Finite Group Databasebeta

← #29592689

Subgroups — #29592689

Order 15616.

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

normal subgroups only

This group has 434 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#21446860C211yesmaximal, characteristic
2#21444855C211yesmaximal, characteristic, complemented
3#21444821C211yesmaximal, characteristic, complemented
4#21443846C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443751C211yesmaximal, characteristic, complemented
7C61×#2593C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9#16840343C2211yescharacteristic
10#16840080—21no—
11#16840075—21no—
12C2×#14519705—21no—
13#16839531C2211yescharacteristic
14#16839495—21no—
15#16839495—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400C2211yescharacteristic
19C61×#398C2211yescharacteristic
20C61×#394—21no—
21C61×#390C2211yescharacteristic
22C61×#388—21no—
23C61×#388—21no—
24C61×#388—21no—
25C61×#388—21no—
26C4×C4⋊C4×C61—21no—
27C2×#11758222—21no—
28#14519803—42no—
29#14519803—42no—
30C2×#11758200—41no—
31C2×#11758199—41no—
32C2×#11758194—21no—
33#14519757—41no—
34#14519752—41no—
35#14519751—21no—
36#14519751—21no—
37#14519710—41no—
38#14519708—41no—
39#14519705—42no—
40#14519697—41no—
41#14519697—41no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22×D4×C61D411yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61—21no—
58C2×C42×C61D411yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61D411yescharacteristic
64#95×C61D411yescharacteristic
65C24×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—41no—
69C2×D4×C61—41no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—41no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82#11758222—41no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×C4×D61—41no—
87C2×Dic122—21no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—81no—
99C22⋊C4×C61—81no—
100C42×C61—42no—
101C42×C61—41no—
102C42×C61—81no—
103#11758200—44no—
104#11758199—44no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109#11758194—22no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61#12011yescharacteristic
122C22×D61—41no—
123D4×C61—42no—
124D4×C61—81no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
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—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C22⋊D61—81no—
149C22⋊D61—81no—
150C2×Dic61—41no—
151D244—41no—
152D244—41no—
153D244—81no—
154D244—81no—
155C4×D61—81no—
156C4×D61—81no—
157Dic122—41no—
158Dic122—41no—
159#92418—42no—
160#92418—81no—
161#92418—81no—
162#12196—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#44911yescharacteristic
173C22×C61#45311yescharacteristic
174C22×C61B(4,𝔽2)11yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—42no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61—81no—
185C4×C61—81no—
186C4×C61—81no—
187Dic61—81no—
188#2593D6111yescharacteristic, complemented
189#2006—611no—
190#1616—611no—
191#1610—611no—
192#1353—611no—
193#1346—611no—
194#1318—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—161no—
198C2×C61#160011yescharacteristic
199C2×C61#219811yescharacteristic
200C2×C61#220411yescharacteristic
201D61—161no—
202C2×AGL(1,ℤ/8)—1221no—
203#537—611no—
204#481—1221no—
205#480—1221no—
206C2×#104—1221no—
207#400C2×D6111yescharacteristic
208#398C2×D6111yescharacteristic
209#394—21no—
210#390C2×D6111yescharacteristic
211#388—21no—
212#388—21no—
213#388—21no—
214#388—21no—
215C4×C4⋊C4—21no—
216#343—611no—
217#327—1221no—
218#327—1221no—
219#324—611no—
220#324—611no—
221C61#1219611yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C22×D4C22⋊D6111yescharacteristic
224AGL(1,ℤ/8)—2442no—
225AGL(1,ℤ/8)—2442no—
226C2×SD16—2441no—
227C2×D8—2441no—
228C2×M16—1221no—
229C22⋊Q8—2441no—
230#121—1221no—
231#121—1221no—
232#121—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C22⋊D6111yescharacteristic
236C2×C4⋊C4C22⋊D6111yescharacteristic
237C2×C4⋊C4C22×D6111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42C22⋊D6111yescharacteristic
247#107—2441no—
248#106—2441no—
249#104—2442no—
250#102—2441no—
251#102—2441no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95C22⋊D6111yescharacteristic
259#95C22⋊D6111yescharacteristic
260C24—21no—
261#41—2441no—
262#41—2441no—
263#41—2441no—
264#41—2441no—
265C2×Q8—1221no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2441no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—2441no—
280C22×C4C2×C22⋊D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282C22×C4C2×C22⋊D6111yescharacteristic
283SD16—2444no—
284D8—2444no—
285M16—1222no—
286M16—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C42—41no—
307C42—42no—
308C42—81no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—2441no—
317C23#1451974611yescharacteristic
318Q8—2441no—
319Q8—2441no—
320D4—42no—
321D4—81no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—4881no—
326D4—2441no—
327D4—2441no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—4881no—
350C2×C4—4881no—
351C2×C4—2441no—
352C2×C4#1451979711yescharacteristic
353C2×C4#1451980211yescharacteristic
354C8—4881no—
355C8—4881no—
356C8—2442no—
357C22—21no—
358C22—21no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22#1683990711yescharacteristic
370C22#1683993011yescharacteristic
371C22#1683994911yescharacteristic
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—4881no—
382C2—21no—
383C2—21no—
384C2—161no—
385C2—9761no—
386C2#2144476511yescharacteristic
387C2#2144781511yescharacteristic
388C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2593C2
socleC22×C61B(4,𝔽2)
prime radical#21446860C2
hypercenter#2593D61
hypocenterC61#12196
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2593

Complements

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

NH ≅ G/Ntype
2. #21444855C2semidirect
3. #21444821C2semidirect
4. #21443846C2semidirect
5. #21443825C2semidirect
6. #21443751C2semidirect
7. C61×#2593C2semidirect
188. #2593D61semidirect
221. C61#12196semidirect

Maximal subgroups

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

subgroupindex
#214468602
#214448552
#214448212
#214438462
#214438252
#214437512
C61×#25932
#1219661