Finite Group Databasebeta

← #29568243

Subgroups — #29568243

Order 15616.

510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 101 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#21448277C211yesmaximal, characteristic
2#21445671C211yesmaximal, characteristic, complemented
3#21445566C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519739C411yescharacteristic
9C2×#14519735—21no—
10C2×#14519706—21no—
11C2×#14519687—21no—
12C2×#14519687—21no—
13#16839664C2211yescharacteristic
14#16839663C411yescharacteristic
15#16839661C411yescharacteristic
16#16839654—21no—
17#16839652—21no—
18C4⋊C4×Dic61C411yescharacteristic
19#16839609—21no—
20C42×Dic61C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519739—22no—
32#14519739—22no—
33#14519735—42no—
34#14519735—42no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—24no—
50#14519687—24no—
51#14519687—42no—
52#14519684—21no—
53#14519684—21no—
54C22×C8×C61—21no—
55C22×C8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60#95×C61—21no—
61C23×D61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C2×D244—21no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244M1612yes—
76C2×C4×D61—24no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C8×C61—22no—
80C2×C8×C61—22no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61M1612yes—
90C42×C61—41no—
91#11758198—24no—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—22no—
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61—42no—
110C2×#92418—22no—
111C2×#92418—22no—
112C2×#92418—41no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—22no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61C2×M1611yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#10412yes—
156C2×Dic61#10412yes—
157D244—42no—
158D244—42no—
159C4×D61—48no—
160C8×C61—42no—
161C8×C61—42no—
162#92418—42no—
163#92418—42no—
164#7628—611nomaximal, Sylow
165C22×C61#40711yescharacteristic
166C22×C61#41011yescharacteristic
167C22×C61#41311yescharacteristic
168C22×C61#41711yescharacteristic
169C22×C61#41811yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C22×C61C2×#10411yescharacteristic
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—42no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—22no—
189Dic61—41no—
190Dic61—41no—
191Dic61—81no—
192#2293—611no—
193#1767—611no—
194#1745—611no—
195#1271—611no—
196#1271D6111yescharacteristic, complemented
197#1270—611no—
198#1270—611no—
199C2×C61#146411yescharacteristic
200C2×C61#148911yescharacteristic
201C2×C61#149011yescharacteristic
202C2×C61#150511yescharacteristic
203C2×C61#150911yescharacteristic
204C2×C61#152411yescharacteristic
205C2×C61#155711yescharacteristic
206D61—82no—
207C2×C4×D4—611no—
208C2×#117—1221no—
209C2×C4⋊C8—1221no—
210C2×#97—1221no—
211C2×#97—1221no—
212#390—611no—
213#390—611no—
214#389—611no—
215#389C2×D6111yescharacteristic
216#388—1221no—
217#388—1221no—
218C4×C4⋊C4—611no—
219C4×C22⋊C4—1221no—
220C43—611no—
221#336—611no—
222#336—611no—
223#336—1221no—
224#336C2×D6111yescharacteristic
225#336C2×D6111yescharacteristic
226C61#762811yescharacteristic, complemented, Sylow
227C22×D4—611no—
228C23×C4—1221no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—1221no—
232C22×C8—1221no—
233C4×D4—1222no—
234C4×D4—1222no—
235#117—2442no—
236#117—2442no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C4⋊C4C4×D6111yescharacteristic
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—1221no—
254C2×C42C22×D6111yescharacteristic
255C4⋊C8—1224no—
256#97—1224no—
257#97—2442no—
258#95—21no—
259#95—1221no—
260#95—1221no—
261C24—1221no—
262C2×D4—612no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4—2441no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1224no—
273C22×C4—1221no—
274C22×C4—2442no—
275C22×C4—2442no—
276C22×C4C2×C4×D6111yescharacteristic
277C22×C4D4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—1222no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C4⋊C4#1175818912yes—
298C22⋊C4—1224no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C42—41no—
306C42—1222no—
307C42—1222no—
308C42—1221no—
309C42—1221no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42—2441no—
315C42—2442no—
316C23—1222no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23C22⋊C4×D6111yescharacteristic
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2448no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4M16×D6111yescharacteristic
355C2×C4C2×#1175818911yescharacteristic
356C2×C4#1451980111yescharacteristic
357C2×C4#1451980411yescharacteristic
358C2×C4#1451980411yescharacteristic
359C2×C4#1451980911yescharacteristic
360C8—42no—
361C8—42no—
362C8—2442no—
363C8—2442no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—2442no—
369C22—2442no—
370C22—2442no—
371C22#1683972411yescharacteristic
372C22#1683973411yescharacteristic
373C22#1683974511yescharacteristic
374C22#1683976211yescharacteristic
375C22#1683976511yescharacteristic
376C22#104×D6111yescharacteristic
377C22#104×D6111yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—81no—
386C4—1222no—
387C4—1222no—
388C4—4881no—
389C4—2441no—
390C4—2441no—
391C2—4882no—
392C2#2144415211yescharacteristic
393C2#2144425711yescharacteristic
394C2#2144426011yescharacteristic
395C2#2144432511yescharacteristic
396C2#2144434311yescharacteristic
397C2#2144440611yescharacteristic
398C2#2144454011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7628
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21445671C2semidirect
3. #21445566C2semidirect
4. #21443642C2semidirect
7. C61×#1271C2semidirect
196. #1271D61semidirect
226. C61#7628semidirect

Maximal subgroups

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

subgroupindex
#214482772
#214456712
#214455662
#214436422
#214436392
C61×#12712
#762861