Finite Group Databasebeta

← #30603808

Subgroups — #30603808

Order 15616.

528 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462047C211yesmaximal, characteristic, complemented
2D61⋊(C22⋊C16)C211yesmaximal, characteristic, complemented
3#21460742C212yesmaximal, complemented
4#21460741C212yesmaximal, complemented
5#408×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×D61⋊C16—21no—
8#16840657—21no—
9#16840657—21no—
10C22⋊#11758187C2212yescomplemented
11C22⋊#11758187C2212yescomplemented
12C2×#41×D61C411yescharacteristic
13C2×M16×D61C411yescharacteristic
14C22×C8×D61C2211yescharacteristic
15#16839730C2211yescharacteristic
16#16839729C2211yescharacteristic
17#16839728C411yescharacteristic
18#16839727—21no—
19#16839727—21no—
20C22⋊C8×D61—21no—
21C22⋊C8×D61—21no—
22C61×#408C411yescharacteristic
23#14519852—42no—
24D61⋊C16—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×#11758226C811yescharacteristic
28C2×#11758222—21no—
29C2×#11758222C2×C411yescharacteristic
30C2×#11758224—21no—
31C2×#11758224C811yescharacteristic
32#41×D61—42no—
33#41×D61—42no—
34C2×Q8×D61C811yescharacteristic
35C2×D4×D61—21no—
36C2×D4×D61C811yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61C2×C411yescharacteristic
39C2×#11758194C2×C411yescharacteristic
40C2×#11758189—21no—
41M16×D61—42no—
42C22×#92418C2311yescharacteristic
43C2×C8×D61—21no—
44C2×C8×D61—42no—
45C2×C8×D61D411yescharacteristic
46C2×C8×D61D411yescharacteristic
47C2×C8×D61D411yescharacteristic
48C2×C8×D61D411yescharacteristic
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519689—21no—
52#14519689—21no—
53#14519689—21no—
54#14519689—21no—
55C2×#41×C61C2×C411yescharacteristic
56C2×M16×C61C2×C411yescharacteristic
57C22×C8×C61C2×C411yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60C23×D61—21no—
61C23×D61M1611yescharacteristic
62#41×C61—41no—
63#41×C61—41no—
64C2×Q8×C61C2×C811yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61C2×C811yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C22×Dic61—21no—
73C22×Dic61M1611yescharacteristic
74#11758226—42no—
75Q8×D61—42no—
76#11758224—42no—
77#11758224—44no—
78D4×D61—42no—
79D4×D61—44no—
80#11758222—42no—
81#11758222—42no—
82#11758222—41no—
83#11758222—41no—
84C2×D244—21no—
85C2×D244C2×C811yescharacteristic
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61C2×C811yescharacteristic
96C2×C4×D61C2×C811yescharacteristic
97C2×Dic122—21no—
98C2×Dic122C2×C811yescharacteristic
99M16×C61—41no—
100C2×C8×C61—21no—
101C2×C8×C61—41no—
102C2×C8×C61C22⋊C411yescharacteristic
103C2×C8×C61C22⋊C411yescharacteristic
104#11758194—41no—
105C2×#92418—21no—
106C2×#92418—41no—
107C2×#92418C2×D411yescharacteristic
108C2×#92418C2×D411yescharacteristic
109#11758189—42no—
110C8×D61—22no—
111C8×D61—22no—
112C8×D61—41no—
113C8×D61—41no—
114C8×D61—42no—
115#11758187—42no—
116#11758187—42no—
117C23×C61—21no—
118C23×C61C2×M1611yescharacteristic
119C22×D61—22no—
120C22×D61—22no—
121C22×D61—21no—
122C22×D61—41no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61C22⋊C811yescharacteristic
127C22×D61C22⋊C811yescharacteristic
128Q8×C61—41no—
129D4×C61—41no—
130D4×C61—42no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C22×C811yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—22no—
142C2×Dic61—21no—
143C2×Dic61—42no—
144C2×Dic61C22⋊C811yescharacteristic
145C2×Dic61C22⋊C811yescharacteristic
146D244—41no—
147D244—42no—
148C4×D61—22no—
149C4×D61—21no—
150C4×D61—21no—
151C4×D61—22no—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61#9912yes—
157C4×D61#10012yes—
158Dic122—42no—
159Dic122—41no—
160C8×C61—21no—
161C8×C61—21no—
162C8×C61—41no—
163#92418—21no—
164#92418—21no—
165#92418—41no—
166#11422—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C2×C22⋊C811yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—44no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—84no—
183C2×D61#32312yes—
184C2×D61#35012yes—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61C2×#9911yescharacteristic
188C4×C61C2×#10011yescharacteristic
189Dic61—21no—
190Dic61—41no—
191Dic61#32312yes—
192C2×#408—611no—
193#2112—611no—
194C2×C22⋊C16—611no—
195#1315—612no—
196#1315—612no—
197C2×C61—41no—
198C2×C61—81no—
199C2×C61C2×#32311yescharacteristic
200C2×C61C2×#35011yescharacteristic
201C2×C61#211711yescharacteristic
202D61—22no—
203D61—22no—
204D61—81no—
205C22×#41—611no—
206C22×M16—611no—
207C23×C8—611no—
208C2×M32—1221no—
209C22×C16—1221no—
210#408—611no—
211#408—611no—
212#408—611no—
213#408—1221no—
214#408—1221no—
215#408#692311yescharacteristic
216C2×C22⋊C8—1221no—
217C2×C22⋊C8—1221no—
218C22⋊C16—612no—
219C22⋊C16—612no—
220C22⋊C16—1221no—
221C22⋊C16—1221no—
222C61#1142211yescharacteristic, complemented, Sylow
223C2×#41—611no—
224C2×#41—611no—
225C2×#41—611no—
226C2×#41—1221no—
227C2×#41—1221no—
228C2×#41—2442no—
229C2×#41—2442no—
230C2×#41C2×#692311yescharacteristic
231C22×Q8—611no—
232C22×D4—611no—
233C22×D4—1221no—
234C23×C4—611no—
235C23×C4—1221no—
236C2×M16—611no—
237C2×M16—1221no—
238C2×M16—2442no—
239C2×M16C2×#692311yescharacteristic
240C22×C8—611no—
241C22×C8—611no—
242C22×C8—611no—
243C22×C8—611no—
244C22×C8—611no—
245C22×C8—1221no—
246C22×C8—2442no—
247C22×C8C2×#692311yescharacteristic
248M32—2442no—
249C2×C16—1222no—
250C2×C16—1222no—
251C2×C16—2442no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256C22⋊C8—1221no—
257C22⋊C8—1221no—
258C22⋊C8—1221no—
259C22⋊C8—1221no—
260C24—611no—
261C24—1221no—
262#41—41no—
263#41—41no—
264#41—2441no—
265#41—2441no—
266#41—2442no—
267#41—2442no—
268#41—2444no—
269#41—2442no—
270#41—2442no—
271C2×Q8—611no—
272C2×Q8—1221no—
273C2×Q8—2442no—
274C2×Q8D61⋊C811yescharacteristic
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—2442no—
282C2×D4—2444no—
283C2×D4D61⋊C811yescharacteristic
284C22×C4—21no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—1222no—
291C22×C4—1222no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4C22×#692311yescharacteristic
299M16—41no—
300M16—2442no—
301M16—2441no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—611no—
305C2×C8—611no—
306C2×C8—1222no—
307C2×C8—1222no—
308C2×C8—1221no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2442no—
312C2×C8—2441no—
313C2×C8C22⋊#692311yescharacteristic
314C2×C8C22⋊#692311yescharacteristic
315C16—2442no—
316C16—2442no—
317C23—21no—
318C23—611no—
319C23—611no—
320C23—1222no—
321C23—1222no—
322C23—1221no—
323C23—2441no—
324C23—2442no—
325C23—2442no—
326C23—2442no—
327C23D61⋊M1611yescharacteristic
328Q8—41no—
329Q8—2441no—
330Q8—2442no—
331D4—41no—
332D4—42no—
333D4—2441no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—612no—
346C2×C4—611no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4C2×C22⋊#692311yescharacteristic
359C2×C4C2×D61⋊C811yescharacteristic
360C8—21no—
361C8—21no—
362C8—41no—
363C8—1221no—
364C8—1221no—
365C8—2441no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—612no—
373C22—612no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—4884no—
379C22—2444no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22D61⋊(C22⋊C8)11yescharacteristic
384C4—21no—
385C4—41no—
386C4—612no—
387C4—1221no—
388C4—2441no—
389C4D61⋊#9911yescharacteristic
390C4D61⋊#10011yescharacteristic
391C2—41no—
392C2—81no—
393C2—1222no—
394C2—1222no—
395C2—4881no—
396C2D61⋊#32311yescharacteristic
397C2D61⋊#35011yescharacteristic
398C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#41×D61C4
cosocleC22×#92418C23
hypercenter#408#6923
hypocenterC61#11422
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #21462047C2semidirect
2. D61⋊(C22⋊C16)C2semidirect
3. #21460742C2semidirect
4. #21460741C2semidirect
10. C22⋊#11758187C22semidirect
11. C22⋊#11758187C22semidirect
222. C61#11422semidirect

Maximal subgroups

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

subgroupindex
#214620472
D61⋊(C22⋊C16)2
#214607422
#214607412
#408×D612
#1142261