Finite Group Databasebeta

← C2×#21460816 #30604811

Subgroups — C2×#21460816 #30604811

Order 15616.

712 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 104 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×#16840640C211yesmaximal, characteristic
2C2×#16840606C211yesmaximal, characteristic
3#21460816C214yesmaximal, direct product factor
4C2×#16839697C211yesmaximal, characteristic
5C22×C22⋊#6923—21no—
6C2×C22⋊#92420—21no—
7#16840640—21no—
8#16840640C2212yes—
9#16840606—21no—
10#16840606C2212yes—
11C22×#11758196—21no—
12C22×#11758198—21no—
13C22×#11758198C2211yescharacteristic
14#16839697—21no—
15#16839697—21no—
16#16839697C412yescomplemented
17#16839697C2212yes—
18C2×#14519684C411yescharacteristic, complemented
19C22×C4⋊C4×C61C411yescharacteristic, complemented
20C23×#6923—41no—
21C22×#92420—41no—
22C2×C22⋊#6923—24no—
23C2×C22⋊#6923—22no—
24C2×C22⋊#6923—41no—
25C2×C22⋊#6923—42no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C24×D61D411yescharacteristic
29C23×Dic61—21no—
30C23×Dic61D411yescharacteristic
31C2×#11758196—22no—
32C2×#11758196—22no—
33C2×#11758196—44no—
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198—41no—
37C2×#11758198—41no—
38C2×#11758198—44no—
39C2×#11758198C2×C411yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×#11758198D411yescharacteristic
42C2×#11758198C2311yescharacteristic
43#14519684—21no—
44#14519684C2×C412yescomplemented
45C23×C4×C61—21no—
46C23×C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C412yescomplemented
51C24×C61C22⋊C411yescharacteristic
52C23×D61—21no—
53C23×D61—21no—
54C23×D61—22no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61C22⋊C411yescharacteristic
58C23×D61SD1612yes—
59C23×D61Q1612yes—
60C23×D61C2×D411yescharacteristic
61C22×#6923—44no—
62C22×#6923—42no—
63C22×#6923—82no—
64C22×#6923—82no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—42no—
69C22×C4×C61—42no—
70C22×C4×C61—42no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—24no—
76C22×Dic61—21no—
77C22×Dic61—22no—
78C22×Dic61—21no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C22⋊#6923—24no—
85C22⋊#6923—44no—
86C22⋊#6923—42no—
87C2×#92420—42no—
88C2×#92420—82no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—41no—
95#11758198—44no—
96#11758198—44no—
97#11758196—44no—
98#11758196—44no—
99C23×C61—22no—
100C23×C61—22no—
101C23×C61#9911yescharacteristic
102C23×C61#9911yescharacteristic
103C23×C61#10312yes—
104C23×C61#10412yes—
105C23×C61C2×C22⋊C411yescharacteristic
106C22×D61—22no—
107C22×D61—22no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—22no—
111C22×D61—22no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—44no—
120C22×D61—44no—
121C22×D61—41no—
122C22×D61—81no—
123C22×D61—84no—
124C22×D61—81no—
125C22×D61#10312yes—
126C22×D61C2×SD1611yescharacteristic
127C22×D61C2×Q1611yescharacteristic
128C2×#6923—44no—
129C2×#6923—82no—
130C2×#6923—88no—
131C2×#6923—82no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×Dic61—24no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61—48no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—81no—
153#92420—82no—
154C2×#1352—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—24no—
158C22×C61—24no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#32812yes—
162C22×C61#32812yes—
163C22×C61#35212yes—
164C22×C61#35312yes—
165C22×C61C2×#9911yescharacteristic
166C22×C61C2×#10311yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C2×D61—21no—
169C2×D61—22no—
170C2×D61—21no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—44no—
174C2×D61—44no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—42no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—81no—
181C2×D61—82no—
182C2×D61—81no—
183C2×D61—82no—
184#6923—84no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—82no—
188Dic61—44no—
189Dic61—41no—
190Dic61—41no—
191C2×#399—611no—
192C2×#342—611no—
193C2×#323—611no—
194#1352—614no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—22no—
198C2×C61#135214yescomplemented
199C2×C61C2×#32811yescharacteristic
200C2×C61C2×#35211yescharacteristic
201C2×C61C2×#35311yescharacteristic
202D61—41no—
203D61—42no—
204D61—41no—
205C22×C4⋊C4—1221no—
206C22×C4⋊C4#692311yescharacteristic, complemented
207C22×C22⋊C4—611no—
208C22×C22⋊C4—1221no—
209C22×C22⋊C4—1221no—
210C2×C22⋊C8—1221no—
211#399—612no—
212#399—612no—
213#399—1221no—
214#399—1221no—
215C2×#95—611no—
216#342—612no—
217#342—1221no—
218#323—612no—
219#323—1221no—
220C61C2×#135211yescharacteristic, complemented, Sylow
221C25—611no—
222C23×C4—21no—
223C23×C4—611no—
224C23×C4—1221no—
225C23×C4—2441no—
226C23×C4C2×#692311yescharacteristic
227C22×C8—2441no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—1222no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4—2444no—
234C2×C4⋊C4C2×#692312yescomplemented
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1224no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—2441no—
244C2×C22⋊C4—2441no—
245C2×C22⋊C4—2444no—
246C2×C22⋊C4—2442no—
247C2×C22⋊C4—2441no—
248C22⋊C8—1222no—
249C22⋊C8—2441no—
250#95—612no—
251#95—1221no—
252C24—612no—
253C24—612no—
254C24—611no—
255C24—611no—
256C24—1221no—
257C24—1222no—
258C24—1221no—
259C24—2442no—
260C24—2442no—
261C24C22⋊#692311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1224no—
274C22×C4—1221no—
275C22×C4—1222no—
276C22×C4—4882no—
277C22×C4—4882no—
278C22×C4—2442no—
279C22×C4—2444no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4—2442no—
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22×#692311yescharacteristic
285C2×C8—4882no—
286C2×C8—2442no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—2444no—
290C4⋊C4—2444no—
291C22⋊C4—1224no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2444no—
297C22⋊C4—2444no—
298C22⋊C4—2442no—
299C22⋊C4—2444no—
300C23—22no—
301C23—22no—
302C23—612no—
303C23—611no—
304C23—611no—
305C23—1221no—
306C23—1221no—
307C23—1222no—
308C23—1222no—
309C23—1221no—
310C23—1221no—
311C23—1222no—
312C23—1222no—
313C23—4881no—
314C23—4881no—
315C23—4884no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2444no—
321C23—2444no—
322C23—2442no—
323C23—2442no—
324C23#1451983511yescharacteristic
325C23#1451983511yescharacteristic
326C23#1451984012yes—
327C23#1451984212yes—
328C23C2×C22⋊#692311yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—1224no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4882no—
344C2×C4—4882no—
345C2×C4—4888no—
346C2×C4—4881no—
347C2×C4—2444no—
348C2×C4—2442no—
349C2×C4—2448no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C8—4882no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—24no—
361C22—1221no—
362C22—1222no—
363C22—1221no—
364C22—4881no—
365C22—4881no—
366C22—4882no—
367C22—4882no—
368C22—2441no—
369C22—2442no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2444no—
376C22—2444no—
377C22#1684061612yes—
378C22#1684061612yes—
379C22#1684066412yes—
380C22#1684066612yes—
381C22C2×#1451983511yescharacteristic
382C22C2×#1451984011yescharacteristic
383C22C2×#1451984211yescharacteristic
384C4—41no—
385C4—41no—
386C4—82no—
387C4—4884no—
388C4—2444no—
389C4—2441no—
390C4—2441no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2—2441no—
395C2—2441no—
396C2—2442no—
397C2#2146081614yesdirect product factor
398C2C2×#1684061611yescharacteristic
399C2C2×#1684066411yescharacteristic
400C2C2×#1684066611yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC24×D61D4
cosocleC2×#11758198C23
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1352
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460816C2direct (N × H)
16. #16839697C4semidirect
18. C2×#14519684C4semidirect
19. C22×C4⋊C4×C61C4semidirect
44. #14519684C2×C4semidirect
50. C2×C4⋊C4×C61C2×C4semidirect
198. C2×C61#1352semidirect
206. C22×C4⋊C4#6923semidirect
220. C61C2×#1352semidirect
234. C2×C4⋊C4C2×#6923semidirect
397. C2#21460816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406402
C2×#168406062
#214608162
C2×#168396972
C2×#135261