Finite Group Databasebeta

← #29663875

Subgroups — #29663875

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic
2#21455941C211yesmaximal, characteristic
3C2×Q8×#92418C211yesmaximal, characteristic, complemented
4#21445275C212yesmaximal, complemented
5#21445265C212yesmaximal, complemented
6#21445199C212yesmaximal, complemented
7#21445169C212yesmaximal, complemented
8#21444580C211yesmaximal, characteristic, complemented
9#21444519C211yesmaximal, characteristic, complemented
10#21444515C211yesmaximal, characteristic
11C61×#3113C211yesmaximal, characteristic, complemented
12#16840312C2211yescharacteristic
13#16840158C2211yescharacteristic
14#16840136C2211yescharacteristic
15#16840112C2211yescharacteristic
16#16840110C2211yescharacteristic
17#16840075—21no—
18#16840057C2212yes—
19#16839993—21no—
20#16839993—21no—
21#16839962C2212yes—
22#16839901—21no—
23Q8×#92418—21no—
24Q8×#92418—21no—
25Q8×#92418C2212yes—
26Q8×#92418C2212yes—
27#16839860—22no—
28C4×#11758201—21no—
29C4×#11758201—21no—
30#16839819C2211yescharacteristic
31C2×C4⋊#92418—21no—
32C2×C4⋊#92418C2211yescharacteristic
33C2×C4×#92418—21no—
34C2×C4×#92418C2211yescharacteristic
35#16839514C2212yes—
36#16839512C2212yes—
37#16839510C2212yes—
38#16839508C2212yes—
39#16839508C2212yes—
40#16839505C2212yes—
41C61×#533C2211yescharacteristic
42C2×C4×Q8×C61C2211yescharacteristic
43C61×#483—21no—
44C61×#475C2212yes—
45C61×#462C2212yes—
46C61×#451—21no—
47C61×#441—22no—
48C61×#432C2211yescharacteristic
49C2×#11758222—21no—
50C2×#11758201—22no—
51C2×#11758201—21no—
52C2×#11758201—21no—
53C22×#92418—21no—
54C22×#92418D411yescharacteristic
55C22×#92418D411yescharacteristic
56#14519777C2311yescharacteristic
57#14519774C2311yescharacteristic
58#14519765—21no—
59#14519751—21no—
60#14519751—21no—
61C4×D244—21no—
62C4×D244—21no—
63#14519710—22no—
64#14519708—21no—
65#14519708—21no—
66C4⋊#92418—21no—
67C4⋊#92418—22no—
68C4⋊#92418—22no—
69C4⋊#92418C2312yes—
70C4⋊#92418C2312yes—
71#14519701—22no—
72#14519701—21no—
73#14519701—21no—
74#14519697—22no—
75#14519697—21no—
76#14519697—21no—
77C22⋊#92418—21no—
78#14519688—21no—
79C4×#92418—22no—
80C4×#92418—22no—
81C4×#92418D411yescharacteristic
82C4×#92418D411yescharacteristic
83C4×#92418C2311yescharacteristic
84C4×#92418C2311yescharacteristic
85C22×Q8×C61D411yescharacteristic
86C2×Q16×C61—22no—
87C4⋊Q8×C61C2311yescharacteristic
88C4⋊Q8×C61C2311yescharacteristic
89#125×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×Q8×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61D412yes—
97C4×Q8×C61C2312yes—
98#117×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C42×C61—21no—
102C2×C42×C61C2311yescharacteristic
103#106×C61—22no—
104C4⋊C8×C61C2312yes—
105#103×C61—22no—
106#103×C61—22no—
107C22⋊C8×C61—21no—
108#97×C61—21no—
109C2×Q8×C61—24no—
110C2×Q8×C61—21no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61C2×D412yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C2×C22⋊D61—41no—
120#11758222—82no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244—21no—
124C2×C4×D61—41no—
125C2×Dic122—21no—
126Q16×C61—44no—
127C2×C8×C61—22no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61C2×D412yes—
138C22⋊C4×C61—41no—
139C42×C61—22no—
140C42×C61—22no—
141C42×C61—41no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61#4111yescharacteristic
145C42×C61C2411yescharacteristic
146#11758201—42no—
147#11758201—44no—
148#11758201—42no—
149#11758198—41no—
150#11758198—41no—
151C4⋊Dic61—21no—
152C4⋊Dic61—21no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418—41no—
157C2×#92418—42no—
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C23×C61#12111yescharacteristic
163C22×D61—41no—
164Q8×C61—24no—
165Q8×C61—22no—
166Q8×C61—42no—
167Q8×C61—41no—
168Q8×C61—41no—
169Q8×C61#13514yes—
170C2×C4×C61—24no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—22no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—22no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C2×#4111yescharacteristic
186C22⋊D61—82no—
187C2×Dic61—41no—
188D244—42no—
189D244—41no—
190D244—41no—
191D244—81no—
192C4×D61—82no—
193Dic122—81no—
194C8×C61—42no—
195#92418—21no—
196#92418—21no—
197#92418—21no—
198#92418—42no—
199#92418—42no—
200#92418#13712yes—
201#19263—611nomaximal, Sylow
202C22×C61—21no—
203C22×C61—21no—
204C22×C61#47112yes—
205C22×C61C2×#12111yescharacteristic
206C2×D61—81no—
207C2×D61—81no—
208C2×D61—81no—
209C4×C61—21no—
210C4×C61—24no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—42no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61C2×#13512yes—
218C4×C61C2×#13711yescharacteristic
219C4×C61#57511yescharacteristic
220Dic61—81no—
221#3167—611no—
222#3113D6111yescharacteristic, complemented
223#3112—611no—
224C2×C8×Q8—611no—
225#1684—612no—
226#1682—612no—
227#1672—612no—
228#1666—612no—
229#1568—611no—
230#1552—611no—
231#1551—611no—
232C2×C61—22no—
233C2×C61#303711yescharacteristic
234C2×C61#305011yescharacteristic
235C2×C61C2×#47111yescharacteristic
236D61—161no—
237#533C2×D6111yescharacteristic
238#532—611no—
239C2×C4×Q8C2×D6111yescharacteristic
240#498—611no—
241#492—611no—
242#487—611no—
243#486—611no—
244#483—21no—
245#480—1221no—
246#477—612no—
247#475C2×D6112yes—
248#465—1221no—
249#465—1221no—
250#462C2×D6112yes—
251#460—612no—
252#451—21no—
253#448—1221no—
254C8×Q8—612no—
255C8×Q8—612no—
256C8×Q8—1221no—
257C8×Q8—1221no—
258#441—22no—
259#440—1222no—
260C4×SD16—1221no—
261C4×SD16—1221no—
262#432—611no—
263#432C2×D6111yescharacteristic
264C2×C4⋊C8—611no—
265C2×C4⋊C8—1221no—
266C2×C4×C8—611no—
267C2×C4×C8—1221no—
268#335—612no—
269#334—612no—
270#333—612no—
271#332—612no—
272#332—612no—
273#331—612no—
274C61#1926311yescharacteristic, complemented, Sylow
275C2×#41—1221no—
276C22×Q8C22⋊D6111yescharacteristic
277C2×Q16—22no—
278C2×SD16—1221no—
279C2×SD16—1221no—
280C2×SD16—1222no—
281C22×C8—611no—
282C22×C8—611no—
283C22×C8—1221no—
284C4⋊Q8—611no—
285C4⋊Q8C22×D6111yescharacteristic
286C4⋊Q8C22×D6111yescharacteristic
287#127—611no—
288#125—21no—
289#124—1221no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292#121—1221no—
293#121—1221no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C22⋊D6112yes—
299C4×Q8C22×D6112yes—
300C4×D4—1221no—
301C4×D4—1221no—
302#117—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C22⋊D6111yescharacteristic
305C2×C42—21no—
306C2×C42C22×D6111yescharacteristic
307#107—1222no—
308#106—22no—
309#106—1221no—
310#106—1221no—
311C4⋊C8—612no—
312C4⋊C8—612no—
313C4⋊C8—1222no—
314C4⋊C8—1222no—
315C4⋊C8—1221no—
316C4⋊C8C22×D6112yes—
317#103—22no—
318#103—22no—
319#103—1221no—
320#103—1221no—
321#103—1222no—
322#102—1221no—
323#102—1221no—
324#102—1222no—
325C22⋊C8—21no—
326C22⋊C8—1221no—
327#97—21no—
328#97—1221no—
329C4×C8—611no—
330C4×C8—611no—
331C4×C8—611no—
332C4×C8—611no—
333C4×C8—1222no—
334C4×C8—1222no—
335#41—4882no—
336C2×Q8—24no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—1221no—
341C2×Q8C2×C22⋊D6112yes—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—2441no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—2441no—
349C22×C4D4×D6111yescharacteristic
350C22×C4#1175822411yescharacteristic
351C22×C4C2×C22⋊D6111yescharacteristic
352Q16—44no—
353SD16—2442no—
354SD16—2442no—
355SD16—2444no—
356C2×C8—22no—
357C2×C8—611no—
358C2×C8—611no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—1222no—
364C2×C8—2441no—
365C2×C8—2442no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4C2×C22⋊D6112yes—
378C22⋊C4—41no—
379C22⋊C4—2441no—
380C22⋊C4—2441no—
381C42—22no—
382C42—22no—
383C42—41no—
384C42D4×D6111yescharacteristic
385C42#1175822411yescharacteristic
386C42C2×C22⋊D6111yescharacteristic
387C42C23×D6111yescharacteristic
388C23—2441no—
389C23#1451974911yescharacteristic
390Q8—24no—
391Q8—22no—
392Q8—42no—
393Q8—41no—
394Q8—41no—
395Q8—4881no—
396Q8#1451979714yes—
397D4—4881no—
398D4—4882no—
399D4—2442no—
400D4—2441no—
401D4—2441no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—4882no—
413C2×C4—2441no—
414C2×C4#1451974911yescharacteristic
415C2×C4#1451974911yescharacteristic
416C2×C4#1451974911yescharacteristic
417C2×C4C2×D4×D6111yescharacteristic
418C2×C4C22×C22⋊D6111yescharacteristic
419C2×C4C2×#1175822411yescharacteristic
420C8—42no—
421C8—612no—
422C8—1221no—
423C8—1221no—
424C8—1221no—
425C8—2442no—
426C8—2442no—
427C22—21no—
428C22—21no—
429C22—4881no—
430C22—4881no—
431C22—4881no—
432C22#1684002712yes—
433C22C2×#1451974911yescharacteristic
434C4—24no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—4881no—
443C4C2×#1451979712yes—
444C4#137×D6111yescharacteristic
445C4#1684056111yescharacteristic
446C2—22no—
447C2—9761no—
448C2#2145528811yescharacteristic
449C2#2145539711yescharacteristic
450C2C2×#1684002711yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3113C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#3113D61
hypocenterC61#19263
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
3. C2×Q8×#92418C2semidirect
4. #21445275C2semidirect
5. #21445265C2semidirect
6. #21445199C2semidirect
7. #21445169C2semidirect
8. #21444580C2semidirect
9. #21444519C2semidirect
11. C61×#3113C2semidirect
222. #3113D61semidirect
274. C61#19263semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214559412
C2×Q8×#924182
#214452752
#214452652
#214451992
#214451692
#214445802
#214445192
#214445152
C61×#31132
#1926361