Finite Group Databasebeta

← #15684903

Subgroups — #15684903

Order 2944.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625122C211yesmaximal, characteristic, complemented
2C22×#67273C211yesmaximal, characteristic, complemented
3D4×Dic46C211yesmaximal, characteristic, complemented
4#13092812C211yesmaximal, characteristic, complemented
5#13092661C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092636C211yesmaximal, characteristic, complemented
8#13092622C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092572C211yesmaximal, characteristic, complemented
11#13092568C211yesmaximal, characteristic, complemented
12#13092555C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic
16C2×#41×C23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C22×Dic46C2211yescharacteristic
19C22×Dic46C2211yescharacteristic, complemented
20C23×#124C2211yescharacteristic
21C23×#123—21no—
22C23×C22⋊Q8C2211yescharacteristic
23C23×#121—21no—
24C23×#121C2211yescharacteristic
25C23×#120—21no—
26C4×D4×C23C2211yescharacteristic
27C4×D4×C23C2211yescharacteristic
28C2×C22⋊C4×C23—21no—
29#10625122—24no—
30C2×#67275C2211yescharacteristic, complemented
31C2×#67275C2211yescharacteristic, complemented
32C2×#67275C2211yescharacteristic, complemented
33D4×Dic23—21no—
34C2×#67273—24no—
35C2×#67273C2211yescharacteristic
36C2×#67273C2211yescharacteristic
37C2×#67273C2211yescharacteristic
38C2×#67273C2211yescharacteristic
39C2×#67273C2211yescharacteristic
40C2×#67273C2211yescharacteristic
41#10625095C2211yescharacteristic
42#10625095C2211yescharacteristic, complemented
43C2×#67267C2211yescharacteristic, complemented
44C22×C23⋊C8C2211yescharacteristic
45#10625059—21no—
46#10625049—21no—
47#10625049—21no—
48#10625040C2211yescharacteristic, complemented
49C4×Dic46C2211yescharacteristic, complemented
50#10625017C2211yescharacteristic, complemented
51#10625014C2211yescharacteristic
52#10625014C2211yescharacteristic
53C22⋊(C23⋊C8)C2211yescharacteristic
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C24×C23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23—22no—
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23—41no—
70C2×D4×C23D411yescharacteristic
71C2×D4×C23C2311yescharacteristic
72C2×D4×C23C2311yescharacteristic
73C22×C4×C23—21no—
74C22×C4×C23—21no—
75C22×C4×C23C2311yescharacteristic
76C22×C4×C23C2311yescharacteristic
77C22×Dic23—21no—
78C22×Dic23—21no—
79C2×Dic46—22no—
80C2×Dic46—22no—
81C2×Dic46—21no—
82C2×Dic46—21no—
83C2×Dic46—41no—
84C2×Dic46—41no—
85C2×Dic46C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88C4⋊C4×C23—21no—
89C4⋊C4×C23D411yescharacteristic
90C4⋊C4×C23C2311yescharacteristic
91C22⋊C4×C23—21no—
92C22⋊C4×C23—21no—
93C22⋊C4×C23—21no—
94C22⋊C4×C23—21no—
95C22⋊C4×C23—21no—
96C22⋊C4×C23D411yescharacteristic
97C22⋊C4×C23D411yescharacteristic
98C42×C23C2311yescharacteristic
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101#67275—22no—
102#67275—22no—
103#67275—41no—
104#67273—22no—
105#67273—22no—
106#67273—22no—
107#67273—22no—
108#67273—41no—
109#67273D414yescomplemented
110C4⋊Dic23—21no—
111C4⋊Dic23—21no—
112C4⋊Dic23C2311yescharacteristic
113Dic23⋊C4—21no—
114Dic23⋊C4—21no—
115Dic23⋊C4—21no—
116C4×Dic23—21no—
117#67267—22no—
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—42no—
126C23×C23—42no—
127C23×C23—81no—
128C23×C23C2×D411yescharacteristic
129C23×C23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23—21no—
132D4×C23—22no—
133D4×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—42no—
137D4×C23—42no—
138D4×C23—81no—
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—42no—
147C2×C4×C23—81no—
148C2×C4×C23C2×D411yescharacteristic
149C2×C4×C23C2×D411yescharacteristic
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2411yescharacteristic
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—42no—
158C2×Dic23—42no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—42no—
165Dic46—42no—
166Dic46C2×D412yes—
167C23⋊C8—21no—
168C23⋊C8—21no—
169C23⋊C8—21no—
170C23⋊C8C2×D412yes—
171#3266—231nomaximal, Sylow
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—22no—
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—41no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—84no—
184C22×C23#13712yescomplemented
185C22×C23C22×D411yescharacteristic
186C4×C23—21no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23—41no—
191C4×C23—41no—
192C4×C23C22×D411yescharacteristic
193C4×C23H(5,𝔽2)11yescharacteristic
194Dic23—22no—
195Dic23—41no—
196Dic23—41no—
197Dic23—41no—
198C2×#137—231no—
199C22×SD16—231no—
200D4×Q8—231no—
201#546D2311yescharacteristic
202#497—231no—
203#468—231no—
204#467—231no—
205#464—231no—
206#461—231no—
207#452—231no—
208#451—231no—
209#450—231no—
210#448—231no—
211#440—231no—
212#435—231no—
213C2×C23—22no—
214C2×C23—41no—
215C2×C23—42no—
216C2×C23—81no—
217C2×C23D4211yescharacteristic
218C2×C23C2×#13711yescharacteristic
219C2×C23#57711yescharacteristic
220C2×#41C2×D2311yescharacteristic
221C22×Q8—231no—
222C22×Q8—231no—
223C22×D4C2×D2311yescharacteristic
224#137—464no—
225C2×Q16—231no—
226C2×Q16—231no—
227C2×Q16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16—231no—
231C2×SD16—231no—
232C2×SD16—231no—
233C2×SD16—231no—
234C2×SD16—464no—
235C2×M16—231no—
236C22×C8—231no—
237C4⋊Q8—231no—
238C4⋊Q8—461no—
239#124C2×D2311yescharacteristic
240#123—21no—
241C22⋊Q8—231no—
242C22⋊Q8—231no—
243C22⋊Q8—461no—
244C22⋊Q8—461no—
245C22⋊Q8C2×D2311yescharacteristic
246#121—21no—
247#121C2×D2311yescharacteristic
248#120—21no—
249C4×Q8—231no—
250C4×D4—461no—
251C4×D4C2×D2311yescharacteristic
252C4×D4C2×D2311yescharacteristic
253C2×C22⋊C4—21no—
254#107—231no—
255C4⋊C8—231no—
256#103—231no—
257#103—231no—
258#103—231no—
259#103—231no—
260#102—231no—
261#102—231no—
262C22⋊C8—231no—
263C22⋊C8—231no—
264#97—231no—
265C23#326611yescharacteristic, complemented, Sylow
266C24—21no—
267#41—22no—
268#41—41no—
269C2×Q8—231no—
270C2×Q8—231no—
271C2×Q8—231no—
272C2×Q8—462no—
273C2×Q8—462no—
274C2×Q8—461no—
275C2×Q8—461no—
276C2×Q8—921no—
277C2×Q8—921no—
278C2×Q8C22×D2311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D2311yescharacteristic
285C2×D4C22×D2311yescharacteristic
286C2×D4C22×D2311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4C22×D2311yescharacteristic
292C22×C4C22×D2311yescharacteristic
293Q16—462no—
294Q16—462no—
295Q16—921no—
296SD16—234no—
297SD16—462no—
298SD16—462no—
299SD16—462no—
300SD16—462no—
301SD16—921no—
302M16—462no—
303C2×C8—231no—
304C2×C8—231no—
305C2×C8—231no—
306C2×C8—231no—
307C2×C8—462no—
308C4⋊C4—21no—
309C4⋊C4—231no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4C22⋊D2311yescharacteristic
316C4⋊C4C22×D2311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4C22⋊D2311yescharacteristic
325C22⋊C4C22⋊D2311yescharacteristic
326C42—461no—
327C42C22×D2311yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D2311yescharacteristic
334C23C2×C22⋊D2311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—232no—
338Q8—461no—
339Q8—461no—
340Q8—461no—
341Q8—461no—
342Q8—461no—
343Q8—922no—
344Q8—922no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D2312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—922no—
366C2×C4—922no—
367C2×C4C2×C22⋊D2311yescharacteristic
368C2×C4C2×C22⋊D2311yescharacteristic
369C2×C4C2×C22⋊D2311yescharacteristic
370C2×C4C2×C22⋊D2311yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—232no—
373C8—461no—
374C8—461no—
375C8—461no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1062512212yescomplemented
389C22C22×C22⋊D2311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—462no—
397C4—921no—
398C4—921no—
399C4—921no—
400C4C2×D4×D2311yescharacteristic
401C4#1062515511yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D2311yescharacteristic
407C2C2×#1062512211yescharacteristic
408C2#1309322811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C22×#67273C2semidirect
3. D4×Dic46C2semidirect
4. #13092812C2semidirect
5. #13092661C2semidirect
6. #13092656C2semidirect
7. #13092636C2semidirect
8. #13092622C2semidirect
9. #13092579C2semidirect
10. #13092572C2semidirect
11. #13092568C2semidirect
12. #13092555C2semidirect
13. #13092517C2semidirect
14. #13092489C2semidirect
19. C22×Dic46C22semidirect
30. C2×#67275C22semidirect
31. C2×#67275C22semidirect
32. C2×#67275C22semidirect
42. #10625095C22semidirect
43. C2×#67267C22semidirect
48. #10625040C22semidirect
49. C4×Dic46C22semidirect
50. #10625017C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624992C22semidirect
56. #10624992C22semidirect
57. #10624992C22semidirect
58. #10624989C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
109. #67273D4semidirect
184. C22×C23#137semidirect
265. C23#3266semidirect
388. C22#10625122semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
C22×#672732
D4×Dic462
#130928122
#130926612
#130926562
#130926362
#130926222
#130925792
#130925722
#130925682
#130925552
#130925172
#130924892
C23×#5462
#326623