Finite Group Databasebeta

← #29576010

Subgroups — #29576010

Order 15616.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454903C211yesmaximal, characteristic
2#21451698C211yesmaximal, characteristic
3C4×#14519695C211yesmaximal, characteristic
4#21444422C211yesmaximal, characteristic
5#21444420C211yesmaximal, characteristic
6#21443683C211yesmaximal, characteristic
7C61×#1288C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839816—21no—
14#16839812—21no—
15C2×#14519695—21no—
16C4×#11758194C2211yescharacteristic
17#16839702—21no—
18#16839702C411yescharacteristic
19#16839702C411yescharacteristic
20#16839694C411yescharacteristic
21#16839694C411yescharacteristic
22#16839683—21no—
23#16839647—21no—
24#16839647—21no—
25#16839530—21no—
26#16839503—22no—
27#16839503—22no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#383C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C2×#11758194—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519769—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196C2×C411yescharacteristic
49C2×#11758196C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C4⋊#92418—21no—
53#14519706—22no—
54#14519706—22no—
55#14519695—24no—
56C22⋊#92418—21no—
57#14519688—21no—
58#14519688D412yes—
59#14519687—22no—
60C4×#92418—21no—
61C8×Dic61—22no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C2×M16×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#97×C61—21no—
73#97×C61D412yes—
74C4×C8×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—22no—
93C2×Dic122—41no—
94M16×C61—22no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—42no—
109C4⋊Dic61—42no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—41no—
115#11758196—41no—
116#11758196—41no—
117#11758196—41no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122#11758194—22no—
123#11758194—41no—
124C2×#92418—22no—
125C2×#92418—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#10412yes—
158Dic122—42no—
159Dic122—42no—
160C8×C61—42no—
161C8×C61—42no—
162#92418—42no—
163#92418—42no—
164#9190—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61C2×#10411yescharacteristic
169C22×C61#42111yescharacteristic
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—81no—
177C4×C61—81no—
178Dic61—22no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—81no—
183Dic61—81no—
184#2983—611no—
185#2634—611no—
186C4×#101—611no—
187#1528—611no—
188#1528—611no—
189#1288—611no—
190#1288D6111yescharacteristic
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#187111yescharacteristic
194C2×C61#191211yescharacteristic
195C2×C61#191511yescharacteristic
196C2×#125—611no—
197C2×C4×Q8—611no—
198#446—1222no—
199#446—1222no—
200#432—611no—
201#432—1221no—
202#432C2×D6111yescharacteristic
203#431—1221no—
204C2×#101—1221no—
205C4×M16—611no—
206C4×M16C2×D6111yescharacteristic
207#400—611no—
208#400—611no—
209#400—1221no—
210#398—611no—
211#398—611no—
212#395—1221no—
213#387—1221no—
214#387—1221no—
215#383C2×D6111yescharacteristic
216#343—1221no—
217#330—1222no—
218#330—1222no—
219C61#919011yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C2×M16—21no—
222C2×M16—1221no—
223#125—1221no—
224#125—1221no—
225#125—1221no—
226#125—1221no—
227C4×Q8—1221no—
228C4×Q8—1221no—
229C4×Q8—1221no—
230C4×Q8—1221no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42C22×D6111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—1222no—
245C4⋊C8—1222no—
246C4⋊C8—1221no—
247#101—1224no—
248C22⋊C8—21no—
249C22⋊C8—1221no—
250#97—21no—
251#97—612no—
252#97—1222no—
253#97—1221no—
254#97D24412yes—
255C4×C8—21no—
256C4×C8—1222no—
257C4×C8—1221no—
258#95—21no—
259#95—21no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266#95C4×D6111yescharacteristic
267#95C4×D6111yescharacteristic
268C2×Q8—1222no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×Q8—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C22×C4D4×D6111yescharacteristic
283M16—22no—
284M16—41no—
285M16—1222no—
286M16—2441no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—1222no—
290C2×C8—2441no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C42—1221no—
308C42—1221no—
309C42—1221no—
310C42—1221no—
311C42C2×D24411yescharacteristic
312C42#1175822211yescharacteristic
313C42D4×D6111yescharacteristic
314C42#1175822611yescharacteristic
315C23C22⋊C4×D6111yescharacteristic
316Q8—2442no—
317Q8—2442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—612no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4#1451973911yescharacteristic
344C2×C4C4×D24411yescharacteristic
345C2×C4#1451974711yescharacteristic
346C2×C4#1451975011yescharacteristic
347C2×C4#1451975211yescharacteristic
348C2×C4#1451976211yescharacteristic
349C8—42no—
350C8—42no—
351C8—2442no—
352C8—2442no—
353C22—21no—
354C22—21no—
355C22#1683964011yescharacteristic
356C22#104×D6111yescharacteristic
357C22#1683977711yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—1222no—
367C4—4881no—
368C4—4881no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2#2144612011yescharacteristic
375C2#2144635511yescharacteristic
376C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1288C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1288D61
hypocenterC61#9190
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
219. C61#9190semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214516982
C4×#145196952
#214444222
#214444202
#214436832
C61×#12882
#919061