Finite Group Databasebeta

← C2×#21461167 #30610571

Subgroups — C2×#21461167 #30610571

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840765C211yesmaximal, characteristic
2C22×C4×#92420C211yesmaximal, characteristic
3#21461167C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×Q8⋊#92420C212yesmaximal, complemented
6C2×#16840314C211yesmaximal, characteristic
7C22×#11758217—21no—
8C23×#92420—21no—
9#16840765—22no—
10#16840765C2214yes—
11C2×#14519844—21no—
12C2×C4⋊#92420C2212yes—
13C2×C4×#92420—21no—
14C2×C4×#92420—22no—
15C2×C4×#92420C2212yes—
16C2×C4×#92420C2214yes—
17#16840612C2218yescomplemented
18Q8⋊#92420C2218yescomplemented
19#16840314—22no—
20#16840314—22no—
21#16840314C414yes—
22#16840314C2214yes—
23C2×#14519776C411yescharacteristic
24C2×#14519775C411yescharacteristic
25C2×#14519767—21no—
26C2×#14519756C411yescharacteristic
27C2×#14519754—21no—
28C2×Q8×Dic61C2211yescharacteristic
29C2×#14519742—21no—
30C2×#14519742C2211yescharacteristic
31C2×#14519733—21no—
32C22×C4×Dic61C2211yescharacteristic
33C2×C22⋊Q8×C61C411yescharacteristic
34C2×#11758217—24no—
35C2×#11758217—44no—
36C22×#92420—28no—
37C22×#92420—22no—
38C22×#92420—24no—
39C22×#92420—22no—
40#14519844—24no—
41C4⋊#92420—22no—
42C4⋊#92420C2314yes—
43C4×#92420—22no—
44C4×#92420—24no—
45C4×#92420C2314yes—
46C22×Dic122—21no—
47C22×Dic122C2×C411yescharacteristic
48C23×Dic61D411yescharacteristic
49C23×Dic61D411yescharacteristic
50#14519776—22no—
51#14519776C2×C414yes—
52#14519775—22no—
53#14519775C2×C414yes—
54#14519767—24no—
55#14519767—24no—
56#14519756—22no—
57#14519756C2×C414yes—
58#14519754—24no—
59#14519754—24no—
60Q8×Dic61—21no—
61Q8×Dic61—21no—
62Q8×Dic61C2×C412yes—
63Q8×Dic61C2312yes—
64#14519742—24no—
65#14519742—24no—
66#14519742—21no—
67#14519742—21no—
68#14519742C2×C412yes—
69#14519742C2312yes—
70#14519733—24no—
71#14519733—24no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2×C412yes—
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D412yes—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D412yes—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2312yes—
90C22×Q8×C61C2×C411yescharacteristic
91C23×C4×C61C2×C411yescharacteristic
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61C2×C414yes—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61C2×C411yescharacteristic
96C2×C22⋊C4×C61—21no—
97C24×C61C22⋊C411yescharacteristic
98C2×Q8×C61—21no—
99C2×Q8×C61—24no—
100C2×Q8×C61C22×C412yes—
101C22×C4×C61—24no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61C22⋊C411yescharacteristic
105C22×C4×C61C22⋊C412yes—
106C22×C4×C61C22×C412yes—
107C22×C4×C61C22×C411yescharacteristic
108C22×Dic61—24no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61C22⋊C412yes—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C412yes—
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61SD1614yes—
116C22×Dic61Q1614yes—
117C22×Dic61C2×D411yescharacteristic
118C22×Dic61C2×D412yes—
119C22×Dic61C2×D411yescharacteristic
120C22×Dic61C2×D412yes—
121C2×Dic122—24no—
122C2×Dic122—21no—
123C2×Dic122—24no—
124C2×Dic122—44no—
125C2×Dic122C22×C412yes—
126#11758217—48no—
127C2×#92420—28no—
128C2×#92420—216no—
129C2×#92420—24no—
130C2×#92420—24no—
131C2×#92420—44no—
132C4⋊C4×C61—24no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61C22×C412yes—
135C22⋊C4×C61—24no—
136C22⋊Dic61—24no—
137C4⋊Dic61—21no—
138C4⋊Dic61—22no—
139C4⋊Dic61—22no—
140C4⋊Dic61C22×C412yes—
141#11758196—24no—
142#11758196—24no—
143#11758196—24no—
144#11758196—24no—
145#11758196—22no—
146#11758196—22no—
147C4×Dic61—22no—
148C4×Dic61—22no—
149C4×Dic61—22no—
150C4×Dic61—22no—
151C4×Dic61C22⋊C412yes—
152C4×Dic61C22⋊C412yes—
153C4×Dic61C22⋊C412yes—
154C4×Dic61C22×C411yescharacteristic
155C4×Dic61C22×C412yes—
156C4×Dic61C2×D411yescharacteristic
157C4×Dic61C2×D412yes—
158C4×Dic61C2×D411yescharacteristic
159C4×Dic61C2×D412yes—
160C4×Dic61C2411yescharacteristic
161C23×C61—22no—
162C23×C61—22no—
163C23×C61#10314yes—
164C23×C61C2×C22⋊C412yes—
165C23×C61C2×C22⋊C411yescharacteristic
166Q8×C61—24no—
167Q8×C61—42no—
168C2×C4×C61—22no—
169C2×C4×C61—24no—
170C2×C4×C61—24no—
171C2×C4×C61—22no—
172C2×C4×C61—22no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61C2×C22⋊C412yes—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61#13114yes—
178C2×C4×C61C23×C411yescharacteristic
179C2×Dic61—22no—
180C2×Dic61—24no—
181C2×Dic61—24no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61#10318yes—
187C2×Dic61#10314yes—
188C2×Dic61#10414yes—
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×C22⋊C411yescharacteristic
191C2×Dic61C2×C22⋊C412yes—
192C2×Dic61C2×C22⋊C412yes—
193C2×Dic61C2×SD1612yes—
194C2×Dic61C2×SD1614yes—
195C2×Dic61C2×Q1614yes—
196C2×Dic61C2×Q1612yes—
197C2×Dic61C22×D411yescharacteristic
198C2×Dic61C22×D411yescharacteristic
199Dic122—24no—
200Dic122—42no—
201Dic122—48no—
202#92420—28no—
203#92420—44no—
204C2×#1493—611nomaximal, Sylow
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—28no—
208C22×C61#40812yes—
209C22×C61C2×#10314yes—
210C22×C61C2×#10312yes—
211C22×C61C2×#10412yes—
212C22×C61C22×C22⋊C411yescharacteristic
213C4×C61—22no—
214C4×C61—42no—
215C4×C61—42no—
216C4×C61#40812yes—
217C4×C61C2×#13112yes—
218Dic61—21no—
219Dic61—21no—
220Dic61—42no—
221Dic61—42no—
222Dic61C2×#10312yes—
223Dic61C2×#10314yes—
224Dic61C2×#10414yes—
225Dic61C22×SD1611yescharacteristic
226Dic61C22×Q1611yescharacteristic
227C2×#533—611no—
228C2×#423—611no—
229C22×C4×C8—611no—
230#1493—618no—
231C2×Q8⋊C8—612no—
232C2×Q8⋊C8—612no—
233C2×C61—24no—
234C2×C61#149314yescomplemented
235C2×C61C2×#40811yescharacteristic
236C2×C61C22×#10311yescharacteristic
237C2×C61C22×#10411yescharacteristic
238C22×M16—1221no—
239C23×C8—1221no—
240#533—614no—
241#533—614no—
242#533—1222no—
243#533—1222no—
244C2×C4⋊Q8—611no—
245C2×C4⋊Q8—611no—
246C2×#125—1221no—
247C2×C22⋊Q8—611no—
248C2×C22⋊Q8—1221no—
249C2×C22⋊Q8#692311yescharacteristic
250C2×C4×Q8—611no—
251C2×C4×Q8—611no—
252C2×C4×Q8—1221no—
253C2×#117—1221no—
254C22×C42—611no—
255#423—614no—
256#423—1222no—
257C2×C4⋊C8—612no—
258C2×C4⋊C8—1221no—
259C2×C4×C8—612no—
260C2×C4×C8—614no—
261C2×C4×C8—1221no—
262C2×C4×C8—1222no—
263Q8⋊C8—618no—
264Q8⋊C8—618no—
265C61C2×#149311yescharacteristic, complemented, Sylow
266C22×Q8—611no—
267C22×Q8—1221no—
268C22×Q8C2×#692311yescharacteristic
269C23×C4—611no—
270C23×C4—611no—
271C23×C4C2×#692311yescharacteristic
272C2×M16—1224no—
273C2×M16—2444no—
274C22×C8—1224no—
275C22×C8—1222no—
276C22×C8—1228no—
277C22×C8—1222no—
278C4⋊Q8—614no—
279C4⋊Q8—614no—
280C4⋊Q8—1222no—
281C4⋊Q8—1222no—
282#125—1224no—
283#125—1224no—
284C22⋊Q8—22no—
285C22⋊Q8—614no—
286C22⋊Q8—1224no—
287C22⋊Q8—1224no—
288C22⋊Q8—1222no—
289C22⋊Q8C2×#692314yes—
290C4×Q8—612no—
291C4×Q8—612no—
292C4×Q8—612no—
293C4×Q8—612no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296C4×Q8—1224no—
297C4×Q8—1224no—
298C4×Q8—1221no—
299C4×Q8—1221no—
300#117—1224no—
301#117—1224no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4C2×#692311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—1221no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—612no—
316C2×C42—612no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—612no—
320C2×C42—612no—
321C2×C42—1221no—
322C2×C42—1221no—
323C4⋊C8—614no—
324C4⋊C8—1222no—
325C4⋊C8—1224no—
326C4×C8—614no—
327C4×C8—1222no—
328C4×C8—1224no—
329C24C22⋊#692311yescharacteristic
330C2×Q8—21no—
331C2×Q8—24no—
332C2×Q8—612no—
333C2×Q8—1224no—
334C2×Q8—1221no—
335C2×Q8—1224no—
336C2×Q8—2444no—
337C2×Q8C22×#692312yes—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—614no—
342C22×C4—614no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—612no—
349C22×C4—612no—
350C22×C4—611no—
351C22×C4—1224no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4C22⋊#692312yes—
355C22×C4C22⋊#692311yescharacteristic
356C22×C4C22×#692312yes—
357C22×C4C22×#692311yescharacteristic
358M16—2448no—
359C2×C8—1224no—
360C2×C8—12216no—
361C2×C8—1228no—
362C2×C8—1224no—
363C2×C8—2444no—
364C4⋊C4—24no—
365C4⋊C4—21no—
366C4⋊C4—612no—
367C4⋊C4—1224no—
368C4⋊C4—1224no—
369C4⋊C4—1222no—
370C4⋊C4—1222no—
371C4⋊C4—1224no—
372C4⋊C4—1222no—
373C4⋊C4—1222no—
374C4⋊C4—1221no—
375C4⋊C4—1224no—
376C4⋊C4C22×#692312yes—
377C22⋊C4—24no—
378C22⋊C4—1224no—
379C42—611no—
380C42—612no—
381C42—612no—
382C42—611no—
383C42—612no—
384C42—612no—
385C42—612no—
386C42—611no—
387C42—611no—
388C42—612no—
389C42—1222no—
390C42—1222no—
391C42—1222no—
392C42—1222no—
393C23—22no—
394C23—22no—
395C23#1451984014yes—
396C23C2×C22⋊#692312yes—
397C23C2×C22⋊#692311yescharacteristic
398Q8—24no—
399Q8—42no—
400Q8—1224no—
401Q8—2448no—
402Q8—2442no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—618no—
411C2×C4—614no—
412C2×C4—612no—
413C2×C4—614no—
414C2×C4—614no—
415C2×C4—612no—
416C2×C4—614no—
417C2×C4—611no—
418C2×C4—612no—
419C2×C4—612no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—611no—
423C2×C4—1224no—
424C2×C4—1224no—
425C2×C4—1222no—
426C2×C4—1222no—
427C2×C4—1222no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4C2×C22⋊#692312yes—
431C2×C4C2×C22⋊#692311yescharacteristic
432C2×C4#1451986414yes—
433C2×C4C23×#692311yescharacteristic
434C8—1228no—
435C8—2444no—
436C22—22no—
437C22—22no—
438C22—28no—
439C22#1684073512yes—
440C22C2×#1451984014yes—
441C22C2×#1451984012yes—
442C22D61⋊#10412yes—
443C22C22×C22⋊#692311yescharacteristic
444C4—22no—
445C4—42no—
446C4—42no—
447C4—611no—
448C4—611no—
449C4—612no—
450C4—614no—
451C4—614no—
452C4—1221no—
453C4—1221no—
454C4—2442no—
455C4—2442no—
456C4#1684073512yes—
457C4C2×#1451986412yes—
458C2—24no—
459C2#2146116714yesdirect product factor
460C2C2×#1684073511yescharacteristic
461C2C22×#1451984011yescharacteristic
462C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61C2×#1493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461167C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×Q8⋊#92420C2semidirect
17. #16840612C22semidirect
18. Q8⋊#92420C22semidirect
234. C2×C61#1493semidirect
265. C61C2×#1493semidirect
459. C2#21461167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407652
C22×C4×#924202
#214611672
C2×#168406122
C2×Q8⋊#924202
C2×#168403142
C2×#149361