Finite Group Databasebeta

← C2×#21444846 #29652148

Subgroups — C2×#21444846 #29652148

Order 15616.

1180 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1180 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×#16840098C212yesmaximal, complemented
3C2×#16839698C211yesmaximal, characteristic
4#21444846C218yesmaximal, 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×#11758196—21no—
16C22×C22⋊Dic61—21no—
17C22×C22⋊Dic61—21no—
18#16840098—24no—
19#16840098C2218yescomplemented
20C2×#14519711—22no—
21C2×#14519702—22no—
22#16839698—22no—
23#16839698C2214yes—
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×#11758196—24no—
54C2×#11758196—44no—
55C2×C22⋊Dic61—22no—
56C2×C22⋊Dic61—24no—
57C2×C22⋊Dic61—22no—
58C2×C22⋊Dic61—24no—
59C2×C22⋊Dic61—24no—
60C2×C22⋊Dic61—44no—
61#14519711—28no—
62#14519702—28no—
63#14519684—21no—
64#14519684C2312yes—
65C25×C61D411yescharacteristic
66C23×C4×C61D411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C22×C8×C61—22no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61D412yes—
72C2×C22⋊C4×C61C2312yes—
73C22⋊C8×C61—22no—
74C22⋊C8×C61C2314yes—
75C24×C61—21no—
76C24×C61—21no—
77C24×C61—22no—
78C24×C61—42no—
79C24×C61—42no—
80C24×C61Q1614yes—
81C24×C61C2×D411yescharacteristic
82C24×C61C2×D412yes—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—42no—
86C22×C4×C61—42no—
87C22×C4×C61C2×D412yes—
88C22×C4×C61C2×D412yes—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2411yescharacteristic
92C22×Dic61—24no—
93C22×Dic61—22no—
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—24no—
97C22×Dic61—24no—
98C22×Dic61—22no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—82no—
106C22×Dic61—82no—
107C2×Dic122—24no—
108C2×Dic122—22no—
109C2×Dic122—44no—
110C2×Dic122—82no—
111C2×Dic122C2×D414yes—
112C2×C8×C61—24no—
113C2×C8×C61—44no—
114C22⋊C4×C61—24no—
115C22⋊C4×C61—24no—
116C22⋊Dic61—28no—
117C22⋊Dic61—24no—
118C22⋊Dic61—24no—
119C22⋊Dic61—48no—
120C4⋊Dic61—24no—
121C4⋊Dic61—22no—
122C4⋊Dic61—24no—
123C4⋊Dic61—42no—
124C4⋊Dic61C2×D414yes—
125#11758196—28no—
126#11758196—24no—
127#11758196—24no—
128#11758196—48no—
129C23×C61—22no—
130C23×C61—22no—
131C23×C61—22no—
132C23×C61—24no—
133C23×C61—22no—
134C23×C61—24no—
135C23×C61—42no—
136C23×C61—48no—
137C23×C61—42no—
138C23×C61—42no—
139C23×C61—42no—
140C23×C61—84no—
141C23×C61—81no—
142C23×C61—81no—
143C23×C61#12011yescharacteristic
144C23×C61#12011yescharacteristic
145C23×C61C2×Q1612yes—
146C23×C61C2×Q1614yes—
147C23×C61#13712yes—
148C23×C61C22×D411yescharacteristic
149C2×C4×C61—24no—
150C2×C4×C61—22no—
151C2×C4×C61—42no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—81no—
157C2×C4×C61#12012yes—
158C2×C4×C61C22×D412yes—
159C2×Dic61—24no—
160C2×Dic61—24no—
161C2×Dic61—24no—
162C2×Dic61—48no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—44no—
166C2×Dic61—44no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C2×Dic61—42no—
170C2×Dic61—84no—
171C2×Dic61—84no—
172C2×Dic61—82no—
173C2×Dic61—82no—
174Dic122—44no—
175Dic122—82no—
176Dic122—84no—
177C8×C61—44no—
178C2×#1614—611nomaximal, Sylow
179C22×C61—24no—
180C22×C61—24no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—24no—
186C22×C61—44no—
187C22×C61—48no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—82no—
191C22×C61—84no—
192C22×C61#45112yes—
193C22×C61#45112yes—
194C22×C61#45312yes—
195C22×C61#45812yes—
196C22×C61C2×#12011yescharacteristic
197C22×C61C22×Q1611yescharacteristic
198C22×C61C2×#13711yescharacteristic
199C4×C61—22no—
200C4×C61—22no—
201C4×C61—42no—
202Dic61—44no—
203Dic61—44no—
204Dic61—44no—
205Dic61—82no—
206C2×#543—611no—
207C2×#484—612no—
208C2×#399—611no—
209#1614—618no—
210C2×#328—612no—
211C2×#323D6111yescharacteristic
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—22no—
215C2×C61—44no—
216C2×C61#161414yescomplemented
217C2×C61C2×#45111yescharacteristic
218C2×C61C2×#45311yescharacteristic
219C2×C61C2×#45811yescharacteristic
220#543—614no—
221#543—1224no—
222#543—1222no—
223C2×C22⋊Q8—612no—
224C2×C22⋊Q8—1222no—
225C2×C22⋊Q8—1222no—
226C2×C22⋊Q8—1221no—
227C22×C4⋊C4—611no—
228C22×C4⋊C4—1221no—
229C22×C22⋊C4—1221no—
230C22×C22⋊C4—1221no—
231C22×C22⋊C4C2×D6111yescharacteristic
232#484—618no—
233#484—1224no—
234C2×#107—1222no—
235C2×#103—1222no—
236C2×C22⋊C8C2×D6112yes—
237#399—614no—
238#399—1222no—
239C2×#95—611no—
240#328—618no—
241#323C2×D6114yes—
242C61C2×#161411yescharacteristic, complemented, Sylow
243C25D24411yescharacteristic
244C22×Q8—612no—
245C22×Q8—1221no—
246C23×C4—1221no—
247C23×C4—1221no—
248C23×C4—1221no—
249C23×C4—1221no—
250C23×C4D24411yescharacteristic
251C23×C4C22×D6111yescharacteristic
252C22×C8—22no—
253C22⋊Q8—614no—
254C22⋊Q8—614no—
255C22⋊Q8—1228no—
256C22⋊Q8—1228no—
257C22⋊Q8—1228no—
258C22⋊Q8—1228no—
259C22⋊Q8—1224no—
260C22⋊Q8—1222no—
261C22⋊Q8—1224no—
262C22⋊Q8—1222no—
263C2×C4⋊C4—612no—
264C2×C4⋊C4—612no—
265C2×C4⋊C4—1222no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1222no—
268C2×C4⋊C4—1222no—
269C2×C4⋊C4—1222no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1224no—
272C2×C4⋊C4—2444no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—1222no—
276C2×C22⋊C4—1224no—
277C2×C22⋊C4—1222no—
278C2×C22⋊C4—1224no—
279C2×C22⋊C4—1224no—
280C2×C22⋊C4—2444no—
281C2×C22⋊C4D24412yes—
282C2×C22⋊C4C22×D6112yes—
283#107—1228no—
284#103—1228no—
285C22⋊C8—22no—
286C22⋊C8C22×D6114yes—
287#95—612no—
288#95—1221no—
289C24—21no—
290C24—22no—
291C24—21no—
292C24—42no—
293C24—42no—
294C24Dic24414yes—
295C24C2×D24411yescharacteristic
296C24C2×D24412yes—
297C2×Q8—614no—
298C2×Q8—1224no—
299C2×Q8—1222no—
300C2×Q8—4882no—
301C2×Q8—2444no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—1224no—
307C22×C4—1224no—
308C22×C4—1224no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1222no—
312C22×C4—1222no—
313C22×C4—4882no—
314C22×C4—4882no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2441no—
318C22×C4—2441no—
319C22×C4—2442no—
320C22×C4—2442no—
321C22×C4C2×D24412yes—
322C22×C4C2×D24411yescharacteristic
323C22×C4D4×D6112yes—
324C22×C4D4×D6112yes—
325C22×C4C23×D6111yescharacteristic
326C2×C8—24no—
327C2×C8—44no—
328C4⋊C4—614no—
329C4⋊C4—1228no—
330C4⋊C4—1224no—
331C4⋊C4—1224no—
332C4⋊C4—1222no—
333C4⋊C4—1224no—
334C4⋊C4—1224no—
335C4⋊C4—2448no—
336C4⋊C4—2442no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—1228no—
340C22⋊C4—1224no—
341C22⋊C4—1224no—
342C22⋊C4—2448no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—22no—
348C23—24no—
349C23—42no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—81no—
356C23—84no—
357C23#1451974711yescharacteristic
358C23#1451974711yescharacteristic
359C23C2×Dic24412yes—
360C23C2×Dic24414yes—
361C23#1451981012yes—
362C23C22×D24411yescharacteristic
363Q8—4882no—
364Q8—4884no—
365Q8—2444no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—81no—
374C2×C4—1224no—
375C2×C4—1224no—
376C2×C4—1224no—
377C2×C4—4882no—
378C2×C4—4882no—
379C2×C4—4884no—
380C2×C4—4884no—
381C2×C4—2442no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4—2448no—
386C2×C4—2444no—
387C2×C4—2442no—
388C2×C4—2444no—
389C2×C4#1451974712yes—
390C2×C4C2×D4×D6112yes—
391C8—44no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—24no—
398C22—24no—
399C22—44no—
400C22—42no—
401C22—42no—
402C22—48no—
403C22—82no—
404C22—84no—
405C22#1683992012yes—
406C22#1683992012yes—
407C22#1683993212yes—
408C22#1683995312yes—
409C22C2×#1451974711yescharacteristic
410C22C22×Dic24411yescharacteristic
411C22C2×#1451981011yescharacteristic
412C4—22no—
413C4—22no—
414C4—42no—
415C4—4882no—
416C4—2444no—
417C4—2444no—
418C4—2444no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—44no—
423C2#2144484614yesdirect product factor
424C2C2×#1683992011yescharacteristic
425C2C2×#1683993211yescharacteristic
426C2C2×#1683995311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#323C2
socleC23×C61#120
prime radicalC25×C61D4
hypercenterC2×#323D61
hypocenterC61C2×#1614
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×#16840098C2semidirect
4. #21444846C2direct (N × H)
5. C2×#16839500C2semidirect
19. #16840098C22semidirect
25. #16839500C22semidirect
216. C2×C61#1614semidirect
242. C61C2×#1614semidirect
423. C2#21444846direct (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×#168400982
C2×#168396982
#214448462
C2×#168395002
C2×C61×#3232
C2×#161461