Finite Group Databasebeta

← #29700192

Subgroups — #29700192

Order 15616.

1178 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×#16839833C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839727C211yesmaximal, characteristic, complemented
4C2×#16839727C211yesmaximal, characteristic, complemented
5#21449034C211yesmaximal, characteristic
6#21446614C211yesmaximal, characteristic, complemented
7#21446435C211yesmaximal, characteristic, complemented
8#21446428C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21446003C211yesmaximal, characteristic, complemented
12#21445998C211yesmaximal, characteristic, complemented
13#21445599C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23#16839833—24no—
24C8×C22⋊D61—24no—
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28#16839727—24no—
29#16839727—24no—
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519687C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40C2×C8×Dic61C2211yescharacteristic
41#16839682C411yescharacteristic
42#16839679C411yescharacteristic
43#16839677C411yescharacteristic
44#16839677C411yescharacteristic
45#16839674C411yescharacteristic
46#16839671C411yescharacteristic
47#16839670C411yescharacteristic
48#16839670C411yescharacteristic
49C4×#11758198C2211yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×C22⋊Dic61C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C23×C8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
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×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—41no—
82C2×#11758189—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—22no—
88C2×C8×D61—22no—
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—41no—
92C2×C8×D61—41no—
93C4×C22⋊D61—22no—
94C4×C22⋊D61—22no—
95C4×C22⋊D61—22no—
96C4×C22⋊D61—22no—
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C4⋊#92418—41no—
112#14519706—22no—
113#14519706—22no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118#14519689—22no—
119#14519689—22no—
120#14519689D414yescomplemented
121#14519689D414yescomplemented
122#14519687—22no—
123C4×#92418—41no—
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×C61—22no—
135C22×C8×C61—22no—
136C22×C8×C61—41no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×D4×C61—41no—
142C4×D4×C61—41no—
143C2×C4⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C22⋊C8×C61—22no—
148C22⋊C8×C61—22no—
149C22⋊C8×C61—41no—
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C2×D4×C61—22no—
155C2×D4×C61—22no—
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—22no—
182C2×C22⋊D61—22no—
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×C61—44no—
225C2×C8×C61C2×D412yes—
226C2×C8×C61C2×D412yes—
227C4⋊C4×C61—41no—
228C22⋊C4×C61—41no—
229C22⋊C4×C61—41no—
230C42×C61—21no—
231C42×C61—21no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235C22⋊Dic61—41no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—41no—
242#11758196—22no—
243#11758196—22no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
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#13112yes—
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—41no—
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#13112yes—
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—28no—
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#22847—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
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×C61C2×#13111yescharacteristic
380C22×C61C2×#13111yescharacteristic
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—22no—
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×#435—611no—
411C2×C8×D4—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388—611no—
415#1954—611no—
416#1924—611no—
417#1923—611no—
418#1870—611no—
419#1869—611no—
420#1869D6111yescharacteristic, complemented
421#1851—611no—
422#1850—611no—
423#1753—611no—
424C8×C22⋊C4—611no—
425C2×C61—42no—
426C2×C61—81no—
427C2×C61#235811yescharacteristic
428C2×C61#292911yescharacteristic
429C2×C61#293111yescharacteristic
430C2×C61#293311yescharacteristic
431C2×C61#293511yescharacteristic
432C2×C61#297711yescharacteristic
433C2×C61#298111yescharacteristic
434D61—42no—
435D61—42no—
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439C23×C8—611no—
440C23×C8—611no—
441C23×C8C2×D6111yescharacteristic
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4C2×D6111yescharacteristic
445#435—1224no—
446C8×D4—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
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⋊C8—611no—
460C2×C22⋊C8C2×D6111yescharacteristic
461C2×C22⋊C8C2×D6111yescharacteristic
462C2×C22⋊C8C2×D6111yescharacteristic
463C2×#97—611no—
464C2×C4×C8—611no—
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#336C2×D6111yescharacteristic
482#336C2×D6111yescharacteristic
483C61#2284711yescharacteristic, 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—2441no—
506C2×M16—2441no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
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—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554C22⋊C8—614no—
555C22⋊C8—614no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—1222no—
562#97—1222no—
563C4×C8—1222no—
564C4×C8—2441no—
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—22no—
583C2×D4—22no—
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—1222no—
595C2×D4—1222no—
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—
637C2×C8—21no—
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—44no—
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—1222no—
676C22⋊C4—1222no—
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—612no—
699C23—612no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23#1451978512yes—
713C23C22×C4×D6111yescharacteristic
714Q8—2444no—
715D4—44no—
716D4—1228no—
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—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1221no—
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#1451978312yes—
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—22no—
782C22—22no—
783C22—22no—
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
813C22C2×#1451978311yescharacteristic
814C22C2×#1451978511yescharacteristic
815C22#1684052711yescharacteristic
816C4—22no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—1222no—
821C4—1222no—
822C4—1222no—
823C4—2441no—
824C4—2441no—
825C4—2441no—
826C4#1684039411yescharacteristic
827C4#1684040911yescharacteristic
828C4#1684040911yescharacteristic
829C4#1684044011yescharacteristic
830C2—42no—
831C2—81no—
832C2—2442no—
833C2—2442no—
834C2#2144880211yescharacteristic
835C2#2145451011yescharacteristic
836C2#2145452611yescharacteristic
837C2#2145454511yescharacteristic
838C2#2145455811yescharacteristic
839C2#2145487311yescharacteristic
840C2#2145489211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1869C2
prime radical#21449034C2
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#22847
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#16839833C2semidirect
2. C2×C8×C22⋊D61C2semidirect
3. C2×#16839727C2semidirect
4. C2×#16839727C2semidirect
6. #21446614C2semidirect
7. #21446435C2semidirect
8. #21446428C2semidirect
9. #21446113C2semidirect
10. #21446108C2semidirect
11. #21446003C2semidirect
12. #21445998C2semidirect
13. #21445599C2semidirect
14. #21445589C2semidirect
15. C61×#1869C2semidirect
120. #14519689D4semidirect
121. #14519689D4semidirect
420. #1869D61semidirect
483. C61#22847semidirect

Maximal subgroups

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

subgroupindex
C2×#168398332
C2×C8×C22⋊D612
C2×#168397272
#214490342
#214466142
#214464352
#214464282
#214461132
#214461082
#214460032
#214459982
#214455992
#214455892
C61×#18692
#2284761