Finite Group Databasebeta

← #29590689

Subgroups — #29590689

Order 15616.

402 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451584C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic
3#21444150C211yesmaximal, characteristic
4#21443820C211yesmaximal, characteristic
5#21443819C211yesmaximal, characteristic
6#21443818C211yesmaximal, characteristic
7C61×#1344C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic, complemented
9C2×#14519754—21no—
10C2×#14519733C2211yescharacteristic
11#16839816—21no—
12#16839696—21no—
13#16839694C411yescharacteristic, complemented
14#16839693C411yescharacteristic, complemented
15#16839690—21no—
16#16839687C2211yescharacteristic
17#16839666—21no—
18#16839626C411yescharacteristic, complemented
19#16839623—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×Dic122—21no—
28C23×Dic61D411yescharacteristic
29#14519776—41no—
30#14519776—41no—
31#14519754—42no—
32#14519754—42no—
33#14519733—41no—
34#14519733—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—41no—
48C22⋊#92418—21no—
49#14519687—41no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—41no—
55#14519684—41no—
56#14519684C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61C2×D411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×Dic122—42no—
83C2×Dic122—42no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103#11758196—42no—
104#11758196—42no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C2×#92418—41no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C23×C61AGL(1,ℤ/8)11yescharacteristic
116C23×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152C2×Dic61#9911yescharacteristic
153C2×Dic61#9911yescharacteristic
154Dic122—82no—
155Dic122—82no—
156C8×C61—81no—
157#92418—81no—
158#11801—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—81no—
168C22×C61C2×#9911yescharacteristic
169C22×C61#41811yescharacteristic
170C22×C61#42111yescharacteristic
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61—81no—
175C4×C61—161no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—81no—
182Dic61—81no—
183Dic61—161no—
184#2621—611no—
185#1820—611no—
186#1464—611no—
187#1344—611no—
188#1344—611no—
189#1344—611no—
190#1344D6111yescharacteristic
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—41no—
194C2×C61—41no—
195C2×C61#151011yescharacteristic
196C2×C61#212311yescharacteristic
197C2×C61#212911yescharacteristic
198C2×C4⋊Q8—611no—
199C2×C22⋊Q8—1221no—
200C2×#117—611no—
201#432—1221no—
202#398—611no—
203#398—611no—
204#398—1221no—
205#397—611no—
206#397—1221no—
207#397C2×D6111yescharacteristic
208#391—1221no—
209#382—611no—
210#381—1221no—
211#342—611no—
212#342—1221no—
213#342C2×D6111yescharacteristic
214#324—1221no—
215#323—611no—
216#323C2×D6111yescharacteristic
217C61#1180111yescharacteristic, complemented, Sylow
218C22×Q8—1221no—
219C23×C4—611no—
220C4⋊Q8—2441no—
221C4⋊Q8—2441no—
222C22⋊Q8—2442no—
223C22⋊Q8—2442no—
224#117—2441no—
225#117—2441no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C4×D6111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4C22×D6111yescharacteristic
240C2×C42—611no—
241C2×C42—611no—
242C4⋊C8—2441no—
243C22⋊C8—21no—
244C22⋊C8—1221no—
245#97—2441no—
246#95—21no—
247#95—611no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95—2441no—
253#95—2441no—
254#95C4×D6111yescharacteristic
255C24D4×D6111yescharacteristic
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2442no—
259C2×Q8—2442no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4C2×C4×D6111yescharacteristic
276C22×C4D4×D6111yescharacteristic
277C2×C8—41no—
278C2×C8—2441no—
279C4⋊C4—41no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2442no—
284C4⋊C4—2442no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23C22⋊C4×D6111yescharacteristic
306C23#1451980111yescharacteristic
307C23#1451980411yescharacteristic
308Q8—4882no—
309Q8—4882no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C8—81no—
348C8—4881no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22#99×D6111yescharacteristic
359C22#1683976511yescharacteristic
360C22#1683977711yescharacteristic
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—161no—
366C4—1221no—
367C4—1221no—
368C4—9761no—
369C4—4881no—
370C4—4881no—
371C4—2441no—
372C4—2441no—
373C4—2441no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#2144434611yescharacteristic
379C2#2144747111yescharacteristic
380C2#2144749211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11801
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#14519776C4semidirect
13. #16839694C4semidirect
14. #16839693C4semidirect
18. #16839626C4semidirect
217. C61#11801semidirect

Maximal subgroups

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

subgroupindex
#214515842
#214458952
#214441502
#214438202
#214438192
#214438182
C61×#13442
#1180161