Finite Group Databasebeta

← #33112548

Subgroups — #33112548

Order 18688.

882 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613210C211yesmaximal, characteristic
2#22610229C211yesmaximal, characteristic, complemented
3#22610228C211yesmaximal, characteristic, complemented
4#22610228C211yesmaximal, characteristic, complemented
5#22610227C211yesmaximal, characteristic, complemented
6#22610226C211yesmaximal, characteristic, complemented
7#22610226C211yesmaximal, characteristic, complemented
8#22610225C211yesmaximal, characteristic, complemented
9#22610225C211yesmaximal, characteristic, complemented
10#22610222C211yesmaximal, characteristic, complemented
11#22610220C211yesmaximal, characteristic, complemented
12#22610220C211yesmaximal, characteristic, complemented
13#22610075C211yesmaximal, characteristic, complemented
14#22610075C211yesmaximal, characteristic, complemented
15C73×#1870C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C2×C4×D292C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×C4×C22⋊D73C2211yescharacteristic
22C2×C4×C22⋊D73C2211yescharacteristic
23C2×C4×C22⋊D73C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33#17988523C411yescharacteristic
34#17988523C411yescharacteristic
35#17988522C411yescharacteristic
36#17988522C411yescharacteristic
37#17988496C411yescharacteristic
38#17988496C411yescharacteristic
39#17988495C411yescharacteristic
40#17988495C411yescharacteristic
41#17988433C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C22×M16×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D292C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C22×C4×D73C2311yescharacteristic
66C2×#11924012—41no—
67C2×#11924012—41no—
68C2×#11924012—41no—
69C2×#11924011—41no—
70C2×#11924011—41no—
71C2×#11924011—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C2×C8×D73—41no—
77C2×C8×D73—41no—
78C2×C8×D73—41no—
79C4×D292—41no—
80C4×D292—41no—
81C4×C22⋊D73—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C4×C22⋊D73—41no—
86C4×C22⋊D73—41no—
87C4×C22⋊D73—41no—
88C4×C22⋊D73—41no—
89C2×C4⋊Dic73C2×C411yescharacteristic
90C2×#11924007C2×C411yescharacteristic
91C2×#11924007C2×C411yescharacteristic
92C2×#11924007C2×C411yescharacteristic
93C2×#11924007C2×C411yescharacteristic
94C2×C22⋊Dic73C2×C411yescharacteristic
95C2×C22⋊Dic73C2×C411yescharacteristic
96C2×C22⋊Dic73C2×C411yescharacteristic
97C2×C22⋊Dic73C2×C411yescharacteristic
98C2×#11924005C2×C411yescharacteristic
99C2×#11924005C2×C411yescharacteristic
100C2×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×C4×Dic73C2311yescharacteristic
105C2×C4×Dic73C2311yescharacteristic
106C22⋊#10596831—41no—
107C22⋊#10596831—41no—
108C22⋊#10596831—41no—
109#14556503—41no—
110#14556503—41no—
111#14556503—41no—
112#14556503—41no—
113#14556503—41no—
114#14556503—41no—
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×D4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C2×M16×C73—41no—
123C2×M16×C73—41no—
124C2×M16×C73—41no—
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C4×D4×C73—41no—
130C4×D4×C73—41no—
131C2×C4⋊C4×C73C2×C411yescharacteristic
132C2×C22⋊C4×C73C2×C411yescharacteristic
133C2×C22⋊C4×C73C2×C411yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C23×D73C22×C411yescharacteristic
139C23×D73C22×C411yescharacteristic
140C2×D292—22no—
141C2×D292—41no—
142C2×D292—41no—
143C2×C22⋊D73—22no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—41no—
146C2×C22⋊D73—41no—
147C2×C22⋊D73—41no—
148C2×C22⋊D73—41no—
149C2×C22⋊D73—41no—
150C2×C22⋊D73—41no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173#11924012—44no—
174#11924011—44no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C8×D73—44no—
188C4⋊Dic73—41no—
189#11924007—41no—
190#11924007—41no—
191#11924007—41no—
192#11924007—41no—
193C22⋊Dic73—41no—
194C22⋊Dic73—41no—
195C22⋊Dic73—41no—
196C22⋊Dic73—41no—
197#11924005—41no—
198#11924005—41no—
199#11924005—41no—
200#11924005—41no—
201#11924005—41no—
202#11924005—41no—
203C4×Dic73—21no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C24×C73C22×C411yescharacteristic
208C24×C73C22×C411yescharacteristic
209C2×D4×C73—41no—
210C2×D4×C73—41no—
211C2×D4×C73—41no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73C22×C411yescharacteristic
225C22×C4×C73C22×C411yescharacteristic
226C22×C4×C73C22×C411yescharacteristic
227C22×C4×C73C22×C411yescharacteristic
228C22×C4×C73C2411yescharacteristic
229M16×C73—44no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C4⋊C4×C73—41no—
243C22⋊C4×C73—41no—
244C22⋊C4×C73—41no—
245C42×C73—21no—
246C42×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73C23×C411yescharacteristic
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73#13112yes—
276D4×C73—44no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C22⋊D73—44no—
304C22⋊D73—44no—
305C22⋊D73—44no—
306C22⋊D73—44no—
307C2×Dic73—21no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325D292—44no—
326C4×D73—41no—
327C4×D73—41no—
328C4×D73—41no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C8×C73—41no—
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338#10596831—41no—
339#10596831—41no—
340#10596831—41no—
341#10596831—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73#51811yescharacteristic
357C22×C73#51811yescharacteristic
358C22×C73#51811yescharacteristic
359C22×C73C2×#13111yescharacteristic
360C22×C73#56811yescharacteristic
361C22×C73#56811yescharacteristic
362C22×C73#56811yescharacteristic
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—22no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C2×D73—41no—
377C4×C73—41no—
378C4×C73—41no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73#56011yescharacteristic
382C4×C73#56011yescharacteristic
383C4×C73#56011yescharacteristic
384C4×C73#56011yescharacteristic
385Dic73—41no—
386Dic73—41no—
387Dic73—41no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391#23359—731nomaximal, Sylow
392C2×C73—81no—
393C2×C73—81no—
394C2×C73#238011yescharacteristic
395C2×C73#297611yescharacteristic
396C2×C73#297611yescharacteristic
397C2×C73#297611yescharacteristic
398C2×C73#297811yescharacteristic
399C2×C73#297811yescharacteristic
400C2×C73#297811yescharacteristic
401D73—42no—
402D73—81no—
403#2397—731no—
404#1870—731no—
405#1870—731no—
406#1870—731no—
407#1870—731no—
408#1870—731no—
409#1870—731no—
410#1870—731no—
411#1870—731no—
412#1870D7311yescharacteristic, complemented
413#1869—731no—
414#1869—731no—
415#1869—731no—
416#1840—731no—
417#1840—731no—
418C73#2335911yescharacteristic, complemented, Sylow
419C22×M16—731no—
420C22×M16—731no—
421C22×M16C2×D7311yescharacteristic
422C23×C8—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4—731no—
426C2×C4×D4—731no—
427C2×C4×D4—731no—
428C2×C4×D4C2×D7311yescharacteristic
429C2×C22⋊C8—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C22⋊C8—731no—
433C2×C22⋊C8—731no—
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×C22⋊C8—731no—
438C2×C22⋊C8C2×D7311yescharacteristic
439C2×C22⋊C8C2×D7311yescharacteristic
440C2×C22⋊C8C2×D7311yescharacteristic
441#399—731no—
442#399—731no—
443#399—731no—
444#399—731no—
445#392—731no—
446#392—731no—
447#392—731no—
448#392—731no—
449#376—731no—
450#336—731no—
451#336—731no—
452#336—731no—
453#336—731no—
454#336—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336C2×D7311yescharacteristic
461#336C2×D7311yescharacteristic
462C22×D4—731no—
463C22×D4—731no—
464C22×D4—731no—
465C22×D4—731no—
466C22×D4—731no—
467C22×D4C4×D7311yescharacteristic
468C23×C4—731no—
469C23×C4—731no—
470C23×C4C22×D7311yescharacteristic
471C23×C4C22×D7311yescharacteristic
472C2×M16—41no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16—2921no—
476C2×M16—2921no—
477C2×M16—2921no—
478C2×M16—2921no—
479C2×M16—2921no—
480C2×M16—2921no—
481C22×C8—2921no—
482C22×C8—2921no—
483C22×C8—2921no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C4×D4—41no—
493C4×D4—41no—
494C4×D4—2921no—
495C4×D4—2921no—
496C4×D4—2921no—
497C4×D4—2921no—
498C4×D4—2921no—
499C4×D4—2921no—
500C4×D4—2921no—
501C4×D4—2921no—
502C4×D4—2921no—
503C4×D4—2921no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4—731no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4C4×D7311yescharacteristic
510C2×C22⋊C4—731no—
511C2×C22⋊C4—731no—
512C2×C22⋊C4—731no—
513C2×C22⋊C4—731no—
514C2×C22⋊C4—731no—
515C2×C22⋊C4—731no—
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4C4×D7311yescharacteristic
521C2×C22⋊C4C4×D7311yescharacteristic
522C2×C42—731no—
523C2×C42—731no—
524C2×C42C22×D7311yescharacteristic
525C22⋊C8—41no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528C22⋊C8—2921no—
529C22⋊C8—2921no—
530C22⋊C8—2921no—
531C22⋊C8—2921no—
532C22⋊C8—2921no—
533C22⋊C8—2921no—
534C22⋊C8—2921no—
535C22⋊C8—2921no—
536C22⋊C8—2921no—
537#95—731no—
538#95—731no—
539#95—731no—
540#95—731no—
541C24—731no—
542C24—731no—
543C24C2×C4×D7311yescharacteristic
544C24C2×C4×D7311yescharacteristic
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—2921no—
549C2×D4—2921no—
550C2×D4—2921no—
551C2×D4—2921no—
552C2×D4—2921no—
553C2×D4—2921no—
554C2×D4—2921no—
555C2×D4—2921no—
556C2×D4—2921no—
557C2×D4—2921no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—1462no—
561C2×D4—1462no—
562C2×D4—1462no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—731no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4C2×C4×D7311yescharacteristic
594C22×C4C2×C4×D7311yescharacteristic
595C22×C4C2×C4×D7311yescharacteristic
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598M16—44no—
599M16—2924no—
600M16—2924no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—2924no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8—1461no—
618C2×C8—1461no—
619C2×C8—1461no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C4⋊C4—41no—
627C4⋊C4—2921no—
628C4⋊C4—2921no—
629C4⋊C4—2921no—
630C4⋊C4—2921no—
631C4⋊C4—2921no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—2921no—
635C22⋊C4—2921no—
636C22⋊C4—2921no—
637C22⋊C4—2921no—
638C22⋊C4—2921no—
639C22⋊C4—2921no—
640C22⋊C4—2921no—
641C22⋊C4—2921no—
642C22⋊C4—2921no—
643C22⋊C4—2921no—
644C42—21no—
645C42—21no—
646C42—1461no—
647C42—1461no—
648C42—1461no—
649C42—1461no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—732no—
665C23—1461no—
666C23—1461no—
667C23—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23C22×C4×D7311yescharacteristic
679D4—44no—
680D4—2924no—
681D4—2924no—
682D4—2924no—
683D4—2924no—
684D4—2924no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—1461no—
714C2×C4—1461no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4#1455663611yescharacteristic
732C2×C4#1455663611yescharacteristic
733C2×C4#1455663611yescharacteristic
734C2×C4#1455663611yescharacteristic
735C2×C4#1455663711yescharacteristic
736C2×C4#1455663711yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—2921no—
742C8—2921no—
743C8—2921no—
744C8—2921no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—2921no—
760C22—2921no—
761C22—2921no—
762C22—2921no—
763C22—2921no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—2921no—
768C22—2921no—
769C22—2921no—
770C22—1462no—
771C22—1462no—
772C22—1462no—
773C22#1798905911yescharacteristic
774C22#1798905911yescharacteristic
775C22#1798906011yescharacteristic
776C22#131×D7311yescharacteristic
777C22#1798935211yescharacteristic
778C22#1798935311yescharacteristic
779C22#1798935311yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—2921no—
785C4—2921no—
786C4—2921no—
787C4—2921no—
788C4—2921no—
789C4—2921no—
790C4#1798932511yescharacteristic
791C4#1798932511yescharacteristic
792C4#1798932611yescharacteristic
793C4#1798932711yescharacteristic
794C2—81no—
795C2—81no—
796C2—2922no—
797C2—5841no—
798C2#2261310611yescharacteristic
799C2#2261897411yescharacteristic
800C2#2261897511yescharacteristic
801C2#2261897811yescharacteristic
802C2#2261898811yescharacteristic
803C2#2261899011yescharacteristic
804C2#2261899111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1870C2
prime radical#22613210C2
cosocleC22×C4×C73C24
hypercenter#1870D73
hypocenterC73#23359
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #22610229C2semidirect
3. #22610228C2semidirect
4. #22610228C2semidirect
5. #22610227C2semidirect
6. #22610226C2semidirect
7. #22610226C2semidirect
8. #22610225C2semidirect
9. #22610225C2semidirect
10. #22610222C2semidirect
11. #22610220C2semidirect
12. #22610220C2semidirect
13. #22610075C2semidirect
14. #22610075C2semidirect
15. C73×#1870C2semidirect
412. #1870D73semidirect
418. C73#23359semidirect

Maximal subgroups

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

subgroupindex
#226132102
#226102292
#226102282
#226102272
#226102262
#226102252
#226102222
#226102202
#226100752
C73×#18702
#2335973