Finite Group Databasebeta

← C2×#21444863 #29652250

Subgroups — C2×#21444863 #29652250

Order 15616.

984 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C2×#16840393C211yesmaximal, characteristic
2C2×#16840098C212yesmaximal
3C2×#16839701C211yesmaximal, characteristic
4#21444863C218yesmaximal, direct product factor
5C2×#16839500C212yesmaximal
6C2×C61×#324C211yesmaximal, characteristic
7#16840393—24no—
8#16840393—22no—
9#16840393C2214yes—
10C2×#14519776—22no—
11C2×#14519768—22no—
12C2×#14519756—21no—
13C2×#14519756C2212yes—
14C2×#14519736—21no—
15C22×C4⋊Dic61C2211yescharacteristic
16#16840098—24no—
17#16840098C2218yes—
18C2×#14519711—22no—
19C2×#14519702—22no—
20#16839701—22no—
21#16839701C2214yes—
22C2×#14519684—21no—
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839500C2218yes—
26C22×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2212yes—
28C61×#324C2214yes—
29C22×Dic122—21no—
30C22×Dic122D412yes—
31C23×Dic61—21no—
32C23×Dic61—21no—
33#14519776—28no—
34#14519776—28no—
35#14519768—28no—
36#14519768—28no—
37#14519756—24no—
38#14519756—24no—
39#14519756—22no—
40#14519756—22no—
41#14519756D414yes—
42#14519756C2314yes—
43#14519736—24no—
44#14519736—24no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61D412yes—
52C2×C4⋊Dic61C2312yes—
53C2×#11758196—22no—
54C2×#11758196—22no—
55C2×C22⋊Dic61—22no—
56C2×C4×Dic61—22no—
57#14519711—28no—
58#14519702—28no—
59#14519684—21no—
60#14519684—24no—
61#14519684—24no—
62#14519684C2312yes—
63C23×C4×C61D411yescharacteristic
64C23×C4×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—22no—
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61D412yes—
70C2×C4⋊C4×C61C2312yes—
71C22⋊C8×C61—22no—
72C22⋊C8×C61C2314yes—
73C24×C61C2×D411yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—42no—
80C22×C4×C61—42no—
81C22×C4×C61Q1614yes—
82C22×C4×C61C2×D412yes—
83C22×C4×C61C2×D412yes—
84C22×C4×C61C2×D412yes—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D412yes—
87C22×C4×C61C2411yescharacteristic
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—22no—
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61—44no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—42no—
98C2×Dic122—24no—
99C2×Dic122—22no—
100C2×Dic122—44no—
101C2×Dic122—82no—
102C2×Dic122C2×D414yes—
103C2×C8×C61—24no—
104C2×C8×C61—44no—
105C4⋊C4×C61—24no—
106C4⋊C4×C61—24no—
107C22⋊Dic61—24no—
108C22⋊Dic61—24no—
109C4⋊Dic61—24no—
110C4⋊Dic61—24no—
111C4⋊Dic61—24no—
112C4⋊Dic61—22no—
113C4⋊Dic61—24no—
114C4⋊Dic61—42no—
115C4⋊Dic61C2×D414yes—
116#11758196—28no—
117#11758196—24no—
118#11758196—24no—
119C4×Dic61—28no—
120C23×C61—22no—
121C23×C61—22no—
122C23×C61#12011yescharacteristic
123C23×C61#12011yescharacteristic
124C23×C61C2×Q1612yes—
125C23×C61#13712yes—
126C23×C61C22×D411yescharacteristic
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—24no—
130C2×C4×C61—24no—
131C2×C4×C61—24no—
132C2×C4×C61—22no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61#12012yes—
140C2×C4×C61C2×Q1614yes—
141C2×C4×C61C22×D412yes—
142C2×Dic61—24no—
143C2×Dic61—24no—
144C2×Dic61—44no—
145C2×Dic61—44no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—44no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—84no—
152C2×Dic61—82no—
153C2×Dic61—82no—
154Dic122—44no—
155Dic122—82no—
156Dic122—84no—
157C8×C61—44no—
158C2×#1617—611nomaximal, Sylow
159C22×C61—24no—
160C22×C61—24no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#45112yes—
166C22×C61#45112yes—
167C22×C61#45412yes—
168C22×C61#45812yes—
169C22×C61C2×#12011yescharacteristic
170C22×C61C22×Q1611yescharacteristic
171C22×C61C2×#13711yescharacteristic
172C4×C61—24no—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—42no—
176Dic61—44no—
177Dic61—44no—
178Dic61—82no—
179Dic61—82no—
180C2×#544—611no—
181C2×#484—612no—
182C2×#400—611no—
183#1617—618no—
184C2×#328—612no—
185C2×#324D6111yescharacteristic
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—22no—
189C2×C61#161714yescomplemented
190C2×C61C2×#45111yescharacteristic
191C2×C61C2×#45411yescharacteristic
192C2×C61C2×#45811yescharacteristic
193#544—614no—
194#544—1224no—
195#544—1222no—
196C2×C4⋊Q8—1222no—
197C2×#125—1222no—
198C2×C22⋊Q8—612no—
199C2×C22⋊Q8—1221no—
200C2×#117—1221no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4C2×D6111yescharacteristic
203#484—618no—
204#484—1224no—
205C2×#107—1222no—
206C2×#103—1222no—
207C2×C22⋊C8C2×D6112yes—
208#400—614no—
209#400—1222no—
210C2×#95—611no—
211C2×#95—1221no—
212C2×#95—1221no—
213#328—618no—
214#324C2×D6114yes—
215C61C2×#161711yescharacteristic, complemented, Sylow
216C22×Q8—612no—
217C22×Q8—1221no—
218C23×C4—1221no—
219C23×C4—1221no—
220C23×C4D24411yescharacteristic
221C23×C4D24411yescharacteristic
222C23×C4C22×D6111yescharacteristic
223C22×C8—22no—
224C4⋊Q8—1228no—
225C4⋊Q8—1228no—
226#125—1228no—
227#125—1228no—
228C22⋊Q8—614no—
229C22⋊Q8—614no—
230C22⋊Q8—1224no—
231C22⋊Q8—1222no—
232C22⋊Q8—1224no—
233C22⋊Q8—1222no—
234#117—1224no—
235#117—1224no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—612no—
239C2×C4⋊C4—612no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4—1222no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4D24412yes—
249C2×C4⋊C4C22×D6112yes—
250C2×C22⋊C4—1222no—
251C2×C42—1222no—
252#107—1228no—
253#103—1228no—
254C22⋊C8—22no—
255C22⋊C8C22×D6114yes—
256#95—612no—
257#95—1221no—
258#95—1224no—
259#95—1224no—
260C24C2×D24411yescharacteristic
261C2×Q8—614no—
262C2×Q8—1224no—
263C2×Q8—1222no—
264C2×Q8—4882no—
265C2×Q8—2444no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—2442no—
278C22×C4—2442no—
279C22×C4—2444no—
280C22×C4—2442no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4Dic24414yes—
284C22×C4C2×D24412yes—
285C22×C4C2×D24412yes—
286C22×C4C2×D24411yescharacteristic
287C22×C4D4×D6112yes—
288C22×C4D4×D6112yes—
289C22×C4C23×D6111yescharacteristic
290C2×C8—24no—
291C2×C8—44no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—614no—
295C4⋊C4—1228no—
296C4⋊C4—1224no—
297C4⋊C4—1224no—
298C4⋊C4—1224no—
299C4⋊C4—1224no—
300C4⋊C4—1222no—
301C4⋊C4—1224no—
302C4⋊C4—1224no—
303C4⋊C4—2442no—
304C22⋊C4—1224no—
305C22⋊C4—1224no—
306C42—1228no—
307C23—22no—
308C23—22no—
309C23#1451974711yescharacteristic
310C23#1451974711yescharacteristic
311C23C2×Dic24412yes—
312C23#1451981012yes—
313C23C22×D24411yescharacteristic
314Q8—4882no—
315Q8—4884no—
316Q8—2444no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4—1224no—
330C2×C4—1224no—
331C2×C4—4884no—
332C2×C4—4882no—
333C2×C4—4882no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2444no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2444no—
340C2×C4—2444no—
341C2×C4#1451974712yes—
342C2×C4C2×Dic24414yes—
343C2×C4C2×D4×D6112yes—
344C8—44no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—24no—
350C22—24no—
351C22#1683992012yes—
352C22#1683992012yes—
353C22#1683993712yes—
354C22#1683995312yes—
355C22C2×#1451974711yescharacteristic
356C22C22×Dic24411yescharacteristic
357C22C2×#1451981011yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—4882no—
363C4—4882no—
364C4—2444no—
365C4—2444no—
366C2—21no—
367C2—21no—
368C2—22no—
369C2#2144486314yesdirect product factor
370C2C2×#1683992011yescharacteristic
371C2C2×#1683993711yescharacteristic
372C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#324D61
hypocenterC61C2×#1617
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #21444863C2direct (N × H)
189. C2×C61#1617semidirect
215. C61C2×#1617semidirect
369. C2#21444863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403932
C2×#168400982
C2×#168397012
#214448632
C2×#168395002
C2×C61×#3242
C2×#161761