Finite Group Databasebeta

← C2×#21460703 #30596990

Subgroups — C2×#21460703 #30596990

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840779C211yesmaximal, characteristic
2C2×C4×#11758217C211yesmaximal, characteristic
3#21460703C214yesmaximal, direct product factor
4C2×#16839785C211yesmaximal, characteristic
5C22×#11758217—21no—
6#16840779—21no—
7#16840779—21no—
8#16840779C412yes—
9#16840779C2212yes—
10C2×#14519844C412yes—
11C2×C22⋊#92420—21no—
12C4×#11758217—21no—
13C4×#11758217—21no—
14C4×#11758217C412yes—
15C4×#11758217C2212yes—
16C2×#14519832C412yes—
17C2×C4×#92420—21no—
18C2×C4×#92420—21no—
19C22×#11758194C411yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839785—21no—
22#16839785—21no—
23#16839785C412yes—
24#16839785C2212yes—
25C2×#14519706—21no—
26C2×#14519706—21no—
27C22×M16×C61C411yescharacteristic
28C2×#11758217—28no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C22×#92420—22no—
32C22×#92420—22no—
33#14519844—22no—
34#14519844C2×C414yes—
35C22⋊#92420—22no—
36C22⋊#92420—22no—
37#14519832—22no—
38#14519832C2×C414yes—
39C4×#92420—22no—
40C4×#92420—22no—
41C4×#92420—22no—
42C4×#92420—22no—
43C23×Dic61D411yescharacteristic
44C23×Dic61Q811yescharacteristic
45C2×#11758194—21no—
46C2×#11758194—42no—
47C2×#11758194C2×C412yes—
48C22×#92418—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61Q811yescharacteristic
60C2×C4×Dic61C2311yescharacteristic
61#14519706—22no—
62#14519706—22no—
63#14519706—22no—
64#14519706—22no—
65C23×C4×C61C2×C411yescharacteristic
66C2×M16×C61—21no—
67C2×M16×C61—42no—
68C2×M16×C61C2×C412yes—
69C22×C8×C61—21no—
70C24×C61C4⋊C411yescharacteristic
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C4211yescharacteristic
74C22×C4×C61C4211yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C22×Dic61—24no—
80C22×Dic61—24no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C4⋊C411yescharacteristic
90C22×Dic61C4⋊C411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×Q811yescharacteristic
93#11758217—28no—
94#11758217—28no—
95C2×#92420—28no—
96C2×#92420—24no—
97C2×#92420—24no—
98C2×#92420—44no—
99M16×C61—42no—
100M16×C61—42no—
101C2×C8×C61—22no—
102C2×C8×C61—42no—
103C4×Dic61C4211yescharacteristic
104C4×Dic61C4211yescharacteristic
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C4⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C22×C411yescharacteristic
116C4×Dic61C22×C411yescharacteristic
117C4×Dic61C2×D411yescharacteristic
118C4×Dic61C2×D411yescharacteristic
119#11758194—42no—
120#11758194—42no—
121C2×#92418—22no—
122C2×#92418—42no—
123C23×C61—22no—
124C23×C61—22no—
125C23×C61—22no—
126C23×C61#9511yescharacteristic
127C23×C61#9511yescharacteristic
128C23×C61C2×C4⋊C411yescharacteristic
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#10012yes—
139C2×C4×C61#10112yes—
140C2×C4×C61C2×C4211yescharacteristic
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61#9511yescharacteristic
153C2×Dic61#9511yescharacteristic
154C2×Dic61#9511yescharacteristic
155C2×Dic61#9511yescharacteristic
156C2×Dic61#10414yes—
157C2×Dic61#10814yes—
158C2×Dic61C2×C22⋊C411yescharacteristic
159C2×Dic61C2×C22⋊C411yescharacteristic
160C2×Dic61C2×C4⋊C411yescharacteristic
161C2×Dic61C2×C4⋊C411yescharacteristic
162#92420—28no—
163#92420—44no—
164C8×C61—42no—
165#92418—42no—
166C2×#1299—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—44no—
174C22×C61#33912yes—
175C22×C61#34112yes—
176C22×C61#34312yes—
177C22×C61C2×#9511yescharacteristic
178C4×C61—21no—
179C4×C61—21no—
180C4×C61#34312yes—
181C4×C61C2×#10011yescharacteristic
182C4×C61C2×#10111yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61#33912yes—
188Dic61#34112yes—
189Dic61C2×#10412yes—
190Dic61C2×#10812yes—
191C2×#431—611no—
192C2×#423—611no—
193C2×C4×M16—611no—
194#1299—614no—
195C2×C61—41no—
196C2×C61—41no—
197C2×C61#129914yescomplemented
198C2×C61C2×#33911yescharacteristic
199C2×C61C2×#34111yescharacteristic
200C2×C61C2×#34311yescharacteristic
201C22×M16—611no—
202C22×M16—1221no—
203C22×M16#692311yescharacteristic
204C22×C42—611no—
205#431—612no—
206#431—612no—
207#431—1221no—
208#431—1221no—
209#423—612no—
210#423—612no—
211#423—1221no—
212#423—1221no—
213C2×C4⋊C8—612no—
214C2×C4⋊C8—1221no—
215C2×C4⋊C8—1221no—
216C2×C22⋊C8—1221no—
217C4×M16—612no—
218C4×M16—612no—
219C4×M16—1221no—
220C4×M16—1221no—
221C2×#97—612no—
222C2×C4×C8—1221no—
223C2×C4×C8—1221no—
224C61C2×#129911yescharacteristic, complemented, Sylow
225C23×C4—611no—
226C23×C4—611no—
227C23×C4C2×#692311yescharacteristic
228C2×M16—21no—
229C2×M16—42no—
230C2×M16—612no—
231C2×M16—1222no—
232C2×M16—1222no—
233C2×M16—1228no—
234C2×M16—1221no—
235C2×M16—2442no—
236C2×M16C2×#692312yes—
237C22×C8—21no—
238C22×C8—1222no—
239C22×C8—1222no—
240C22×C8—1221no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C4⋊C8—614no—
254C4⋊C8—1222no—
255C4⋊C8—1222no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8—1222no—
259C22⋊C8—1222no—
260C22⋊C8—1222no—
261#97—614no—
262#97—1222no—
263C4×C8—1222no—
264C4×C8—1222no—
265C4×C8—1222no—
266C4×C8—1222no—
267C24C4⋊#692311yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1224no—
283C22×C4—1224no—
284C22×C4C4×#692311yescharacteristic
285C22×C4C4×#692311yescharacteristic
286C22×C4C4⋊#692311yescharacteristic
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22⋊#692311yescharacteristic
289C22×C4C22×#692311yescharacteristic
290M16—42no—
291M16—42no—
292M16—1228no—
293M16—1228no—
294M16—2442no—
295M16—2442no—
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—1224no—
299C2×C8—1228no—
300C2×C8—1224no—
301C2×C8—1222no—
302C2×C8—2444no—
303C2×C8—2442no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23(C2×#6923)⋊C411yescharacteristic
324C23(C2×#6923)⋊C411yescharacteristic
325C23C2×C4⋊#692311yescharacteristic
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—614no—
334C2×C4—614no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4(C2×#6923)⋊C411yescharacteristic
354C2×C4(C2×#6923)⋊C411yescharacteristic
355C2×C4#1451983712yes—
356C2×C4#1451983812yes—
357C2×C4C2×C4×#692311yescharacteristic
358C2×C4C2×C22⋊#692311yescharacteristic
359C8—42no—
360C8—1228no—
361C8—2444no—
362C8—2442no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—44no—
370C22#1684063412yes—
371C22#1684063712yes—
372C22#1684064212yes—
373C22C2×(C2×#6923)⋊C411yescharacteristic
374C4—21no—
375C4—21no—
376C4—612no—
377C4—612no—
378C4—612no—
379C4—612no—
380C4—1221no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4#1684064212yes—
385C4C2×#1451983711yescharacteristic
386C4C2×#1451983811yescharacteristic
387C2—41no—
388C2—41no—
389C2#2146070314yesdirect product factor
390C2C2×#1684063411yescharacteristic
391C2C2×#1684063711yescharacteristic
392C2C2×#1684064211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC23×C61#95
prime radicalC24×C61C4⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×M16#6923
hypocenterC61C2×#1299
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460703C2direct (N × H)
197. C2×C61#1299semidirect
224. C61C2×#1299semidirect
389. C2#21460703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407792
C2×C4×#117582172
#214607032
C2×#168397852
C2×#129961