Finite Group Databasebeta

← C73×#35079 #32944483

Subgroups — C73×#35079 #32944483

Order 18688.

2098 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2857C212yesmaximal, complemented
2C73×#2851C212yesmaximal, complemented
3C73×#2667C212yesmaximal, complemented
4C73×#2665C212yesmaximal, complemented
5C73×#2569C212yesmaximal, complemented
6C73×#2549C212yesmaximal, complemented
7C73×#2442C212yesmaximal, complemented
8C73×#2441C212yesmaximal, complemented
9C73×#2440C212yesmaximal, complemented
10C73×#2439C212yesmaximal, complemented
11C73×#2437C214yesmaximal
12C73×#2329C214yesmaximal, complemented
13C73×#2280C211yesmaximal, characteristic
14C2×#380×C73C211yesmaximal, characteristic
15C2×C4×C22⋊C4×C73C211yesmaximal, characteristic
16C24×C4×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2212yescomplemented
18C2×#125×C73C2212yescomplemented
19C2×C22⋊Q8×C73C2214yes—
20C2×C22⋊Q8×C73C2214yes—
21C2×#117×C73C2212yes—
22C22×C4⋊C4×C73C2212yes—
23C22×C22⋊C4×C73C2212yes—
24C22×C22⋊C4×C73C2212yes—
25C22×C42×C73C2212yes—
26#400×C73C2214yescomplemented
27#399×C73C2214yes—
28#398×C73C2214yescomplemented
29#398×C73C2214yescomplemented
30#396×C73C2214yes—
31#396×C73C2214yes—
32#395×C73C2214yescomplemented
33#393×C73C2214yes—
34#391×C73C2214yescomplemented
35#391×C73C2214yescomplemented
36#389×C73C2212yescomplemented
37#389×C73C2212yescomplemented
38#389×C73C2212yescomplemented
39#389×C73C2212yescomplemented
40#389×C73C2214yescomplemented
41#389×C73C2214yescomplemented
42#387×C73C2214yescomplemented
43#387×C73C2214yescomplemented
44#387×C73C2214yescomplemented
45#387×C73C2214yescomplemented
46#385×C73C2214yes—
47#385×C73C2214yes—
48#385×C73C2214yes—
49#385×C73C2214yes—
50#384×C73C2212yescomplemented
51#382×C73C2212yescomplemented
52#381×C73C2212yes—
53#380×C73C2211yescharacteristic
54#380×C73C2212yes—
55#380×C73C2211yescharacteristic
56#380×C73C2214yes—
57#380×C73C2212yes—
58#380×C73C2212yes—
59#380×C73C2212yes—
60#380×C73C2211yescharacteristic
61#380×C73C2211yescharacteristic
62#380×C73C2214yes—
63#379×C73C2212yes—
64C4×C22⋊C4×C73C2212yes—
65C4×C22⋊C4×C73C2211yescharacteristic
66C4×C22⋊C4×C73C2211yescharacteristic
67C4×C22⋊C4×C73C2212yes—
68C4×C22⋊C4×C73C2211yescharacteristic
69C4×C22⋊C4×C73C2211yescharacteristic
70C4×C22⋊C4×C73C2212yes—
71C4×C22⋊C4×C73C2212yes—
72C2×#95×C73C2211yescharacteristic
73C2×#95×C73C2211yescharacteristic
74C2×#95×C73C2212yes—
75C25×C73C2311yescharacteristic
76C22×Q8×C73C2314yes—
77C23×C4×C73—44no—
78C23×C4×C73Q818yescomplemented
79C23×C4×C73C2312yes—
80C23×C4×C73C2312yes—
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2311yescharacteristic
84C23×C4×C73C2314yes—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2311yescharacteristic
88C4⋊Q8×C73—44no—
89#125×C73—44no—
90C22⋊Q8×C73—216no—
91C22⋊Q8×C73—48no—
92#117×C73—44no—
93C2×C4⋊C4×C73—44no—
94C2×C4⋊C4×C73C2312yes—
95C2×C4⋊C4×C73C2312yes—
96C2×C4⋊C4×C73C2312yes—
97C2×C4⋊C4×C73C2312yes—
98C2×C4⋊C4×C73C2314yes—
99C2×C4⋊C4×C73C2314yes—
100C2×C4⋊C4×C73C2314yes—
101C2×C4⋊C4×C73C2314yes—
102C2×C4⋊C4×C73C2314yes—
103C2×C4⋊C4×C73C2314yes—
104C2×C4⋊C4×C73C2314yes—
105C2×C4⋊C4×C73C2314yes—
106C2×C4⋊C4×C73C2314yes—
107C2×C4⋊C4×C73C2314yes—
108C2×C22⋊C4×C73—28no—
109C2×C22⋊C4×C73—44no—
110C2×C22⋊C4×C73C2312yes—
111C2×C22⋊C4×C73C2312yes—
112C2×C22⋊C4×C73C2312yes—
113C2×C22⋊C4×C73C2312yes—
114C2×C22⋊C4×C73C2314yes—
115C2×C22⋊C4×C73C2312yes—
116C2×C22⋊C4×C73C2314yes—
117C2×C22⋊C4×C73C2314yes—
118C2×C22⋊C4×C73C2312yes—
119C2×C22⋊C4×C73C2312yes—
120C2×C22⋊C4×C73C2312yes—
121C2×C42×C73—44no—
122C2×C42×C73C2312yes—
123C2×C42×C73C2312yes—
124C2×C42×C73C2312yes—
125C2×C42×C73C2314yes—
126C2×C42×C73C2312yes—
127#95×C73C2312yes—
128#95×C73C2312yes—
129#95×C73C2311yescharacteristic
130#95×C73C2311yescharacteristic
131#95×C73C2311yescharacteristic
132#95×C73C2311yescharacteristic
133#95×C73C2312yes—
134#95×C73C2312yes—
135#95×C73C2314yes—
136#95×C73C2312yes—
137#95×C73C2314yes—
138#95×C73C2312yes—
139#95×C73C2314yes—
140#95×C73C2314yes—
141#95×C73C2314yes—
142#95×C73C2314yes—
143#95×C73C2314yes—
144#95×C73C2314yes—
145C24×C73—24no—
146C24×C73—22no—
147C24×C73—22no—
148C24×C73—42no—
149C24×C73C2×Q814yes—
150C24×C73C2411yescharacteristic
151C24×C73C2411yescharacteristic
152C24×C73C2411yescharacteristic
153C2×Q8×C73—28no—
154C2×Q8×C73—44no—
155C2×Q8×C73—44no—
156C22×C4×C73—24no—
157C22×C4×C73—24no—
158C22×C4×C73—24no—
159C22×C4×C73—24no—
160C22×C4×C73—24no—
161C22×C4×C73—28no—
162C22×C4×C73—24no—
163C22×C4×C73—24no—
164C22×C4×C73—416no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—44no—
171C22×C4×C73—44no—
172C22×C4×C73C2×Q814yes—
173C22×C4×C73C2×Q814yes—
174C22×C4×C73C2×Q814yes—
175C22×C4×C73C2×Q814yes—
176C22×C4×C73C2×Q814yes—
177C22×C4×C73C2×Q814yes—
178C22×C4×C73C2412yes—
179C22×C4×C73C2414yes—
180C22×C4×C73C2414yes—
181C22×C4×C73C2412yes—
182C22×C4×C73C2414yes—
183C22×C4×C73C2414yes—
184C22×C4×C73C2411yescharacteristic
185C22×C4×C73C2411yescharacteristic
186C22×C4×C73C2411yescharacteristic
187C22×C4×C73C2412yes—
188C22×C4×C73C2412yes—
189C22×C4×C73C2411yescharacteristic
190C4⋊C4×C73—28no—
191C4⋊C4×C73—28no—
192C4⋊C4×C73—28no—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—24no—
195C4⋊C4×C73—24no—
196C4⋊C4×C73—24no—
197C4⋊C4×C73—44no—
198C4⋊C4×C73—44no—
199C4⋊C4×C73—44no—
200C4⋊C4×C73—44no—
201C4⋊C4×C73—44no—
202C4⋊C4×C73—44no—
203C4⋊C4×C73—44no—
204C22⋊C4×C73—24no—
205C22⋊C4×C73—28no—
206C22⋊C4×C73—28no—
207C22⋊C4×C73—24no—
208C22⋊C4×C73—24no—
209C22⋊C4×C73—24no—
210C22⋊C4×C73—24no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—44no—
214C22⋊C4×C73#4118yes—
215C42×C73—24no—
216C42×C73—24no—
217C42×C73—42no—
218C42×C73—42no—
219C42×C73—44no—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—22no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—28no—
226C23×C73—28no—
227C23×C73—22no—
228C23×C73—21no—
229C23×C73—22no—
230C23×C73—21no—
231C23×C73—44no—
232C23×C73—48no—
233C23×C73—48no—
234C23×C73C22×Q812yes—
235C23×C73C22×Q812yes—
236C23×C73C22×Q812yes—
237C23×C73C2×#4114yes—
238C23×C73H(5,𝔽2)12yes—
239C23×C732−1+412yes—
240C23×C73C2511yescharacteristic
241Q8×C73—88no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—28no—
250C2×C4×C73—28no—
251C2×C4×C73—28no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—24no—
255C2×C4×C73—24no—
256C2×C4×C73—24no—
257C2×C4×C73—24no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—24no—
261C2×C4×C73—24no—
262C2×C4×C73—24no—
263C2×C4×C73—24no—
264C2×C4×C73—24no—
265C2×C4×C73—24no—
266C2×C4×C73—24no—
267C2×C4×C73—22no—
268C2×C4×C73—24no—
269C2×C4×C73—22no—
270C2×C4×C73—44no—
271C2×C4×C73—44no—
272C2×C4×C73—44no—
273C2×C4×C73—48no—
274C2×C4×C73—48no—
275C2×C4×C73—88no—
276C2×C4×C73C22×Q812yes—
277C2×C4×C73C22×Q812yes—
278C2×C4×C73C22×Q812yes—
279C2×C4×C73C22×Q812yes—
280C2×C4×C73C2×#4114yes—
281C2×C4×C73C2×#4114yes—
282C2×C4×C73H(5,𝔽2)14yes—
283C22×C73—22no—
284C22×C73—22no—
285C22×C73—22no—
286C22×C73—22no—
287C22×C73—24no—
288C22×C73—24no—
289C22×C73—24no—
290C22×C73—24no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—416no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73#53314yes—
298C22×C73#54414yes—
299C22×C73C23×Q811yescharacteristic
300C22×C73C22×#4112yes—
301C22×C73C2×H(5,𝔽2)12yes—
302C22×C73C2×H(5,𝔽2)11yescharacteristic
303C22×C73C2×2−1+411yescharacteristic
304C4×C73—22no—
305C4×C73—22no—
306C4×C73—22no—
307C4×C73—24no—
308C4×C73—24no—
309C4×C73—42no—
310C4×C73—44no—
311C4×C73—44no—
312C4×C73—44no—
313C4×C73—44no—
314C4×C73—42no—
315C4×C73#54314yes—
316#35079C7311yesmaximal, characteristic, direct product factor, Sylow
317C2×C73—24no—
318C2×C73—24no—
319C2×C73—42no—
320C2×C73C2×#53311yescharacteristic
321C2×C73C2×#54311yescharacteristic
322C2×C73C2×#54411yescharacteristic
323C2×C73#351912yes—
324C2×C73#352012yes—
325#2857C2×C7312yescomplemented
326#2851C2×C7312yescomplemented
327#2667C2×C7312yescomplemented
328#2665C2×C7312yescomplemented
329#2569C2×C7312yescomplemented
330#2549C2×C7312yescomplemented
331#2442C2×C7312yescomplemented
332#2441C2×C7312yescomplemented
333#2440C2×C7312yescomplemented
334#2439C2×C7312yescomplemented
335#2437C2×C7314yes—
336#2329C2×C7314yescomplemented
337#2280C2×C7311yescharacteristic
338C2×#380C2×C7311yescharacteristic
339C2×C4×C22⋊C4C2×C7311yescharacteristic
340C73#3507911yescharacteristic, direct product factor, Sylow
341C24×C4C22×C7311yescharacteristic
342C2×C4⋊Q8C22×C7312yescomplemented
343C2×#125C22×C7312yescomplemented
344C2×C22⋊Q8C22×C7314yes—
345C2×C22⋊Q8C22×C7314yes—
346C2×#117C22×C7312yes—
347C22×C4⋊C4C22×C7312yes—
348C22×C22⋊C4C22×C7312yes—
349C22×C22⋊C4C22×C7312yes—
350C22×C42C22×C7312yes—
351#400C22×C7314yescomplemented
352#399C22×C7314yes—
353#398C22×C7314yescomplemented
354#398C22×C7314yescomplemented
355#396C22×C7314yes—
356#396C22×C7314yes—
357#395C22×C7314yescomplemented
358#393C22×C7314yes—
359#391C22×C7314yescomplemented
360#391C22×C7314yescomplemented
361#389C22×C7314yescomplemented
362#389C22×C7314yescomplemented
363#389C22×C7312yescomplemented
364#389C22×C7312yescomplemented
365#389C22×C7312yescomplemented
366#389C22×C7312yescomplemented
367#387C22×C7314yescomplemented
368#387C22×C7314yescomplemented
369#387C22×C7314yescomplemented
370#387C22×C7314yescomplemented
371#385C22×C7314yes—
372#385C22×C7314yes—
373#385C22×C7314yes—
374#385C22×C7314yes—
375#384C22×C7312yescomplemented
376#382C22×C7312yescomplemented
377#381C22×C7312yes—
378#380C22×C7314yes—
379#380C22×C7312yes—
380#380C22×C7314yes—
381#380C22×C7311yescharacteristic
382#380C22×C7312yes—
383#380C22×C7311yescharacteristic
384#380C22×C7312yes—
385#380C22×C7311yescharacteristic
386#380C22×C7312yes—
387#380C22×C7311yescharacteristic
388#379C22×C7312yes—
389C4×C22⋊C4C22×C7312yes—
390C4×C22⋊C4C22×C7312yes—
391C4×C22⋊C4C22×C7312yes—
392C4×C22⋊C4C22×C7311yescharacteristic
393C4×C22⋊C4C22×C7311yescharacteristic
394C4×C22⋊C4C22×C7312yes—
395C4×C22⋊C4C22×C7311yescharacteristic
396C4×C22⋊C4C22×C7311yescharacteristic
397C2×#95C22×C7311yescharacteristic
398C2×#95C22×C7312yes—
399C2×#95C22×C7311yescharacteristic
400C25C23×C7311yescharacteristic
401C22×Q8C23×C7314yes—
402C23×C4—44no—
403C23×C4Q8×C7318yescomplemented
404C23×C4C23×C7312yes—
405C23×C4C23×C7312yes—
406C23×C4C23×C7311yescharacteristic
407C23×C4C23×C7311yescharacteristic
408C23×C4C23×C7311yescharacteristic
409C23×C4C23×C7314yes—
410C23×C4C23×C7311yescharacteristic
411C23×C4C23×C7311yescharacteristic
412C23×C4C23×C7311yescharacteristic
413C4⋊Q8—44no—
414#125—44no—
415C22⋊Q8—216no—
416C22⋊Q8—48no—
417#117—44no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4C23×C7312yes—
420C2×C4⋊C4C23×C7312yes—
421C2×C4⋊C4C23×C7312yes—
422C2×C4⋊C4C23×C7312yes—
423C2×C4⋊C4C23×C7314yes—
424C2×C4⋊C4C23×C7314yes—
425C2×C4⋊C4C23×C7314yes—
426C2×C4⋊C4C23×C7314yes—
427C2×C4⋊C4C23×C7314yes—
428C2×C4⋊C4C23×C7314yes—
429C2×C4⋊C4C23×C7314yes—
430C2×C4⋊C4C23×C7314yes—
431C2×C4⋊C4C23×C7314yes—
432C2×C4⋊C4C23×C7314yes—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4C23×C7314yes—
436C2×C22⋊C4C23×C7312yes—
437C2×C22⋊C4C23×C7312yes—
438C2×C22⋊C4C23×C7312yes—
439C2×C22⋊C4C23×C7312yes—
440C2×C22⋊C4C23×C7314yes—
441C2×C22⋊C4C23×C7312yes—
442C2×C22⋊C4C23×C7312yes—
443C2×C22⋊C4C23×C7312yes—
444C2×C22⋊C4C23×C7314yes—
445C2×C22⋊C4C23×C7312yes—
446C2×C42—44no—
447C2×C42C23×C7312yes—
448C2×C42C23×C7312yes—
449C2×C42C23×C7314yes—
450C2×C42C23×C7312yes—
451C2×C42C23×C7312yes—
452#95C23×C7312yes—
453#95C23×C7312yes—
454#95C23×C7311yescharacteristic
455#95C23×C7311yescharacteristic
456#95C23×C7311yescharacteristic
457#95C23×C7311yescharacteristic
458#95C23×C7312yes—
459#95C23×C7314yes—
460#95C23×C7312yes—
461#95C23×C7312yes—
462#95C23×C7312yes—
463#95C23×C7314yes—
464#95C23×C7314yes—
465#95C23×C7314yes—
466#95C23×C7314yes—
467#95C23×C7314yes—
468#95C23×C7314yes—
469#95C23×C7314yes—
470C24—24no—
471C24—22no—
472C24—22no—
473C24—42no—
474C24C2×Q8×C7314yes—
475C24C24×C7311yescharacteristic
476C24C24×C7311yescharacteristic
477C24C24×C7311yescharacteristic
478C2×Q8—28no—
479C2×Q8—44no—
480C2×Q8—44no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—28no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—416no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4C2×Q8×C7314yes—
498C22×C4C2×Q8×C7314yes—
499C22×C4C2×Q8×C7314yes—
500C22×C4C2×Q8×C7314yes—
501C22×C4C2×Q8×C7314yes—
502C22×C4C2×Q8×C7314yes—
503C22×C4C24×C7312yes—
504C22×C4C24×C7314yes—
505C22×C4C24×C7314yes—
506C22×C4C24×C7312yes—
507C22×C4C24×C7314yes—
508C22×C4C24×C7314yes—
509C22×C4C24×C7311yescharacteristic
510C22×C4C24×C7311yescharacteristic
511C22×C4C24×C7311yescharacteristic
512C22×C4C24×C7312yes—
513C22×C4C24×C7312yes—
514C22×C4C24×C7311yescharacteristic
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—28no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C4⋊C4—44no—
528C4⋊C4—44no—
529C22⋊C4—24no—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—44no—
539C22⋊C4#41×C7318yes—
540C42—24no—
541C42—24no—
542C42—42no—
543C42—42no—
544C42—44no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—21no—
549C23—21no—
550C23—28no—
551C23—28no—
552C23—22no—
553C23—21no—
554C23—22no—
555C23—21no—
556C23—44no—
557C23—48no—
558C23—48no—
559C23C22×Q8×C7312yes—
560C23C22×Q8×C7312yes—
561C23C22×Q8×C7312yes—
562C23C2×#41×C7314yes—
563C23H(5,𝔽2)×C7312yes—
564C232−1+4×C7312yes—
565C23C25×C7311yescharacteristic
566Q8—88no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—48no—
600C2×C4—88no—
601C2×C4C22×Q8×C7312yes—
602C2×C4C22×Q8×C7312yes—
603C2×C4C22×Q8×C7312yes—
604C2×C4C22×Q8×C7312yes—
605C2×C4C2×#41×C7314yes—
606C2×C4C2×#41×C7314yes—
607C2×C4H(5,𝔽2)×C7314yes—
608C22—24no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—416no—
620C22—42no—
621C22—42no—
622C22#533×C7314yes—
623C22#544×C7314yes—
624C22C23×Q8×C7311yescharacteristic
625C22C22×#41×C7312yes—
626C22C2×H(5,𝔽2)×C7311yescharacteristic
627C22C2×H(5,𝔽2)×C7312yes—
628C22C2×2−1+4×C7311yescharacteristic
629C4—24no—
630C4—24no—
631C4—22no—
632C4—22no—
633C4—22no—
634C4—42no—
635C4—44no—
636C4—44no—
637C4—44no—
638C4—42no—
639C4—44no—
640C4#543×C7314yes—
641C2—24no—
642C2—24no—
643C2—42no—
644C2C2×#533×C7311yescharacteristic
645C2C2×#543×C7311yescharacteristic
646C2C2×#544×C7311yescharacteristic
647C2C73×#351912yes—
648C2C73×#352012yes—
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC25×C73C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2857C2semidirect
2. C73×#2851C2semidirect
3. C73×#2667C2semidirect
4. C73×#2665C2semidirect
5. C73×#2569C2semidirect
6. C73×#2549C2semidirect
7. C73×#2442C2semidirect
8. C73×#2441C2semidirect
9. C73×#2440C2semidirect
10. C73×#2439C2semidirect
12. C73×#2329C2semidirect
17. C2×C4⋊Q8×C73C22semidirect
18. C2×#125×C73C22semidirect
26. #400×C73C22semidirect
28. #398×C73C22semidirect
29. #398×C73C22semidirect
32. #395×C73C22semidirect
34. #391×C73C22semidirect
35. #391×C73C22semidirect
36. #389×C73C22semidirect
37. #389×C73C22semidirect
38. #389×C73C22semidirect
39. #389×C73C22semidirect
40. #389×C73C22semidirect
41. #389×C73C22semidirect
42. #387×C73C22semidirect
43. #387×C73C22semidirect
44. #387×C73C22semidirect
45. #387×C73C22semidirect
50. #384×C73C22semidirect
51. #382×C73C22semidirect
78. C23×C4×C73Q8semidirect
316. #35079C73direct (N × H)
325. #2857C2×C73semidirect
326. #2851C2×C73semidirect
327. #2667C2×C73semidirect
328. #2665C2×C73semidirect
329. #2569C2×C73semidirect
330. #2549C2×C73semidirect
331. #2442C2×C73semidirect
332. #2441C2×C73semidirect
333. #2440C2×C73semidirect
334. #2439C2×C73semidirect
336. #2329C2×C73semidirect
340. C73#35079direct (N × H)
342. C2×C4⋊Q8C22×C73semidirect
343. C2×#125C22×C73semidirect
351. #400C22×C73semidirect
353. #398C22×C73semidirect
354. #398C22×C73semidirect
357. #395C22×C73semidirect
359. #391C22×C73semidirect
360. #391C22×C73semidirect
361. #389C22×C73semidirect
362. #389C22×C73semidirect
363. #389C22×C73semidirect
364. #389C22×C73semidirect
365. #389C22×C73semidirect
366. #389C22×C73semidirect
367. #387C22×C73semidirect
368. #387C22×C73semidirect
369. #387C22×C73semidirect
370. #387C22×C73semidirect
375. #384C22×C73semidirect
376. #382C22×C73semidirect
403. C23×C4Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28572
C73×#28512
C73×#26672
C73×#26652
C73×#25692
C73×#25492
C73×#24422
C73×#24412
C73×#24402
C73×#24392
C73×#24372
C73×#23292
C73×#22802
C2×#380×C732
C2×C4×C22⋊C4×C732
#3507973