Finite Group Databasebeta

← #29590323

Subgroups — #29590323

Order 15616.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451631C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic, complemented
5#21443847C211yesmaximal, characteristic, complemented
6#21443845C211yesmaximal, characteristic, complemented
7C61×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519753C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11C22⋊C8×D61—21no—
12#16839702C411yescharacteristic
13#16839701C2211yescharacteristic
14#16839696—21no—
15#16839693—21no—
16#16839681C411yescharacteristic
17#16839633—21no—
18#16839624—21no—
19#16839621C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#395C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758189—41no—
32M16×D61—24no—
33M16×D61—42no—
34C2×C8×D61—41no—
35C2×C8×D61—41no—
36#14519753—41no—
37#14519753—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C411yescharacteristic
44C2×#11758196D411yescharacteristic
45C4⋊C4×D61—41no—
46C4⋊C4×D61—41no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C2×M16×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61C2311yescharacteristic
61C22⋊C8×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—41no—
66C2×Q8×C61—81no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85C2×C4×D61—81no—
86C2×C4×D61SD1612yes—
87C2×C4×D61Q1612yes—
88M16×C61—22no—
89M16×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—81no—
94#11758198—41no—
95#11758198—41no—
96#11758198—42no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—42no—
102#11758196—81no—
103#11758196—81no—
104#11758194—22no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108#11758189—44no—
109C8×D61—44no—
110C8×D61—82no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—41no—
113C22×D61—41no—
114C22×D61#9911yescharacteristic
115C22×D61#9911yescharacteristic
116C22×D61#10312yes—
117C22×D61#10412yes—
118Q8×C61—82no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C2×SD1611yescharacteristic
132C2×C4×C61C2×Q1611yescharacteristic
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#10312yes—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—42no—
150C4×D61—81no—
151C4×D61—81no—
152C4×D61—81no—
153C8×C61—42no—
154C8×C61—81no—
155#92418—42no—
156#92418—81no—
157#11722—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61C2×#9911yescharacteristic
161C22×C61C2×#10311yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—42no—
168C2×D61—42no—
169C2×D61#32812yes—
170C2×D61#32812yes—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—81no—
176C4×C61—81no—
177Dic61—22no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181Dic61—81no—
182#2627—611no—
183C2×#343—611no—
184C2×#324—611no—
185#1354—611no—
186#1354D6111yescharacteristic, complemented
187#1353—611no—
188#1353—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61C2×#32811yescharacteristic
192C2×C61#212111yescharacteristic
193C2×C61#213311yescharacteristic
194D61—22no—
195D61—22no—
196C22×M16—1221no—
197C2×C22⋊Q8—611no—
198C22×C4⋊C4—611no—
199C2×C22⋊C8—1221no—
200#400—611no—
201#400—611no—
202#398—1221no—
203#398—1221no—
204#395—611no—
205#395C2×D6111yescharacteristic
206#385—1221no—
207#381—1221no—
208#380—611no—
209#343—611no—
210#343—1221no—
211#343C2×D6111yescharacteristic
212#324—611no—
213#324—1221no—
214#324C2×D6111yescharacteristic
215C61#1172211yescharacteristic, complemented, Sylow
216C22×Q8C4×D6111yescharacteristic
217C23×C4—611no—
218C23×C4—611no—
219C23×C4—611no—
220C2×M16—21no—
221C2×M16—1224no—
222C2×M16—1221no—
223C2×M16—2441no—
224C2×M16—2442no—
225C22×C8—2441no—
226C22×C8—2441no—
227C22⋊Q8—2441no—
228C22⋊Q8—2441no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—2441no—
238C2×C4⋊C4—2441no—
239C2×C4⋊C4C22×D6111yescharacteristic
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C22⋊C8—21no—
243C22⋊C8—1221no—
244C22⋊C8—2441no—
245#95—21no—
246#95—611no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95C4×D6111yescharacteristic
253C24—611no—
254C2×Q8—41no—
255C2×Q8—81no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—611no—
259C22×C4—612no—
260C22×C4—612no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1222no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—4881no—
273C22×C4—4881no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4D4×D6111yescharacteristic
277M16—22no—
278M16—41no—
279M16—1222no—
280M16—2444no—
281M16—2441no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—4882no—
285C2×C8—2444no—
286C2×C8—2441no—
287C2×C8—2441no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—4881no—
291C4⋊C4—4881no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C23—611no—
301C23—611no—
302C23—612no—
303C23—612no—
304C23—2441no—
305C23—2441no—
306C23C22⋊C4×D6111yescharacteristic
307Q8—82no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—612no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4SD16×D6111yescharacteristic
341C2×C4Q16×D6111yescharacteristic
342C8—42no—
343C8—81no—
344C8—4881no—
345C8—2442no—
346C22—21no—
347C22—21no—
348C22—612no—
349C22—612no—
350C22—1221no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—2442no—
355C22—2442no—
356C22#99×D6111yescharacteristic
357C22#103×D6111yescharacteristic
358C22#104×D6111yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—1222no—
366C4—4881no—
367C4—4881no—
368C4—2441no—
369C4—2441no—
370C2—21no—
371C2—21no—
372C2—1222no—
373C2—1222no—
374C2#328×D6111yescharacteristic
375C2#2144746211yescharacteristic
376C2#2144750711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1354C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1354D61
hypocenterC61#11722
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #21443849C2semidirect
5. #21443847C2semidirect
6. #21443845C2semidirect
7. C61×#1354C2semidirect
186. #1354D61semidirect
215. C61#11722semidirect

Maximal subgroups

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

subgroupindex
#214516312
#343×D612
#324×D612
#214438492
#214438472
#214438452
C61×#13542
#1172261