Finite Group Databasebeta

← C2×#21461191 #30610901

Subgroups — C2×#21461191 #30610901

Order 15616.

1182 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840780C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461191C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal, complemented
5C2×#16840613C212yesmaximal
6C2×#16840291C211yesmaximal, characteristic
7C22×C4×#6923—21no—
8#16840780—22no—
9#16840780C2214yescomplemented
10C2×#14519844—21no—
11C2×#14519834C2212yes—
12C2×C4×#92420—21no—
13#16840698—22no—
14#16840698C2214yescomplemented
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4C2212yes—
17#16840616C2218yescomplemented
18#16840613C2218yes—
19#16840291—22no—
20#16840291—22no—
21#16840291C414yescomplemented
22#16840291C2214yes—
23C2×#14519770—21no—
24C2×#14519769C411yescharacteristic, complemented
25C2×#14519759—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519748C2211yescharacteristic
28C2×Q8×Dic61C411yescharacteristic, complemented
29C2×D4×Dic61C411yescharacteristic, complemented
30C2×#14519737—21no—
31C2×#14519733—21no—
32C2×C42×D61C2211yescharacteristic
33C2×#124×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4×#6923—28no—
37C2×C4×#6923—24no—
38#14519844—24no—
39#14519834—22no—
40#14519834C2314yes—
41C4×#92420—24no—
42(C2×#6923)⋊C4—24no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4C2314yes—
45C22×C22⋊D61—21no—
46C23×Dic61—21no—
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×C4×D61C2311yescharacteristic
50#14519770—24no—
51#14519770—24no—
52#14519769—22no—
53#14519769C2×C414yescomplemented
54#14519759—24no—
55#14519759—24no—
56#14519753—21no—
57#14519753—21no—
58#14519753C2×C412yes—
59#14519753C2312yes—
60#14519748—21no—
61#14519748—21no—
62#14519748C2×C412yes—
63#14519748C2312yes—
64Q8×Dic61—22no—
65Q8×Dic61C2×C414yescomplemented
66D4×Dic61—22no—
67D4×Dic61C2×C414yescomplemented
68#14519737—24no—
69#14519737—24no—
70#14519733—24no—
71#14519733—24no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C42×D61C2×C412yes—
86C42×D61D412yes—
87C42×D61D412yes—
88C42×D61C2312yes—
89C22×Q8×C61C2×C411yescharacteristic
90C22×D4×C61C2×C411yescharacteristic
91#124×C61—22no—
92#124×C61C2×C414yescomplemented
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C42×C61C2×C411yescharacteristic
96C24×C61—21no—
97C23×D61C2×D411yescharacteristic
98C22×#6923—28no—
99C22×#6923—24no—
100C22×#6923—44no—
101C22×#6923—44no—
102C2×Q8×C61—21no—
103C2×Q8×C61—42no—
104C2×Q8×C61C22×C412yes—
105C2×D4×C61—21no—
106C2×D4×C61—42no—
107C2×D4×C61C22×C412yes—
108C22×C4×C61—21no—
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22⋊C411yescharacteristic
111C22×C4×C61C22×C411yescharacteristic
112C2×C22⋊D61—22no—
113C2×C22⋊D61—22no—
114C2×C22⋊D61—44no—
115C22×Dic61—21no—
116C22×Dic61—21no—
117C22×Dic61—24no—
118C22×Dic61—44no—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C2×D411yescharacteristic
122C2×C4×D61—24no—
123C2×C4×D61—24no—
124C2×C4×D61—42no—
125C2×C4×D61C22⋊C412yes—
126C2×C4×D61C22⋊C412yes—
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C2×D412yes—
129C2×C4×D61C2×D412yes—
130C2×C4×D61C2×D411yescharacteristic
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2411yescharacteristic
133C2×#92420—24no—
134C2×#92420—44no—
135C4×#6923—216no—
136C22⋊C4×C61—24no—
137C22⋊C4×C61—24no—
138C42×C61C22⋊C412yes—
139C42×C61C22×C412yes—
140C22⋊Dic61—22no—
141C22⋊Dic61—24no—
142C22⋊Dic61—22no—
143#11758198—22no—
144#11758198—22no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—24no—
148C4⋊Dic61C22×C412yes—
149C4⋊Dic61C22×C412yes—
150#11758196—24no—
151#11758196—24no—
152#11758196—22no—
153#11758196—22no—
154C4×Dic61—24no—
155C4×Dic61C22⋊C412yes—
156C4×Dic61C22⋊C412yes—
157C4×Dic61C22⋊C412yes—
158C4×Dic61C22×C412yes—
159C4×Dic61C2×D412yes—
160C4×Dic61C2×D412yes—
161C23×C61—22no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61C2×C22⋊C411yescharacteristic
166C22×D61—22no—
167C22×D61—22no—
168C22×D61C2×C22⋊C411yescharacteristic
169C22×D61#13514yes—
170C22×D61C22×D411yescharacteristic
171C2×#6923—28no—
172C2×#6923—44no—
173C2×#6923—416no—
174C2×#6923—44no—
175Q8×C61—42no—
176Q8×C61—42no—
177D4×C61—42no—
178D4×C61—42no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—42no—
184C2×C4×C61C2×C22⋊C411yescharacteristic
185C2×C4×C61C2×C22⋊C412yes—
186C2×C4×C61C2×C22⋊C412yes—
187C2×C4×C61C23×C411yescharacteristic
188C22⋊D61—44no—
189C22⋊D61—44no—
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—48no—
197C2×Dic61#10414yes—
198C2×Dic61C2×C22⋊C411yescharacteristic
199C2×Dic61C2×C22⋊C412yes—
200C2×Dic61C2×C22⋊C412yes—
201C2×Dic61C22×D411yescharacteristic
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—24no—
205C4×D61—24no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210#92420—44no—
211C2×#1500—611nomaximal, Sylow
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—84no—
216C22×C61#41012yes—
217C22×C61#41612yes—
218C22×C61C2×#10412yes—
219C22×C61C22×C22⋊C411yescharacteristic
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—21no—
223C2×D61—21no—
224C2×D61—28no—
225C2×D61#41612yes—
226C2×D61C2×#13512yes—
227#6923—48no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—22no—
231C4×C61—22no—
232C4×C61—42no—
233Dic61—21no—
234Dic61—21no—
235Dic61—22no—
236Dic61—42no—
237Dic61—42no—
238Dic61C2×#10414yes—
239C2×#529—611no—
240C2×#431—611no—
241C2×#376—611no—
242#1500—618no—
243C2×#328—612no—
244C2×#327—612no—
245C2×C61—82no—
246C2×C61#150014yescomplemented
247C2×C61C2×#41011yescharacteristic
248C2×C61C2×#41611yescharacteristic
249C2×C61C22×#10411yescharacteristic
250D61—22no—
251D61—22no—
252#529—614no—
253#529—614no—
254#529—1222no—
255#529—1222no—
256C2×#126—1221no—
257C2×#125—611no—
258C2×#124#692311yescharacteristic, complemented
259C2×#123—1221no—
260C2×C22⋊Q8—611no—
261C2×#121—611no—
262C2×C4×Q8—611no—
263C2×C4×D4—611no—
264C2×C4×D4—1221no—
265C2×#117—1221no—
266C22×C42—611no—
267C22×C42—1221no—
268#431—614no—
269#431—1222no—
270C2×C4⋊C8—1221no—
271C2×C22⋊C8—612no—
272C2×C4×C8—1221no—
273#376—614no—
274#376—1222no—
275C2×#95—612no—
276C2×#95—1221no—
277#328—618no—
278#327—618no—
279C61C2×#150011yescharacteristic, complemented, Sylow
280C22×Q8C2×#692311yescharacteristic
281C22×D4—1221no—
282C22×D4C2×#692311yescharacteristic
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—1221no—
287C23×C4—1222no—
288C22×C8—1222no—
289#126—1224no—
290#126—1224no—
291#125—614no—
292#125—1222no—
293#124—22no—
294#124C2×#692314yescomplemented
295#123—1224no—
296#123—1224no—
297C22⋊Q8—612no—
298C22⋊Q8—612no—
299C22⋊Q8—1221no—
300C22⋊Q8—1221no—
301#121—612no—
302#121—612no—
303#121—1221no—
304#121—1221no—
305C4×Q8—614no—
306C4×Q8—1222no—
307C4×D4—614no—
308C4×D4—1222no—
309C4×D4—1224no—
310C4×D4—1224no—
311#117—1224no—
312#117—1224no—
313C2×C4⋊C4—611no—
314C2×C4⋊C4—611no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C42—611no—
325C2×C42—611no—
326C2×C42—611no—
327C2×C42—612no—
328C2×C42—612no—
329C2×C42—612no—
330C2×C42—612no—
331C2×C42—1221no—
332C2×C42—1224no—
333C2×C42—1228no—
334C2×C42C2×#692311yescharacteristic
335C4⋊C8—1224no—
336C22⋊C8—614no—
337C22⋊C8—1222no—
338C4×C8—1224no—
339#95—614no—
340#95—1222no—
341#95—1224no—
342C24—21no—
343C24—611no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8C22×#692312yes—
347C2×D4—21no—
348C2×D4—42no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—2444no—
352C2×D4C22×#692312yes—
353C22×C4—21no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—1224no—
366C22×C4—1224no—
367C22×C4—1224no—
368C22×C4—1224no—
369C22×C4—1228no—
370C22×C4—1221no—
371C22×C4—1221no—
372C22×C4—2442no—
373C22×C4—2444no—
374C22×C4—2444no—
375C22×C4—2444no—
376C22×C4C22⋊#692311yescharacteristic
377C22×C4C22⋊#692311yescharacteristic
378C22×C4C22×#692311yescharacteristic
379C2×C8—1224no—
380C2×C8—2444no—
381C4⋊C4—612no—
382C4⋊C4—612no—
383C4⋊C4—1222no—
384C4⋊C4—1222no—
385C4⋊C4—1224no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C4⋊C4—1224no—
389C4⋊C4—1224no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—1222no—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1224no—
397C42—612no—
398C42—612no—
399C42—612no—
400C42—612no—
401C42—612no—
402C42—612no—
403C42—1224no—
404C42—12216no—
405C42C22⋊#692312yes—
406C42C22×#692312yes—
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—614no—
412C23—611no—
413C23—611no—
414C23—1222no—
415C23—1222no—
416C23C2×C22⋊#692311yescharacteristic
417Q8—42no—
418Q8—42no—
419D4—42no—
420D4—42no—
421D4—2444no—
422D4—2444no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—614no—
429C2×C4—612no—
430C2×C4—611no—
431C2×C4—612no—
432C2×C4—611no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—1222no—
438C2×C4—1222no—
439C2×C4—1228no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2448no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—24416no—
450C2×C4—2442no—
451C2×C4—2442no—
452C2×C4C2×C22⋊#692311yescharacteristic
453C2×C4C2×C22⋊#692312yes—
454C2×C4C2×C22⋊#692312yes—
455C2×C4C23×#692311yescharacteristic
456C8—2444no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—612no—
462C22—612no—
463C22—1221no—
464C22—1221no—
465C22—1221no—
466C22—1221no—
467C22—1228no—
468C22#1684074212yes—
469C22#1684075212yes—
470C22D61⋊#10412yes—
471C22C22×C22⋊#692311yescharacteristic
472C4—21no—
473C4—21no—
474C4—22no—
475C4—22no—
476C4—42no—
477C4—614no—
478C4—1221no—
479C4—1221no—
480C4—1222no—
481C4—2448no—
482C4—2442no—
483C4—2442no—
484C2—82no—
485C2—1222no—
486C2—1222no—
487C2#2146119114yesdirect product factor
488C2C2×#1684074211yescharacteristic
489C2C2×#1684075211yescharacteristic
490C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C22
cosocleC2×C4×D61C24
hypercenterC2×#124#6923
hypocenterC61C2×#1500
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840780C2semidirect
2. C2×#16840698C2semidirect
3. #21461191C2direct (N × H)
4. C2×#16840616C2semidirect
9. #16840780C22semidirect
14. #16840698C22semidirect
17. #16840616C22semidirect
21. #16840291C4semidirect
24. C2×#14519769C4semidirect
28. C2×Q8×Dic61C4semidirect
29. C2×D4×Dic61C4semidirect
33. C2×#124×C61C4semidirect
53. #14519769C2×C4semidirect
65. Q8×Dic61C2×C4semidirect
67. D4×Dic61C2×C4semidirect
92. #124×C61C2×C4semidirect
246. C2×C61#1500semidirect
258. C2×#124#6923semidirect
279. C61C2×#1500semidirect
294. #124C2×#6923semidirect
487. C2#21461191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407802
C2×#168406982
#214611912
C2×#168406162
C2×#168406132
C2×#168402912
C2×#150061