Finite Group Databasebeta

← #30601162

Subgroups — #30601162

Order 15616.

554 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462296C211yesmaximal, characteristic, complemented
2#21461719C211yesmaximal, characteristic, complemented
3#21461224C212yesmaximal
4#21460667C212yesmaximal, complemented
5#21450310C211yesmaximal, characteristic
6#16840734C2212yes—
7#16840711—24no—
8#16840705C2212yes—
9#16840704—21no—
10C4×C22⋊#6923—21no—
11#16840642—21no—
12#16840642—21no—
13#16840613—24no—
14C2×#14519748C2211yescharacteristic
15C2×C4⋊C4×D61C2211yescharacteristic
16#16839690—21no—
17#16839690—21no—
18#16839665C411yescharacteristic, complemented
19#16839638—21no—
20#16839638—21no—
21#16839628C411yescharacteristic, complemented
22#16839627C411yescharacteristic, complemented
23C4×#11758198C2211yescharacteristic
24C61×#390C411yescharacteristic, complemented
25C2×#11758217—22no—
26C2×C4⋊#6923—22no—
27C2×C22⋊#6923—22no—
28C2×C4×#6923—22no—
29#14519834—22no—
30#14519834—22no—
31(C2×#6923)⋊C4—22no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4D414yes—
35C22×C22⋊D61—21no—
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61C2311yescharacteristic
39#14519748—22no—
40#14519748—22no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×#11758196D411yescharacteristic
45C4⋊C4×D61—22no—
46C4⋊C4×D61—22no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×D4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C411yescharacteristic
62C24×C61—21no—
63C23×D61C2×D411yescharacteristic
64C22×#6923—24no—
65C2×D4×C61—22no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89C2×C4×D61C2×D412yes—
90C2×C4×D61#4112yes—
91C22⋊#6923—42no—
92C22⋊#6923—42no—
93#11758217—42no—
94#11758217—42no—
95C2×#92420—42no—
96C4⋊#6923—82no—
97C4×#6923—82no—
98C4⋊C4×C61—22no—
99C22⋊C4×C61—81no—
100C22⋊C4×C61—81no—
101C42×C61—41no—
102C22⋊Dic61—42no—
103C22⋊Dic61—81no—
104C22⋊Dic61—81no—
105#11758198—42no—
106C4⋊Dic61—22no—
107C4⋊Dic61—22no—
108#11758196—22no—
109#11758196—22no—
110C4×Dic61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—22no—
122C22×D61—41no—
123C22×D61#12011yescharacteristic
124C22×D61#12311yescharacteristic
125C2×#6923—44no—
126C2×#6923—44no—
127C2×#6923—44no—
128D4×C61—82no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61C4×D412yes—
139C22⋊D61—82no—
140C22⋊D61—82no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61#12112yes—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—81no—
159C4×D61—81no—
160#92420—82no—
161#9465—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61#38611yescharacteristic
172C22×C61#41011yescharacteristic
173C22×C61#41011yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—42no—
180C2×D61—42no—
181C2×D61#45412yes—
182#6923—84no—
183C4×C61—22no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—41no—
189Dic61—41no—
190Dic61—81no—
191Dic61—81no—
192#2504—611no—
193#2313—611no—
194#1821—611no—
195#1510—612no—
196#1284—612no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—161no—
200C2×C61#188811yescharacteristic
201C2×C61#189911yescharacteristic
202C2×C61#191111yescharacteristic
203D61—22no—
204D61—41no—
205C2×#121—611no—
206C22×C4⋊C4—611no—
207#407—612no—
208#397—1221no—
209#397—1221no—
210#390—611no—
211#390#692311yescharacteristic, complemented
212#387—1224no—
213#386—1221no—
214#386—1221no—
215#382—611no—
216#382—611no—
217#381—612no—
218#380—1221no—
219C4×C22⋊C4—611no—
220C4×C22⋊C4—1221no—
221#343—1221no—
222#343—1221no—
223#327—1224no—
224C61#946511yescharacteristic, complemented, Sylow
225C22×D4—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C2×M16—1222no—
231#121—1222no—
232#121—1222no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4C2×#692311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1222no—
248C2×C42—611no—
249C2×C42—1222no—
250C2×C42C2×#692311yescharacteristic
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253#95—614no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1222no—
258#95—1222no—
259#95—1222no—
260#95—1221no—
261#95—1221no—
262C24—21no—
263C24—611no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2442no—
270C2×D4—2442no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1224no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—4881no—
285C22×C4—4881no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4C22⋊#692311yescharacteristic
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22×#692311yescharacteristic
291M16—2442no—
292M16—2442no—
293C2×C8—2442no—
294C4⋊C4—22no—
295C4⋊C4—1222no—
296C4⋊C4—1222no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—4882no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—4881no—
303C22⋊C4—4881no—
304C22⋊C4—2442no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C42—41no—
309C42—4882no—
310C42—2441no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—611no—
319C23—611no—
320C23—1222no—
321C23—1221no—
322C23—1221no—
323C23—2441no—
324C23C2×C22⋊#692311yescharacteristic
325D4—82no—
326D4—4882no—
327D4—4882no—
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—612no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—4881no—
343C2×C4—4881no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2444no—
353C2×C4—2444no—
354C2×C4—2444no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4D4×#692312yes—
360C8—4882no—
361C22—21no—
362C22—21no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—612no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—2442no—
377C22—2442no—
378C22#1684071011yescharacteristic
379C22#1684074111yescharacteristic
380C22#1684074211yescharacteristic
381C4—22no—
382C4—41no—
383C4—41no—
384C4—81no—
385C4—1222no—
386C4—4881no—
387C4—4884no—
388C4—4881no—
389C4—2441no—
390C4—2441no—
391C2—21no—
392C2—21no—
393C2—161no—
394C2—1222no—
395C2—2441no—
396C2#2146182711yescharacteristic
397C2#2146184211yescharacteristic
398C2#2146186511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61#386
prime radicalC2×#14519748C22
cosocleC22×C4×D61C23
hypercenter#390#6923
hypocenterC61#9465
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21462296C2semidirect
2. #21461719C2semidirect
4. #21460667C2semidirect
18. #16839665C4semidirect
21. #16839628C4semidirect
22. #16839627C4semidirect
24. C61×#390C4semidirect
211. #390#6923semidirect
224. C61#9465semidirect

Maximal subgroups

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

subgroupindex
#214622962
#214617192
#214612242
#214606672
#214503102
#946561