Finite Group Databasebeta

← #29590215

Subgroups — #29590215

Order 15616.

536 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 115 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#21445558C211yesmaximal, characteristic, complemented
2#21444133C211yesmaximal, characteristic, complemented
3#21443825C212yesmaximal, complemented
4#21443822C212yesmaximal, complemented
5C61×#2392C211yesmaximal, characteristic
6C22×#11758194—21no—
7#16839815—21no—
8#16839531—21no—
9#16839531C2212yes—
10#16839488C2212yes—
11#16839486—21no—
12C2×C4×D4×C61—21no—
13C2×C4×D4×C61C411yescharacteristic
14C2×#117×C61C2211yescharacteristic
15C61×#398C2211yescharacteristic
16C61×#397C411yescharacteristic
17C61×#396—21no—
18C61×#394—21no—
19C61×#394C2211yescharacteristic
20C61×#392C411yescharacteristic
21C4×C4⋊C4×C61C411yescharacteristic
22C4×C22⋊C4×C61—21no—
23C2×#11758194—24no—
24C2×#11758194—22no—
25C2×#11758194—41no—
26C2×#11758194—42no—
27C22×#92418—41no—
28C4⋊#92418—41no—
29C22⋊#92418—22no—
30C4×#92418—41no—
31C22×D4×C61—21no—
32C22×D4×C61C2×C411yescharacteristic
33C23×C4×C61—21no—
34C23×C4×C61D411yescharacteristic
35C4×D4×C61—41no—
36C4×D4×C61—41no—
37C4×D4×C61—42no—
38C4×D4×C61—42no—
39#117×C61—41no—
40#117×C61—41no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61C2311yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61—21no—
54C2×C42×C61C2×C411yescharacteristic
55C2×C42×C61D411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59#95×C61C2×C411yescharacteristic
60C24×C61—21no—
61C24×C61C22⋊C411yescharacteristic
62C2×D4×C61—42no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61—41no—
75C22×C4×C61—42no—
76C22×C4×C61—42no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×C4×C61D812yes—
81C22×C4×C61SD1612yes—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—42no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61—21no—
100C42×C61—21no—
101C42×C61—21no—
102C42×C61—21no—
103C42×C61—42no—
104#11758194—24no—
105#11758194—44no—
106#11758194—42no—
107C2×#92418—42no—
108C2×#92418—44no—
109C2×#92418—42no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61#10212yes—
122C23×C61C2×C22⋊C411yescharacteristic
123D4×C61—42no—
124D4×C61—48no—
125D4×C61—42no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
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—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—82no—
150C2×C4×C61—82no—
151C2×C4×C61#9911yescharacteristic
152C2×C4×C61#9911yescharacteristic
153C2×C4×C61#10212yes—
154C2×C4×C61#10412yes—
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157#92418—44no—
158#92418—82no—
159#11697—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—42no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—42no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186C4×C61#32712yes—
187C4×C61#32712yes—
188#2392D6111yescharacteristic
189#1742—611no—
190#1458—611no—
191#1346—612no—
192#1345—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—42no—
196C2×C61—82no—
197C2×C61C2×#32711yescharacteristic
198C2×C61#212011yescharacteristic
199C2×C61#213211yescharacteristic
200C22×M16—1221no—
201C2×C4×D4—21no—
202C2×C4×D4Dic6111yescharacteristic
203C2×#117C2×D6111yescharacteristic
204#431—1221no—
205#398C2×D6111yescharacteristic
206#397Dic6111yescharacteristic
207#396—21no—
208#394—21no—
209#394C2×D6111yescharacteristic
210#392Dic6111yescharacteristic
211C4×C4⋊C4Dic6111yescharacteristic
212C4×C22⋊C4—21no—
213#343—612no—
214#343—1221no—
215#324—612no—
216#323—1221no—
217C61#1169711yescharacteristic, complemented, Sylow
218C22×D4—21no—
219C22×D4C2×Dic6111yescharacteristic
220C23×C4—21no—
221C23×C4C22⋊D6111yescharacteristic
222C2×M16—1224no—
223C2×M16—1222no—
224C2×M16—2441no—
225C2×M16—2442no—
226C22×C8—2441no—
227C4×D4—41no—
228C4×D4—41no—
229C4×D4—42no—
230C4×D4—42no—
231#117—41no—
232#117—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×Dic6111yescharacteristic
236C2×C4⋊C4C22⋊D6111yescharacteristic
237C2×C4⋊C4C22×D6111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4C2×Dic6111yescharacteristic
244C2×C22⋊C4C22⋊D6111yescharacteristic
245C2×C42—21no—
246C2×C42C2×Dic6111yescharacteristic
247C2×C42C22⋊D6111yescharacteristic
248C4⋊C8—2441no—
249C22⋊C8—1222no—
250C4×C8—2441no—
251#95—21no—
252#95—21no—
253#95C2×Dic6111yescharacteristic
254#95C2×Dic6111yescharacteristic
255C24—21no—
256C24C22⋊Dic6111yescharacteristic
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4#1175819912yes—
273C22×C4#1175820012yes—
274C22×C4C22⋊Dic6111yescharacteristic
275C22×C4C22⋊Dic6111yescharacteristic
276C22×C4C22⋊Dic6111yescharacteristic
277C22×C4C22×Dic6111yescharacteristic
278C22×C4C2×C22⋊D6111yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280M16—1224no—
281M16—2444no—
282M16—2442no—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2444no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—21no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—42no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23#1451969812yes—
317C23C2×C22⋊Dic6111yescharacteristic
318D4—42no—
319D4—48no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4#1451969211yescharacteristic
347C2×C4#1451969211yescharacteristic
348C2×C4#1451969812yes—
349C2×C4#1451970412yes—
350C2×C4C2×#1175819911yescharacteristic
351C2×C4C2×#1175820011yescharacteristic
352C8—4882no—
353C8—2444no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C2×#1451969211yescharacteristic
369C22C2×#1451969811yescharacteristic
370C22C2×#1451970411yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4#1683949612yes—
381C4#1683949612yes—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—82no—
386C2C2×#1683949611yescharacteristic
387C2#2144746011yescharacteristic
388C2#2144750411yescharacteristic
subgroupG/H
centerC2×C4#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2392C2
socleC22×C61C2×#99
prime radicalC61×#392C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2392D61
hypocenterC61#11697
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #21445558C2semidirect
2. #21444133C2semidirect
3. #21443825C2semidirect
4. #21443822C2semidirect
217. C61#11697semidirect

Maximal subgroups

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

subgroupindex
#214455582
#214441332
#214438252
#214438222
C61×#23922
#1169761