Finite Group Databasebeta

← #33112021

Subgroups — #33112021

Order 18688.

1052 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556560C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610727C211yesmaximal, characteristic, complemented
4#22610723C211yesmaximal, characteristic, complemented
5#22610547C211yesmaximal, characteristic, complemented
6#22610547C211yesmaximal, characteristic, complemented
7#22610541C211yesmaximal, characteristic, complemented
8#22610541C211yesmaximal, characteristic, complemented
9#22610540C211yesmaximal, characteristic, complemented
10#22610534C211yesmaximal, characteristic, complemented
11#22610220C211yesmaximal, characteristic, complemented
12#22610220C211yesmaximal, characteristic, complemented
13#22610220C211yesmaximal, characteristic, complemented
14#22609841C211yesmaximal, characteristic, complemented
15C73×#1779C211yesmaximal, characteristic, complemented
16C22×C8×D73C2211yescharacteristic, complemented
17C2×#14556560C411yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×#14556520C2211yescharacteristic, complemented
22C2×#14556520C2211yescharacteristic, complemented
23C2×#14556520C2211yescharacteristic, complemented
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×#14556503C2211yescharacteristic, complemented
31C2×#14556503C2211yescharacteristic, complemented
32C2×#14556503C2211yescharacteristic, complemented
33C2×#14556501C2211yescharacteristic, complemented
34C2×#14556501C2211yescharacteristic, complemented
35C2×C8×Dic73C2211yescharacteristic, complemented
36#17988466C411yescharacteristic
37#17988466C411yescharacteristic
38#17988466C411yescharacteristic
39#17988460C411yescharacteristic
40#17988460C411yescharacteristic
41#17988460C411yescharacteristic
42#17988443C411yescharacteristic
43C4×C22⋊Dic73C2211yescharacteristic
44C4×C22⋊Dic73C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988341C2211yescharacteristic, complemented
47#17988341C2211yescharacteristic, complemented
48#17988341C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52C24×C4×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C22×C22⋊D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C8×D73—41no—
68C2×C8×D73—41no—
69C2×C8×D73—41no—
70#14556560—24no—
71C4×C22⋊D73—41no—
72C4×C22⋊D73—41no—
73C4×C22⋊D73—41no—
74C4×C22⋊D73—41no—
75C4×C22⋊D73—41no—
76C4×C22⋊D73—41no—
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×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95#14556520—41no—
96#14556520—41no—
97#14556520—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103C22⋊#10596831—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556501—41no—
108#14556501—41no—
109C8×Dic73—41no—
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116C25×C73C2×C411yescharacteristic
117C23×C4×C73—41no—
118C23×C4×C73—41no—
119C23×C4×C73—41no—
120C23×C4×C73—41no—
121C23×C4×C73—41no—
122C23×C4×C73—41no—
123C23×C4×C73C2×C411yescharacteristic
124C23×C4×C73C2×C411yescharacteristic
125C23×C4×C73C2×C411yescharacteristic
126C23×C4×C73C2311yescharacteristic
127C23×C4×C73C2311yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C22×C8×C73C2311yescharacteristic
133C22⋊C8×C73—41no—
134C22⋊C8×C73—41no—
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C22⋊C8×C73—41no—
139C23×D73C22×C411yescharacteristic
140C2×C22⋊D73—22no—
141C2×C22⋊D73—22no—
142C2×C22⋊D73—22no—
143C2×C22⋊D73—22no—
144C2×C22⋊D73—41no—
145C2×C22⋊D73—41no—
146C2×C22⋊D73—41no—
147C2×C22⋊D73—41no—
148C2×C22⋊D73M1614yes—
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—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—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C8×D73—44no—
175#11924007—41no—
176#11924007—41no—
177#11924007—41no—
178C22⋊Dic73—22no—
179C22⋊Dic73—22no—
180C22⋊Dic73—22no—
181C22⋊Dic73—22no—
182C22⋊Dic73—22no—
183C22⋊Dic73—41no—
184C22⋊Dic73—41no—
185C22⋊Dic73—41no—
186C22⋊Dic73—41no—
187#11924005—41no—
188#11924005—41no—
189#11924005—41no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C24×C73—22no—
197C24×C73—22no—
198C24×C73—22no—
199C24×C73—41no—
200C24×C73—41no—
201C24×C73—41no—
202C24×C73—41no—
203C24×C73C22×C411yescharacteristic
204C24×C73C22×C411yescharacteristic
205C24×C73C22×C411yescharacteristic
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
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×C73—41no—
225C22×C4×C73—41no—
226C22×C4×C73—41no—
227C22×C4×C73—41no—
228C22×C4×C73—41no—
229C22×C4×C73—41no—
230C22×C4×C73—41no—
231C22×C4×C73—41no—
232C22×C4×C73—41no—
233C22×C4×C73—44no—
234C22×C4×C73—44no—
235C22×C4×C73—44no—
236C22×C4×C73—44no—
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C22×C411yescharacteristic
240C22×C4×C73C2411yescharacteristic
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×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×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—44no—
272C23×C73—44no—
273C23×C73—44no—
274C23×C73—44no—
275C23×C73—44no—
276C23×C73—44no—
277C23×C73—44no—
278C23×C73C2×M1612yes—
279C23×C73#13112yes—
280C23×C73#13112yes—
281C23×C73C23×C411yescharacteristic
282C22×D73—21no—
283C22×D73—21no—
284C22×D73—21no—
285C22×D73—21no—
286C22×D73—21no—
287C22×D73—21no—
288C22×D73C2×M1612yes—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—44no—
299C2×C4×C73—44no—
300C2×C4×C73—44no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C2×C4×C73H(5,𝔽2)11yescharacteristic
316C2×C4×C73H(5,𝔽2)11yescharacteristic
317C2×C4×C73H(5,𝔽2)11yescharacteristic
318C2×C4×C73H(5,𝔽2)11yescharacteristic
319C22⋊D73—44no—
320C22⋊D73—44no—
321C22⋊D73—44no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—21no—
334C2×Dic73—21no—
335C2×Dic73—21no—
336C2×Dic73—21no—
337C2×Dic73—21no—
338C2×Dic73—21no—
339C2×Dic73—21no—
340C2×Dic73—21no—
341C2×Dic73—21no—
342C2×Dic73C2×M1612yes—
343C4×D73—41no—
344C4×D73—41no—
345C4×D73—41no—
346C4×D73—41no—
347C8×C73—41no—
348C8×C73—41no—
349C8×C73—41no—
350C8×C73—41no—
351#10596831—41no—
352#10596831—41no—
353#10596831—41no—
354#10596831—41no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—22no—
363C22×C73—22no—
364C22×C73—416no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73#51811yescharacteristic
378C22×C73#51811yescharacteristic
379C22×C73#51811yescharacteristic
380C22×C73C22×M1611yescharacteristic
381C22×C73C2×#13111yescharacteristic
382C22×C73C2×#13111yescharacteristic
383C22×C73#56811yescharacteristic
384C2×D73—22no—
385C2×D73—22no—
386C2×D73—22no—
387C2×D73—41no—
388C2×D73—41no—
389C2×D73—41no—
390C2×D73—41no—
391C4×C73—41no—
392C4×C73—41no—
393C4×C73—41no—
394C4×C73#56011yescharacteristic
395C4×C73#56011yescharacteristic
396C4×C73#56011yescharacteristic
397C4×C73H(3,𝔽4)11yescharacteristic
398Dic73—22no—
399Dic73—41no—
400Dic73—41no—
401Dic73—41no—
402Dic73—41no—
403Dic73—41no—
404Dic73—41no—
405#23307—731nomaximal, Sylow
406C2×C73—42no—
407C2×C73—42no—
408C2×C73—42no—
409C2×C73#237511yescharacteristic
410C2×C73#297311yescharacteristic
411C2×C73#297411yescharacteristic
412C2×C73#297411yescharacteristic
413C2×C73#297611yescharacteristic
414C2×C73#297611yescharacteristic
415C2×C73#297711yescharacteristic
416D73—42no—
417C4×#120—731no—
418#1955—731no—
419#1955—731no—
420#1954—731no—
421#1924—731no—
422#1924—731no—
423#1924—731no—
424#1924—731no—
425#1923—731no—
426#1923—731no—
427#1869—731no—
428#1869—731no—
429#1869—731no—
430#1779—731no—
431#1779D7311yescharacteristic, complemented
432C73#2330711yescharacteristic, complemented, Sylow
433C24×C4C2×D7311yescharacteristic
434C23×C8—731no—
435C2×#120—731no—
436C2×C4×D4—731no—
437C2×C4×D4—731no—
438C2×C4×D4—731no—
439C2×C4⋊C8—731no—
440C2×C4⋊C8—731no—
441C2×C4⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×C22⋊C8C2×D7311yescharacteristic
452C2×C22⋊C8C2×D7311yescharacteristic
453C2×C22⋊C8C2×D7311yescharacteristic
454C2×C22⋊C8C2×D7311yescharacteristic
455C2×C22⋊C8C2×D7311yescharacteristic
456C2×C22⋊C8C2×D7311yescharacteristic
457C2×#97—731no—
458C2×#97—731no—
459C2×C4×C8—731no—
460#386—731no—
461#386—731no—
462#386—731no—
463#385—731no—
464#385—731no—
465#385—731no—
466#379—731no—
467C4×C22⋊C4—731no—
468C4×C22⋊C4—731no—
469C4×C22⋊C4—731no—
470#336—731no—
471#336—731no—
472#336—731no—
473#336—731no—
474#336—731no—
475#336—731no—
476C25C4×D7311yescharacteristic
477C22×D4—731no—
478C22×D4—731no—
479C22×D4—731no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—731no—
487C23×C4C4×D7311yescharacteristic
488C23×C4C4×D7311yescharacteristic
489C23×C4C4×D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7311yescharacteristic
493C22×C8—2921no—
494C22×C8—2921no—
495C22×C8—2921no—
496C22×C8—731no—
497C22×C8—731no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8C22×D7311yescharacteristic
501C22×C8C22×D7311yescharacteristic
502C22×C8C22×D7311yescharacteristic
503C22×C8C22×D7311yescharacteristic
504#120—1464no—
505C4×D4—2921no—
506C4×D4—2921no—
507C4×D4—2921no—
508C4×D4—2921no—
509C4×D4—2921no—
510C4×D4—2921no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊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⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4—731no—
525C2×C22⋊C4—731no—
526C2×C42—731no—
527C2×C42—731no—
528C2×C42—731no—
529C4⋊C8—2921no—
530C4⋊C8—2921no—
531C4⋊C8—2921no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—41no—
537C22⋊C8—41no—
538C22⋊C8—2921no—
539C22⋊C8—2921no—
540C22⋊C8—2921no—
541C22⋊C8—2921no—
542C22⋊C8—2921no—
543C22⋊C8—2921no—
544C22⋊C8—2921no—
545C22⋊C8—2921no—
546C22⋊C8—2921no—
547#97—2921no—
548#97—2921no—
549C4×C8—2921no—
550#95—731no—
551#95—731no—
552#95—731no—
553#95—731no—
554#95—731no—
555#95—731no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—41no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—731no—
564C24C2×C4×D7311yescharacteristic
565C24C2×C4×D7311yescharacteristic
566C24C2×C4×D7311yescharacteristic
567C2×D4—2921no—
568C2×D4—2921no—
569C2×D4—2921no—
570C2×D4—2921no—
571C2×D4—734no—
572C2×D4—1462no—
573C2×D4—1462no—
574C2×D4—1462no—
575C2×D4—1462no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—731no—
608C22×C4—731no—
609C22×C4—731no—
610C22×C4—731no—
611C22×C4—731no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—1461no—
615C22×C4—1461no—
616C22×C4—1461no—
617C22×C4—1461no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4C2×C4×D7311yescharacteristic
621C22×C4C2×C4×D7311yescharacteristic
622C22×C4C2×C4×D7311yescharacteristic
623C22×C4C23×D7311yescharacteristic
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—2924no—
637C2×C8—1461no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8—1461no—
645C2×C8—1461no—
646C2×C8—1461no—
647C2×C8—1461no—
648C2×C8—1461no—
649C4⋊C4—2921no—
650C4⋊C4—2921no—
651C4⋊C4—2921no—
652C22⋊C4—2921no—
653C22⋊C4—2921no—
654C22⋊C4—2921no—
655C22⋊C4—2921no—
656C22⋊C4—2921no—
657C22⋊C4—2921no—
658C22⋊C4—2921no—
659C22⋊C4—1462no—
660C22⋊C4—1462no—
661C22⋊C4—1462no—
662C22⋊C4—1462no—
663C22⋊C4—1462no—
664C42—1461no—
665C42—1461no—
666C42—1461no—
667C42—1461no—
668C42—1461no—
669C42—1461no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—732no—
696C23—1461no—
697C23—1461no—
698C23—1461no—
699C23—1461no—
700C23—1461no—
701C23—1461no—
702C23M16×D7312yes—
703C23#1455659712yes—
704C23#1455659912yes—
705C23C22×C4×D7311yescharacteristic
706D4—2924no—
707D4—2924no—
708D4—2924no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—2921no—
734C2×C4—2921no—
735C2×C4—2921no—
736C2×C4—2921no—
737C2×C4—732no—
738C2×C4—1461no—
739C2×C4—1461no—
740C2×C4—1461no—
741C2×C4—1461no—
742C2×C4—1461no—
743C2×C4—1461no—
744C2×C4—1461no—
745C2×C4—1461no—
746C2×C4—1461no—
747C2×C4—1461no—
748C2×C4—1461no—
749C2×C4—1461no—
750C2×C4—1461no—
751C2×C4—1461no—
752C2×C4—1461no—
753C2×C4—1461no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4—1461no—
757C2×C4—1461no—
758C2×C4#1455663611yescharacteristic
759C2×C4#1455663611yescharacteristic
760C2×C4#1455663611yescharacteristic
761C2×C4#1455663611yescharacteristic
762C2×C4#1455663611yescharacteristic
763C2×C4#1455663611yescharacteristic
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C8—2921no—
769C8—2921no—
770C8—2921no—
771C8—2921no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
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—2921no—
795C22—2921no—
796C22—2921no—
797C22—2921no—
798C22—1462no—
799C22—1462no—
800C22—1462no—
801C22#1798906011yescharacteristic
802C22#1798906011yescharacteristic
803C22#1798906011yescharacteristic
804C22C2×M16×D7311yescharacteristic
805C22C2×#1455659711yescharacteristic
806C22C2×#1455659911yescharacteristic
807C22#1798935311yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—2921no—
812C4—2921no—
813C4—2921no—
814C4—2921no—
815C4—2921no—
816C4—2921no—
817C4—1462no—
818C4#1798932611yescharacteristic
819C4#1798932611yescharacteristic
820C4#1798932611yescharacteristic
821C4#1798933011yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—2922no—
826C2#2261307011yescharacteristic
827C2#2261895811yescharacteristic
828C2#2261896211yescharacteristic
829C2#2261896711yescharacteristic
830C2#2261897611yescharacteristic
831C2#2261898111yescharacteristic
832C2#2261898511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1779C2
prime radicalC2×#14556560C4
cosocleC22×C4×C73C24
hypercenter#1779D73
hypocenterC73#23307
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610547C2semidirect
6. #22610547C2semidirect
7. #22610541C2semidirect
8. #22610541C2semidirect
9. #22610540C2semidirect
10. #22610534C2semidirect
11. #22610220C2semidirect
12. #22610220C2semidirect
13. #22610220C2semidirect
14. #22609841C2semidirect
15. C73×#1779C2semidirect
16. C22×C8×D73C22semidirect
21. C2×#14556520C22semidirect
22. C2×#14556520C22semidirect
23. C2×#14556520C22semidirect
30. C2×#14556503C22semidirect
31. C2×#14556503C22semidirect
32. C2×#14556503C22semidirect
33. C2×#14556501C22semidirect
34. C2×#14556501C22semidirect
35. C2×C8×Dic73C22semidirect
46. #17988341C22semidirect
47. #17988341C22semidirect
48. #17988341C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
431. #1779D73semidirect
432. C73#23307semidirect

Maximal subgroups

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

subgroupindex
C4×#145565602
#226107272
#226107232
#226105472
#226105412
#226105402
#226105342
#226102202
#226098412
C73×#17792
#2330773