Finite Group Databasebeta

← #29663338

Subgroups — #29663338

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457164C211yesmaximal, characteristic, complemented
2#21457136C211yesmaximal, characteristic
3#21456142C211yesmaximal, characteristic
4#21454753C211yesmaximal, characteristic, complemented
5#21445374C212yesmaximal, complemented
6#21445360C212yesmaximal, complemented
7#21445278C212yesmaximal, complemented
8#21445264C212yesmaximal, complemented
9#21444507C211yesmaximal, characteristic, complemented
10#21444494C211yesmaximal, characteristic
11C2×C61×#335C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840319C2211yescharacteristic
14#16840312C2211yescharacteristic
15#16840117—21no—
16#16840117—21no—
17#16840113C2211yescharacteristic
18#16840113C2211yescharacteristic
19#16840109C2211yescharacteristic
20#16840109C2211yescharacteristic
21#16840058—21no—
22#16840058C2212yes—
23#16840053—21no—
24#16840048C2212yes—
25#16840003—22no—
26#16839991—22no—
27#16839973—21no—
28#16839973C2212yes—
29#16839968—21no—
30#16839963C2212yes—
31#16839892—21no—
32#16839892C2212yes—
33C8×Dic122—21no—
34C8×Dic122C2212yes—
35#16839788—21no—
36#16839786C2211yescharacteristic
37#16839759—21no—
38#16839759—21no—
39#16839717—21no—
40#16839510C2212yes—
41#16839509C2212yes—
42#16839507C2212yes—
43#16839505C2212yes—
44C2×C4⋊C8×C61C2211yescharacteristic
45C2×C4⋊C8×C61C2211yescharacteristic
46C2×C4×C8×C61C2211yescharacteristic
47C61×#335C2212yes—
48C61×#335C2212yes—
49C2×#11758222—21no—
50C2×Dic244—22no—
51C2×#11758190—22no—
52C2×#11758194—21no—
53#14519777D411yescharacteristic
54#14519777D411yescharacteristic
55#14519777C2311yescharacteristic
56#14519777C2311yescharacteristic
57#14519777C2311yescharacteristic
58#14519774C2311yescharacteristic
59#14519769—21no—
60#14519769—21no—
61#14519765—21no—
62#14519756—21no—
63#14519756—21no—
64#14519756—21no—
65#14519756D412yes—
66#14519751—21no—
67#14519751—21no—
68C4×Dic122—21no—
69C4×Dic122—21no—
70C4×Dic122—21no—
71C4×Dic122C2312yes—
72C4×D244—21no—
73C4×D244—21no—
74#14519736—21no—
75#14519736—21no—
76#14519711—22no—
77#14519709—22no—
78C4⋊#92418—21no—
79C4⋊#92418C2312yes—
80#14519706—22no—
81#14519706—22no—
82#14519702—22no—
83#14519702—22no—
84#14519702—21no—
85#14519702—21no—
86#14519702—21no—
87#14519702—21no—
88#14519702—22no—
89#14519699—21no—
90#14519699—21no—
91#14519699—21no—
92#14519699—21no—
93#14519699—22no—
94#14519687—22no—
95C8×Dic61—22no—
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61D411yescharacteristic
99C22×C8×C61D411yescharacteristic
100C2×C42×C61C2311yescharacteristic
101C4⋊C8×C61—21no—
102C4⋊C8×C61—21no—
103C4⋊C8×C61C2312yes—
104C4⋊C8×C61C2312yes—
105C4×C8×C61D411yescharacteristic
106C4×C8×C61D411yescharacteristic
107C4×C8×C61C2311yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—41no—
113#11758222—42no—
114#11758222—42no—
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—21no—
118C2×C4×D61—41no—
119C2×Dic122—21no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122C2×D412yes—
124C2×C8×C61—22no—
125C2×C8×C61—22no—
126C2×C8×C61—22no—
127C2×C8×C61—22no—
128C2×C8×C61—81no—
129C2×C8×C61—81no—
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61#4111yescharacteristic
137C42×C61C2411yescharacteristic
138C22⋊Dic61—22no—
139C22⋊Dic61—41no—
140#11758198—41no—
141#11758198—41no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61—21no—
151C4⋊Dic61C2×D412yes—
152#11758196—22no—
153#11758196—22no—
154#11758196—41no—
155#11758196—41no—
156C4×Dic61—22no—
157C4×Dic61—41no—
158#11758194—42no—
159C2×#92418—22no—
160Dic244—82no—
161#11758190—82no—
162C23×C61#12111yescharacteristic
163C22×D61—41no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#13512yes—
171C2×C4×C61#13712yes—
172C2×C4×C61C22×D411yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C2×#4111yescharacteristic
175C22⋊D61—82no—
176C2×Dic61—22no—
177C2×Dic61—22no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181D244—41no—
182D244—41no—
183D244—41no—
184D244—41no—
185D244—81no—
186C4×D61—82no—
187Dic122—22no—
188Dic122—22no—
189Dic122—42no—
190Dic122—41no—
191Dic122—41no—
192Dic122—41no—
193Dic122—41no—
194Dic122—81no—
195C8×C61—21no—
196C8×C61—21no—
197C8×C61—21no—
198C8×C61—21no—
199C8×C61—42no—
200C8×C61—42no—
201#92418—42no—
202#19217—611nomaximal, Sylow
203C22×C61—21no—
204C22×C61—21no—
205C22×C61#46412yes—
206C22×C61C2×#12111yescharacteristic
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61#46412yes—
214C4×C61C2×#13511yescharacteristic
215C4×C61C2×#13711yescharacteristic
216C4×C61#57611yescharacteristic
217C4×C61#57811yescharacteristic
218Dic61—42no—
219Dic61—42no—
220Dic61—81no—
221Dic61—81no—
222Dic61—81no—
223#3249—611no—
224#3246—611no—
225#3131—611no—
226#2960—611no—
227#1700—612no—
228#1698—612no—
229#1684—612no—
230#1682—612no—
231C2×#335D6111yescharacteristic, complemented
232#1550—611no—
233#1547—611no—
234C2×C61—22no—
235C2×C61C2×#46411yescharacteristic
236C2×C61#306111yescharacteristic
237C2×C61#306711yescharacteristic
238D61—161no—
239#533—611no—
240#533—611no—
241#532—611no—
242#488—1221no—
243#488—1221no—
244#487—611no—
245#487—611no—
246#486—611no—
247#486—611no—
248#477—612no—
249#477—1221no—
250#476—1221no—
251#475—612no—
252#467—1222no—
253#465—1222no—
254#462—612no—
255#462—1221no—
256#461—1221no—
257#460—612no—
258#446—612no—
259#446—1221no—
260C8×Q8—612no—
261C8×Q8—1221no—
262#424—1221no—
263#423—611no—
264C2×C4⋊C8C2×D6111yescharacteristic
265C2×C4⋊C8C2×D6111yescharacteristic
266#416—1221no—
267#416—1221no—
268#405—1221no—
269C2×C4×C8C2×D6111yescharacteristic
270#335C2×D6112yes—
271#335C2×D6112yes—
272#333—612no—
273#332—612no—
274#332—612no—
275#331—612no—
276C61#1921711yescharacteristic, complemented, Sylow
277C2×#41—1221no—
278C2×Q16—1222no—
279C2×SD16—1222no—
280C2×M16—1221no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8D24411yescharacteristic
284C22×C8D24411yescharacteristic
285C4⋊Q8—611no—
286C4⋊Q8—611no—
287C4⋊Q8—611no—
288C4⋊Q8—611no—
289C4⋊Q8—611no—
290#127—611no—
291#125—1221no—
292#125—1221no—
293#124—1221no—
294C22⋊Q8—612no—
295C22⋊Q8—1221no—
296C22⋊Q8—1221no—
297C22⋊Q8—1221no—
298#121—1221no—
299#121—1221no—
300C4×Q8—612no—
301C4×Q8—1221no—
302C4×Q8—1221no—
303C4×Q8—1221no—
304C4×D4—1221no—
305C4×D4—1221no—
306#117—1221no—
307#117—1221no—
308C2×C42C22×D6111yescharacteristic
309#107—1222no—
310#106—1222no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313C4⋊C8—612no—
314C4⋊C8—1222no—
315C4⋊C8—1222no—
316C4⋊C8—1221no—
317C4⋊C8C22×D6112yes—
318C4⋊C8C22×D6112yes—
319#103—1222no—
320#103—1222no—
321#103—1222no—
322#103—1221no—
323#103—1221no—
324#103—1221no—
325#103—1221no—
326#102—1222no—
327#102—1221no—
328#102—1221no—
329#102—1221no—
330#102—1221no—
331#97—1222no—
332C4×C8—1222no—
333C4×C8D24411yescharacteristic
334C4×C8D24411yescharacteristic
335C4×C8C22×D6111yescharacteristic
336C4×C8C22×D6111yescharacteristic
337#41—2442no—
338#41—2442no—
339C2×Q8—612no—
340C2×Q8—1221no—
341C2×Q8—1221no—
342C2×Q8—1221no—
343C2×Q8—1221no—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—2441no—
348C22×C4—2441no—
349C22×C4C2×D24411yescharacteristic
350C22×C4D4×D6111yescharacteristic
351C22×C4#1175822611yescharacteristic
352Q16—4882no—
353SD16—4882no—
354M16—2442no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—81no—
360C2×C8—81no—
361C2×C8—1222no—
362C2×C8C2×D24411yescharacteristic
363C2×C8C2×D24411yescharacteristic
364C2×C8C2×D24411yescharacteristic
365C2×C8C2×D24411yescharacteristic
366C4⋊C4—612no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C4⋊C4—1221no—
370C4⋊C4—1221no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C22⋊C4—1222no—
381C22⋊C4—2441no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C42—1222no—
385C42—2441no—
386C42C2×D24411yescharacteristic
387C42D4×D6111yescharacteristic
388C42#1175822611yescharacteristic
389C42C23×D6111yescharacteristic
390C23—2441no—
391C23#1451975211yescharacteristic
392Q8—1222no—
393Q8—1222no—
394Q8—4881no—
395Q8—2442no—
396Q8—2441no—
397Q8—2441no—
398Q8—2441no—
399Q8—2441no—
400D4—4881no—
401D4—4882no—
402D4—2441no—
403D4—2441no—
404D4—2441no—
405D4—2441no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—1222no—
410C2×C4—1222no—
411C2×C4—4882no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4#1451975211yescharacteristic
416C2×C4#1451975211yescharacteristic
417C2×C4#1451975211yescharacteristic
418C2×C4#1451979912yes—
419C2×C4#1451981012yes—
420C2×C4C2×D4×D6111yescharacteristic
421C2×C4C22×D24411yescharacteristic
422C2×C4C2×#1175822611yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—42no—
429C8—2442no—
430C22—21no—
431C22—21no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22#1683998512yes—
436C22C2×#1451975211yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—4881no—
441C4—4881no—
442C4—4881no—
443C4—2442no—
444C4—2442no—
445C4#1683998512yes—
446C4C2×#1451979911yescharacteristic
447C4C2×#1451981011yescharacteristic
448C4#1684056311yescharacteristic
449C4#1684057511yescharacteristic
450C2—22no—
451C2—9761no—
452C2C2×#1683998511yescharacteristic
453C2#2145549111yescharacteristic
454C2#2145554011yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#335C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenterC2×#335D61
hypocenterC61#19217
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
1. #21457164C2semidirect
4. #21454753C2semidirect
5. #21445374C2semidirect
6. #21445360C2semidirect
7. #21445278C2semidirect
8. #21445264C2semidirect
9. #21444507C2semidirect
11. C2×C61×#335C2semidirect
231. C2×#335D61semidirect
276. C61#19217semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214571362
#214561422
#214547532
#214453742
#214453602
#214452782
#214452642
#214445072
#214444942
C2×C61×#3352
#1921761