Finite Group Databasebeta

← #15683590

Subgroups — #15683590

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#13092897C211yesmaximal, characteristic, complemented
2#13092733C211yesmaximal, characteristic, complemented
3#13092728C211yesmaximal, characteristic, complemented
4#13092721C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092614C211yesmaximal, characteristic, complemented
7#13092609C211yesmaximal, characteristic, complemented
8#13092560C211yesmaximal, characteristic, complemented
9#13092560C211yesmaximal, characteristic, complemented
10#13092527C211yesmaximal, characteristic, complemented
11#13092517C211yesmaximal, characteristic, complemented
12C4×#67273C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#540C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C23×#127C2211yescharacteristic
18C23×#125C2211yescharacteristic
19C23×#123—21no—
20C23×#123—21no—
21C23×#121—21no—
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C23×#121C2211yescharacteristic
25C4×D4×C23C2211yescharacteristic
26C4×D4×C23C2211yescharacteristic
27C23×#117C2211yescharacteristic
28C2×#67273C2211yescharacteristic
29C2×#67273C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33#10625063—21no—
34C4⋊C4×D23—21no—
35(C22⋊D23)⋊C4—21no—
36(C22⋊D23)⋊C4—21no—
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41#10625014C2211yescharacteristic
42#10625014C2211yescharacteristic
43#10625014C2211yescharacteristic
44#10625014C2211yescharacteristic
45C22⋊(C23⋊C8)C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10624992C2211yescharacteristic
48#10624992C2211yescharacteristic
49#10624991C2211yescharacteristic
50#10624991C2211yescharacteristic
51#10624990C2211yescharacteristic
52#10624990C2211yescharacteristic
53#10624989C2211yescharacteristic
54#10624989C2211yescharacteristic
55C4⋊(C23⋊C8)C2211yescharacteristic
56C4⋊(C23⋊C8)C2211yescharacteristic
57#10624985C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23—21no—
61C2×D4×C23—21no—
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23C2311yescharacteristic
68C2×C22⋊D23—21no—
69C22×Dic23—21no—
70#67288—22no—
71#67288—22no—
72C2×D92C2311yescharacteristic
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×Dic46C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23D411yescharacteristic
80C4⋊C4×C23D411yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C22⋊C4×C23—21no—
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊C4×C23D411yescharacteristic
88C22⋊C4×C23D411yescharacteristic
89C42×C23C2311yescharacteristic
90C42×C23C2311yescharacteristic
91#67273—22no—
92#67273—22no—
93#67272—22no—
94#67272—22no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97C4⋊Dic23—21no—
98C4⋊Dic23C2311yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C2×D411yescharacteristic
111C22×D23—21no—
112D4×C23—21no—
113D4×C23—21no—
114D4×C23—21no—
115D4×C23—21no—
116D4×C23—81no—
117D4×C23—81no—
118D4×C23—81no—
119D4×C23—81no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—81no—
125C2×C4×C23—81no—
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2411yescharacteristic
132C22⋊D23—24no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—81no—
137D92—21no—
138D92#4112yes—
139C4×D23—24no—
140C4×D23—81no—
141C4×D23—81no—
142Dic46—21no—
143Dic46#4112yes—
144C23⋊C8—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23C22×D411yescharacteristic
159C2×D23—22no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—21no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—41no—
168C4×C23—41no—
169C4×C23C2×#4111yescharacteristic
170C4×C23C2×#4111yescharacteristic
171Dic23—22no—
172Dic23—41no—
173Dic23—41no—
174#540D2311yescharacteristic, complemented
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#433—231no—
189C2×C23—41no—
190C2×C23—81no—
191C2×C23—81no—
192C2×C23#52511yescharacteristic
193C2×C23#57611yescharacteristic
194C2×C23#57711yescharacteristic
195D23—42no—
196C2×#41—231no—
197C2×SD16—231no—
198C2×SD16—231no—
199C2×D8—231no—
200C2×D8—231no—
201#127C2×D2311yescharacteristic
202#125C2×D2311yescharacteristic
203#123—21no—
204#123—21no—
205#121—21no—
206#121—21no—
207#121C2×D2311yescharacteristic
208#121C2×D2311yescharacteristic
209C4×Q8—231no—
210C4×Q8—231no—
211C4×D4—231no—
212C4×D4—231no—
213C4×D4—461no—
214C4×D4—461no—
215C4×D4C2×D2311yescharacteristic
216C4×D4C2×D2311yescharacteristic
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⋊C8—231no—
226C4⋊C8—231no—
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⋊C8—231no—
236C22⋊C8—231no—
237#97—231no—
238C4×C8—231no—
239C23#311911yescharacteristic, complemented, Sylow
240#41—462no—
241#41—462no—
242C2×Q8—231no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—231no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4C22×D2311yescharacteristic
258SD16—462no—
259SD16—462no—
260D8—462no—
261D8—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8—231no—
265C2×C8—231no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4C22⋊D2311yescharacteristic
274C4⋊C4C22⋊D2311yescharacteristic
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4C22⋊D2311yescharacteristic
284C22⋊C4C22⋊D2311yescharacteristic
285C42—461no—
286C42—461no—
287C42C22×D2311yescharacteristic
288C42C22×D2311yescharacteristic
289C23—21no—
290C23—21no—
291C23—461no—
292C23C2×C22⋊D2311yescharacteristic
293Q8—232no—
294Q8—461no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—232no—
304D4—464no—
305D4—461no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—464no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—1841no—
317C2×C4—1841no—
318C2×C4—1841no—
319C2×C4C2×C22⋊D2311yescharacteristic
320C2×C4C2×C22⋊D2311yescharacteristic
321C2×C4C2×C22⋊D2311yescharacteristic
322C2×C4C2×C22⋊D2311yescharacteristic
323C2×C4C2×C22⋊D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—461no—
326C8—461no—
327C8—461no—
328C8—461no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—462no—
339C22—921no—
340C22—921no—
341C22C22×C22⋊D2311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—462no—
350C4—921no—
351C4—921no—
352C4#41×D2311yescharacteristic
353C4#41×D2311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—922no—
358C2#1309292411yescharacteristic
359C2#1309322011yescharacteristic
360C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#540C2
socleC22×C23C22×D4
hypercenter#540D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #13092897C2semidirect
2. #13092733C2semidirect
3. #13092728C2semidirect
4. #13092721C2semidirect
5. #13092714C2semidirect
6. #13092614C2semidirect
7. #13092609C2semidirect
8. #13092560C2semidirect
9. #13092560C2semidirect
10. #13092527C2semidirect
11. #13092517C2semidirect
12. C4×#67273C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#540C2semidirect
174. #540D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130928972
#130927332
#130927282
#130927212
#130927142
#130926142
#130926092
#130925602
#130925272
#130925172
C4×#672732
C4×#672722
#130924782
C23×#5402
#311923