Finite Group Databasebeta

← C2×#21461321 #30611714

Subgroups — C2×#21461321 #30611714

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840779C211yesmaximal, characteristic
2C22×#14519844C211yesmaximal, characteristic
3#21461321C218yesmaximal, direct product factor
4C2×#16840622C212yesmaximal, complemented
5C2×#16840621C212yesmaximal, complemented
6C2×#16840314C211yesmaximal, characteristic
7C23×#92420—21no—
8#16840779—22no—
9#16840779C2214yes—
10C2×#14519844—21no—
11C2×#14519844—22no—
12C2×#14519844C2212yes—
13C2×#14519844C2212yes—
14C2×#14519844C2214yes—
15C2×C22⋊#92420—21no—
16C2×C4×#92420—21no—
17#16840622C2218yescomplemented
18#16840621C2218yescomplemented
19#16840314—22no—
20#16840314—22no—
21#16840314C414yes—
22#16840314C2214yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519775C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519756C411yescharacteristic
27C2×#14519754—21no—
28C2×Q8×Dic61C411yescharacteristic
29C2×#14519742—21no—
30C2×#14519742C411yescharacteristic
31C2×#14519733—21no—
32C22×C4×Dic61C2211yescharacteristic
33C2×C22⋊Q8×C61C411yescharacteristic
34C22×#92420—22no—
35C22×#92420—22no—
36C22×#92420—24no—
37C22×#92420—44no—
38#14519844—24no—
39#14519844—22no—
40#14519844—22no—
41#14519844C2314yes—
42#14519844C2314yes—
43C22⋊#92420—24no—
44C4×#92420—24no—
45C22×Dic122—21no—
46C22×Dic122C2×C411yescharacteristic
47C23×Dic61D411yescharacteristic
48C23×Dic61D411yescharacteristic
49#14519776—21no—
50#14519776—21no—
51#14519776C2×C412yes—
52#14519776C2312yes—
53#14519775—21no—
54#14519775—21no—
55#14519775C2×C412yes—
56#14519775C2312yes—
57#14519767—24no—
58#14519767—24no—
59#14519756—22no—
60#14519756C2×C414yes—
61#14519754—24no—
62#14519754—24no—
63Q8×Dic61—22no—
64Q8×Dic61C2×C414yes—
65#14519742—24no—
66#14519742—22no—
67#14519742—24no—
68#14519742C2×C414yes—
69#14519733—24no—
70#14519733—24no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C412yes—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D412yes—
86C2×C4×Dic61D412yes—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2312yes—
89C22×Q8×C61C2×C411yescharacteristic
90C23×C4×C61C2×C411yescharacteristic
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61C2×C414yes—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61C2×C411yescharacteristic
95C2×C22⋊C4×C61—21no—
96C24×C61C22⋊C411yescharacteristic
97C2×Q8×C61—21no—
98C2×Q8×C61—42no—
99C2×Q8×C61C22×C412yes—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—42no—
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22⋊C412yes—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C412yes—
107C22×Dic61—24no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C412yes—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C412yes—
114C22×Dic61SD1614yes—
115C22×Dic61Q1614yes—
116C22×Dic61C2×D412yes—
117C22×Dic61C2×D411yescharacteristic
118C22×Dic61C2×D412yes—
119C22×Dic61C2×D411yescharacteristic
120C2×Dic122—21no—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—44no—
124C2×Dic122—42no—
125C2×Dic122C22×C412yes—
126C2×#92420—24no—
127C2×#92420—24no—
128C2×#92420—48no—
129C2×#92420—44no—
130C2×#92420—44no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61C22×C412yes—
134C22⋊C4×C61—24no—
135C22⋊Dic61—24no—
136C4⋊Dic61—21no—
137C4⋊Dic61—24no—
138C4⋊Dic61C22×C412yes—
139#11758196—24no—
140#11758196—22no—
141#11758196—22no—
142#11758196—22no—
143#11758196—24no—
144#11758196—22no—
145#11758196—22no—
146#11758196—22no—
147C4×Dic61—24no—
148C4×Dic61—24no—
149C4×Dic61C22⋊C412yes—
150C4×Dic61C22⋊C412yes—
151C4×Dic61C22⋊C412yes—
152C4×Dic61C22×C412yes—
153C4×Dic61C22×C411yescharacteristic
154C4×Dic61C2×D412yes—
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D411yescharacteristic
157C4×Dic61C2×D411yescharacteristic
158C4×Dic61C2411yescharacteristic
159C23×C61—22no—
160C23×C61—22no—
161C23×C61#10314yes—
162C23×C61C2×C22⋊C412yes—
163C23×C61C2×C22⋊C411yescharacteristic
164Q8×C61—42no—
165Q8×C61—42no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61C2×C22⋊C412yes—
175C2×C4×C61C2×C22⋊C411yescharacteristic
176C2×C4×C61C23×C411yescharacteristic
177C2×Dic61—22no—
178C2×Dic61—24no—
179C2×Dic61—24no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61#10318yes—
185C2×Dic61#10314yes—
186C2×Dic61C2×C22⋊C412yes—
187C2×Dic61C2×C22⋊C412yes—
188C2×Dic61C2×C22⋊C411yescharacteristic
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×SD1614yes—
191C2×Dic61C2×SD1612yes—
192C2×Dic61C2×Q1614yes—
193C2×Dic61C2×Q1612yes—
194C2×Dic61#13514yes—
195C2×Dic61C22×D411yescharacteristic
196C2×Dic61C22×D411yescharacteristic
197Dic122—42no—
198Dic122—44no—
199Dic122—44no—
200Dic122—42no—
201#92420—44no—
202#92420—44no—
203C2×#1542—611nomaximal, Sylow
204C22×C61—28no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61#41312yes—
208C22×C61C2×#10314yes—
209C22×C61C2×#10312yes—
210C22×C61#41612yes—
211C22×C61C22×C22⋊C411yescharacteristic
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—22no—
215C4×C61—42no—
216C4×C61—42no—
217Dic61—22no—
218Dic61—42no—
219Dic61—42no—
220Dic61C2×#10314yes—
221Dic61C2×#10312yes—
222Dic61#41612yes—
223Dic61C22×SD1611yescharacteristic
224Dic61C22×Q1611yescharacteristic
225Dic61C2×#13512yes—
226C2×#533—611no—
227C2×#431—611no—
228C22×C4⋊C8—611no—
229#1542—618no—
230C2×#333—612no—
231C2×#332—612no—
232C2×C61—24no—
233C2×C61#154214yescomplemented
234C2×C61C2×#41311yescharacteristic
235C2×C61C22×#10311yescharacteristic
236C2×C61C2×#41611yescharacteristic
237C23×C8—1221no—
238#533—614no—
239#533—614no—
240#533—1222no—
241#533—1222no—
242C2×C4⋊Q8—611no—
243C2×C4⋊Q8—611no—
244C2×#125—1221no—
245C2×C22⋊Q8—611no—
246C2×C22⋊Q8—1221no—
247C2×C22⋊Q8#692311yescharacteristic
248C2×C4×Q8—611no—
249C2×C4×Q8—611no—
250C2×C4×Q8—1221no—
251C2×#117—1221no—
252C22×C42—611no—
253#431—614no—
254#431—1222no—
255C2×C4⋊C8—612no—
256C2×C4⋊C8—612no—
257C2×C4⋊C8—614no—
258C2×C4⋊C8—1221no—
259C2×C4⋊C8—1222no—
260C2×C22⋊C8—1221no—
261C2×C4×C8—1221no—
262#333—618no—
263#332—618no—
264C61C2×#154211yescharacteristic, complemented, Sylow
265C22×Q8—611no—
266C22×Q8—1221no—
267C22×Q8C2×#692311yescharacteristic
268C23×C4—611no—
269C23×C4—611no—
270C23×C4C2×#692311yescharacteristic
271C22×C8—1224no—
272C22×C8—1222no—
273C22×C8—1222no—
274C22×C8—2444no—
275C4⋊Q8—612no—
276C4⋊Q8—612no—
277C4⋊Q8—612no—
278C4⋊Q8—612no—
279C4⋊Q8—1221no—
280C4⋊Q8—1221no—
281C4⋊Q8—1221no—
282C4⋊Q8—1221no—
283#125—1224no—
284#125—1224no—
285C22⋊Q8—22no—
286C22⋊Q8—614no—
287C22⋊Q8—1224no—
288C22⋊Q8—1224no—
289C22⋊Q8—1222no—
290C22⋊Q8C2×#692314yes—
291C4×Q8—614no—
292C4×Q8—614no—
293C4×Q8—1222no—
294C4×Q8—1224no—
295C4×Q8—1224no—
296C4×Q8—1222no—
297#117—1224no—
298#117—1224no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4C2×#692311yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—1221no—
310C2×C42—611no—
311C2×C42—611no—
312C2×C42—612no—
313C2×C42—612no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—612no—
317C2×C42—612no—
318C2×C42—1221no—
319C2×C42—1221no—
320C4⋊C8—614no—
321C4⋊C8—614no—
322C4⋊C8—1224no—
323C4⋊C8—1222no—
324C4⋊C8—1222no—
325C22⋊C8—1224no—
326C4×C8—1224no—
327C24C22⋊#692311yescharacteristic
328C2×Q8—21no—
329C2×Q8—42no—
330C2×Q8—612no—
331C2×Q8—1222no—
332C2×Q8—1222no—
333C2×Q8—1221no—
334C2×Q8—2442no—
335C2×Q8—2444no—
336C2×Q8C22×#692312yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—42no—
340C22×C4—614no—
341C22×C4—614no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—612no—
348C22×C4—612no—
349C22×C4—611no—
350C22×C4—1224no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4C22⋊#692311yescharacteristic
354C22×C4C22⋊#692312yes—
355C22×C4C22×#692311yescharacteristic
356C22×C4C22×#692312yes—
357C2×C8—1224no—
358C2×C8—1224no—
359C2×C8—2448no—
360C2×C8—2444no—
361C2×C8—2444no—
362C4⋊C4—24no—
363C4⋊C4—21no—
364C4⋊C4—612no—
365C4⋊C4—1222no—
366C4⋊C4—1222no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C4⋊C4—1224no—
370C4⋊C4—1222no—
371C4⋊C4—1222no—
372C4⋊C4—1224no—
373C4⋊C4—1221no—
374C4⋊C4—1224no—
375C4⋊C4C22×#692312yes—
376C22⋊C4—24no—
377C22⋊C4—1224no—
378C42—612no—
379C42—612no—
380C42—611no—
381C42—611no—
382C42—612no—
383C42—612no—
384C42—612no—
385C42—611no—
386C42—612no—
387C42—611no—
388C42—1224no—
389C42—1224no—
390C23—22no—
391C23—22no—
392C23#1451984014yes—
393C23C2×C22⋊#692312yes—
394C23C2×C22⋊#692311yescharacteristic
395Q8—42no—
396Q8—42no—
397Q8—2442no—
398Q8—2442no—
399Q8—2444no—
400Q8—2444no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—618no—
410C2×C4—614no—
411C2×C4—614no—
412C2×C4—612no—
413C2×C4—614no—
414C2×C4—612no—
415C2×C4—614no—
416C2×C4—612no—
417C2×C4—611no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—612no—
422C2×C4—1224no—
423C2×C4—1224no—
424C2×C4—1222no—
425C2×C4—1222no—
426C2×C4—1222no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4C2×C22⋊#692312yes—
430C2×C4C2×C22⋊#692311yescharacteristic
431C2×C4C23×#692311yescharacteristic
432C8—2444no—
433C8—2444no—
434C22—28no—
435C22—22no—
436C22—22no—
437C22#1684074912yes—
438C22C2×#1451984014yes—
439C22C2×#1451984012yes—
440C22#1684075212yes—
441C22C22×C22⋊#692311yescharacteristic
442C4—22no—
443C4—21no—
444C4—21no—
445C4—42no—
446C4—42no—
447C4—611no—
448C4—611no—
449C4—614no—
450C4—612no—
451C4—612no—
452C4—612no—
453C4—1222no—
454C4—2442no—
455C4—2442no—
456C2—24no—
457C2#2146132114yesdirect product factor
458C2C2×#1684074911yescharacteristic
459C2C22×#1451984011yescharacteristic
460C2C2×#1684075211yescharacteristic
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×#1542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #21461321C2direct (N × H)
4. C2×#16840622C2semidirect
5. C2×#16840621C2semidirect
17. #16840622C22semidirect
18. #16840621C22semidirect
233. C2×C61#1542semidirect
264. C61C2×#1542semidirect
457. C2#21461321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407792
C22×#145198442
#214613212
C2×#168406222
C2×#168406212
C2×#168403142
C2×#154261