Finite Group Databasebeta

← #15682687

Subgroups — #15682687

Order 2944.

700 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625158C211yesmaximal, characteristic
2C2×#10625089C211yesmaximal, characteristic, complemented
3C2×Q16×D23C211yesmaximal, characteristic, complemented
4#13092990C211yesmaximal, characteristic, complemented
5#13092582C211yesmaximal, characteristic, complemented
6#13092581C211yesmaximal, characteristic, complemented
7#13092578C211yesmaximal, characteristic, complemented
8#13092577C211yesmaximal, characteristic, complemented
9#13092574C211yesmaximal, characteristic, complemented
10#13092573C211yesmaximal, characteristic, complemented
11#13092571C211yesmaximal, characteristic, complemented
12#13092424C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14#13092382C211yesmaximal, characteristic, complemented
15C23×#451C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17#10625158—24no—
18#10625158—24no—
19C2×#67292—21no—
20C2×#67292C2211yescharacteristic
21C2×#67292C2211yescharacteristic
22C2×Q8×D23—21no—
23C2×Q8×D23C2211yescharacteristic
24C2×Q8×D23C2211yescharacteristic
25C2×Q8×D23C2211yescharacteristic
26C2×#67288—21no—
27C2×#67288—21no—
28C2×#67288C2211yescharacteristic
29C2×#67288C2211yescharacteristic
30C2×Q16×C23C2211yescharacteristic
31C2×Q16×C23C2211yescharacteristic
32C23×C22⋊Q8C2211yescharacteristic
33#10625117C2211yescharacteristic
34C2×#67275C2211yescharacteristic
35C2×#67275C2211yescharacteristic
36C2×#67275C2211yescharacteristic
37C2×#67274C2211yescharacteristic
38#10625095C2211yescharacteristic
39#10625089—24no—
40Q16×D23—24no—
41C2×Dic92C2211yescharacteristic
42C2×#67263C2211yescharacteristic
43C2×#67262C2211yescharacteristic
44C2×C8×D23C2211yescharacteristic
45#10625068C2211yescharacteristic
46#10625065—21no—
47#10625063C2211yescharacteristic
48#10625059—21no—
49#10625056—21no—
50#10625054—21no—
51C23×#103C2211yescharacteristic
52C23×#103C2211yescharacteristic
53C23×C22⋊C8C2211yescharacteristic
54#10625017C2211yescharacteristic
55#10625017C2211yescharacteristic
56C22⋊(C23⋊C8)C2211yescharacteristic
57#10625003C2211yescharacteristic
58(C2×D23)⋊C8C2211yescharacteristic
59(C2×D23)⋊C8C2211yescharacteristic
60#10624998C2211yescharacteristic
61#10624992C2211yescharacteristic
62#10624991C2211yescharacteristic
63C2×Q8×C23—22no—
64C2×Q8×C23—22no—
65C2×Q8×C23—21no—
66C2×Q8×C23C2311yescharacteristic
67C2×Q8×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C22×C4×C23—21no—
70C22×C4×C23C2311yescharacteristic
71C2×C22⋊D23—21no—
72C2×C22⋊D23D411yescharacteristic
73C2×C22⋊D23D411yescharacteristic
74#67292—28no—
75#67292—22no—
76#67292—22no—
77#67292—22no—
78#67292D414yes—
79Q8×D23—28no—
80Q8×D23—22no—
81Q8×D23—22no—
82Q8×D23—22no—
83Q8×D23—22no—
84Q8×D23—22no—
85Q8×D23D414yes—
86#67288—28no—
87#67288—28no—
88#67288—22no—
89#67288—22no—
90#67288—22no—
91#67288—22no—
92C2×D92—21no—
93C2×D92—21no—
94C2×D92D411yescharacteristic
95C2×D92C2311yescharacteristic
96C2×C4×D23—21no—
97C2×C4×D23—21no—
98C2×C4×D23—21no—
99C2×C4×D23—21no—
100C2×C4×D23—21no—
101C2×C4×D23—21no—
102C2×C4×D23C2311yescharacteristic
103C2×C4×D23C2311yescharacteristic
104C2×Dic46—21no—
105C2×Dic46—21no—
106C2×Dic46—21no—
107C2×Dic46D411yescharacteristic
108C2×Dic46C2311yescharacteristic
109C2×Dic46C2311yescharacteristic
110Q16×C23—22no—
111Q16×C23—22no—
112C2×C8×C23C2311yescharacteristic
113C2×C8×C23C2311yescharacteristic
114C4⋊C4×C23—21no—
115C4⋊C4×C23C2311yescharacteristic
116C22⋊C4×C23—21no—
117C22⋊Dic23—21no—
118#67275—22no—
119#67275—22no—
120#67275—22no—
121#67274—22no—
122(C2×D23)⋊C4—21no—
123(C2×D23)⋊C4—21no—
124(C2×D23)⋊C4—21no—
125C4⋊Dic23—21no—
126C4⋊Dic23C2311yescharacteristic
127Dic23⋊C4—21no—
128Dic23⋊C4—21no—
129C4×Dic23—21no—
130C2×C23⋊C8C2311yescharacteristic
131C2×C23⋊C8C2311yescharacteristic
132Dic92—22no—
133#67263—22no—
134#67262—22no—
135C8×D23—22no—
136C23×C23C2×D411yescharacteristic
137C22×D23—21no—
138C22×D23C2×D411yescharacteristic
139C22×D23C2×D411yescharacteristic
140Q8×C23—24no—
141Q8×C23—21no—
142Q8×C23—21no—
143Q8×C23—21no—
144Q8×C23—21no—
145Q8×C23C2×D412yes—
146Q8×C23C2×D412yes—
147C2×C4×C23—24no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—21no—
154C2×C4×C23C2×D411yescharacteristic
155C2×C4×C23C2411yescharacteristic
156C22⋊D23—24no—
157C22⋊D23—22no—
158C22⋊D23—22no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23C2×D411yescharacteristic
163C2×Dic23C2×D411yescharacteristic
164D92—24no—
165D92—24no—
166D92—22no—
167D92—21no—
168D92C2×D412yes—
169C4×D23—24no—
170C4×D23—24no—
171C4×D23—24no—
172C4×D23—24no—
173C4×D23—21no—
174C4×D23—21no—
175C4×D23—24no—
176C4×D23—42no—
177C4×D23C2×D412yes—
178C4×D23C2×D412yes—
179Dic46—24no—
180Dic46—21no—
181Dic46—24no—
182Dic46—22no—
183Dic46—21no—
184Dic46—21no—
185Dic46—42no—
186Dic46C2×D412yes—
187C8×C23—21no—
188C8×C23—21no—
189C23⋊C8—21no—
190C23⋊C8—21no—
191#3011—231nomaximal, Sylow
192C22×C23—21no—
193C22×C23—21no—
194C22×C23—21no—
195C22×C23C22×D411yescharacteristic
196C2×D23—21no—
197C2×D23—21no—
198C2×D23—21no—
199C2×D23—22no—
200C2×D23—21no—
201C2×D23—21no—
202C2×D23—41no—
203C2×D23—41no—
204C2×D23#12012yes—
205C4×C23—22no—
206C4×C23—22no—
207C4×C23—21no—
208C4×C23—41no—
209C4×C23—41no—
210C4×C23C22×D411yescharacteristic
211C4×C23C22×D411yescharacteristic
212Dic23—21no—
213Dic23—22no—
214Dic23—41no—
215Dic23—41no—
216Dic23#12012yes—
217C2×2−1+4—231no—
218C2×#137—231no—
219C22×Q16—231no—
220#536—231no—
221#452—231no—
222#452—231no—
223#452—231no—
224#452—231no—
225#451—231no—
226#451—231no—
227#451—231no—
228#451D2311yescharacteristic, complemented
229#419—231no—
230#416—231no—
231#408—231no—
232C2×C23—41no—
233C2×C23C2×#12011yescharacteristic
234C2×C23#57811yescharacteristic
235C2×C23#57811yescharacteristic
236D23—22no—
237D23—41no—
238D23—42no—
2392−1+4—464no—
2402−1+4—464no—
241C2×#41—231no—
242C2×#41—231no—
243C2×#41—231no—
244C2×#41—231no—
245C2×#41—461no—
246C2×#41—461no—
247C2×#41—461no—
248C22×Q8—231no—
249C22×Q8—231no—
250C22×Q8—231no—
251C22×Q8—461no—
252C22×Q8C2×D2311yescharacteristic
253#137—464no—
254C2×Q16—231no—
255C2×Q16—231no—
256C2×Q16—231no—
257C2×Q16—231no—
258C2×Q16—464no—
259C2×Q16C2×D2311yescharacteristic
260C2×Q16C2×D2311yescharacteristic
261C2×SD16—231no—
262C2×SD16—231no—
263C2×M16—231no—
264C22×C8—231no—
265C4⋊Q8—461no—
266#124—461no—
267#123—461no—
268#123—461no—
269C22⋊Q8—231no—
270C22⋊Q8—231no—
271C22⋊Q8—231no—
272C22⋊Q8C2×D2311yescharacteristic
273#117—231no—
274#103—231no—
275#103—231no—
276#103—231no—
277#103—231no—
278#103C2×D2311yescharacteristic
279#103C2×D2311yescharacteristic
280#102—231no—
281#102—231no—
282C22⋊C8—231no—
283C22⋊C8—231no—
284C22⋊C8—231no—
285C22⋊C8C2×D2311yescharacteristic
286C23#301111yescharacteristic, complemented, Sylow
287#41—234no—
288#41—462no—
289#41—462no—
290#41—462no—
291#41—462no—
292#41—468no—
293#41—468no—
294#41—462no—
295#41—462no—
296#41—468no—
297#41—462no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—21no—
301C2×Q8—231no—
302C2×Q8—234no—
303C2×Q8—231no—
304C2×Q8—231no—
305C2×Q8—461no—
306C2×Q8—461no—
307C2×Q8—461no—
308C2×Q8—462no—
309C2×Q8—462no—
310C2×Q8—462no—
311C2×Q8—462no—
312C2×Q8—468no—
313C2×Q8—462no—
314C2×Q8C22×D2311yescharacteristic
315C2×Q8C22×D2311yescharacteristic
316C2×Q8C22×D2311yescharacteristic
317C2×D4—231no—
318C2×D4—231no—
319C2×D4—231no—
320C2×D4—231no—
321C2×D4—461no—
322C2×D4—461no—
323C2×D4—461no—
324C22×C4—21no—
325C22×C4—231no—
326C22×C4—231no—
327C22×C4—461no—
328C22×C4—461no—
329C22×C4—461no—
330C22×C4—461no—
331C22×C4—461no—
332C22×C4—461no—
333C22×C4C22×D2311yescharacteristic
334Q16—22no—
335Q16—22no—
336Q16—462no—
337Q16—462no—
338Q16—462no—
339Q16—462no—
340SD16—462no—
341SD16—462no—
342M16—462no—
343C2×C8—231no—
344C2×C8—231no—
345C2×C8—462no—
346C2×C8C22×D2311yescharacteristic
347C2×C8C22×D2311yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—231no—
350C4⋊C4—461no—
351C4⋊C4—461no—
352C4⋊C4—461no—
353C4⋊C4C22×D2311yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—461no—
356C22⋊C4—461no—
357C22⋊C4—461no—
358C22⋊C4—461no—
359C42—461no—
360C23—231no—
361C23—231no—
362C23—461no—
363C23D4×D2311yescharacteristic
364Q8—24no—
365Q8—21no—
366Q8—21no—
367Q8—21no—
368Q8—21no—
369Q8—232no—
370Q8—464no—
371Q8—462no—
372Q8—464no—
373Q8—461no—
374Q8—461no—
375Q8—461no—
376Q8—922no—
377Q8D4×D2312yes—
378Q8D4×D2312yes—
379D4—232no—
380D4—462no—
381D4—464no—
382D4—464no—
383D4—462no—
384D4—462no—
385D4—464no—
386D4—461no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—231no—
395C2×C4—232no—
396C2×C4—232no—
397C2×C4—231no—
398C2×C4—464no—
399C2×C4—464no—
400C2×C4—464no—
401C2×C4—464no—
402C2×C4—464no—
403C2×C4—461no—
404C2×C4—461no—
405C2×C4—461no—
406C2×C4—461no—
407C2×C4—461no—
408C2×C4—922no—
409C2×C4D4×D2311yescharacteristic
410C2×C4C23×D2311yescharacteristic
411C8—21no—
412C8—21no—
413C8—461no—
414C8—461no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—232no—
419C22—461no—
420C22—461no—
421C22—462no—
422C22—461no—
423C22—461no—
424C22—461no—
425C22—921no—
426C22—921no—
427C22C2×D4×D2311yescharacteristic
428C4—22no—
429C4—22no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—232no—
434C4—461no—
435C4—462no—
436C4—921no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—41no—
441C2—462no—
442C2—921no—
443C2—922no—
444C2#120×D2311yescharacteristic
445C2#1309323011yescharacteristic
446C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#451C2
socleC22×C23C22×D4
prime radicalC2×#10625158C2
hypercenter#451D23
hypocenterC23#3011
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×#10625089C2semidirect
3. C2×Q16×D23C2semidirect
4. #13092990C2semidirect
5. #13092582C2semidirect
6. #13092581C2semidirect
7. #13092578C2semidirect
8. #13092577C2semidirect
9. #13092574C2semidirect
10. #13092573C2semidirect
11. #13092571C2semidirect
12. #13092424C2semidirect
13. #13092412C2semidirect
14. #13092382C2semidirect
15. C23×#451C2semidirect
228. #451D23semidirect
286. C23#3011semidirect

Maximal subgroups

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

subgroupindex
C2×#106251582
C2×#106250892
C2×Q16×D232
#130929902
#130925822
#130925812
#130925782
#130925772
#130925742
#130925732
#130925712
#130924242
#130924122
#130923822
C23×#4512
#301123