Finite Group Databasebeta

← #29574916

Subgroups — #29574916

Order 15616.

452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454989C211yesmaximal, characteristic, complemented
2#21446652C211yesmaximal, characteristic, complemented
3#21444305C211yesmaximal, characteristic, complemented
4#21444288C211yesmaximal, characteristic, complemented
5#21443713C211yesmaximal, characteristic, complemented
6#21443709C211yesmaximal, characteristic, complemented
7C61×#3171C211yesmaximal, characteristic
8#16839893—21no—
9#16839840—21no—
10#16839834—21no—
11#16839834—21no—
12#16839823—21no—
13#16839819C2211yescharacteristic
14#16839815C2211yescharacteristic
15#16839789—21no—
16#16839786C2211yescharacteristic
17C2×#14519704—21no—
18C2×#14519704—21no—
19#16839608C2211yescharacteristic
20#16839499—21no—
21#16839496—21no—
22D4⋊#92418—21no—
23D4⋊#92418—21no—
24C61×#532C2211yescharacteristic
25C61×#529C2211yescharacteristic
26C61×#501C411yescharacteristic, complemented
27C61×#496C411yescharacteristic, complemented
28C61×#490C411yescharacteristic, complemented
29C61×#489C411yescharacteristic, complemented
30C61×#469—21no—
31C61×#468—21no—
32C4×SD16×C61—21no—
33C4×D8×C61—21no—
34C4×M16×C61C2211yescharacteristic
35C2×#11758194—21no—
36C2×#11758194D411yescharacteristic
37C2×#11758194D411yescharacteristic
38C22×#92418—21no—
39C2×C4×Dic61—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46C4⋊#92418D411yescharacteristic
47#14519704—42no—
48#14519704—42no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519688—21no—
54#14519688—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57#14519684—21no—
58#14519684—21no—
59C2×#41×C61—21no—
60C2×SD16×C61—21no—
61C2×D8×C61—21no—
62C2×M16×C61—21no—
63C4⋊Q8×C61C2×C411yescharacteristic
64#127×C61C2×C411yescharacteristic
65#126×C61—21no—
66#125×C61C2×C411yescharacteristic
67#124×C61—21no—
68#124×C61C2×C411yescharacteristic
69#123×C61—21no—
70C22⋊Q8×C61D411yescharacteristic
71#121×C61—21no—
72#121×C61—21no—
73#121×C61D411yescharacteristic
74C4×Q8×C61D411yescharacteristic
75C4×D4×C61—21no—
76C4×D4×C61—21no—
77C4×D4×C61—21no—
78C4×D4×C61D411yescharacteristic
79#117×C61—21no—
80C2×C42×C61C2311yescharacteristic
81#107×C61—21no—
82#106×C61—21no—
83#103×C61—21no—
84#102×C61—21no—
85#102×C61—21no—
86#102×C61—21no—
87#97×C61C2×C411yescharacteristic
88#97×C61C2×C411yescharacteristic
89C4×C8×C61—21no—
90#41×C61—41no—
91#41×C61—41no—
92#41×C61—41no—
93#41×C61—41no—
94C2×Q8×C61—21no—
95C2×Q8×C61C22⋊C411yescharacteristic
96C2×D4×C61—21no—
97C2×D4×C61—21no—
98C2×D4×C61—21no—
99C2×D4×C61—21no—
100C2×D4×C61—41no—
101C2×D4×C61C22⋊C411yescharacteristic
102C22×C4×C61—21no—
103C22×C4×C61—41no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C22×Dic61—41no—
108SD16×C61—42no—
109D8×C61—42no—
110M16×C61—42no—
111C2×C8×C61—21no—
112C2×C8×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61C22⋊C411yescharacteristic
120C4⋊C4×C61C22⋊C411yescharacteristic
121C22⋊C4×C61—21no—
122C22⋊C4×C61—21no—
123C22⋊C4×C61—21no—
124C22⋊C4×C61—21no—
125C22⋊C4×C61—21no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C42×C61—21no—
129C42×C61C22×C411yescharacteristic
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61#4111yescharacteristic
133C4×Dic61—22no—
134C4×Dic61—41no—
135#11758194—41no—
136#11758194—41no—
137#11758194—81no—
138C2×#92418—21no—
139C2×#92418—21no—
140C2×#92418—21no—
141C2×#92418—21no—
142C2×#92418—41no—
143C2×#92418—81no—
144C23×C61—21no—
145C23×C61—41no—
146C23×C61#12111yescharacteristic
147Q8×C61—41no—
148Q8×C61—41no—
149Q8×C61—41no—
150D4×C61—41no—
151D4×C61—41no—
152D4×C61—41no—
153D4×C61—42no—
154D4×C61—41no—
155D4×C61—41no—
156D4×C61—81no—
157D4×C61—81no—
158D4×C61—81no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61C2×C22⋊C411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61C4×D411yescharacteristic
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12311yescharacteristic
177C2×Dic61—42no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C8×C61—22no—
181C8×C61—41no—
182#92418—41no—
183#92418—41no—
184#92418—41no—
185#92418—41no—
186#92418—81no—
187#8997—611nomaximal, Sylow
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61#38611yescharacteristic
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—81no—
207C4×C61#45311yescharacteristic
208C4×C61#45411yescharacteristic
209Dic61—82no—
210#3171D6111yescharacteristic
211#2995—611no—
212#1963—611no—
213#1500—611no—
214#1496—611no—
215#1300—611no—
216#1299—611no—
217C2×C61—41no—
218C2×C61—81no—
219C2×C61—161no—
220C2×C61#188111yescharacteristic
221C2×C61#188311yescharacteristic
222C2×C61#188411yescharacteristic
223#532C2×D6111yescharacteristic
224#529C2×D6111yescharacteristic
225#501Dic6111yescharacteristic, complemented
226#496Dic6111yescharacteristic, complemented
227#490Dic6111yescharacteristic, complemented
228#489Dic6111yescharacteristic, complemented
229#469—21no—
230#468—21no—
231#446—1221no—
232C4×SD16—21no—
233C4×D8—21no—
234#436—1221no—
235#435—1221no—
236#435—1221no—
237#433—1221no—
238#432—611no—
239#431—611no—
240#424—1221no—
241#423—611no—
242C2×#104—1221no—
243C2×#104—1221no—
244C4×M16C2×D6111yescharacteristic
245#376—611no—
246#328—1221no—
247#327—1221no—
248D4⋊C8—1221no—
249D4⋊C8—1221no—
250C61#899711yescharacteristic, complemented, Sylow
251C2×#41—21no—
252C2×SD16—21no—
253C2×D8—21no—
254C2×M16—21no—
255C2×M16—611no—
256C2×M16—611no—
257C2×M16—1221no—
258C22×C8—1221no—
259C4⋊Q8C2×Dic6111yescharacteristic
260#127C2×Dic6111yescharacteristic
261#126—21no—
262#125C2×Dic6111yescharacteristic
263#124—21no—
264#124C2×Dic6111yescharacteristic
265#123—21no—
266C22⋊Q8C22⋊D6111yescharacteristic
267#121—21no—
268#121—21no—
269#121C22⋊D6111yescharacteristic
270C4×Q8C22⋊D6111yescharacteristic
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4C22⋊D6111yescharacteristic
275#117—21no—
276C2×C42—1221no—
277C2×C42C22×D6111yescharacteristic
278#107—21no—
279#106—21no—
280C4⋊C8—611no—
281C4⋊C8—611no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C4⋊C8—1221no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287#104—2442no—
288#104—2442no—
289#103—21no—
290#102—21no—
291#102—21no—
292#102—21no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297#97—1221no—
298#97—1221no—
299#97C2×Dic6111yescharacteristic
300#97C2×Dic6111yescharacteristic
301C4×C8—21no—
302C4×C8—1221no—
303C4×C8—1221no—
304#95—1221no—
305#95—1221no—
306#41—41no—
307#41—41no—
308#41—41no—
309#41—41no—
310C2×Q8—21no—
311C2×Q8C22⋊Dic6111yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4C22⋊Dic6111yescharacteristic
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—2441no—
321C22×C4D4×D6111yescharacteristic
322C22×C4#1175822411yescharacteristic
323C22×C4C2×C22⋊D6111yescharacteristic
324SD16—42no—
325D8—42no—
326M16—42no—
327M16—4881no—
328M16—2441no—
329M16—2441no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—1221no—
336C2×C8—4881no—
337C2×C8—2441no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4C22⋊Dic6111yescharacteristic
345C4⋊C4C22⋊Dic6111yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C42—21no—
354C42—1222no—
355C42—2441no—
356C42D4×D6111yescharacteristic
357C42#1175822411yescharacteristic
358C42C22×Dic6111yescharacteristic
359C42C2×C22⋊D6111yescharacteristic
360C23—21no—
361C23—41no—
362C23#1451974911yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—4881no—
388C2×C4—4881no—
389C2×C4—2442no—
390C2×C4C2×C22⋊Dic6111yescharacteristic
391C2×C4D4×Dic6111yescharacteristic
392C2×C4D4×Dic6111yescharacteristic
393C2×C4#1451974511yescharacteristic
394C2×C4#1451974911yescharacteristic
395C2×C4#1451975811yescharacteristic
396C8—22no—
397C8—41no—
398C8—4881no—
399C8—2441no—
400C8—2441no—
401C8—2441no—
402C8—2441no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1683964211yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—81no—
422C4—4882no—
423C4#1683992811yescharacteristic
424C4#1683993311yescharacteristic
425C2—41no—
426C2—81no—
427C2—161no—
428C2#2144618311yescharacteristic
429C2#2144619711yescharacteristic
430C2#2144620311yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3171C2
socleC22×C61#386
cosocleC2×C42×C61C23
hypercenter#3171D61
hypocenterC61#8997
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3171

Complements

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

NH ≅ G/Ntype
1. #21454989C2semidirect
2. #21446652C2semidirect
3. #21444305C2semidirect
4. #21444288C2semidirect
5. #21443713C2semidirect
6. #21443709C2semidirect
26. C61×#501C4semidirect
27. C61×#496C4semidirect
28. C61×#490C4semidirect
29. C61×#489C4semidirect
225. #501Dic61semidirect
226. #496Dic61semidirect
227. #490Dic61semidirect
228. #489Dic61semidirect
250. C61#8997semidirect

Maximal subgroups

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

subgroupindex
#214549892
#214466522
#214443052
#214442882
#214437132
#214437092
C61×#31712
#899761