Finite Group Databasebeta

← C2×C73×#3532 #32972122

Subgroups — C2×C73×#3532 #32972122

Order 18688.

9542 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3532C2132yesmaximal, direct product factor
2C2×H(3,𝔽4)×C73C211yesmaximal, characteristic, complemented
3C2×#560×C73C213yesmaximal, complemented
4C2×#551×C73C213yesmaximal, complemented
5C2×#546×C73C216yesmaximal, complemented
6C2×D42×C73C213yesmaximal, complemented
7C2×#538×C73C216yesmaximal, complemented
8C2×#535×C73C213yesmaximal, complemented
9C2×#534×C73C213yesmaximal, complemented
10C22×#120×C73C213yesmaximal, complemented
11C26×C73C2211yescharacteristic, complemented
12C22×#41×C73C2213yescomplemented
13C23×D4×C73C2216yescomplemented
14C23×D4×C73C2213yescomplemented
15C23×D4×C73C2213yescomplemented
16H(3,𝔽4)×C73C22116yescomplemented
17#560×C73C22148yescomplemented
18#551×C73C22148yescomplemented
19#546×C73C22196yescomplemented
20D42×C73C22148yescomplemented
21#538×C73C22196yescomplemented
22#535×C73C22148yescomplemented
23#534×C73C22148yescomplemented
24C2×#127×C73C2213yescomplemented
25C2×#127×C73C2211yescharacteristic, complemented
26C2×#126×C73C2216yescomplemented
27C2×#126×C73C2212yescomplemented
28C2×#124×C73C2216yescomplemented
29C2×#124×C73C2213yescomplemented
30C2×#124×C73C2213yescomplemented
31C2×#123×C73C2216yescomplemented
32C2×#123×C73C2213yescomplemented
33C2×#123×C73C2213yescomplemented
34C2×#123×C73C2216yescomplemented
35C2×C22⋊Q8×C73C2216yescomplemented
36C2×#121×C73C2216yescomplemented
37C2×#121×C73C2216yescomplemented
38C2×#121×C73C2216yescomplemented
39C2×#121×C73C2216yescomplemented
40C2×#121×C73C2216yescomplemented
41C2×#120×C73C2213yes—
42C2×#120×C73C2213yescomplemented
43C2×#120×C73C2213yescomplemented
44C2×#120×C73C2213yescomplemented
45C2×#120×C73C2216yescomplemented
46C2×#120×C73C2216yescomplemented
47C2×#120×C73C2216yescomplemented
48C2×#120×C73C22148yescomplemented
49C2×#120×C73C2213yescomplemented
50C2×#120×C73C2211yescharacteristic, complemented
51C2×C4×D4×C73C2216yescomplemented
52C2×C4×D4×C73C2216yescomplemented
53C2×#117×C73C2213yescomplemented
54C22×C22⋊C4×C73C2216yescomplemented
55C22×C22⋊C4×C73C2213yescomplemented
56C22×C22⋊C4×C73C2213yescomplemented
57C25×C73—412no—
58C25×C73C2313yes—
59C25×C73C2313yes—
60C25×C73C2313yes—
61C25×C73C2311yescharacteristic
62C25×C73C2318yescomplemented
63C25×C73C2311yescharacteristic, complemented
64C2×#41×C73—412no—
65C2×#41×C73C23124yescomplemented
66C22×Q8×C73C2313yescomplemented
67C22×D4×C73—412no—
68C22×D4×C73—424no—
69C22×D4×C73—412no—
70C22×D4×C73C2316yes—
71C22×D4×C73C2316yes—
72C22×D4×C73C2313yes—
73C22×D4×C73C2313yes—
74C22×D4×C73C2316yes—
75C22×D4×C73C2313yes—
76C22×D4×C73C2316yes—
77C22×D4×C73C2313yes—
78C22×D4×C73C23124yescomplemented
79C22×D4×C73C23148yescomplemented
80C22×D4×C73C2313yescomplemented
81C22×D4×C73C2316yescomplemented
82C22×D4×C73C23124yescomplemented
83C23×C4×C73C2313yes—
84C23×C4×C73C2316yes—
85C23×C4×C73C2316yescomplemented
86C23×C4×C73C2313yescomplemented
87#127×C73C2318yescomplemented
88#127×C73C23124yescomplemented
89#126×C73C23116yescomplemented
90#126×C73C23148yescomplemented
91#124×C73C23124yescomplemented
92#124×C73C23124yescomplemented
93#124×C73C23148yescomplemented
94#123×C73C23124yescomplemented
95#123×C73C23124yescomplemented
96#123×C73C23148yescomplemented
97#123×C73C23148yescomplemented
98C22⋊Q8×C73C23148yescomplemented
99#121×C73C23148yescomplemented
100#121×C73C23148yescomplemented
101#121×C73C23148yescomplemented
102#121×C73C23148yescomplemented
103#121×C73C23148yescomplemented
104#120×C73C23124yes—
105#120×C73C23148yescomplemented
106#120×C73C23148yescomplemented
107#120×C73C23124yescomplemented
108#120×C73C23124yescomplemented
109#120×C73C23124yescomplemented
110#120×C73C23148yescomplemented
111#120×C73C2318yescomplemented
112#120×C73C23124yescomplemented
113C4×D4×C73C23148yescomplemented
114C4×D4×C73C23148yescomplemented
115#117×C73C23124yescomplemented
116C2×C4⋊C4×C73C2316yescomplemented
117C2×C4⋊C4×C73C2316yescomplemented
118C2×C4⋊C4×C73C2316yescomplemented
119C2×C22⋊C4×C73C2316yes—
120C2×C22⋊C4×C73C2316yes—
121C2×C22⋊C4×C73C2313yes—
122C2×C22⋊C4×C73C2316yes—
123C2×C22⋊C4×C73C2316yes—
124C2×C22⋊C4×C73C2316yes—
125C2×C22⋊C4×C73C2313yes—
126C2×C22⋊C4×C73C23124yescomplemented
127C2×C22⋊C4×C73C23148yescomplemented
128C2×C22⋊C4×C73C23124yescomplemented
129C2×C22⋊C4×C73C2313yescomplemented
130C2×C22⋊C4×C73C2313yescomplemented
131C2×C22⋊C4×C73C2316yescomplemented
132C2×C22⋊C4×C73C2316yescomplemented
133C2×C42×C73C2311yescharacteristic, complemented
134C2×C42×C73C2313yescomplemented
135C2×C42×C73C2312yescomplemented
136C24×C73—224no—
137C24×C73—212no—
138C24×C73—212no—
139C24×C73—46no—
140C24×C73—412no—
141C24×C73—46no—
142C24×C73—448no—
143C24×C73—412no—
144C24×C73—46no—
145C24×C73—464no—
146C24×C73C2413yes—
147C24×C73C2411yescharacteristic
148C24×C73C2413yes—
149C24×C73C2413yes—
150C24×C73C24112yes—
151C24×C73C2413yes—
152C24×C73C24112yes—
153C24×C73C24112yes—
154C24×C73C2414yes—
155C24×C73C2414yescomplemented
156#41×C73—448no—
157C2×Q8×C73—46no—
158C2×Q8×C73C24112yescomplemented
159C2×D4×C73—224no—
160C2×D4×C73—224no—
161C2×D4×C73—46no—
162C2×D4×C73—46no—
163C2×D4×C73—46no—
164C2×D4×C73—46no—
165C2×D4×C73—412no—
166C2×D4×C73—412no—
167C2×D4×C73—448no—
168C2×D4×C73—412no—
169C2×D4×C73—46no—
170C2×D4×C73—496no—
171C2×D4×C73—448no—
172C2×D4×C73C24124yes—
173C2×D4×C73C24124yes—
174C2×D4×C73C24112yes—
175C2×D4×C73C24112yes—
176C2×D4×C73C24124yes—
177C2×D4×C73C24112yes—
178C2×D4×C73C24124yes—
179C2×D4×C73C24112yes—
180C2×D4×C73C24112yescomplemented
181C2×D4×C73C24124yescomplemented
182C22×C4×C73—212no—
183C22×C4×C73—412no—
184C22×C4×C73—46no—
185C22×C4×C73—412no—
186C22×C4×C73C24112yes—
187C22×C4×C73C2413yes—
188C22×C4×C73C2416yes—
189C22×C4×C73C2416yes—
190C22×C4×C73C2413yes—
191C22×C4×C73C24124yes—
192C22×C4×C73C24124yescomplemented
193C22×C4×C73C24112yescomplemented
194C4⋊C4×C73C24124yescomplemented
195C4⋊C4×C73C24124yescomplemented
196C4⋊C4×C73C24124yescomplemented
197C22⋊C4×C73C24124yes—
198C22⋊C4×C73C24124yes—
199C22⋊C4×C73C24112yes—
200C22⋊C4×C73C24124yes—
201C22⋊C4×C73C24124yes—
202C22⋊C4×C73C24124yes—
203C22⋊C4×C73C24112yes—
204C22⋊C4×C73C24112yescomplemented
205C22⋊C4×C73C24112yescomplemented
206C22⋊C4×C73C24124yescomplemented
207C22⋊C4×C73C24124yescomplemented
208C42×C73C2414yescomplemented
209C42×C73C24112yescomplemented
210C42×C73C2418yescomplemented
211C23×C73—212no—
212C23×C73—212no—
213C23×C73—26no—
214C23×C73—212no—
215C23×C73—26no—
216C23×C73—248no—
217C23×C73—224no—
218C23×C73—26no—
219C23×C73—212no—
220C23×C73—26no—
221C23×C73—224no—
222C23×C73—412no—
223C23×C73—424no—
224C23×C73—412no—
225C23×C73—424no—
226C23×C73—412no—
227C23×C73—448no—
228C23×C73—448no—
229C23×C73—4128no—
230C23×C73—416no—
231C23×C73—824no—
232C23×C73—88no—
233C23×C73H(5,𝔽2)112yes—
234C23×C73C2516yes—
235C23×C73C2512yes—
236C23×C73C2516yes—
237C23×C73C2516yes—
238C23×C73C2516yes—
239C23×C73C2511yescharacteristic
240Q8×C73—412no—
241D4×C73—248no—
242D4×C73—248no—
243D4×C73—412no—
244D4×C73—412no—
245D4×C73—412no—
246D4×C73—412no—
247D4×C73—424no—
248D4×C73—424no—
249D4×C73—424no—
250D4×C73—412no—
251C2×C4×C73—26no—
252C2×C4×C73—26no—
253C2×C4×C73—224no—
254C2×C4×C73—212no—
255C2×C4×C73—212no—
256C2×C4×C73—424no—
257C2×C4×C73—412no—
258C2×C4×C73—424no—
259C2×C4×C73C2516yes—
260C2×C4×C73C25112yes—
261C2×C4×C73C25112yes—
262C2×C4×C73C2516yes—
263C22×C73—212no—
264C22×C73—224no—
265C22×C73—212no—
266C22×C73—26no—
267C22×C73—212no—
268C22×C73—26no—
269C22×C73—26no—
270C22×C73—212no—
271C22×C73—26no—
272C22×C73—448no—
273C22×C73—448no—
274C22×C73—416no—
275C22×C73—412no—
276C22×C73—44no—
277C22×C73—412no—
278C22×C73—412no—
279C22×C73—824no—
280C22×C73—88no—
281C22×C73C2×H(5,𝔽2)112yes—
282C22×C73C2×H(5,𝔽2)16yes—
283C22×C73C2611yescharacteristic
284C4×C73—26no—
285C4×C73—26no—
286C4×C73—212no—
287C4×C73—212no—
288C2×#3532C7311yesmaximal, characteristic, direct product factor, Sylow
289C2×C73—212no—
290C2×C73—46no—
291C2×C73—42no—
292C2×C73—46no—
293C2×C73—46no—
294C2×C73#353214yesdirect product factor
295C2×C73C22×H(5,𝔽2)13yes—
296#3532C2×C73132yesdirect product factor
297C2×H(3,𝔽4)C2×C7311yescharacteristic, complemented
298C2×#560C2×C7313yescomplemented
299C2×#551C2×C7313yescomplemented
300C2×#546C2×C7316yescomplemented
301C2×D42C2×C7313yescomplemented
302C2×#538C2×C7316yescomplemented
303C2×#535C2×C7313yescomplemented
304C2×#534C2×C7313yescomplemented
305C22×#120C2×C7313yescomplemented
306C73C2×#353211yescharacteristic, direct product factor, Sylow
307C26C22×C7311yescharacteristic, complemented
308C22×#41C22×C7313yescomplemented
309C23×D4C22×C7313yescomplemented
310C23×D4C22×C7316yescomplemented
311C23×D4C22×C7313yescomplemented
312H(3,𝔽4)C22×C73116yescomplemented
313#560C22×C73148yescomplemented
314#551C22×C73148yescomplemented
315#546C22×C73196yescomplemented
316D42C22×C73148yescomplemented
317#538C22×C73196yescomplemented
318#535C22×C73148yescomplemented
319#534C22×C73148yescomplemented
320C2×#127C22×C7311yescharacteristic, complemented
321C2×#127C22×C7313yescomplemented
322C2×#126C22×C7312yescomplemented
323C2×#126C22×C7316yescomplemented
324C2×#124C22×C7313yescomplemented
325C2×#124C22×C7313yescomplemented
326C2×#124C22×C7316yescomplemented
327C2×#123C22×C7313yescomplemented
328C2×#123C22×C7313yescomplemented
329C2×#123C22×C7316yescomplemented
330C2×#123C22×C7316yescomplemented
331C2×C22⋊Q8C22×C7316yescomplemented
332C2×#121C22×C7316yescomplemented
333C2×#121C22×C7316yescomplemented
334C2×#121C22×C7316yescomplemented
335C2×#121C22×C7316yescomplemented
336C2×#121C22×C7316yescomplemented
337C2×#120C22×C7313yes—
338C2×#120C22×C7316yescomplemented
339C2×#120C22×C7316yescomplemented
340C2×#120C22×C7313yescomplemented
341C2×#120C22×C7313yescomplemented
342C2×#120C22×C7313yescomplemented
343C2×#120C22×C7316yescomplemented
344C2×#120C22×C73148yescomplemented
345C2×#120C22×C7311yescharacteristic, complemented
346C2×#120C22×C7313yescomplemented
347C2×C4×D4C22×C7316yescomplemented
348C2×C4×D4C22×C7316yescomplemented
349C2×#117C22×C7313yescomplemented
350C22×C22⋊C4C22×C7313yescomplemented
351C22×C22⋊C4C22×C7316yescomplemented
352C22×C22⋊C4C22×C7313yescomplemented
353C25—412no—
354C25C23×C7313yes—
355C25C23×C7313yes—
356C25C23×C7313yes—
357C25C23×C7311yescharacteristic
358C25C23×C7318yescomplemented
359C25C23×C7311yescharacteristic, complemented
360C2×#41—412no—
361C2×#41C23×C73124yescomplemented
362C22×Q8C23×C7313yescomplemented
363C22×D4—412no—
364C22×D4—424no—
365C22×D4—412no—
366C22×D4C23×C7316yes—
367C22×D4C23×C7316yes—
368C22×D4C23×C7313yes—
369C22×D4C23×C7313yes—
370C22×D4C23×C7316yes—
371C22×D4C23×C7313yes—
372C22×D4C23×C7316yes—
373C22×D4C23×C7313yes—
374C22×D4C23×C73124yescomplemented
375C22×D4C23×C73148yescomplemented
376C22×D4C23×C7313yescomplemented
377C22×D4C23×C7316yescomplemented
378C22×D4C23×C73124yescomplemented
379C23×C4C23×C7313yes—
380C23×C4C23×C7316yes—
381C23×C4C23×C7316yescomplemented
382C23×C4C23×C7313yescomplemented
383#127C23×C7318yescomplemented
384#127C23×C73124yescomplemented
385#126C23×C73116yescomplemented
386#126C23×C73148yescomplemented
387#124C23×C73124yescomplemented
388#124C23×C73124yescomplemented
389#124C23×C73148yescomplemented
390#123C23×C73124yescomplemented
391#123C23×C73124yescomplemented
392#123C23×C73148yescomplemented
393#123C23×C73148yescomplemented
394C22⋊Q8C23×C73148yescomplemented
395#121C23×C73148yescomplemented
396#121C23×C73148yescomplemented
397#121C23×C73148yescomplemented
398#121C23×C73148yescomplemented
399#121C23×C73148yescomplemented
400#120C23×C73124yes—
401#120C23×C73148yescomplemented
402#120C23×C73148yescomplemented
403#120C23×C73124yescomplemented
404#120C23×C73124yescomplemented
405#120C23×C73124yescomplemented
406#120C23×C73148yescomplemented
407#120C23×C7318yescomplemented
408#120C23×C73124yescomplemented
409C4×D4C23×C73148yescomplemented
410C4×D4C23×C73148yescomplemented
411#117C23×C73124yescomplemented
412C2×C4⋊C4C23×C7316yescomplemented
413C2×C4⋊C4C23×C7316yescomplemented
414C2×C4⋊C4C23×C7316yescomplemented
415C2×C22⋊C4C23×C7316yes—
416C2×C22⋊C4C23×C7316yes—
417C2×C22⋊C4C23×C7313yes—
418C2×C22⋊C4C23×C7316yes—
419C2×C22⋊C4C23×C7316yes—
420C2×C22⋊C4C23×C7316yes—
421C2×C22⋊C4C23×C7313yes—
422C2×C22⋊C4C23×C73124yescomplemented
423C2×C22⋊C4C23×C73148yescomplemented
424C2×C22⋊C4C23×C73124yescomplemented
425C2×C22⋊C4C23×C7313yescomplemented
426C2×C22⋊C4C23×C7313yescomplemented
427C2×C22⋊C4C23×C7316yescomplemented
428C2×C22⋊C4C23×C7316yescomplemented
429C2×C42C23×C7311yescharacteristic, complemented
430C2×C42C23×C7313yescomplemented
431C2×C42C23×C7312yescomplemented
432C24—224no—
433C24—212no—
434C24—212no—
435C24—46no—
436C24—412no—
437C24—46no—
438C24—448no—
439C24—412no—
440C24—46no—
441C24—464no—
442C24C24×C7313yes—
443C24C24×C7311yescharacteristic
444C24C24×C7313yes—
445C24C24×C7313yes—
446C24C24×C73112yes—
447C24C24×C7313yes—
448C24C24×C73112yes—
449C24C24×C73112yes—
450C24C24×C7314yes—
451C24C24×C7314yescomplemented
452#41—448no—
453C2×Q8—46no—
454C2×Q8C24×C73112yescomplemented
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—46no—
458C2×D4—46no—
459C2×D4—46no—
460C2×D4—46no—
461C2×D4—412no—
462C2×D4—412no—
463C2×D4—448no—
464C2×D4—412no—
465C2×D4—46no—
466C2×D4—496no—
467C2×D4—448no—
468C2×D4C24×C73124yes—
469C2×D4C24×C73124yes—
470C2×D4C24×C73112yes—
471C2×D4C24×C73112yes—
472C2×D4C24×C73124yes—
473C2×D4C24×C73112yes—
474C2×D4C24×C73124yes—
475C2×D4C24×C73112yes—
476C2×D4C24×C73112yescomplemented
477C2×D4C24×C73124yescomplemented
478C22×C4—212no—
479C22×C4—412no—
480C22×C4—46no—
481C22×C4—412no—
482C22×C4C24×C7313yes—
483C22×C4C24×C7316yes—
484C22×C4C24×C7316yes—
485C22×C4C24×C7313yes—
486C22×C4C24×C73112yes—
487C22×C4C24×C73124yes—
488C22×C4C24×C73124yescomplemented
489C22×C4C24×C73112yescomplemented
490C4⋊C4C24×C73124yescomplemented
491C4⋊C4C24×C73124yescomplemented
492C4⋊C4C24×C73124yescomplemented
493C22⋊C4C24×C73124yes—
494C22⋊C4C24×C73124yes—
495C22⋊C4C24×C73112yes—
496C22⋊C4C24×C73124yes—
497C22⋊C4C24×C73124yes—
498C22⋊C4C24×C73124yes—
499C22⋊C4C24×C73112yes—
500C22⋊C4C24×C73112yescomplemented
501C22⋊C4C24×C73112yescomplemented
502C22⋊C4C24×C73124yescomplemented
503C22⋊C4C24×C73124yescomplemented
504C42C24×C7314yescomplemented
505C42C24×C73112yescomplemented
506C42C24×C7318yescomplemented
507C23—212no—
508C23—212no—
509C23—26no—
510C23—212no—
511C23—26no—
512C23—248no—
513C23—224no—
514C23—26no—
515C23—212no—
516C23—26no—
517C23—224no—
518C23—412no—
519C23—424no—
520C23—412no—
521C23—424no—
522C23—412no—
523C23—448no—
524C23—448no—
525C23—4128no—
526C23—416no—
527C23—824no—
528C23—88no—
529C23H(5,𝔽2)×C73112yes—
530C23C25×C7316yes—
531C23C25×C7312yes—
532C23C25×C7316yes—
533C23C25×C7316yes—
534C23C25×C7316yes—
535C23C25×C7311yescharacteristic
536Q8—412no—
537D4—248no—
538D4—248no—
539D4—412no—
540D4—412no—
541D4—412no—
542D4—412no—
543D4—424no—
544D4—424no—
545D4—424no—
546D4—412no—
547C2×C4—26no—
548C2×C4—26no—
549C2×C4—224no—
550C2×C4—212no—
551C2×C4—212no—
552C2×C4—424no—
553C2×C4—412no—
554C2×C4—424no—
555C2×C4C25×C7316yes—
556C2×C4C25×C73112yes—
557C2×C4C25×C73112yes—
558C2×C4C25×C7316yes—
559C22—224no—
560C22—212no—
561C22—212no—
562C22—26no—
563C22—212no—
564C22—26no—
565C22—26no—
566C22—212no—
567C22—26no—
568C22—448no—
569C22—448no—
570C22—416no—
571C22—412no—
572C22—44no—
573C22—412no—
574C22—412no—
575C22—824no—
576C22—88no—
577C22C2×H(5,𝔽2)×C73112yes—
578C22C2×H(5,𝔽2)×C7316yes—
579C22C26×C7311yescharacteristic
580C4—26no—
581C4—26no—
582C4—212no—
583C4—212no—
584C2—212no—
585C2—46no—
586C2—42no—
587C2—46no—
588C2—46no—
589C2C73×#353214yesdirect product factor
590C2C22×H(5,𝔽2)×C7313yes—
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC22C26×C73
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3532C2direct (N × H)
2. C2×H(3,𝔽4)×C73C2semidirect
3. C2×#560×C73C2semidirect
4. C2×#551×C73C2semidirect
5. C2×#546×C73C2semidirect
6. C2×D42×C73C2semidirect
7. C2×#538×C73C2semidirect
8. C2×#535×C73C2semidirect
9. C2×#534×C73C2semidirect
10. C22×#120×C73C2semidirect
11. C26×C73C22semidirect
12. C22×#41×C73C22semidirect
13. C23×D4×C73C22semidirect
14. C23×D4×C73C22semidirect
15. C23×D4×C73C22semidirect
16. H(3,𝔽4)×C73C22semidirect
17. #560×C73C22semidirect
18. #551×C73C22semidirect
19. #546×C73C22semidirect
20. D42×C73C22semidirect
21. #538×C73C22semidirect
22. #535×C73C22semidirect
23. #534×C73C22semidirect
24. C2×#127×C73C22semidirect
25. C2×#127×C73C22semidirect
26. C2×#126×C73C22semidirect
27. C2×#126×C73C22semidirect
28. C2×#124×C73C22semidirect
29. C2×#124×C73C22semidirect
30. C2×#124×C73C22semidirect
31. C2×#123×C73C22semidirect
32. C2×#123×C73C22semidirect
33. C2×#123×C73C22semidirect
34. C2×#123×C73C22semidirect
35. C2×C22⋊Q8×C73C22semidirect
36. C2×#121×C73C22semidirect
37. C2×#121×C73C22semidirect
38. C2×#121×C73C22semidirect
39. C2×#121×C73C22semidirect
40. C2×#121×C73C22semidirect
42. C2×#120×C73C22semidirect
43. C2×#120×C73C22semidirect
44. C2×#120×C73C22semidirect
45. C2×#120×C73C22semidirect
46. C2×#120×C73C22semidirect
47. C2×#120×C73C22semidirect
48. C2×#120×C73C22semidirect
49. C2×#120×C73C22semidirect
50. C2×#120×C73C22semidirect
51. C2×C4×D4×C73C22semidirect
52. C2×C4×D4×C73C22semidirect
53. C2×#117×C73C22semidirect
54. C22×C22⋊C4×C73C22semidirect
55. C22×C22⋊C4×C73C22semidirect
56. C22×C22⋊C4×C73C22semidirect
62. C25×C73C23semidirect
63. C25×C73C23semidirect
65. C2×#41×C73C23semidirect
66. C22×Q8×C73C23semidirect
78. C22×D4×C73C23semidirect
79. C22×D4×C73C23semidirect
80. C22×D4×C73C23semidirect
81. C22×D4×C73C23semidirect
82. C22×D4×C73C23semidirect
85. C23×C4×C73C23semidirect
86. C23×C4×C73C23semidirect
87. #127×C73C23semidirect
88. #127×C73C23semidirect
89. #126×C73C23semidirect
90. #126×C73C23semidirect
91. #124×C73C23semidirect
92. #124×C73C23semidirect
93. #124×C73C23semidirect
94. #123×C73C23semidirect
95. #123×C73C23semidirect
96. #123×C73C23semidirect
97. #123×C73C23semidirect
98. C22⋊Q8×C73C23semidirect
99. #121×C73C23semidirect
100. #121×C73C23semidirect
101. #121×C73C23semidirect
102. #121×C73C23semidirect
103. #121×C73C23semidirect
105. #120×C73C23semidirect
106. #120×C73C23semidirect
107. #120×C73C23semidirect
108. #120×C73C23semidirect
109. #120×C73C23semidirect
110. #120×C73C23semidirect
111. #120×C73C23semidirect
112. #120×C73C23semidirect
113. C4×D4×C73C23semidirect
114. C4×D4×C73C23semidirect
115. #117×C73C23semidirect
116. C2×C4⋊C4×C73C23semidirect
117. C2×C4⋊C4×C73C23semidirect
118. C2×C4⋊C4×C73C23semidirect
126. C2×C22⋊C4×C73C23semidirect
127. C2×C22⋊C4×C73C23semidirect
128. C2×C22⋊C4×C73C23semidirect
129. C2×C22⋊C4×C73C23semidirect
130. C2×C22⋊C4×C73C23semidirect
131. C2×C22⋊C4×C73C23semidirect
132. C2×C22⋊C4×C73C23semidirect
133. C2×C42×C73C23semidirect
134. C2×C42×C73C23semidirect
135. C2×C42×C73C23semidirect
155. C24×C73C24semidirect
158. C2×Q8×C73C24semidirect
180. C2×D4×C73C24semidirect
181. C2×D4×C73C24semidirect
192. C22×C4×C73C24semidirect
193. C22×C4×C73C24semidirect
194. C4⋊C4×C73C24semidirect
195. C4⋊C4×C73C24semidirect
196. C4⋊C4×C73C24semidirect
204. C22⋊C4×C73C24semidirect
205. C22⋊C4×C73C24semidirect
206. C22⋊C4×C73C24semidirect
207. C22⋊C4×C73C24semidirect
208. C42×C73C24semidirect
209. C42×C73C24semidirect
210. C42×C73C24semidirect
288. C2×#3532C73direct (N × H)
294. C2×C73#3532direct (N × H)
296. #3532C2×C73direct (N × H)
297. C2×H(3,𝔽4)C2×C73semidirect
298. C2×#560C2×C73semidirect
299. C2×#551C2×C73semidirect
300. C2×#546C2×C73semidirect
301. C2×D42C2×C73semidirect
302. C2×#538C2×C73semidirect
303. C2×#535C2×C73semidirect
304. C2×#534C2×C73semidirect
305. C22×#120C2×C73semidirect
306. C73C2×#3532direct (N × H)
307. C26C22×C73semidirect
308. C22×#41C22×C73semidirect
309. C23×D4C22×C73semidirect
310. C23×D4C22×C73semidirect
311. C23×D4C22×C73semidirect
312. H(3,𝔽4)C22×C73semidirect
313. #560C22×C73semidirect
314. #551C22×C73semidirect
315. #546C22×C73semidirect
316. D42C22×C73semidirect
317. #538C22×C73semidirect
318. #535C22×C73semidirect
319. #534C22×C73semidirect
320. C2×#127C22×C73semidirect
321. C2×#127C22×C73semidirect
322. C2×#126C22×C73semidirect
323. C2×#126C22×C73semidirect
324. C2×#124C22×C73semidirect
325. C2×#124C22×C73semidirect
326. C2×#124C22×C73semidirect
327. C2×#123C22×C73semidirect
328. C2×#123C22×C73semidirect
329. C2×#123C22×C73semidirect
330. C2×#123C22×C73semidirect
331. C2×C22⋊Q8C22×C73semidirect
332. C2×#121C22×C73semidirect
333. C2×#121C22×C73semidirect
334. C2×#121C22×C73semidirect
335. C2×#121C22×C73semidirect
336. C2×#121C22×C73semidirect
338. C2×#120C22×C73semidirect
339. C2×#120C22×C73semidirect
340. C2×#120C22×C73semidirect
341. C2×#120C22×C73semidirect
342. C2×#120C22×C73semidirect
343. C2×#120C22×C73semidirect
344. C2×#120C22×C73semidirect
345. C2×#120C22×C73semidirect
346. C2×#120C22×C73semidirect
347. C2×C4×D4C22×C73semidirect
348. C2×C4×D4C22×C73semidirect
349. C2×#117C22×C73semidirect
350. C22×C22⋊C4C22×C73semidirect
351. C22×C22⋊C4C22×C73semidirect
352. C22×C22⋊C4C22×C73semidirect
358. C25C23×C73semidirect
359. C25C23×C73semidirect
361. C2×#41C23×C73semidirect
362. C22×Q8C23×C73semidirect
374. C22×D4C23×C73semidirect
375. C22×D4C23×C73semidirect
376. C22×D4C23×C73semidirect
377. C22×D4C23×C73semidirect
378. C22×D4C23×C73semidirect
381. C23×C4C23×C73semidirect
382. C23×C4C23×C73semidirect
383. #127C23×C73semidirect
384. #127C23×C73semidirect
385. #126C23×C73semidirect
386. #126C23×C73semidirect
387. #124C23×C73semidirect
388. #124C23×C73semidirect
389. #124C23×C73semidirect
390. #123C23×C73semidirect
391. #123C23×C73semidirect
392. #123C23×C73semidirect
393. #123C23×C73semidirect
394. C22⋊Q8C23×C73semidirect
395. #121C23×C73semidirect
396. #121C23×C73semidirect
397. #121C23×C73semidirect
398. #121C23×C73semidirect
399. #121C23×C73semidirect
401. #120C23×C73semidirect
402. #120C23×C73semidirect
403. #120C23×C73semidirect
404. #120C23×C73semidirect
405. #120C23×C73semidirect
406. #120C23×C73semidirect
407. #120C23×C73semidirect
408. #120C23×C73semidirect
409. C4×D4C23×C73semidirect
410. C4×D4C23×C73semidirect
411. #117C23×C73semidirect
412. C2×C4⋊C4C23×C73semidirect
413. C2×C4⋊C4C23×C73semidirect
414. C2×C4⋊C4C23×C73semidirect
422. C2×C22⋊C4C23×C73semidirect
423. C2×C22⋊C4C23×C73semidirect
424. C2×C22⋊C4C23×C73semidirect
425. C2×C22⋊C4C23×C73semidirect
426. C2×C22⋊C4C23×C73semidirect
427. C2×C22⋊C4C23×C73semidirect
428. C2×C22⋊C4C23×C73semidirect
429. C2×C42C23×C73semidirect
430. C2×C42C23×C73semidirect
431. C2×C42C23×C73semidirect
451. C24C24×C73semidirect
454. C2×Q8C24×C73semidirect
476. C2×D4C24×C73semidirect
477. C2×D4C24×C73semidirect
488. C22×C4C24×C73semidirect
489. C22×C4C24×C73semidirect
490. C4⋊C4C24×C73semidirect
491. C4⋊C4C24×C73semidirect
492. C4⋊C4C24×C73semidirect
500. C22⋊C4C24×C73semidirect
501. C22⋊C4C24×C73semidirect
502. C22⋊C4C24×C73semidirect
503. C22⋊C4C24×C73semidirect
504. C42C24×C73semidirect
505. C42C24×C73semidirect
506. C42C24×C73semidirect
589. C2C73×#3532direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35322
C2×H(3,𝔽4)×C732
C2×#560×C732
C2×#551×C732
C2×#546×C732
C2×D42×C732
C2×#538×C732
C2×#535×C732
C2×#534×C732
C22×#120×C732
C2×#353273