Finite Group Databasebeta

← #29583231

Subgroups — #29583231

Order 15616.

438 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21452016C211yesmaximal, characteristic, complemented
2#21444348C211yesmaximal, characteristic
3#21444335C211yesmaximal, characteristic
4#21443725C211yesmaximal, characteristic, complemented
5#21443705C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1964C211yesmaximal, characteristic
8#16839726C2211yescharacteristic
9#16839726C2211yescharacteristic
10#16839698—21no—
11#16839695—21no—
12#16839695—21no—
13#16839685—21no—
14#16839659—21no—
15#16839645—21no—
16#16839625C2211yescharacteristic
17C4×C22⋊Dic61C2211yescharacteristic
18#16839496—21no—
19#16839496—21no—
20#16839496—21no—
21#16839496—21no—
22C2×#121×C61C2211yescharacteristic
23C2×#99×C61—21no—
24C2×#99×C61—21no—
25C61×#380C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C2×#11758194—21no—
28C2×#11758194—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22⋊#92418—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684D411yescharacteristic
46#14519684D411yescharacteristic
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C22×D4×C61—21no—
50C22×D4×C61Q811yescharacteristic
51C23×C4×C61C2311yescharacteristic
52#121×C61—21no—
53#121×C61—21no—
54#121×C61—21no—
55#121×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61Q811yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61D411yescharacteristic
62C2×C42×C61—21no—
63#99×C61—42no—
64#99×C61—42no—
65#95×C61—21no—
66#95×C61—21no—
67C24×C61—21no—
68C24×C61C2×D411yescharacteristic
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—81no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—81no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×Q811yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—81no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C42×C61—81no—
103C22⋊Dic61—42no—
104C22⋊Dic61—81no—
105C4⋊Dic61—42no—
106C4⋊Dic61—81no—
107#11758196—42no—
108#11758196—81no—
109#11758196—81no—
110#11758196—81no—
111C4×Dic61—81no—
112#11758194—81no—
113#11758194—81no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—81no—
124C23×C61—81no—
125C23×C61#12011yescharacteristic
126C23×C61C22⋊Q811yescharacteristic
127C23×C61#12411yescharacteristic
128D4×C61—81no—
129D4×C61—81no—
130D4×C61—81no—
131D4×C61—81no—
132D4×C61—81no—
133D4×C61—81no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—81no—
151C2×C4×C61—81no—
152C2×C4×C61C22⋊Q811yescharacteristic
153C2×C4×C61C22⋊Q811yescharacteristic
154C2×C4×C61#12411yescharacteristic
155C2×C4×C61#12411yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168#92418—81no—
169#92418—81no—
170#10384—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—161no—
185C22×C61—161no—
186C22×C61#39311yescharacteristic
187C22×C61#45311yescharacteristic
188C22×C61#45411yescharacteristic
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—81no—
194C4×C61—81no—
195C4×C61—82no—
196C4×C61—81no—
197Dic61—42no—
198Dic61—81no—
199Dic61—81no—
200Dic61—81no—
201#2667—611no—
202#1964D6111yescharacteristic
203#1510—611no—
204#1507—611no—
205#1305—611no—
206#1297—611no—
207#1284—611no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—41no—
212C2×C61—161no—
213C2×C61#202711yescharacteristic
214C2×C61#203111yescharacteristic
215C2×C61#203211yescharacteristic
216C2×#121C2×D6111yescharacteristic
217C2×#99—21no—
218C2×#99—21no—
219#407—611no—
220#407—611no—
221#399—1221no—
222#398—1221no—
223#398—1221no—
224#396—1221no—
225#389—1221no—
226#387—1221no—
227#381—611no—
228#380C2×D6111yescharacteristic
229C4×C22⋊C4—611no—
230C4×C22⋊C4C2×D6111yescharacteristic
231#327—1221no—
232#327—1221no—
233#327—1221no—
234#327—1221no—
235C61#1038411yescharacteristic, complemented, Sylow
236C22×D4—21no—
237C22×D4Dic12211yescharacteristic
238C23×C4C22×D6111yescharacteristic
239C2×M16—1221no—
240C2×M16—1221no—
241#121—21no—
242#121—21no—
243#121—21no—
244#121—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4Dic12211yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4C22⋊D6111yescharacteristic
258C2×C22⋊C4C22⋊D6111yescharacteristic
259C2×C42—21no—
260C2×C42—1221no—
261#99—42no—
262#99—42no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266C22⋊C8—1221no—
267#95—21no—
268#95—21no—
269#95—611no—
270#95—611no—
271#95—611no—
272#95—611no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276C24—21no—
277C24C2×C22⋊D6111yescharacteristic
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—81no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4C2×Dic12211yescharacteristic
297C22×C4#1175822211yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300C22×C4#1175822411yescharacteristic
301C22×C4#1175822411yescharacteristic
302M16—4881no—
303M16—4881no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—81no—
309C4⋊C4—4881no—
310C4⋊C4—4881no—
311C4⋊C4—4881no—
312C4⋊C4—4881no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—4881no—
322C22⋊C4—2442no—
323C42—81no—
324C42—4881no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—81no—
333C23—81no—
334C23#1451974511yescharacteristic
335C23#1451975611yescharacteristic
336C23#1451976411yescharacteristic
337D4—81no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—1222no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451975411yescharacteristic
374C2×C4#1451975411yescharacteristic
375C2×C4#1451976311yescharacteristic
376C2×C4#1451976311yescharacteristic
377C8—4881no—
378C8—4881no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22—161no—
394C22#1683967411yescharacteristic
395C22#1683992911yescharacteristic
396C22#1683993411yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—82no—
404C4—81no—
405C4—4881no—
406C4—4881no—
407C4—4881no—
408C4—2442no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—161no—
414C2#2144697511yescharacteristic
415C2#2144699311yescharacteristic
416C2#2144699611yescharacteristic
subgroupG/H
centerC22#16839674
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1964C2
socleC22×C61#393
prime radicalC2×#121×C61C22
hypercenter#1964D61
hypocenterC61#10384
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
1. #21452016C2semidirect
4. #21443725C2semidirect
5. #21443705C2semidirect
6. #21443672C2semidirect
235. C61#10384semidirect

Maximal subgroups

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

subgroupindex
#214520162
#214443482
#214443352
#214437252
#214437052
#214436722
C61×#19642
#1038461