Finite Group Databasebeta

← #33097087

Subgroups — #33097087

Order 18688.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988663C211yesmaximal, characteristic, complemented
2C4×#14556560C211yesmaximal, characteristic
3#22610727C211yesmaximal, characteristic, complemented
4#22610723C211yesmaximal, characteristic, complemented
5#22610547C211yesmaximal, characteristic, complemented
6#22610540C211yesmaximal, characteristic, complemented
7#22610534C211yesmaximal, characteristic, complemented
8#22610534C211yesmaximal, characteristic, complemented
9#22610228C211yesmaximal, characteristic, complemented
10#22610225C211yesmaximal, characteristic, complemented
11#22610225C211yesmaximal, characteristic, complemented
12#22610114C211yesmaximal, characteristic, complemented
13#22609841C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#407×C73C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic, complemented
17C2×#14556560C411yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21#17988663—24no—
22C2×#14556520C2211yescharacteristic, complemented
23C2×#14556520C2211yescharacteristic, complemented
24C2×#14556520C2211yescharacteristic, complemented
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×C22⋊#10596831C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×#14556503C2211yescharacteristic, complemented
32C2×#14556503C2211yescharacteristic, complemented
33C2×#14556503C2211yescharacteristic, complemented
34C2×#14556501C2211yescharacteristic, complemented
35C2×C8×Dic73C2211yescharacteristic, complemented
36C2×C8×Dic73C2211yescharacteristic, complemented
37#17988466C411yescharacteristic
38#17988466C411yescharacteristic
39#17988466C411yescharacteristic
40#17988460C411yescharacteristic
41#17988460C411yescharacteristic
42#17988460C411yescharacteristic
43#17988443C411yescharacteristic
44C4×C22⋊Dic73C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47#17988341C2211yescharacteristic, complemented
48#17988341C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52#17988341C2211yescharacteristic, complemented
53C24×C4×C73C2211yescharacteristic
54C22×M16×C73C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56#407×C73—24no—
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C22×C22⋊D73C2×C411yescharacteristic
63C22×C22⋊D73C2×C411yescharacteristic
64C22×C4×D73C2311yescharacteristic
65C2×#11924011—22no—
66C2×#11924011—41no—
67C2×#11924011—41no—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72#14556560—24no—
73C4×C22⋊D73—22no—
74C4×C22⋊D73—22no—
75C4×C22⋊D73—41no—
76C4×C22⋊D73—41no—
77C4×C22⋊D73—41no—
78C4×C22⋊D73—41no—
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×#11924007C2×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×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97#14556520—22no—
98#14556520—41no—
99#14556520—41no—
100C22⋊#10596831—22no—
101C22⋊#10596831—22no—
102C22⋊#10596831—41no—
103C22⋊#10596831—41no—
104C22⋊#10596831—41no—
105C22⋊#10596831—41no—
106#14556503—22no—
107#14556503—41no—
108#14556503—41no—
109#14556501—41no—
110C8×Dic73—22no—
111C8×Dic73—41no—
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118C25×C73C2×C411yescharacteristic
119C23×C4×C73—22no—
120C23×C4×C73—22no—
121C23×C4×C73—41no—
122C23×C4×C73—41no—
123C23×C4×C73—41no—
124C23×C4×C73—41no—
125C23×C4×C73C2×C411yescharacteristic
126C23×C4×C73C2×C411yescharacteristic
127C23×C4×C73C2×C411yescharacteristic
128C23×C4×C73C2311yescharacteristic
129C23×C4×C73C2311yescharacteristic
130C23×C4×C73C2311yescharacteristic
131C2×M16×C73—22no—
132C2×M16×C73—41no—
133C2×M16×C73—41no—
134C2×M16×C73—41no—
135C2×M16×C73—41no—
136C2×M16×C73D414yescomplemented
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C22×C8×C73C2311yescharacteristic
140C22×C8×C73C2311yescharacteristic
141C22⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144C22⋊C8×C73—22no—
145C23×D73C22×C411yescharacteristic
146C2×C22⋊D73—22no—
147C2×C22⋊D73—22no—
148C2×C22⋊D73—22no—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—22no—
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
161C22×Dic73C22×C411yescharacteristic
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168#11924011—44no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181#11924007—22no—
182#11924007—41no—
183#11924007—41no—
184C22⋊Dic73—22no—
185C22⋊Dic73—22no—
186C22⋊Dic73—22no—
187C22⋊Dic73—22no—
188C22⋊Dic73—41no—
189C22⋊Dic73—41no—
190C22⋊Dic73—41no—
191C22⋊Dic73—41no—
192C22⋊Dic73M1614yescomplemented
193#11924005—22no—
194#11924005—41no—
195#11924005—41no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C24×C73—22no—
203C24×C73—22no—
204C24×C73—22no—
205C24×C73—41no—
206C24×C73—41no—
207C24×C73—41no—
208C24×C73—41no—
209C24×C73C22×C411yescharacteristic
210C24×C73C22×C411yescharacteristic
211C24×C73C22×C411yescharacteristic
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—41no—
232C22×C4×C73—41no—
233C22×C4×C73—41no—
234C22×C4×C73—41no—
235C22×C4×C73—41no—
236C22×C4×C73—41no—
237C22×C4×C73—44no—
238C22×C4×C73—44no—
239C22×C4×C73—44no—
240C22×C4×C73—44no—
241C22×C4×C73C22×C411yescharacteristic
242C22×C4×C73C22×C411yescharacteristic
243C22×C4×C73C22×C411yescharacteristic
244C22×C4×C73C2×D412yes—
245C22×C4×C73#4112yes—
246C22×C4×C73C2411yescharacteristic
247M16×C73—44no—
248M16×C73—44no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—21no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73C2×D412yes—
260C2×C8×C73C2×D412yes—
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—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—44no—
280C23×C73—44no—
281C23×C73—44no—
282C23×C73—44no—
283C23×C73—44no—
284C23×C73—44no—
285C23×C73—44no—
286C23×C73C4×D412yes—
287C23×C73C2×M1612yes—
288C23×C73#13112yes—
289C23×C73C23×C411yescharacteristic
290C22×D73—21no—
291C22×D73—21no—
292C22×D73—21no—
293C22×D73—21no—
294C22×D73—21no—
295C22×D73—21no—
296C22×D73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—44no—
310C2×C4×C73—44no—
311C2×C4×C73—44no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73C4×D412yes—
321C2×C4×C73C22×D411yescharacteristic
322C2×C4×C73C2×#4111yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C2×C4×C73H(5,𝔽2)11yescharacteristic
325C2×C4×C73H(5,𝔽2)11yescharacteristic
326C2×C4×C73H(5,𝔽2)11yescharacteristic
327C22⋊D73—44no—
328C22⋊D73—44no—
329C22⋊D73—44no—
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×Dic73—21no—
343C2×Dic73—21no—
344C2×Dic73—21no—
345C2×Dic73—21no—
346C2×Dic73—21no—
347C2×Dic73—21no—
348C2×Dic73—21no—
349C2×Dic73C2×M1612yes—
350C2×Dic73C2×M1612yes—
351C4×D73—41no—
352C4×D73—41no—
353C4×D73—41no—
354C4×D73—41no—
355C8×C73—22no—
356C8×C73—22no—
357C8×C73—41no—
358C8×C73—41no—
359#10596831—41no—
360#10596831—41no—
361#10596831—41no—
362#10596831—41no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—416no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—41no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73C2×C4×D411yescharacteristic
386C22×C73#51811yescharacteristic
387C22×C73#51811yescharacteristic
388C22×C73C22×M1611yescharacteristic
389C22×C73C2×#13111yescharacteristic
390C22×C73#56811yescharacteristic
391C22×C73#56811yescharacteristic
392C2×D73—41no—
393C2×D73—41no—
394C2×D73—41no—
395C2×D73—41no—
396C2×D73—41no—
397C2×D73—41no—
398C2×D73—41no—
399C4×C73—22no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73#53411yescharacteristic
403C4×C73#53511yescharacteristic
404C4×C73#53811yescharacteristic
405C4×C73#53811yescharacteristic
406Dic73—22no—
407Dic73—22no—
408Dic73—41no—
409Dic73—41no—
410Dic73—41no—
411Dic73—41no—
412Dic73—41no—
413#22038—731nomaximal, Sylow
414C2×C73—42no—
415C2×C73—42no—
416C2×C73—42no—
417C2×C73#232111yescharacteristic
418C2×C73#293311yescharacteristic
419C2×C73D4×M1611yescharacteristic
420C2×C73#297411yescharacteristic
421C2×C73#297511yescharacteristic
422C2×C73#297611yescharacteristic
423C2×C73#297811yescharacteristic
424D73—81no—
425C2×#436—731no—
426C2×#407D7311yescharacteristic, complemented
427C4×#120—731no—
428#1955—731no—
429#1954—731no—
430#1924—731no—
431#1923—731no—
432#1923—731no—
433#1923—731no—
434#1870—731no—
435#1870—731no—
436#1870—731no—
437#1851—731no—
438#1779—731no—
439#1753—731no—
440C73#2203811yescharacteristic, complemented, Sylow
441C24×C4C2×D7311yescharacteristic
442C22×M16—731no—
443C22×M16C2×D7311yescharacteristic
444C22×M16C2×D7311yescharacteristic
445C2×#120—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4—731no—
449#436—1464no—
450C2×C4⋊C8—731no—
451C2×C4⋊C8—731no—
452C2×C4⋊C8—731no—
453#407—24no—
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×C22⋊C8—731no—
457C2×C22⋊C8—731no—
458C2×C22⋊C8—731no—
459C2×C22⋊C8—731no—
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×C22⋊C8—731no—
463C2×C22⋊C8C2×D7311yescharacteristic
464C2×C22⋊C8C2×D7311yescharacteristic
465C2×C22⋊C8C2×D7311yescharacteristic
466C2×C22⋊C8C2×D7311yescharacteristic
467C2×#97—731no—
468C2×C4×C8—731no—
469C2×C4×C8—731no—
470#386—731no—
471#386—731no—
472#386—731no—
473#385—731no—
474#385—731no—
475#385—731no—
476#379—731no—
477C4×C22⋊C4—731no—
478C4×C22⋊C4—731no—
479C4×C22⋊C4—731no—
480#336—731no—
481#336—731no—
482#336—731no—
483#336—731no—
484#336—731no—
485#336—731no—
486C25C4×D7311yescharacteristic
487C22×D4—731no—
488C22×D4—731no—
489C22×D4—731no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4—731no—
497C23×C4C4×D7311yescharacteristic
498C23×C4C4×D7311yescharacteristic
499C23×C4C4×D7311yescharacteristic
500C23×C4C22×D7311yescharacteristic
501C23×C4C22×D7311yescharacteristic
502C23×C4C22×D7311yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—2921no—
509C2×M16—2921no—
510C2×M16—1462no—
511C2×M16C22⋊D7314yescomplemented
512C22×C8—731no—
513C22×C8—731no—
514C22×C8—731no—
515C22×C8—731no—
516C22×C8C22×D7311yescharacteristic
517C22×C8C22×D7311yescharacteristic
518C22×C8C22×D7311yescharacteristic
519C22×C8C22×D7311yescharacteristic
520#120—1464no—
521C4×D4—2921no—
522C4×D4—2921no—
523C4×D4—2921no—
524C4×D4—2921no—
525C4×D4—1462no—
526C4×D4—1462no—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—731no—
534C2×C22⋊C4—731no—
535C2×C22⋊C4—731no—
536C2×C22⋊C4—731no—
537C2×C22⋊C4—731no—
538C2×C22⋊C4—731no—
539C2×C22⋊C4—731no—
540C2×C22⋊C4—731no—
541C2×C22⋊C4—731no—
542C2×C42—731no—
543C2×C42—731no—
544C2×C42—731no—
545C4⋊C8—2921no—
546C4⋊C8—2921no—
547C4⋊C8—1462no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—2921no—
553C22⋊C8—2921no—
554C22⋊C8—2921no—
555C22⋊C8—2921no—
556C22⋊C8—2921no—
557C22⋊C8—2921no—
558C22⋊C8—1462no—
559C22⋊C8—1462no—
560C22⋊C8—1462no—
561#97—2921no—
562C4×C8—2921no—
563C4×C8—1462no—
564#95—731no—
565#95—731no—
566#95—731no—
567#95—731no—
568#95—731no—
569#95—731no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24—731no—
578C24C2×C4×D7311yescharacteristic
579C24C2×C4×D7311yescharacteristic
580C24C2×C4×D7311yescharacteristic
581C2×D4—2921no—
582C2×D4—2921no—
583C2×D4—2921no—
584C2×D4—2921no—
585C2×D4—1462no—
586C2×D4—1462no—
587C2×D4—1462no—
588C2×D4—1462no—
589C2×D4—1462no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
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—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—731no—
624C22×C4—731no—
625C22×C4—731no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4C2×C4×D7311yescharacteristic
633C22×C4C2×C4×D7311yescharacteristic
634C22×C4C2×C4×D7311yescharacteristic
635C22×C4C2×C22⋊D7312yes—
636C22×C4#1192402812yes—
637C22×C4C23×D7311yescharacteristic
638M16—44no—
639M16—44no—
640M16—2924no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—1461no—
652C2×C8—1461no—
653C2×C8—1461no—
654C2×C8—1461no—
655C2×C8—1461no—
656C2×C8—1461no—
657C2×C8—1461no—
658C2×C8—1461no—
659C2×C8—1461no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8C2×C22⋊D7312yes—
664C2×C8C2×C22⋊D7312yes—
665C4⋊C4—2921no—
666C4⋊C4—2921no—
667C4⋊C4—1462no—
668C22⋊C4—2921no—
669C22⋊C4—2921no—
670C22⋊C4—2921no—
671C22⋊C4—2921no—
672C22⋊C4—2921no—
673C22⋊C4—2921no—
674C22⋊C4—734no—
675C22⋊C4—1462no—
676C22⋊C4—1462no—
677C22⋊C4—1462no—
678C22⋊C4—1462no—
679C22⋊C4—1462no—
680C42—1461no—
681C42—1461no—
682C42—1461no—
683C42—1461no—
684C42—1461no—
685C42—1461no—
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—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—1461no—
712C23—1461no—
713C23—1461no—
714C23—1461no—
715C23—1461no—
716C23—1461no—
717C23—1461no—
718C23C4×C22⋊D7312yes—
719C23M16×D7312yes—
720C23#1455659912yes—
721C23C22×C4×D7311yescharacteristic
722D4—2924no—
723D4—2924no—
724D4—2924no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—732no—
753C2×C4—732no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4—1461no—
757C2×C4—1461no—
758C2×C4—1461no—
759C2×C4—1461no—
760C2×C4—1461no—
761C2×C4—1461no—
762C2×C4—1461no—
763C2×C4—1461no—
764C2×C4—1461no—
765C2×C4—1461no—
766C2×C4—1461no—
767C2×C4—1461no—
768C2×C4—1461no—
769C2×C4—1461no—
770C2×C4—1461no—
771C2×C4—1461no—
772C2×C4—1461no—
773C2×C4C4×C22⋊D7312yes—
774C2×C4C22×C22⋊D7311yescharacteristic
775C2×C4C2×#1192402811yescharacteristic
776C2×C4#1455663611yescharacteristic
777C2×C4#1455663611yescharacteristic
778C2×C4#1455663611yescharacteristic
779C2×C4#1455663611yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—2921no—
785C8—2921no—
786C8—2921no—
787C8—2921no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—2921no—
811C22—2921no—
812C22—2921no—
813C22—2921no—
814C22—2921no—
815C22—2921no—
816C22—2921no—
817C22C2×C4×C22⋊D7311yescharacteristic
818C22#1798906011yescharacteristic
819C22#1798906011yescharacteristic
820C22C2×M16×D7311yescharacteristic
821C22C2×#1455659911yescharacteristic
822C22#1798935311yescharacteristic
823C22#1798935311yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—2921no—
828C4—2921no—
829C4—2921no—
830C4—2921no—
831C4—2921no—
832C4—1462no—
833C4—1462no—
834C4#1798914611yescharacteristic
835C4#1798915411yescharacteristic
836C4#1798917511yescharacteristic
837C4#1798917511yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—5841no—
842C2#2261258911yescharacteristic
843C2#2261865611yescharacteristic
844C2M16×C22⋊D7311yescharacteristic
845C2#2261896711yescharacteristic
846C2#2261897011yescharacteristic
847C2#2261898111yescharacteristic
848C2#2261899111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#407×C73C2
prime radicalC2×#14556560C4
cosocleC22×C4×C73C24
hypercenterC2×#407D73
hypocenterC73#22038
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#17988663C2semidirect
3. #22610727C2semidirect
4. #22610723C2semidirect
5. #22610547C2semidirect
6. #22610540C2semidirect
7. #22610534C2semidirect
8. #22610534C2semidirect
9. #22610228C2semidirect
10. #22610225C2semidirect
11. #22610225C2semidirect
12. #22610114C2semidirect
13. #22609841C2semidirect
14. #22609712C2semidirect
15. C2×#407×C73C2semidirect
16. C22×#11924011C22semidirect
22. C2×#14556520C22semidirect
23. C2×#14556520C22semidirect
24. C2×#14556520C22semidirect
31. C2×#14556503C22semidirect
32. C2×#14556503C22semidirect
33. C2×#14556503C22semidirect
34. C2×#14556501C22semidirect
35. C2×C8×Dic73C22semidirect
36. C2×C8×Dic73C22semidirect
47. #17988341C22semidirect
48. #17988341C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
52. #17988341C22semidirect
136. C2×M16×C73D4semidirect
192. C22⋊Dic73M16semidirect
426. C2×#407D73semidirect
440. C73#22038semidirect
511. C2×M16C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886632
C4×#145565602
#226107272
#226107232
#226105472
#226105402
#226105342
#226102282
#226102252
#226101142
#226098412
#226097122
C2×#407×C732
#2203873