Finite Group Databasebeta

← #15676106

Subgroups — #15676106

Order 2944.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625056C211yesmaximal, characteristic
2C2×C4×Dic46C211yesmaximal, characteristic, complemented
3C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
4#13092321C211yesmaximal, characteristic, complemented
5#13092317C211yesmaximal, characteristic
6#13092309C211yesmaximal, characteristic, complemented
7#13092308C211yesmaximal, characteristic, complemented
8#13092305C211yesmaximal, characteristic, complemented
9#13092292C211yesmaximal, characteristic, complemented
10#13092291C211yesmaximal, characteristic, complemented
11#13092289C211yesmaximal, characteristic, complemented
12#13092288C211yesmaximal, characteristic, complemented
13#13092286C211yesmaximal, characteristic, complemented
14#13092262C211yesmaximal, characteristic, complemented
15C23×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D23C2211yescharacteristic
17C23×Dic23C2211yescharacteristic
18C22×C4×D23C2211yescharacteristic
19C22×Dic46C2211yescharacteristic
20C2×C4⋊C4×C23C2211yescharacteristic
21C2×C22⋊C4×C23C2211yescharacteristic
22C2×C22⋊C4×C23C2211yescharacteristic
23C2×C22⋊C4×C23C2211yescharacteristic
24C2×C42×C23C2211yescharacteristic
25C2×C22⋊Dic23C2211yescharacteristic
26C2×C22⋊Dic23C2211yescharacteristic
27C2×(C2×D23)⋊C4C2211yescharacteristic
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×(C2×D23)⋊C4C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33C2×C4⋊Dic23C2211yescharacteristic
34C2×Dic23⋊C4C2211yescharacteristic
35C2×Dic23⋊C4C2211yescharacteristic
36C2×Dic23⋊C4C2211yescharacteristic
37C2×Dic23⋊C4C2211yescharacteristic
38C2×Dic23⋊C4C2211yescharacteristic
39C2×C4×Dic23C2211yescharacteristic
40C2×C4×Dic23C2211yescharacteristic
41C2×C4×Dic23C2211yescharacteristic
42C2×C4×Dic23C2211yescharacteristic
43#10625056C418yescomplemented
44(C22⋊D23)⋊C4—24no—
45C4×Dic46—24no—
46C23×#95C2211yescharacteristic
47C23×#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C24×C23C2311yescharacteristic
55C23×D23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23—22no—
63C2×C22⋊D23—22no—
64C2×C22⋊D23C2×C414yes—
65C22×Dic23—22no—
66C22×Dic23—41no—
67C22×Dic23—41no—
68C22×Dic23C2311yescharacteristic
69C22×Dic23C2311yescharacteristic
70C22×Dic23C2311yescharacteristic
71C22×Dic23C2311yescharacteristic
72C22×Dic23C2311yescharacteristic
73C22×Dic23C2311yescharacteristic
74C22×Dic23C2311yescharacteristic
75C2×C4×D23—22no—
76C2×C4×D23—41no—
77C2×C4×D23—41no—
78C2×Dic46—22no—
79C2×Dic46—22no—
80C2×Dic46C2×C414yescomplemented
81C4⋊C4×C23—41no—
82C22⋊C4×C23—22no—
83C22⋊C4×C23—41no—
84C22⋊C4×C23C2×C414yescomplemented
85C42×C23—22no—
86C22⋊Dic23—41no—
87C22⋊Dic23C2×C414yescomplemented
88(C2×D23)⋊C4—22no—
89(C2×D23)⋊C4—41no—
90(C2×D23)⋊C4—41no—
91(C2×D23)⋊C4C2×C414yescomplemented
92(C2×D23)⋊C4C2×C414yescomplemented
93C4⋊Dic23—22no—
94C4⋊Dic23—41no—
95Dic23⋊C4—22no—
96Dic23⋊C4—22no—
97Dic23⋊C4—22no—
98Dic23⋊C4—41no—
99Dic23⋊C4—41no—
100C4×Dic23—22no—
101C4×Dic23—22no—
102C4×Dic23C2×C414yescomplemented
103C4×Dic23D414yes—
104C23×C23—21no—
105C23×C23—21no—
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C22×C412yes—
111C23×C23C2411yescharacteristic
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—21no—
117C22×D23—21no—
118C22×D23C22×C412yes—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23C22×C412yes—
135C2×C4×C23C22×C412yes—
136C2×C4×C23C2×D412yes—
137C22⋊D23—28no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—44no—
154C2×Dic23C22×C412yes—
155C2×Dic23C22×C412yes—
156C2×Dic23C22×C412yes—
157C2×Dic23C2×D412yes—
158C2×Dic23C2×D412yes—
159C2×Dic23#4112yes—
160C4×D23—44no—
161Dic46—28no—
162#2326—231nomaximal, Sylow
163C22×C23—22no—
164C22×C23—22no—
165C22×C23—22no—
166C22×C23—41no—
167C22×C23—41no—
168C22×C23—41no—
169C22×C23—41no—
170C22×C23C23×C411yescharacteristic
171C22×C23C22×D411yescharacteristic
172C22×C23C2×#4111yescharacteristic
173C22×C23H(5,𝔽2)11yescharacteristic
174C22×C23H(5,𝔽2)11yescharacteristic
175C22×C232−1+411yescharacteristic
176C22×C232−1+411yescharacteristic
177C2×D23—22no—
178C2×D23—22no—
179C2×D23—22no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—41no—
184C4×C23—22no—
185C4×C23—22no—
186C4×C23—22no—
187C4×C23—41no—
188C4×C23—41no—
189C4×C23—41no—
190Dic23—22no—
191Dic23—22no—
192Dic23—22no—
193Dic23—41no—
194Dic23—41no—
195Dic23—41no—
196Dic23C4×D414yes—
197C2×#124—231no—
198C2×C4×Q8—231no—
199C2×C4×D4—231no—
200#391—231no—
201#390—231no—
202#388—231no—
203#388—231no—
204#388—231no—
205#388D2311yescharacteristic, complemented
206#385—231no—
207#385—231no—
208#385—231no—
209#385—231no—
210#384—231no—
211#376—231no—
212C2×C23—42no—
213C2×C23C2×C4×D411yescharacteristic
214C2×C23#52011yescharacteristic
215C2×C23#52011yescharacteristic
216C2×C23#53511yescharacteristic
217C2×C23#53611yescharacteristic
218C2×C23#54211yescharacteristic
219C2×C23#54211yescharacteristic
220D23—42no—
221C22×Q8—231no—
222C22×D4—231no—
223C23×C4—231no—
224C23×C4—231no—
225#124—238no—
226C4×Q8—464no—
227C4×D4—464no—
228C2×C4⋊C4—231no—
229C2×C4⋊C4—231no—
230C2×C4⋊C4—231no—
231C2×C4⋊C4—231no—
232C2×C4⋊C4—231no—
233C2×C4⋊C4—231no—
234C2×C4⋊C4—231no—
235C2×C4⋊C4C2×D2311yescharacteristic
236C2×C22⋊C4—231no—
237C2×C22⋊C4—231no—
238C2×C22⋊C4—231no—
239C2×C22⋊C4—231no—
240C2×C22⋊C4—231no—
241C2×C22⋊C4—231no—
242C2×C22⋊C4—231no—
243C2×C22⋊C4C2×D2311yescharacteristic
244C2×C22⋊C4C2×D2311yescharacteristic
245C2×C22⋊C4C2×D2311yescharacteristic
246C2×C42—231no—
247C2×C42—231no—
248C2×C42—231no—
249C2×C42—231no—
250C2×C42C2×D2311yescharacteristic
251#95—231no—
252#95—231no—
253#95—231no—
254#95—231no—
255#95—231no—
256#95—231no—
257#95C2×D2311yescharacteristic
258#95C2×D2311yescharacteristic
259C23#232611yescharacteristic, complemented, Sylow
260C24—231no—
261C24C22×D2311yescharacteristic
262C2×Q8—234no—
263C2×Q8—462no—
264C2×Q8—462no—
265C2×D4—234no—
266C2×D4—462no—
267C2×D4—462no—
268C22×C4—231no—
269C22×C4—231no—
270C22×C4—231no—
271C22×C4—231no—
272C22×C4—231no—
273C22×C4—231no—
274C22×C4—231no—
275C22×C4—462no—
276C22×C4—462no—
277C22×C4—921no—
278C22×C4—921no—
279C22×C4—921no—
280C22×C4—921no—
281C22×C4C22×D2311yescharacteristic
282C22×C4C22×D2311yescharacteristic
283C22×C4C22×D2311yescharacteristic
284C22×C4C22×D2311yescharacteristic
285C22×C4C22×D2311yescharacteristic
286C22×C4C22×D2311yescharacteristic
287C4⋊C4—41no—
288C4⋊C4—462no—
289C4⋊C4—462no—
290C4⋊C4—462no—
291C4⋊C4—462no—
292C4⋊C4—921no—
293C4⋊C4—921no—
294C4⋊C4—921no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—234no—
298C22⋊C4—234no—
299C22⋊C4—234no—
300C22⋊C4—462no—
301C22⋊C4—921no—
302C22⋊C4—921no—
303C22⋊C4—921no—
304C22⋊C4C4×D2314yescomplemented
305C42—22no—
306C42—234no—
307C42—234no—
308C42—462no—
309C42—462no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—232no—
317C23—461no—
318C23—461no—
319C23—461no—
320C23—461no—
321C23—461no—
322C23—461no—
323C23C2×C4×D2312yes—
324C23C23×D2311yescharacteristic
325Q8—468no—
326D4—468no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—232no—
343C2×C4—232no—
344C2×C4—232no—
345C2×C4—232no—
346C2×C4—232no—
347C2×C4—232no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—461no—
353C2×C4—461no—
354C2×C4—461no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—924no—
364C2×C4—924no—
365C2×C4C2×C4×D2312yes—
366C2×C4C2×C4×D2312yes—
367C2×C4D4×D2312yes—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—462no—
376C22—462no—
377C22—462no—
378C22—921no—
379C22—921no—
380C22—921no—
381C22—921no—
382C22C22×C4×D2311yescharacteristic
383C22C2×D4×D2311yescharacteristic
384C22#1062515511yescharacteristic
385C22#41×D2311yescharacteristic
386C22#1062516011yescharacteristic
387C22#1062516111yescharacteristic
388C22#1062516111yescharacteristic
389C4—22no—
390C4—22no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—234no—
396C4—462no—
397C4—462no—
398C4—462no—
399C4—921no—
400C4—921no—
401C4—921no—
402C2—42no—
403C2—922no—
404C2C4×D4×D2311yescharacteristic
405C2#1309289611yescharacteristic
406C2#1309289711yescharacteristic
407C2#1309298311yescharacteristic
408C2#1309298911yescharacteristic
409C2#1309303111yescharacteristic
410C2#1309303311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#388C2
socle, cosocleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenter#388D23
hypocenterC23#2326
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic46C2semidirect
4. #13092321C2semidirect
6. #13092309C2semidirect
7. #13092308C2semidirect
8. #13092305C2semidirect
9. #13092292C2semidirect
10. #13092291C2semidirect
11. #13092289C2semidirect
12. #13092288C2semidirect
13. #13092286C2semidirect
14. #13092262C2semidirect
15. C23×#388C2semidirect
43. #10625056C4semidirect
80. C2×Dic46C2×C4semidirect
84. C22⋊C4×C23C2×C4semidirect
87. C22⋊Dic23C2×C4semidirect
91. (C2×D23)⋊C4C2×C4semidirect
92. (C2×D23)⋊C4C2×C4semidirect
102. C4×Dic23C2×C4semidirect
205. #388D23semidirect
259. C23#2326semidirect
304. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250562
C2×C4×Dic462
C2×(C22⋊D23)⋊C42
#130923212
#130923172
#130923092
#130923082
#130923052
#130922922
#130922912
#130922892
#130922882
#130922862
#130922622
C23×#3882
#232623