Finite Group Databasebeta

← #29594999

Subgroups — #29594999

Order 15616.

794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#16839745C212yesmaximal
2#21448410C211yesmaximal, characteristic
3#21443946C211yesmaximal, characteristic, complemented
4#21443945C212yesmaximal, complemented
5C61×#1394C211yesmaximal, characteristic, complemented
6C22×#11758226C2211yescharacteristic
7C2×M16×D61—22no—
8C2×#14519734C411yescharacteristic
9C2×C4⋊C4×D61C411yescharacteristic
10#16839745—24no—
11#16839745C418yescomplemented
12C2×#14519696C2212yes—
13C2×#14519693—22no—
14#16839669C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839663C411yescharacteristic
17#16839640—22no—
18#16839621—22no—
19C2×#101×C61C2212yes—
20C61×#391C2211yescharacteristic
21C2×#11758226—42no—
22C2×#11758226—42no—
23C2×#11758226C2×C414yes—
24C2×#11758226D412yes—
25C2×#11758226Q812yes—
26C22×D244C2×C411yescharacteristic
27C22×D244D412yes—
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D412yes—
31C2×#11758194—22no—
32C2×#11758189—42no—
33M16×D61—28no—
34M16×D61—44no—
35C2×C8×D61—42no—
36#14519734—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C4⋊C4×D61—42no—
41C2×#11758198—21no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×C4×Dic61C2×C411yescharacteristic
45#14519696—22no—
46#14519696C2×C414yescomplemented
47#14519693—28no—
48#14519684—22no—
49C22×Q8×C61C2311yescharacteristic
50C2×M16×C61—22no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#101×C61—22no—
54#101×C61C2×C414yescomplemented
55#95×C61—22no—
56C23×D61C22⋊C411yescharacteristic
57C23×D61C22⋊C412yes—
58C2×Q8×C61—41no—
59C2×Q8×C61—41no—
60C2×Q8×C61C22×C412yes—
61C2×Q8×C61C2×D411yescharacteristic
62C2×Q8×C61C2×Q811yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D412yes—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70#11758226—44no—
71#11758226—44no—
72#11758226—44no—
73#11758226—44no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—42no—
77C2×D244—42no—
78C2×D244C4212yes—
79C2×D244C22⋊C414yes—
80C2×D244C4⋊C412yes—
81C2×D244C4⋊C414yes—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—24no—
86C2×C4×D61—22no—
87C2×C4×D61—42no—
88C2×C4×D61—82no—
89C2×C4×D61C4212yes—
90C2×C4×D61C22⋊C414yes—
91C2×C4×D61C4⋊C412yes—
92C2×C4×D61C4⋊C414yes—
93M16×C61—24no—
94M16×C61—42no—
95C2×C8×C61—42no—
96C4⋊C4×C61—41no—
97C42×C61—41no—
98#11758198—42no—
99#11758198—82no—
100#11758198—82no—
101C4⋊Dic61—41no—
102#11758196—42no—
103#11758196—42no—
104C4×Dic61—41no—
105#11758194—24no—
106#11758194—42no—
107C2×#92418—42no—
108#11758189—48no—
109C8×D61—48no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61#9512yes—
120C22×D61#9514yes—
121Q8×C61—42no—
122Q8×C61—41no—
123Q8×C61—41no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C4211yescharacteristic
134C2×C4×C61C2×C22⋊C412yes—
135C2×C4×C61C2×C4⋊C411yescharacteristic
136C2×C4×C61C2×C4⋊C412yes—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#9512yes—
143C2×Dic61#9912yes—
144C2×Dic61#9912yes—
145D244—42no—
146D244—44no—
147D244—42no—
148D244—44no—
149C4×D61—24no—
150C4×D61—24no—
151C4×D61—24no—
152C4×D61—24no—
153C4×D61—24no—
154C4×D61—24no—
155C4×D61—84no—
156C8×C61—44no—
157#92418—44no—
158#12587—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61C2×#9511yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C2×D61—22no—
165C2×D61—24no—
166C2×D61—42no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61—41no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—44no—
173C2×D61—82no—
174C4×C61—22no—
175C4×C61—21no—
176C4×C61—22no—
177C4×C61—21no—
178C4×C61—81no—
179C4×C61—81no—
180Dic61—81no—
181Dic61—81no—
182Dic61#34214yes—
183C2×#413—612no—
184#2311—611no—
185#1394—612no—
186#1394—611no—
187#1394D6111yescharacteristic, complemented
188C2×C61—21no—
189C2×C61—21no—
190C2×C61C2×#34211yescharacteristic
191C2×C61#213411yescharacteristic
192C2×C61#213511yescharacteristic
193D61—42no—
194D61—44no—
195C22×#41—611no—
196C22×M16—1222no—
197C2×#117—611no—
198C22×C4⋊C4—611no—
199#413—618no—
200#413—1224no—
201C2×#101—612no—
202C2×#101C2×D6112yes—
203C2×#100—1222no—
204#391—611no—
205#391C2×D6111yescharacteristic
206#390—611no—
207#390—611no—
208#386—1222no—
209#380—1222no—
210C61#1258711yescharacteristic, complemented, Sylow
211C2×#41—614no—
212C2×#41—612no—
213C2×#41—612no—
214C2×#41—2442no—
215C2×#41—2442no—
216C22×Q8C22×D6111yescharacteristic
217C22×D4—611no—
218C22×D4—612no—
219C23×C4—611no—
220C23×C4—612no—
221C23×C4—1221no—
222C2×M16—22no—
223C2×M16—1228no—
224C2×M16—1222no—
225C2×M16—2442no—
226C2×M16—2444no—
227C22×C8—2442no—
228#117—2442no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—2442no—
233C2×C4⋊C4C4×D6111yescharacteristic
234C2×C22⋊C4—1222no—
235C2×C22⋊C4—1222no—
236C2×C22⋊C4—1221no—
237C2×C42—611no—
238C2×C42C4×D6111yescharacteristic
239#101—22no—
240#101—614no—
241#101—1222no—
242#101C4×D6114yescomplemented
243#100—1228no—
244#95—22no—
245#95—1222no—
246C24—612no—
247C24—611no—
248#41—2444no—
249#41—2444no—
250#41—2444no—
251#41—2444no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8C2×C4×D6112yes—
255C2×Q8D4×D6111yescharacteristic
256C2×Q8Q8×D6111yescharacteristic
257C2×D4—612no—
258C2×D4—614no—
259C2×D4—612no—
260C2×D4—614no—
261C2×D4—2441no—
262C2×D4—2442no—
263C2×D4—2441no—
264C2×D4—2442no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—612no—
269C22×C4—614no—
270C22×C4—612no—
271C22×C4—614no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1224no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—4882no—
280C22×C4—2442no—
281C22×C4C2×C4×D6111yescharacteristic
282C22×C4D4×D6112yes—
283M16—24no—
284M16—42no—
285M16—1224no—
286M16—2448no—
287M16—2442no—
288C2×C8—42no—
289C2×C8—2448no—
290C2×C8—2442no—
291C4⋊C4—41no—
292C4⋊C4—2441no—
293C4⋊C4—2442no—
294C4⋊C4—2442no—
295C22⋊C4—4882no—
296C22⋊C4—4882no—
297C22⋊C4—2442no—
298C42—41no—
299C42—2441no—
300C23—612no—
301C23—614no—
302C23—1222no—
303C23—1221no—
304C23—1221no—
305C23—1222no—
306C23—2442no—
307C23—2442no—
308C23—2441no—
309C23—2441no—
310C23C22⋊C4×D6111yescharacteristic
311Q8—42no—
312Q8—41no—
313Q8—41no—
314D4—2444no—
315D4—2442no—
316D4—2442no—
317D4—2444no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—1224no—
331C2×C4—1224no—
332C2×C4—1224no—
333C2×C4—1224no—
334C2×C4—1224no—
335C2×C4—1224no—
336C2×C4—4884no—
337C2×C4—2441no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4C42×D6111yescharacteristic
343C2×C4C22⋊C4×D6112yes—
344C2×C4C4⋊C4×D6111yescharacteristic
345C2×C4C4⋊C4×D6112yes—
346C8—44no—
347C8—2444no—
348C22—21no—
349C22—21no—
350C22—1224no—
351C22—1222no—
352C22—4882no—
353C22—2444no—
354C22—2442no—
355C22—2442no—
356C22—2441no—
357C22—2442no—
358C22—2442no—
359C22—2441no—
360C22#95×D6111yescharacteristic
361C22#99×D6111yescharacteristic
362C22#99×D6111yescharacteristic
363C4—22no—
364C4—21no—
365C4—21no—
366C4—22no—
367C4—81no—
368C4—81no—
369C4—614no—
370C4—4881no—
371C4—4881no—
372C2—21no—
373C2—21no—
374C2—2444no—
375C2—2442no—
376C2#342×D6111yescharacteristic
377C2#2144750911yescharacteristic
378C2#2144751211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC22×#11758226C22
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#12587
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
3. #21443946C2semidirect
4. #21443945C2semidirect
5. C61×#1394C2semidirect
11. #16839745C4semidirect
46. #14519696C2×C4semidirect
54. #101×C61C2×C4semidirect
187. #1394D61semidirect
210. C61#12587semidirect
242. #101C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397452
#214484102
#214439462
#214439452
C61×#13942
#1258761