Finite Group Databasebeta

← C2×#21461190 #30610899

Subgroups — C2×#21461190 #30610899

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×#16840781C211yesmaximal, characteristic, complemented
2C2×#16840698C211yesmaximal, characteristic, complemented
3#21461190C218yesmaximal, direct product factor
4C2×#16840615C212yesmaximal, complemented
5C2×#16840613C212yesmaximal
6C2×#16840294C211yesmaximal, characteristic
7C22×C4×#6923—21no—
8#16840781—22no—
9#16840781C2214yescomplemented
10C2×C4⋊#92420—21no—
11C2×#14519834C2212yes—
12C2×C4×#92420—21no—
13#16840698—22no—
14#16840698C2214yescomplemented
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4C2212yes—
17#16840615C2218yescomplemented
18#16840613C2218yes—
19#16840294—22no—
20#16840294—22no—
21#16840294C414yescomplemented
22#16840294C2214yes—
23C2×#14519770—21no—
24C2×#14519768C411yescharacteristic, complemented
25C2×#14519764C411yescharacteristic, complemented
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519748C2211yescharacteristic
29C2×C4×Dic122C411yescharacteristic, complemented
30C2×C4×C22⋊D61—21no—
31C2×#14519736—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×D4×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C22×#92420—22no—
36C2×C4×#6923—28no—
37C2×C4×#6923—24no—
38C4⋊#92420—24no—
39#14519834—22no—
40#14519834C2314yes—
41C4×#92420—24no—
42(C2×#6923)⋊C4—24no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4C2314yes—
45C22×Dic122C2×C411yescharacteristic
46C22×C22⋊D61—21no—
47C22×C4×D61D411yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×C4×D61C2311yescharacteristic
50#14519770—24no—
51#14519770—24no—
52#14519768—22no—
53#14519768C2×C414yescomplemented
54#14519764—22no—
55#14519764C2×C414yescomplemented
56#14519759—24no—
57#14519759—24no—
58#14519757—21no—
59#14519757—21no—
60#14519757C2×C412yes—
61#14519757C2312yes—
62#14519748—21no—
63#14519748—21no—
64#14519748C2×C412yes—
65#14519748C2312yes—
66C4×Dic122—22no—
67C4×Dic122C2×C414yescomplemented
68C4×C22⋊D61—24no—
69C4×C22⋊D61—24no—
70#14519736—24no—
71#14519736—24no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—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×D4×C61C2×C411yescharacteristic
90C23×C4×C61—21no—
91C4×D4×C61—22no—
92C4×D4×C61C2×C414yescomplemented
93C2×C4⋊C4×C61C2×C411yescharacteristic
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×D4×C61—21no—
103C2×D4×C61—42no—
104C2×D4×C61C22×C412yes—
105C22×C4×C61—21no—
106C22×C4×C61—24no—
107C22×C4×C61—44no—
108C22×C4×C61C22⋊C411yescharacteristic
109C22×C4×C61C22⋊C411yescharacteristic
110C22×C4×C61C22×C411yescharacteristic
111C2×C22⋊D61—22no—
112C2×C22⋊D61—22no—
113C2×C22⋊D61—44no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22⋊C411yescharacteristic
118C22×Dic61C2×D411yescharacteristic
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—42no—
122C2×C4×D61C22⋊C412yes—
123C2×C4×D61C22⋊C412yes—
124C2×C4×D61C22×C411yescharacteristic
125C2×C4×D61C2×D412yes—
126C2×C4×D61C2×D412yes—
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2411yescharacteristic
130C2×Dic122—21no—
131C2×Dic122—42no—
132C2×Dic122C22×C412yes—
133C2×#92420—24no—
134C2×#92420—44no—
135C4×#6923—216no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61C22×C412yes—
138C22⋊C4×C61—24no—
139C42×C61C22⋊C412yes—
140C42×C61C22×C412yes—
141C22⋊Dic61—22no—
142C22⋊Dic61—24no—
143C22⋊Dic61—24no—
144C22⋊Dic61—22no—
145#11758198—22no—
146#11758198—22no—
147C4⋊Dic61—21no—
148C4⋊Dic61—22no—
149C4⋊Dic61—24no—
150C4⋊Dic61—22no—
151C4⋊Dic61C22×C412yes—
152#11758196—24no—
153#11758196—24no—
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—
175D4×C61—42no—
176D4×C61—42no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—42no—
181C2×C4×C61—48no—
182C2×C4×C61#10414yes—
183C2×C4×C61C2×C22⋊C411yescharacteristic
184C2×C4×C61C2×C22⋊C412yes—
185C2×C4×C61C2×C22⋊C412yes—
186C2×C4×C61C23×C411yescharacteristic
187C22⋊D61—44no—
188C22⋊D61—44no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61C2×C22⋊C411yescharacteristic
197C2×Dic61C2×C22⋊C412yes—
198C2×Dic61C2×C22⋊C412yes—
199C2×Dic61C22×D411yescharacteristic
200C4×D61—24no—
201C4×D61—24no—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208Dic122—42no—
209Dic122—42no—
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—42no—
232C4×C61C2×#10414yes—
233Dic61—21no—
234Dic61—21no—
235Dic61—22no—
236Dic61—22no—
237Dic61—42no—
238Dic61—42no—
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—611no—
259C2×#123—1221no—
260C2×C22⋊Q8—611no—
261C2×#121—611no—
262C2×C4×Q8—611no—
263C2×C4×D4—1221no—
264C2×C4×D4#692311yescharacteristic, complemented
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×Q8—611no—
281C22×D4—1221no—
282C22×D4C2×#692311yescharacteristic
283C23×C4—21no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—611no—
287C23×C4—1222no—
288C22×C8—1222no—
289#126—1224no—
290#126—1224no—
291#125—614no—
292#125—1222no—
293#124—614no—
294#124—1222no—
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—22no—
308C4×D4—1224no—
309C4×D4—1224no—
310C4×D4C2×#692314yescomplemented
311#117—1224no—
312#117—1224no—
313C2×C4⋊C4—611no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4C2×#692311yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—1221no—
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—1224no—
332C2×C42—1228no—
333C2×C42—1221no—
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—612no—
345C2×Q8—1221no—
346C2×Q8—2442no—
347C2×D4—21no—
348C2×D4—42no—
349C2×D4—1222no—
350C2×D4—1222no—
351C2×D4—2444no—
352C2×D4C22×#692312yes—
353C22×C4—21no—
354C22×C4—24no—
355C22×C4—44no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—612no—
362C22×C4—612no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—1224no—
368C22×C4—1224no—
369C22×C4—1224no—
370C22×C4—1228no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—2442no—
374C22×C4—2444no—
375C22×C4—2444no—
376C22×C4C22⋊#692311yescharacteristic
377C22×C4C22⋊#692311yescharacteristic
378C22×C4C22×#692311yescharacteristic
379C2×C8—1224no—
380C2×C8—2444no—
381C4⋊C4—21no—
382C4⋊C4—612no—
383C4⋊C4—1224no—
384C4⋊C4—1222no—
385C4⋊C4—1222no—
386C4⋊C4—1224no—
387C4⋊C4—1221no—
388C4⋊C4—1224no—
389C4⋊C4C22×#692312yes—
390C22⋊C4—24no—
391C22⋊C4—1222no—
392C22⋊C4—1222no—
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C22⋊C4—1224no—
396C22⋊C4—1224no—
397C42—612no—
398C42—612no—
399C42—612no—
400C42—612no—
401C42—612no—
402C42—612no—
403C42—12216no—
404C42—1224no—
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—2442no—
418Q8—2442no—
419D4—42no—
420D4—42no—
421D4—2444no—
422D4—2444no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—48no—
428C2×C4—611no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—611no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1222no—
435C2×C4—1222no—
436C2×C4—1222no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—1228no—
440C2×C4—1222no—
441C2×C4—1222no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2444no—
447C2×C4—2444no—
448C2×C4—24416no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4#1451984114yes—
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#1684074112yes—
469C22#1684075212yes—
470C22C2×#1451984112yes—
471C22C22×C22⋊#692311yescharacteristic
472C4—21no—
473C4—21no—
474C4—22no—
475C4—42no—
476C4—1221no—
477C4—1221no—
478C4—1222no—
479C4—1222no—
480C4—2448no—
481C4—2442no—
482C4—2442no—
483C4C2×#1451984114yes—
484C2—82no—
485C2—1222no—
486C2—1222no—
487C2#2146119014yesdirect product factor
488C2C2×#1684074111yescharacteristic
489C2C2×#1684075211yescharacteristic
490C2C22×#1451984111yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1500
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840781C2semidirect
2. C2×#16840698C2semidirect
3. #21461190C2direct (N × H)
4. C2×#16840615C2semidirect
9. #16840781C22semidirect
14. #16840698C22semidirect
17. #16840615C22semidirect
21. #16840294C4semidirect
24. C2×#14519768C4semidirect
25. C2×#14519764C4semidirect
29. C2×C4×Dic122C4semidirect
33. C2×C4×D4×C61C4semidirect
53. #14519768C2×C4semidirect
55. #14519764C2×C4semidirect
67. C4×Dic122C2×C4semidirect
92. C4×D4×C61C2×C4semidirect
246. C2×C61#1500semidirect
264. C2×C4×D4#6923semidirect
279. C61C2×#1500semidirect
310. C4×D4C2×#6923semidirect
487. C2#21461190direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407812
C2×#168406982
#214611902
C2×#168406152
C2×#168406132
C2×#168402942
C2×#150061