Finite Group Databasebeta

← #29568490

Subgroups — #29568490

Order 15616.

464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454187C211yesmaximal, characteristic
2#21445671C211yesmaximal, characteristic, complemented
3#21445667C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443639C211yesmaximal, characteristic
6#21443639C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic, complemented
8C2×#14519772—21no—
9C2×#14519706—21no—
10C2×#14519706—21no—
11C2×#14519687—21no—
12C2×C8×Dic61—21no—
13#16839664C2211yescharacteristic
14#16839663C411yescharacteristic
15#16839663C411yescharacteristic
16#16839661C411yescharacteristic
17#16839658C411yescharacteristic
18#16839654—21no—
19#16839652—21no—
20#16839651—21no—
21C42×Dic61C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30#14519772—42no—
31#14519772—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519706—24no—
48#14519706—24no—
49#14519687—42no—
50C8×Dic61—42no—
51#14519684—21no—
52#14519684—21no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—41no—
74C2×D244—41no—
75C2×C8×C61—22no—
76C2×C8×C61—22no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61—41no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—41no—
97#11758196—42no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C4×Dic61D812yes—
106C4×Dic61SD1612yes—
107C2×#92418—22no—
108C2×#92418—22no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61C2×C22⋊C411yescharacteristic
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
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#13111yescharacteristic
134C2×C4×C61#13111yescharacteristic
135C2×C4×C61C2×D811yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61#13711yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61#10212yes—
151C2×Dic61#10212yes—
152C2×Dic61#10412yes—
153C2×Dic61#10412yes—
154D244—81no—
155D244—81no—
156C8×C61—42no—
157C8×C61—42no—
158#92418—42no—
159#92418—42no—
160#7686—611nomaximal, Sylow
161C22×C61#40811yescharacteristic
162C22×C61#41011yescharacteristic
163C22×C61#41311yescharacteristic
164C22×C61C2×#10211yescharacteristic
165C22×C61#41711yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—81no—
182C4×C61—81no—
183Dic61—22no—
184Dic61—22no—
185Dic61—22no—
186Dic61—22no—
187Dic61—81no—
188#2860—611no—
189#1767—611no—
190C4×C4⋊C8—611no—
191#1271—611no—
192#1271D6111yescharacteristic, complemented
193#1270—611no—
194#1270—611no—
195C2×C61#147311yescharacteristic
196C2×C61#148311yescharacteristic
197C2×C61#149211yescharacteristic
198C2×C61#150211yescharacteristic
199C2×C61#150911yescharacteristic
200C2×C61#152411yescharacteristic
201C2×C61#154711yescharacteristic
202D61—161no—
203C2×#126—1221no—
204C2×C4⋊C8—1221no—
205C2×C4⋊C8—1221no—
206C2×#97—1221no—
207C2×C4×C8—1221no—
208#390—611no—
209#390—611no—
210#390—611no—
211#389—611no—
212#389—611no—
213#389C2×D6111yescharacteristic
214#388—1221no—
215#388—1221no—
216#388—1221no—
217C43—611no—
218#336—611no—
219#336—611no—
220#336C2×D6111yescharacteristic
221#336C2×D6111yescharacteristic
222C61#768611yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—1221no—
227C22×C8—1221no—
228#126—2442no—
229#126—2442no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4C4×D6111yescharacteristic
235C2×C4⋊C4C4×D6111yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42C22×D6111yescharacteristic
249C4⋊C8—1224no—
250C4⋊C8—1224no—
251#97—2442no—
252C4×C8—2442no—
253#95—21no—
254#95—1221no—
255#95—1221no—
256C24—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—2441no—
260C2×D4—2441no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4D4×D6111yescharacteristic
270C22×C4D4×D6111yescharacteristic
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—1222no—
278C2×C8—1222no—
279C2×C8—2441no—
280C2×C8—2441no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C22⋊C4—2442no—
292C22⋊C4—2442no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C42—41no—
300C42—612no—
301C42—612no—
302C42—1222no—
303C42—1222no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C42—2441no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23C22⋊C4×D6111yescharacteristic
317D4—4881no—
318D4—4881no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—612no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4#1451978311yescharacteristic
347C2×C4#1451978511yescharacteristic
348C2×C4D8×D6111yescharacteristic
349C2×C4SD16×D6111yescharacteristic
350C2×C4#1451980411yescharacteristic
351C2×C4#1451980911yescharacteristic
352C8—42no—
353C8—42no—
354C8—2442no—
355C8—2442no—
356C22—4881no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22#1683972711yescharacteristic
364C22#1683973411yescharacteristic
365C22#1683974511yescharacteristic
366C22#102×D6111yescharacteristic
367C22#1683976211yescharacteristic
368C22#104×D6111yescharacteristic
369C22#104×D6111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—1222no—
379C4—1222no—
380C4—1222no—
381C4—1222no—
382C4—4881no—
383C2—9761no—
384C2#2144418711yescharacteristic
385C2#2144423111yescharacteristic
386C2#2144426811yescharacteristic
387C2#2144431211yescharacteristic
388C2#2144434311yescharacteristic
389C2#2144440611yescharacteristic
390C2#2144449511yescharacteristic
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#7686
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. #21445667C2semidirect
4. #21443642C2semidirect
7. C61×#1271C2semidirect
192. #1271D61semidirect
222. C61#7686semidirect

Maximal subgroups

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

subgroupindex
#214541872
#214456712
#214456672
#214436422
#214436392
C61×#12712
#768661