Finite Group Databasebeta

← #15682689

Subgroups — #15682689

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×#10625161C211yesmaximal, characteristic
2C2×#10625086C211yesmaximal, characteristic, complemented
3C2×Q16×D23C211yesmaximal, characteristic, complemented
4#13092990C211yesmaximal, characteristic, complemented
5#13092580C211yesmaximal, characteristic, complemented
6#13092579C211yesmaximal, characteristic, complemented
7#13092576C211yesmaximal, characteristic, complemented
8#13092575C211yesmaximal, characteristic, complemented
9#13092574C211yesmaximal, characteristic, complemented
10#13092572C211yesmaximal, characteristic, complemented
11#13092571C211yesmaximal, characteristic, complemented
12#13092424C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14#13092382C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17#10625161—24no—
18#10625161—24no—
19C2×Q8×D23C2211yescharacteristic
20C2×Q8×D23C2211yescharacteristic
21C2×Q8×D23C2211yescharacteristic
22C2×#67290—21no—
23C2×#67290—21no—
24C2×#67290C2211yescharacteristic
25C2×#67290C2211yescharacteristic
26C2×#67288—21no—
27C2×#67288C2211yescharacteristic
28C22×Dic46—21no—
29C22×Dic46C2211yescharacteristic
30C2×Q16×C23C2211yescharacteristic
31C2×SD16×C23C2211yescharacteristic
32C23×C22⋊Q8C2211yescharacteristic
33#10625117C2211yescharacteristic
34C2×#67275C2211yescharacteristic
35C2×#67275C2211yescharacteristic
36C2×#67275C2211yescharacteristic
37C2×#67273C2211yescharacteristic
38#10625095C2211yescharacteristic
39Q16×D23—24no—
40#10625086—24no—
41C2×Dic92C2211yescharacteristic
42C2×Dic92C2211yescharacteristic
43C2×#67262C2211yescharacteristic
44C2×C8×D23C2211yescharacteristic
45#10625068C2211yescharacteristic
46#10625065—21no—
47#10625063C2211yescharacteristic
48#10625059—21no—
49#10625056—21no—
50#10625054—21no—
51C23×#103C2211yescharacteristic
52C23×#102C2211yescharacteristic
53C23×C22⋊C8C2211yescharacteristic
54#10625017C2211yescharacteristic
55#10625014C2211yescharacteristic
56C22⋊(C23⋊C8)C2211yescharacteristic
57(C2×D23)⋊C8C2211yescharacteristic
58(C2×D23)⋊C8C2211yescharacteristic
59#10624998C2211yescharacteristic
60#10624998C2211yescharacteristic
61#10624992C2211yescharacteristic
62#10624992C2211yescharacteristic
63#41×C23—22no—
64#41×C23—22no—
65C2×Q8×C23C2311yescharacteristic
66C2×Q8×C23C2311yescharacteristic
67C2×D4×C23—21no—
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23—21no—
70C22×C4×C23C2311yescharacteristic
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23D411yescharacteristic
74C2×C22⋊D23D411yescharacteristic
75C22×Dic23—21no—
76C22×Dic23—21no—
77C22×Dic23—21no—
78Q8×D23—22no—
79Q8×D23—22no—
80Q8×D23—22no—
81Q8×D23—22no—
82Q8×D23—22no—
83Q8×D23D414yes—
84#67290—28no—
85#67290—28no—
86#67290—22no—
87#67290—22no—
88#67290—22no—
89#67290D414yes—
90#67288—28no—
91#67288—22no—
92#67288—22no—
93C2×D92D411yescharacteristic
94C2×C4×D23—21no—
95C2×C4×D23—21no—
96C2×C4×D23—21no—
97C2×C4×D23C2311yescharacteristic
98C2×C4×D23C2311yescharacteristic
99C2×Dic46—28no—
100C2×Dic46—21no—
101C2×Dic46—21no—
102C2×Dic46—21no—
103C2×Dic46—22no—
104C2×Dic46—22no—
105C2×Dic46—21no—
106C2×Dic46D411yescharacteristic
107C2×Dic46C2311yescharacteristic
108C2×Dic46C2311yescharacteristic
109C2×Dic46C2311yescharacteristic
110Q16×C23—22no—
111SD16×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#67273—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—
133Dic92—22no—
134#67262—22no—
135C8×D23—22no—
136C23×C23—21no—
137C23×C23C2×D411yescharacteristic
138C22×D23C2×D411yescharacteristic
139C22×D23C2×D411yescharacteristic
140Q8×C23—21no—
141Q8×C23—21no—
142Q8×C23—21no—
143Q8×C23C2×D412yes—
144D4×C23—24no—
145D4×C23—21no—
146D4×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×C23C2×D411yescharacteristic
154C2×C4×C23C2411yescharacteristic
155C22⋊D23—24no—
156C22⋊D23—22no—
157C22⋊D23—24no—
158C22⋊D23—22no—
159C2×Dic23—24no—
160C2×Dic23—24no—
161C2×Dic23—21no—
162C2×Dic23—21no—
163C2×Dic23—24no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23C2×D411yescharacteristic
167C2×Dic23C2×D411yescharacteristic
168D92—22no—
169C4×D23—24no—
170C4×D23—24no—
171C4×D23—21no—
172C4×D23—21no—
173C4×D23—42no—
174C4×D23C2×D412yes—
175C4×D23C2×D412yes—
176Dic46—24no—
177Dic46—24no—
178Dic46—21no—
179Dic46—21no—
180Dic46—22no—
181Dic46—24no—
182Dic46—21no—
183Dic46—21no—
184Dic46—42no—
185Dic46C2×D412yes—
186Dic46C2×D412yes—
187C8×C23—21no—
188C8×C23—21no—
189C23⋊C8—21no—
190C23⋊C8—21no—
191#3011—231nomaximal, Sylow
192C22×C23—21no—
193C22×C23—22no—
194C22×C23—21no—
195C22×C23—21no—
196C22×C23—41no—
197C22×C23—41no—
198C22×C23C22×D411yescharacteristic
199C2×D23—21no—
200C2×D23—21no—
201C2×D23—21no—
202C2×D23—21no—
203C2×D23—21no—
204C2×D23#12012yes—
205C4×C23—21no—
206C4×C23—22no—
207C4×C23—41no—
208C4×C23—41no—
209C4×C23C22×D411yescharacteristic
210C4×C23C22×D411yescharacteristic
211Dic23—21no—
212Dic23—22no—
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#452D2311yescharacteristic, complemented
225#451—231no—
226#451—231no—
227#451—231no—
228#451—231no—
229#419—231no—
230#416—231no—
231#408—231no—
232C2×C23—41no—
233C2×C23—42no—
234C2×C23C2×#12011yescharacteristic
235C2×C23#57811yescharacteristic
236C2×C23#57811yescharacteristic
237D23—22no—
238D23—41no—
2392−1+4—464no—
2402−1+4—464no—
241C2×#41—231no—
242C2×#41—231no—
243C2×#41—231no—
244C2×#41—461no—
245C2×#41—461no—
246C2×#41—461no—
247C2×#41C2×D2311yescharacteristic
248C22×Q8—231no—
249C22×Q8—231no—
250C22×Q8—231no—
251C22×Q8—231no—
252C22×Q8—461no—
253#137—464no—
254C2×Q16—231no—
255C2×Q16—231no—
256C2×Q16—231no—
257C2×Q16—231no—
258C2×Q16—231no—
259C2×Q16—464no—
260C2×Q16C2×D2311yescharacteristic
261C2×SD16—231no—
262C2×SD16C2×D2311yescharacteristic
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#103—231no—
279#103C2×D2311yescharacteristic
280#102—231no—
281#102C2×D2311yescharacteristic
282C22⋊C8—231no—
283C22⋊C8—231no—
284C22⋊C8—231no—
285C22⋊C8C2×D2311yescharacteristic
286C23#301111yescharacteristic, complemented, Sylow
287#41—22no—
288#41—22no—
289#41—234no—
290#41—462no—
291#41—462no—
292#41—468no—
293#41—462no—
294#41—462no—
295#41—468no—
296#41—468no—
297#41—462no—
298C2×Q8—231no—
299C2×Q8—234no—
300C2×Q8—231no—
301C2×Q8—231no—
302C2×Q8—231no—
303C2×Q8—461no—
304C2×Q8—461no—
305C2×Q8—461no—
306C2×Q8—462no—
307C2×Q8—462no—
308C2×Q8—468no—
309C2×Q8—462no—
310C2×Q8—462no—
311C2×Q8—462no—
312C2×Q8—462no—
313C2×Q8—462no—
314C2×Q8—461no—
315C2×Q8C22×D2311yescharacteristic
316C2×Q8C22×D2311yescharacteristic
317C2×D4—21no—
318C2×D4—231no—
319C2×D4—231no—
320C2×D4—231no—
321C2×D4—461no—
322C2×D4—461no—
323C2×D4C22×D2311yescharacteristic
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—462no—
336Q16—462no—
337Q16—462no—
338Q16—462no—
339Q16—462no—
340SD16—22no—
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—21no—
361C23—231no—
362C23—231no—
363C23D4×D2311yescharacteristic
364Q8—21no—
365Q8—21no—
366Q8—21no—
367Q8—232no—
368Q8—232no—
369Q8—462no—
370Q8—464no—
371Q8—464no—
372Q8—464no—
373Q8—461no—
374Q8—461no—
375Q8—461no—
376Q8—461no—
377Q8—922no—
378Q8D4×D2312yes—
379D4—24no—
380D4—21no—
381D4—462no—
382D4—462no—
383D4—462no—
384D4—464no—
385D4—464no—
386D4D4×D2312yes—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—231no—
394C2×C4—232no—
395C2×C4—232no—
396C2×C4—231no—
397C2×C4—464no—
398C2×C4—464no—
399C2×C4—464no—
400C2×C4—464no—
401C2×C4—464no—
402C2×C4—461no—
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—22no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—232no—
422C22—461no—
423C22—461no—
424C22—461no—
425C22—461no—
426C22—461no—
427C22C2×D4×D2311yescharacteristic
428C4—21no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—232no—
433C4—461no—
434C4—462no—
435C4—462no—
436C4—921no—
437C4—921no—
438C4C2×D4×D2311yescharacteristic
439C4C2×D4×D2311yescharacteristic
440C2—41no—
441C2—42no—
442C2—462no—
443C2—921no—
444C2#120×D2311yescharacteristic
445C2#1309323111yescharacteristic
446C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
prime radicalC2×#10625161C2
hypercenter#452D23
hypocenterC23#3011
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×#10625086C2semidirect
3. C2×Q16×D23C2semidirect
4. #13092990C2semidirect
5. #13092580C2semidirect
6. #13092579C2semidirect
7. #13092576C2semidirect
8. #13092575C2semidirect
9. #13092574C2semidirect
10. #13092572C2semidirect
11. #13092571C2semidirect
12. #13092424C2semidirect
13. #13092410C2semidirect
14. #13092382C2semidirect
15. C23×#452C2semidirect
224. #452D23semidirect
286. C23#3011semidirect

Maximal subgroups

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

subgroupindex
C2×#106251612
C2×#106250862
C2×Q16×D232
#130929902
#130925802
#130925792
#130925762
#130925752
#130925742
#130925722
#130925712
#130924242
#130924102
#130923822
C23×#4522
#301123