Finite Group Databasebeta

← #15684923

Subgroups — #15684923

Order 2944.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625120C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13093063C211yesmaximal, characteristic, complemented
4#13092809C211yesmaximal, characteristic, complemented
5#13092673C211yesmaximal, characteristic, complemented
6#13092648C211yesmaximal, characteristic, complemented
7#13092632C211yesmaximal, characteristic, complemented
8#13092619C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092577C211yesmaximal, characteristic, complemented
11#13092567C211yesmaximal, characteristic, complemented
12#13092562C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15C23×#547C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#41×C23C2211yescharacteristic, complemented
18C2×#67288C2211yescharacteristic
19C22×D92C2211yescharacteristic
20C23×C4⋊Q8C2211yescharacteristic, complemented
21C23×#123—21no—
22C23×#123—21no—
23C23×C22⋊Q8C2211yescharacteristic
24C23×C22⋊Q8C2211yescharacteristic, complemented
25C23×#121—21no—
26C4×D4×C23C2211yescharacteristic
27C4×D4×C23C2211yescharacteristic, complemented
28C2×C4⋊C4×C23—21no—
29#10625121—24no—
30#10625120—24no—
31C2×#67275C2211yescharacteristic, complemented
32C2×#67275C2211yescharacteristic, complemented
33C2×#67274C2211yescharacteristic
34C2×#67274C2211yescharacteristic
35C2×#67274C2211yescharacteristic
36C2×#67274C2211yescharacteristic
37#10625108—21no—
38C2×#67273C2211yescharacteristic, complemented
39C2×#67272C2211yescharacteristic
40C2×#67272C2211yescharacteristic
41#10625101C2211yescharacteristic
42#10625095C2211yescharacteristic
43C2×#67267C2211yescharacteristic
44C22×C23⋊C8C2211yescharacteristic, complemented
45#10625065—21no—
46#10625055—21no—
47C22⋊C4×D23—21no—
48#10625046C2211yescharacteristic
49C4×D92C2211yescharacteristic
50#10625017C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625014C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic
57#10624991C2211yescharacteristic
58#10624990C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—22no—
64#41×C23—41no—
65#41×C23—41no—
66C2×Q8×C23C2311yescharacteristic
67C2×Q8×C23C2311yescharacteristic
68C2×D4×C23—21no—
69C2×D4×C23—21no—
70C2×D4×C23D411yescharacteristic
71C2×D4×C23C2311yescharacteristic
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23—21no—
75C22×C4×C23C2311yescharacteristic
76C22×C4×C23C2311yescharacteristic
77C2×C22⋊D23—21no—
78C2×C22⋊D23—21no—
79#67288—22no—
80#67288—41no—
81C2×D92—22no—
82C2×D92—21no—
83C2×D92—41no—
84C2×D92C2311yescharacteristic
85C2×D92C2311yescharacteristic
86C2×C4×D23—21no—
87C2×C4×D23—21no—
88C2×Dic46C2311yescharacteristic
89C4⋊C4×C23—21no—
90C4⋊C4×C23—21no—
91C4⋊C4×C23—21no—
92C4⋊C4×C23—21no—
93C4⋊C4×C23D411yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊C4×C23D411yescharacteristic
99C22⋊C4×C23D411yescharacteristic
100C42×C23C2311yescharacteristic
101C22⋊Dic23—21no—
102#67275—22no—
103#67275—41no—
104#67274—22no—
105#67274—22no—
106#67274—22no—
107#67274—41no—
108#67273—22no—
109#67272—22no—
110#67272D414yescomplemented
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4—21no—
114(C2×D23)⋊C4—21no—
115C4⋊Dic23C2311yescharacteristic
116Dic23⋊C4—21no—
117#67267—22no—
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—81no—
131Q8×C23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135D4×C23—21no—
136D4×C23—41no—
137D4×C23—42no—
138D4×C23—42no—
139D4×C23C2×D412yes—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—42no—
148C2×C4×C23—42no—
149C2×C4×C23—42no—
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2×D411yescharacteristic
153C2×C4×C23C2×D411yescharacteristic
154C2×C4×C23C2411yescharacteristic
155C22⋊D23—42no—
156C22⋊D23—81no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159D92—21no—
160D92—21no—
161D92—21no—
162D92—42no—
163D92C2×D412yes—
164C4×D23—42no—
165C4×D23—81no—
166Dic46—21no—
167Dic46—21no—
168C23⋊C8—21no—
169C23⋊C8—21no—
170C23⋊C8—21no—
171C23⋊C8C2×D412yes—
172#3267—231nomaximal, Sylow
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—22no—
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—21no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23C22×D411yescharacteristic
183C2×D23—22no—
184C2×D23—41no—
185C2×D23—41no—
186C2×D23—41no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—84no—
190C4×C23—21no—
191C4×C23—21no—
192C4×C23—21no—
193C4×C23—21no—
194C4×C23—41no—
195C4×C23—41no—
196C4×C23—41no—
197C4×C23C22×D411yescharacteristic
198C4×C23H(5,𝔽2)11yescharacteristic
199Dic23—41no—
200Dic23—41no—
201C2×AGL(1,ℤ/8)—231no—
202C2×#135—231no—
203#547D2311yescharacteristic, complemented
204#546—231no—
205#497—231no—
206#470—231no—
207#465—231no—
208#463—231no—
209#461—231no—
210#452—231no—
211#452—231no—
212#450—231no—
213#449—231no—
214#442—231no—
215#435—231no—
216C2×C23—41no—
217C2×C23—41no—
218C2×C23—42no—
219C2×C23D4211yescharacteristic
220C2×C23#57511yescharacteristic
221C2×C23#57711yescharacteristic
222D23—42no—
223D23—81no—
224C2×#41—231no—
225C2×#41C2×D2311yescharacteristic
226C2×#41C2×D2311yescharacteristic, complemented
227C22×D4—231no—
228AGL(1,ℤ/8)—464no—
229#135—464no—
230C2×Q16—231no—
231C2×Q16—231no—
232C2×SD16—231no—
233C2×SD16—231no—
234C2×SD16—231no—
235C2×SD16—231no—
236C2×SD16—231no—
237C2×D8—231no—
238C2×D8—231no—
239C2×M16—231no—
240C22×C8—231no—
241C4⋊Q8C2×D2311yescharacteristic, complemented
242#124—231no—
243#123—21no—
244#123—21no—
245#123—461no—
246C22⋊Q8—231no—
247C22⋊Q8C2×D2311yescharacteristic
248C22⋊Q8C2×D2311yescharacteristic, complemented
249#121—21no—
250#121—231no—
251#121—461no—
252#120—461no—
253C4×D4—231no—
254C4×D4C2×D2311yescharacteristic
255C4×D4C2×D2311yescharacteristic, complemented
256C2×C4⋊C4—21no—
257C2×C22⋊C4—461no—
258#106—231no—
259C4⋊C8—231no—
260#103—231no—
261#103—231no—
262#103—231no—
263#102—231no—
264#102—231no—
265#102—231no—
266C22⋊C8—231no—
267C22⋊C8—231no—
268#97—231no—
269C23#326711yescharacteristic, complemented, Sylow
270C24—461no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—462no—
276#41—921no—
277C2×Q8—231no—
278C2×Q8C22×D2311yescharacteristic
279C2×Q8C22×D2311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—231no—
283C2×D4—231no—
284C2×D4—462no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—461no—
288C2×D4—921no—
289C2×D4C22⋊D2311yescharacteristic
290C2×D4C22×D2311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4C22×D2311yescharacteristic
297C22×C4C22×D2311yescharacteristic
298Q16—462no—
299Q16—921no—
300SD16—462no—
301SD16—462no—
302SD16—462no—
303SD16—462no—
304SD16—921no—
305D8—234no—
306D8—462no—
307M16—462no—
308C2×C8—231no—
309C2×C8—231no—
310C2×C8—231no—
311C2×C8—231no—
312C2×C8—462no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—231no—
318C4⋊C4—461no—
319C4⋊C4C22⋊D2311yescharacteristic
320C4⋊C4C22×D2311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C22⋊C4—461no—
327C22⋊C4—461no—
328C22⋊C4—461no—
329C22⋊C4C22⋊D2311yescharacteristic
330C22⋊C4C22⋊D2311yescharacteristic
331C42C22×D2311yescharacteristic
332C23—21no—
333C23—461no—
334C23—461no—
335C23—922no—
336C23—922no—
337C23—1841no—
338C23C2×C22⋊D2311yescharacteristic
339C23C2×C22⋊D2311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—461no—
345Q8—461no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—232no—
351D4—461no—
352D4—461no—
353D4—461no—
354D4—922no—
355D4—922no—
356D4—1841no—
357D4D4×D2312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—922no—
371C2×C4—1841no—
372C2×C4C2×C22⋊D2311yescharacteristic
373C2×C4C2×C22⋊D2311yescharacteristic
374C2×C4C2×C22⋊D2311yescharacteristic
375C2×C4C2×C22⋊D2311yescharacteristic
376C2×C4C23×D2311yescharacteristic
377C8—232no—
378C8—461no—
379C8—461no—
380C8—461no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—462no—
391C22—921no—
392C22—921no—
393C22—921no—
394C22—921no—
395C22—921no—
396C22—1844no—
397C22C22×C22⋊D2311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—921no—
406C4—921no—
407C4C2×D4×D2311yescharacteristic
408C4#1062515511yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—922no—
413C2—1841no—
414C2D4×C22⋊D2311yescharacteristic
415C2#1309321511yescharacteristic
416C2#1309322511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#547C2
socleC22×C23C22×D4
hypercenter#547D23
hypocenterC23#3267
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#10625120C2semidirect
2. C2×#10625121C2semidirect
3. #13093063C2semidirect
4. #13092809C2semidirect
5. #13092673C2semidirect
6. #13092648C2semidirect
7. #13092632C2semidirect
8. #13092619C2semidirect
9. #13092579C2semidirect
10. #13092577C2semidirect
11. #13092567C2semidirect
12. #13092562C2semidirect
13. #13092527C2semidirect
14. #13092489C2semidirect
15. C23×#547C2semidirect
17. C2×#41×C23C22semidirect
20. C23×C4⋊Q8C22semidirect
24. C23×C22⋊Q8C22semidirect
27. C4×D4×C23C22semidirect
31. C2×#67275C22semidirect
32. C2×#67275C22semidirect
38. C2×#67273C22semidirect
44. C22×C23⋊C8C22semidirect
50. #10625017C22semidirect
51. #10625017C22semidirect
52. #10625014C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624992C22semidirect
58. #10624990C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
110. #67272D4semidirect
203. #547D23semidirect
226. C2×#41C2×D23semidirect
241. C4⋊Q8C2×D23semidirect
248. C22⋊Q8C2×D23semidirect
255. C4×D4C2×D23semidirect
269. C23#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#106251202
C2×#106251212
#130930632
#130928092
#130926732
#130926482
#130926322
#130926192
#130925792
#130925772
#130925672
#130925622
#130925272
#130924892
C23×#5472
#326723