Finite Group Databasebeta

← #29576328

Subgroups — #29576328

Order 15616.

452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#16840104C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic
3#21445916C211yesmaximal, characteristic
4#21444340C211yesmaximal, characteristic
5#21444184C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic
7C61×#1293C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16840104—21no—
11#16840104—21no—
12#16840104—21no—
13#16840104—21no—
14#16839820—22no—
15#16839816—21no—
16#16839812—21no—
17C2×#14519711C411yescharacteristic, complemented
18C2×#14519709C411yescharacteristic, complemented
19#16839790—21no—
20C2×#14519702C411yescharacteristic, complemented
21C2×#14519702C411yescharacteristic, complemented
22C2×C22⋊#92418C2211yescharacteristic
23#16839720—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839523—21no—
26#16839523—21no—
27#16839500—22no—
28#16839487—21no—
29#16839487—21no—
30C61×#407C2211yescharacteristic
31C61×#407C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C22×Dic122C2×C411yescharacteristic
34C22×#92418—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39#14519736—21no—
40#14519736—21no—
41#14519736D411yescharacteristic
42#14519736D411yescharacteristic
43#14519736D411yescharacteristic
44#14519736D411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C4×Dic61—21no—
53C2×C4×Dic61—21no—
54#14519711—21no—
55#14519711—21no—
56#14519709—21no—
57#14519709—21no—
58#14519706—22no—
59#14519706—22no—
60#14519702—21no—
61#14519702—21no—
62#14519702—21no—
63#14519702—21no—
64C22⋊#92418—21no—
65C22⋊#92418D411yescharacteristic
66C22⋊#92418D411yescharacteristic
67#14519687—22no—
68C8×Dic61—22no—
69#14519684—21no—
70C23×C4×C61C2311yescharacteristic
71C2×M16×C61—21no—
72C2×M16×C61—21no—
73C22×C8×C61C2×C411yescharacteristic
74C22×C8×C61C2×C411yescharacteristic
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61D412yes—
81C24×C61#4111yescharacteristic
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—41no—
98C2×Dic122—41no—
99M16×C61—41no—
100M16×C61—41no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—41no—
109C22⋊Dic61—21no—
110C22⋊Dic61—21no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C22⋊Dic61—22no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61C22⋊C411yescharacteristic
122C4⋊Dic61C22⋊C411yescharacteristic
123C4⋊Dic61C22⋊C411yescharacteristic
124C4⋊Dic61C22⋊C411yescharacteristic
125#11758196—41no—
126#11758196—41no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—41no—
136C2×#92418—41no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61C4×D411yescharacteristic
142C23×C61#12111yescharacteristic
143C23×C61#12311yescharacteristic
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61C2×C22⋊C411yescharacteristic
154C2×C4×C61C4×D411yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—81no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172Dic122—41no—
173Dic122—41no—
174Dic122—81no—
175C8×C61—42no—
176C8×C61—41no—
177C8×C61—41no—
178C8×C61—81no—
179#92418—41no—
180#92418—41no—
181#9240—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#38611yescharacteristic
193C22×C61#44311yescharacteristic
194C22×C61#44411yescharacteristic
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61#41011yescharacteristic
199C4×C61#41011yescharacteristic
200Dic61—41no—
201Dic61—41no—
202Dic61—41no—
203Dic61—41no—
204Dic61—82no—
205Dic61—81no—
206Dic61—81no—
207C2×#485—611no—
208#2924—611no—
209#1826—611no—
210#1508—611no—
211#1472—611no—
212#1293D6111yescharacteristic
213#1282—611no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—41no—
217C2×C61—41no—
218C2×C61#187611yescharacteristic
219C2×C61#189911yescharacteristic
220C2×C61#190211yescharacteristic
221C2×C22⋊Q8—611no—
222C2×#117—611no—
223#485—1221no—
224#485—1221no—
225#485—1221no—
226#485—1221no—
227#433—1222no—
228#432—1221no—
229#431—1221no—
230C2×#107—611no—
231C2×#106—611no—
232#424—1221no—
233C2×#103—611no—
234C2×#103—611no—
235#407C2×D6111yescharacteristic
236#407C2×D6111yescharacteristic
237C2×C22⋊C8—611no—
238C2×C22⋊C8C2×D6111yescharacteristic
239#405—1221no—
240C4×C22⋊C4—611no—
241#339—1221no—
242#339—1221no—
243#328—1222no—
244#324—1221no—
245#324—1221no—
246C61#924011yescharacteristic, complemented, Sylow
247C22×Q8—611no—
248C23×C4C22×D6111yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251C22×C8—1221no—
252C22×C8C4×D6111yescharacteristic
253C22×C8C4×D6111yescharacteristic
254C22⋊Q8—1221no—
255C22⋊Q8—1221no—
256C22⋊Q8—1221no—
257C22⋊Q8—1221no—
258#117—611no—
259#117—611no—
260#117—611no—
261#117—611no—
262#117—1221no—
263#117—1221no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1221no—
270C2×C22⋊C4—1221no—
271C2×C42—1221no—
272C2×C42—1221no—
273#107—1221no—
274#107—1221no—
275#106—1221no—
276#106—1221no—
277C4⋊C8—1222no—
278C4⋊C8—1222no—
279#103—1221no—
280#103—1221no—
281#103—1221no—
282#103—1221no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—611no—
289C22⋊C8—611no—
290C22⋊C8—1221no—
291C22⋊C8D24412yes—
292#97—1222no—
293C4×C8—1222no—
294#95—1221no—
295C24#1175822611yescharacteristic
296C2×Q8—1221no—
297C2×Q8—1221no—
298C2×Q8—2441no—
299C2×Q8—2441no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—2441no—
307C22×C4C2×C4×D6111yescharacteristic
308C22×C4C2×D24411yescharacteristic
309C22×C4#1175822211yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—1221no—
324C2×C8—1221no—
325C2×C8—2441no—
326C2×C8—2441no—
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—611no—
330C4⋊C4—611no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1222no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C42—1221no—
346C42—1221no—
347C42—1221no—
348C42—1221no—
349C42—2441no—
350C42—2441no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23#1451973911yescharacteristic
356C23#1451975211yescharacteristic
357C23#1451976211yescharacteristic
358Q8—4881no—
359Q8—2441no—
360Q8—2441no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4C22⋊C4×D6111yescharacteristic
386C2×C4C4×D24411yescharacteristic
387C2×C4#1451974711yescharacteristic
388C2×C4#1451975011yescharacteristic
389C8—42no—
390C8—41no—
391C8—41no—
392C8—81no—
393C8—2441no—
394C8—2441no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1683964011yescharacteristic
406C22#1683987811yescharacteristic
407C22#1683988311yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—4882no—
412C4—4881no—
413C4—4881no—
414C4—2441no—
415C4—2441no—
416C4—2441no—
417C4—2441no—
418C4#1683973411yescharacteristic
419C4#1683973411yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#2144614711yescharacteristic
425C2#2144627611yescharacteristic
426C2#2144629311yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1293C2
socleC22×C61#386
prime radicalC24×C61#41
cosocleC23×C4×C61C23
hypercenter#1293D61
hypocenterC61#9240
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
17. C2×#14519711C4semidirect
18. C2×#14519709C4semidirect
20. C2×#14519702C4semidirect
21. C2×#14519702C4semidirect
246. C61#9240semidirect

Maximal subgroups

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

subgroupindex
C2×#168401042
#214544792
#214459162
#214443402
#214441842
#214436662
C61×#12932
#924061