Finite Group Databasebeta

← #15683596

Subgroups — #15683596

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#13092735C211yesmaximal, characteristic, complemented
3#13092730C211yesmaximal, characteristic, complemented
4#13092724C211yesmaximal, characteristic, complemented
5#13092717C211yesmaximal, characteristic, complemented
6#13092617C211yesmaximal, characteristic, complemented
7#13092612C211yesmaximal, characteristic, complemented
8#13092562C211yesmaximal, characteristic, complemented
9#13092562C211yesmaximal, characteristic, complemented
10#13092527C211yesmaximal, characteristic, complemented
11#13092515C211yesmaximal, characteristic, complemented
12C4×#67274C211yesmaximal, characteristic, complemented
13C4×#67272C211yesmaximal, characteristic, complemented
14#13092478C211yesmaximal, characteristic, complemented
15C23×#520C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C4×Q8×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×D4×C23—21no—
20C4×D4×C23—21no—
21C4×D4×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic
23C23×#117—21no—
24C23×#117C2211yescharacteristic
25C2×C4⋊C4×C23—21no—
26C2×C4⋊C4×C23C2211yescharacteristic
27C2×#67274C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29C2×#67272C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101C2211yescharacteristic
32#10625101C2211yescharacteristic
33#10625065—21no—
34#10625065—21no—
35#10625055—21no—
36#10625055—21no—
37#10625045C2211yescharacteristic
38C4×D92C2211yescharacteristic
39C4×D92C2211yescharacteristic
40#10625041C2211yescharacteristic
41#10625017C2211yescharacteristic
42#10625017C2211yescharacteristic
43#10625014C2211yescharacteristic
44#10625014C2211yescharacteristic
45C22⋊(C23⋊C8)C2211yescharacteristic
46C22⋊(C23⋊C8)C2211yescharacteristic
47#10624991C2211yescharacteristic
48#10624991C2211yescharacteristic
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
59#41×C23—22no—
60#41×C23—22no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C22×C4×C23—21no—
67C22×C4×C23—21no—
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×D92—21no—
72C2×D92—21no—
73C2×D92C2311yescharacteristic
74C2×D92C2311yescharacteristic
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23—21no—
80C4⋊C4×C23D411yescharacteristic
81C4⋊C4×C23D411yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85C22⋊C4×C23—21no—
86C22⋊C4×C23D411yescharacteristic
87C22⋊C4×C23D411yescharacteristic
88C42×C23—21no—
89C42×C23—21no—
90C42×C23C2311yescharacteristic
91C42×C23C2311yescharacteristic
92#67274—22no—
93#67274—22no—
94#67272—22no—
95#67272—22no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4—21no—
99(C2×D23)⋊C4—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23—21no—
109C23×C23C2×D411yescharacteristic
110C22×D23—21no—
111C22×D23—21no—
112Q8×C23—21no—
113Q8×C23#4112yes—
114D4×C23—24no—
115D4×C23—21no—
116D4×C23#4112yes—
117C2×C4×C23—24no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—81no—
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—81no—
133C22⋊D23—81no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136D92—21no—
137D92—21no—
138D92—21no—
139D92—21no—
140D92—81no—
141D92—81no—
142C4×D23—81no—
143C4×D23—81no—
144C23⋊C8—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148#3119—231nomaximal, Sylow
149C22×C23—21no—
150C22×C23—22no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23C22×D411yescharacteristic
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C2×D23—41no—
162C4×C23—21no—
163C4×C23—22no—
164C4×C23—21no—
165C4×C23—21no—
166C4×C23—21no—
167C4×C23—21no—
168C4×C23—41no—
169C4×C23—41no—
170C4×C23C2×#4111yescharacteristic
171C4×C23C2×#4111yescharacteristic
172Dic23—41no—
173Dic23—41no—
174#540—231no—
175#520D2311yescharacteristic, complemented
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—42no—
191C2×C23#52511yescharacteristic
192C2×C23#57611yescharacteristic
193C2×C23#57711yescharacteristic
194D23—81no—
195D23—81no—
196C2×#41C2×D2311yescharacteristic
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×Q8C2×D2311yescharacteristic
210C4×Q8C2×D2311yescharacteristic
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4C2×D2311yescharacteristic
216C4×D4C2×D2311yescharacteristic
217#117—21no—
218#117C2×D2311yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×D2311yescharacteristic
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—22no—
241#41—22no—
242C2×Q8C22×D2311yescharacteristic
243C2×D4—21no—
244C2×D4—231no—
245C2×D4—231no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4—461no—
250C2×D4C22×D2311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
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—21no—
269C4⋊C4—231no—
270C4⋊C4—231no—
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—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4C22⋊D2311yescharacteristic
284C22⋊C4C22⋊D2311yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D2311yescharacteristic
288C42C22×D2311yescharacteristic
289C23—21no—
290C23—461no—
291C23—461no—
292C23C2×C22⋊D2311yescharacteristic
293Q8—21no—
294Q8#6728812yes—
295D4—24no—
296D4—21no—
297D4—461no—
298D4—461no—
299D4—461no—
300D4—461no—
301D4—1841no—
302D4—1841no—
303D4—1841no—
304D4—1841no—
305D4#6728812yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—461no—
316C2×C4—461no—
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—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22—921no—
340C22—921no—
341C22C22×C22⋊D2311yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—921no—
351C4—921no—
352C4C2×#6728811yescharacteristic
353C4C2×#6728811yescharacteristic
354C2—41no—
355C2—42no—
356C2—1841no—
357C2—1841no—
358C2#1309292811yescharacteristic
359C2#1309322011yescharacteristic
360C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#520C2
socleC22×C23C22×D4
hypercenter#520D23
hypocenterC23#3119
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #13093022C2semidirect
2. #13092735C2semidirect
3. #13092730C2semidirect
4. #13092724C2semidirect
5. #13092717C2semidirect
6. #13092617C2semidirect
7. #13092612C2semidirect
8. #13092562C2semidirect
9. #13092562C2semidirect
10. #13092527C2semidirect
11. #13092515C2semidirect
12. C4×#67274C2semidirect
13. C4×#67272C2semidirect
14. #13092478C2semidirect
15. C23×#520C2semidirect
175. #520D23semidirect
239. C23#3119semidirect

Maximal subgroups

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

subgroupindex
#130930222
#130927352
#130927302
#130927242
#130927172
#130926172
#130926122
#130925622
#130925272
#130925152
C4×#672742
C4×#672722
#130924782
C23×#5202
#311923