Finite Group Databasebeta

← #33112217

Subgroups — #33112217

Order 18688.

848 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556563C211yesmaximal, characteristic
2#22610726C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610535C211yesmaximal, characteristic, complemented
5#22610534C211yesmaximal, characteristic, complemented
6#22610491C211yesmaximal, characteristic, complemented
7#22610486C211yesmaximal, characteristic, complemented
8#22610228C211yesmaximal, characteristic, complemented
9#22610225C211yesmaximal, characteristic, complemented
10#22610225C211yesmaximal, characteristic, complemented
11#22610115C211yesmaximal, characteristic, complemented
12#22610114C211yesmaximal, characteristic, complemented
13#22609997C211yesmaximal, characteristic, complemented
14#22609909C211yesmaximal, characteristic, complemented
15C73×#1870C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C2×#14556563C411yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C22×C4×Dic73C2211yescharacteristic
21C2×C4⋊#10596831C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×C4×#10596831C2211yescharacteristic
33C2×C8×Dic73C2211yescharacteristic
34#17988487C411yescharacteristic
35#17988482C411yescharacteristic
36#17988481C411yescharacteristic
37#17988477C411yescharacteristic
38#17988467C411yescharacteristic
39#17988464C411yescharacteristic
40#17988445C411yescharacteristic
41C4×#11924007C2211yescharacteristic
42C4×#11924005C2211yescharacteristic
43C4×C22⋊Dic73C2211yescharacteristic
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×C22⋊D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C23×Dic73C2×C411yescharacteristic
62C23×Dic73C2×C411yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C2×#11924011—41no—
65C2×#11924011—41no—
66C2×#11924011—41no—
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556563—24no—
72C4×C22⋊D73—41no—
73C4×C22⋊D73—41no—
74C4×C22⋊D73—41no—
75C4×C22⋊D73—41no—
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×C22⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×C4×Dic73—41no—
89C2×C4×Dic73—41no—
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2×C411yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C4⋊#10596831—41no—
96#14556520—41no—
97#14556520—41no—
98#14556520—41no—
99C22⋊#10596831—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106C4×#10596831—41no—
107C8×Dic73—41no—
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114C22×D4×C73C2×C411yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C2×M16×C73—41no—
118C2×M16×C73—41no—
119C2×M16×C73—41no—
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C4×D4×C73—41no—
125C4×D4×C73—41no—
126C2×C4⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C22⋊C8×C73—41no—
131C22⋊C8×C73—41no—
132C22⋊C8×C73—41no—
133C23×D73C22×C411yescharacteristic
134C2×C22⋊D73—22no—
135C2×C22⋊D73—22no—
136C2×C22⋊D73—22no—
137C2×C22⋊D73—41no—
138C2×C22⋊D73—41no—
139C2×C22⋊D73—41no—
140C22×Dic73—22no—
141C22×Dic73—22no—
142C22×Dic73—22no—
143C22×Dic73—41no—
144C22×Dic73—41no—
145C22×Dic73—41no—
146C22×Dic73C22×C411yescharacteristic
147C22×Dic73C22×C411yescharacteristic
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159#11924011—44no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172#11924007—41no—
173#11924007—41no—
174#11924007—41no—
175#11924007M1614yescomplemented
176C22⋊Dic73—22no—
177C22⋊Dic73—22no—
178C22⋊Dic73—41no—
179C22⋊Dic73—41no—
180#11924005—22no—
181#11924005—22no—
182#11924005—41no—
183#11924005—41no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—41no—
191C4×Dic73—41no—
192C24×C73C22×C411yescharacteristic
193C24×C73C22×C411yescharacteristic
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—41no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C2411yescharacteristic
214M16×C73—44no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C4⋊C4×C73—41no—
228C22⋊C4×C73—41no—
229C22⋊C4×C73—41no—
230C42×C73—21no—
231C42×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73#13112yes—
246C23×C73C23×C411yescharacteristic
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254D4×C73—44no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73C2×M1612yes—
275C2×C4×C73H(5,𝔽2)11yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C73H(5,𝔽2)11yescharacteristic
280C2×C4×C732−1+411yescharacteristic
281C22⋊D73—44no—
282C22⋊D73—44no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—44no—
302C2×Dic73—44no—
303C2×Dic73C2×M1612yes—
304C2×Dic73C2×M1612yes—
305C2×Dic73#13112yes—
306C4×D73—41no—
307C4×D73—41no—
308C4×D73—41no—
309C4×D73—41no—
310C8×C73—41no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314#10596831—41no—
315#10596831—41no—
316#10596831—41no—
317#10596831—41no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73#51811yescharacteristic
333C22×C73#51811yescharacteristic
334C22×C73#52011yescharacteristic
335C22×C73C22×M1611yescharacteristic
336C22×C73C2×#13111yescharacteristic
337C22×C73C2×#13111yescharacteristic
338C22×C73#56811yescharacteristic
339C2×D73—41no—
340C2×D73—41no—
341C2×D73—41no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C4×C73—22no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73#56011yescharacteristic
351C4×C73#56011yescharacteristic
352C4×C73#56211yescharacteristic
353C4×C73#56211yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—41no—
358Dic73—41no—
359Dic73—41no—
360Dic73—41no—
361#23327—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—81no—
364C2×C73#237711yescharacteristic
365C2×C73#297411yescharacteristic
366C2×C73#297511yescharacteristic
367C2×C73#297711yescharacteristic
368C2×C73#298111yescharacteristic
369C2×C73#299111yescharacteristic
370C2×C73#299211yescharacteristic
371D73—81no—
372C4×#121—731no—
373#1954—731no—
374#1954—731no—
375#1923—731no—
376#1923—731no—
377#1916—731no—
378#1916—731no—
379#1870—731no—
380#1870—731no—
381#1870—731no—
382#1870D7311yescharacteristic, complemented
383#1851—731no—
384#1851—731no—
385#1817—731no—
386#1797—731no—
387C73#2332711yescharacteristic, complemented, Sylow
388C22×M16—731no—
389C22×M16C2×D7311yescharacteristic
390C2×#121—731no—
391C2×C4×D4—731no—
392C2×C4×D4—731no—
393C2×C4×D4C2×D7311yescharacteristic
394C22×C42—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8—731no—
398C2×C4⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8C2×D7311yescharacteristic
407C2×C22⋊C8C2×D7311yescharacteristic
408C2×C22⋊C8C2×D7311yescharacteristic
409C2×C4×C8—731no—
410C2×C4×C8—731no—
411#390—731no—
412#389—731no—
413#388—731no—
414#388—731no—
415#386—731no—
416#386—731no—
417#380—731no—
418C4×C4⋊C4—731no—
419C4×C22⋊C4—731no—
420C4×C22⋊C4—731no—
421#336—731no—
422#336—731no—
423#336—731no—
424#336—731no—
425#336—731no—
426#336—731no—
427#336—731no—
428#336—731no—
429#336C2×D7311yescharacteristic
430#336C2×D7311yescharacteristic
431C22×D4—731no—
432C22×D4—731no—
433C22×D4C4×D7311yescharacteristic
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4C22×D7311yescharacteristic
438C23×C4C22×D7311yescharacteristic
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
442C2×M16—2921no—
443C2×M16—2921no—
444C2×M16—2921no—
445C22×C8—731no—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8C22×D7311yescharacteristic
450C22×C8C22×D7311yescharacteristic
451C22×C8C22×D7311yescharacteristic
452C22×C8C22×D7311yescharacteristic
453#121—1464no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—2921no—
457C4×D4—2921no—
458C4×D4—2921no—
459C4×D4—2921no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4C4×D7311yescharacteristic
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C22⋊C4—731no—
471C2×C22⋊C4—731no—
472C2×C22⋊C4—731no—
473C2×C22⋊C4C4×D7311yescharacteristic
474C2×C22⋊C4C4×D7311yescharacteristic
475C2×C42—2921no—
476C2×C42—2921no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42—731no—
482C2×C42C22×D7311yescharacteristic
483C4⋊C8—2921no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—2921no—
491C22⋊C8—2921no—
492C22⋊C8—2921no—
493C22⋊C8—2921no—
494C22⋊C8—2921no—
495C22⋊C8—2921no—
496C22⋊C8—2921no—
497C4×C8—2921no—
498C4×C8—2921no—
499#95—731no—
500#95—731no—
501#95—731no—
502#95—731no—
503#95—731no—
504#95—731no—
505C24—731no—
506C24C2×C4×D7311yescharacteristic
507C24C2×C4×D7311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—2921no—
512C2×D4—2921no—
513C2×D4—2921no—
514C2×D4—1462no—
515C2×D4—1462no—
516C2×D4—1462no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—2921no—
530C22×C4—2921no—
531C22×C4—2921no—
532C22×C4—731no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—731no—
536C22×C4—731no—
537C22×C4—731no—
538C22×C4—731no—
539C22×C4—1462no—
540C22×C4—1462no—
541C22×C4—1462no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4—1461no—
548C22×C4C2×C4×D7311yescharacteristic
549C22×C4C2×C4×D7311yescharacteristic
550C22×C4C2×C4×D7311yescharacteristic
551C22×C4C2×C4×D7311yescharacteristic
552C22×C4C23×D7311yescharacteristic
553M16—44no—
554M16—2924no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C4⋊C4—41no—
580C4⋊C4—2921no—
581C4⋊C4—2921no—
582C4⋊C4—2921no—
583C4⋊C4—734no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—2921no—
587C22⋊C4—2921no—
588C22⋊C4—2921no—
589C22⋊C4—2921no—
590C22⋊C4—1462no—
591C22⋊C4—1462no—
592C22⋊C4—1462no—
593C22⋊C4—1462no—
594C42—21no—
595C42—21no—
596C42—2921no—
597C42—2921no—
598C42—1461no—
599C42—1461no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23—1461no—
624C23#1455659912yes—
625C23C22×C4×D7311yescharacteristic
626D4—44no—
627D4—2924no—
628D4—2924no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—2924no—
649C2×C4—2924no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—732no—
655C2×C4—732no—
656C2×C4—732no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4M16×D7312yes—
676C2×C4#1455663611yescharacteristic
677C2×C4#1455663611yescharacteristic
678C2×C4#1455663611yescharacteristic
679C2×C4#1455663611yescharacteristic
680C2×C4#1455663711yescharacteristic
681C2×C4#1455663811yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—2921no—
687C8—2921no—
688C8—2921no—
689C8—2921no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—2921no—
705C22—2921no—
706C22—2921no—
707C22—2921no—
708C22—2921no—
709C22—2921no—
710C22—2921no—
711C22#1798905911yescharacteristic
712C22#1798906011yescharacteristic
713C22#1798906611yescharacteristic
714C22C2×M16×D7311yescharacteristic
715C22#131×D7311yescharacteristic
716C22C2×#1455659911yescharacteristic
717C22#1798935211yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—2921no—
723C4—2921no—
724C4—2921no—
725C4—2921no—
726C4—1462no—
727C4—1462no—
728C4—1462no—
729C4#1798932511yescharacteristic
730C4#1798932611yescharacteristic
731C4#1798933211yescharacteristic
732C4#1798933411yescharacteristic
733C2—42no—
734C2—81no—
735C2—5841no—
736C2#2261308911yescharacteristic
737C2#2261896711yescharacteristic
738C2#2261896911yescharacteristic
739C2#2261898211yescharacteristic
740C2#2261900411yescharacteristic
741C2#2261905911yescharacteristic
742C2#2261907111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1870C2
prime radicalC2×#14556563C4
cosocleC22×C4×C73C24
hypercenter#1870D73
hypocenterC73#23327
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #22610726C2semidirect
3. #22610723C2semidirect
4. #22610535C2semidirect
5. #22610534C2semidirect
6. #22610491C2semidirect
7. #22610486C2semidirect
8. #22610228C2semidirect
9. #22610225C2semidirect
10. #22610225C2semidirect
11. #22610115C2semidirect
12. #22610114C2semidirect
13. #22609997C2semidirect
14. #22609909C2semidirect
15. C73×#1870C2semidirect
175. #11924007M16semidirect
382. #1870D73semidirect
387. C73#23327semidirect

Maximal subgroups

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

subgroupindex
C4×#145565632
#226107262
#226107232
#226105352
#226105342
#226104912
#226104862
#226102282
#226102252
#226101152
#226101142
#226099972
#226099092
C73×#18702
#2332773