Finite Group Databasebeta

← C2×#21461194 #30610904

Subgroups — C2×#21461194 #30610904

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊#6923C211yesmaximal, characteristic, complemented
3#21461194C218yesmaximal, direct product factor
4C2×#16840616C212yesmaximal, complemented
5C2×#16840613C212yesmaximal, complemented
6C2×#16840269C211yesmaximal, characteristic
7C22×D61⋊C8—21no—
8C22×C22⋊#6923—21no—
9C22×C4×#6923—21no—
10C2×#14519834C2212yes—
11D61⋊(C22⋊C8)—22no—
12D61⋊(C22⋊C8)C2214yescomplemented
13C2×C22⋊#92420—21no—
14C4×C22⋊#6923—22no—
15C4×C22⋊#6923C2214yescomplemented
16C2×(C2×#6923)⋊C4C2212yes—
17#16840616C2218yescomplemented
18#16840613C2218yescomplemented
19C23×C4×D61C2211yescharacteristic
20#16840269—22no—
21#16840269—22no—
22#16840269C414yescomplemented
23#16840269C2214yes—
24C2×#14519758—21no—
25C2×#14519753C411yescharacteristic, complemented
26C2×#14519753C2211yescharacteristic
27C2×#14519748C411yescharacteristic, complemented
28C2×#14519748C2211yescharacteristic
29C2×#14519745—21no—
30C2×C4×C22⋊D61—21no—
31C2×C4×C22⋊D61—21no—
32C2×#14519736C411yescharacteristic, complemented
33C22×#41×C61C411yescharacteristic, complemented
34C23×#6923—22no—
35C2×D61⋊C8—24no—
36C2×D61⋊C8—44no—
37C22×#92420—22no—
38C2×C22⋊#6923—28no—
39C2×C22⋊#6923—24no—
40C2×C4×#6923—24no—
41C2×C4×#6923—44no—
42#14519834—22no—
43#14519834C2314yes—
44C22⋊#92420—24no—
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4C2314yes—
47C24×D61D411yescharacteristic
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C23×Dic61D411yescharacteristic
51C22×C4×D61—44no—
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C412yes—
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D412yes—
57C22×C4×D61D412yes—
58C22×C4×D61C2312yes—
59C22×C4×D61C2311yescharacteristic
60#14519758—24no—
61#14519758—24no—
62#14519753—22no—
63#14519753—21no—
64#14519753—21no—
65#14519753C2×C412yes—
66#14519753C2×C414yescomplemented
67#14519753C2312yes—
68#14519748—22no—
69#14519748—21no—
70#14519748—21no—
71#14519748C2×C412yes—
72#14519748C2×C414yescomplemented
73#14519748C2312yes—
74#14519745—24no—
75#14519745—24no—
76C4×C22⋊D61—24no—
77C4×C22⋊D61—24no—
78C4×C22⋊D61—24no—
79C4×C22⋊D61—24no—
80#14519736—22no—
81#14519736C2×C414yescomplemented
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92C2×#41×C61—22no—
93C2×#41×C61—44no—
94C2×#41×C61C2×C414yescomplemented
95C22×Q8×C61C2×C411yescharacteristic
96C22×D4×C61—21no—
97C22×D4×C61C2×C411yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61C2×C411yescharacteristic
100C24×C61—21no—
101C24×C61C22⋊C411yescharacteristic
102C23×D61—24no—
103C23×D61—24no—
104C23×D61—42no—
105C23×D61C22⋊C412yes—
106C23×D61C22⋊C411yescharacteristic
107C23×D61C2×D412yes—
108C23×D61C2×D411yescharacteristic
109C22×#6923—28no—
110C22×#6923—24no—
111C22×#6923—44no—
112C22×#6923—44no—
113#41×C61—48no—
114#41×C61—48no—
115C2×Q8×C61—21no—
116C2×Q8×C61—42no—
117C2×Q8×C61C22×C412yes—
118C2×D4×C61—24no—
119C2×D4×C61—21no—
120C2×D4×C61—42no—
121C2×D4×C61—44no—
122C2×D4×C61C22×C412yes—
123C22×C4×C61—24no—
124C22×C4×C61—21no—
125C22×C4×C61—24no—
126C22×C4×C61—44no—
127C22×C4×C61C22⋊C412yes—
128C22×C4×C61C22⋊C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C412yes—
131C2×C22⋊D61—22no—
132C2×C22⋊D61—24no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—44no—
135C2×C22⋊D61—44no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—42no—
139C22×Dic61C22⋊C411yescharacteristic
140C22×Dic61C22⋊C412yes—
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D412yes—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61C22⋊C412yes—
152C2×C4×D61C22⋊C412yes—
153C2×C4×D61C22⋊C412yes—
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C22×C412yes—
156C2×C4×D61C2×D412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2411yescharacteristic
161C22⋊#6923—216no—
162C2×#92420—24no—
163C2×#92420—44no—
164C4×#6923—48no—
165D61⋊C8—48no—
166C22⋊Dic61—24no—
167C22⋊Dic61—22no—
168C22⋊Dic61—24no—
169C22⋊Dic61—22no—
170#11758198—22no—
171#11758198—24no—
172#11758198—22no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61C22×C412yes—
176C4⋊Dic61C22×C412yes—
177#11758196—22no—
178#11758196—24no—
179#11758196—22no—
180C4×Dic61—24no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—22no—
184C23×C61—22no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61C2×C22⋊C412yes—
189C23×C61C2×C22⋊C411yescharacteristic
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—22no—
194C22×D61—24no—
195C22×D61—24no—
196C22×D61—24no—
197C22×D61—24no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—416no—
201C22×D61#10414yes—
202C22×D61C2×C22⋊C411yescharacteristic
203C22×D61C2×C22⋊C412yes—
204C22×D61#13514yes—
205C22×D61C22×D411yescharacteristic
206C2×#6923—28no—
207C2×#6923—44no—
208C2×#6923—416no—
209C2×#6923—44no—
210Q8×C61—42no—
211Q8×C61—42no—
212D4×C61—42no—
213D4×C61—42no—
214D4×C61—48no—
215C2×C4×C61—22no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—42no—
220C2×C4×C61—48no—
221C2×C4×C61#9914yes—
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C2×C4×C61C2×C22⋊C412yes—
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—44no—
226C22⋊D61—44no—
227C22⋊D61—48no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C22×D411yescharacteristic
239C4×D61—24no—
240C4×D61—24no—
241C4×D61—24no—
242C4×D61—24no—
243C4×D61—42no—
244C4×D61—41no—
245C4×D61—42no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—41no—
249#92420—44no—
250C2×#1501—611nomaximal, Sylow
251C22×C61—22no—
252C22×C61—22no—
253C22×C61—22no—
254C22×C61—44no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—84no—
259C22×C61C2×#9912yes—
260C22×C61#41612yes—
261C22×C61C2×#10412yes—
262C22×C61C22×C22⋊C411yescharacteristic
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—28no—
270C2×D61—28no—
271C2×D61—48no—
272C2×D61—48no—
273C2×D61#41612yes—
274C2×D61C2×#10414yes—
275C2×D61C2×#13512yes—
276#6923—48no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—42no—
280C4×C61C2×#9914yes—
281Dic61—21no—
282Dic61—22no—
283Dic61—21no—
284Dic61—42no—
285Dic61—42no—
286C2×#525—611no—
287C22×C22⋊C8—611no—
288C2×C4×C22⋊C4—611no—
289#1501—618no—
290C2×#328—612no—
291C2×#327—612no—
292C2×C61—42no—
293C2×C61—82no—
294C2×C61#150114yescomplemented
295C2×C61C22×#9911yescharacteristic
296C2×C61C2×#41611yescharacteristic
297C2×C61C22×#10411yescharacteristic
298D61—22no—
299D61—22no—
300D61—24no—
301C22×#41#692311yescharacteristic, complemented
302C24×C4—611no—
303C23×C8—1221no—
304#525—614no—
305#525—614no—
306#525—1222no—
307#525—1222no—
308C2×#123—1221no—
309C2×C22⋊Q8—611no—
310C2×C22⋊Q8—611no—
311C2×#121—611no—
312C2×#121—611no—
313C2×#120—1221no—
314C2×C4×D4—1221no—
315C2×C4×D4—1221no—
316C2×#117—611no—
317C22×C22⋊C4—1221no—
318C22×C42—1221no—
319C2×C22⋊C8—614no—
320C2×C22⋊C8—612no—
321C2×C22⋊C8—1221no—
322C2×C22⋊C8—1222no—
323C4×C22⋊C4—614no—
324C4×C22⋊C4—1222no—
325C2×#95—612no—
326#328—618no—
327#327—618no—
328C61C2×#150111yescharacteristic, complemented, Sylow
329C25—611no—
330C2×#41—22no—
331C2×#41—44no—
332C2×#41C2×#692314yescomplemented
333C22×Q8C2×#692311yescharacteristic
334C22×D4—21no—
335C22×D4—1221no—
336C22×D4—1221no—
337C22×D4C2×#692311yescharacteristic
338C23×C4—21no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—612no—
343C23×C4—612no—
344C23×C4—611no—
345C23×C4—612no—
346C23×C4—611no—
347C23×C4—612no—
348C23×C4—1222no—
349C23×C4—2444no—
350C23×C4C2×#692311yescharacteristic
351C22×C8—1222no—
352C22×C8—1224no—
353C22×C8—2444no—
354#123—1224no—
355#123—1224no—
356C22⋊Q8—612no—
357C22⋊Q8—612no—
358C22⋊Q8—614no—
359C22⋊Q8—1221no—
360C22⋊Q8—1221no—
361C22⋊Q8—1222no—
362#121—612no—
363#121—612no—
364#121—614no—
365#121—1221no—
366#121—1221no—
367#121—1222no—
368#120—1224no—
369#120—1224no—
370C4×D4—1224no—
371C4×D4—1224no—
372C4×D4—1224no—
373C4×D4—1224no—
374#117—614no—
375#117—1222no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1224no—
385C2×C22⋊C4—1228no—
386C2×C22⋊C4—1221no—
387C2×C42—1221no—
388C2×C42—1224no—
389C2×C42—2444no—
390C22⋊C8—614no—
391C22⋊C8—1224no—
392C22⋊C8—1222no—
393#95—614no—
394#95—1222no—
395C24—21no—
396C24—611no—
397C24—611no—
398C24—612no—
399C24—612no—
400C24—1224no—
401C24—1224no—
402C24—2442no—
403C24C22⋊#692311yescharacteristic
404#41—48no—
405#41—48no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8C22×#692312yes—
409C2×D4—24no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—1222no—
414C2×D4—1224no—
415C2×D4—1222no—
416C2×D4—2444no—
417C2×D4—2444no—
418C2×D4C22×#692312yes—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—44no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—612no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—612no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—1224no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1228no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—2444no—
444C22×C4—2444no—
445C22×C4—2444no—
446C22×C4—2444no—
447C22×C4—2442no—
448C22×C4—2442no—
449C22×C4—2442no—
450C22×C4—2444no—
451C22×C4—2444no—
452C22×C4C22⋊#692312yes—
453C22×C4C22⋊#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692312yes—
456C2×C8—1224no—
457C2×C8—2448no—
458C2×C8—2444no—
459C4⋊C4—612no—
460C4⋊C4—612no—
461C4⋊C4—1222no—
462C4⋊C4—1224no—
463C4⋊C4—1222no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C22⋊C4—1222no—
467C22⋊C4—1224no—
468C22⋊C4—1222no—
469C22⋊C4—1222no—
470C22⋊C4—1224no—
471C22⋊C4—1222no—
472C22⋊C4—12216no—
473C22⋊C4—1224no—
474C42—1224no—
475C42—2448no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—614no—
484C23—614no—
485C23—611no—
486C23—612no—
487C23—611no—
488C23—1224no—
489C23—1224no—
490C23—1224no—
491C23—1224no—
492C23—1222no—
493C23—1222no—
494C23—1222no—
495C23—1222no—
496C23—2442no—
497C23—2442no—
498C23—24416no—
499C23C2×C22⋊#692312yes—
500C23C2×C22⋊#692311yescharacteristic
501Q8—42no—
502Q8—42no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—2444no—
507D4—2444no—
508D4—2448no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—48no—
515C2×C4—611no—
516C2×C4—612no—
517C2×C4—611no—
518C2×C4—1222no—
519C2×C4—1222no—
520C2×C4—1224no—
521C2×C4—1224no—
522C2×C4—1224no—
523C2×C4—1224no—
524C2×C4—1228no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2442no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2444no—
536C2×C4—2444no—
537C2×C4—24416no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4#1451983514yes—
541C2×C4C2×C22⋊#692311yescharacteristic
542C2×C4C2×C22⋊#692312yes—
543C2×C4C23×#692311yescharacteristic
544C8—2444no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—84no—
553C22—612no—
554C22—612no—
555C22—614no—
556C22—1221no—
557C22—1222no—
558C22—1221no—
559C22—1222no—
560C22—1221no—
561C22—1221no—
562C22—1228no—
563C22—1228no—
564C22—2448no—
565C22—2448no—
566C22C2×#1451983512yes—
567C22#1684075212yes—
568C22D61⋊#10412yes—
569C22C22×C22⋊#692311yescharacteristic
570C4—21no—
571C4—21no—
572C4—42no—
573C4—1221no—
574C4—1221no—
575C4—1222no—
576C4—2448no—
577C4—2442no—
578C4—2442no—
579C4C2×#1451983514yes—
580C2—42no—
581C2—82no—
582C2—1222no—
583C2—1222no—
584C2—1224no—
585C2#2146119414yesdirect product factor
586C2C22×#1451983511yescharacteristic
587C2C2×#1684075211yescharacteristic
588C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×#41×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840269C2
cosocleC2×C4×D61C24
hypercenterC22×#41#6923
hypocenterC61C2×#1501
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊(C22⋊C8)C2semidirect
2. C2×C4×C22⋊#6923C2semidirect
3. #21461194C2direct (N × H)
4. C2×#16840616C2semidirect
5. C2×#16840613C2semidirect
12. D61⋊(C22⋊C8)C22semidirect
15. C4×C22⋊#6923C22semidirect
17. #16840616C22semidirect
18. #16840613C22semidirect
22. #16840269C4semidirect
25. C2×#14519753C4semidirect
27. C2×#14519748C4semidirect
32. C2×#14519736C4semidirect
33. C22×#41×C61C4semidirect
66. #14519753C2×C4semidirect
72. #14519748C2×C4semidirect
81. #14519736C2×C4semidirect
94. C2×#41×C61C2×C4semidirect
294. C2×C61#1501semidirect
301. C22×#41#6923semidirect
328. C61C2×#1501semidirect
332. C2×#41C2×#6923semidirect
585. C2#21461194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
C2×C4×C22⋊#69232
#214611942
C2×#168406162
C2×#168406132
C2×#168402692
C2×#150161