Finite Group Databasebeta

← #29569332

Subgroups — #29569332

Order 15616.

438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453763C211yesmaximal, characteristic
2#21447357C211yesmaximal, characteristic, complemented
3#21447356C211yesmaximal, characteristic, complemented
4#21447351C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic, complemented
8C2×#14519711—21no—
9C2×#14519710—21no—
10C2×#14519709—21no—
11C2×#14519702—21no—
12C2×#14519701—21no—
13C2×#14519699—21no—
14#16839704—21no—
15#16839675—21no—
16#16839673—21no—
17#16839668C2211yescharacteristic
18#16839664C2211yescharacteristic
19#16839640—21no—
20#16839636—21no—
21#16839633—21no—
22#16839632C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×#92418—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42#14519711—42no—
43#14519710—42no—
44#14519709—42no—
45#14519702—42no—
46#14519701—42no—
47#14519699—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×Q8×C61D411yescharacteristic
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60C23×D61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—41no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244Q1612yes—
78C2×C4×D61—81no—
79C2×C4×D61—81no—
80C2×C4×D61—81no—
81C2×Dic122—21no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×C8×C61—22no—
86C2×C8×C61—22no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C42×C61—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—81no—
98#11758198—81no—
99#11758198—81no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108#11758196—81no—
109C2×#92418—22no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61#12011yescharacteristic
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120Q8×C61—42no—
121Q8×C61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
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×C61C2×Q1611yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×C4×C61#13711yescharacteristic
140C2×Dic61—41no—
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—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152D244—42no—
153D244—81no—
154C4×D61—84no—
155Dic122—42no—
156Dic122—81no—
157C8×C61—42no—
158C8×C61—42no—
159#92418—42no—
160#7833—611nomaximal, Sylow
161C22×C61#45111yescharacteristic
162C22×C61#45211yescharacteristic
163C22×C61#45211yescharacteristic
164C22×C61#45311yescharacteristic
165C22×C61#45311yescharacteristic
166C22×C61#45311yescharacteristic
167C22×C61#45811yescharacteristic
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—81no—
182C4×C61—81no—
183Dic61—81no—
184Dic61—81no—
185Dic61—81no—
186Dic61—161no—
187#2804—611no—
188#2095—611no—
189#2095—611no—
190#2094—611no—
191#1272—611no—
192#1272D6111yescharacteristic, complemented
193#1270—611no—
194C2×C61#161411yescharacteristic
195C2×C61#161811yescharacteristic
196C2×C61#161811yescharacteristic
197C2×C61#163011yescharacteristic
198C2×C61#163211yescharacteristic
199C2×C61#163211yescharacteristic
200C2×C61#165511yescharacteristic
201D61—82no—
202C2×#107—1221no—
203C2×#107—1221no—
204C2×#106—1221no—
205C2×#103—1221no—
206C2×#103—1221no—
207C2×#102—1221no—
208#400—1221no—
209#393—1221no—
210#393—1221no—
211#391—611no—
212#391C2×D6111yescharacteristic
213#390—611no—
214#386—1221no—
215#385—1221no—
216#385—1221no—
217#384—611no—
218#336—611no—
219#336C2×D6111yescharacteristic
220#336C2×D6111yescharacteristic
221C61#783311yescharacteristic, complemented, Sylow
222C22×Q8—611no—
223C22×Q8D24411yescharacteristic
224C22×D4—611no—
225C23×C4—1221no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—1221no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4D24411yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C42C22×D6111yescharacteristic
242#107—2442no—
243#107—2442no—
244#106—2442no—
245#103—2442no—
246#103—2442no—
247#102—2442no—
248#95—21no—
249#95—21no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—1221no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—1221no—
261C2×Q8—1221no—
262C2×Q8—2441no—
263C2×Q8—2441no—
264C2×D4—612no—
265C2×D4—1221no—
266C2×D4—2441no—
267C2×D4—2441no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—4881no—
274C22×C4—4881no—
275C22×C4—4881no—
276C22×C4—2441no—
277C22×C4C2×D24411yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C4⋊C4—41no—
290C4⋊C4—4881no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—4881no—
300C22⋊C4—4881no—
301C22⋊C4—4881no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—41no—
307C23—1222no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23#1451974711yescharacteristic
315Q8—42no—
316Q8—81no—
317Q8—4881no—
318Q8—2442no—
319D4—4881no—
320D4—2442no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—4884no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
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×C4Q16×D6111yescharacteristic
347C2×C4#1451979811yescharacteristic
348C2×C4#1451979911yescharacteristic
349C2×C4#1451980611yescharacteristic
350C2×C4#1451980911yescharacteristic
351C2×C4#1451981011yescharacteristic
352C8—42no—
353C8—42no—
354C8—2442no—
355C22—4881no—
356C22—4881no—
357C22—4881no—
358C22—4881no—
359C22—2442no—
360C22—2442no—
361C22—2442no—
362C22#1683991911yescharacteristic
363C22#1683992611yescharacteristic
364C22#1683992711yescharacteristic
365C22#1683993111yescharacteristic
366C22#1683993111yescharacteristic
367C22#1683993211yescharacteristic
368C22#1683995311yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—81no—
377C4—9761no—
378C4—4881no—
379C4—4881no—
380C4—4881no—
381C2—4882no—
382C2#2144484511yescharacteristic
383C2#2144486911yescharacteristic
384C2#2144487011yescharacteristic
385C2#2144494211yescharacteristic
386C2#2144495411yescharacteristic
387C2#2144495611yescharacteristic
388C2#2144510911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1272D61
hypocenterC61#7833
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #21447357C2semidirect
3. #21447356C2semidirect
5. #21443644C2semidirect
7. C61×#1272C2semidirect
192. #1272D61semidirect
221. C61#7833semidirect

Maximal subgroups

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

subgroupindex
#214537632
#214473572
#214473562
#214473512
#214436442
#214436392
C61×#12722
#783361