Finite Group Databasebeta

← #29589593

Subgroups — #29589593

Order 15616.

408 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 69 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#21450278C211yesmaximal, characteristic
2#21444152C211yesmaximal, characteristic, complemented
3#21444132C211yesmaximal, characteristic, complemented
4#21443765C211yesmaximal, characteristic, complemented
5#21443750C211yesmaximal, characteristic, complemented
6#21443750C211yesmaximal, characteristic, complemented
7C61×#1325C211yesmaximal, characteristic, complemented
8C2×#14519752C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839679—21no—
13#16839679—21no—
14#16839664C411yescharacteristic
15#16839663C2211yescharacteristic
16#16839652—21no—
17#16839652—21no—
18#16839627C411yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#384C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61C2×C411yescharacteristic
30#14519752—41no—
31#14519752—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×#11758198D411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46#14519706—41no—
47#14519706—41no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519687—41no—
51C8×Dic61—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C23×D61—21no—
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—42no—
78C2×D244—81no—
79C2×D244—81no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—81no—
90C4⋊C4×C61—81no—
91C42×C61—21no—
92C42×C61—21no—
93#11758198—41no—
94#11758198—41no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—41no—
99#11758198—41no—
100#11758198—81no—
101#11758198—81no—
102C4⋊Dic61—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#13111yescharacteristic
136C2×C4×C61#13111yescharacteristic
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61#9911yescharacteristic
147C2×Dic61#9911yescharacteristic
148D244—81no—
149D244—81no—
150D244—84no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C8×C61—81no—
156C8×C61—81no—
157#92418—81no—
158#92418—81no—
159#11554—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#40811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61#41311yescharacteristic
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—81no—
188#2500—611no—
189#1464—611no—
190#1458—611no—
191#1325—611no—
192#1325D6111yescharacteristic, complemented
193#1318—611no—
194#1318—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#146811yescharacteristic
198C2×C61#212811yescharacteristic
199C2×C61#213211yescharacteristic
200D61—81no—
201D61—161no—
202C2×#121—611no—
203C2×#117—611no—
204#432—1221no—
205#431—1221no—
206#394—1221no—
207#394—1221no—
208#390—611no—
209#390—611no—
210#388—1221no—
211#388—1221no—
212#384C2×D6111yescharacteristic
213#382—611no—
214C4×C22⋊C4—611no—
215#324—611no—
216#324—611no—
217#324C2×D6111yescharacteristic
218#324C2×D6111yescharacteristic
219#323—1221no—
220#323—1221no—
221C61#1155411yescharacteristic, complemented, Sylow
222C22×D4—611no—
223C22×D4—1221no—
224C23×C4—611no—
225#121—2441no—
226#121—2441no—
227#117—2441no—
228#117—2441no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4C4×D6111yescharacteristic
233C2×C4⋊C4C22×D6111yescharacteristic
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42C4×D6111yescharacteristic
246C4⋊C8—2441no—
247C4⋊C8—2441no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—1221no—
251C22⋊C8—1221no—
252#97—2441no—
253C4×C8—2441no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257C24—611no—
258C24—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—4881no—
262C2×D4—4881no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2442no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4C2×C4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—2441no—
289C22⋊C4—4881no—
290C22⋊C4—4881no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—21no—
299C42—21no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C42—2441no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23C22⋊C4×D6111yescharacteristic
318D4—4881no—
319D4—4881no—
320D4—4884no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451978311yescharacteristic
349C2×C4#1451978511yescharacteristic
350C8—81no—
351C8—81no—
352C8—4881no—
353C8—4881no—
354C22—21no—
355C22—21no—
356C22—4881no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1683972711yescharacteristic
369C22#99×D6111yescharacteristic
370C22#1683974511yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—81no—
377C4—1221no—
378C4—1221no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C2—21no—
383C2—21no—
384C2—9761no—
385C2—4881no—
386C2#2144416611yescharacteristic
387C2#2144748911yescharacteristic
388C2#2144750311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1325C2
socleC22×C61C2×#99
prime radicalC2×#14519752C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1325D61
hypocenterC61#11554
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
2. #21444152C2semidirect
3. #21444132C2semidirect
4. #21443765C2semidirect
5. #21443750C2semidirect
6. #21443750C2semidirect
7. C61×#1325C2semidirect
192. #1325D61semidirect
221. C61#11554semidirect

Maximal subgroups

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

subgroupindex
#214502782
#214441522
#214441322
#214437652
#214437502
C61×#13252
#1155461