Finite Group Databasebeta

← #29577761

Subgroups — #29577761

Order 15616.

554 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 93 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#21450311C211yesmaximal, characteristic
2#21448420C211yesmaximal, characteristic, complemented
3#21445897C211yesmaximal, characteristic, complemented
4#21444349C211yesmaximal, characteristic
5#21444347C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10#16839726C2211yescharacteristic
11#16839689—22no—
12#16839664C412yescomplemented
13#16839647—22no—
14#16839645—22no—
15#16839639—21no—
16#16839639—21no—
17#16839628C412yescomplemented
18#16839625C2211yescharacteristic
19#16839620—21no—
20C22⋊C4×Dic61—21no—
21#16839530—22no—
22#16839497—22no—
23#16839495—22no—
24C61×#407C2211yescharacteristic
25C61×#381C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×#11758194—21no—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C412yes—
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198—22no—
47C2×#11758198—22no—
48C2×C4×Dic61—22no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—22no—
52#14519684—22no—
53#14519684—21no—
54#14519684—22no—
55#14519684—22no—
56#14519684D412yes—
57C23×C4×C61C2311yescharacteristic
58C2×M16×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C412yes—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61—21no—
66#95×C61D412yes—
67C24×C61C2×D411yescharacteristic
68C23×D61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—42no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C2×C22⋊D61—44no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—81no—
88C22×Dic61—81no—
89C22×Dic61C22⋊C412yes—
90C22×Dic61C22⋊C412yes—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244—42no—
94M16×C61—42no—
95C2×C8×C61—41no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—42no—
98C42×C61—42no—
99C22⋊Dic61—42no—
100#11758198—41no—
101#11758198—41no—
102#11758198—82no—
103#11758198—82no—
104C4⋊Dic61—22no—
105C4⋊Dic61—22no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758196—82no—
111C4×Dic61—82no—
112#11758194—42no—
113C2×#92418—41no—
114C23×C61—22no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61#12011yescharacteristic
119C23×C61#12311yescharacteristic
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—41no—
123C22×D61—42no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C22⋊D61—82no—
141C22⋊D61—82no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155D244—81no—
156D244—81no—
157C8×C61—81no—
158#92418—81no—
159#9465—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—44no—
168C22×C61#38611yescharacteristic
169C22×C61#41012yes—
170C22×C61#45412yes—
171C2×D61—84no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—82no—
180C4×C61—82no—
181Dic61—42no—
182Dic61—42no—
183Dic61—82no—
184Dic61—81no—
185#2504—611no—
186#2313—611no—
187#1821—611no—
188#1510—611no—
189#1510—611no—
190#1284—611no—
191#1284D6111yescharacteristic, complemented
192C2×C61—22no—
193C2×C61—22no—
194C2×C61—41no—
195C2×C61#188811yescharacteristic
196C2×C61#189911yescharacteristic
197C2×C61#191111yescharacteristic
198D61—161no—
199C2×#121—611no—
200C22×C4⋊C4—611no—
201#407—611no—
202#407C2×D6111yescharacteristic
203#397—1222no—
204#390—612no—
205#387—1222no—
206#387—1222no—
207#386—1221no—
208#386—1221no—
209#382—612no—
210#381—611no—
211#381C2×D6111yescharacteristic
212#380—1221no—
213C4×C22⋊C4—1221no—
214C4×C22⋊C4C2×D6111yescharacteristic
215#343—1222no—
216#327—1222no—
217#327—1222no—
218C61#946511yescharacteristic, complemented, Sylow
219C22×D4—611no—
220C22×D4—1221no—
221C23×C4—611no—
222C23×C4—611no—
223C23×C4C22×D6111yescharacteristic
224C2×M16—21no—
225C2×M16—1221no—
226#121—1221no—
227#121—1221no—
228#121—1221no—
229#121—1221no—
230C2×C4⋊C4—612no—
231C2×C4⋊C4—612no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1222no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—1222no—
245C2×C42C4×D6112yes—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—1221no—
249C22⋊C8—1221no—
250#95—21no—
251#95—21no—
252#95—612no—
253#95—1222no—
254#95—1222no—
255#95—1222no—
256#95—1222no—
257#95—1221no—
258#95D24412yes—
259C24—1221no—
260C24D4×D6111yescharacteristic
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—2442no—
264C2×D4—2444no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1222no—
278C22×C4—4881no—
279C22×C4—4881no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4C2×D24411yescharacteristic
282C22×C4#1175822211yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4#1175822611yescharacteristic
286M16—42no—
287M16—2442no—
288C2×C8—41no—
289C2×C8—2441no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—4882no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—4882no—
300C22⋊C4—4882no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—42no—
305C42—4882no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23—2442no—
310C23—2442no—
311C23—2442no—
312C23—2441no—
313C23C22⋊C4×D6111yescharacteristic
314C23#1451974711yescharacteristic
315C23#1451976211yescharacteristic
316D4—4881no—
317D4—4881no—
318D4—4882no—
319D4—4882no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4#1451973911yescharacteristic
346C2×C4C4×D24411yescharacteristic
347C2×C4#1451975011yescharacteristic
348C2×C4#1451975211yescharacteristic
349C8—81no—
350C8—4881no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—44no—
359C22—4884no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22#1683964011yescharacteristic
364C22#1683973412yes—
365C22#1683993612yes—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—82no—
371C4—82no—
372C4—4882no—
373C4—4881no—
374C4—2442no—
375C4—2442no—
376C2—22no—
377C2—22no—
378C2—41no—
379C2—9761no—
380C2#2144622111yescharacteristic
381C2#2144627611yescharacteristic
382C2#2144635011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#9465
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
2. #21448420C2semidirect
3. #21445897C2semidirect
6. #21443672C2semidirect
7. C61×#1284C2semidirect
12. #16839664C4semidirect
17. #16839628C4semidirect
191. #1284D61semidirect
218. C61#9465semidirect

Maximal subgroups

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

subgroupindex
#214503112
#214484202
#214458972
#214443492
#214443472
#214436722
C61×#12842
#946561