Finite Group Databasebeta

← #30599321

Subgroups — #30599321

Order 15616.

656 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461655C211yesmaximal, characteristic
2#21461648C211yesmaximal, characteristic
3#21460667C212yesmaximal, complemented
4#21460667C212yesmaximal, complemented
5#21448305C211yesmaximal, characteristic
6C2×#14519838—21no—
7C2×#14519837—21no—
8C2×#14519836—21no—
9C2×#14519835—21no—
10#16840734C2212yes—
11#16840705C2212yes—
12C22×#11758222C2211yescharacteristic
13C2×#14519734C411yescharacteristic, complemented
14C2×C42×D61C411yescharacteristic, complemented
15#16839666—21no—
16#16839662—21no—
17#16839640—21no—
18#16839638—21no—
19C4×#11758198C2211yescharacteristic
20C4×#11758198C2211yescharacteristic
21C4×C22⋊Dic61C411yescharacteristic, complemented
22C4×C22⋊C4×C61C411yescharacteristic, complemented
23C2×#11758217—22no—
24C2×C22⋊#6923—22no—
25#14519838—42no—
26#14519837—42no—
27#14519836—42no—
28#14519835—42no—
29#14519834—24no—
30(C2×#6923)⋊C4—24no—
31C2×#11758222—24no—
32C2×#11758222—42no—
33C2×#11758222—42no—
34C22×Dic122D411yescharacteristic
35C22×D244D411yescharacteristic
36C22×C22⋊D61D411yescharacteristic
37C22×C22⋊D61D411yescharacteristic
38C22×C4×D61—21no—
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61C2311yescharacteristic
41#14519734—42no—
42C2×#11758196—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C42×D61—42no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C23×C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61C2×C411yescharacteristic
58#95×C61—21no—
59C24×C61C22⋊C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C22×C4×C61—21no—
64C22×C4×C61—22no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80#11758222—416no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—41no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61#4114yes—
93C2×Dic122—22no—
94C2×Dic122—22no—
95C2×Dic122—41no—
96C22⋊#6923—42no—
97C22⋊#6923—42no—
98#11758217—42no—
99#11758217—42no—
100C2×#92420—42no—
101C22⋊C4×C61—42no—
102C42×C61—41no—
103C42×C61—41no—
104C22⋊Dic61—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—42no—
108#11758196—42no—
109C4×Dic61—42no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61#9912yes—
127C22×D61#12312yes—
128C2×#6923—82no—
129C2×#6923—82no—
130C2×#6923—82no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—44no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61#11712yes—
144C22⋊D61—44no—
145C22⋊D61—44no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—22no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61#9912yes—
157C2×Dic61#12312yes—
158D244—44no—
159C4×D61—28no—
160C4×D61—44no—
161C4×D61—48no—
162Dic122—44no—
163#92420—82no—
164#8738—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#38111yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—42no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—42no—
183C2×D61—81no—
184C2×D61—81no—
185#6923—162no—
186C4×C61—22no—
187C4×C61—42no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—22no—
191Dic61—22no—
192Dic61—42no—
193Dic61—81no—
194#2297—611no—
195#1785—611no—
196#1782—611no—
197#1284—612no—
198#1284—612no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—81no—
202C2×C61#181911yescharacteristic
203C2×C61#182711yescharacteristic
204C2×C61#182711yescharacteristic
205D61—42no—
206D61—42no—
207C22×#41—611no—
208C2×#117—611no—
209C22×C42—611no—
210C2×#101—1221no—
211C2×#100—1221no—
212C2×#99—1221no—
213C2×#99—1221no—
214#407—612no—
215#391—1221no—
216#390—1221no—
217#386—1221no—
218#386—1221no—
219#381—612no—
220C4×C22⋊C4—611no—
221C4×C22⋊C4—611no—
222C4×C22⋊C4—611no—
223C4×C22⋊C4#692311yescharacteristic, complemented
224C61#873811yescharacteristic, complemented, Sylow
225C2×#41—1224no—
226C2×#41—2442no—
227C2×#41—2442no—
228C22×Q8—611no—
229C22×D4—611no—
230C22×D4—611no—
231C22×D4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—1221no—
235C23×C4C2×#692311yescharacteristic
236C2×M16—1222no—
237#117—2442no—
238C2×C4⋊C4—1221no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1222no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1221no—
248C2×C42—2442no—
249C2×C42C2×#692311yescharacteristic
250C2×C42C2×#692311yescharacteristic
251#101—2442no—
252#100—2442no—
253#99—2442no—
254#99—2442no—
255C22⋊C8—1224no—
256#95—21no—
257#95—1221no—
258#95—1221no—
259#95—1224no—
260#95—1221no—
261C24—611no—
262C24—611no—
263C24C22⋊#692311yescharacteristic
264#41—24416no—
265C2×Q8—1222no—
266C2×Q8—1222no—
267C2×Q8—2441no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4—1222no—
274C2×D4—2441no—
275C2×D4—2441no—
276C2×D4—2441no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—614no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298M16—2442no—
299M16—2442no—
300C2×C8—2442no—
301C4⋊C4—2442no—
302C22⋊C4—42no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C42—41no—
310C42—41no—
311C42—2441no—
312C42—2441no—
313C42—2442no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—612no—
320C23—612no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23—1221no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23—2441no—
329C23C2×C22⋊#692311yescharacteristic
330Q8—2444no—
331D4—2444no—
332D4—2444no—
333D4—2444no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—1228no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1222no—
354C2×C4—4882no—
355C2×C4—4882no—
356C2×C4—4882no—
357C2×C4—2444no—
358C2×C4—2448no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4#1451985612yes—
365C8—4882no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—1222no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—4881no—
378C22—4881no—
379C22—2442no—
380C22—2442no—
381C22—2441no—
382C22—2441no—
383C22#1684070511yescharacteristic
384C22D61⋊#9911yescharacteristic
385C22D61⋊#9911yescharacteristic
386C4—22no—
387C4—42no—
388C4—41no—
389C4—81no—
390C4—1222no—
391C4—1222no—
392C4—9762no—
393C4—4881no—
394C4—2442no—
395C2—21no—
396C2—21no—
397C2—81no—
398C2—2442no—
399C2—2442no—
400C2#2146171511yescharacteristic
401C2#2146172811yescharacteristic
402C2#2146172911yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC22×#11758222C22
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8738
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460667C2semidirect
4. #21460667C2semidirect
13. C2×#14519734C4semidirect
14. C2×C42×D61C4semidirect
21. C4×C22⋊Dic61C4semidirect
22. C4×C22⋊C4×C61C4semidirect
223. C4×C22⋊C4#6923semidirect
224. C61#8738semidirect

Maximal subgroups

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

subgroupindex
#214616552
#214616482
#214606672
#214483052
#873861