Finite Group Databasebeta

← #29700391

Subgroups — #29700391

Order 15616.

1134 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×#16839922C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic
4#21448650C211yesmaximal, characteristic
5#21446679C211yesmaximal, characteristic, complemented
6#21446508C211yesmaximal, characteristic, complemented
7#21446460C211yesmaximal, characteristic, complemented
8#21446253C211yesmaximal, characteristic, complemented
9#21446160C211yesmaximal, characteristic, complemented
10#21446156C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446007C211yesmaximal, characteristic, complemented
13C4×#14519697C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#2360C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22#16839922C418yescomplemented
23#16839860—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26#16839761—24no—
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839668C2211yescharacteristic
39#16839668C2211yescharacteristic
40#16839638—21no—
41#16839638—21no—
42#16839624—21no—
43#16839622C2211yescharacteristic
44#95×D61—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×C22⋊Q8×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C61×#391C2211yescharacteristic
55C61×#389—21no—
56C61×#389C2211yescharacteristic
57C61×#387—21no—
58C61×#385—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61—21no—
61C4×C22⋊C4×C61C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yes—
68C22×Dic122C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758202—41no—
75C2×#11758202—41no—
76C2×#11758202C2×C414yescomplemented
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201C2×C414yescomplemented
80C2×#11758194—22no—
81C2×#11758194—22no—
82C2×#11758194—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C4×D244—22no—
88C4×D244—22no—
89C4×D244—41no—
90C4×D244—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96#14519710—22no—
97#14519710—41no—
98#14519701—22no—
99#14519701—41no—
100#14519700—22no—
101#14519700—22no—
102#14519700C2×C414yescomplemented
103#14519697—22no—
104#14519697C2×C414yescomplemented
105#14519697D414yes—
106C22⋊#92418C2×C414yescomplemented
107#14519688—22no—
108C4×#92418—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114C22×Q8×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61C2×C414yescomplemented
119C4×Q8×C61—22no—
120C4×Q8×C61—41no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—22no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—41no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—81no—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61#4112yes—
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176#11758222—28no—
177#11758222—44no—
178#11758222—44no—
179#11758222—44no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244C22×C412yes—
184C2×D244C2×D412yes—
185C2×D244#4112yes—
186C2×C4×D61—24no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122C22×C412yes—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—42no—
207C4⋊C4×C61—42no—
208C4⋊C4×C61—81no—
209C4⋊C4×C61C22×C412yes—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—24no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—41no—
214C42×C61—21no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—21no—
218C42×C61—42no—
219C42×C61—81no—
220C22⋊Dic61—81no—
221#11758202—44no—
222#11758201—28no—
223#11758198—42no—
224#11758198—42no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229#11758194—44no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418C22×C412yes—
240C2×#92418C22×C412yes—
241C2×#92418C2×D412yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—41no—
260Q8×C61—41no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—84no—
291C2×C4×C61C4×D412yes—
292C2×C4×C61#13712yes—
293C2×C4×C61C23×C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C61H(5,𝔽2)11yescharacteristic
299C22⋊D61—48no—
300C2×Dic61—22no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309D244—22no—
310D244—22no—
311D244—22no—
312D244C4×D414yes—
313C4×D61—48no—
314C4×D61—84no—
315C4×D61—84no—
316Dic122—22no—
317Dic122—22no—
318Dic122—41no—
319Dic122—41no—
320#92418—22no—
321#92418—22no—
322#92418—22no—
323#92418—41no—
324#22862—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61C2×C4×D411yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61C2×#13711yescharacteristic
336C22×C61#57511yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57811yescharacteristic
339C2×D61—24no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61—41no—
351C4×C61—42no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61—81no—
355C4×C61C2×C4×D411yescharacteristic
356C4×C61#51811yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#55111yescharacteristic
359Dic61—42no—
360Dic61—81no—
361Dic61—81no—
362C2×#452—611no—
363C2×#440—611no—
364C2×#417—611no—
365#2360D6111yescharacteristic, complemented
366#2339—611no—
367#1969—611no—
368#1935—611no—
369#1928—611no—
370#1894—611no—
371#1878—611no—
372#1877—611no—
373#1862—611no—
374#1852—611no—
375C4×#102—611no—
376#1753—611no—
377C2×C61—42no—
378C2×C61#235811yescharacteristic
379C2×C61C4×#13711yescharacteristic
380C2×C61#295111yescharacteristic
381C2×C61#327311yescharacteristic
382C2×C61#327611yescharacteristic
383C2×C61#331411yescharacteristic
384C2×C61#331511yescharacteristic
385D61—44no—
386C22×#41—611no—
387C22×Q16—611no—
388C22×SD16—611no—
389C22×M16—611no—
390C2×C22⋊Q8C2×D6111yescharacteristic
391C2×C4×Q8C2×D6111yescharacteristic
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C22×C4⋊C4C2×D6111yescharacteristic
395#452—618no—
396#440—1224no—
397C2×#107—611no—
398C2×#107—611no—
399#417—1224no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×C22⋊C8—611no—
409C2×#97—611no—
410C2×C4×C8—611no—
411#391—611no—
412#391—611no—
413#391C2×D6111yescharacteristic
414#389—21no—
415#389C2×D6111yescharacteristic
416#387—21no—
417#386—1221no—
418#386—1221no—
419#385—21no—
420#381—1221no—
421#380—611no—
422C4×C4⋊C4C2×D6111yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4C2×D6111yescharacteristic
425C2×#95—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#336—611no—
431#336—611no—
432C61#2286211yescharacteristic, complemented, Sylow
433C2×#41—614no—
434C2×#41—1222no—
435C2×#41—1222no—
436C2×#41—1222no—
437C2×#41—2441no—
438C2×#41—2441no—
439C22×Q8—611no—
440C22×Q8C22×D6111yescharacteristic
441C22×D4—611no—
442C22×D4—1221no—
443C23×C4—21no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C23×C4C22×D6111yescharacteristic
448C2×Q16—614no—
449C2×Q16—2441no—
450C2×Q16—2441no—
451C2×SD16—614no—
452C2×SD16—1222no—
453C2×SD16—1222no—
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22⋊Q8—22no—
462C22⋊Q8C4×D6114yescomplemented
463C4×Q8—22no—
464C4×Q8—41no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—2441no—
468C4×D4—2441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4C22⋊D6111yescharacteristic
485C2×C22⋊C4C22⋊D6111yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42C22×D6111yescharacteristic
489C2×C42C22×D6111yescharacteristic
490#107—1222no—
491#107—2441no—
492#103—614no—
493#103—1222no—
494#103—1222no—
495#103—1222no—
496#103—2441no—
497#102—614no—
498#102—614no—
499#102—1222no—
500C22⋊C8—614no—
501#97—1222no—
502C4×C8—2441no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95C22⋊D6111yescharacteristic
513#95C22⋊D6111yescharacteristic
514C24—1221no—
515C24C2×C22⋊D6111yescharacteristic
516#41—1228no—
517#41—2444no—
518#41—2444no—
519#41—2444no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—612no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8C2×C4×D6112yes—
532C2×D4—612no—
533C2×D4—612no—
534C2×D4—612no—
535C2×D4—1224no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2442no—
540C2×D4—2442no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—1221no—
553C22×C4—1224no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—4881no—
557C22×C4—4881no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4C2×C4×D6112yes—
565C22×C4#1175822212yes—
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C23×D6111yescharacteristic
572Q16—2444no—
573SD16—1228no—
574M16—2444no—
575C2×C8—612no—
576C2×C8—612no—
577C2×C8—612no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—24no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4C2×C4×D6112yes—
600C4⋊C4D4×D6112yes—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—4881no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—42no—
612C42—81no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23C4×C22⋊D6112yes—
627C23C22×C22⋊D6111yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—1222no—
633Q8—1222no—
634Q8—2441no—
635Q8—2441no—
636D4—614no—
637D4—1222no—
638D4—1222no—
639D4—1222no—
640D4—2448no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—1222no—
672C2×C4—4884no—
673C2×C4—4884no—
674C2×C4—2448no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4C4×C22⋊D6112yes—
684C2×C4#1451980812yes—
685C2×C4C22×C4×D6111yescharacteristic
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822211yescharacteristic
689C2×C4#1451982211yescharacteristic
690C2×C4#1451982311yescharacteristic
691C8—1222no—
692C8—1222no—
693C8—1222no—
694C8—2441no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—1224no—
703C22—2442no—
704C22—2442no—
705C22—2442no—
706C22—2442no—
707C22—2442no—
708C22—2442no—
709C22C2×C4×C22⋊D6111yescharacteristic
710C22D4×C22⋊D6111yescharacteristic
711C22#1684040011yescharacteristic
712C22C2×#1451980811yescharacteristic
713C22#1684056011yescharacteristic
714C22#1684056511yescharacteristic
715C22#1684057711yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—81no—
725C4—4881no—
726C4—4881no—
727C4—2442no—
728C4C4×D4×D6111yescharacteristic
729C4#1684023411yescharacteristic
730C4#1684040811yescharacteristic
731C4#1684044111yescharacteristic
732C2—42no—
733C2—2444no—
734C2#2144879611yescharacteristic
735C2C4×#1451980811yescharacteristic
736C2#2145469211yescharacteristic
737C2#2145742611yescharacteristic
738C2#2145746511yescharacteristic
739C2#2145789411yescharacteristic
740C2#2145790911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2360C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#2360D61
hypocenterC61#22862
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#16839860C2semidirect
5. #21446679C2semidirect
6. #21446508C2semidirect
7. #21446460C2semidirect
8. #21446253C2semidirect
9. #21446160C2semidirect
10. #21446156C2semidirect
11. #21446065C2semidirect
12. #21446007C2semidirect
13. C4×#14519697C2semidirect
14. #21445603C2semidirect
15. C61×#2360C2semidirect
22. #16839922C4semidirect
76. C2×#11758202C2×C4semidirect
79. C2×#11758201C2×C4semidirect
102. #14519700C2×C4semidirect
104. #14519697C2×C4semidirect
106. C22⋊#92418C2×C4semidirect
118. C22⋊Q8×C61C2×C4semidirect
365. #2360D61semidirect
432. C61#22862semidirect
462. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399222
C2×#168398602
C2×#168397612
#214486502
#214466792
#214465082
#214464602
#214462532
#214461602
#214461562
#214460652
#214460072
C4×#145196972
#214456032
C61×#23602
#2286261