Finite Group Databasebeta

← #15683065

Subgroups — #15683065

Order 2944.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625087C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic, complemented
3#13092997C211yesmaximal, characteristic, complemented
4#13092996C211yesmaximal, characteristic, complemented
5#13092664C211yesmaximal, characteristic, complemented
6#13092663C211yesmaximal, characteristic, complemented
7#13092660C211yesmaximal, characteristic, complemented
8#13092657C211yesmaximal, characteristic, complemented
9#13092656C211yesmaximal, characteristic, complemented
10#13092652C211yesmaximal, characteristic, complemented
11#13092651C211yesmaximal, characteristic, complemented
12#107×D23C211yesmaximal, characteristic, complemented
13#13092417C211yesmaximal, characteristic, complemented
14#13092415C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic
21C23×C22⋊Q8C2211yescharacteristic
22C23×#121C2211yescharacteristic
23#10625117C2211yescharacteristic
24C2×#67275C2211yescharacteristic
25#10625110—21no—
26#10625109—21no—
27#10625109C2211yescharacteristic
28C2×#67272C2211yescharacteristic
29#10625101C2211yescharacteristic
30#10625095C2211yescharacteristic
31C22×C23⋊C8C2211yescharacteristic
32#10625087—24no—
33#10625078—24no—
34C2×#67263C2211yescharacteristic
35C2×#67262C2211yescharacteristic
36C2×#67262C2211yescharacteristic
37C2×C8×D23C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic
39#10625068C2211yescharacteristic
40#10625067—21no—
41#10625066—21no—
42#10625066C2211yescharacteristic
43C4⋊C4×D23C2211yescharacteristic
44C4⋊C4×D23C2211yescharacteristic
45#10625055—21no—
46#10625055—21no—
47#10625055—21no—
48#10625049—21no—
49C23×#107C2211yescharacteristic
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52#10625017C2211yescharacteristic
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55#10625000C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624992C2211yescharacteristic
58#10624991C2211yescharacteristic
59#10624989C2211yescharacteristic
60#10624989C2211yescharacteristic
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23D411yescharacteristic
69C2×C22⋊D23D411yescharacteristic
70C22×Dic23—21no—
71#67292—22no—
72#67292—22no—
73#67290—22no—
74#67290—22no—
75#67288—22no—
76#67288—22no—
77C2×D92—21no—
78C2×D92—21no—
79C2×D92D411yescharacteristic
80C2×D92C2311yescharacteristic
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23—21no—
84C2×C4×D23C2311yescharacteristic
85C2×C4×D23C2311yescharacteristic
86C2×Dic46D411yescharacteristic
87C2×Dic46C2311yescharacteristic
88SD16×C23—22no—
89M16×C23—22no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23—21no—
93C4⋊C4×C23C2311yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊Dic23—21no—
98C22⋊Dic23—21no—
99#67275—22no—
100#67272—22no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105C4⋊Dic23—21no—
106C4⋊Dic23C2311yescharacteristic
107C4⋊Dic23C2311yescharacteristic
108Dic23⋊C4—21no—
109Dic23⋊C4—21no—
110Dic23⋊C4—21no—
111Dic23⋊C4—21no—
112C2×C23⋊C8—22no—
113C2×C23⋊C8C2311yescharacteristic
114C2×C23⋊C8C2311yescharacteristic
115#67263—22no—
116#67262—22no—
117#67262—22no—
118C8×D23—22no—
119C8×D23D414yescomplemented
120C23×C23—21no—
121C23×C23C2×D411yescharacteristic
122C22×D23—21no—
123C22×D23C2×D411yescharacteristic
124C22×D23C2×D411yescharacteristic
125Q8×C23—21no—
126Q8×C23—21no—
127D4×C23—21no—
128D4×C23—21no—
129D4×C23—81no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23C2×D411yescharacteristic
136C2×C4×C23C2411yescharacteristic
137C22⋊D23—22no—
138C22⋊D23—22no—
139C22⋊D23—42no—
140C22⋊D23—81no—
141C22⋊D23—81no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—42no—
146C2×Dic23C2×D411yescharacteristic
147C2×Dic23C2×D411yescharacteristic
148D92—22no—
149D92—21no—
150D92—21no—
151D92—42no—
152D92—81no—
153C4×D23—21no—
154C4×D23—21no—
155C4×D23—42no—
156C4×D23—81no—
157C4×D23—81no—
158C4×D23C2×D412yes—
159C4×D23#4112yes—
160Dic46—22no—
161Dic46—21no—
162Dic46—21no—
163C8×C23—21no—
164C8×C23C2×D412yes—
165C23⋊C8—21no—
166C23⋊C8C2×D412yes—
167#3061—231nomaximal, Sylow
168C22×C23—21no—
169C22×C23—21no—
170C22×C23—21no—
171C22×C23—41no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23C22×D411yescharacteristic
175C2×D23—21no—
176C2×D23—21no—
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—21no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23#12112yes—
184C4×C23—21no—
185C4×C23—41no—
186C4×C23—41no—
187C4×C23—41no—
188C4×C23C22×D411yescharacteristic
189C4×C23C2×#4111yescharacteristic
190Dic23—21no—
191Dic23—41no—
192Dic23—41no—
193Dic23—41no—
194Dic23#12112yes—
195C2×#135—231no—
196C2×#131—231no—
197#537—231no—
198#537—231no—
199#468—231no—
200#468—231no—
201#468—231no—
202#468D2311yescharacteristic, complemented
203#467—231no—
204#467—231no—
205#466—231no—
206#466—231no—
207C2×#107—231no—
208#417—231no—
209#417—231no—
210C2×C23—41no—
211C2×C23—81no—
212C2×C23C2×#12111yescharacteristic
213C2×C23#57611yescharacteristic
214C2×C23#57811yescharacteristic
215D23—22no—
216D23—41no—
217D23—81no—
218C2×#41—231no—
219C2×#41—231no—
220C2×#41—231no—
221#135—464no—
222C2×Q16—231no—
223C2×SD16—231no—
224C2×SD16C2×D2311yescharacteristic
225C2×D8—231no—
226#131—464no—
227C2×M16—231no—
228C2×M16—231no—
229C2×M16C2×D2311yescharacteristic
230C22×C8—231no—
231C22×C8—231no—
232C22×C8—231no—
233C22⋊Q8—231no—
234C22⋊Q8—231no—
235C22⋊Q8—231no—
236C22⋊Q8—461no—
237C22⋊Q8—461no—
238C22⋊Q8C2×D2311yescharacteristic
239#121—231no—
240#121—231no—
241#121—231no—
242#121—461no—
243#121—461no—
244#121—461no—
245#121—461no—
246#121—461no—
247#121—461no—
248#121C2×D2311yescharacteristic
249C2×C4⋊C4—231no—
250C2×C4⋊C4—231no—
251#107—231no—
252#107—231no—
253#107—231no—
254#107C2×D2311yescharacteristic
255#103—231no—
256#103—231no—
257#103—231no—
258#103C2×D2311yescharacteristic
259#102—231no—
260#102—231no—
261#102—231no—
262#102C2×D2311yescharacteristic
263C23#306111yescharacteristic, complemented, Sylow
264#41—462no—
265#41—462no—
266#41—462no—
267#41—462no—
268#41—462no—
269#41—462no—
270C2×Q8—231no—
271C2×Q8—231no—
272C2×Q8C22×D2311yescharacteristic
273C2×D4—21no—
274C2×D4—231no—
275C2×D4—231no—
276C2×D4—231no—
277C2×D4—231no—
278C2×D4—461no—
279C2×D4—461no—
280C2×D4—461no—
281C2×D4—461no—
282C2×D4—461no—
283C2×D4C22×D2311yescharacteristic
284C22×C4—231no—
285C22×C4—231no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4C22×D2311yescharacteristic
291Q16—462no—
292SD16—22no—
293SD16—462no—
294D8—462no—
295M16—22no—
296M16—462no—
297M16—462no—
298C2×C8—231no—
299C2×C8—234no—
300C2×C8—231no—
301C2×C8—462no—
302C2×C8—462no—
303C2×C8C22×D2311yescharacteristic
304C2×C8C22×D2311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—231no—
307C4⋊C4—231no—
308C4⋊C4—461no—
309C4⋊C4—461no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4C22×D2311yescharacteristic
314C4⋊C4C22×D2311yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C23—21no—
324C23—231no—
325C23—231no—
326C23—461no—
327C23D4×D2311yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—462no—
331Q8—461no—
332Q8—461no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—462no—
337D4—462no—
338D4—462no—
339D4—461no—
340D4—461no—
341D4—922no—
342D4—922no—
343D4—1841no—
344D4—1841no—
345D4—1841no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—231no—
352C2×C4—232no—
353C2×C4—232no—
354C2×C4—231no—
355C2×C4—461no—
356C2×C4—461no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—922no—
361C2×C4—922no—
362C2×C4—1841no—
363C2×C4—1841no—
364C2×C4D4×D2311yescharacteristic
365C2×C4C23×D2311yescharacteristic
366C8—21no—
367C8—232no—
368C8—461no—
369C8D4×D2312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—232no—
377C22—461no—
378C22—461no—
379C22—461no—
380C22—461no—
381C22—461no—
382C22—921no—
383C22—921no—
384C22—921no—
385C22C2×D4×D2311yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—232no—
391C4—461no—
392C4—921no—
393C4—921no—
394C4—921no—
395C4C2×D4×D2311yescharacteristic
396C4#41×D2311yescharacteristic
397C2—41no—
398C2—81no—
399C2—462no—
400C2—921no—
401C2—1841no—
402C2#121×D2311yescharacteristic
403C2#1309322111yescharacteristic
404C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
hypercenter#468D23
hypocenterC23#3061
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10625087C2semidirect
2. C2×#10625078C2semidirect
3. #13092997C2semidirect
4. #13092996C2semidirect
5. #13092664C2semidirect
6. #13092663C2semidirect
7. #13092660C2semidirect
8. #13092657C2semidirect
9. #13092656C2semidirect
10. #13092652C2semidirect
11. #13092651C2semidirect
12. #107×D23C2semidirect
13. #13092417C2semidirect
14. #13092415C2semidirect
15. C23×#468C2semidirect
119. C8×D23D4semidirect
202. #468D23semidirect
263. C23#3061semidirect

Maximal subgroups

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

subgroupindex
C2×#106250872
C2×#106250782
#130929972
#130929962
#130926642
#130926632
#130926602
#130926572
#130926562
#130926522
#130926512
#107×D232
#130924172
#130924152
C23×#4682
#306123