Finite Group Databasebeta

← C73×#14488 #32923892

Subgroups — C73×#14488 #32923892

Order 18688.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C73C211yesmaximal, characteristic
2C2×#388×C73C211yesmaximal, characteristic
3C2×#385×C73C211yesmaximal, characteristic
4C73×#1444C211yesmaximal, characteristic, complemented
5C73×#1442C211yesmaximal, characteristic, complemented
6C73×#1442C211yesmaximal, characteristic, complemented
7C73×#1441C211yesmaximal, characteristic, complemented
8C73×#1439C211yesmaximal, characteristic
9C73×#1439C211yesmaximal, characteristic
10C73×#1436C211yesmaximal, characteristic, complemented
11C73×C4⋊#95C211yesmaximal, characteristic, complemented
12C73×C4⋊#95C211yesmaximal, characteristic, complemented
13C73×#1434C211yesmaximal, characteristic, complemented
14C73×C22⋊#95C211yesmaximal, characteristic
15C73×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C73C2211yescharacteristic
17C22×C4⋊C4×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C42×C73C2211yescharacteristic
30C22×C42×C73C2211yescharacteristic
31#388×C73—24no—
32#388×C73C418yescomplemented
33#385×C73—24no—
34C2×#95×C73C2211yescharacteristic
35C2×#95×C73C2211yescharacteristic
36C2×#95×C73C2211yescharacteristic
37C2×#95×C73C2211yescharacteristic
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C2×#95×C73C2211yescharacteristic
42C2×#95×C73C2211yescharacteristic
43C2×#95×C73C2211yescharacteristic
44C2×#95×C73C2211yescharacteristic
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C25×C73C2311yescharacteristic
55C23×C4×C73—22no—
56C23×C4×C73—22no—
57C23×C4×C73—22no—
58C23×C4×C73—41no—
59C23×C4×C73—41no—
60C23×C4×C73—41no—
61C23×C4×C73—41no—
62C23×C4×C73C2311yescharacteristic
63C23×C4×C73C2311yescharacteristic
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C23×C4×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C2×C4⋊C4×C73—22no—
77C2×C4⋊C4×C73—22no—
78C2×C4⋊C4×C73—22no—
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—41no—
84C2×C4⋊C4×C73—41no—
85C2×C4⋊C4×C73—41no—
86C2×C4⋊C4×C73—41no—
87C2×C4⋊C4×C73—41no—
88C2×C4⋊C4×C73—41no—
89C2×C4⋊C4×C73—41no—
90C2×C4⋊C4×C73—41no—
91C2×C4⋊C4×C73—41no—
92C2×C4⋊C4×C73—41no—
93C2×C4⋊C4×C73C2×C414yescomplemented
94C2×C22⋊C4×C73—22no—
95C2×C22⋊C4×C73—22no—
96C2×C22⋊C4×C73—22no—
97C2×C22⋊C4×C73—22no—
98C2×C22⋊C4×C73—22no—
99C2×C22⋊C4×C73—41no—
100C2×C22⋊C4×C73—41no—
101C2×C22⋊C4×C73—41no—
102C2×C22⋊C4×C73—41no—
103C2×C22⋊C4×C73—41no—
104C2×C22⋊C4×C73—41no—
105C2×C22⋊C4×C73—41no—
106C2×C22⋊C4×C73—41no—
107C2×C22⋊C4×C73C2×C414yes—
108C2×C22⋊C4×C73C2×C414yes—
109C2×C22⋊C4×C73C2×C414yes—
110C2×C22⋊C4×C73D414yes—
111C2×C22⋊C4×C73Q814yes—
112C2×C42×C73—22no—
113C2×C42×C73—22no—
114C2×C42×C73—41no—
115C2×C42×C73—41no—
116C2×C42×C73—41no—
117C2×C42×C73C2×C414yescomplemented
118#95×C73—22no—
119#95×C73—22no—
120#95×C73—22no—
121#95×C73—22no—
122#95×C73—22no—
123#95×C73—22no—
124#95×C73—22no—
125#95×C73—41no—
126#95×C73—41no—
127#95×C73—41no—
128#95×C73—41no—
129#95×C73—41no—
130#95×C73—41no—
131#95×C73—41no—
132#95×C73—41no—
133#95×C73—41no—
134#95×C73—41no—
135#95×C73—41no—
136#95×C73C2×C414yescomplemented
137#95×C73C2×C414yescomplemented
138C24×C73—21no—
139C24×C73—21no—
140C24×C73—21no—
141C24×C73—21no—
142C24×C73—21no—
143C24×C73—21no—
144C24×C73—21no—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73—21no—
148C24×C73—21no—
149C24×C73—21no—
150C24×C73C22×C412yes—
151C24×C73C2×D412yes—
152C24×C73C2×Q812yes—
153C24×C73C2411yescharacteristic
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
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×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—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—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—44no—
239C22×C4×C73—44no—
240C22×C4×C73—44no—
241C22×C4×C73—44no—
242C22×C4×C73—44no—
243C22×C4×C73—44no—
244C22×C4×C73—44no—
245C22×C4×C73C22×C412yes—
246C22×C4×C73C22×C412yes—
247C22×C4×C73C22×C412yes—
248C22×C4×C73C22×C412yes—
249C22×C4×C73C22×C412yes—
250C22×C4×C73C22×C412yes—
251C22×C4×C73C2×D412yes—
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2×Q812yes—
254C22×C4×C73C2×Q812yes—
255C22×C4×C73#4112yes—
256C22×C4×C73#4112yes—
257C22×C4×C73#4112yes—
258C22×C4×C73#4112yes—
259C4⋊C4×C73—44no—
260C4⋊C4×C73—44no—
261C4⋊C4×C73—44no—
262C4⋊C4×C73—44no—
263C4⋊C4×C73—44no—
264C4⋊C4×C73—44no—
265C22⋊C4×C73—44no—
266C22⋊C4×C73—44no—
267C22⋊C4×C73—44no—
268C22⋊C4×C73—44no—
269C22⋊C4×C73—44no—
270C22⋊C4×C73C4⋊C4116yescomplemented
271C42×C73—44no—
272C42×C73—44no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73C2×C4⋊C414yes—
308C23×C73C23×C411yescharacteristic
309C23×C73C22×D411yescharacteristic
310C23×C73C22×Q811yescharacteristic
311C23×C73C2×#4111yescharacteristic
312C23×C73C2×#4111yescharacteristic
313C23×C73C2×#4111yescharacteristic
314C23×C73C2×#4111yescharacteristic
315C23×C73H(5,𝔽2)11yescharacteristic
316C23×C73H(5,𝔽2)11yescharacteristic
317C23×C73H(5,𝔽2)11yescharacteristic
318C23×C73H(5,𝔽2)11yescharacteristic
319C23×C73H(5,𝔽2)11yescharacteristic
320C23×C73H(5,𝔽2)11yescharacteristic
321C23×C732−1+411yescharacteristic
322C23×C732−1+411yescharacteristic
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—416no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73—41no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—41no—
406C2×C4×C73—41no—
407C2×C4×C73—41no—
408C2×C4×C73—41no—
409C2×C4×C73—41no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—41no—
414C2×C4×C73—41no—
415C2×C4×C73—41no—
416C2×C4×C73—41no—
417C2×C4×C73—41no—
418C2×C4×C73—41no—
419C2×C4×C73—41no—
420C2×C4×C73C2×C4⋊C414yes—
421C2×C4×C73C2×C4⋊C414yes—
422C22×C73—24no—
423C22×C73—24no—
424C22×C73—24no—
425C22×C73—42no—
426C22×C73—42no—
427C22×C73—42no—
428C22×C73—42no—
429C22×C73—42no—
430C22×C73—42no—
431C22×C73—42no—
432C22×C73—42no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73C22×C4⋊C411yescharacteristic
438C22×C73C4×#4111yescharacteristic
439C22×C73C4×#4111yescharacteristic
440C22×C73#51811yescharacteristic
441C22×C73#51811yescharacteristic
442C22×C73#52011yescharacteristic
443C22×C73#52011yescharacteristic
444C22×C73#53511yescharacteristic
445C22×C73#53611yescharacteristic
446C22×C73#53811yescharacteristic
447C22×C73#53811yescharacteristic
448C22×C73#53811yescharacteristic
449C22×C73#53911yescharacteristic
450C22×C73#54011yescharacteristic
451C22×C73#54211yescharacteristic
452C22×C73#54211yescharacteristic
453C22×C73#54211yescharacteristic
454C22×C73#54411yescharacteristic
455C22×C73#54411yescharacteristic
456C22×C73#54611yescharacteristic
457C22×C73#54611yescharacteristic
458C22×C73#54611yescharacteristic
459C22×C73#54611yescharacteristic
460C22×C73#55111yescharacteristic
461C22×C73#55211yescharacteristic
462C22×C73#55311yescharacteristic
463C22×C73#55411yescharacteristic
464C22×C73#55411yescharacteristic
465C22×C73#55411yescharacteristic
466C22×C73#55411yescharacteristic
467C22×C73#55611yescharacteristic
468C22×C73#56011yescharacteristic
469C22×C73#56011yescharacteristic
470C22×C73#56211yescharacteristic
471C22×C73#56211yescharacteristic
472C4×C73—24no—
473C4×C73—24no—
474C4×C73—42no—
475C4×C73—42no—
476C4×C73—42no—
477C4×C73—42no—
478C4×C73—42no—
479C4×C73—42no—
480C4×C73—42no—
481C4×C73—42no—
482C4×C73—81no—
483C4×C73—81no—
484C4×C73—81no—
485C4×C73—81no—
486#14488C7311yesmaximal, characteristic, direct product factor, Sylow
487C2×C73—44no—
488C2×C73#231711yescharacteristic
489C2×C73#233511yescharacteristic
490C2×C73#233711yescharacteristic
491C2×C73#234911yescharacteristic
492C2×C73#234911yescharacteristic
493C2×C73#237311yescharacteristic
494C2×C73#237711yescharacteristic
495C2×C73#268511yescharacteristic
496C2×C73#268711yescharacteristic
497C2×C73#270011yescharacteristic
498C2×C73#270311yescharacteristic
499C2×C73#274211yescharacteristic
500C2×C73#276811yescharacteristic
501C2×C73#278811yescharacteristic
502C2×C73#279011yescharacteristic
503C2×#388C2×C7311yescharacteristic
504C2×#388C2×C7311yescharacteristic
505C2×#385C2×C7311yescharacteristic
506#1444C2×C7311yescharacteristic, complemented
507#1442C2×C7311yescharacteristic, complemented
508#1442C2×C7311yescharacteristic, complemented
509#1441C2×C7311yescharacteristic, complemented
510#1439C2×C7311yescharacteristic
511#1439C2×C7311yescharacteristic
512#1436C2×C7311yescharacteristic, complemented
513C4⋊#95C2×C7311yescharacteristic, complemented
514C4⋊#95C2×C7311yescharacteristic, complemented
515#1434C2×C7311yescharacteristic, complemented
516C22⋊#95C2×C7311yescharacteristic
517C22⋊#95C2×C7311yescharacteristic
518C73#1448811yescharacteristic, direct product factor, Sylow
519C24×C4C22×C7311yescharacteristic
520C22×C4⋊C4C22×C7311yescharacteristic
521C22×C4⋊C4C22×C7311yescharacteristic
522C22×C4⋊C4C22×C7311yescharacteristic
523C22×C4⋊C4C22×C7311yescharacteristic
524C22×C4⋊C4C22×C7311yescharacteristic
525C22×C4⋊C4C22×C7311yescharacteristic
526C22×C22⋊C4C22×C7311yescharacteristic
527C22×C22⋊C4C22×C7311yescharacteristic
528C22×C22⋊C4C22×C7311yescharacteristic
529C22×C22⋊C4C22×C7311yescharacteristic
530C22×C22⋊C4C22×C7311yescharacteristic
531C22×C22⋊C4C22×C7311yescharacteristic
532C22×C42C22×C7311yescharacteristic
533C22×C42C22×C7311yescharacteristic
534#388—24no—
535#388C4×C7318yescomplemented
536#385—24no—
537C2×#95C22×C7311yescharacteristic
538C2×#95C22×C7311yescharacteristic
539C2×#95C22×C7311yescharacteristic
540C2×#95C22×C7311yescharacteristic
541C2×#95C22×C7311yescharacteristic
542C2×#95C22×C7311yescharacteristic
543C2×#95C22×C7311yescharacteristic
544C2×#95C22×C7311yescharacteristic
545C2×#95C22×C7311yescharacteristic
546C2×#95C22×C7311yescharacteristic
547C2×#95C22×C7311yescharacteristic
548C2×#95C22×C7311yescharacteristic
549C2×#95C22×C7311yescharacteristic
550C2×#95C22×C7311yescharacteristic
551C2×#95C22×C7311yescharacteristic
552C2×#95C22×C7311yescharacteristic
553C2×#95C22×C7311yescharacteristic
554C2×#95C22×C7311yescharacteristic
555C2×#95C22×C7311yescharacteristic
556C2×#95C22×C7311yescharacteristic
557C25C23×C7311yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C7311yescharacteristic
566C23×C4C23×C7311yescharacteristic
567C23×C4C23×C7311yescharacteristic
568C23×C4C23×C7311yescharacteristic
569C23×C4C23×C7311yescharacteristic
570C23×C4C23×C7311yescharacteristic
571C23×C4C23×C7311yescharacteristic
572C23×C4C23×C7311yescharacteristic
573C23×C4C23×C7311yescharacteristic
574C23×C4C23×C7311yescharacteristic
575C23×C4C23×C7311yescharacteristic
576C23×C4C23×C7311yescharacteristic
577C23×C4C23×C7311yescharacteristic
578C23×C4C23×C7311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C2×C4×C7314yescomplemented
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4C2×C4×C7314yes—
611C2×C22⋊C4C2×C4×C7314yes—
612C2×C22⋊C4C2×C4×C7314yes—
613C2×C22⋊C4D4×C7314yes—
614C2×C22⋊C4Q8×C7314yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C7314yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C7314yescomplemented
640#95C2×C4×C7314yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C7312yes—
654C24C2×D4×C7312yes—
655C24C2×Q8×C7312yes—
656C24C24×C7311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4C22×C4×C7312yes—
749C22×C4C22×C4×C7312yes—
750C22×C4C22×C4×C7312yes—
751C22×C4C22×C4×C7312yes—
752C22×C4C22×C4×C7312yes—
753C22×C4C22×C4×C7312yes—
754C22×C4C2×D4×C7312yes—
755C22×C4C2×D4×C7312yes—
756C22×C4C2×Q8×C7312yes—
757C22×C4C2×Q8×C7312yes—
758C22×C4#41×C7312yes—
759C22×C4#41×C7312yes—
760C22×C4#41×C7312yes—
761C22×C4#41×C7312yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4C4⋊C4×C73116yescomplemented
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C7314yes—
811C23C23×C4×C7311yescharacteristic
812C23C22×D4×C7311yescharacteristic
813C23C22×Q8×C7311yescharacteristic
814C23C2×#41×C7311yescharacteristic
815C23C2×#41×C7311yescharacteristic
816C23C2×#41×C7311yescharacteristic
817C23C2×#41×C7311yescharacteristic
818C23H(5,𝔽2)×C7311yescharacteristic
819C23H(5,𝔽2)×C7311yescharacteristic
820C23H(5,𝔽2)×C7311yescharacteristic
821C23H(5,𝔽2)×C7311yescharacteristic
822C23H(5,𝔽2)×C7311yescharacteristic
823C23H(5,𝔽2)×C7311yescharacteristic
824C232−1+4×C7311yescharacteristic
825C232−1+4×C7311yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—416no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4C2×C4⋊C4×C7314yes—
924C2×C4C2×C4⋊C4×C7314yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C7311yescharacteristic
941C22C4×#41×C7311yescharacteristic
942C22C4×#41×C7311yescharacteristic
943C22#518×C7311yescharacteristic
944C22#518×C7311yescharacteristic
945C22#520×C7311yescharacteristic
946C22#520×C7311yescharacteristic
947C22#535×C7311yescharacteristic
948C22#536×C7311yescharacteristic
949C22#538×C7311yescharacteristic
950C22#538×C7311yescharacteristic
951C22#538×C7311yescharacteristic
952C22#539×C7311yescharacteristic
953C22#540×C7311yescharacteristic
954C22#542×C7311yescharacteristic
955C22#542×C7311yescharacteristic
956C22#542×C7311yescharacteristic
957C22#544×C7311yescharacteristic
958C22#544×C7311yescharacteristic
959C22#546×C7311yescharacteristic
960C22#546×C7311yescharacteristic
961C22#546×C7311yescharacteristic
962C22#546×C7311yescharacteristic
963C22#551×C7311yescharacteristic
964C22#552×C7311yescharacteristic
965C22#553×C7311yescharacteristic
966C22#554×C7311yescharacteristic
967C22#554×C7311yescharacteristic
968C22#554×C7311yescharacteristic
969C22#554×C7311yescharacteristic
970C22#556×C7311yescharacteristic
971C22#560×C7311yescharacteristic
972C22#560×C7311yescharacteristic
973C22#562×C7311yescharacteristic
974C22#562×C7311yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C73×#231711yescharacteristic
991C2C73×#233511yescharacteristic
992C2C73×#233711yescharacteristic
993C2C73×#234911yescharacteristic
994C2C73×#234911yescharacteristic
995C2C73×#237311yescharacteristic
996C2C73×#237711yescharacteristic
997C2C73×#268511yescharacteristic
998C2C73×#268711yescharacteristic
999C2C73×#270011yescharacteristic
1000C2C73×#270311yescharacteristic
1001C2C73×#274211yescharacteristic
1002C2C73×#276811yescharacteristic
1003C2C73×#278811yescharacteristic
1004C2C73×#279011yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC24C24×C73
prime radicalC25×C73C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1444C2semidirect
5. C73×#1442C2semidirect
6. C73×#1442C2semidirect
7. C73×#1441C2semidirect
10. C73×#1436C2semidirect
11. C73×C4⋊#95C2semidirect
12. C73×C4⋊#95C2semidirect
13. C73×#1434C2semidirect
32. #388×C73C4semidirect
93. C2×C4⋊C4×C73C2×C4semidirect
117. C2×C42×C73C2×C4semidirect
136. #95×C73C2×C4semidirect
137. #95×C73C2×C4semidirect
270. C22⋊C4×C73C4⋊C4semidirect
486. #14488C73direct (N × H)
506. #1444C2×C73semidirect
507. #1442C2×C73semidirect
508. #1442C2×C73semidirect
509. #1441C2×C73semidirect
512. #1436C2×C73semidirect
513. C4⋊#95C2×C73semidirect
514. C4⋊#95C2×C73semidirect
515. #1434C2×C73semidirect
518. C73#14488direct (N × H)
535. #388C4×C73semidirect
596. C2×C4⋊C4C2×C4×C73semidirect
620. C2×C42C2×C4×C73semidirect
639. #95C2×C4×C73semidirect
640. #95C2×C4×C73semidirect
773. C22⋊C4C4⋊C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C732
C2×#385×C732
C73×#14442
C73×#14422
C73×#14412
C73×#14392
C73×#14362
C73×C4⋊#952
C73×#14342
C73×C22⋊#952
#1448873