Finite Group Databasebeta

← C2×#21462091 #30623954

Subgroups — C2×#21462091 #30623954

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840743C212yesmaximal, complemented
2#21462091C218yesmaximal, direct product factor
3C2×#16840669C212yesmaximal, complemented
4C2×#16840666C212yesmaximal, complemented
5C2×#16840311C211yesmaximal, characteristic
6C2×#14519856—22no—
7#16840743—24no—
8#16840743C2218yescomplemented
9C2×#14519836—22no—
10C2×#14519836C2214yes—
11#16840669C2218yescomplemented
12#16840666C2218yescomplemented
13C22×#11758226C2211yescharacteristic
14C22×#11758224C411yescharacteristic, complemented
15#16840311—24no—
16#16840311C414yescomplemented
17#16840311C2214yes—
18C2×#14519775C411yescharacteristic, complemented
19C2×#14519773C2211yescharacteristic
20C2×#14519765C2211yescharacteristic
21C2×#14519750—22no—
22C2×#14519737—22no—
23C2×C42×D61C411yescharacteristic, complemented
24C2×#124×C61C411yescharacteristic, complemented
25#14519856—28no—
26#14519856—44no—
27C2×C4⋊#6923—42no—
28C2×C22⋊#6923—24no—
29C2×C4×#6923—42no—
30#14519836—28no—
31#14519836—24no—
32#14519836C2318yes—
33C2×#11758226—41no—
34C2×#11758226—41no—
35C2×#11758226—42no—
36C2×#11758226C2×C412yes—
37C2×#11758226D414yes—
38C2×#11758226C2312yes—
39C2×#11758224—22no—
40C2×#11758224—42no—
41C2×#11758224—41no—
42C2×#11758224—41no—
43C2×#11758224C2×C414yescomplemented
44C22×Dic122C2×C411yescharacteristic
45C22×D244D412yes—
46C22×D244C2311yescharacteristic
47C22×C22⋊D61—21no—
48C22×C22⋊D61—22no—
49C23×Dic61—21no—
50C22×C4×D61—21no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D412yes—
53#14519775—22no—
54#14519775C2×C414yescomplemented
55#14519773—22no—
56#14519773C2×C412yes—
57#14519773C2312yes—
58#14519765—22no—
59#14519765C2×C412yes—
60#14519765C2312yes—
61#14519750—28no—
62#14519750—28no—
63#14519737—28no—
64#14519737—28no—
65C2×#11758196—22no—
66C2×#11758198—22no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61C2×C411yescharacteristic
69C42×D61—22no—
70C42×D61C2×C414yescomplemented
71C22×Q8×C61C2×C411yescharacteristic
72C22×D4×C61C2×C411yescharacteristic
73#124×C61—22no—
74#124×C61C2×C414yescomplemented
75C2×C22⋊C4×C61—22no—
76C2×C42×C61C2×C411yescharacteristic
77C24×C61—21no—
78C23×D61C22⋊C411yescharacteristic
79C23×D61C2×D412yes—
80C22×#6923—44no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C2×Q8×C61C22⋊C412yes—
84C2×Q8×C61C22×C412yes—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61C22×C412yes—
89C22×C4×C61—21no—
90C22×C4×C61C22⋊C412yes—
91C22×C4×C61C22×C411yescharacteristic
92C2×C22⋊D61—24no—
93C2×C22⋊D61—24no—
94C2×C22⋊D61—24no—
95C2×C22⋊D61—48no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—24no—
101C22×Dic61—42no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61C22⋊C411yescharacteristic
105#11758226—42no—
106#11758226—42no—
107#11758226—44no—
108#11758226—44no—
109#11758226—42no—
110#11758226—42no—
111#11758224—44no—
112#11758224—44no—
113#11758224—44no—
114#11758224—44no—
115C2×D244—42no—
116C2×D244—42no—
117C2×D244—41no—
118C2×D244—41no—
119C2×D244C22⋊C414yes—
120C2×D244C22×C411yescharacteristic
121C2×D244C2×D414yes—
122C2×D244C2×D412yes—
123C2×D244C2411yescharacteristic
124C2×C4×D61—22no—
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—24no—
130C2×C4×D61—24no—
131C2×C4×D61—44no—
132C2×C4×D61C22⋊C412yes—
133C2×C4×D61C22⋊C414yes—
134C2×C4×D61C22×C412yes—
135C2×C4×D61C2×D414yes—
136C2×Dic122—21no—
137C2×Dic122—41no—
138C2×Dic122—41no—
139C2×Dic122C22×C412yes—
140C22⋊#6923—28no—
141C22⋊#6923—44no—
142C4⋊#6923—48no—
143C4×#6923—48no—
144C22⋊C4×C61—28no—
145C42×C61—21no—
146C42×C61C22×C412yes—
147#11758198—24no—
148#11758198—24no—
149#11758196—28no—
150C4×Dic61—21no—
151C4×Dic61—24no—
152C4×Dic61C22×C412yes—
153C23×C61—22no—
154C23×C61—44no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61C2×C22⋊C411yescharacteristic
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—42no—
163C22×D61—44no—
164C22×D61C2×C22⋊C412yes—
165C22×D61C2×C22⋊C412yes—
166C22×D61C22×D412yes—
167C2×#6923—48no—
168C2×#6923—88no—
169Q8×C61—42no—
170Q8×C61—42no—
171D4×C61—42no—
172D4×C61—42no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—42no—
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C2×C22⋊C414yes—
181C2×C4×C61C23×C411yescharacteristic
182C22⋊D61—48no—
183C22⋊D61—48no—
184C22⋊D61—48no—
185C2×Dic61—24no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—44no—
191C2×Dic61—44no—
192C2×Dic61#9912yes—
193C2×Dic61#9911yescharacteristic
194C2×Dic61#9911yescharacteristic
195C2×Dic61C2×C22⋊C412yes—
196D244—44no—
197D244—41no—
198D244—42no—
199D244—44no—
200D244—41no—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—24no—
206C4×D61—24no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—48no—
210Dic122—42no—
211Dic122—42no—
212C2×#2126—611nomaximal, Sylow
213C22×C61—22no—
214C22×C61—44no—
215C22×C61—42no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61C2×#9911yescharacteristic
219C22×C61C2×#9911yescharacteristic
220C22×C61C22×C22⋊C411yescharacteristic
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—42no—
225C2×D61—44no—
226C2×D61—42no—
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—82no—
231#6923—88no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—24no—
235C4×C61—42no—
236Dic61—24no—
237Dic61—42no—
238Dic61C2×#9912yes—
239Dic61C2×#9912yes—
240C2×#532—611no—
241C2×#410—612no—
242#2126—618no—
243C2×#354—612no—
244C2×#353—612no—
245C2×C61—21no—
246C2×C61—21no—
247C2×C61—82no—
248C2×C61#212612yescomplemented
249C2×C61C22×#9911yescharacteristic
250D61—42no—
251D61—42no—
252D61—42no—
253C22×#41—611no—
254C22×#41—611no—
255#532—614no—
256#532—614no—
257#532—1224no—
258C2×C4⋊Q8—611no—
259C2×#127—611no—
260C2×#124—611no—
261C2×#124#692311yescharacteristic, complemented
262C2×#121—1222no—
263C2×C4×D4—1222no—
264C2×#117—1222no—
265C22×C42—611no—
266#410—618no—
267#410—1224no—
268C2×#99—614no—
269C2×#99—1222no—
270#354—618no—
271#353—618no—
272C61C2×#212611yescharacteristic, complemented, Sylow
273C2×#41—614no—
274C2×#41—612no—
275C2×#41—612no—
276C2×#41—614no—
277C2×#41—1222no—
278C2×#41—2441no—
279C2×#41—2441no—
280C2×#41—2442no—
281C2×#41—2442no—
282C2×#41—2441no—
283C2×#41—2441no—
284C22×Q8—611no—
285C22×Q8C2×#692311yescharacteristic
286C22×D4—612no—
287C22×D4—611no—
288C22×D4—1222no—
289C22×D4—1221no—
290C22×D4C2×#692311yescharacteristic
291C23×C4—612no—
292C23×C4—611no—
293C23×C4—1221no—
294C23×C4—1221no—
295C4⋊Q8—614no—
296C4⋊Q8—1222no—
297#127—612no—
298#127—612no—
299#127—1222no—
300#124—22no—
301#124—612no—
302#124—612no—
303#124—1222no—
304#124C2×#692314yescomplemented
305#121—1228no—
306#121—1228no—
307C4×D4—1228no—
308C4×D4—1228no—
309#117—1228no—
310#117—2444no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4—2442no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1224no—
316C2×C42—611no—
317C2×C42—614no—
318C2×C42—1222no—
319C2×C42—1221no—
320C2×C42—2442no—
321C2×C42C2×#692311yescharacteristic
322#99—618no—
323#99—1224no—
324#99—1228no—
325C24—21no—
326C24—612no—
327C24—611no—
328#41—2442no—
329#41—2444no—
330#41—2442no—
331#41—2444no—
332#41—2442no—
333#41—2442no—
334#41—2444no—
335#41—2444no—
336#41—2444no—
337#41—2444no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—612no—
341C2×Q8—1221no—
342C2×Q8—2441no—
343C2×Q8—2441no—
344C2×Q8C22⋊#692312yes—
345C2×Q8C22×#692312yes—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—614no—
350C2×D4—612no—
351C2×D4—614no—
352C2×D4—611no—
353C2×D4—611no—
354C2×D4—1224no—
355C2×D4—1224no—
356C2×D4—1224no—
357C2×D4—2442no—
358C2×D4—2441no—
359C2×D4—2442no—
360C2×D4—2441no—
361C2×D4—2448no—
362C2×D4—2442no—
363C2×D4—2442no—
364C2×D4C22×#692312yes—
365C22×C4—21no—
366C22×C4—611no—
367C22×C4—612no—
368C22×C4—614no—
369C22×C4—614no—
370C22×C4—612no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1224no—
374C22×C4—1222no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1224no—
378C22×C4—1224no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—2444no—
382C22×C4—2442no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2444no—
386C22×C4C22⋊#692312yes—
387C22×C4C22×#692311yescharacteristic
388C4⋊C4—1228no—
389C4⋊C4—2448no—
390C22⋊C4—28no—
391C22⋊C4—1224no—
392C22⋊C4—1224no—
393C22⋊C4—1228no—
394C22⋊C4—2444no—
395C42—21no—
396C42—612no—
397C42—1224no—
398C42—1221no—
399C42—2448no—
400C42C22×#692312yes—
401C23—22no—
402C23—44no—
403C23—41no—
404C23—41no—
405C23—612no—
406C23—612no—
407C23—612no—
408C23—1222no—
409C23—1221no—
410C23—1222no—
411C23—1221no—
412C23—2444no—
413C23—2442no—
414C23C2×C22⋊#692311yescharacteristic
415Q8—42no—
416Q8—42no—
417Q8—2442no—
418Q8—2442no—
419D4—42no—
420D4—42no—
421D4—2442no—
422D4—2444no—
423D4—2444no—
424D4—2441no—
425D4—2441no—
426D4—2448no—
427D4—2448no—
428D4—2448no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—612no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—612no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1222no—
444C2×C4—1222no—
445C2×C4—1222no—
446C2×C4—1222no—
447C2×C4—1224no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—4888no—
451C2×C4—2448no—
452C2×C4—2444no—
453C2×C4—2444no—
454C2×C4—2448no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4C2×C22⋊#692311yescharacteristic
458C2×C4C2×C22⋊#692314yes—
459C2×C4C23×#692311yescharacteristic
460C22—22no—
461C22—44no—
462C22—42no—
463C22—82no—
464C22—82no—
465C22—1222no—
466C22—1222no—
467C22—1222no—
468C22—4882no—
469C22—2442no—
470C22—2442no—
471C22—2442no—
472C22—2442no—
473C22—2444no—
474C22—2442no—
475C22D61⋊#9911yescharacteristic
476C22D61⋊#9911yescharacteristic
477C22C22×C22⋊#692311yescharacteristic
478C4—21no—
479C4—24no—
480C4—21no—
481C4—42no—
482C4—612no—
483C4—612no—
484C4—1224no—
485C4—4888no—
486C4—2442no—
487C2—21no—
488C2—21no—
489C2—82no—
490C2—2442no—
491C2—2442no—
492C2—2442no—
493C2#2146209112yesdirect product factor
494C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840311C2
cosocleC2×D244C24
hypercenterC2×#124#6923
hypocenterC61C2×#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840743C2semidirect
2. #21462091C2direct (N × H)
3. C2×#16840669C2semidirect
4. C2×#16840666C2semidirect
8. #16840743C22semidirect
11. #16840669C22semidirect
12. #16840666C22semidirect
14. C22×#11758224C4semidirect
16. #16840311C4semidirect
18. C2×#14519775C4semidirect
23. C2×C42×D61C4semidirect
24. C2×#124×C61C4semidirect
43. C2×#11758224C2×C4semidirect
54. #14519775C2×C4semidirect
70. C42×D61C2×C4semidirect
74. #124×C61C2×C4semidirect
248. C2×C61#2126semidirect
261. C2×#124#6923semidirect
272. C61C2×#2126semidirect
304. #124C2×#6923semidirect
493. C2#21462091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407432
#214620912
C2×#168406692
C2×#168406662
C2×#168403112
C2×#212661