Finite Group Databasebeta

← #29580673

Subgroups — #29580673

Order 15616.

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

normal subgroups only

This group has 502 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#21455767C211yesmaximal, characteristic
2#21453854C211yesmaximal, characteristic
3#21445896C211yesmaximal, characteristic
4#21444353C211yesmaximal, characteristic
5#21444352C211yesmaximal, characteristic
6#21443728C211yesmaximal, characteristic
7C61×#3095C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840103—22no—
10#16840097—21no—
11#16840092—21no—
12#16839805—21no—
13#16839770—21no—
14#16839726C2211yescharacteristic
15#16839701—21no—
16#16839700—21no—
17#16839690—22no—
18#16839682—21no—
19#16839681—21no—
20#16839625C2211yescharacteristic
21#16839625C2211yescharacteristic
22#16839529—22no—
23#16839500—22no—
24#16839499—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#485—22no—
28C61×#484—21no—
29C61×#483—21no—
30C61×#428—21no—
31C61×#419—21no—
32C61×#407C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758194—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—22no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D412yes—
45#14519710—22no—
46#14519708—22no—
47#14519700—22no—
48#14519700—22no—
49C22⋊#92418—21no—
50C22⋊#92418D412yes—
51#14519684—22no—
52#14519684—22no—
53#14519684—22no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×Q8×C61D411yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C2×M16×C61—21no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65#117×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76#107×C61—22no—
77#106×C61—22no—
78#103×C61—22no—
79#103×C61—22no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61D412yes—
82C24×C61C2×D411yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—42no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—42no—
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×Dic61—21no—
98C22×Dic61—22no—
99C22×Dic61—21no—
100C22×Dic61—41no—
101C2×Dic122—21no—
102C2×Dic122—21no—
103C2×Dic122—42no—
104M16×C61—42no—
105C2×C8×C61—22no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—41no—
118C42×C61—41no—
119C42×C61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—41no—
122C22⋊Dic61—42no—
123C22⋊Dic61—42no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126#11758196—41no—
127#11758196—41no—
128#11758196—82no—
129#11758194—42no—
130C2×#92418—22no—
131C23×C61—22no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61#12011yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61#12711yescharacteristic
137Q8×C61—42no—
138Q8×C61—81no—
139C2×C4×C61—22no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—81no—
152C2×C4×C61—81no—
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—81no—
165C2×Dic61—81no—
166C2×Dic61—81no—
167Dic122—42no—
168Dic122—81no—
169C8×C61—42no—
170#92418—42no—
171#9985—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—82no—
181C22×C61#39211yescharacteristic
182C22×C61#45812yes—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—81no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61—81no—
191Dic61—82no—
192Dic61—81no—
193Dic61—81no—
194Dic61—161no—
195#3095—611no—
196#3095D6111yescharacteristic
197#2817—611no—
198#1820—611no—
199#1511—611no—
200#1511—611no—
201#1306—611no—
202C2×C61—22no—
203C2×C61—41no—
204C2×C61—41no—
205C2×C61#200911yescharacteristic
206C2×C61#200911yescharacteristic
207C2×C61#202211yescharacteristic
208C2×C22⋊Q8—611no—
209C2×C22⋊Q8C2×D6111yescharacteristic
210C2×#117C2×D6111yescharacteristic
211#485—22no—
212#485—1222no—
213#484—21no—
214#484—1221no—
215#483—21no—
216#483—1221no—
217#428—21no—
218#428—1221no—
219#419—21no—
220#419—1221no—
221#407—611no—
222#407C2×D6111yescharacteristic
223#400—1221no—
224#400—1221no—
225#397—1222no—
226#395—1221no—
227#395—1221no—
228#381—611no—
229#381—611no—
230#342—1222no—
231#328—1222no—
232#328—1222no—
233C61#998511yescharacteristic, complemented, Sylow
234C22×Q8—611no—
235C22×Q8C22⋊D6111yescharacteristic
236C23×C4C22×D6111yescharacteristic
237C2×M16—21no—
238C2×M16—1221no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—1221no—
244C22⋊Q8—1221no—
245C22⋊Q8—1221no—
246C22⋊Q8—1221no—
247#117—21no—
248#117—21no—
249#117—21no—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—1222no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4C22⋊D6111yescharacteristic
256C2×C4⋊C4C22⋊D6111yescharacteristic
257C2×C4⋊C4C22⋊D6111yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—612no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C42—21no—
264#107—22no—
265#107—1222no—
266#106—22no—
267#106—1222no—
268#103—22no—
269#103—22no—
270#103—1222no—
271#103—1222no—
272C22⋊C8—21no—
273C22⋊C8—612no—
274C22⋊C8—1221no—
275C22⋊C8C22⋊D6112yes—
276#95—1222no—
277#95—1222no—
278#95—1222no—
279#95—1221no—
280#95—1221no—
281#95—1221no—
282#95—1221no—
283C24D4×D6111yescharacteristic
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×Q8—1221no—
288C2×Q8—1221no—
289C2×Q8—2442no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—42no—
295C22×C4—1222no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4D4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4#1175822411yescharacteristic
302C22×C4C2×C22⋊D6111yescharacteristic
303C22×C4C2×C22⋊D6111yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305M16—42no—
306M16—2442no—
307C2×C8—22no—
308C2×C8—1222no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—4882no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—2442no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2442no—
330C42—41no—
331C42—41no—
332C23—22no—
333C23—41no—
334C23—41no—
335C23#1451974511yescharacteristic
336C23#1451974911yescharacteristic
337C23#1451977311yescharacteristic
338Q8—42no—
339Q8—81no—
340Q8—4881no—
341Q8—2442no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—4881no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4#1451974511yescharacteristic
367C2×C4#1451974611yescharacteristic
368C2×C4#1451974811yescharacteristic
369C2×C4#1451974911yescharacteristic
370C8—42no—
371C8—2442no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—82no—
381C22#1683967011yescharacteristic
382C22#1683995112yes—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—9761no—
392C4—4882no—
393C4—4881no—
394C4—4881no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2#2144687611yescharacteristic
399C2#2144687711yescharacteristic
400C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#3095C2
socleC22×C61#392
prime radicalC24×C61C2×D4
hypercenter#3095D61
hypocenterC61#9985
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
233. C61#9985semidirect

Maximal subgroups

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

subgroupindex
#214557672
#214538542
#214458962
#214443532
#214443522
#214437282
C61×#30952
#998561