Finite Group Databasebeta

← #15683602

Subgroups — #15683602

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#13093018C211yesmaximal, characteristic, complemented
2#13092899C211yesmaximal, characteristic, complemented
3#13092737C211yesmaximal, characteristic, complemented
4#13092729C211yesmaximal, characteristic, complemented
5#13092726C211yesmaximal, characteristic, complemented
6#13092716C211yesmaximal, characteristic, complemented
7#13092615C211yesmaximal, characteristic, complemented
8#13092611C211yesmaximal, characteristic, complemented
9#13092565C211yesmaximal, characteristic, complemented
10#13092561C211yesmaximal, characteristic, complemented
11#13092527C211yesmaximal, characteristic, complemented
12#13092515C211yesmaximal, characteristic, complemented
13C4×D184C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×SD16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67274C2211yescharacteristic
22#10625111C2211yescharacteristic
23#10625109C2211yescharacteristic
24C2×#67272C2211yescharacteristic
25#10625101—21no—
26#10625100—21no—
27C2×D184C2211yescharacteristic
28#10625066C2211yescharacteristic
29#10625064—21no—
30#10625064C2211yescharacteristic
31C4⋊C4×D23—21no—
32C4⋊C4×D23C2211yescharacteristic
33#10625061C2211yescharacteristic
34#10625055—21no—
35#10625054—21no—
36C4×D92—21no—
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic
39#10625043—21no—
40#10625043C2211yescharacteristic
41C23×#106C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625014C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51#10625000C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65#67292—22no—
66#67292—22no—
67C2×D92—21no—
68C2×D92—21no—
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×C4×D23C2311yescharacteristic
77SD16×C23—22no—
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C4⋊C4×C23—21no—
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C42×C23—21no—
85C42×C23C2311yescharacteristic
86C22⋊Dic23—21no—
87#67274—22no—
88#67272—22no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23—21no—
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107D184—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—21no—
111C22×D23C2×D411yescharacteristic
112Q8×C23—21no—
113Q8×C23#4112yes—
114D4×C23—21no—
115D4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—81no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2411yescharacteristic
123C22⋊D23—81no—
124C22⋊D23—81no—
125C22⋊D23—81no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131D92—24no—
132D92—21no—
133D92—21no—
134D92—21no—
135D92—81no—
136D92#4112yes—
137C4×D23—24no—
138C4×D23—21no—
139C4×D23—21no—
140C4×D23—81no—
141C4×D23—81no—
142C4×D23—81no—
143C4×D23—81no—
144C8×C23—21no—
145C8×C23—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23—41no—
150C22×C23—41no—
151C22×C23—41no—
152C22×C23C22×D411yescharacteristic
153C2×D23—21no—
154C2×D23—22no—
155C2×D23—21no—
156C2×D23—21no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—22no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23C2×#4111yescharacteristic
168C4×C23C2×#4111yescharacteristic
169Dic23—21no—
170Dic23—21no—
171Dic23—21no—
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×SD16D2311yescharacteristic, complemented
187C4×D8—231no—
188#433—231no—
189C2×C23—81no—
190C2×C23#52511yescharacteristic
191C2×C23#57611yescharacteristic
192C2×C23#57711yescharacteristic
193D23—41no—
194D23—42no—
195D23—81no—
196C2×#41—231no—
197C2×SD16—231no—
198C2×SD16C2×D2311yescharacteristic
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×Q8C2×D2311yescharacteristic
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—461no—
215C4×D4—461no—
216C4×D4C2×D2311yescharacteristic
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—461no—
221#107—231no—
222#107—231no—
223#106—231no—
224#106C2×D2311yescharacteristic
225C4⋊C8—231no—
226C4⋊C8—231no—
227#103—231no—
228#103C2×D2311yescharacteristic
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234#102C2×D2311yescharacteristic
235C22⋊C8—231no—
236C22⋊C8—231no—
237#97—231no—
238C4×C8C2×D2311yescharacteristic
239C23#311911yescharacteristic, complemented, Sylow
240#41—462no—
241#41—462no—
242C2×Q8C22×D2311yescharacteristic
243C2×D4—231no—
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4—461no—
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—231no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258SD16—22no—
259SD16—462no—
260D8—462no—
261D8—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—231no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—231no—
279C22⋊C4—231no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C42—21no—
286C42—231no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C23—21no—
290C23—231no—
291C23—461no—
292C23—461no—
293Q8—21no—
294Q8#6728812yes—
295D4—21no—
296D4—21no—
297D4—232no—
298D4—464no—
299D4—461no—
300D4—461no—
301D4—461no—
302D4—1841no—
303D4—1841no—
304D4—1841no—
305D4—1841no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—231no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—464no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4—1841no—
322C2×C4D4×D2311yescharacteristic
323C2×C4D4×D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—21no—
327C8—461no—
328C8—461no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—462no—
333C22—461no—
334C22—461no—
335C22—461no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22C2×D4×D2311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—461no—
348C4—461no—
349C4—461no—
350C4—921no—
351C4—921no—
352C4C2×#6728811yescharacteristic
353C4#41×D2311yescharacteristic
354C2—81no—
355C2—921no—
356C2—922no—
357C2—1841no—
358C2#1309292611yescharacteristic
359C2#1309321911yescharacteristic
360C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×SD16×C23C2
socleC22×C23C22×D4
hypercenterC4×SD16D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #13093018C2semidirect
2. #13092899C2semidirect
3. #13092737C2semidirect
4. #13092729C2semidirect
5. #13092726C2semidirect
6. #13092716C2semidirect
7. #13092615C2semidirect
8. #13092611C2semidirect
9. #13092565C2semidirect
10. #13092561C2semidirect
11. #13092527C2semidirect
12. #13092515C2semidirect
13. C4×D184C2semidirect
14. #13092476C2semidirect
15. C4×SD16×C23C2semidirect
186. C4×SD16D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930182
#130928992
#130927372
#130927292
#130927262
#130927162
#130926152
#130926112
#130925652
#130925612
#130925272
#130925152
C4×D1842
#130924762
C4×SD16×C232
#311923