Finite Group Databasebeta

← C2×#21462102 #30623968

Subgroups — C2×#21462102 #30623968

Order 15616.

1230 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 216 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×#16840743C212yesmaximal
2#21462102C218yesmaximal, direct product factor
3C2×#16840669C212yesmaximal, complemented
4C2×#16840668C212yesmaximal, complemented
5C2×#16840337C211yesmaximal, characteristic
6C2×#14519856—22no—
7#16840743—24no—
8#16840743C2218yes—
9C2×#14519836—22no—
10C2×#14519836C2214yes—
11#16840669C2218yescomplemented
12#16840668C2218yescomplemented
13C22×#11758226C2211yescharacteristic
14C22×Q8×D61C411yescharacteristic, complemented
15#16840337—24no—
16#16840337C414yescomplemented
17#16840337C2214yes—
18C2×#14519775C411yescharacteristic, complemented
19C2×#14519766C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519762—22no—
22C2×#14519755—22no—
23C2×#14519734C411yescharacteristic, complemented
24C2×C4⋊Q8×C61C411yescharacteristic, complemented
25#14519856—28no—
26#14519856—44no—
27C2×C4⋊#6923—42no—
28C2×C22⋊#6923—24no—
29C2×C4×#6923—42no—
30#14519836—28no—
31#14519836—24no—
32#14519836C2318yes—
33C2×#11758226—42no—
34C2×#11758226—42no—
35C2×#11758226C2×C412yes—
36C2×#11758226D414yes—
37C2×#11758226C2312yes—
38C22×Dic122—21no—
39C22×Dic122C2×C411yescharacteristic
40C2×Q8×D61—22no—
41C2×Q8×D61—42no—
42C2×Q8×D61—42no—
43C2×Q8×D61C2×C414yescomplemented
44C22×D244D412yes—
45C22×D244C2311yescharacteristic
46C22×C4×D61—21no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61D412yes—
49#14519775—22no—
50#14519775C2×C414yescomplemented
51#14519766—22no—
52#14519766C2×C412yes—
53#14519766C2312yes—
54#14519765—22no—
55#14519765C2×C412yes—
56#14519765C2312yes—
57#14519762—28no—
58#14519762—28no—
59#14519755—28no—
60#14519755—28no—
61#14519734—22no—
62#14519734C2×C414yescomplemented
63C2×#11758196—22no—
64C2×#11758196—21no—
65C2×#11758198—21no—
66C2×#11758198—22no—
67C2×#11758198—22no—
68C2×C4×Dic61C2×C411yescharacteristic
69C22×Q8×C61C2×C411yescharacteristic
70C22×Q8×C61C2×C411yescharacteristic
71C4⋊Q8×C61—22no—
72C4⋊Q8×C61C2×C414yescomplemented
73C2×C4⋊C4×C61—22no—
74C2×C42×C61C2×C411yescharacteristic
75C23×D61C22⋊C411yescharacteristic
76C23×D61C2×D412yes—
77C22×#6923—44no—
78C2×Q8×C61—21no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C2×Q8×C61C22⋊C412yes—
84C2×Q8×C61C22×C412yes—
85C2×Q8×C61C22×C412yes—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61C22⋊C412yes—
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61C22⋊C411yescharacteristic
93#11758226—44no—
94#11758226—44no—
95#11758226—44no—
96#11758226—44no—
97Q8×D61—48no—
98Q8×D61—48no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244C22⋊C414yes—
104C2×D244C22×C411yescharacteristic
105C2×D244C2×D414yes—
106C2×D244C2×D412yes—
107C2×D244C2411yescharacteristic
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—24no—
113C2×C4×D61—24no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61C22⋊C412yes—
117C2×C4×D61C22⋊C414yes—
118C2×C4×D61C22×C412yes—
119C2×C4×D61C2×D414yes—
120C2×Dic122—21no—
121C2×Dic122—24no—
122C2×Dic122—42no—
123C2×Dic122—42no—
124C2×Dic122—41no—
125C2×Dic122—41no—
126C2×Dic122C22×C412yes—
127C22⋊#6923—28no—
128C22⋊#6923—44no—
129C4⋊#6923—48no—
130C4×#6923—48no—
131C4⋊C4×C61—28no—
132C42×C61—21no—
133C42×C61C22×C412yes—
134#11758198—24no—
135#11758198—24no—
136#11758198—24no—
137#11758198—24no—
138#11758198—24no—
139#11758196—28no—
140#11758196—24no—
141C4×Dic61—21no—
142C4×Dic61C22×C412yes—
143C23×C61C2×C22⋊C411yescharacteristic
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—22no—
147C22×D61—22no—
148C22×D61—42no—
149C22×D61—44no—
150C22×D61C2×C22⋊C412yes—
151C22×D61C2×C22⋊C412yes—
152C22×D61C22×D412yes—
153C2×#6923—48no—
154C2×#6923—88no—
155Q8×C61—42no—
156Q8×C61—42no—
157Q8×C61—42no—
158Q8×C61—42no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61C2×C22⋊C411yescharacteristic
169C2×C4×C61C2×C22⋊C414yes—
170C2×C4×C61C23×C411yescharacteristic
171C2×Dic61—22no—
172C2×Dic61—22no—
173C2×Dic61—42no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61#9912yes—
177C2×Dic61#9912yes—
178C2×Dic61C2×C22⋊C412yes—
179D244—44no—
180D244—41no—
181D244—42no—
182D244—44no—
183D244—41no—
184C4×D61—24no—
185C4×D61—24no—
186C4×D61—24no—
187C4×D61—24no—
188C4×D61—24no—
189C4×D61—24no—
190C4×D61—48no—
191Dic122—42no—
192Dic122—48no—
193Dic122—42no—
194C2×#2129—611nomaximal, Sylow
195C22×C61—22no—
196C22×C61C2×#9911yescharacteristic
197C22×C61C2×#9911yescharacteristic
198C22×C61C22×C22⋊C411yescharacteristic
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—42no—
203C2×D61—44no—
204C2×D61—42no—
205C2×D61—42no—
206C2×D61—42no—
207C2×D61—42no—
208C2×D61—82no—
209#6923—88no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—24no—
213C4×C61—42no—
214C4×C61—42no—
215Dic61—42no—
216Dic61—42no—
217Dic61C2×#9914yes—
218C2×#536—611no—
219C2×#410—612no—
220#2129—618no—
221C2×#354—612no—
222C2×#354—612no—
223C2×C61—21no—
224C2×C61—21no—
225C2×C61#212912yescomplemented
226C2×C61C22×#9911yescharacteristic
227D61—42no—
228D61—42no—
229D61—42no—
230C22×#41—611no—
231C23×Q8—611no—
232#536—614no—
233#536—614no—
234#536—1224no—
235C2×C4⋊Q8—611no—
236C2×C4⋊Q8#692311yescharacteristic, complemented
237C2×#124—611no—
238C2×#124—611no—
239C2×#123—1222no—
240C2×C22⋊Q8—1222no—
241C2×#117—611no—
242C2×#117—1222no—
243#410—618no—
244#410—1224no—
245C2×#99—614no—
246C2×#99—1222no—
247#354—618no—
248#354—618no—
249C61C2×#212911yescharacteristic, complemented, Sylow
250C2×#41—614no—
251C2×#41—612no—
252C2×#41—612no—
253C2×#41—2442no—
254C2×#41—2442no—
255C22×Q8—614no—
256C22×Q8—611no—
257C22×Q8—1221no—
258C22×Q8—1222no—
259C22×Q8—2442no—
260C22×Q8—2442no—
261C22×Q8C2×#692311yescharacteristic
262C22×Q8C2×#692311yescharacteristic
263C22×D4—612no—
264C22×D4—611no—
265C23×C4—612no—
266C23×C4—611no—
267C23×C4—1221no—
268C4⋊Q8—22no—
269C4⋊Q8—614no—
270C4⋊Q8—1222no—
271C4⋊Q8C2×#692314yescomplemented
272#124—612no—
273#124—612no—
274#124—612no—
275#124—612no—
276#124—1222no—
277#124—1222no—
278#123—1228no—
279#123—1228no—
280C22⋊Q8—1228no—
281C22⋊Q8—1228no—
282#117—614no—
283#117—1222no—
284#117—1228no—
285#117—2444no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—1222no—
289C2×C4⋊C4—2442no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1222no—
292C2×C22⋊C4—1222no—
293C2×C22⋊C4—1224no—
294C2×C42—611no—
295C2×C42—2442no—
296C2×C42C2×#692311yescharacteristic
297#99—618no—
298#99—1224no—
299#99—1228no—
300C24—612no—
301C24—611no—
302#41—2444no—
303#41—2444no—
304#41—2444no—
305#41—2444no—
306C2×Q8—21no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—612no—
312C2×Q8—1224no—
313C2×Q8—1221no—
314C2×Q8—2441no—
315C2×Q8—2441no—
316C2×Q8—2442no—
317C2×Q8—2442no—
318C2×Q8—2448no—
319C2×Q8—2448no—
320C2×Q8C22⋊#692312yes—
321C2×Q8C22×#692312yes—
322C2×Q8C22×#692312yes—
323C2×D4—614no—
324C2×D4—612no—
325C2×D4—614no—
326C2×D4—611no—
327C2×D4—611no—
328C2×D4—2442no—
329C2×D4—2441no—
330C2×D4—2442no—
331C2×D4—2441no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—611no—
335C22×C4—614no—
336C22×C4—612no—
337C22×C4—614no—
338C22×C4—612no—
339C22×C4—1222no—
340C22×C4—1222no—
341C22×C4—1224no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1224no—
345C22×C4—1221no—
346C22×C4—1221no—
347C22×C4—2442no—
348C22×C4—2442no—
349C22×C4—2444no—
350C22×C4C22⋊#692312yes—
351C22×C4C22×#692311yescharacteristic
352C4⋊C4—28no—
353C4⋊C4—1224no—
354C4⋊C4—1228no—
355C4⋊C4—2448no—
356C22⋊C4—1224no—
357C22⋊C4—1224no—
358C22⋊C4—1224no—
359C22⋊C4—1224no—
360C22⋊C4—1224no—
361C22⋊C4—1228no—
362C22⋊C4—2444no—
363C42—21no—
364C42—612no—
365C42—1221no—
366C42—2448no—
367C42C22×#692312yes—
368C23—612no—
369C23—612no—
370C23—612no—
371C23—1222no—
372C23—1221no—
373C23—1221no—
374C23—1222no—
375C23—2444no—
376C23—2442no—
377C23C2×C22⋊#692311yescharacteristic
378Q8—42no—
379Q8—42no—
380Q8—42no—
381Q8—42no—
382Q8—2442no—
383Q8—2442no—
384Q8—2448no—
385D4—2444no—
386D4—2444no—
387D4—2442no—
388D4—2441no—
389D4—2441no—
390C2×C4—22no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—612no—
400C2×C4—612no—
401C2×C4—612no—
402C2×C4—1224no—
403C2×C4—1224no—
404C2×C4—1224no—
405C2×C4—1224no—
406C2×C4—1224no—
407C2×C4—1224no—
408C2×C4—1222no—
409C2×C4—1222no—
410C2×C4—4888no—
411C2×C4—2448no—
412C2×C4—2448no—
413C2×C4—2442no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4C2×C22⋊#692311yescharacteristic
417C2×C4C2×C22⋊#692314yes—
418C2×C4C23×#692311yescharacteristic
419C22—22no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—4882no—
424C22—2442no—
425C22—2442no—
426C22—2442no—
427C22—2442no—
428C22—2444no—
429C22—2442no—
430C22D61⋊#9911yescharacteristic
431C22D61⋊#9911yescharacteristic
432C22C22×C22⋊#692311yescharacteristic
433C4—24no—
434C4—21no—
435C4—21no—
436C4—42no—
437C4—42no—
438C4—614no—
439C4—4888no—
440C4—2442no—
441C4—2442no—
442C2—21no—
443C2—21no—
444C2—2442no—
445C2—2442no—
446C2—2442no—
447C2#2146210212yesdirect product factor
448C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758226C22
cosocleC2×D244C24
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21462102C2direct (N × H)
3. C2×#16840669C2semidirect
4. C2×#16840668C2semidirect
11. #16840669C22semidirect
12. #16840668C22semidirect
14. C22×Q8×D61C4semidirect
16. #16840337C4semidirect
18. C2×#14519775C4semidirect
23. C2×#14519734C4semidirect
24. C2×C4⋊Q8×C61C4semidirect
43. C2×Q8×D61C2×C4semidirect
50. #14519775C2×C4semidirect
62. #14519734C2×C4semidirect
72. C4⋊Q8×C61C2×C4semidirect
225. C2×C61#2129semidirect
236. C2×C4⋊Q8#6923semidirect
249. C61C2×#2129semidirect
271. C4⋊Q8C2×#6923semidirect
447. C2#21462102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407432
#214621022
C2×#168406692
C2×#168406682
C2×#168403372
C2×#212961