Finite Group Databasebeta

← #29592136

Subgroups — #29592136

Order 15616.

428 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 63 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#21456612C211yesmaximal, characteristic
2#21447753C211yesmaximal, characteristic, complemented
3#21447736C211yesmaximal, characteristic, complemented
4#21443830C211yesmaximal, characteristic, complemented
5#21443827C211yesmaximal, characteristic, complemented
6#21443743C211yesmaximal, characteristic, complemented
7C61×#2001C211yesmaximal, characteristic, complemented
8#16840273—21no—
9C2×#14519723—21no—
10C2×#14519720—21no—
11#16840104—21no—
12#16840087—21no—
13#16840003C2211yescharacteristic
14#16839998C2211yescharacteristic
15#16839991—21no—
16#16839926—21no—
17#16839909—21no—
18#16839566—21no—
19#16839566—21no—
20C22⋊#11758185C2211yescharacteristic
21C22⋊#11758185C2211yescharacteristic
22C22×Q16×C61C2211yescharacteristic
23C2×C22⋊Q8×C61—21no—
24C2×#103×C61—21no—
25C2×C22⋊C8×C61C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×#11758222—21no—
28C2×Dic244D411yescharacteristic
29C2×#11758190—21no—
30C2×D488D411yescharacteristic
31#14519760—41no—
32#14519756—21no—
33#14519756—21no—
34#14519751—21no—
35#14519751—21no—
36#14519746—41no—
37C4×C22⋊D61—41no—
38C4×C22⋊D61—41no—
39#14519736—21no—
40#14519723—42no—
41#14519720—42no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519709—21no—
47#14519702—21no—
48#14519702—21no—
49#14519699—21no—
50#14519699—21no—
51C22×Q8×C61—21no—
52C23×C4×C61D411yescharacteristic
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—42no—
56C22×C8×C61D411yescharacteristic
57C22×C8×C61C2311yescharacteristic
58C22⋊Q8×C61—42no—
59C22⋊Q8×C61—42no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—41no—
62C2×C22⋊C4×C61—41no—
63#103×C61—42no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C24×C61D811yescharacteristic
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61D811yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84#11758222—81no—
85#11758222—81no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89Q16×C61—22no—
90Q16×C61—22no—
91Q16×C61—41no—
92Q16×C61—41no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C4⋊C4×C61—22no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—44no—
101C22⋊C4×C61—44no—
102C22⋊Dic61—41no—
103C22⋊Dic61—41no—
104C22⋊Dic61—41no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—41no—
112Dic244—41no—
113D488—41no—
114#11758190—81no—
115#11758185—41no—
116#11758185—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×D811yescharacteristic
123C22×D61—41no—
124Q8×C61—42no—
125Q8×C61—42no—
126Q8×C61—81no—
127Q8×C61—81no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C22⋊D61—82no—
144C22⋊D61—82no—
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150D244—41no—
151D244—41no—
152C4×D61—82no—
153Dic122—41no—
154Dic122—41no—
155C8×C61—21no—
156C8×C61—21no—
157C8×C61—41no—
158#12107—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—42no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—81no—
166C22×C61#44711yescharacteristic
167C22×C61#50811yescharacteristic
168C22×C61#51011yescharacteristic
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—82no—
175C4×C61—82no—
176C4×C61#45311yescharacteristic
177C4×C61B(4,𝔽2)11yescharacteristic
178Dic61—81no—
179Dic61—81no—
180Dic61—81no—
181#3191—611no—
182#2188—611no—
183#2185—611no—
184#2001D6111yescharacteristic, complemented
185#1348—611no—
186#1347—611no—
187#1314—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61—81no—
191C2×C61#159511yescharacteristic
192C2×C61#218911yescharacteristic
193C2×C61#219111yescharacteristic
194D61—161no—
195C22×Q16C2×D6111yescharacteristic
196#525—1221no—
197C2×C22⋊Q8—21no—
198C2×Q32—1221no—
199C2×SD32—1221no—
200#485—1221no—
201#482—1221no—
202#467—611no—
203#466—611no—
204#465—1221no—
205#452—1221no—
206#449—1221no—
207C2×#103—21no—
208C2×C22⋊C8C2×D6111yescharacteristic
209#358—1221no—
210#358—1221no—
211C22⋊C16—611no—
212C22⋊C16—611no—
213#340C2×D6111yescharacteristic
214C61#1210711yescharacteristic, complemented, Sylow
215C2×#41—1221no—
216C22×Q8—21no—
217C23×C4C22⋊D6111yescharacteristic
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—42no—
221C2×Q16—611no—
222C2×SD16—1221no—
223C2×D8—611no—
224C22×C8C22⋊D6111yescharacteristic
225C22×C8C22×D6111yescharacteristic
226#123—2441no—
227C22⋊Q8—42no—
228C22⋊Q8—42no—
229C22⋊Q8—1221no—
230C22⋊Q8—1221no—
231#121—1221no—
232#121—1221no—
233#120—2441no—
234C4×D4—2441no—
235C4×D4—2441no—
236#117—1221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—41no—
239C2×C22⋊C4—41no—
240Q32—2442no—
241SD32—2442no—
242C2×C16—1221no—
243C2×C16—1221no—
244#107—611no—
245#107—611no—
246#106—1221no—
247#103—42no—
248#103—1221no—
249#103—1221no—
250#102—1221no—
251#102—1221no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C24#1175819911yescharacteristic
255#41—4881no—
256#41—4881no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—1221no—
264C2×D4—1221no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—2441no—
275C22×C4#1175819911yescharacteristic
276C22×C4C2×C22⋊D6111yescharacteristic
277Q16—22no—
278Q16—22no—
279Q16—41no—
280Q16—41no—
281Q16—2441no—
282SD16—4881no—
283D8—2441no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8D4×D6111yescharacteristic
288C2×C8D4×D6111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—44no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C22⋊C4—44no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—2441no—
303C16—2441no—
304C16—2441no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—2441no—
311C23C2×#1175819911yescharacteristic
312Q8—42no—
313Q8—42no—
314Q8—81no—
315Q8—81no—
316Q8—2441no—
317Q8—2441no—
318D4—4882no—
319D4—4882no—
320D4—4881no—
321D4—4881no—
322D4—2441no—
323D4—2441no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—4882no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451974511yescharacteristic
342C2×C4#1451980211yescharacteristic
343C8—21no—
344C8—21no—
345C8—41no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—81no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22#1683989511yescharacteristic
357C22#1684019211yescharacteristic
358C22#1684020311yescharacteristic
359C4—21no—
360C4—41no—
361C4—82no—
362C4—82no—
363C4—4881no—
364C4—4881no—
365C4—4881no—
366C4#1683992911yescharacteristic
367C4#1683994811yescharacteristic
368C2—21no—
369C2—21no—
370C2—81no—
371C2—9761no—
372C2#2144473611yescharacteristic
373C2#2144775711yescharacteristic
374C2#2144776911yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2001C2
socleC22×C61#447
prime radical#21456612C2
hypercenter#2001D61
hypocenterC61#12107
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. #21447753C2semidirect
3. #21447736C2semidirect
4. #21443830C2semidirect
5. #21443827C2semidirect
6. #21443743C2semidirect
7. C61×#2001C2semidirect
184. #2001D61semidirect
214. C61#12107semidirect

Maximal subgroups

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

subgroupindex
#214566122
#214477532
#214477362
#214438302
#214438272
#214437432
C61×#20012
#1210761