Finite Group Databasebeta

← #30605418

Subgroups — #30605418

Order 15616.

510 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461684C211yesmaximal, characteristic, complemented
2#21461057C211yesmaximal, characteristic, complemented
3#21460804C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21450774C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8C2×C22⋊#92420—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519748—21no—
13C2×#14519748C411yescharacteristic
14C2×#14519737C2211yescharacteristic
15#16839694C2211yescharacteristic
16#16839687C411yescharacteristic
17#16839676C2211yescharacteristic
18#16839655—21no—
19#16839642—21no—
20#16839638—21no—
21#95×D61C411yescharacteristic
22C61×#392C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28C22⋊#92420—22no—
29C22⋊#92420—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35#14519748—42no—
36#14519748—42no—
37#14519748—41no—
38#14519748—41no—
39#14519737—41no—
40#14519737—41no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C22×D4×C61—21no—
55C22×D4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61C22⋊C411yescharacteristic
62C2×D4×C61—42no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C2×D4×C61—81no—
66C2×D4×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61D812yes—
76C2×C22⋊D61SD1612yes—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—81no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—81no—
90C2×C4×D61—81no—
91#11758217—42no—
92#11758217—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—82no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61—81no—
104#11758198—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108#11758196—41no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C23×C61—21no—
112C23×C61—21no—
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—41no—
122C23×C61#10212yes—
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#10212yes—
129D4×C61—84no—
130D4×C61—82no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—84no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61#9911yescharacteristic
155C2×Dic61#9911yescharacteristic
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61C2×SD1611yescharacteristic
158C4×D61—81no—
159C4×D61—81no—
160C4×D61—84no—
161#92420—82no—
162#92420—82no—
163#11884—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—22no—
167C22×C61—42no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61C2×#9911yescharacteristic
179C22×C61C2×#10211yescharacteristic
180C22×C61#42111yescharacteristic
181C2×D61—22no—
182C2×D61—42no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—42no—
186C4×C61—42no—
187C4×C61—41no—
188C4×C61—41no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194Dic61—81no—
195Dic61—81no—
196#2543—611no—
197#1800—611no—
198#1459—611no—
199#1346—612no—
200#1345—612no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—42no—
204C2×C61—161no—
205C2×C61#151911yescharacteristic
206C2×C61#212111yescharacteristic
207C2×C61#213211yescharacteristic
208D61—42no—
209C2×#121—611no—
210C2×#121—1221no—
211C2×C4×D4—611no—
212#423—1221no—
213C2×#100—1221no—
214C2×C22⋊C8—1221no—
215#398—611no—
216#397—611no—
217#394—611no—
218#392#692311yescharacteristic
219#388—1221no—
220#386—1221no—
221#386—1221no—
222C2×#95—611no—
223#343—612no—
224#324—612no—
225#323—1221no—
226C61#1188411yescharacteristic, complemented, Sylow
227C22×D4—21no—
228C22×D4—611no—
229C22×D4—1221no—
230C22×D4C2×#692311yescharacteristic
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1221no—
234C2×M16—1222no—
235C22×C8—2441no—
236#121—2442no—
237#121—2442no—
238#121—2441no—
239#121—2441no—
240C4×D4—2441no—
241C4×D4—2441no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4C2×#692311yescharacteristic
252C2×C42—611no—
253C4⋊C8—2441no—
254C4⋊C8—2441no—
255#100—2442no—
256C22⋊C8—1222no—
257C22⋊C8—2441no—
258#95—611no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95C2×#692311yescharacteristic
263C24—21no—
264C24—611no—
265C24C22⋊#692311yescharacteristic
266C2×D4—41no—
267C2×D4—42no—
268C2×D4—42no—
269C2×D4—81no—
270C2×D4—81no—
271C2×D4—612no—
272C2×D4—612no—
273C2×D4—2441no—
274C2×D4—2441no—
275C2×D4—2442no—
276C2×D4—2442no—
277C2×D4—2442no—
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—4881no—
289C22×C4—4881no—
290C22×C4—4881no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22×#692311yescharacteristic
295M16—2442no—
296M16—2442no—
297C2×C8—4882no—
298C2×C8—2442no—
299C2×C8—2442no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—4881no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2442no—
313C42—1221no—
314C42—1221no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—612no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23#1451983912yes—
332C23C2×C22⋊#692311yescharacteristic
333D4—84no—
334D4—82no—
335D4—4884no—
336D4—2442no—
337D4—2442no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—4881no—
353C2×C4—4881no—
354C2×C4—4884no—
355C2×C4—4881no—
356C2×C4—2441no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C8—4882no—
366C8—4882no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—42no—
371C22—41no—
372C22—41no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—1222no—
382C22—2442no—
383C22—2442no—
384C22—2441no—
385C22—2441no—
386C22D61⋊#9911yescharacteristic
387C22C2×#1451983911yescharacteristic
388C22#1684075911yescharacteristic
389C4—42no—
390C4—41no—
391C4—41no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—4881no—
397C4—4881no—
398C4—2441no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—161no—
403C2—2442no—
404C2#2146125411yescharacteristic
405C2#2146207511yescharacteristic
406C2#2146211111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61C2×#99
prime radical#21450774C2
cosocleC2×#11758196C23
hypercenter#392#6923
hypocenterC61#11884
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21461684C2semidirect
2. #21461057C2semidirect
3. #21460804C2semidirect
4. #21460801C2semidirect
226. C61#11884semidirect

Maximal subgroups

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

subgroupindex
#214616842
#214610572
#214608042
#214608012
#214507742
#1188461