Finite Group Databasebeta

← #30598397

Subgroups — #30598397

Order 15616.

706 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461685C211yesmaximal, characteristic
2#21461332C212yesmaximal
3#21461149C212yesmaximal
4#21461061C211yesmaximal, characteristic
5C2×#16840490C211yesmaximal, characteristic
6#16840779C2212yes—
7#16840765C2212yes—
8C2×#14519838—21no—
9#16840642—21no—
10#16840622—24no—
11#16840612—24no—
12#16840608—21no—
13#16840607—21no—
14#16840490—24no—
15#16840490—24no—
16C2×#14519777C411yescharacteristic
17C2×#14519775C411yescharacteristic
18C2×#14519775C2211yescharacteristic
19C2×#14519769—21no—
20C2×#14519767—21no—
21C2×#14519767—21no—
22C2×C4×Dic122—21no—
23C2×C4×Dic122C2211yescharacteristic
24C2×#14519742C411yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×C4×Q8×C61C411yescharacteristic
27C2×#11758217—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31#14519838—42no—
32C22⋊#92420—22no—
33C4×#92420—22no—
34C22×Dic122C2×C411yescharacteristic
35C22×Dic122C2×C411yescharacteristic
36C22×Dic122D411yescharacteristic
37#14519777—22no—
38#14519777—22no—
39#14519775—22no—
40#14519775—22no—
41#14519775—22no—
42#14519775D414yes—
43#14519769—28no—
44#14519767—28no—
45#14519767—28no—
46C4×Dic122—28no—
47C4×Dic122—22no—
48C4×Dic122—22no—
49#14519742—22no—
50#14519742—22no—
51#14519742—22no—
52#14519742D414yes—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61D411yescharacteristic
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196—21no—
59C2×#11758196—21no—
60C2×#11758196—21no—
61C2×#11758196—21no—
62C2×#11758196D411yescharacteristic
63C2×#11758196D411yescharacteristic
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2×C411yescharacteristic
67C2×C4×Dic61C2311yescharacteristic
68C22×Q8×C61C2×C411yescharacteristic
69C4×Q8×C61—22no—
70C4×Q8×C61—22no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C42×C61—21no—
74C2×C42×C61C2×C411yescharacteristic
75C2×Q8×C61—21no—
76C2×Q8×C61—42no—
77C2×Q8×C61C22⋊C412yes—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22⋊C411yescharacteristic
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—42no—
94C2×Dic122—42no—
95C2×Dic122C22⋊C412yes—
96C2×Dic122C22⋊C412yes—
97C2×Dic122SD1612yes—
98C2×Dic122Q1612yes—
99#11758217—42no—
100#11758217—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C4⋊C4×C61—24no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61C22⋊C412yes—
106C42×C61—24no—
107C42×C61—21no—
108C42×C61—21no—
109C4⋊Dic61—24no—
110C4⋊Dic61—24no—
111C4⋊Dic61—22no—
112#11758196—24no—
113#11758196—24no—
114#11758196—24no—
115#11758196—24no—
116#11758196—24no—
117#11758196—24no—
118#11758196—22no—
119#11758196—22no—
120C4×Dic61—24no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—24no—
124C4×Dic61C2×D412yes—
125C4×Dic61C2×D412yes—
126C23×C61C2×C22⋊C411yescharacteristic
127Q8×C61—42no—
128Q8×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61#10312yes—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150C2×Dic61#10312yes—
151C2×Dic61#12012yes—
152C2×Dic61#12012yes—
153C2×Dic61C2×SD1611yescharacteristic
154C2×Dic61C2×Q1611yescharacteristic
155C2×Dic61#13712yes—
156Dic122—24no—
157Dic122—24no—
158Dic122—24no—
159Dic122—42no—
160Dic122—42no—
161Dic122—42no—
162#92420—82no—
163#92420—82no—
164#8392—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#37911yescharacteristic
168C22×C61C2×#10311yescharacteristic
169C22×C61#41911yescharacteristic
170C4×C61—21no—
171C4×C61—22no—
172C4×C61—41no—
173C4×C61—42no—
174C4×C61—42no—
175C4×C61#41312yes—
176Dic61—22no—
177Dic61—22no—
178Dic61—41no—
179Dic61—42no—
180Dic61—42no—
181Dic61#44812yes—
182Dic61#45112yes—
183C2×#557—611no—
184#1801—611no—
185#1548—612no—
186#1487—612no—
187#1461—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#178511yescharacteristic
191C2×C61#178711yescharacteristic
192C2×C61#179611yescharacteristic
193#557—1224no—
194#557—1224no—
195C2×C4⋊Q8—611no—
196C2×C4⋊Q8—611no—
197C2×C4⋊Q8—611no—
198C2×#125—1221no—
199C2×#125—1221no—
200C2×#125—1221no—
201C2×C4×Q8—611no—
202C2×C4×Q8—611no—
203C2×C4×Q8—611no—
204C2×C4×Q8—1221no—
205C2×C4×Q8#692311yescharacteristic
206#431—612no—
207#423—612no—
208C2×#101—1221no—
209#343—1221no—
210#333—1224no—
211Q8⋊C8—1224no—
212#324—1221no—
213#324—1221no—
214C61#839211yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×Q8—611no—
217C22×Q8—611no—
218C22×Q8C2×#692311yescharacteristic
219C2×M16—1222no—
220C4⋊Q8—614no—
221C4⋊Q8—1222no—
222C4⋊Q8—1222no—
223C4⋊Q8—1222no—
224C4⋊Q8—1222no—
225C4⋊Q8—1222no—
226#125—1228no—
227#125—1228no—
228#125—1228no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8—614no—
232C4×Q8—1222no—
233C4×Q8—1222no—
234C4×Q8—1228no—
235C4×Q8—1222no—
236C4×Q8—1222no—
237C4×Q8—1222no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4C2×#692311yescharacteristic
251C2×C42—21no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42C2×#692311yescharacteristic
257C4⋊C8—1222no—
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260#101—2442no—
261C22⋊C8—1222no—
262C4×C8—1222no—
263C2×Q8—21no—
264C2×Q8—42no—
265C2×Q8—612no—
266C2×Q8—612no—
267C2×Q8—612no—
268C2×Q8—612no—
269C2×Q8—1222no—
270C2×Q8—1222no—
271C2×Q8—1221no—
272C2×Q8—1221no—
273C2×Q8—2442no—
274C2×Q8—2442no—
275C2×Q8C22⋊#692312yes—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287M16—2442no—
288M16—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C4⋊C4—24no—
292C4⋊C4—21no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—1224no—
297C4⋊C4—1224no—
298C4⋊C4—1224no—
299C4⋊C4—1224no—
300C4⋊C4—1224no—
301C4⋊C4—1224no—
302C4⋊C4—1224no—
303C4⋊C4—1224no—
304C4⋊C4C22⋊#692312yes—
305C42—24no—
306C42—21no—
307C42—21no—
308C42—612no—
309C42—612no—
310C42—1224no—
311C42—1224no—
312C42—1221no—
313C42—1221no—
314C23C2×C22⋊#692311yescharacteristic
315Q8—42no—
316Q8—42no—
317Q8—1224no—
318Q8—1224no—
319Q8—1224no—
320Q8—2442no—
321Q8—2442no—
322Q8—2442no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—612no—
337C2×C4—612no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—2441no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2441no—
347C2×C4#1451984012yes—
348C2×C4C2×C22⋊#692311yescharacteristic
349C2×C4C2×C22⋊#692311yescharacteristic
350C8—4882no—
351C8—4882no—
352C22—21no—
353C22—21no—
354C22#1684070311yescharacteristic
355C22C2×#1451984011yescharacteristic
356C22#1684075511yescharacteristic
357C4—21no—
358C4—22no—
359C4—42no—
360C4—41no—
361C4—42no—
362C4—612no—
363C4—612no—
364C4—1222no—
365C4—1222no—
366C4—2442no—
367C4—2442no—
368C4—2441no—
369C4#1684074812yes—
370C2—21no—
371C2—21no—
372C2#2146165511yescharacteristic
373C2#2146165811yescharacteristic
374C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61#379
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#8392
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
214. C61#8392semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214613322
#214611492
#214610612
C2×#168404902
#839261