Finite Group Databasebeta

← #15683598

Subgroups — #15683598

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093022C211yesmaximal, characteristic, complemented
2#13092897C211yesmaximal, characteristic, complemented
3#13092736C211yesmaximal, characteristic, complemented
4#13092731C211yesmaximal, characteristic, complemented
5#13092725C211yesmaximal, characteristic, complemented
6#13092718C211yesmaximal, characteristic, complemented
7#13092618C211yesmaximal, characteristic, complemented
8#13092613C211yesmaximal, characteristic, complemented
9#13092564C211yesmaximal, characteristic, complemented
10#13092564C211yesmaximal, characteristic, complemented
11#13092530C211yesmaximal, characteristic, complemented
12#13092519C211yesmaximal, characteristic, complemented
13C4×#67263C211yesmaximal, characteristic, complemented
14C4×D184C211yesmaximal, characteristic, complemented
15C23×#433C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C23×#117C2211yescharacteristic
18#10625101C2211yescharacteristic
19#10625101C2211yescharacteristic
20C2×C4⋊Dic23C2211yescharacteristic
21C2×D184C2211yescharacteristic
22C2×D184C2211yescharacteristic
23C2×#67263C2211yescharacteristic
24C2×#67263C2211yescharacteristic
25#10625065—21no—
26#10625065—21no—
27#10625063—21no—
28C4⋊C4×D23—21no—
29#10625055—21no—
30#10625055—21no—
31(C22⋊D23)⋊C4—21no—
32(C22⋊D23)⋊C4—21no—
33#10625045C2211yescharacteristic
34C4×D92C2211yescharacteristic
35C4×D92C2211yescharacteristic
36C4×D92C2211yescharacteristic
37C4×D92C2211yescharacteristic
38#10625041C2211yescharacteristic
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#10625003C2211yescharacteristic
52#10625003C2211yescharacteristic
53#10625000C2211yescharacteristic
54#10625000C2211yescharacteristic
55#10624999C2211yescharacteristic
56#10624999C2211yescharacteristic
57#10624998C2211yescharacteristic
58#10624998C2211yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C2×C22⋊D23—21no—
61C2×C22⋊D23—21no—
62C2×C22⋊D23—21no—
63C22×Dic23—21no—
64#67288—22no—
65#67288—22no—
66C2×D92—21no—
67C2×D92—21no—
68C2×D92C2311yescharacteristic
69C2×D92C2311yescharacteristic
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×Dic46C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23D411yescharacteristic
82C4⋊C4×C23D411yescharacteristic
83C22⋊C4×C23D411yescharacteristic
84C22⋊C4×C23D411yescharacteristic
85C42×C23C2311yescharacteristic
86C42×C23C2311yescharacteristic
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23C2311yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104D184—22no—
105D184—22no—
106#67263—22no—
107#67263—22no—
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110C22×D23—21no—
111C22×D23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23C2×D411yescharacteristic
115C2×C4×C23C2×D411yescharacteristic
116C2×C4×C23C2×D411yescharacteristic
117C2×C4×C23C2×D411yescharacteristic
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2411yescharacteristic
120C22⋊D23—24no—
121C22⋊D23—81no—
122C22⋊D23—81no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—81no—
129D92—21no—
130D92—21no—
131D92—21no—
132D92—21no—
133D92—21no—
134D92—81no—
135D92—81no—
136D92#4112yes—
137C4×D23—24no—
138C4×D23—81no—
139C4×D23—81no—
140C4×D23—81no—
141C4×D23—81no—
142Dic46—21no—
143Dic46#4112yes—
144C8×C23—21no—
145C8×C23—21no—
146C8×C23—21no—
147C8×C23—21no—
148#3119—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—21no—
151C22×C23—21no—
152C22×C23C22×D411yescharacteristic
153C2×D23—22no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—21no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23C2×#4111yescharacteristic
168C4×C23C2×#4111yescharacteristic
169Dic23—22no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173Dic23—41no—
174#540—231no—
175#520—231no—
176#481—231no—
177#480—231no—
178#479—231no—
179#478—231no—
180#460—231no—
181#459—231no—
182#449—231no—
183#449—231no—
184#442—231no—
185#440—231no—
186C4×SD16—231no—
187C4×D8—231no—
188#433D2311yescharacteristic, complemented
189C2×C23—41no—
190C2×C23#52511yescharacteristic
191C2×C23#57611yescharacteristic
192C2×C23#57711yescharacteristic
193D23—42no—
194D23—81no—
195D23—81no—
196C2×#41—231no—
197C2×SD16—231no—
198C2×SD16—231no—
199C2×D8—231no—
200C2×D8—231no—
201#127—231no—
202#125—231no—
203#123—461no—
204#123—461no—
205#121—231no—
206#121—231no—
207#121—461no—
208#121—461no—
209C4×Q8—231no—
210C4×Q8—231no—
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—461no—
216C4×D4—461no—
217#117—461no—
218#117C2×D2311yescharacteristic
219C2×C4⋊C4—231no—
220C2×C4⋊C4—461no—
221#107—231no—
222#107—231no—
223#106—231no—
224#106—231no—
225C4⋊C8C2×D2311yescharacteristic
226C4⋊C8C2×D2311yescharacteristic
227#103—231no—
228#103—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102—231no—
235C22⋊C8C2×D2311yescharacteristic
236C22⋊C8C2×D2311yescharacteristic
237#97C2×D2311yescharacteristic
238C4×C8C2×D2311yescharacteristic
239C23#311911yescharacteristic, complemented, Sylow
240#41—462no—
241#41—462no—
242C2×Q8—231no—
243C2×D4—231no—
244C2×D4—231no—
245C2×D4—231no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4—461no—
250C2×D4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4C22×D2311yescharacteristic
258SD16—462no—
259SD16—462no—
260D8—462no—
261D8—462no—
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4D9211yescharacteristic
276C4⋊C4D9211yescharacteristic
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4D9211yescharacteristic
284C22⋊C4D9211yescharacteristic
285C42—461no—
286C42—461no—
287C42C22×D2311yescharacteristic
288C42C22×D2311yescharacteristic
289C23—461no—
290C23—461no—
291C23—461no—
292C23C2×D9211yescharacteristic
293Q8—232no—
294Q8—461no—
295D4—232no—
296D4—464no—
297D4—461no—
298D4—461no—
299D4—461no—
300D4—461no—
301D4—461no—
302D4—1841no—
303D4—1841no—
304D4—1841no—
305D4—1841no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—464no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—461no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—1841no—
315C2×C4—1841no—
316C2×C4—1841no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4C2×D9211yescharacteristic
320C2×C4C2×D9211yescharacteristic
321C2×C4C2×D9211yescharacteristic
322C2×C4C2×D9211yescharacteristic
323C2×C4C2×D9211yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—462no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22C22×D9211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—462no—
348C4—921no—
349C4—921no—
350C4—921no—
351C4—921no—
352C4#41×D2311yescharacteristic
353C4#41×D2311yescharacteristic
354C2—41no—
355C2—922no—
356C2—1841no—
357C2—1841no—
358C2#1309292911yescharacteristic
359C2#1309322211yescharacteristic
360C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#433C2
socleC22×C23C22×D4
hypercenter#433D23
hypocenterC23#3119
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. #13093022C2semidirect
2. #13092897C2semidirect
3. #13092736C2semidirect
4. #13092731C2semidirect
5. #13092725C2semidirect
6. #13092718C2semidirect
7. #13092618C2semidirect
8. #13092613C2semidirect
9. #13092564C2semidirect
10. #13092564C2semidirect
11. #13092530C2semidirect
12. #13092519C2semidirect
13. C4×#67263C2semidirect
14. C4×D184C2semidirect
15. C23×#433C2semidirect
188. #433D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930222
#130928972
#130927362
#130927312
#130927252
#130927182
#130926182
#130926132
#130925642
#130925302
#130925192
C4×#672632
C4×D1842
C23×#4332
#311923