Finite Group Databasebeta

← C2×#21444812 #29652142

Subgroups — C2×#21444812 #29652142

Order 15616.

1136 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1136 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×#16840388C211yesmaximal, characteristic
2C2×#16840093C212yesmaximal, complemented
3C2×#16839687C211yesmaximal, characteristic
4#21444812C218yesmaximal, direct product factor
5C2×#16839500C212yesmaximal, complemented
6C2×C61×#323C211yesmaximal, characteristic
7#16840388—24no—
8#16840388—22no—
9#16840388C2214yes—
10C2×#14519756—21no—
11C2×#14519756C2212yes—
12C2×#14519754—22no—
13C2×#14519754—22no—
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C22⋊Dic61—21no—
16C22×C22⋊Dic61—21no—
17#16840093—24no—
18#16840093C2218yescomplemented
19C2×#14519709—22no—
20C2×#14519702—22no—
21#16839687—22no—
22#16839687C2214yes—
23C2×#14519684—21no—
24C2×#14519684C2211yescharacteristic
25#16839500C2218yescomplemented
26C22×C22⋊C4×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2212yes—
28C61×#323C2214yes—
29C22×Dic122—21no—
30C22×Dic122D412yes—
31C23×Dic61—21no—
32C23×Dic61—21no—
33C23×Dic61—21no—
34C23×Dic61—21no—
35#14519756—24no—
36#14519756—24no—
37#14519756—22no—
38#14519756—22no—
39#14519756D414yes—
40#14519756C2314yes—
41#14519754—28no—
42#14519754—28no—
43#14519754—28no—
44#14519754—28no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61D412yes—
50C2×C4⋊Dic61C2312yes—
51C2×#11758196—22no—
52C2×#11758196—22no—
53C2×C22⋊Dic61—22no—
54C2×C22⋊Dic61—24no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—24no—
58C2×C22⋊Dic61—44no—
59#14519709—28no—
60#14519702—28no—
61#14519684—21no—
62#14519684—24no—
63#14519684C2312yes—
64C25×C61D411yescharacteristic
65C23×C4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—22no—
68C2×C22⋊C4×C61—22no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61D412yes—
71C2×C22⋊C4×C61C2312yes—
72C22⋊C8×C61—22no—
73C22⋊C8×C61C2314yes—
74C24×C61—21no—
75C24×C61—21no—
76C24×C61—22no—
77C24×C61—42no—
78C24×C61—42no—
79C24×C61SD1614yes—
80C24×C61C2×D411yescharacteristic
81C24×C61C2×D412yes—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61C2×D412yes—
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D412yes—
90C22×C4×C61C2411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—24no—
94C22×Dic61—24no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—42no—
98C22×Dic61—42no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—42no—
104C22×Dic61—82no—
105C22×Dic61—82no—
106C2×Dic122—24no—
107C2×Dic122—22no—
108C2×Dic122—44no—
109C2×Dic122—82no—
110C2×Dic122C2×D414yes—
111C2×C8×C61—24no—
112C2×C8×C61—44no—
113C22⋊C4×C61—24no—
114C22⋊C4×C61—24no—
115C22⋊Dic61—28no—
116C22⋊Dic61—24no—
117C22⋊Dic61—24no—
118C22⋊Dic61—48no—
119C4⋊Dic61—24no—
120C4⋊Dic61—22no—
121C4⋊Dic61—24no—
122C4⋊Dic61—42no—
123C4⋊Dic61C2×D414yes—
124#11758196—28no—
125#11758196—24no—
126#11758196—24no—
127C23×C61—22no—
128C23×C61—22no—
129C23×C61—22no—
130C23×C61—24no—
131C23×C61—22no—
132C23×C61—24no—
133C23×C61—48no—
134C23×C61—42no—
135C23×C61—42no—
136C23×C61—42no—
137C23×C61—42no—
138C23×C61—84no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61#12011yescharacteristic
142C23×C61#12011yescharacteristic
143C23×C61C2×SD1612yes—
144C23×C61C2×SD1614yes—
145C23×C61#13712yes—
146C23×C61C22×D411yescharacteristic
147C2×C4×C61—24no—
148C2×C4×C61—22no—
149C2×C4×C61—42no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—81no—
155C2×C4×C61#12012yes—
156C2×C4×C61C22×D412yes—
157C2×Dic61—24no—
158C2×Dic61—24no—
159C2×Dic61—44no—
160C2×Dic61—44no—
161C2×Dic61—42no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—84no—
168C2×Dic61—84no—
169C2×Dic61—84no—
170C2×Dic61—82no—
171C2×Dic61—82no—
172Dic122—44no—
173Dic122—82no—
174Dic122—84no—
175C8×C61—44no—
176C2×#1608—611nomaximal, Sylow
177C22×C61—24no—
178C22×C61—24no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—24no—
184C22×C61—44no—
185C22×C61—48no—
186C22×C61—42no—
187C22×C61—42no—
188C22×C61—82no—
189C22×C61—84no—
190C22×C61#44812yes—
191C22×C61#44812yes—
192C22×C61#45512yes—
193C22×C61#45812yes—
194C22×C61C2×#12011yescharacteristic
195C22×C61C22×SD1611yescharacteristic
196C22×C61C2×#13711yescharacteristic
197C4×C61—22no—
198C4×C61—22no—
199C4×C61—42no—
200Dic61—44no—
201Dic61—44no—
202Dic61—82no—
203Dic61—82no—
204C2×#543—611no—
205C2×#483—612no—
206C2×#397—611no—
207#1608—618no—
208C2×#328—612no—
209C2×#323D6111yescharacteristic
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—22no—
213C2×C61—44no—
214C2×C61#160814yescomplemented
215C2×C61C2×#44811yescharacteristic
216C2×C61C2×#45511yescharacteristic
217C2×C61C2×#45811yescharacteristic
218#543—614no—
219#543—1224no—
220#543—1222no—
221C2×C22⋊Q8—612no—
222C2×C22⋊Q8—1222no—
223C2×C22⋊Q8—1222no—
224C2×C22⋊Q8—1221no—
225C22×C4⋊C4—611no—
226C22×C22⋊C4—1221no—
227C22×C22⋊C4—1221no—
228C22×C22⋊C4C2×D6111yescharacteristic
229#483—618no—
230#483—1224no—
231C2×#106—1222no—
232C2×#103—1222no—
233C2×C22⋊C8C2×D6112yes—
234#397—614no—
235#397—1222no—
236C2×#95—611no—
237C2×#95—1221no—
238#328—618no—
239#323C2×D6114yes—
240C61C2×#160811yescharacteristic, complemented, Sylow
241C25D24411yescharacteristic
242C22×Q8—612no—
243C22×Q8—1221no—
244C23×C4—1221no—
245C23×C4—1221no—
246C23×C4—1221no—
247C23×C4—1221no—
248C23×C4D24411yescharacteristic
249C23×C4C22×D6111yescharacteristic
250C22×C8—22no—
251C22⋊Q8—614no—
252C22⋊Q8—614no—
253C22⋊Q8—1228no—
254C22⋊Q8—1228no—
255C22⋊Q8—1228no—
256C22⋊Q8—1228no—
257C22⋊Q8—1224no—
258C22⋊Q8—1222no—
259C22⋊Q8—1224no—
260C22⋊Q8—1222no—
261C2×C4⋊C4—612no—
262C2×C4⋊C4—612no—
263C2×C4⋊C4—1222no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1222no—
267C2×C4⋊C4—1222no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—1222no—
272C2×C22⋊C4—1224no—
273C2×C22⋊C4—1222no—
274C2×C22⋊C4—1224no—
275C2×C22⋊C4—1224no—
276C2×C22⋊C4—2444no—
277C2×C22⋊C4D24412yes—
278C2×C22⋊C4C22×D6112yes—
279#106—1228no—
280#103—1228no—
281C22⋊C8—22no—
282C22⋊C8C22×D6114yes—
283#95—612no—
284#95—1221no—
285#95—1224no—
286C24—21no—
287C24—22no—
288C24—21no—
289C24—42no—
290C24—42no—
291C24#1175819014yes—
292C24C2×D24411yescharacteristic
293C24C2×D24412yes—
294C2×Q8—614no—
295C2×Q8—1224no—
296C2×Q8—1222no—
297C2×Q8—4882no—
298C2×Q8—2444no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—1224no—
304C22×C4—1224no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—1222no—
308C22×C4—1222no—
309C22×C4—4882no—
310C22×C4—4882no—
311C22×C4—2442no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2441no—
315C22×C4—2441no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4C2×D24412yes—
319C22×C4C2×D24411yescharacteristic
320C22×C4D4×D6112yes—
321C22×C4D4×D6112yes—
322C22×C4C23×D6111yescharacteristic
323C2×C8—24no—
324C2×C8—44no—
325C4⋊C4—614no—
326C4⋊C4—1228no—
327C4⋊C4—1224no—
328C4⋊C4—1224no—
329C4⋊C4—1222no—
330C4⋊C4—1224no—
331C4⋊C4—1224no—
332C4⋊C4—2442no—
333C22⋊C4—24no—
334C22⋊C4—24no—
335C22⋊C4—1228no—
336C22⋊C4—1224no—
337C22⋊C4—1224no—
338C22⋊C4—2448no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—22no—
344C23—24no—
345C23—48no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—84no—
353C23#1451974711yescharacteristic
354C23#1451974711yescharacteristic
355C23C2×#1175819012yes—
356C23C2×#1175819014yes—
357C23#1451981012yes—
358C23C22×D24411yescharacteristic
359Q8—4882no—
360Q8—4884no—
361Q8—2444no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—1224no—
371C2×C4—1224no—
372C2×C4—4884no—
373C2×C4—4882no—
374C2×C4—4882no—
375C2×C4—4884no—
376C2×C4—4884no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2444no—
384C2×C4—2444no—
385C2×C4#1451974712yes—
386C2×C4C2×D4×D6112yes—
387C8—44no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—24no—
393C22—24no—
394C22—24no—
395C22—44no—
396C22—42no—
397C22—42no—
398C22—48no—
399C22—82no—
400C22—84no—
401C22#1683990312yes—
402C22#1683990312yes—
403C22#1683994212yes—
404C22#1683995312yes—
405C22C2×#1451974711yescharacteristic
406C22C22×#1175819011yescharacteristic
407C22C2×#1451981011yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—4882no—
412C4—4882no—
413C4—2444no—
414C4—2444no—
415C2—21no—
416C2—21no—
417C2—22no—
418C2—44no—
419C2#2144481214yesdirect product factor
420C2C2×#1683990311yescharacteristic
421C2C2×#1683994211yescharacteristic
422C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61#120
prime radicalC25×C61D4
hypercenterC2×#323D61
hypocenterC61C2×#1608
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#16840093C2semidirect
4. #21444812C2direct (N × H)
5. C2×#16839500C2semidirect
18. #16840093C22semidirect
25. #16839500C22semidirect
214. C2×C61#1608semidirect
240. C61C2×#1608semidirect
419. C2#21444812direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403882
C2×#168400932
C2×#168396872
#214448122
C2×#168395002
C2×C61×#3232
C2×#160861