Finite Group Databasebeta

← #30595708

Subgroups — #30595708

Order 15616.

568 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 124 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#21461675C211yesmaximal, characteristic
2C2×#16840628C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460639C212yesmaximal, complemented
5#21454167C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×#14519844—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519775C411yescharacteristic
13C2×#14519756C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839669C2211yescharacteristic
16#16839667C2211yescharacteristic
17#16839657—21no—
18#16839657—21no—
19#16839631C411yescharacteristic
20#16839620—21no—
21#16839620—21no—
22C2×C22⋊Q8×C61C411yescharacteristic
23C22×#92420—24no—
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—42no—
27C22×#92420—42no—
28#14519844—42no—
29C22⋊#92420—42no—
30C22×Dic122C2×C411yescharacteristic
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519775—42no—
34#14519756—42no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×Q8×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C22⋊Q8×C61—42no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×Q8×C61—22no—
59C2×Q8×C61—41no—
60C2×Q8×C61—41no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61SD1612yes—
77C22×Dic61SD1612yes—
78C22×Dic61Q1612yes—
79C22×Dic61Q1612yes—
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×Dic122—22no—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×#92420—24no—
86C2×#92420—42no—
87C2×#92420—48no—
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—42no—
95C22⋊Dic61—42no—
96C4⋊Dic61—41no—
97#11758196—42no—
98#11758196—42no—
99#11758196—42no—
100#11758196—42no—
101#11758196—42no—
102C4×Dic61—22no—
103C4×Dic61—22no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61#10012yes—
111C23×C61#10312yes—
112C23×C61#10312yes—
113C23×C61C2×C22⋊C411yescharacteristic
114Q8×C61—82no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—44no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#13112yes—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—24no—
135C2×Dic61—24no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9912yes—
145C2×Dic61#10312yes—
146C2×Dic61#10312yes—
147C2×Dic61#10412yes—
148C2×Dic61C2×SD1611yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61C2×Q1611yescharacteristic
151C2×Dic61C2×Q1611yescharacteristic
152Dic122—82no—
153#92420—44no—
154#92420—82no—
155#7667—611nomaximal, Sylow
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61#33314yes—
163C22×C61#40811yescharacteristic
164C22×C61C2×#9911yescharacteristic
165C22×C61C2×#10011yescharacteristic
166C22×C61C2×#10311yescharacteristic
167C22×C61C2×#10311yescharacteristic
168C22×C61C2×#10411yescharacteristic
169C22×C61#42111yescharacteristic
170C4×C61—22no—
171C4×C61—41no—
172C4×C61—81no—
173C4×C61—81no—
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—22no—
178Dic61—21no—
179Dic61—81no—
180Dic61—81no—
181Dic61#32814yes—
182#2857—611no—
183#1797—611no—
184C2×#336—611no—
185#1272—612no—
186#1272—612no—
187C2×C61—24no—
188C2×C61#147111yescharacteristic
189C2×C61#148111yescharacteristic
190C2×C61#149311yescharacteristic
191C2×C61C2×#32811yescharacteristic
192C2×C61#152011yescharacteristic
193C2×C61#153011yescharacteristic
194C2×C61C2×#33311yescharacteristic
195C23×C8—1221no—
196C2×C4⋊Q8—611no—
197C2×C22⋊Q8—611no—
198C2×C22⋊Q8#692311yescharacteristic
199C22×C42—611no—
200C2×C4⋊C8—1221no—
201C2×C22⋊C8—1221no—
202#391—611no—
203#391—611no—
204#389—1221no—
205#389—1221no—
206#384—611no—
207#380—1221no—
208#380—1221no—
209#336—612no—
210#336—612no—
211#336—1221no—
212C61#766711yescharacteristic, complemented, Sylow
213C22×Q8—611no—
214C22×Q8C2×#692311yescharacteristic
215C23×C4—611no—
216C23×C4—611no—
217C23×C4C2×#692311yescharacteristic
218C22×C8—1222no—
219C22×C8—1224no—
220C22×C8—1222no—
221C22×C8—2442no—
222C22×C8—2442no—
223C4⋊Q8—2442no—
224C22⋊Q8—42no—
225C22⋊Q8—2442no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4C2×#692311yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—1221no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—2442no—
241C4⋊C8—2442no—
242C22⋊C8—2442no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247C24C22⋊#692311yescharacteristic
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—1222no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—612no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—612no—
266C22×C4—612no—
267C22×C4—1222no—
268C22×C4—1222no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4C22⋊#692311yescharacteristic
274C22×C4C22×#692311yescharacteristic
275C2×C8—1224no—
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C2×C8—2442no—
280C2×C8—2448no—
281C2×C8—2442no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—2441no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C4⋊C4—2442no—
290C22⋊C4—42no—
291C22⋊C4—2442no—
292C42—1222no—
293C42—1222no—
294C42—2441no—
295C42—2441no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#1451983712yes—
301C23#1451984012yes—
302C23#1451984012yes—
303C23C2×C22⋊#692311yescharacteristic
304Q8—82no—
305Q8—4882no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—1224no—
327C2×C4—1224no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4#1451986412yes—
343C8—4882no—
344C8—2444no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22#1684062214yes—
352C22#1684073511yescharacteristic
353C22D61⋊#9911yescharacteristic
354C22C2×#1451983711yescharacteristic
355C22C2×#1451984011yescharacteristic
356C22C2×#1451984011yescharacteristic
357C22D61⋊#10411yescharacteristic
358C22#1684075911yescharacteristic
359C4—22no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—614no—
364C4—1221no—
365C4—1222no—
366C4—1221no—
367C4—1221no—
368C4—1221no—
369C4—4881no—
370C4—4881no—
371C2—24no—
372C2#2146109511yescharacteristic
373C2#2146112711yescharacteristic
374C2#2146116711yescharacteristic
375C2D61⋊#32811yescharacteristic
376C2#2146125711yescharacteristic
377C2#2146128811yescharacteristic
378C2C2×#1684062211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊Q8#6923
hypocenterC61#7667
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460639C2semidirect
212. C61#7667semidirect

Maximal subgroups

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

subgroupindex
#214616752
C2×#168406282
#214606402
#214606392
#214541672
#766761