Finite Group Databasebeta

← C2×#21461127 #30610493

Subgroups — C2×#21461127 #30610493

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840779C211yesmaximal, characteristic
2C22×C4⋊#92420C211yesmaximal, characteristic
3#21461127C218yesmaximal, direct product factor
4C2×#16840612C212yesmaximal, complemented
5C2×Q8⋊#92420C212yesmaximal, complemented
6C2×#16840314C211yesmaximal, characteristic
7C23×#92420—21no—
8#16840779—22no—
9#16840779C2214yes—
10C2×#14519844—21no—
11C2×C4⋊#92420—21no—
12C2×C4⋊#92420—22no—
13C2×C4⋊#92420C2212yes—
14C2×C4⋊#92420C2214yes—
15C2×C22⋊#92420—21no—
16C2×C4×#92420C2212yes—
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
34C22×#92420—22no—
35C22×#92420—22no—
36C22×#92420—24no—
37C22×#92420—44no—
38#14519844—24no—
39C4⋊#92420—24no—
40C4⋊#92420—22no—
41C4⋊#92420C2314yes—
42C22⋊#92420—24no—
43C4×#92420—22no—
44C4×#92420C2314yes—
45C22×Dic122—21no—
46C22×Dic122C2×C411yescharacteristic
47C23×Dic61D411yescharacteristic
48C23×Dic61D411yescharacteristic
49#14519776—22no—
50#14519776C2×C414yes—
51#14519775—22no—
52#14519775C2×C414yes—
53#14519767—24no—
54#14519767—24no—
55#14519756—22no—
56#14519756C2×C414yes—
57#14519754—24no—
58#14519754—24no—
59Q8×Dic61—21no—
60Q8×Dic61—21no—
61Q8×Dic61C2×C412yes—
62Q8×Dic61C2312yes—
63#14519742—24no—
64#14519742—24no—
65#14519742—21no—
66#14519742—21no—
67#14519742C2×C412yes—
68#14519742C2312yes—
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×Dic61D412yes—
85C2×C4×Dic61D411yescharacteristic
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—24no—
99C2×Q8×C61C22×C412yes—
100C22×C4×C61—24no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22⋊C412yes—
105C22×C4×C61C22×C412yes—
106C22×C4×C61C22×C411yescharacteristic
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—42no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C412yes—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C412yes—
114C22×Dic61SD1614yes—
115C22×Dic61Q1614yes—
116C22×Dic61C2×D411yescharacteristic
117C22×Dic61C2×D412yes—
118C22×Dic61C2×D411yescharacteristic
119C22×Dic61C2×D412yes—
120C2×Dic122—24no—
121C2×Dic122—21no—
122C2×Dic122—24no—
123C2×Dic122—44no—
124C2×Dic122C22×C412yes—
125C2×#92420—24no—
126C2×#92420—24no—
127C2×#92420—44no—
128C2×#92420—48no—
129C2×#92420—44no—
130C4⋊C4×C61—24no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61C22×C412yes—
133C22⋊C4×C61—24no—
134C22⋊Dic61—24no—
135C4⋊Dic61—21no—
136C4⋊Dic61—22no—
137C4⋊Dic61—22no—
138C4⋊Dic61C22×C412yes—
139#11758196—24no—
140#11758196—24no—
141#11758196—24no—
142#11758196—24no—
143#11758196—22no—
144#11758196—22no—
145C4×Dic61—22no—
146C4×Dic61—22no—
147C4×Dic61—22no—
148C4×Dic61—22no—
149C4×Dic61C22⋊C412yes—
150C4×Dic61C22⋊C412yes—
151C4×Dic61C22⋊C412yes—
152C4×Dic61C22×C411yescharacteristic
153C4×Dic61C22×C412yes—
154C4×Dic61C2×D411yescharacteristic
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D411yescharacteristic
157C4×Dic61C2×D412yes—
158C4×Dic61C2411yescharacteristic
159C23×C61—22no—
160C23×C61—22no—
161C23×C61#10314yes—
162C23×C61C2×C22⋊C412yes—
163C23×C61C2×C22⋊C411yescharacteristic
164Q8×C61—24no—
165Q8×C61—42no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—24no—
169C2×C4×C61—22no—
170C2×C4×C61—22no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61C2×C22⋊C412yes—
174C2×C4×C61C2×C22⋊C411yescharacteristic
175C2×C4×C61#13114yes—
176C2×C4×C61C23×C411yescharacteristic
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61#10318yes—
186C2×Dic61#10314yes—
187C2×Dic61C2×C22⋊C411yescharacteristic
188C2×Dic61C2×C22⋊C412yes—
189C2×Dic61C2×C22⋊C411yescharacteristic
190C2×Dic61C2×C22⋊C412yes—
191C2×Dic61C2×SD1614yes—
192C2×Dic61C2×SD1612yes—
193C2×Dic61C2×Q1614yes—
194C2×Dic61C2×Q1612yes—
195C2×Dic61C22×D411yescharacteristic
196C2×Dic61C22×D411yescharacteristic
197Dic122—24no—
198Dic122—48no—
199Dic122—42no—
200#92420—44no—
201#92420—44no—
202C2×#1481—611nomaximal, Sylow
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—28no—
206C22×C61#40812yes—
207C22×C61C2×#10314yes—
208C22×C61C2×#10312yes—
209C22×C61#42112yes—
210C22×C61C22×C22⋊C411yescharacteristic
211C4×C61—22no—
212C4×C61—42no—
213C4×C61—42no—
214C4×C61#40812yes—
215C4×C61C2×#13112yes—
216Dic61—21no—
217Dic61—22no—
218Dic61—21no—
219Dic61—42no—
220Dic61—42no—
221Dic61C2×#10312yes—
222Dic61C2×#10314yes—
223Dic61C22×SD1611yescharacteristic
224Dic61C22×Q1611yescharacteristic
225C2×#533—611no—
226C2×#431—611no—
227C22×C4⋊C8—611no—
228#1481—618no—
229C2×Q8⋊C8—612no—
230C2×Q8⋊C8—612no—
231C2×C61—24no—
232C2×C61#148114yescomplemented
233C2×C61C2×#40811yescharacteristic
234C2×C61C22×#10311yescharacteristic
235C2×C61C2×#42111yescharacteristic
236C23×C8—1221no—
237#533—614no—
238#533—614no—
239#533—1222no—
240#533—1222no—
241C2×C4⋊Q8—611no—
242C2×C4⋊Q8—611no—
243C2×#125—1221no—
244C2×C22⋊Q8—611no—
245C2×C22⋊Q8—1221no—
246C2×C22⋊Q8#692311yescharacteristic
247C2×C4×Q8—611no—
248C2×C4×Q8—611no—
249C2×C4×Q8—1221no—
250C2×#117—1221no—
251C22×C42—611no—
252#431—614no—
253#431—1222no—
254C2×C4⋊C8—612no—
255C2×C4⋊C8—614no—
256C2×C4⋊C8—1221no—
257C2×C4⋊C8—1222no—
258C2×C4⋊C8—1221no—
259C2×C22⋊C8—1221no—
260C2×C4×C8—612no—
261Q8⋊C8—618no—
262Q8⋊C8—618no—
263C61C2×#148111yescharacteristic, complemented, Sylow
264C22×Q8—611no—
265C22×Q8—1221no—
266C22×Q8C2×#692311yescharacteristic
267C23×C4—611no—
268C23×C4—611no—
269C23×C4C2×#692311yescharacteristic
270C22×C8—1224no—
271C22×C8—1222no—
272C22×C8—1222no—
273C22×C8—2444no—
274C4⋊Q8—614no—
275C4⋊Q8—614no—
276C4⋊Q8—1222no—
277C4⋊Q8—1222no—
278#125—1224no—
279#125—1224no—
280C22⋊Q8—22no—
281C22⋊Q8—614no—
282C22⋊Q8—1224no—
283C22⋊Q8—1224no—
284C22⋊Q8—1222no—
285C22⋊Q8C2×#692314yes—
286C4×Q8—612no—
287C4×Q8—612no—
288C4×Q8—612no—
289C4×Q8—612no—
290C4×Q8—1221no—
291C4×Q8—1221no—
292C4×Q8—1224no—
293C4×Q8—1224no—
294C4×Q8—1221no—
295C4×Q8—1221no—
296#117—1224no—
297#117—1224no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—1221no—
301C2×C4⋊C4—1221no—
302C2×C4⋊C4—1221no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4C2×#692311yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—1221no—
309C2×C42—611no—
310C2×C42—611no—
311C2×C42—612no—
312C2×C42—612no—
313C2×C42—611no—
314C2×C42—611no—
315C2×C42—612no—
316C2×C42—612no—
317C2×C42—1221no—
318C2×C42—1221no—
319C4⋊C8—614no—
320C4⋊C8—1222no—
321C4⋊C8—1224no—
322C4⋊C8—1224no—
323C22⋊C8—1224no—
324C4×C8—614no—
325C4×C8—1222no—
326C24C22⋊#692311yescharacteristic
327C2×Q8—21no—
328C2×Q8—24no—
329C2×Q8—612no—
330C2×Q8—1224no—
331C2×Q8—1221no—
332C2×Q8—1224no—
333C2×Q8—2444no—
334C2×Q8C22×#692312yes—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—614no—
339C22×C4—614no—
340C22×C4—612no—
341C22×C4—612no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—612no—
347C22×C4—612no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—2442no—
351C22×C4C22⋊#692312yes—
352C22×C4C22⋊#692311yescharacteristic
353C22×C4C22×#692312yes—
354C22×C4C22×#692311yescharacteristic
355C2×C8—1224no—
356C2×C8—1224no—
357C2×C8—2448no—
358C2×C8—2444no—
359C2×C8—2444no—
360C4⋊C4—24no—
361C4⋊C4—21no—
362C4⋊C4—612no—
363C4⋊C4—1224no—
364C4⋊C4—1224no—
365C4⋊C4—1222no—
366C4⋊C4—1222no—
367C4⋊C4—1224no—
368C4⋊C4—1222no—
369C4⋊C4—1222no—
370C4⋊C4—1221no—
371C4⋊C4—1224no—
372C4⋊C4C22×#692312yes—
373C22⋊C4—24no—
374C22⋊C4—1224no—
375C42—611no—
376C42—611no—
377C42—612no—
378C42—612no—
379C42—612no—
380C42—612no—
381C42—612no—
382C42—611no—
383C42—611no—
384C42—612no—
385C42—1222no—
386C42—1222no—
387C42—1222no—
388C42—1222no—
389C23—22no—
390C23—22no—
391C23#1451984014yes—
392C23C2×C22⋊#692312yes—
393C23C2×C22⋊#692311yescharacteristic
394Q8—24no—
395Q8—42no—
396Q8—1224no—
397Q8—2448no—
398Q8—2442no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—618no—
407C2×C4—614no—
408C2×C4—614no—
409C2×C4—612no—
410C2×C4—614no—
411C2×C4—612no—
412C2×C4—611no—
413C2×C4—612no—
414C2×C4—611no—
415C2×C4—611no—
416C2×C4—612no—
417C2×C4—611no—
418C2×C4—1222no—
419C2×C4—1222no—
420C2×C4—1222no—
421C2×C4—1222no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4C2×C22⋊#692312yes—
427C2×C4C2×C22⋊#692311yescharacteristic
428C2×C4#1451986414yes—
429C2×C4C23×#692311yescharacteristic
430C8—2444no—
431C8—2444no—
432C22—22no—
433C22—28no—
434C22—22no—
435C22#1684073512yes—
436C22C2×#1451984014yes—
437C22C2×#1451984012yes—
438C22#1684075912yes—
439C22C22×C22⋊#692311yescharacteristic
440C4—22no—
441C4—42no—
442C4—42no—
443C4—611no—
444C4—611no—
445C4—612no—
446C4—614no—
447C4—1221no—
448C4—1221no—
449C4—1222no—
450C4—2442no—
451C4—2442no—
452C4#1684073512yes—
453C4C2×#1451986412yes—
454C2—24no—
455C2#2146112714yesdirect product factor
456C2C2×#1684073511yescharacteristic
457C2C22×#1451984011yescharacteristic
458C2C2×#1684075911yescharacteristic
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×#1481
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. #21461127C2direct (N × H)
4. C2×#16840612C2semidirect
5. C2×Q8⋊#92420C2semidirect
17. #16840612C22semidirect
18. Q8⋊#92420C22semidirect
232. C2×C61#1481semidirect
263. C61C2×#1481semidirect
455. C2#21461127direct (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×C4⋊#924202
#214611272
C2×#168406122
C2×Q8⋊#924202
C2×#168403142
C2×#148161