Finite Group Databasebeta

← C2×#21460764 #30603902

Subgroups — C2×#21460764 #30603902

Order 15616.

770 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 770 conjugacy classes of subgroups — too many to draw. Only its 120 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×#16840605C211yesmaximal, characteristic
2C2×#16840605C211yesmaximal, characteristic
3#21460764C214yesmaximal, direct product factor
4C2×#16839635C211yesmaximal, characteristic
5C2×C22⋊#92420—21no—
6C2×C22⋊#92420—21no—
7#16840605—21no—
8#16840605—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C22×#11758196—21no—
12C22×C22⋊Dic61C411yescharacteristic
13C22×C22⋊Dic61C2211yescharacteristic
14#16839635—21no—
15#16839635—21no—
16#16839635C412yes—
17#16839635C2212yes—
18C2×#14519684—21no—
19C24×C4×C61C411yescharacteristic
20C22×#92420—41no—
21C22×#92420—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24C22⋊#92420—41no—
25C22⋊#92420—41no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×#11758196—44no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—41no—
35C2×C22⋊Dic61—41no—
36C2×C22⋊Dic61C814yescomplemented
37C2×C22⋊Dic61C2×C412yes—
38C2×C22⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61D411yescharacteristic
40C2×C22⋊Dic61D411yescharacteristic
41C2×C22⋊Dic61C2311yescharacteristic
42#14519684—22no—
43#14519684—22no—
44C25×C61C2×C411yescharacteristic
45C23×C4×C61—21no—
46C23×C4×C61—21no—
47C23×C4×C61—44no—
48C23×C4×C61—41no—
49C23×C4×C61—41no—
50C23×C4×C61C2×C412yes—
51C24×C61—21no—
52C24×C61—21no—
53C24×C61—22no—
54C24×C61—42no—
55C24×C61—42no—
56C24×C61C22⋊C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×C812yes—
59C24×C61M1612yes—
60C24×C61C22×C411yescharacteristic
61C22×C4×C61—24no—
62C22×C4×C61—22no—
63C22×C4×C61—44no—
64C22×C4×C61—44no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61—48no—
68C22×C4×C61—44no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—42no—
72C22×C4×C61—44no—
73C22×Dic61—24no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C22×Dic61C2×D411yescharacteristic
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—82no—
90C2×#92420—82no—
91C22⋊Dic61—24no—
92C22⋊Dic61—22no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61C2×C814yescomplemented
98#11758196—44no—
99#11758196—44no—
100C23×C61—22no—
101C23×C61—22no—
102C23×C61—22no—
103C23×C61—22no—
104C23×C61—22no—
105C23×C61—22no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—42no—
111C23×C61—48no—
112C23×C61—42no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—44no—
117C23×C61—44no—
118C23×C61—41no—
119C23×C61—42no—
120C23×C61—42no—
121C23×C61C22⋊C812yes—
122C23×C61C22⋊C812yes—
123C23×C61#9911yescharacteristic
124C23×C61#9911yescharacteristic
125C23×C61#10112yes—
126C23×C61C2×C22⋊C411yescharacteristic
127C23×C61C22×C811yescharacteristic
128C23×C61C2×M1611yescharacteristic
129C2×C4×C61—24no—
130C2×C4×C61—42no—
131C2×C4×C61—44no—
132C2×C4×C61—48no—
133C2×C4×C61—44no—
134C2×C4×C61—44no—
135C2×C4×C61—42no—
136C2×C4×C61—44no—
137C2×Dic61—24no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61—48no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153#92420—82no—
154#92420—82no—
155C2×#1326—611nomaximal, Sylow
156C22×C61—24no—
157C22×C61—24no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—22no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—42no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—44no—
169C22×C61—44no—
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—44no—
173C22×C61—44no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61#32412yes—
179C22×C61#32412yes—
180C22×C61AΣL(1,𝔽16)12yes—
181C22×C61#35212yes—
182C22×C61C2×C22⋊C811yescharacteristic
183C22×C61C2×#9911yescharacteristic
184C22×C61C2×#10111yescharacteristic
185C4×C61—44no—
186Dic61—44no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191C2×#385—611no—
192C2×#323—611no—
193C2×#323—611no—
194#1326—614no—
195C2×C61—21no—
196C2×C61—22no—
197C2×C61—21no—
198C2×C61—42no—
199C2×C61—41no—
200C2×C61—41no—
201C2×C61#132614yescomplemented
202C2×C61C2×#32411yescharacteristic
203C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
204C2×C61C2×#35211yescharacteristic
205C24×C4#692311yescharacteristic
206C22×C4⋊C4—1221no—
207C22×C22⋊C4—611no—
208C22×C22⋊C4—611no—
209C2×C22⋊C8—1221no—
210C2×C22⋊C8—1221no—
211#385—612no—
212#385—612no—
213#385—1221no—
214#385—1221no—
215C2×#95—1221no—
216#323—612no—
217#323—612no—
218#323—1221no—
219#323—1221no—
220C61C2×#132611yescharacteristic, complemented, Sylow
221C25C2×#692311yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—44no—
225C23×C4—41no—
226C23×C4—41no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—1221no—
230C23×C4C2×#692312yes—
231C22×C8—2441no—
232C22×C8—2441no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—2444no—
236C2×C22⋊C4—614no—
237C2×C22⋊C4—612no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—2441no—
245C2×C22⋊C4—2441no—
246C22⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—2441no—
249C22⋊C8—2441no—
250#95—1222no—
251#95—1222no—
252C24—21no—
253C24—21no—
254C24—22no—
255C24—42no—
256C24—42no—
257C24D61⋊C812yes—
258C24#1175821312yes—
259C24C22⋊#692311yescharacteristic
260C24C22⋊#692311yescharacteristic
261C24C22×#692311yescharacteristic
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—48no—
269C22×C4—44no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1224no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—2442no—
285C22×C4—2442no—
286C22×C4—2442no—
287C22×C4—2442no—
288C2×C8—4882no—
289C2×C8—4882no—
290C2×C8—2442no—
291C2×C8—2442no—
292C4⋊C4—2444no—
293C4⋊C4—2444no—
294C22⋊C4—614no—
295C22⋊C4—1224no—
296C22⋊C4—1222no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C23—22no—
302C23—22no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—41no—
312C23—41no—
313C23—44no—
314C23—44no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—48no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23#1451983412yes—
323C23#1451983412yes—
324C23#1451983511yescharacteristic
325C23#1451983511yescharacteristic
326C23#1451983812yes—
327C23C2×C22⋊#692311yescharacteristic
328C23C2×D61⋊C811yescharacteristic
329C23C2×#1175821311yescharacteristic
330C2×C4—24no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—48no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—1224no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2442no—
346C2×C4—2448no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C8—4882no—
355C8—4882no—
356C22—24no—
357C22—24no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—21no—
364C22—21no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—42no—
370C22—44no—
371C22—44no—
372C22—44no—
373C22—44no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1684060812yes—
379C22#1684060812yes—
380C22#1684066212yes—
381C22#1684066412yes—
382C22C2×#1451983411yescharacteristic
383C22C2×#1451983511yescharacteristic
384C22C2×#1451983811yescharacteristic
385C4—44no—
386C4—2444no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—42no—
395C2—41no—
396C2—41no—
397C2#2146076414yesdirect product factor
398C2C2×#1684060811yescharacteristic
399C2C2×#1684066211yescharacteristic
400C2C2×#1684066411yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC24×C4×C61C4
socleC23×C61#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC24×C4#6923
hypocenterC61C2×#1326
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
3. #21460764C2direct (N × H)
36. C2×C22⋊Dic61C8semidirect
97. C22⋊Dic61C2×C8semidirect
201. C2×C61#1326semidirect
220. C61C2×#1326semidirect
397. C2#21460764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406052
#214607642
C2×#168396352
C2×#132661