Finite Group Databasebeta

← C2×#21444795 #29652199

Subgroups — C2×#21444795 #29652199

Order 15616.

1200 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1200 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×#16839920C212yesmaximal
3C2×#16839682C211yesmaximal, characteristic
4#21444795C218yesmaximal, direct product factor
5C2×#16839500C212yesmaximal
6C2×C61×#324C211yesmaximal, characteristic
7C23×Dic122C2211yescharacteristic
8C22×Dic244—22no—
9#16840393—24no—
10#16840393—22no—
11#16840393C2214yes—
12C2×#14519776—22no—
13C2×#14519768—22no—
14C2×#14519756—21no—
15C2×#14519756C2212yes—
16C2×#14519736—21no—
17C22×#11758196—21no—
18#16839920—24no—
19#16839920C2218yes—
20C2×#14519702—22no—
21#16839682—22no—
22#16839682C2214yes—
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839500C2218yes—
26C22×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2212yes—
28C61×#324C2214yes—
29C22×Dic122—22no—
30C22×Dic122—21no—
31C22×Dic122—22no—
32C22×Dic122—21no—
33C22×Dic122—44no—
34C22×Dic122D412yes—
35C22×Dic122C2312yes—
36C23×Dic61—21no—
37C23×Dic61—21no—
38C2×Dic244—28no—
39C2×Dic244—48no—
40#14519776—28no—
41#14519776—28no—
42#14519768—28no—
43#14519768—28no—
44#14519756—24no—
45#14519756—24no—
46#14519756—22no—
47#14519756—22no—
48#14519756D414yes—
49#14519756C2314yes—
50#14519736—24no—
51#14519736—24no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61D412yes—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196—24no—
59C2×#11758196—44no—
60C2×C22⋊Dic61—22no—
61C2×C4×Dic61—22no—
62#14519702—28no—
63#14519684—21no—
64#14519684—24no—
65#14519684C2312yes—
66C23×C4×C61D411yescharacteristic
67C23×C4×C61D411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—22no—
70C2×C4⋊C4×C61—22no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61D412yes—
73C2×C4⋊C4×C61C2312yes—
74C22⋊C8×C61—22no—
75C22⋊C8×C61C2314yes—
76C24×C61C2×D411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—42no—
83C22×C4×C61—42no—
84C22×C4×C61Q1614yescomplemented
85C22×C4×C61C2×D412yes—
86C22×C4×C61C2×D412yes—
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D412yes—
90C22×C4×C61C2411yescharacteristic
91C22×Dic61—24no—
92C22×Dic61—24no—
93C22×Dic61—22no—
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—42no—
98C22×Dic61—42no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—42no—
102C2×Dic122—28no—
103C2×Dic122—24no—
104C2×Dic122—24no—
105C2×Dic122—22no—
106C2×Dic122—44no—
107C2×Dic122—48no—
108C2×Dic122—44no—
109C2×Dic122—44no—
110C2×Dic122—42no—
111C2×Dic122—44no—
112C2×Dic122—82no—
113C2×Dic122C2×D414yes—
114C2×C8×C61—24no—
115C2×C8×C61—44no—
116C4⋊C4×C61—24no—
117C4⋊C4×C61—24no—
118C22⋊Dic61—24no—
119C22⋊Dic61—24no—
120C4⋊Dic61—24no—
121C4⋊Dic61—24no—
122C4⋊Dic61—24no—
123C4⋊Dic61—22no—
124C4⋊Dic61C2×D414yes—
125#11758196—28no—
126#11758196—24no—
127#11758196—24no—
128#11758196—48no—
129C4×Dic61—28no—
130Dic244—416no—
131C23×C61—22no—
132C23×C61—22no—
133C23×C61#12011yescharacteristic
134C23×C61#12011yescharacteristic
135C23×C61C2×Q1612yes—
136C23×C61#13712yes—
137C23×C61C22×D411yescharacteristic
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—24no—
141C2×C4×C61—24no—
142C2×C4×C61—24no—
143C2×C4×C61—22no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—42no—
149C2×C4×C61—81no—
150C2×C4×C61#12012yes—
151C2×C4×C61C2×Q1614yescomplemented
152C2×C4×C61C22×D412yes—
153C2×Dic61—24no—
154C2×Dic61—24no—
155C2×Dic61—24no—
156C2×Dic61—24no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—44no—
160C2×Dic61—48no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—44no—
164C2×Dic61—44no—
165C2×Dic61—44no—
166Dic122—28no—
167Dic122—44no—
168Dic122—48no—
169Dic122—44no—
170Dic122—82no—
171Dic122—84no—
172C8×C61—44no—
173C2×#1605—611nomaximal, Sylow
174C22×C61—24no—
175C22×C61—24no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#45112yes—
181C22×C61#45112yes—
182C22×C61#45612yes—
183C22×C61B(4,𝔽2)12yes—
184C22×C61C2×#12011yescharacteristic
185C22×C61C22×Q1611yescharacteristic
186C22×C61C2×#13711yescharacteristic
187C4×C61—24no—
188C4×C61—22no—
189C4×C61—22no—
190C4×C61—42no—
191Dic61—44no—
192Dic61—44no—
193Dic61—44no—
194Dic61—44no—
195C2×#544—611no—
196C2×#451—612no—
197C2×#395—611no—
198#1605—618no—
199C2×#328—612no—
200C2×#324D6111yescharacteristic
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—22no—
204C2×C61#160514yescomplemented
205C2×C61C2×#45111yescharacteristic
206C2×C61C2×#45611yescharacteristic
207C2×C61C2×B(4,𝔽2)11yescharacteristic
208C23×Q8—611no—
209C22×Q16—1222no—
210#544—614no—
211#544—1224no—
212#544—1222no—
213C2×C4⋊Q8—1222no—
214C2×#125—1222no—
215C2×C22⋊Q8—612no—
216C2×C22⋊Q8—1221no—
217C2×#117—1221no—
218C22×C4⋊C4—1221no—
219C22×C4⋊C4C2×D6111yescharacteristic
220#451—618no—
221#451—1224no—
222C2×#103—1222no—
223C2×C22⋊C8C2×D6112yes—
224#395—614no—
225#395—1222no—
226C2×#95—611no—
227C2×#95—1221no—
228#328—618no—
229#324C2×D6114yes—
230C61C2×#160511yescharacteristic, complemented, Sylow
231C22×Q8—612no—
232C22×Q8—612no—
233C22×Q8—1221no—
234C22×Q8—1221no—
235C22×Q8—1222no—
236C22×Q8—1222no—
237C22×Q8—2444no—
238C23×C4—1221no—
239C23×C4—1221no—
240C23×C4D24411yescharacteristic
241C23×C4D24411yescharacteristic
242C23×C4C22×D6111yescharacteristic
243C2×Q16—1228no—
244C2×Q16—2448no—
245C22×C8—22no—
246C4⋊Q8—1228no—
247C4⋊Q8—1228no—
248#125—1228no—
249#125—1228no—
250C22⋊Q8—614no—
251C22⋊Q8—614no—
252C22⋊Q8—1224no—
253C22⋊Q8—1222no—
254C22⋊Q8—1224no—
255C22⋊Q8—1222no—
256#117—1224no—
257#117—1224no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—612no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1224no—
267C2×C4⋊C4—2444no—
268C2×C4⋊C4D24412yes—
269C2×C4⋊C4C22×D6112yes—
270C2×C22⋊C4—1222no—
271C2×C42—1222no—
272#103—1228no—
273C22⋊C8—22no—
274C22⋊C8C22×D6114yes—
275#95—612no—
276#95—1221no—
277#95—1224no—
278C24C2×D24411yescharacteristic
279C2×Q8—614no—
280C2×Q8—1224no—
281C2×Q8—1228no—
282C2×Q8—1222no—
283C2×Q8—1224no—
284C2×Q8—4882no—
285C2×Q8—2444no—
286C2×Q8—2444no—
287C2×Q8—2444no—
288C2×Q8—2444no—
289C2×Q8—2448no—
290C2×Q8—2442no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—1224no—
299C22×C4—1224no—
300C22×C4—1222no—
301C22×C4—1222no—
302C22×C4—1222no—
303C22×C4—1222no—
304C22×C4—2442no—
305C22×C4—2442no—
306C22×C4—2442no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4Dic24414yescomplemented
310C22×C4C2×D24412yes—
311C22×C4C2×D24412yes—
312C22×C4C2×D24411yescharacteristic
313C22×C4D4×D6112yes—
314C22×C4D4×D6112yes—
315C22×C4C23×D6111yescharacteristic
316Q16—24416no—
317C2×C8—24no—
318C2×C8—44no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—614no—
322C4⋊C4—1228no—
323C4⋊C4—1224no—
324C4⋊C4—1224no—
325C4⋊C4—1224no—
326C4⋊C4—1224no—
327C4⋊C4—1222no—
328C4⋊C4—1224no—
329C4⋊C4—2448no—
330C22⋊C4—1224no—
331C22⋊C4—1224no—
332C42—1228no—
333C23—22no—
334C23—22no—
335C23#1451974711yescharacteristic
336C23#1451974711yescharacteristic
337C23C2×Dic24412yes—
338C23#1451981012yes—
339C23C22×D24411yescharacteristic
340Q8—1228no—
341Q8—4882no—
342Q8—4884no—
343Q8—2444no—
344Q8—2444no—
345Q8—2448no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—1224no—
359C2×C4—1224no—
360C2×C4—1224no—
361C2×C4—1224no—
362C2×C4—2442no—
363C2×C4—2448no—
364C2×C4—2442no—
365C2×C4—2444no—
366C2×C4—2444no—
367C2×C4—2444no—
368C2×C4—2444no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4#1451974712yes—
372C2×C4C2×Dic24414yescomplemented
373C2×C4C2×D4×D6112yes—
374C8—44no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—24no—
381C22#1683992012yes—
382C22#1683992012yes—
383C22#1683994712yes—
384C22#1683995012yes—
385C22C2×#1451974711yescharacteristic
386C22C22×Dic24411yescharacteristic
387C22C2×#1451981011yescharacteristic
388C4—22no—
389C4—22no—
390C4—24no—
391C4—42no—
392C4—2444no—
393C4—2444no—
394C4—2444no—
395C4—2444no—
396C2—21no—
397C2—21no—
398C2—22no—
399C2#2144479514yesdirect product factor
400C2C2×#1683992011yescharacteristic
401C2C2×#1683994711yescharacteristic
402C2C2×#1683995011yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#324D61
hypocenterC61C2×#1605
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. #21444795C2direct (N × H)
84. C22×C4×C61Q16semidirect
151. C2×C4×C61C2×Q16semidirect
204. C2×C61#1605semidirect
230. C61C2×#1605semidirect
309. C22×C4Dic244semidirect
372. C2×C4C2×Dic244semidirect
399. C2#21444795direct (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×#168399202
C2×#168396822
#214447952
C2×#168395002
C2×C61×#3242
C2×#160561