Finite Group Databasebeta

← #29702239

Subgroups — #29702239

Order 15616.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839838C211yesmaximal, characteristic, complemented
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839788C211yesmaximal, characteristic, complemented
4#21449061C211yesmaximal, characteristic
5#21446615C211yesmaximal, characteristic, complemented
6#21446534C211yesmaximal, characteristic, complemented
7#21446432C211yesmaximal, characteristic, complemented
8#21446422C211yesmaximal, characteristic, complemented
9#21446117C211yesmaximal, characteristic, complemented
10#21446111C211yesmaximal, characteristic, complemented
11#21446002C211yesmaximal, characteristic, complemented
12#21446000C211yesmaximal, characteristic, complemented
13#21445695C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C2×C61×#435C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×C4×C22⋊D61C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839838—24no—
22#16839837—24no—
23#16839788—24no—
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839695C411yescharacteristic
39#16839690C411yescharacteristic
40#16839685C411yescharacteristic
41#16839684C411yescharacteristic
42#16839678C411yescharacteristic
43#16839677C411yescharacteristic
44#16839676C411yescharacteristic
45#16839670C411yescharacteristic
46C4×#11758196C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×C22⋊Dic61C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#435—24no—
59C2×C4⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—41no—
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80#14519736—22no—
81#14519736—22no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×C22⋊Dic61C2×C411yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×C22⋊Dic61C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519706—22no—
102#14519706—22no—
103#14519706—22no—
104#14519706—22no—
105#14519706D414yescomplemented
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C22⋊#92418—41no—
109#14519689—22no—
110#14519689—22no—
111#14519689—41no—
112#14519687—22no—
113C8×Dic61—22no—
114C8×Dic61—22no—
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121C22×D4×C61C2×C411yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C2×M16×C61—22no—
125C2×M16×C61—22no—
126C2×M16×C61—41no—
127C22×C8×C61—22no—
128C22×C8×C61—22no—
129C22×C8×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C4×D4×C61—22no—
135C4×D4×C61—22no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61—22no—
141C22⋊C8×C61—22no—
142C22⋊C8×C61D414yescomplemented
143#97×C61—22no—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C2×D4×C61—22no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C22×C4×C61—21no—
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—21no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186M16×C61—44no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—44no—
197C2×C8×C61C2×D412yes—
198C2×C8×C61C2×D412yes—
199C2×C8×C61C2×D412yes—
200C4⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C42×C61—21no—
204C42×C61—21no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—41no—
211#11758198—22no—
212#11758198—22no—
213#11758198—41no—
214#11758198—41no—
215C4⋊Dic61—22no—
216C4⋊Dic61—22no—
217#11758196—22no—
218#11758196—22no—
219#11758196—22no—
220#11758196—41no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61C2×D412yes—
226C4×Dic61#4112yes—
227#11758194—44no—
228C2×#92418—21no—
229C2×#92418—21no—
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×#92418C2×D412yes—
240#11758189—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61C4×D412yes—
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263D4×C61—44no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C612−1+411yescharacteristic
290C22⋊D61—44no—
291C22⋊D61—44no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61C4×D412yes—
311C2×Dic61C4×D412yes—
312C2×Dic61#13112yes—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C8×C61—22no—
318C8×C61—22no—
319C8×C61—22no—
320C8×C61—41no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#92418—41no—
325#22994—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61#52011yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61#56811yescharacteristic
345C22×C61#56811yescharacteristic
346C22×C61#56811yescharacteristic
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—22no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61D4211yescharacteristic
359C4×C61#54711yescharacteristic
360C4×C61#54811yescharacteristic
361C4×C61#55311yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369C2×#436—611no—
370C2×#436—611no—
371C2×#435D6111yescharacteristic, complemented
372C2×#424—611no—
373#2392—611no—
374#1955—611no—
375#1939—611no—
376#1924—611no—
377#1923—611no—
378#1870—611no—
379#1869—611no—
380#1851—611no—
381#1851—611no—
382#1771—611no—
383#1750—611no—
384C2×C61—42no—
385C2×C61—81no—
386C2×C61#236111yescharacteristic
387C2×C61#293011yescharacteristic
388C2×C61#293011yescharacteristic
389C2×C61#293311yescharacteristic
390C2×C61#293511yescharacteristic
391C2×C61#299311yescharacteristic
392C2×C61#299511yescharacteristic
393D61—81no—
394C22×M16—611no—
395C22×M16—611no—
396C22×M16C2×D6111yescharacteristic
397C23×C8C2×D6111yescharacteristic
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4C2×D6111yescharacteristic
401C2×#117—611no—
402#436—1224no—
403#436—1224no—
404#435—24no—
405#424—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8C2×D6111yescharacteristic
419C2×C22⋊C8C2×D6111yescharacteristic
420C2×#97—611no—
421C2×#97C2×D6111yescharacteristic
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424#398—611no—
425#397—611no—
426#396—611no—
427#396—611no—
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—611no—
434C4×C22⋊C4—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441C61#2299411yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4C4×D6111yescharacteristic
445C23×C4—611no—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—41no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—2441no—
456C2×M16—2441no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4C4×D6111yescharacteristic
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C4×D6111yescharacteristic
494C2×C22⋊C4C4×D6111yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—614no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504C4⋊C8—1222no—
505C22⋊C8—22no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—2441no—
511C22⋊C8—2441no—
512C22⋊C8C22⋊D6114yescomplemented
513#97—22no—
514#97—1222no—
515C4×C8—1222no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523C24—611no—
524C24C2×C4×D6111yescharacteristic
525C24C2×C4×D6111yescharacteristic
526C2×D4—22no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4#1175822212yes—
563C22×C4C2×C22⋊D6112yes—
564C22×C4C23×D6111yescharacteristic
565M16—44no—
566M16—2444no—
567M16—2444no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8—612no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8D4×D6112yes—
591C2×C8C2×C22⋊D6112yes—
592C2×C8C2×C22⋊D6112yes—
593C4⋊C4—22no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C42—21no—
613C42—21no—
614C42—612no—
615C42—612no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23C4×C22⋊D6112yes—
641C23C22×C4×D6111yescharacteristic
642D4—44no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
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—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4C4×C22⋊D6112yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C22×C22⋊D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4C2×#1175822211yescharacteristic
694C2×C4#1451982211yescharacteristic
695C2×C4#1451982411yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—1222no—
701C8—2441no—
702C8—2441no—
703C8—2441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C4×D4×D6111yescharacteristic
726C22C2×C4×C22⋊D6111yescharacteristic
727C22#1684024111yescharacteristic
728C22#131×D6111yescharacteristic
729C22#1684052711yescharacteristic
730C22#1684052811yescharacteristic
731C22#1684052811yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—1222no—
737C4—1222no—
738C4—1222no—
739C4—2441no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4D4×C22⋊D6111yescharacteristic
744C4#1684041111yescharacteristic
745C4#1684042111yescharacteristic
746C4#1684046111yescharacteristic
747C2—42no—
748C2—81no—
749C2—4881no—
750C2#2144883611yescharacteristic
751C2#2145451711yescharacteristic
752C2#2145452211yescharacteristic
753C2#2145454111yescharacteristic
754C2#2145456011yescharacteristic
755C2#2145496111yescharacteristic
756C2#2145498511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#435C2
prime radical#16839670C4
cosocleC22×C4×C61C24
hypercenterC2×#435D61
hypocenterC61#22994
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16839838C2semidirect
2. C2×#16839837C2semidirect
3. C2×#16839788C2semidirect
5. #21446615C2semidirect
6. #21446534C2semidirect
7. #21446432C2semidirect
8. #21446422C2semidirect
9. #21446117C2semidirect
10. #21446111C2semidirect
11. #21446002C2semidirect
12. #21446000C2semidirect
13. #21445695C2semidirect
14. #21445587C2semidirect
15. C2×C61×#435C2semidirect
105. #14519706D4semidirect
142. C22⋊C8×C61D4semidirect
371. C2×#435D61semidirect
441. C61#22994semidirect
512. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398382
C2×#168398372
C2×#168397882
#214490612
#214466152
#214465342
#214464322
#214464222
#214461172
#214461112
#214460022
#214460002
#214456952
#214455872
C2×C61×#4352
#2299461