Finite Group Databasebeta

← C73×#25576 #32934980

Subgroups — C73×#25576 #32934980

Order 18688.

1174 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
1C2×#552×C73C211yesmaximal, characteristic, complemented
2C2×#488×C73C211yesmaximal, characteristic, complemented
3C2×#464×C73C211yesmaximal, characteristic, complemented
4C73×#2540C211yesmaximal, characteristic
5C73×#2001C211yesmaximal, characteristic, complemented
6C73×#2001C211yesmaximal, characteristic, complemented
7C73×#2000C211yesmaximal, characteristic, complemented
8C73×#2000C211yesmaximal, characteristic, complemented
9C73×#1989C211yesmaximal, characteristic, complemented
10C73×#1954C211yesmaximal, characteristic, complemented
11C73×#1875C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1872C211yesmaximal, characteristic, complemented
15C4×#103×C73C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18#552×C73—24no—
19#552×C73—24no—
20C2×#126×C73—21no—
21C2×#125×C73—21no—
22C2×#125×C73C2211yescharacteristic
23C2×#124×C73C2211yescharacteristic
24C2×#123×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C22⋊Q8×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×#121×C73C2211yescharacteristic
31C2×C4×Q8×C73C2211yescharacteristic
32C2×C4×D4×C73C2211yescharacteristic
33C2×#117×C73—21no—
34C2×#117×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36#488×C73—24no—
37#464×C73—24no—
38C2×C4⋊C8×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#103×C73C2211yescharacteristic
43C2×#103×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C22⋊C8×C73C2211yescharacteristic
50C2×C22⋊C8×C73C2211yescharacteristic
51C2×C4×C8×C73C2211yescharacteristic
52#399×C73—21no—
53#392×C73—21no—
54#390×C73—21no—
55#390×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73C2311yescharacteristic
71C23×C4×C73C2311yescharacteristic
72C2×Q16×C73—22no—
73C2×Q16×C73—41no—
74C2×Q16×C73—41no—
75C2×SD16×C73—22no—
76C2×SD16×C73—41no—
77C2×SD16×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#126×C73—28no—
83#125×C73—28no—
84#125×C73—22no—
85#125×C73D414yescomplemented
86#124×C73—22no—
87#124×C73—22no—
88#123×C73—28no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73—22no—
91C22⋊Q8×C73—22no—
92C22⋊Q8×C73—22no—
93C22⋊Q8×C73—22no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—41no—
96C22⋊Q8×C73—41no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—41no—
100#121×C73—41no—
101C4×Q8×C73—22no—
102C4×Q8×C73D414yescomplemented
103C4×D4×C73—22no—
104C4×D4×C73—22no—
105#117×C73—28no—
106#117×C73—22no—
107#117×C73—22no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—22no—
115C2×C4⋊C4×C73—22no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73D411yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C42×C73—21no—
136C2×C42×C73—21no—
137C2×C42×C73—21no—
138C2×C42×C73C2311yescharacteristic
139C4⋊C8×C73—22no—
140#103×C73—22no—
141#103×C73—22no—
142#103×C73—22no—
143#103×C73—22no—
144#103×C73—22no—
145#102×C73—22no—
146#102×C73—22no—
147#102×C73—22no—
148C22⋊C8×C73—41no—
149C22⋊C8×C73—41no—
150C22⋊C8×C73—41no—
151C22⋊C8×C73—41no—
152C4×C8×C73—22no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73C2×D411yescharacteristic
156C24×C73C2×D411yescharacteristic
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73C2×D412yes—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—41no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—81no—
183C2×D4×C73—81no—
184C22×C4×C73—24no—
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—42no—
205C22×C4×C73—42no—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2411yescharacteristic
211Q16×C73—44no—
212SD16×C73—44no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
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—
225C4⋊C4×C73—24no—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—24no—
228C4⋊C4×C73—24no—
229C4⋊C4×C73—24no—
230C4⋊C4×C73—24no—
231C4⋊C4×C73—22no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—42no—
238C4⋊C4×C73—42no—
239C4⋊C4×C73C2×D412yes—
240C4⋊C4×C73C2×D412yes—
241C4⋊C4×C73C2×D412yes—
242C4⋊C4×C73#4112yes—
243C4⋊C4×C73#4112yes—
244C22⋊C4×C73—24no—
245C22⋊C4×C73—24no—
246C22⋊C4×C73—24no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C42×C73—24no—
256C42×C73—24no—
257C42×C73—81no—
258C42×C73C2×D412yes—
259C42×C73C2×D412yes—
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—21no—
272C23×C73—21no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73#13512yes—
281C23×C73C22×D411yescharacteristic
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73—41no—
290D4×C73—44no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—84no—
296D4×C73—84no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—48no—
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×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73#12012yes—
338C2×C4×C73#12012yes—
339C2×C4×C73C22×D411yescharacteristic
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C2×#4111yescharacteristic
342C2×C4×C73C2×#4111yescharacteristic
343C2×C4×C73H(5,𝔽2)11yescharacteristic
344C2×C4×C73H(5,𝔽2)11yescharacteristic
345C8×C73—41no—
346C8×C73—41no—
347C8×C73—41no—
348C8×C73—41no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—81no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73C2×#12011yescharacteristic
371C22×C73#54611yescharacteristic
372C22×C73#54611yescharacteristic
373C22×C73C2×#13511yescharacteristic
374C22×C73#57511yescharacteristic
375C22×C73#57711yescharacteristic
376C22×C73#57811yescharacteristic
377C4×C73—22no—
378C4×C73—22no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73—42no—
382C4×C73—42no—
383C4×C73—42no—
384C4×C73—42no—
385C4×C73—42no—
386C4×C73—42no—
387C4×C73—81no—
388C4×C73#53211yescharacteristic
389C4×C73#53511yescharacteristic
390C4×C73#55011yescharacteristic
391C4×C73#55011yescharacteristic
392#25576C7311yesmaximal, characteristic, direct product factor, Sylow
393C2×C73—42no—
394C2×C73—81no—
395C2×C73—161no—
396C2×C73#243111yescharacteristic
397C2×C73#300211yescharacteristic
398C2×C73#301311yescharacteristic
399C2×C73#329611yescharacteristic
400C2×C73#330011yescharacteristic
401C2×C73#332311yescharacteristic
402C2×C73#332711yescharacteristic
403C2×#552C2×C7311yescharacteristic, complemented
404C2×#488C2×C7311yescharacteristic, complemented
405C2×#464C2×C7311yescharacteristic, complemented
406#2540C2×C7311yescharacteristic
407#2001C2×C7311yescharacteristic, complemented
408#2001C2×C7311yescharacteristic, complemented
409#2000C2×C7311yescharacteristic, complemented
410#2000C2×C7311yescharacteristic, complemented
411#1989C2×C7311yescharacteristic, complemented
412#1954C2×C7311yescharacteristic, complemented
413#1875C2×C7311yescharacteristic, complemented
414#1874C2×C7311yescharacteristic, complemented
415#1873C2×C7311yescharacteristic, complemented
416#1872C2×C7311yescharacteristic, complemented
417C4×#103C2×C7311yescharacteristic, complemented
418C73#2557611yescharacteristic, direct product factor, Sylow
419C22×Q16C22×C7311yescharacteristic
420C22×SD16C22×C7311yescharacteristic
421#552—24no—
422#552—24no—
423C2×#126—21no—
424C2×#125—21no—
425C2×#125C22×C7311yescharacteristic
426C2×#124C22×C7311yescharacteristic
427C2×#123—21no—
428C2×C22⋊Q8C22×C7311yescharacteristic
429C2×C22⋊Q8C22×C7311yescharacteristic
430C2×C22⋊Q8C22×C7311yescharacteristic
431C2×C22⋊Q8C22×C7311yescharacteristic
432C2×#121C22×C7311yescharacteristic
433C2×#121C22×C7311yescharacteristic
434C2×C4×Q8C22×C7311yescharacteristic
435C2×C4×D4C22×C7311yescharacteristic
436C2×#117—21no—
437C2×#117C22×C7311yescharacteristic
438C22×C4⋊C4C22×C7311yescharacteristic
439#488—24no—
440#464—24no—
441C2×C4⋊C8C22×C7311yescharacteristic
442C2×#103C22×C7311yescharacteristic
443C2×#103C22×C7311yescharacteristic
444C2×#103C22×C7311yescharacteristic
445C2×#103C22×C7311yescharacteristic
446C2×#103C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×#102C22×C7311yescharacteristic
449C2×#102C22×C7311yescharacteristic
450C2×C22⋊C8C22×C7311yescharacteristic
451C2×C22⋊C8C22×C7311yescharacteristic
452C2×C22⋊C8C22×C7311yescharacteristic
453C2×C22⋊C8C22×C7311yescharacteristic
454C2×C4×C8C22×C7311yescharacteristic
455#399—21no—
456#392—21no—
457#390—21no—
458#390—21no—
459C4×C4⋊C4C22×C7311yescharacteristic
460#340C22×C7311yescharacteristic
461#340C22×C7311yescharacteristic
462#340C22×C7311yescharacteristic
463#340C22×C7311yescharacteristic
464#340C22×C7311yescharacteristic
465#340C22×C7311yescharacteristic
466C22×Q8C23×C7311yescharacteristic
467C22×Q8C23×C7311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4D4×C7311yescharacteristic
471C22×D4C23×C7311yescharacteristic
472C23×C4—21no—
473C23×C4C23×C7311yescharacteristic
474C23×C4C23×C7311yescharacteristic
475C2×Q16—22no—
476C2×Q16—41no—
477C2×Q16—41no—
478C2×SD16—22no—
479C2×SD16—41no—
480C2×SD16—41no—
481C22×C8C23×C7311yescharacteristic
482C22×C8C23×C7311yescharacteristic
483C22×C8C23×C7311yescharacteristic
484C22×C8C23×C7311yescharacteristic
485#126—28no—
486#125—28no—
487#125—22no—
488#125D4×C7314yescomplemented
489#124—22no—
490#124—22no—
491#123—28no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—41no—
499C22⋊Q8—41no—
500#121—22no—
501#121—22no—
502#121—41no—
503#121—41no—
504C4×Q8—22no—
505C4×Q8D4×C7314yescomplemented
506C4×D4—22no—
507C4×D4—22no—
508#117—28no—
509#117—22no—
510#117—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4D4×C7311yescharacteristic
522C2×C4⋊C4C23×C7311yescharacteristic
523C2×C4⋊C4C23×C7311yescharacteristic
524C2×C4⋊C4C23×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C7311yescharacteristic
537C2×C22⋊C4D4×C7311yescharacteristic
538C2×C42—21no—
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C7311yescharacteristic
542C4⋊C8—22no—
543#103—22no—
544#103—22no—
545#103—22no—
546#103—22no—
547#103—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—41no—
552C22⋊C8—41no—
553C22⋊C8—41no—
554C22⋊C8—41no—
555C4×C8—22no—
556#95—21no—
557C24—21no—
558C24C2×D4×C7311yescharacteristic
559C24C2×D4×C7311yescharacteristic
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C2×D4×C7312yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
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—42no—
608C22×C4—42no—
609C22×C4C2×D4×C7311yescharacteristic
610C22×C4C2×D4×C7311yescharacteristic
611C22×C4C2×D4×C7311yescharacteristic
612C22×C4C2×D4×C7311yescharacteristic
613C22×C4C24×C7311yescharacteristic
614Q16—44no—
615SD16—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4C2×D4×C7312yes—
643C4⋊C4C2×D4×C7312yes—
644C4⋊C4C2×D4×C7312yes—
645C4⋊C4#41×C7312yes—
646C4⋊C4#41×C7312yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C42—24no—
659C42—24no—
660C42—81no—
661C42C2×D4×C7312yes—
662C42C2×D4×C7312yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23#135×C7312yes—
684C23C22×D4×C7311yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
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—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4#120×C7312yes—
741C2×C4#120×C7312yes—
742C2×C4C22×D4×C7311yescharacteristic
743C2×C4C22×D4×C7311yescharacteristic
744C2×C4C2×#41×C7311yescharacteristic
745C2×C4C2×#41×C7311yescharacteristic
746C2×C4H(5,𝔽2)×C7311yescharacteristic
747C2×C4H(5,𝔽2)×C7311yescharacteristic
748C8—41no—
749C8—41no—
750C8—41no—
751C8—41no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22C2×#120×C7311yescharacteristic
774C22#546×C7311yescharacteristic
775C22#546×C7311yescharacteristic
776C22C2×#135×C7311yescharacteristic
777C22#575×C7311yescharacteristic
778C22#577×C7311yescharacteristic
779C22#578×C7311yescharacteristic
780C4—22no—
781C4—22no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—42no—
790C4—81no—
791C4#532×C7311yescharacteristic
792C4#535×C7311yescharacteristic
793C4#550×C7311yescharacteristic
794C4#550×C7311yescharacteristic
795C2—42no—
796C2—81no—
797C2—161no—
798C2C73×#243111yescharacteristic
799C2C73×#300211yescharacteristic
800C2C73×#301311yescharacteristic
801C2C73×#329611yescharacteristic
802C2C73×#330011yescharacteristic
803C2C73×#332311yescharacteristic
804C2C73×#332711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#552×C73C2semidirect
2. C2×#488×C73C2semidirect
3. C2×#464×C73C2semidirect
5. C73×#2001C2semidirect
6. C73×#2001C2semidirect
7. C73×#2000C2semidirect
8. C73×#2000C2semidirect
9. C73×#1989C2semidirect
10. C73×#1954C2semidirect
11. C73×#1875C2semidirect
12. C73×#1874C2semidirect
13. C73×#1873C2semidirect
14. C73×#1872C2semidirect
15. C4×#103×C73C2semidirect
85. #125×C73D4semidirect
102. C4×Q8×C73D4semidirect
392. #25576C73direct (N × H)
403. C2×#552C2×C73semidirect
404. C2×#488C2×C73semidirect
405. C2×#464C2×C73semidirect
407. #2001C2×C73semidirect
408. #2001C2×C73semidirect
409. #2000C2×C73semidirect
410. #2000C2×C73semidirect
411. #1989C2×C73semidirect
412. #1954C2×C73semidirect
413. #1875C2×C73semidirect
414. #1874C2×C73semidirect
415. #1873C2×C73semidirect
416. #1872C2×C73semidirect
417. C4×#103C2×C73semidirect
418. C73#25576direct (N × H)
488. #125D4×C73semidirect
505. C4×Q8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C732
C2×#488×C732
C2×#464×C732
C73×#25402
C73×#20012
C73×#20002
C73×#19892
C73×#19542
C73×#18752
C73×#18742
C73×#18732
C73×#18722
C4×#103×C732
#2557673