yescharacteristic
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×Dic46—21no—
72C2×Dic46C2311yescharacteristic
73C2×Dic46C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23D411yescharacteristic
79C4⋊C4×C23D411yescharacteristic
80C22⋊C4×C23D411yescharacteristic
81C22⋊C4×C23D411yescharacteristic
82C42×C23C2311yescharacteristic
83C42×C23C2311yescharacteristic
84C22⋊Dic23—21no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23—21no—
93C4⋊Dic23C2311yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104Dic92—22no—
105D184—22no—
106#67263—22no—
107#67263—22no—
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110C22×D23—21no—
111C2×C4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23C2×D411yescharacteristic
114C2×C4×C23C2×D411yescharacteristic
115C2×C4×C23C2×D411yescharacteristic
116C2×C4×C23C2×D411yescharacteristic
117C2×C4×C23C2×D411yescharacteristic
118C2×C4×C23C2411yescharacteristic
119C22⋊D23—24no—
120C22⋊D23—81no—
121C2×Dic23—21no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—81no—
128D92—21no—
129D92—21no—
130D92—21no—
131D92#4112yes—
132C4×D23—24no—
133C4×D23—81no—
134C4×D23—81no—
135C4×D23—81no—
136Dic46—21no—
137Dic46—21no—
138Dic46—21no—
139Dic46—81no—
140Dic46#4112yes—
141C8×C23—21no—
142C8×C23—21no—
143C8×C23—21no—
144C8×C23—21no—
145#3124—231nomaximal, Sylow
146C22×C23—21no—
147C22×C23—21no—
148C22×C23—21no—
149C22×C23C22×D411yescharacteristic
150C2×D23—22no—
151C2×D23—41no—
152C2×D23—41no—
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C4×C23—21no—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—21no—
160C4×C23—21no—
161C4×C23C2×#4111yescharacteristic
162C4×C23C2×#4111yescharacteristic
163Dic23—22no—
164Dic23—41no—
165Dic23—41no—
166Dic23—41no—
167Dic23—41no—
168Dic23—41no—
169#542—231no—
170#520—231no—
171#484—231no—
172#480—231no—
173#477—231no—
174#474—231no—
175#464—231no—
176#463—231no—
177#452—231no—
178#449—231no—
179#440—231no—
180#440—231no—
181C4×Q16—231no—
182C4×D8—231no—
183#433D2311yescharacteristic, complemented
184C2×C23—41no—
185C2×C23#52511yescharacteristic
186C2×C23#57611yescharacteristic
187C2×C23#57811yescharacteristic
188D23—42no—
189D23—81no—
190C2×#41—231no—
191C2×Q16—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×D8—231no—
195C4⋊Q8—231no—
196#126—461no—
197#124—231no—
198#124—461no—
199#123—461no—
200C22⋊Q8—231no—
201C22⋊Q8—461no—
202#121—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8—231no—
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211#117—461no—
212#117C2×D2311yescharacteristic
213C2×C4⋊C4—231no—
214C2×C4⋊C4—461no—
215#107—231no—
216#107—231no—
217#107—231no—
218#107—231no—
219C4⋊C8C2×D2311yescharacteristic
220C4⋊C8C2×D2311yescharacteristic
221#103—231no—
222#103—231no—
223#103—231no—
224#103—231no—
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229C22⋊C8C2×D2311yescharacteristic
230C22⋊C8C2×D2311yescharacteristic
231#97C2×D2311yescharacteristic
232C4×C8C2×D2311yescharacteristic
233C23#312411yescharacteristic, complemented, Sylow
234#41—462no—
235#41—462no—
236C2×Q8—231no—
237C2×Q8—231no—
238C2×Q8—461no—
239C2×D4—231no—
240C2×D4—231no—
241C2×D4—461no—
242C2×D4—461no—
243C22×C4—461no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4C22×D2311yescharacteristic
249Q16—462no—
250SD16—462no—
251SD16—462no—
252D8—462no—
253C2×C8C22×D2311yescharacteristic
254C2×C8C22×D2311yescharacteristic
255C2×C8C22×D2311yescharacteristic
256C2×C8C22×D2311yescharacteristic
257C4⋊C4—231no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4D9211yescharacteristic
268C4⋊C4D9211yescharacteristic
269C22⋊C4—461no—
270C22⋊C4—461no—
271C22⋊C4—461no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4D9211yescharacteristic
277C22⋊C4D9211yescharacteristic
278C42—461no—
279C42—461no—
280C42—461no—
281C42C22×D2311yescharacteristic
282C42C22×D2311yescharacteristic
283C23—461no—
284C23—461no—
285C23C2×D9211yescharacteristic
286Q8—232no—
287Q8—461no—
288Q8—461no—
289Q8—461no—
290Q8—1841no—
291D4—232no—
292D4—464no—
293D4—461no—
294D4—461no—
295D4—461no—
296D4—1841no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—464no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—461no—
305C2×C4—461no—
306C2×C4—1841no—
307C2×C4—1841no—
308C2×C4—1841no—
309C2×C4—1841no—
310C2×C4C2×D9211yescharacteristic
311C2×C4C2×D9211yescharacteristic
312C2×C4C2×D9211yescharacteristic
313C2×C4C2×D9211yescharacteristic
314C2×C4C2×D9211yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—462no—
324C22—921no—
325C22—921no—
326C22—921no—
327C22—921no—
328C22—921no—
329C22C22×D9211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—462no—
336C4—921no—
337C4—921no—
338C4—921no—
339C4—921no—
340C4—921no—
341C4#41×D2311yescharacteristic
342C4#41×D2311yescharacteristic
343C2—41no—
344C2—922no—
345C2—1841no—
346C2#1309292911yescharacteristic
347C2#1309322211yescharacteristic
348C2#1309323411yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
prime radical#13092564C2
hypercenter#433D23
hypocenterC23#3124
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #13093038C2semidirect
2. #13092897C2semidirect
3. #13092753C2semidirect
4. #13092731C2semidirect
5. #13092713C2semidirect
6. #13092698C2semidirect
7. #13092640C2semidirect
8. #13092633C2semidirect
9. #13092581C2semidirect
11. #13092519C2semidirect
12. #13092519C2semidirect
13. C4×Dic92C2semidirect
14. C4×D184C2semidirect
15. C23×#433C2semidirect
183. #433D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930382
#130928972
#130927532
#130927312
#130927132
#130926982
#130926402
#130926332
#130925812
#130925642
#130925192
C4×Dic922
C4×D1842
C23×#4332
#312423