Finite Group Databasebeta

← #29706561

Subgroups — #29706561

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519773C211yesmaximal, characteristic
2#21446117C211yesmaximal, characteristic, complemented
3#21446115C211yesmaximal, characteristic, complemented
4#21446114C211yesmaximal, characteristic, complemented
5#21446114C211yesmaximal, characteristic, complemented
6#21446113C211yesmaximal, characteristic, complemented
7#21446113C211yesmaximal, characteristic, complemented
8#21446111C211yesmaximal, characteristic, complemented
9#21446111C211yesmaximal, characteristic, complemented
10#21446110C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic, complemented
12#21446108C211yesmaximal, characteristic, complemented
13#21445961C211yesmaximal, characteristic, complemented
14#21445961C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519773C411yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×C4×C22⋊D61C2211yescharacteristic
24C2×C4×C22⋊D61C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839665C411yescharacteristic
35#16839663C411yescharacteristic
36#16839662C411yescharacteristic
37#16839662C411yescharacteristic
38#16839662C411yescharacteristic
39#16839662C411yescharacteristic
40#16839631C411yescharacteristic
41C42×Dic61C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C23×C8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194—41no—
67C2×#11758194—41no—
68C2×#11758194—41no—
69C2×#11758189—41no—
70C2×#11758189—41no—
71C2×#11758189—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—41no—
77C2×C8×D61—41no—
78C2×C8×D61—41no—
79#14519773—24no—
80C4×D244—41no—
81C4×D244—41no—
82C4×C22⋊D61—41no—
83C4×C22⋊D61—41no—
84C4×C22⋊D61—41no—
85C4×C22⋊D61—41no—
86C4×C22⋊D61—41no—
87C4×C22⋊D61—41no—
88C4×C22⋊D61—41no—
89C4×C22⋊D61—41no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C22⋊#92418—41no—
112C22⋊#92418—41no—
113C22⋊#92418—41no—
114#14519689—41no—
115#14519689—41no—
116#14519689—41no—
117#14519689—41no—
118#14519689—41no—
119#14519689—41no—
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C22×C8×C61—41no—
124C22×C8×C61—41no—
125C22×C8×C61—41no—
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×D4×C61—41no—
131C4×D4×C61—41no—
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C22⋊C8×C61—41no—
137C22⋊C8×C61—41no—
138C22⋊C8×C61—41no—
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C23×D61C22×C411yescharacteristic
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—41no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
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×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61M1614yescomplemented
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—41no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—44no—
209C4⋊C4×C61—41no—
210C22⋊C4×C61—41no—
211C22⋊C4×C61—41no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61—41no—
217C22⋊Dic61—41no—
218#11758198—41no—
219#11758198—41no—
220#11758198—41no—
221#11758198—41no—
222#11758198—41no—
223#11758198—41no—
224C4⋊Dic61—41no—
225#11758196—41no—
226#11758196—41no—
227#11758196—41no—
228#11758196—41no—
229C4×Dic61—22no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C4×Dic61—41no—
237#11758194—44no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250#11758189—44no—
251C8×D61—44no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61C2×M1612yes—
266C23×C61C23×C411yescharacteristic
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61C2×M1612yes—
281D4×C61—44no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61#13112yes—
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—44no—
310C22⋊D61—44no—
311C22⋊D61—44no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61C2×M1612yes—
329C2×Dic61#13112yes—
330D244—44no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#23356—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61#51811yescharacteristic
363C22×C61#51811yescharacteristic
364C22×C61#51811yescharacteristic
365C22×C61C22×M1611yescharacteristic
366C22×C61C2×#13111yescharacteristic
367C22×C61C2×#13111yescharacteristic
368C22×C61#56811yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C4×C61—22no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61#56011yescharacteristic
388C4×C61#56011yescharacteristic
389C4×C61#56011yescharacteristic
390C4×C61#56011yescharacteristic
391Dic61—22no—
392Dic61—22no—
393Dic61—41no—
394Dic61—41no—
395Dic61—41no—
396Dic61—41no—
397C4×#127—611no—
398#1870—611no—
399#1870—611no—
400#1870—611no—
401#1870—611no—
402#1870—611no—
403#1870—611no—
404#1869—611no—
405#1869—611no—
406#1869—611no—
407#1869—611no—
408#1869—611no—
409#1869D6111yescharacteristic, complemented
410#1839—611no—
411#1839—611no—
412C2×C61—42no—
413C2×C61—81no—
414C2×C61#238011yescharacteristic
415C2×C61#297311yescharacteristic
416C2×C61#297411yescharacteristic
417C2×C61#297411yescharacteristic
418C2×C61#297911yescharacteristic
419C2×C61#298111yescharacteristic
420C2×C61#298111yescharacteristic
421D61—42no—
422D61—81no—
423C22×M16—611no—
424C22×M16—611no—
425C23×C8—611no—
426C23×C8C2×D6111yescharacteristic
427C2×#127—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4C2×D6111yescharacteristic
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8C2×D6111yescharacteristic
444C2×C22⋊C8C2×D6111yescharacteristic
445C2×C22⋊C8C2×D6111yescharacteristic
446#390—611no—
447#390—611no—
448#390—611no—
449#390—611no—
450#390—611no—
451#390—611no—
452#384—611no—
453C43—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336—611no—
461#336—611no—
462#336—611no—
463#336—611no—
464#336C2×D6111yescharacteristic
465#336C2×D6111yescharacteristic
466C61#2335611yescharacteristic, complemented, Sylow
467C22×D4—611no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—611no—
471C22×D4—611no—
472C22×D4C4×D6111yescharacteristic
473C23×C4—611no—
474C23×C4—611no—
475C23×C4C22×D6111yescharacteristic
476C23×C4C22×D6111yescharacteristic
477C2×M16—2441no—
478C2×M16—2441no—
479C2×M16—2441no—
480C2×M16—2441no—
481C2×M16—2441no—
482C2×M16—2441no—
483C22×C8—41no—
484C22×C8—41no—
485C22×C8—41no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—2441no—
491C22×C8—2441no—
492C22×C8—2441no—
493C22×C8C22×D6111yescharacteristic
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496C22×C8C22×D6111yescharacteristic
497#127—1224no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—2441no—
501C4×D4—2441no—
502C4×D4—2441no—
503C4×D4—2441no—
504C4×D4—2441no—
505C4×D4—2441no—
506C4×D4—2441no—
507C4×D4—2441no—
508C4×D4—2441no—
509C4×D4—2441no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4C4×D6111yescharacteristic
516C2×C22⋊C4—611no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4C4×D6111yescharacteristic
527C2×C22⋊C4C4×D6111yescharacteristic
528C2×C42—611no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—611no—
534C2×C42C22×D6111yescharacteristic
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—2441no—
539C22⋊C8—2441no—
540C22⋊C8—2441no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C22⋊C8—2441no—
547C24—611no—
548C24—611no—
549C24C2×C4×D6111yescharacteristic
550C24C2×C4×D6111yescharacteristic
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—41no—
554C2×D4—614no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—2441no—
563C2×D4—2441no—
564C2×D4—2441no—
565C2×D4—2441no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4C2×C4×D6111yescharacteristic
600C22×C4C2×C4×D6111yescharacteristic
601C22×C4C2×C4×D6111yescharacteristic
602C22×C4C2×C4×D6111yescharacteristic
603C22×C4C23×D6111yescharacteristic
604M16—2444no—
605M16—2444no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—44no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—2444no—
632C4⋊C4—41no—
633C4⋊C4—2441no—
634C4⋊C4—2441no—
635C4⋊C4—2441no—
636C4⋊C4—2441no—
637C4⋊C4—2441no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—2441no—
641C22⋊C4—2441no—
642C22⋊C4—2441no—
643C22⋊C4—2441no—
644C22⋊C4—2441no—
645C22⋊C4—2441no—
646C22⋊C4—2441no—
647C22⋊C4—2441no—
648C22⋊C4—2441no—
649C22⋊C4—2441no—
650C42—21no—
651C42—21no—
652C42—1222no—
653C42—1222no—
654C42—1221no—
655C42—1221no—
656C42—1221no—
657C42—1221no—
658C42—1222no—
659C42—2441no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—612no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23M16×D6112yes—
688C23C22×C4×D6111yescharacteristic
689D4—44no—
690D4—2444no—
691D4—2444no—
692D4—2444no—
693D4—2444no—
694D4—2444no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—612no—
715C2×C4—612no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4#1451978312yes—
741C2×C4#1451982211yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982211yescharacteristic
744C2×C4#1451982211yescharacteristic
745C2×C4#1451982311yescharacteristic
746C2×C4#1451982311yescharacteristic
747C8—41no—
748C8—41no—
749C8—41no—
750C8—41no—
751C8—2441no—
752C8—2441no—
753C8—2441no—
754C8—2441no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—1222no—
770C22—1222no—
771C22—1222no—
772C22—2441no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22#1684023411yescharacteristic
784C22#1684023411yescharacteristic
785C22#1684023511yescharacteristic
786C22C2×M16×D6111yescharacteristic
787C22#131×D6111yescharacteristic
788C22C2×#1451978311yescharacteristic
789C22#1684052711yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—1222no—
795C4—1222no—
796C4—2441no—
797C4—2441no—
798C4—2441no—
799C4—2441no—
800C4#1684050011yescharacteristic
801C4#1684050011yescharacteristic
802C4#1684050111yescharacteristic
803C4#1684050211yescharacteristic
804C2—42no—
805C2—81no—
806C2—4881no—
807C2—2442no—
808C2#2144899411yescharacteristic
809C2#2145484411yescharacteristic
810C2#2145484911yescharacteristic
811C2#2145485011yescharacteristic
812C2#2145488211yescharacteristic
813C2#2145489211yescharacteristic
814C2#2145489311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1869C2
prime radicalC2×#14519773C4
cosocleC22×C4×C61C24
hypercenter#1869D61
hypocenterC61#23356
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #21446117C2semidirect
3. #21446115C2semidirect
4. #21446114C2semidirect
5. #21446114C2semidirect
6. #21446113C2semidirect
7. #21446113C2semidirect
8. #21446111C2semidirect
9. #21446111C2semidirect
10. #21446110C2semidirect
11. #21446108C2semidirect
12. #21446108C2semidirect
13. #21445961C2semidirect
14. #21445961C2semidirect
15. C61×#1869C2semidirect
174. C2×C22⋊D61M16semidirect
409. #1869D61semidirect
466. C61#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#145197732
#214461172
#214461152
#214461142
#214461132
#214461112
#214461102
#214461082
#214459612
C61×#18692
#2335661