Finite Group Databasebeta

← C2×#21460691 #30596772

Subgroups — C2×#21460691 #30596772

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C212yesmaximal
2#21460691C214yesmaximal, direct product factor
3C22×#14519689C211yesmaximal, characteristic
4C22×#11758213—22no—
5#16840733—22no—
6#16840733—22no—
7#16840733C414yes—
8#16840733C2214yes—
9C2×#14519834C414yes—
10C2×C22⋊#92420—22no—
11C23×C4×D61C2211yescharacteristic
12C23×#92418C411yescharacteristic
13C2×#14519689—22no—
14C2×#14519689—22no—
15C2×#14519689C412yes—
16C2×#14519689C2212yes—
17C23×C8×C61C411yescharacteristic
18C2×#11758213—24no—
19C2×#11758213—24no—
20C2×#11758213—44no—
21C2×#11758213—44no—
22C22×#92420—24no—
23#14519834—24no—
24#14519834C2×C418yes—
25C22⋊#92420—24no—
26C22⋊#92420—24no—
27C24×D61Q811yescharacteristic
28C23×Dic61D411yescharacteristic
29C22×C4×D61—42no—
30C22×C4×D61—42no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61C2×C412yes—
33C22×C4×D61C2×C412yes—
34C22×C4×D61D412yes—
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D412yes—
37C22×C4×D61Q811yescharacteristic
38C22×C4×D61C2311yescharacteristic
39C22×#92418—21no—
40C22×#92418—21no—
41C22×#92418—42no—
42C22×#92418C2×C412yes—
43#14519689—24no—
44#14519689—24no—
45C23×C4×C61C2×C411yescharacteristic
46C22×C8×C61—21no—
47C22×C8×C61—21no—
48C22×C8×C61—42no—
49C22×C8×C61C2×C412yes—
50C24×C61C4⋊C411yescharacteristic
51C23×D61—22no—
52C23×D61—22no—
53C23×D61—42no—
54C23×D61—42no—
55C23×D61C4⋊C412yes—
56C23×D61C4⋊C411yescharacteristic
57C23×D61C4⋊C412yes—
58C23×D61C2×Q811yescharacteristic
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61C4211yescharacteristic
62C22×C4×C61C4211yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C4⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—42no—
68C22×Dic61C22⋊C412yes—
69C22×Dic61C22⋊C412yes—
70C22×Dic61C4⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×C4×D61—24no—
73C2×C4×D61—24no—
74C2×C4×D61—44no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—44no—
84C2×C4×D61C4212yes—
85C2×C4×D61C22⋊C412yes—
86C2×C4×D61C22⋊C412yes—
87C2×C4×D61C22⋊C412yes—
88C2×C4×D61C4⋊C412yes—
89C2×C4×D61C4⋊C412yes—
90C2×C4×D61C22×C412yes—
91C2×C4×D61C2×D412yes—
92C2×#92420—28no—
93C2×#92420—48no—
94#11758213—48no—
95#11758213—44no—
96#11758213—44no—
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99C2×C8×C61—42no—
100C2×C8×C61—42no—
101C2×#92418—22no—
102C2×#92418—42no—
103C2×#92418—42no—
104C2×#92418—42no—
105C23×C61—22no—
106C23×C61—22no—
107C23×C61#9511yescharacteristic
108C23×C61#9511yescharacteristic
109C23×C61#10812yes—
110C23×C61#10812yes—
111C23×C61C2×C4⋊C411yescharacteristic
112C22×D61—24no—
113C22×D61—24no—
114C22×D61—24no—
115C22×D61—24no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—42no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—42no—
125C22×D61—41no—
126C22×D61—48no—
127C22×D61—48no—
128C22×D61#9512yes—
129C22×D61C2×C4⋊C412yes—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9912yes—
140C2×C4×C61#9912yes—
141C2×C4×C61C2×C4211yescharacteristic
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C2×Dic61—24no—
144C2×Dic61—42no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9512yes—
148C2×Dic61C2×C22⋊C412yes—
149C4×D61—24no—
150C4×D61—24no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159#92420—48no—
160C8×C61—42no—
161#92418—42no—
162C2×#1293—611nomaximal, Sylow
163C22×C61—24no—
164C22×C61—24no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#33812yes—
170C22×C61#34112yes—
171C22×C61#34112yes—
172C22×C61#34212yes—
173C22×C61C2×#9511yescharacteristic
174C22×C61C2×#10811yescharacteristic
175C22×C61C2×#10811yescharacteristic
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—48no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—48no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61#34212yes—
191C4×C61C2×#9911yescharacteristic
192C4×C61C2×#9911yescharacteristic
193Dic61—22no—
194Dic61—22no—
195C2×#407—612no—
196C22×C22⋊C8—611no—
197#1293—614no—
198C2×C61—22no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61#129314yescomplemented
202C2×C61C2×#33811yescharacteristic
203C2×C61C2×#34111yescharacteristic
204C2×C61C2×#34211yescharacteristic
205D61—42no—
206D61—42no—
207C24×C4—611no—
208C22×M16—1222no—
209C23×C8—611no—
210C23×C8#692311yescharacteristic
211#407—614no—
212#407—614no—
213#407—1222no—
214#407—1222no—
215C2×C22⋊C8—614no—
216C2×C22⋊C8—612no—
217C2×C22⋊C8—612no—
218C2×C22⋊C8—1222no—
219C2×C22⋊C8—1222no—
220C2×C22⋊C8—1222no—
221C61C2×#129311yescharacteristic, complemented, Sylow
222C25—611no—
223C23×C4—611no—
224C23×C4—612no—
225C23×C4—612no—
226C23×C4—612no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—612no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—2442no—
233C23×C4—2442no—
234C23×C4C2×#692311yescharacteristic
235C2×M16—1224no—
236C2×M16—1224no—
237C2×M16—2444no—
238C2×M16—2444no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—42no—
242C22×C8—612no—
243C22×C8—1224no—
244C22×C8—1221no—
245C22×C8—1221no—
246C22×C8—2442no—
247C22×C8C2×#692312yes—
248C22⋊C8—618no—
249C22⋊C8—1224no—
250C22⋊C8—1224no—
251C22⋊C8—1224no—
252C22⋊C8—1224no—
253C22⋊C8—1224no—
254C24—612no—
255C24—612no—
256C24—611no—
257C24—611no—
258C24—1222no—
259C24—1222no—
260C24—2442no—
261C24—2442no—
262C24C4⋊#692311yescharacteristic
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—612no—
266C22×C4—612no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—1224no—
278C22×C4—1224no—
279C22×C4—2442no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2442no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4—2444no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4—2444no—
289C22×C4—2442no—
290C22×C4C4×#692311yescharacteristic
291C22×C4C4×#692311yescharacteristic
292C22×C4C4⋊#692311yescharacteristic
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22×#692311yescharacteristic
296M16—2444no—
297M16—2444no—
298M16—2448no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—1228no—
304C2×C8—1222no—
305C2×C8—2442no—
306C2×C8—2448no—
307C2×C8—2442no—
308C2×C8—2442no—
309C23—22no—
310C23—22no—
311C23—612no—
312C23—612no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1224no—
318C23—1224no—
319C23—1224no—
320C23—1224no—
321C23—2442no—
322C23—2441no—
323C23—2441no—
324C23—2442no—
325C23—2441no—
326C23—2441no—
327C23—2448no—
328C23—2448no—
329C23(C2×#6923)⋊C411yescharacteristic
330C23(C2×#6923)⋊C411yescharacteristic
331C23#1451984712yes—
332C23#1451984812yes—
333C23C2×C4⋊#692311yescharacteristic
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—612no—
342C2×C4—612no—
343C2×C4—1224no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1224no—
349C2×C4—1224no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4(C2×#6923)⋊C411yescharacteristic
358C2×C4(C2×#6923)⋊C411yescharacteristic
359C2×C4#1451983512yes—
360C2×C4#1451983612yes—
361C2×C4C2×C4×#692311yescharacteristic
362C2×C4C2×C22⋊#692311yescharacteristic
363C8—42no—
364C8—2448no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—24no—
369C22—24no—
370C22—21no—
371C22—21no—
372C22—1222no—
373C22—1222no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—1222no—
378C22—2442no—
379C22—2442no—
380C22—2442no—
381C22—2442no—
382C22—2448no—
383C22—2448no—
384C22#1684063112yes—
385C22#1684063812yes—
386C22#1684063812yes—
387C22#1684064012yes—
388C22C2×(C2×#6923)⋊C411yescharacteristic
389C22C2×#1451984711yescharacteristic
390C22C2×#1451984811yescharacteristic
391C4—21no—
392C4—21no—
393C4—1222no—
394C4—1222no—
395C4#1684064012yes—
396C4C2×#1451983511yescharacteristic
397C4C2×#1451983611yescharacteristic
398C2—21no—
399C2—21no—
400C2—22no—
401C2—2442no—
402C2—2442no—
403C2#2146069114yesdirect product factor
404C2C2×#1684063111yescharacteristic
405C2C2×#1684063811yescharacteristic
406C2C2×#1684064011yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC23×C8×C61C4
socleC23×C61#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC23×C8#6923
hypocenterC61C2×#1293
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #21460691C2direct (N × H)
201. C2×C61#1293semidirect
221. C61C2×#1293semidirect
403. C2#21460691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407332
#214606912
C22×#145196892
C2×#129361