Finite Group Databasebeta

← #30599011

Subgroups — #30599011

Order 15616.

460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461699C211yesmaximal, characteristic, complemented
2#21461698C211yesmaximal, characteristic, complemented
3#21461074C212yesmaximal
4#21460691C212yesmaximal, complemented
5C2×#16839831C211yesmaximal, characteristic
6C2×#14519848—21no—
7C2×#14519847—21no—
8#16840733C2212yes—
9#16840733C2212yes—
10#16840638—21no—
11#16840638—21no—
12#16840608—22no—
13#16840605—22no—
14C22×C8×D61C2211yescharacteristic
15C2×C4×C22⋊D61C2211yescharacteristic
16#16839831—21no—
17#16839831—21no—
18#16839831—21no—
19#16839831—21no—
20C2×#14519706C411yescharacteristic
21C2×C22⋊#92418C411yescharacteristic
22C2×#14519689C2211yescharacteristic
23C2×#14519687C411yescharacteristic
24C22×M16×C61C411yescharacteristic
25C2×#11758213—22no—
26C2×#11758213—22no—
27#14519848—42no—
28#14519847—42no—
29#14519834—22no—
30#14519834—22no—
31C22⋊#92420—22no—
32C22⋊#92420—22no—
33C22×C22⋊D61Q811yescharacteristic
34C22×C4×D61C2311yescharacteristic
35C22×#92418C2×C411yescharacteristic
36C22×#92418C2×C411yescharacteristic
37C2×C8×D61—42no—
38C2×C8×D61D411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61D411yescharacteristic
41C2×C8×D61D411yescharacteristic
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C2×#11758196D411yescharacteristic
47C2×C22⋊Dic61D411yescharacteristic
48C2×#11758198Q811yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50#14519706—21no—
51#14519706—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519689—21no—
55#14519689—21no—
56#14519687—21no—
57#14519687—21no—
58C23×C4×C61C2×C411yescharacteristic
59C2×M16×C61—21no—
60C2×M16×C61—21no—
61C2×M16×C61—42no—
62C22×C8×C61C2×C411yescharacteristic
63C22×C8×C61C2×C411yescharacteristic
64C24×C61C4⋊C411yescharacteristic
65C23×D61C2×Q811yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C4⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—42no—
75C22×Dic61C4⋊C411yescharacteristic
76C22×Dic61C4⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61C2×D411yescharacteristic
81C2×C4×D61C2×D411yescharacteristic
82C2×C4×D61#4111yescharacteristic
83C2×C4×D61#4111yescharacteristic
84C2×#92420—42no—
85C2×#92420—42no—
86#11758213—42no—
87#11758213—42no—
88#11758213—42no—
89#11758213—42no—
90M16×C61—42no—
91M16×C61—42no—
92C2×C8×C61—22no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C2×C8×C61C22⋊C411yescharacteristic
96C2×C8×C61C22⋊C411yescharacteristic
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99#11758198—21no—
100#11758198—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C2×#92418—21no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110C8×D61—22no—
111C8×D61—22no—
112C8×D61—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C4⋊C411yescharacteristic
119C22×D61—22no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61C22⋊Q811yescharacteristic
123C22×D61C22⋊Q811yescharacteristic
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C2×C22⋊C411yescharacteristic
132C2×C4×C61#11711yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#12111yescharacteristic
141C2×Dic61#12111yescharacteristic
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—41no—
147C4×D61—41no—
148#92420—82no—
149#92420—82no—
150C8×C61—21no—
151C8×C61—41no—
152C8×C61#9912yes—
153#92418—21no—
154#92418—21no—
155#92418—41no—
156#8613—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—82no—
163C22×C61#38011yescharacteristic
164C22×C61#43012yes—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—44no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61C2×#9911yescharacteristic
175C4×C61#41011yescharacteristic
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180C2×#435—611no—
181#1810—611no—
182#1810—611no—
183#1465—612no—
184#1293—612no—
185C2×C61—22no—
186C2×C61—81no—
187C2×C61#179911yescharacteristic
188C2×C61#181111yescharacteristic
189C2×C61#181311yescharacteristic
190D61—41no—
191D61—41no—
192C22×M16#692311yescharacteristic
193C23×C8—611no—
194C2×C4×D4—611no—
195#435—1221no—
196#435—1221no—
197#435—1221no—
198#435—1221no—
199C2×#108—1221no—
200C2×#108—1221no—
201C2×C4⋊C8—611no—
202#407—612no—
203#407—612no—
204C2×C22⋊C8—611no—
205C2×C22⋊C8—611no—
206C2×#97—611no—
207#341—1221no—
208#341—1221no—
209#324—1222no—
210#323—1222no—
211C61#861311yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C23×C4—611no—
214C23×C4C2×#692311yescharacteristic
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—42no—
218C2×M16—1222no—
219C2×M16—1222no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8—611no—
224C22×C8—611no—
225C22×C8—611no—
226C22×C8—2442no—
227C22×C8C2×#692311yescharacteristic
228C22×C8C2×#692311yescharacteristic
229C4×D4—1221no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233C2×C4⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C42—611no—
237#108—2442no—
238#108—2442no—
239C4⋊C8—1221no—
240C4⋊C8—1221no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244C22⋊C8—1221no—
245C22⋊C8—1222no—
246C22⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—1222no—
249#97—1221no—
250#97—1221no—
251C24—611no—
252C24C4⋊#692311yescharacteristic
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—2442no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4C4⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271M16—42no—
272M16—42no—
273M16—2442no—
274M16—2442no—
275M16—2442no—
276M16—2442no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—1221no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2441no—
291C2×C8C22⋊#692311yescharacteristic
292C2×C8C22⋊#692311yescharacteristic
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—1221no—
300C42—1221no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—611no—
306C23—611no—
307C23—1222no—
308C23—2441no—
309C23—2441no—
310C23C2×C4⋊#692311yescharacteristic
311D4—2442no—
312D4—2442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1222no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4C2×C22⋊#692311yescharacteristic
334C2×C4#1451985611yescharacteristic
335C8—21no—
336C8—41no—
337C8—1221no—
338C8—1221no—
339C8—4882no—
340C8—4882no—
341C8—2441no—
342C8#1451983512yes—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—82no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—1221no—
355C22—2444no—
356C22#1684070411yescharacteristic
357C22#1684077712yes—
358C4—21no—
359C4—41no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4C2×#1451983511yescharacteristic
365C4#1684074111yescharacteristic
366C2—22no—
367C2—81no—
368C2—2441no—
369C2—2441no—
370C2#2146167911yescharacteristic
371C2#2146170011yescharacteristic
372C2#2146170411yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61#380
prime radicalC22×C22⋊D61Q8
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8613
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. #21461699C2semidirect
2. #21461698C2semidirect
4. #21460691C2semidirect
211. C61#8613semidirect

Maximal subgroups

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

subgroupindex
#214616992
#214616982
#214610742
#214606912
C2×#168398312
#861361