Finite Group Databasebeta

← #29577899

Subgroups — #29577899

Order 15616.

458 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454455C211yesmaximal, characteristic
2#21451390C211yesmaximal, characteristic
3#21444266C211yesmaximal, characteristic, complemented
4#21444151C211yesmaximal, characteristic
5#21443685C211yesmaximal, characteristic, complemented
6#21443684C211yesmaximal, characteristic, complemented
7C61×#1491C211yesmaximal, characteristic, complemented
8C2×#14519734C2211yescharacteristic
9#16839824—22no—
10#16839821—22no—
11#16839819C2211yescharacteristic
12#16839785—21no—
13#16839725—21no—
14C4×#11758194C2211yescharacteristic
15#16839693C411yescharacteristic
16#16839688C411yescharacteristic
17#16839681C411yescharacteristic
18#16839673C411yescharacteristic
19#16839653—21no—
20#16839646—21no—
21#16839643—21no—
22#16839633—21no—
23#16839630C2211yescharacteristic
24Q8⋊#92418—22no—
25#16839487—21no—
26#16839485—21no—
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×C4×D61D411yescharacteristic
32C2×#11758194—21no—
33#14519734—21no—
34#14519734—21no—
35#14519734—21no—
36#14519734—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198C2×C411yescharacteristic
44C2×#11758198D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C4⋊#92418—21no—
47#14519706—24no—
48C22⋊#92418—21no—
49#14519689—24no—
50#14519688—21no—
51#14519688—21no—
52C4×#92418D412yes—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684C2×C411yescharacteristic
60#14519684C2×C411yescharacteristic
61C22×Q8×C61C2×C411yescharacteristic
62C2×M16×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74#97×C61—21no—
75C4×C8×C61D412yes—
76C23×D61C22⋊C411yescharacteristic
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—42no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94M16×C61—41no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C42×C61—41no—
103C42×C61—41no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—42no—
113#11758198—42no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196—21no—
118#11758196—42no—
119#11758196—42no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122#11758194—41no—
123#11758194—41no—
124C2×#92418—22no—
125C2×#92418—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—41no—
131C22×D61—41no—
132Q8×C61—22no—
133Q8×C61—22no—
134Q8×C61—41no—
135Q8×C61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—22no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C4×D61—42no—
166C4×D61—42no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—42no—
170#92418—81no—
171#9493—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38611yescharacteristic
175C22×C61#42111yescharacteristic
176C22×C61#42111yescharacteristic
177C2×D61—42no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—42no—
189C4×C61—81no—
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61—81no—
194Dic61—81no—
195#2921—611no—
196#2599—611no—
197#1491—611no—
198#1491D6111yescharacteristic, complemented
199#1464—611no—
200#1288—611no—
201#1288—611no—
202C2×C61—21no—
203C2×C61—21no—
204C2×C61#189111yescharacteristic
205C2×C61#189711yescharacteristic
206C2×C61#190911yescharacteristic
207D61—81no—
208C2×C4×Q8C2×D6111yescharacteristic
209C2×#117—611no—
210#433—1222no—
211#433—1222no—
212#432—611no—
213#432C2×D6111yescharacteristic
214#423—1221no—
215#407—1221no—
216C4×M16—611no—
217C4×M16C2×D6111yescharacteristic
218#398—611no—
219#397—611no—
220#395—611no—
221#393—611no—
222#388—1221no—
223#387—1221no—
224#387—1221no—
225#385—1221no—
226#383—611no—
227Q8⋊C8—22no—
228Q8⋊C8—1222no—
229#324—1221no—
230#323—1221no—
231C61#949311yescharacteristic, complemented, Sylow
232C22×Q8C4×D6111yescharacteristic
233C23×C4—611no—
234C2×M16—21no—
235C2×M16—1221no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240#117—1221no—
241#117—1221no—
242#117—1221no—
243#117—1221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4C4×D6111yescharacteristic
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—21no—
255C2×C42—611no—
256C2×C42C22×D6111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—1224no—
259C4⋊C8—1221no—
260C22⋊C8—21no—
261C22⋊C8—1224no—
262C22⋊C8—1221no—
263#97—21no—
264#97—21no—
265#97—1221no—
266#97—1221no—
267C4×C8—612no—
268C4×C8C22⋊D6112yes—
269#95—611no—
270#95—611no—
271#95—1221no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276#95—1221no—
277C24—611no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4C2×C4×D6111yescharacteristic
293C22×C4D4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295M16—41no—
296M16—41no—
297M16—2441no—
298M16—2441no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—1222no—
302C2×C8—2441no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—2442no—
312C4⋊C4—2442no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—2442no—
318C22⋊C4—2442no—
319C42—41no—
320C42—41no—
321C42—1221no—
322C42—1221no—
323C42#1175822211yescharacteristic
324C42D4×D6111yescharacteristic
325C42#1175822411yescharacteristic
326C42C2×C22⋊D6111yescharacteristic
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—2441no—
331C23—2441no—
332C23C22⋊C4×D6111yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—41no—
336Q8—41no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4#1451973711yescharacteristic
363C2×C4C4×C22⋊D6111yescharacteristic
364C2×C4#1451974511yescharacteristic
365C2×C4#1451974811yescharacteristic
366C2×C4#1451975011yescharacteristic
367C2×C4#1451975911yescharacteristic
368C8—42no—
369C8—81no—
370C8—4881no—
371C8—2442no—
372C22—21no—
373C22—21no—
374C22—4881no—
375C22—2442no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22#1683963811yescharacteristic
380C22#1683977711yescharacteristic
381C22#1683977711yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—4881no—
391C4—4881no—
392C4—2441no—
393C4—2441no—
394C4—2441no—
395C2—21no—
396C2—21no—
397C2—4881no—
398C2#2144623411yescharacteristic
399C2#2144626411yescharacteristic
400C2#2144633811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1491C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1491D61
hypocenterC61#9493
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. #21444266C2semidirect
5. #21443685C2semidirect
6. #21443684C2semidirect
7. C61×#1491C2semidirect
198. #1491D61semidirect
231. C61#9493semidirect

Maximal subgroups

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

subgroupindex
#214544552
#214513902
#214442662
#214441512
#214436852
#214436842
C61×#14912
#949361