Finite Group Databasebeta

← #29663592

Subgroups — #29663592

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457131C211yesmaximal, characteristic
2#21456276C211yesmaximal, characteristic
3#21454768C211yesmaximal, characteristic, complemented
4#21445311C212yesmaximal, complemented
5#21445293C212yesmaximal, complemented
6#21445187C212yesmaximal, complemented
7#21445169C212yesmaximal, complemented
8#21444572C211yesmaximal, characteristic, complemented
9#21444466C211yesmaximal, characteristic
10C2×#16839508C211yesmaximal, characteristic, complemented
11C61×#3229C211yesmaximal, characteristic, complemented
12C2×#14519808—21no—
13C2×#14519808—21no—
14#16840312C2211yescharacteristic
15#16840154—22no—
16#16840141C2212yes—
17#16840136C2212yes—
18#16840049—21no—
19#16840047C2212yes—
20#16839993—22no—
21#16839964—21no—
22#16839962C2212yes—
23#16839893—22no—
24#16839893C2212yes—
25Q8×#92418C2212yes—
26#16839789—21no—
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29#16839718—21no—
30C4×#11758194C2211yescharacteristic
31#16839514C2212yes—
32#16839512C2212yes—
33#16839508C2212yes—
34#16839508C2212yes—
35#16839507C2211yescharacteristic
36#16839507C2211yescharacteristic
37#16839505C2211yescharacteristic
38#16839505C2211yescharacteristic
39C61×#533C2211yescharacteristic
40C2×C4⋊Q8×C61C2211yescharacteristic
41C61×#498—21no—
42C61×#487—21no—
43C61×#483—22no—
44C61×#475C2212yes—
45C61×#475C2212yes—
46C61×#431C2211yescharacteristic
47C2×#11758222—21no—
48#14519808—44no—
49#14519808—44no—
50C2×#11758202—22no—
51C2×#11758202—22no—
52C2×#11758201—22no—
53C2×#11758201—22no—
54C2×#11758201—22no—
55C2×#11758194D411yescharacteristic
56C2×#11758194D411yescharacteristic
57C22×#92418—21no—
58C22×#92418—21no—
59#14519777C2311yescharacteristic
60#14519774C2311yescharacteristic
61#14519765—21no—
62#14519751—21no—
63#14519751—21no—
64C4×D244—21no—
65C4×D244—21no—
66#14519708—22no—
67C4⋊#92418—21no—
68C4⋊#92418—21no—
69C4⋊#92418—22no—
70C4⋊#92418—22no—
71C4⋊#92418C2312yes—
72C4⋊#92418C2311yescharacteristic
73C4⋊#92418C2311yescharacteristic
74#14519701—22no—
75#14519697—22no—
76#14519688—22no—
77#14519688D412yes—
78C4×#92418—22no—
79C4×#92418C2312yes—
80C22×Q8×C61—21no—
81C4⋊Q8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61D411yescharacteristic
85C4⋊Q8×C61D411yescharacteristic
86C4⋊Q8×C61C2312yes—
87#125×C61—21no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61D412yes—
90C4×Q8×C61—21no—
91C4×Q8×C61C2312yes—
92#117×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96#106×C61—22no—
97#106×C61—22no—
98C4⋊C8×C61C2311yescharacteristic
99C4⋊C8×C61C2311yescharacteristic
100#103×C61—22no—
101#103×C61—22no—
102C22⋊C8×C61—21no—
103C4×C8×C61—21no—
104C2×Q8×C61—21no—
105C2×Q8×C61—22no—
106C2×Q8×C61—41no—
107C2×Q8×C61—42no—
108C2×Q8×C61—42no—
109C2×Q8×C61C2×D412yes—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C2×C22⋊D61—41no—
115#11758222—42no—
116#11758222—42no—
117C2×D244—21no—
118C2×D244—21no—
119C2×D244—21no—
120C2×C4×D61—41no—
121C2×Dic122—21no—
122C2×C8×C61—21no—
123C2×C8×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—22no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61C2×D412yes—
134C22⋊C4×C61—22no—
135C42×C61—22no—
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61#4111yescharacteristic
139C42×C61C2411yescharacteristic
140#11758202—44no—
141#11758202—44no—
142#11758201—44no—
143#11758201—44no—
144#11758201—82no—
145#11758198—41no—
146#11758198—41no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149#11758194—22no—
150#11758194SD1614yescomplemented
151C2×#92418—21no—
152C2×#92418—21no—
153C2×#92418—22no—
154C2×#92418—42no—
155C2×#92418—81no—
156C2×#92418C2×D412yes—
157C2×#92418C2×D412yes—
158C23×C61#12111yescharacteristic
159C22×D61—41no—
160Q8×C61—22no—
161Q8×C61—22no—
162Q8×C61—42no—
163Q8×C61—42no—
164Q8×C61—81no—
165Q8×C61—82no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—82no—
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61C2×SD1612yes—
177C2×C4×C61AGL(1,ℤ/8)12yes—
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C2×#4111yescharacteristic
181C22⋊D61—82no—
182C2×Dic61—41no—
183D244—41no—
184D244—41no—
185D244—41no—
186D244—41no—
187D244—81no—
188C4×D61—82no—
189Dic122—41no—
190Dic122—41no—
191C8×C61—41no—
192C8×C61—41no—
193#92418—22no—
194#92418—41no—
195#92418—41no—
196#92418—42no—
197#92418C2×SD1614yes—
198#19239—611nomaximal, Sylow
199C22×C61—21no—
200C22×C61—21no—
201C22×C61#46012yes—
202C22×C61C2×#12111yescharacteristic
203C2×D61—81no—
204C2×D61—81no—
205C2×D61—81no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—42no—
211C4×C61—82no—
212C4×C61#46012yes—
213C4×C61C22×SD1611yescharacteristic
214C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
215C4×C61#57711yescharacteristic
216C4×C61#57811yescharacteristic
217Dic61—81no—
218#3246—611no—
219#3229D6111yescharacteristic, complemented
220#3152—611no—
221#2962—611no—
222#1690—612no—
223#1686—612no—
224#1670—612no—
225#1666—612no—
226#1565—611no—
227#1540—611no—
228C2×#332—611no—
229C2×C61—22no—
230C2×C61C2×#46011yescharacteristic
231C2×C61#306311yescharacteristic
232C2×C61#306911yescharacteristic
233D61—161no—
234C2×#137—1221no—
235C2×#137—1221no—
236#533C2×D6111yescharacteristic
237#532—611no—
238C2×C4⋊Q8C2×D6111yescharacteristic
239#498—21no—
240#497—1222no—
241#494—612no—
242#492—612no—
243#487—21no—
244#483—22no—
245#476—1221no—
246#475—612no—
247#475C2×D6112yes—
248#475C2×D6112yes—
249#465—1222no—
250#461—1221no—
251#460—612no—
252#446—612no—
253#446—1222no—
254C8×Q8—612no—
255#431C2×D6111yescharacteristic
256#424—1221no—
257C2×C4⋊C8—611no—
258C2×C4⋊C8—611no—
259#405—1221no—
260C4×M16—611no—
261#335—612no—
262#334—612no—
263#332—612no—
264#332—612no—
265#332—611no—
266#332—611no—
267#331—611no—
268#331—611no—
269C61#1923911yescharacteristic, complemented, Sylow
270C2×#41—1221no—
271C22×Q8—21no—
272#137—2444no—
273#137—2444no—
274C2×Q16—1222no—
275C2×Q16—1222no—
276C2×SD16—1222no—
277C2×SD16—1222no—
278C2×SD16—1222no—
279C2×M16—611no—
280C2×M16—611no—
281C22×C8—1221no—
282C22×C8—1221no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—611no—
287C4⋊Q8C22⋊D6111yescharacteristic
288C4⋊Q8C22⋊D6111yescharacteristic
289C4⋊Q8C22×D6112yes—
290#127—611no—
291#125—21no—
292#124—1221no—
293C22⋊Q8—21no—
294C22⋊Q8C22⋊D6112yes—
295#121—1221no—
296#121—1221no—
297C4×Q8—21no—
298C4×Q8C22×D6112yes—
299C4×D4—1221no—
300C4×D4—1221no—
301#117—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C42C22×D6111yescharacteristic
305#106—22no—
306#106—22no—
307#106—1222no—
308C4⋊C8—611no—
309C4⋊C8—611no—
310C4⋊C8—612no—
311C4⋊C8—1222no—
312C4⋊C8—1222no—
313C4⋊C8—1221no—
314C4⋊C8—1221no—
315C4⋊C8C22×D6111yescharacteristic
316C4⋊C8C22×D6111yescharacteristic
317#103—22no—
318#103—22no—
319#103—1222no—
320#102—1222no—
321C22⋊C8—21no—
322#97—612no—
323#97—1222no—
324C4×C8—21no—
325C4×C8—612no—
326C4×C8—1222no—
327#41—2442no—
328#41—2442no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8—41no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—1221no—
335C2×Q8C2×C22⋊D6112yes—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—2441no—
340C22×C4—41no—
341C22×C4—2441no—
342C22×C4D4×D6111yescharacteristic
343C22×C4#1175822411yescharacteristic
344C22×C4C2×C22⋊D6111yescharacteristic
345Q16—2444no—
346Q16—2444no—
347SD16—4882no—
348SD16—2444no—
349SD16—2444no—
350M16—614no—
351M16—1222no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—612no—
355C2×C8—612no—
356C2×C8—1221no—
357C2×C8—1221no—
358C2×C8—1222no—
359C2×C8—4881no—
360C2×C8—2442no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4C2×C22⋊D6112yes—
373C22⋊C4—22no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—22no—
377C42D4×D6111yescharacteristic
378C42#1175822411yescharacteristic
379C42C2×C22⋊D6111yescharacteristic
380C42C23×D6111yescharacteristic
381C23—2441no—
382C23#1451974911yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—42no—
386Q8—42no—
387Q8—81no—
388Q8—82no—
389Q8—2441no—
390Q8—2441no—
391D4—4881no—
392D4—4882no—
393D4—2441no—
394D4—2441no—
395D4—2441no—
396D4—2441no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—82no—
404C2×C4—4882no—
405C2×C4—2441no—
406C2×C4#1451974911yescharacteristic
407C2×C4#1451974911yescharacteristic
408C2×C4#1451974911yescharacteristic
409C2×C4SD16×D6112yes—
410C2×C4#1451980412yes—
411C2×C4C2×D4×D6111yescharacteristic
412C2×C4C22×C22⋊D6111yescharacteristic
413C2×C4C2×#1175822411yescharacteristic
414C8—41no—
415C8—41no—
416C8—614no—
417C8—1222no—
418C8—2441no—
419C8—2441no—
420C8—2442no—
421C22—21no—
422C22—21no—
423C22—4881no—
424C22—4881no—
425C22—4881no—
426C22#1683996012yes—
427C22C2×#1451974911yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—82no—
434C4—4881no—
435C4#1683996012yes—
436C4C2×SD16×D6111yescharacteristic
437C4C2×#1451980411yescharacteristic
438C4#1684057011yescharacteristic
439C4#1684057711yescharacteristic
440C2—22no—
441C2—9761no—
442C2C2×#1683996011yescharacteristic
443C2#2145550611yescharacteristic
444C2#2145555311yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3229C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#3229D61
hypocenterC61#19239
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
3. #21454768C2semidirect
4. #21445311C2semidirect
5. #21445293C2semidirect
6. #21445187C2semidirect
7. #21445169C2semidirect
8. #21444572C2semidirect
10. C2×#16839508C2semidirect
11. C61×#3229C2semidirect
150. #11758194SD16semidirect
219. #3229D61semidirect
269. C61#19239semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214562762
#214547682
#214453112
#214452932
#214451872
#214451692
#214445722
#214444662
C2×#168395082
C61×#32292
#1923961