Finite Group Databasebeta

← #29700218

Subgroups — #29700218

Order 15616.

1144 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839837C211yesmaximal, characteristic, complemented
2C2×#16839836C211yesmaximal, characteristic, complemented
3C2×#16839727C211yesmaximal, characteristic, complemented
4C2×#16839727C211yesmaximal, characteristic, complemented
5#21449034C211yesmaximal, characteristic
6#21446429C211yesmaximal, characteristic, complemented
7#21446422C211yesmaximal, characteristic, complemented
8#21446117C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21446000C211yesmaximal, characteristic, complemented
12#21445995C211yesmaximal, characteristic, complemented
13#21445604C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C61×#1955C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24#16839837—24no—
25#16839836—24no—
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28#16839727—24no—
29#16839727—24no—
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39#16839682C411yescharacteristic
40#16839679C411yescharacteristic
41#16839677C411yescharacteristic
42#16839677C411yescharacteristic
43#16839674C411yescharacteristic
44#16839671C411yescharacteristic
45#16839670C411yescharacteristic
46#16839670C411yescharacteristic
47C4×#11758198C2211yescharacteristic
48C4×#11758198C2211yescharacteristic
49C4×C22⋊Dic61C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2×C411yescharacteristic
70C22×D244C2×C411yescharacteristic
71C22×C22⋊D61C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C22×C22⋊D61C2×C411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758194—22no—
78C2×#11758194—22no—
79C2×#11758194—41no—
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—41no—
85C2×#11758189—41no—
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61—41no—
95C2×C8×D61—41no—
96C4×C22⋊D61—22no—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519706—22no—
115#14519706—22no—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118C22⋊#92418—41no—
119#14519689—22no—
120#14519689—22no—
121#14519689D414yescomplemented
122#14519689D414yescomplemented
123#14519687—22no—
124C8×Dic61—22no—
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×D4×C61—41no—
139C4×D4×C61—41no—
140C2×C4⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C4⋊C8×C61—41no—
145C22⋊C8×C61—22no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C22⋊C8×C61—22no—
149#97×C61—41no—
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—41no—
182C2×C22⋊D61—41no—
183C2×C22⋊D61—41no—
184C2×C22⋊D61—41no—
185C2×C22⋊D61—41no—
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192#11758222—44no—
193#11758222—44no—
194#11758222—44no—
195#11758222—44no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—41no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61#4112yes—
210C2×C4×D61#4112yes—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—41no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61C2×D412yes—
225C2×C8×C61C2×D412yes—
226C4⋊C4×C61—41no—
227C22⋊C4×C61—41no—
228C22⋊C4×C61—41no—
229C42×C61—21no—
230C42×C61—21no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—41no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—41no—
239#11758198—41no—
240#11758198—41no—
241#11758196—22no—
242#11758196—22no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247#11758194—44no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418C2×D412yes—
259C2×#92418C2×D412yes—
260#11758189—44no—
261#11758189—44no—
262C8×D61—44no—
263C8×D61—44no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61C23×C411yescharacteristic
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61C4×D412yes—
292C22×D61C4×D412yes—
293D4×C61—44no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C22⋊D61—44no—
321C22⋊D61—44no—
322C22⋊D61—44no—
323C22⋊D61—44no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61C4×D412yes—
340C2×Dic61C4×D412yes—
341C2×Dic61#13112yes—
342D244—44no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351Dic122—44no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—41no—
355C8×C61—41no—
356#92418—22no—
357#92418—22no—
358#92418—41no—
359#92418—41no—
360#22849—611nomaximal, Sylow
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61C2×C4×D411yescharacteristic
376C22×C61C2×C4×D411yescharacteristic
377C22×C61#51811yescharacteristic
378C22×C61C2×#13111yescharacteristic
379C22×C61#56811yescharacteristic
380C22×C61#56811yescharacteristic
381C22×C61#56811yescharacteristic
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61D4211yescharacteristic
401C4×C61#54611yescharacteristic
402C4×C61#54611yescharacteristic
403C4×C61#55111yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—22no—
407Dic61—41no—
408Dic61—41no—
409Dic61—41no—
410C2×#436—611no—
411C2×#435—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388—611no—
415#1955D6111yescharacteristic, complemented
416#1924—611no—
417#1923—611no—
418#1870—611no—
419#1870—611no—
420#1869—611no—
421#1851—611no—
422#1850—611no—
423#1753—611no—
424#1752—611no—
425C2×C61—81no—
426C2×C61—81no—
427C2×C61#235811yescharacteristic
428C2×C61#293011yescharacteristic
429C2×C61#293211yescharacteristic
430C2×C61#293311yescharacteristic
431C2×C61#293511yescharacteristic
432C2×C61#297811yescharacteristic
433C2×C61#298111yescharacteristic
434D61—42no—
435D61—42no—
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439C22×M16—611no—
440C23×C8—611no—
441C23×C8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4C2×D6111yescharacteristic
445#436—1224no—
446#435—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8C2×D6111yescharacteristic
450#408—1224no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8C2×D6111yescharacteristic
460C2×C22⋊C8C2×D6111yescharacteristic
461C2×C22⋊C8C2×D6111yescharacteristic
462C2×C22⋊C8C2×D6111yescharacteristic
463C2×#97—611no—
464C2×#97C2×D6111yescharacteristic
465C2×C4×C8—611no—
466#395—611no—
467#394—611no—
468#394—611no—
469#394—611no—
470#393—611no—
471#392—611no—
472#392—611no—
473#392—611no—
474C4×C22⋊C4—611no—
475C4×C22⋊C4—611no—
476C4×C22⋊C4—611no—
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483C61#2284911yescharacteristic, complemented, Sylow
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8—611no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4C4×D6111yescharacteristic
497C23×C4—611no—
498C23×C4—611no—
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—1222no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—1222no—
517C22×C8—1222no—
518C22×C8—2441no—
519C22×C8—2441no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4C4×D6111yescharacteristic
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4C4×D6111yescharacteristic
544C2×C22⋊C4C4×D6111yescharacteristic
545C2×C42—611no—
546C2×C42—611no—
547C2×C42C22×D6111yescharacteristic
548C4⋊C8—41no—
549C4⋊C8—1222no—
550C4⋊C8—1222no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—614no—
556C22⋊C8—614no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—2441no—
562#97—41no—
563#97—1222no—
564C4×C8—1222no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95—611no—
569#95—611no—
570#95—611no—
571C24—611no—
572C24—611no—
573C24C2×C4×D6111yescharacteristic
574C24C2×C4×D6111yescharacteristic
575#41—2444no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—2441no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4C2×C4×D6111yescharacteristic
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4C23×D6111yescharacteristic
635M16—2444no—
636M16—2444no—
637M16—2444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—612no—
649C2×C8—612no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—2444no—
661C2×C8—2444no—
662C2×C8D4×D6112yes—
663C2×C8D4×D6112yes—
664C4⋊C4—41no—
665C4⋊C4—1222no—
666C4⋊C4—1222no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—2441no—
676C22⋊C4—2441no—
677C22⋊C4—2441no—
678C22⋊C4—2441no—
679C42—21no—
680C42—21no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—612no—
700C23—612no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23C22×C4×D6111yescharacteristic
714Q8—2444no—
715D4—44no—
716D4—2444no—
717D4—2444no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4#41×D6111yescharacteristic
770C2×C4#41×D6111yescharacteristic
771C2×C4#1451982211yescharacteristic
772C2×C4#1451982211yescharacteristic
773C8—22no—
774C8—22no—
775C8—41no—
776C8—41no—
777C8—1222no—
778C8—1222no—
779C8—2441no—
780C8—2441no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C4×D4×D6111yescharacteristic
810C22C4×D4×D6111yescharacteristic
811C22#1684023511yescharacteristic
812C22#131×D6111yescharacteristic
813C22#1684052711yescharacteristic
814C22#1684052811yescharacteristic
815C22#1684052811yescharacteristic
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—2441no—
824C4—2441no—
825C4—2441no—
826C4#1684039711yescharacteristic
827C4#1684040111yescharacteristic
828C4#1684040111yescharacteristic
829C4#1684044211yescharacteristic
830C2—81no—
831C2—81no—
832C2—2442no—
833C2—2442no—
834C2#2144880011yescharacteristic
835C2#2145451711yescharacteristic
836C2#2145453311yescharacteristic
837C2#2145454211yescharacteristic
838C2#2145456011yescharacteristic
839C2#2145487911yescharacteristic
840C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1955C2
prime radical#21449034C2
cosocleC22×C4×C61C24
hypercenter#1955D61
hypocenterC61#22849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#16839837C2semidirect
2. C2×#16839836C2semidirect
3. C2×#16839727C2semidirect
4. C2×#16839727C2semidirect
6. #21446429C2semidirect
7. #21446422C2semidirect
8. #21446117C2semidirect
9. #21446113C2semidirect
10. #21446108C2semidirect
11. #21446000C2semidirect
12. #21445995C2semidirect
13. #21445604C2semidirect
14. #21445596C2semidirect
15. C61×#1955C2semidirect
121. #14519689D4semidirect
122. #14519689D4semidirect
415. #1955D61semidirect
483. C61#22849semidirect

Maximal subgroups

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

subgroupindex
C2×#168398372
C2×#168398362
C2×#168397272
#214490342
#214464292
#214464222
#214461172
#214461132
#214461082
#214460002
#214459952
#214456042
#214455962
C61×#19552
#2284961