Finite Group Databasebeta

← #29696564

Subgroups — #29696564

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic
2#21448696C211yesmaximal, characteristic, complemented
3#21446804C211yesmaximal, characteristic, complemented
4#21446804C212yesmaximal, complemented
5#21446803C211yesmaximal, characteristic, complemented
6#21446803C212yesmaximal, complemented
7#21445804C211yesmaximal, characteristic
8#21445804C212yesmaximal
9C4×#14519691C211yesmaximal, characteristic
10C4×#14519691C212yesmaximal
11C61×#2345C211yesmaximal, characteristic, complemented
12#16840467—21no—
13#16840467—22no—
14#16840467—21no—
15#16840467—21no—
16#16840467—22no—
17#16840467—21no—
18C2×#14519776C411yescharacteristic, complemented
19C2×#14519767C412yescomplemented
20C2×#14519757C411yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic
22C2×#14519756C2212yes—
23C2×#14519755C412yescomplemented
24C2×#14519742C411yescharacteristic, complemented
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×C4×C22⋊D61C2212yes—
27C2×C4⋊C4×D61C411yescharacteristic, complemented
28C2×#14519691C2211yescharacteristic
29C2×#14519691C2212yes—
30C2×#14519691C2211yescharacteristic
31#16839661—21no—
32#16839648—22no—
33#16839622C2211yescharacteristic
34#16839622C2212yes—
35C4⋊C4×Dic61—21no—
36C4×C22⋊Dic61C2211yescharacteristic
37C4×C22⋊Dic61C2212yes—
38#16839528C2212yes—
39#16839528C2211yescharacteristic
40#16839528C2212yes—
41#16839528C2212yes—
42#16839528C2212yes—
43#16839528C2212yes—
44#16839528C2211yescharacteristic
45C22×C4⋊C4×C61C2211yescharacteristic
46C61×#389—21no—
47C61×#387—22no—
48C61×#380C2212yes—
49C61×#380C2211yescharacteristic
50C4×C4⋊C4×C61—21no—
51C4×C22⋊C4×C61C2211yescharacteristic
52C4×C22⋊C4×C61C2212yes—
53C22×Dic122C2×C411yescharacteristic
54C22×Dic122C2×C412yes—
55C22×C22⋊D61C2311yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C412yes—
58#14519776—22no—
59#14519776—21no—
60#14519776—21no—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519757—22no—
66#14519757—21no—
67#14519757—21no—
68#14519756—22no—
69#14519756—22no—
70#14519756—22no—
71#14519756—22no—
72#14519756—21no—
73#14519756—21no—
74#14519756—21no—
75#14519756—21no—
76#14519755—22no—
77#14519755—22no—
78#14519755—22no—
79#14519755—22no—
80#14519742—22no—
81#14519742—21no—
82#14519742—21no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—22no—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C412yes—
98C2×#11758196C2×C412yes—
99C2×#11758196C2×C412yes—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C2×C22⋊Dic61C2311yescharacteristic
104C2×C22⋊Dic61C2312yes—
105C2×C22⋊Dic61C2312yes—
106C2×C22⋊Dic61C2311yescharacteristic
107C2×C22⋊Dic61C2311yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C412yes—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61C2×C412yes—
113C2×C4×Dic61C2×C411yescharacteristic
114#14519691—22no—
115#14519691—24no—
116#14519691Q814yescomplemented
117#14519684—21no—
118#14519684—22no—
119#14519684—22no—
120#14519684—21no—
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2312yes—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—22no—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C412yes—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61D412yes—
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61D412yes—
133C2×C4⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2312yes—
136C2×C22⋊C4×C61C2311yescharacteristic
137C2×C42×C61—21no—
138C2×C42×C61—22no—
139#95×C61—21no—
140#95×C61—22no—
141#95×C61—22no—
142#95×C61—21no—
143C24×C61C2411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—42no—
149C22×C4×C61—82no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C412yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—21no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61C2×Q812yes—
167C2×C22⋊D61#4112yes—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C412yes—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C412yes—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—42no—
181C2×C4×D61—82no—
182C2×Dic122—21no—
183C2×Dic122—21no—
184C2×Dic122—22no—
185C2×Dic122—22no—
186C2×Dic122—42no—
187C2×Dic122—82no—
188C4⋊C4×C61—42no—
189C4⋊C4×C61—82no—
190C4⋊C4×C61C22⋊C412yes—
191C4⋊C4×C61C22⋊C411yescharacteristic
192C4⋊C4×C61C22⋊C411yescharacteristic
193C4⋊C4×C61C22⋊C412yes—
194C4⋊C4×C61C22⋊C412yes—
195C4⋊C4×C61C22⋊C412yes—
196C4⋊C4×C61C22⋊C412yes—
197C4⋊C4×C61C22⋊C412yes—
198C4⋊C4×C61C22⋊C411yescharacteristic
199C4⋊C4×C61C22⋊C411yescharacteristic
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—21no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61C2×Q812yes—
206C42×C61—42no—
207C42×C61—82no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—21no—
211C22⋊Dic61—21no—
212C22⋊Dic61—21no—
213C22⋊Dic61—21no—
214C22⋊Dic61—22no—
215C22⋊Dic61—21no—
216C22⋊Dic61—22no—
217C22⋊Dic61C2×Q812yes—
218#11758198—21no—
219#11758198—21no—
220#11758198—22no—
221#11758198—22no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—22no—
225C4⋊Dic61—22no—
226C4⋊Dic61—42no—
227C4⋊Dic61—82no—
228#11758196—22no—
229#11758196—22no—
230#11758196—21no—
231#11758196—21no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238C4×Dic61—22no—
239C4×Dic61—22no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—42no—
243C4×Dic61—82no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C23×C411yescharacteristic
247C23×C61C22×D411yescharacteristic
248C23×C61C22×D411yescharacteristic
249C23×C61C22×Q811yescharacteristic
250C23×C61C2×#4111yescharacteristic
251C23×C612−1+411yescharacteristic
252C23×C612−1+411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61C4×Q812yes—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—42no—
279C2×C4×C61C2×C22⋊C412yes—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C2×C22⋊C411yescharacteristic
282C2×C4×C61C2×C22⋊C411yescharacteristic
283C2×C4×C61C2×C22⋊C411yescharacteristic
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C2×C22⋊C411yescharacteristic
287C22⋊D61—22no—
288C22⋊D61—22no—
289C22⋊D61—22no—
290C22⋊D61—22no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—42no—
301C2×Dic61—41no—
302C2×Dic61—42no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—42no—
310C2×Dic61C4×Q812yes—
311C4×D61—42no—
312C4×D61—42no—
313C4×D61—82no—
314C4×D61—82no—
315Dic122—42no—
316Dic122—42no—
317Dic122—82no—
318Dic122—82no—
319#22513—611nomaximal, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61C2×C4×Q811yescharacteristic
332C22×C61#51911yescharacteristic
333C22×C61#54811yescharacteristic
334C22×C61#54811yescharacteristic
335C22×C61D4×Q811yescharacteristic
336C22×C61D4×Q811yescharacteristic
337C2×D61—22no—
338C2×D61—42no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—42no—
342C4×C61—21no—
343C4×C61—21no—
344C4×C61—21no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—81no—
351C4×C61—82no—
352C4×C61#41012yes—
353Dic61—22no—
354Dic61—42no—
355Dic61—42no—
356Dic61—41no—
357Dic61—41no—
358Dic61—42no—
359Dic61—81no—
360Dic61—82no—
361C2×#554—611no—
362#2345—611no—
363#2345D6111yescharacteristic, complemented
364#1996—612no—
365#1996—611no—
366#1996—612no—
367#1996—611no—
368#1799—612no—
369#1799—611no—
370C4×#99—612no—
371C4×#99—611no—
372C2×C61—21no—
373C2×C61—21no—
374C2×C61—21no—
375C2×C61—21no—
376C2×C61—21no—
377C2×C61—21no—
378C2×C61Q8×C22⋊C411yescharacteristic
379C2×C61C2×#41011yescharacteristic
380C2×C61#288311yescharacteristic
381D61—42no—
382#554—1221no—
383#554—1222no—
384#554—1221no—
385#554—1221no—
386#554—1222no—
387#554—1221no—
388C2×C4⋊Q8—611no—
389C2×#125—612no—
390C2×C22⋊Q8—612no—
391C2×C22⋊Q8—611no—
392C2×C22⋊Q8—612no—
393C2×C22⋊Q8—611no—
394C2×C4×Q8—611no—
395C2×C4×D4—612no—
396C2×C4×D4—611no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4C2×D6111yescharacteristic
399C2×#99—611no—
400C2×#99—612no—
401C2×#99—611no—
402#389—21no—
403#389—1221no—
404#387—22no—
405#387—1222no—
406#380—612no—
407#380—611no—
408#380C2×D6112yes—
409#380C2×D6111yescharacteristic
410C4×C4⋊C4—21no—
411C4×C4⋊C4—1221no—
412C4×C22⋊C4—611no—
413C4×C22⋊C4—612no—
414C4×C22⋊C4C2×D6111yescharacteristic
415C4×C22⋊C4C2×D6112yes—
416#342—612no—
417#342—612no—
418#342—612no—
419#342—612no—
420#342—611no—
421#342—612no—
422#342—611no—
423C61#2251311yescharacteristic, complemented, Sylow
424C22×Q8—612no—
425C22×Q8—611no—
426C22×D4—611no—
427C23×C4—612no—
428C23×C4—611no—
429C23×C4C22×D6111yescharacteristic
430C23×C4C22×D6112yes—
431C4⋊Q8—1222no—
432C4⋊Q8—1221no—
433C4⋊Q8—1221no—
434#125—1222no—
435#125—1222no—
436#125—1222no—
437#125—1222no—
438C22⋊Q8—1222no—
439C22⋊Q8—1222no—
440C22⋊Q8—1221no—
441C22⋊Q8—1221no—
442C22⋊Q8—1222no—
443C22⋊Q8—1222no—
444C22⋊Q8—1221no—
445C22⋊Q8—1221no—
446C22⋊Q8—1222no—
447C22⋊Q8—1222no—
448C22⋊Q8—1222no—
449C22⋊Q8—1222no—
450C22⋊Q8—1222no—
451C22⋊Q8—1221no—
452C22⋊Q8—1221no—
453C4×Q8—1222no—
454C4×Q8—1221no—
455C4×Q8—1221no—
456C4×D4—1222no—
457C4×D4—1222no—
458C4×D4—1221no—
459C4×D4—1221no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1221no—
463C4×D4—1221no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—612no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—612no—
472C2×C4⋊C4—612no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1222no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4C4×D6111yescharacteristic
479C2×C4⋊C4C4×D6112yes—
480C2×C4⋊C4C4×D6111yescharacteristic
481C2×C4⋊C4D24411yescharacteristic
482C2×C4⋊C4D24412yes—
483C2×C4⋊C4D24411yescharacteristic
484C2×C4⋊C4C22⋊D6111yescharacteristic
485C2×C4⋊C4C22⋊D6112yes—
486C2×C4⋊C4C22⋊D6111yescharacteristic
487C2×C22⋊C4—611no—
488C2×C22⋊C4—612no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—612no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4C22×D6111yescharacteristic
495C2×C22⋊C4C22×D6112yes—
496C2×C22⋊C4C22×D6111yescharacteristic
497C2×C42—21no—
498C2×C42—22no—
499C2×C42—612no—
500C2×C42—611no—
501C2×C42—1222no—
502C2×C42—1221no—
503#99—614no—
504#99—1222no—
505#99—1224no—
506#95—21no—
507#95—22no—
508#95—22no—
509#95—21no—
510#95—1221no—
511#95—1222no—
512#95—1222no—
513#95—1221no—
514C24—611no—
515C24C23×D6111yescharacteristic
516C2×Q8—1222no—
517C2×Q8—1222no—
518C2×Q8—1221no—
519C2×Q8—1221no—
520C2×Q8—4882no—
521C2×Q8—2442no—
522C2×D4—612no—
523C2×D4—612no—
524C2×D4—1221no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—82no—
533C22×C4—611no—
534C22×C4—612no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—612no—
538C22×C4—1221no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1222no—
544C22×C4—1221no—
545C22×C4—4882no—
546C22×C4—2442no—
547C22×C4C2×C4×D6111yescharacteristic
548C22×C4C2×C4×D6112yes—
549C22×C4C2×C4×D6111yescharacteristic
550C22×C4C2×C4×D6112yes—
551C22×C4C2×D24411yescharacteristic
552C22×C4C2×D24411yescharacteristic
553C22×C4C2×D24412yes—
554C22×C4C2×D24412yes—
555C22×C4C2×C22⋊D6111yescharacteristic
556C22×C4C2×C22⋊D6111yescharacteristic
557C22×C4C2×C22⋊D6112yes—
558C22×C4C2×C22⋊D6112yes—
559C4⋊C4—42no—
560C4⋊C4—82no—
561C4⋊C4—1222no—
562C4⋊C4—1222no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1222no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—4882no—
576C4⋊C4—2442no—
577C4⋊C4#1175819812yes—
578C4⋊C4#1175819811yescharacteristic
579C4⋊C4#1175819811yescharacteristic
580C4⋊C4#1175819812yes—
581C4⋊C4#1175819812yes—
582C4⋊C4#1175819812yes—
583C4⋊C4#1175819812yes—
584C4⋊C4#1175819812yes—
585C4⋊C4#1175819811yescharacteristic
586C4⋊C4#1175819811yescharacteristic
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—22no—
592C22⋊C4—612no—
593C22⋊C4—1222no—
594C22⋊C4—1221no—
595C22⋊C4—1222no—
596C22⋊C4—1221no—
597C22⋊C4—1221no—
598C22⋊C4—1222no—
599C22⋊C4—1222no—
600C22⋊C4—1221no—
601C22⋊C4—1221no—
602C22⋊C4—1222no—
603C22⋊C4—1221no—
604C22⋊C4—1222no—
605C22⋊C4—1221no—
606C22⋊C4Q8×D6112yes—
607C42—42no—
608C42—82no—
609C42—1222no—
610C42—1222no—
611C42—1221no—
612C42—1221no—
613C42—4882no—
614C42—2442no—
615C23—41no—
616C23—41no—
617C23—612no—
618C23—1221no—
619C23—1221no—
620C23—2441no—
621C23—2441no—
622C23C22×C4×D6111yescharacteristic
623C23C22×C22⋊D6111yescharacteristic
624C23C22×D24411yescharacteristic
625C23C2×Q8×D6111yescharacteristic
626C23#41×D6111yescharacteristic
627C23#1451982411yescharacteristic
628C23#1451982511yescharacteristic
629Q8—4882no—
630Q8—4882no—
631Q8—2442no—
632Q8—2442no—
633D4—1222no—
634D4—1222no—
635D4—1222no—
636D4—1222no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—612no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—4882no—
667C2×C4—4882no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2442no—
682C2×C4C2×#1175819812yes—
683C2×C4C2×#1175819812yes—
684C2×C4C2×#1175819811yescharacteristic
685C2×C4C2×#1175819811yescharacteristic
686C2×C4C2×#1175819811yescharacteristic
687C2×C4C2×#1175819812yes—
688C2×C4C2×#1175819812yes—
689C2×C4C2×#1175819811yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—1222no—
701C22—2442no—
702C22—2442no—
703C22—2441no—
704C22—2441no—
705C22C22×#1175819811yescharacteristic
706C22C4×Q8×D6111yescharacteristic
707C22#1684023811yescharacteristic
708C22#1684041911yescharacteristic
709C22#1684042411yescharacteristic
710C22Q8×C22⋊D6111yescharacteristic
711C22Q8×D24411yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—42no—
720C4—81no—
721C4—82no—
722C4—1222no—
723C4—4882no—
724C4—4881no—
725C4—2442no—
726C4—2441no—
727C4—2442no—
728C4—2442no—
729C4—2441no—
730C4#1683973512yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—2442no—
738C2Q8×#1175819811yescharacteristic
739C2C2×#1683973511yescharacteristic
740C2#2145427911yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#2345C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C23
cosocleC24×C61C24
hypercenter#2345D61
hypocenterC61#22513
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #21448696C2semidirect
3. #21446804C2semidirect
4. #21446804C2semidirect
5. #21446803C2semidirect
6. #21446803C2semidirect
11. C61×#2345C2semidirect
18. C2×#14519776C4semidirect
19. C2×#14519767C4semidirect
20. C2×#14519757C4semidirect
23. C2×#14519755C4semidirect
24. C2×#14519742C4semidirect
27. C2×C4⋊C4×D61C4semidirect
116. #14519691Q8semidirect
363. #2345D61semidirect
423. C61#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#168404672
#214486962
#214468042
#214468032
#214458042
C4×#145196912
C61×#23452
#2251361