Finite Group Databasebeta

← #30595516

Subgroups — #30595516

Order 15616.

656 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461674C211yesmaximal, characteristic, complemented
2#21461546C211yesmaximal, characteristic, complemented
3#21460639C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21448308C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×#14519832—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×#11758226C411yescharacteristic
13C2×#14519735C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839669C2211yescharacteristic
16#16839664C411yescharacteristic
17#16839663C2211yescharacteristic
18#16839640—21no—
19#16839640—21no—
20#16839609—21no—
21#16839609—21no—
22C61×#391C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519834—24no—
27#14519834—42no—
28#14519832—42no—
29C2×#11758226—22no—
30C2×#11758226—22no—
31C2×#11758226—42no—
32C2×#11758226—42no—
33C22×D244—21no—
34C22×D244C2×C411yescharacteristic
35C22×C4×D61—21no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61D411yescharacteristic
38C22×C4×D61D411yescharacteristic
39#14519735—42no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50C42×D61—42no—
51#14519684—21no—
52#14519684—21no—
53C22×Q8×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C23×D61—21no—
59C23×D61C22⋊C411yescharacteristic
60C2×Q8×C61—21no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×Q8×C61M1612yes—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73#11758226—48no—
74#11758226—48no—
75C2×D244—24no—
76C2×D244—21no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—42no—
80C2×D244—42no—
81C2×D244M1612yes—
82C2×C4×D61—22no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—24no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—41no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61—42no—
95C2×C4×D61—42no—
96C2×#92420—24no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C4⋊C4×C61—41no—
103C42×C61—41no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—42no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—41no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—41no—
114C4×Dic61—42no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61#10012yes—
130Q8×C61—42no—
131Q8×C61—42no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61#10412yes—
146C2×C4×C61C2×M1611yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9912yes—
158C2×Dic61#13512yes—
159C2×Dic61AGL(1,ℤ/8)11yescharacteristic
160C2×Dic61#13711yescharacteristic
161D244—42no—
162D244—42no—
163D244—48no—
164C4×D61—24no—
165C4×D61—24no—
166C4×D61—44no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—48no—
170#92420—44no—
171#92420—82no—
172#7612—611nomaximal, Sylow
173C22×C61#40711yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C22×C61C2×#10011yescharacteristic
176C22×C61#41611yescharacteristic
177C22×C61#41711yescharacteristic
178C22×C61C2×#10411yescharacteristic
179C22×C61#42111yescharacteristic
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—42no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—22no—
197C4×C61—42no—
198C4×C61—41no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—22no—
202Dic61—21no—
203Dic61—21no—
204Dic61—81no—
205#2297—611no—
206#1797—611no—
207#1749—611no—
208#1272—612no—
209#1270—612no—
210C2×C61#146211yescharacteristic
211C2×C61#148811yescharacteristic
212C2×C61#148911yescharacteristic
213C2×C61#150111yescharacteristic
214C2×C61#151311yescharacteristic
215C2×C61#153011yescharacteristic
216C2×C61#155111yescharacteristic
217D61—42no—
218D61—82no—
219C22×#41—611no—
220C2×#117—611no—
221C22×C42—611no—
222C2×C4⋊C8—1221no—
223C2×C22⋊C8—1221no—
224C2×C22⋊C8—1221no—
225C2×#97—1221no—
226#391—611no—
227#391#692311yescharacteristic
228#390—611no—
229#390—611no—
230#386—1221no—
231#386—1221no—
232C4×C22⋊C4—1221no—
233C4×C22⋊C4—1221no—
234#336—612no—
235#336—612no—
236C61#761211yescharacteristic, complemented, Sylow
237C2×#41—1222no—
238C2×#41—1222no—
239C2×#41—2442no—
240C2×#41—2442no—
241C22×Q8C2×#692311yescharacteristic
242C22×D4—611no—
243C22×D4—1221no—
244C23×C4—611no—
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—1221no—
248C22×C8—1222no—
249C22×C8—1222no—
250#117—2442no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—1221no—
262C2×C42—2442no—
263C2×C42C2×#692311yescharacteristic
264C4⋊C8—2442no—
265C22⋊C8—1224no—
266C22⋊C8—2442no—
267#97—2442no—
268#95—21no—
269#95—21no—
270#95—1221no—
271#95—1221no—
272C24—611no—
273C24—1221no—
274#41—2448no—
275#41—2448no—
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8#1175821312yes—
280C2×D4—612no—
281C2×D4—1224no—
282C2×D4—1221no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2442no—
286C2×D4—2442no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1222no—
293C22×C4—1221no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1222no—
297C22×C4—1224no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4—1221no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2442no—
306C22×C4—2442no—
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22⋊#692311yescharacteristic
309C22×C4C22×#692311yescharacteristic
310C2×C8—1224no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—41no—
317C4⋊C4—2441no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—41no—
325C42—1222no—
326C42—1222no—
327C42—2441no—
328C42—2442no—
329C23—612no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1222no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23—2441no—
343C23C2×C22⋊#692311yescharacteristic
344Q8—42no—
345Q8—42no—
346D4—2442no—
347D4—2442no—
348D4—2448no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—1224no—
367C2×C4—1224no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—2444no—
375C2×C4—2442no—
376C2×C4—2442no—
377C2×C4—2448no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451984212yes—
382C2×C4D61⋊M1611yescharacteristic
383C2×C4C2×#1175821311yescharacteristic
384C8—4882no—
385C8—2444no—
386C22—1222no—
387C22—1222no—
388C22—1222no—
389C22—4881no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—2442no—
394C22—2442no—
395C22—2442no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22—2441no—
400C22#1684073311yescharacteristic
401C22D61⋊#9911yescharacteristic
402C22D61⋊#10011yescharacteristic
403C22#1684075211yescharacteristic
404C22#1684075311yescharacteristic
405C22C2×#1451984211yescharacteristic
406C22#1684076111yescharacteristic
407C4—21no—
408C4—21no—
409C4—22no—
410C4—42no—
411C4—41no—
412C4—81no—
413C4—1222no—
414C4—1222no—
415C4—1221no—
416C4—1221no—
417C4—4881no—
418C2—4882no—
419C2—2442no—
420C2#2146106511yescharacteristic
421C2#2146115311yescharacteristic
422C2#2146115711yescharacteristic
423C2#2146119711yescharacteristic
424C2#2146123711yescharacteristic
425C2#2146129011yescharacteristic
426C2#2146133911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #21461674C2semidirect
2. #21461546C2semidirect
3. #21460639C2semidirect
4. #21460636C2semidirect
236. C61#7612semidirect

Maximal subgroups

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

subgroupindex
#214616742
#214615462
#214606392
#214606362
#214483082
#761261