Finite Group Databasebeta

← #29592696

Subgroups — #29592696

Order 15616.

426 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 59 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#21446865C211yesmaximal, characteristic
2#21444821C211yesmaximal, characteristic
3#21444787C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443753C211yesmaximal, characteristic, complemented
7C61×#2586C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9#16840343C2211yescharacteristic
10#16840075—21no—
11#16839901—21no—
12C2×#14519705—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#398C2211yescharacteristic
19C61×#395—21no—
20C61×#395C2211yescharacteristic
21C61×#391—21no—
22C61×#391C2211yescharacteristic
23C61×#389—21no—
24C61×#387—21no—
25C61×#387—21no—
26C4×C4⋊C4×C61—21no—
27C2×#11758222—21no—
28#14519808—42no—
29#14519808—42no—
30C2×#11758202—41no—
31C2×#11758201—41no—
32C2×#11758201—41no—
33C2×#11758194—21no—
34#14519757—41no—
35#14519752—41no—
36#14519751—21no—
37#14519751—21no—
38#14519710—41no—
39#14519705—42no—
40#14519701—41no—
41#14519697—41no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×Q8×C61D411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C4⋊C4×C61C2311yescharacteristic
53C2×C42×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61D411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—42no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C4⋊C4×C61—24no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—81no—
97C4⋊C4×C61—81no—
98C42×C61—42no—
99C42×C61—41no—
100C42×C61—81no—
101#11758202—44no—
102#11758201—44no—
103#11758201—82no—
104#11758198—41no—
105#11758198—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758194—22no—
109#11758194—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114C22×D61—41no—
115Q8×C61—42no—
116Q8×C61—42no—
117Q8×C61—81no—
118Q8×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
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×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—41no—
148D244—41no—
149D244—41no—
150D244—81no—
151D244—81no—
152C4×D61—81no—
153C4×D61—81no—
154Dic122—41no—
155Dic122—41no—
156#92418—42no—
157#92418—81no—
158#92418—81no—
159#12197—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#44911yescharacteristic
163C22×C61#45311yescharacteristic
164C22×C61B(4,𝔽2)11yescharacteristic
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—42no—
171C4×C61—42no—
172C4×C61—42no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—42no—
176C4×C61—81no—
177C4×C61—81no—
178Dic61—81no—
179#2586D6111yescharacteristic, complemented
180#2007—611no—
181#1610—611no—
182#1604—611no—
183#1354—611no—
184#1346—611no—
185#1319—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#160011yescharacteristic
189C2×C61#219711yescharacteristic
190C2×C61#220511yescharacteristic
191D61—161no—
192C2×#137—1221no—
193#537—611no—
194#480—1221no—
195#448—1221no—
196C2×#104—1221no—
197#398C2×D6111yescharacteristic
198#395—21no—
199#395C2×D6111yescharacteristic
200#391—21no—
201#391C2×D6111yescharacteristic
202#389—21no—
203#387—21no—
204#387—21no—
205C4×C4⋊C4—21no—
206#343—611no—
207#327—1221no—
208#327—1221no—
209#324—611no—
210#324—611no—
211C61#1219711yescharacteristic, complemented, Sylow
212C2×#41—1221no—
213C22×Q8C22⋊D6111yescharacteristic
214C22×Q8C22⋊D6111yescharacteristic
215#137—2442no—
216#137—2442no—
217C2×Q16—2441no—
218C2×SD16—2441no—
219C2×SD16—2441no—
220C2×M16—1221no—
221C22⋊Q8—2441no—
222#121—1221no—
223#121—1221no—
224#121—2441no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D6111yescharacteristic
231C2×C4⋊C4C22×D6111yescharacteristic
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C22⋊D6111yescharacteristic
235#107—2441no—
236#104—2442no—
237#103—2441no—
238#102—2441no—
239C22⋊C8—1221no—
240C22⋊C8—1221no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C22⋊D6111yescharacteristic
249#95C22⋊D6111yescharacteristic
250#41—2441no—
251#41—2441no—
252#41—2441no—
253#41—2441no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—42no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—2441no—
272C22×C4C2×C22⋊D6111yescharacteristic
273C22×C4C2×C22⋊D6111yescharacteristic
274C22×C4C2×C22⋊D6111yescharacteristic
275Q16—2444no—
276SD16—4882no—
277SD16—2444no—
278M16—1222no—
279M16—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—24no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—41no—
296C42—42no—
297C42—81no—
298C23—2441no—
299C23#1451974611yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304Q8—2441no—
305Q8—2441no—
306D4—4881no—
307D4—4881no—
308D4—4881no—
309D4—4881no—
310D4—2441no—
311D4—2441no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—2441no—
339C2×C4#1451979711yescharacteristic
340C2×C4#1451980211yescharacteristic
341C8—4881no—
342C8—4881no—
343C8—2442no—
344C22—21no—
345C22—21no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22#1683990711yescharacteristic
350C22#1683993011yescharacteristic
351C22#1683994911yescharacteristic
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—42no—
357C4—41no—
358C4—41no—
359C4—42no—
360C4—81no—
361C4—81no—
362C4—4881no—
363C2—21no—
364C2—21no—
365C2—9761no—
366C2#2144476511yescharacteristic
367C2#2144780911yescharacteristic
368C2#2144784911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2586C2
socleC22×C61B(4,𝔽2)
prime radical#16840343C22
hypercenter#2586D61
hypocenterC61#12197
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2586

Complements

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

NH ≅ G/Ntype
4. #21443849C2semidirect
5. #21443825C2semidirect
6. #21443753C2semidirect
7. C61×#2586C2semidirect
179. #2586D61semidirect
211. C61#12197semidirect

Maximal subgroups

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

subgroupindex
#214468652
#214448212
#214447872
#214438492
#214438252
#214437532
C61×#25862
#1219761