Finite Group Databasebeta

← #29589571

Subgroups — #29589571

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#21450283C211yesmaximal, characteristic
2#21444152C211yesmaximal, characteristic, complemented
3#21444132C211yesmaximal, characteristic, complemented
4#21443762C211yesmaximal, characteristic, complemented
5#21443762C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#1318C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839678—21no—
13#16839678—21no—
14#16839665C411yescharacteristic
15#16839655—21no—
16#16839655—21no—
17#16839632C411yescharacteristic
18#16839627C2211yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22#16839485—21no—
23#16839485—21no—
24C61×#390C2211yescharacteristic
25C61×#324C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C4×D61C2×C411yescharacteristic
29#14519748—41no—
30#14519748—41no—
31#14519735—41no—
32#14519735—41no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—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—
55C22×D4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C42×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C22⋊C8×C61—21no—
62C24×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—42no—
73C2×C22⋊D61—81no—
74C2×C22⋊D61—81no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
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—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—42no—
90C42×C61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—81no—
94C22⋊Dic61—81no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—81no—
101C4⋊Dic61—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123D4×C61—81no—
124D4×C61—81no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61#13111yescharacteristic
135C2×C4×C61#13111yescharacteristic
136C22⋊D61—84no—
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—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61#9911yescharacteristic
150C2×Dic61#9911yescharacteristic
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#11550—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61#40811yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61#41311yescharacteristic
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—41no—
181C4×C61—41no—
182Dic61—21no—
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61—81no—
187Dic61—81no—
188#2500—611no—
189#1464—611no—
190#1458—611no—
191#1324—611no—
192#1324—611no—
193#1318—611no—
194#1318D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—161no—
198C2×C61#146811yescharacteristic
199C2×C61#212611yescharacteristic
200C2×C61#213411yescharacteristic
201D61—81no—
202C2×#121—611no—
203C2×#117—611no—
204#432—1221no—
205#431—1221no—
206#394—1221no—
207#394—1221no—
208#390—611no—
209#390C2×D6111yescharacteristic
210#388—1221no—
211#388—1221no—
212#384—611no—
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#1155011yescharacteristic, complemented, Sylow
222C22×D4—1221no—
223C22×D4C4×D6111yescharacteristic
224C23×C4—611no—
225#121—2441no—
226#121—2441no—
227#117—2441no—
228#117—2441no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C22×D6111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
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—21no—
258C24—611no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—4881no—
264C2×D4—4881no—
265C2×D4—2442no—
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1221no—
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—4881no—
286C4⋊C4—4881no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—4881no—
292C22⋊C4—4881no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—41no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—2441no—
316C23—2441no—
317C23C22⋊C4×D6111yescharacteristic
318D4—81no—
319D4—81no—
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—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
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—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—4881no—
364C22—4881no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22#1683972711yescharacteristic
369C22#99×D6111yescharacteristic
370C22#1683974311yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—41no—
375C4—41no—
376C4—1221no—
377C4—1221no—
378C4—4881no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C2—21no—
383C2—21no—
384C2—161no—
385C2—4881no—
386C2#2144416411yescharacteristic
387C2#2144748111yescharacteristic
388C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1318C2
socleC22×C61C2×#99
prime radicalC2×#14519748C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1318D61
hypocenterC61#11550
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #21444152C2semidirect
3. #21444132C2semidirect
4. #21443762C2semidirect
5. #21443762C2semidirect
6. #21443751C2semidirect
7. C61×#1318C2semidirect
194. #1318D61semidirect
221. C61#11550semidirect

Maximal subgroups

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

subgroupindex
#214502832
#214441522
#214441322
#214437622
#214437512
C61×#13182
#1155061