Finite Group Databasebeta

← #29591054

Subgroups — #29591054

Order 15616.

440 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 77 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#21450725C211yesmaximal, characteristic
2#21445814C211yesmaximal, characteristic, complemented
3#21444141C211yesmaximal, characteristic, complemented
4#21443825C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic
6#21443821C211yesmaximal, characteristic
7C61×#1346C211yesmaximal, characteristic, complemented
8C2×#14519755—21no—
9C2×#14519742C2211yescharacteristic
10C2×#14519739C411yescharacteristic
11#16839812—21no—
12#16839785—21no—
13C2×#14519695—21no—
14#16839693C411yescharacteristic
15#16839680C411yescharacteristic
16#16839679C2211yescharacteristic
17#16839652—21no—
18#16839651—21no—
19#16839626C411yescharacteristic
20#16839621—21no—
21#16839531C2211yescharacteristic
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#398C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758194—21no—
31#14519755—42no—
32#14519755—42no—
33#14519742—41no—
34#14519742—41no—
35#14519739—41no—
36#14519739—41no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196C2×C411yescharacteristic
40C2×#11758196D411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50#14519706—41no—
51#14519706—41no—
52#14519695—42no—
53C22⋊#92418—21no—
54C8×Dic61—41no—
55#14519684—21no—
56#14519684—21no—
57#14519684C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61—21no—
64#95×C61C2×C411yescharacteristic
65C23×D61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C2×D244—41no—
77C2×D244—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122D812yes—
84C2×Dic122SD1612yes—
85M16×C61—41no—
86M16×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100#11758196—41no—
101#11758196—41no—
102#11758196—42no—
103#11758196—42no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110#11758194—41no—
111#11758194—41no—
112C2×#92418—41no—
113C2×#92418—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—22no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
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×C61C2×D811yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61#9911yescharacteristic
147C2×Dic61#9911yescharacteristic
148C2×Dic61#10212yes—
149C2×Dic61#10212yes—
150D244—42no—
151D244—42no—
152C4×D61—84no—
153Dic122—42no—
154Dic122—42no—
155C8×C61—81no—
156C8×C61—81no—
157#92418—81no—
158#92418—81no—
159#11879—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10211yescharacteristic
164C22×C61#42111yescharacteristic
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—81no—
177C4×C61—81no—
178Dic61—21no—
179Dic61—21no—
180Dic61—22no—
181Dic61—22no—
182Dic61—41no—
183Dic61—81no—
184#2536—611no—
185#1801—611no—
186#1461—611no—
187#1346—611no—
188#1346D6111yescharacteristic, complemented
189#1345—611no—
190#1345—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#151911yescharacteristic
194C2×C61#212011yescharacteristic
195C2×C61#213311yescharacteristic
196D61—82no—
197C2×C22⋊Q8—1221no—
198C2×C4×Q8—611no—
199C2×C4×D4—611no—
200#431—1221no—
201#423—1221no—
202C2×#101—1221no—
203#398—611no—
204#398C2×D6111yescharacteristic
205#394—611no—
206#394—611no—
207#388—1221no—
208#388—1221no—
209#382—611no—
210#380—1221no—
211#343—611no—
212#343C2×D6111yescharacteristic
213#324—611no—
214#324—1221no—
215#324C2×D6111yescharacteristic
216C61#1187911yescharacteristic, complemented, Sylow
217C22×Q8—611no—
218C22×D4—611no—
219C23×C4—1221no—
220C2×M16—21no—
221C2×M16—1221no—
222C22⋊Q8—2442no—
223C22⋊Q8—2442no—
224C4×Q8—2441no—
225C4×Q8—2441no—
226C4×D4—2441no—
227C4×D4—2441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C4×D6111yescharacteristic
234C2×C4⋊C4C22×D6111yescharacteristic
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C4⋊C8—2441no—
244C4⋊C8—2441no—
245C4⋊C8—2441no—
246#101—2442no—
247C22⋊C8—21no—
248C22⋊C8—1221no—
249C4×C8—2441no—
250#95—21no—
251#95—611no—
252#95—1221no—
253#95—1221no—
254#95C4×D6111yescharacteristic
255C24—1221no—
256C2×Q8—612no—
257C2×Q8—612no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×D4—2441no—
261C2×D4—2442no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—2442no—
270C22×C4—2442no—
271C22×C4—2442no—
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4D4×D6111yescharacteristic
275M16—41no—
276M16—41no—
277M16—2441no—
278M16—2441no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—2441no—
282C2×C8—2441no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C23—1222no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23—2441no—
311C23C22⋊C4×D6111yescharacteristic
312Q8—2442no—
313Q8—2442no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
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—611no—
329C2×C4—611no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4884no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4D8×D6111yescharacteristic
344C2×C4SD16×D6111yescharacteristic
345C8—81no—
346C8—81no—
347C8—4881no—
348C8—4881no—
349C22—21no—
350C22—21no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—2442no—
356C22—2442no—
357C22—2442no—
358C22#99×D6111yescharacteristic
359C22#102×D6111yescharacteristic
360C22#1683977711yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—1222no—
368C4—1222no—
369C4—1221no—
370C4—1221no—
371C4—4881no—
372C4—2441no—
373C2—21no—
374C2—21no—
375C2—4882no—
376C2#2144438511yescharacteristic
377C2#2144745911yescharacteristic
378C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1346C2
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1346D61
hypocenterC61#11879
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
2. #21445814C2semidirect
3. #21444141C2semidirect
4. #21443825C2semidirect
7. C61×#1346C2semidirect
188. #1346D61semidirect
216. C61#11879semidirect

Maximal subgroups

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

subgroupindex
#214507252
#214458142
#214441412
#214438252
#214438232
#214438212
C61×#13462
#1187961