Finite Group Databasebeta

← #29598698

Subgroups — #29598698

Order 15616.

420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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#21451029C211yesmaximal, characteristic
2#21445813C211yesmaximal, characteristic
3#101×Dic61C211yesmaximal, characteristic
4#21443946C211yesmaximal, characteristic
5#21443945C211yesmaximal, characteristic
6#21443945C211yesmaximal, characteristic
7C61×#1394C211yesmaximal, characteristic
8C2×#14519776C411yescharacteristic
9C2×Q8×Dic61C2211yescharacteristic
10#16839785—21no—
11C2×#14519696C2211yescharacteristic
12C2×#14519696C2211yescharacteristic
13M16×Dic61—21no—
14#16839683—21no—
15#16839683—21no—
16#16839669C2211yescharacteristic
17#16839659—21no—
18#16839659—21no—
19#16839632C411yescharacteristic
20#16839631C411yescharacteristic
21C4×#11758196C411yescharacteristic
22#16839530—21no—
23#16839530—21no—
24C2×#101×C61C2211yescharacteristic
25C2×#101×C61C2211yescharacteristic
26C61×#391C2211yescharacteristic
27C22×Dic122—21no—
28C2×#11758194—21no—
29C2×#11758194—21no—
30#14519776—41no—
31#14519776—41no—
32Q8×Dic61—41no—
33Q8×Dic61—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519706—41no—
49#14519706—41no—
50#14519696—21no—
51#14519696—21no—
52#14519696—21no—
53#14519696Q812yescomplemented
54#14519687—41no—
55C8×Dic61—41no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59C22×Q8×C61C2311yescharacteristic
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61C2×C411yescharacteristic
64#101×C61—21no—
65#101×C61—21no—
66#101×C61—21no—
67#101×C61Q812yescomplemented
68#95×C61—21no—
69#95×C61—21no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61C2×Q811yescharacteristic
73C2×Q8×C61C2×Q811yescharacteristic
74C2×Q8×C61#4111yescharacteristic
75C2×Q8×C61#4111yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C2×Dic122—42no—
88C2×Dic122—81no—
89C2×Dic122—81no—
90M16×C61—22no—
91M16×C61—41no—
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—41no—
97C42×C61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—81no—
103C4⋊Dic61—81no—
104#11758196—24no—
105#11758196—41no—
106#11758196—41no—
107#11758196—81no—
108#11758196—81no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—41no—
116#11758194—22no—
117#11758194—41no—
118#11758194—41no—
119#11758194—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123Q8×C61—41no—
124Q8×C61—41no—
125Q8×C61—41no—
126Q8×C61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C4×Q811yescharacteristic
140C2×C4×C61C4×Q811yescharacteristic
141C2×C4×C61C22⋊Q811yescharacteristic
142C2×C4×C61C22⋊Q811yescharacteristic
143C2×C4×C61#12411yescharacteristic
144C2×C4×C61C4⋊Q811yescharacteristic
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61#9911yescharacteristic
159C2×Dic61#9911yescharacteristic
160Dic122—84no—
161C8×C61—42no—
162C8×C61—81no—
163#92418—42no—
164#92418—81no—
165#13302—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61#39111yescharacteristic
169C22×C61C2×#9911yescharacteristic
170C22×C61#41011yescharacteristic
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—81no—
179Dic61—21no—
180Dic61—42no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61—81no—
185Dic61#35612yes—
186#2567—611no—
187#1801—611no—
188C4×#101—611no—
189#1394—611no—
190#1394—611no—
191#1394—611no—
192#1394D6111yescharacteristic
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#199611yescharacteristic
196C2×C61C2×#35611yescharacteristic
197C2×C61#213411yescharacteristic
198C2×C4⋊Q8—611no—
199C2×C4×Q8—611no—
200#423—1221no—
201C2×#101—611no—
202C2×#101—611no—
203C2×#101C2×D6111yescharacteristic
204C2×#101C2×D6111yescharacteristic
205C4×M16—1221no—
206#395—1221no—
207#395—1221no—
208#391—611no—
209#391C2×D6111yescharacteristic
210#389—1221no—
211#389—1221no—
212#384—611no—
213#384—611no—
214C4×C4⋊C4—611no—
215#343—1221no—
216#343—1221no—
217C61#1330211yescharacteristic, complemented, Sylow
218C22×Q8—1221no—
219C22×Q8C22×D6111yescharacteristic
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—1221no—
223C2×M16—1221no—
224C4⋊Q8—2441no—
225C4⋊Q8—2441no—
226C4×Q8—2441no—
227C4×Q8—2441no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4C4×D6111yescharacteristic
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42C4×D6111yescharacteristic
244C4⋊C8—2441no—
245C4⋊C8—2441no—
246#101—21no—
247#101—21no—
248#101—21no—
249#101—612no—
250#101—1221no—
251#101—1221no—
252#101—1221no—
253#101Dic12212yescomplemented
254#97—2441no—
255C4×C8—2441no—
256#95—21no—
257#95—21no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—4881no—
264C2×Q8—4881no—
265C2×Q8—2442no—
266C2×Q8C2×Dic12211yescharacteristic
267C2×Q8#1175822211yescharacteristic
268C2×Q8#1175822411yescharacteristic
269C2×Q8Q8×D6111yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4C2×C4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281M16—22no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—1222no—
286M16—2441no—
287M16—2441no—
288M16—2441no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—41no—
294C4⋊C4—1224no—
295C4⋊C4—4881no—
296C4⋊C4—4881no—
297C4⋊C4—4881no—
298C4⋊C4—4881no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C42—41no—
306C42—1221no—
307C42—1221no—
308C42—1221no—
309C42—1221no—
310C42—1221no—
311C42—1221no—
312C42—2441no—
313C23C22⋊C4×D6111yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—41no—
317Q8—41no—
318Q8—4884no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4#1451974211yescharacteristic
347C2×C4C4×Dic12211yescharacteristic
348C2×C4#1451975411yescharacteristic
349C2×C4#1451975511yescharacteristic
350C2×C4#1451976311yescharacteristic
351C2×C4#1451977611yescharacteristic
352C8—42no—
353C8—81no—
354C8—4881no—
355C8—2442no—
356C22—21no—
357C22—21no—
358C22#1683966611yescharacteristic
359C22#99×D6111yescharacteristic
360C22#1683973411yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—612no—
370C4—1221no—
371C4—4881no—
372C4—2442no—
373C4—2441no—
374C4—2441no—
375C4—2441no—
376C2—21no—
377C2—21no—
378C2#2144680211yescharacteristic
379C2#356×D6111yescharacteristic
380C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Q8×C61C23
hypercenter#1394D61
hypocenterC61#13302
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
53. #14519696Q8semidirect
67. #101×C61Q8semidirect
217. C61#13302semidirect
253. #101Dic122semidirect

Maximal subgroups

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

subgroupindex
#214510292
#214458132
#101×Dic612
#214439462
#214439452
C61×#13942
#1330261