Finite Group Databasebeta

← C73×#62863 #32972267

Subgroups — C73×#62863 #32972267

Order 18688.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3560C218yesmaximal, complemented
2C73×#3558C218yesmaximal, complemented
3C73×#3537C218yesmaximal, complemented
4C73×#3534C218yesmaximal, complemented
5C73×#3533C218yesmaximal, complemented
6C73×#3532C218yesmaximal, complemented
7C73×#3505C214yesmaximal, complemented
8C73×#3496C214yesmaximal, complemented
9C73×#3484C214yesmaximal, complemented
10C2×#538×C73C212yesmaximal, complemented
11C2×#534×C73C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C73C2214yescomplemented
13C23×D4×C73C2212yescomplemented
14#563×C73C2218yescomplemented
15#562×C73C22116yescomplemented
16H(3,𝔽4)×C73C2218yescomplemented
17#560×C73C22116yescomplemented
18#560×C73C2218yescomplemented
19#560×C73C2218yescomplemented
20#559×C73C2218yescomplemented
21#553×C73C22116yescomplemented
22#553×C73C2218yescomplemented
23#553×C73C22116yescomplemented
24#552×C73C2218yescomplemented
25#551×C73C22116yescomplemented
26#551×C73C2218yescomplemented
27#551×C73C2218yescomplemented
28#548×C73C2218yescomplemented
29#547×C73C2218yescomplemented
30#547×C73C2218yescomplemented
31#546×C73C2218yescomplemented
32#546×C73C22116yescomplemented
33#546×C73C22116yescomplemented
34#546×C73C22116yescomplemented
35#546×C73C22116yescomplemented
36#546×C73C22116yescomplemented
37D42×C73C2218yescomplemented
38D42×C73C22116yescomplemented
39D42×C73C22116yescomplemented
40D42×C73C2218yescomplemented
41D42×C73C2218yescomplemented
42#542×C73C22116yescomplemented
43#540×C73C22116yescomplemented
44#539×C73C22116yescomplemented
45#539×C73C2218yescomplemented
46#538×C73C22116yescomplemented
47#538×C73C2218yescomplemented
48#538×C73C2218yescomplemented
49#538×C73C22116yescomplemented
50#538×C73C22116yescomplemented
51#538×C73C22116yescomplemented
52#538×C73C2218yescomplemented
53#537×C73C2218yescomplemented
54#535×C73C2218yescomplemented
55#535×C73C22116yescomplemented
56#534×C73C2218yescomplemented
57#534×C73C2218yescomplemented
58#534×C73C2218yescomplemented
59#534×C73C2218yescomplemented
60#534×C73C22116yescomplemented
61#534×C73C2218yescomplemented
62#532×C73C2218yescomplemented
63#529×C73C2218yescomplemented
64C2×#126×C73C2214yescomplemented
65C2×#124×C73C2214yescomplemented
66#525×C73C2218yescomplemented
67#525×C73C2218yescomplemented
68C2×#123×C73C2214yescomplemented
69C2×#123×C73C2214yescomplemented
70C2×C22⋊Q8×C73C2212yescomplemented
71C2×#121×C73C2214yescomplemented
72C2×#121×C73C2214yescomplemented
73C2×#121×C73C2212yescomplemented
74C2×#121×C73C2218yescomplemented
75C2×#120×C73C2214yescomplemented
76C2×#120×C73C2214yescomplemented
77C2×#120×C73C2218yescomplemented
78#518×C73C2214yescomplemented
79C2×C4×D4×C73C2214yescomplemented
80C22×C22⋊C4×C73C2211yescharacteristic, complemented
81C25×C73C2311yescharacteristic
82C25×C73C2312yes—
83H(5,𝔽2)×C73—416no—
84C2×#41×C73C2318yes—
85C2×#41×C73C23116yescomplemented
86C2×#41×C73C2318yescomplemented
87C22×Q8×C73C2312yescomplemented
88C22×D4×C73—48no—
89C22×D4×C73C2314yes—
90C22×D4×C73C2314yes—
91C22×D4×C73C2314yes—
92C22×D4×C73C2318yes—
93C22×D4×C73C23116yes—
94C22×D4×C73C2314yes—
95C22×D4×C73C2314yes—
96C22×D4×C73C2314yes—
97C22×D4×C73C23116yescomplemented
98C22×D4×C73C23116yescomplemented
99C22×D4×C73C2312yescomplemented
100C22×D4×C73C2318yescomplemented
101C23×C4×C73C2312yes—
102C23×C4×C73C2312yes—
103C23×C4×C73C2314yescomplemented
104C4⋊Q8×C73C2318yescomplemented
105#127×C73C2318yes—
106#127×C73C2318yes—
107#127×C73C2318yescomplemented
108#126×C73C23116yescomplemented
109#126×C73C23116yescomplemented
110#126×C73C23116yescomplemented
111#126×C73C23116yescomplemented
112#126×C73C23116yescomplemented
113#125×C73C2318yescomplemented
114#125×C73C23116yescomplemented
115#124×C73C2318yes—
116#124×C73C2318yes—
117#124×C73C23116yescomplemented
118#124×C73C23116yescomplemented
119#124×C73C2318yescomplemented
120#124×C73C23116yescomplemented
121#124×C73C23116yescomplemented
122#123×C73C23116yes—
123#123×C73C2318yes—
124#123×C73C2318yes—
125#123×C73C23116yes—
126#123×C73C2318yes—
127#123×C73C2318yes—
128#123×C73C23116yescomplemented
129#123×C73C23116yescomplemented
130#123×C73C23116yescomplemented
131#123×C73C23116yescomplemented
132#123×C73C23116yescomplemented
133#123×C73C23116yescomplemented
134#123×C73C23116yescomplemented
135#123×C73C23116yescomplemented
136C22⋊Q8×C73C2318yes—
137C22⋊Q8×C73C2318yescomplemented
138C22⋊Q8×C73C2318yescomplemented
139C22⋊Q8×C73C23116yescomplemented
140C22⋊Q8×C73C23116yescomplemented
141C22⋊Q8×C73C23116yescomplemented
142C22⋊Q8×C73C23116yescomplemented
143#121×C73C2318yes—
144#121×C73C2318yes—
145#121×C73C2318yes—
146#121×C73C2318yes—
147#121×C73C2318yes—
148#121×C73C23116yes—
149#121×C73C23116yes—
150#121×C73C23116yes—
151#121×C73C23116yes—
152#121×C73C2318yescomplemented
153#121×C73C23116yescomplemented
154#121×C73C23116yescomplemented
155#121×C73C23116yescomplemented
156#121×C73C2318yescomplemented
157#121×C73C23116yescomplemented
158#121×C73C2318yescomplemented
159#121×C73C2318yescomplemented
160#121×C73C23116yescomplemented
161#121×C73C23116yescomplemented
162#121×C73C23116yescomplemented
163#121×C73C23116yescomplemented
164#121×C73C23116yescomplemented
165#120×C73C23116yes—
166#120×C73C23116yes—
167#120×C73C2318yes—
168#120×C73C2318yes—
169#120×C73C23116yes—
170#120×C73C23116yes—
171#120×C73C2318yes—
172#120×C73C2318yes—
173#120×C73C23116yescomplemented
174#120×C73C23116yescomplemented
175#120×C73C23116yescomplemented
176#120×C73C23116yescomplemented
177#120×C73C23116yescomplemented
178C4×Q8×C73C2318yescomplemented
179C4×D4×C73C2318yes—
180C4×D4×C73C2318yes—
181C4×D4×C73C2318yescomplemented
182C4×D4×C73C2318yescomplemented
183C4×D4×C73C23116yescomplemented
184C4×D4×C73C23116yescomplemented
185C4×D4×C73C23116yescomplemented
186C4×D4×C73C23116yescomplemented
187C4×D4×C73C23116yescomplemented
188C4×D4×C73C2318yescomplemented
189C4×D4×C73C2318yescomplemented
190C4×D4×C73C2318yescomplemented
191C4×D4×C73C23116yescomplemented
192#117×C73C2318yes—
193#117×C73C2318yescomplemented
194#117×C73C23116yescomplemented
195C2×C4⋊C4×C73C2314yes—
196C2×C4⋊C4×C73C2314yescomplemented
197C2×C4⋊C4×C73C2314yescomplemented
198C2×C4⋊C4×C73C2312yescomplemented
199C2×C4⋊C4×C73C2318yescomplemented
200C2×C4⋊C4×C73C2312yescomplemented
201C2×C22⋊C4×C73C2314yes—
202C2×C22⋊C4×C73C2314yes—
203C2×C22⋊C4×C73C2314yes—
204C2×C22⋊C4×C73C2314yes—
205C2×C22⋊C4×C73C2318yes—
206C2×C22⋊C4×C73C2318yes—
207C2×C22⋊C4×C73C2314yes—
208C2×C22⋊C4×C73C2314yes—
209C2×C22⋊C4×C73C2314yescomplemented
210C2×C22⋊C4×C73C23116yescomplemented
211C2×C22⋊C4×C73C2314yescomplemented
212C2×C22⋊C4×C73C23116yescomplemented
213C2×C42×C73C2314yescomplemented
214C24×C73—24no—
215C24×C73—44no—
216C24×C73—82no—
217C24×C73—84no—
218C24×C73C2414yes—
219C24×C73C2414yes—
220C24×C73C2412yes—
221C24×C73C2414yes—
222C24×C73C2418yes—
223C24×C73C2418yes—
224C24×C73C2411yescharacteristic
225#41×C73—416no—
226#41×C73—432no—
227#41×C73—88no—
228C2×Q8×C73—82no—
229C2×Q8×C73C2418yes—
230C2×Q8×C73C2418yes—
231C2×D4×C73—216no—
232C2×D4×C73—216no—
233C2×D4×C73—48no—
234C2×D4×C73—432no—
235C2×D4×C73—416no—
236C2×D4×C73—432no—
237C2×D4×C73—84no—
238C2×D4×C73—84no—
239C2×D4×C73—84no—
240C2×D4×C73—82no—
241C2×D4×C73—88no—
242C2×D4×C73—816no—
243C2×D4×C73C2418yes—
244C2×D4×C73C2418yes—
245C2×D4×C73C24116yes—
246C2×D4×C73C2418yes—
247C2×D4×C73C2418yes—
248C2×D4×C73C24116yes—
249C2×D4×C73C24116yes—
250C2×D4×C73C24116yes—
251C2×D4×C73C24116yes—
252C2×D4×C73C2418yes—
253C2×D4×C73C2418yes—
254C2×D4×C73C2418yes—
255C2×D4×C73C24116yes—
256C2×D4×C73C2418yes—
257C22×C4×C73—44no—
258C22×C4×C73—82no—
259C22×C4×C73—84no—
260C22×C4×C73C2414yes—
261C22×C4×C73C2414yes—
262C22×C4×C73C2414yes—
263C22×C4×C73C2414yes—
264C22×C4×C73C2414yes—
265C22×C4×C73C2412yes—
266C22×C4×C73C2412yes—
267C22×C4×C73C2414yes—
268C22×C4×C73C24116yes—
269C22×C4×C73C2418yes—
270C22×C4×C73C2418yes—
271C22×C4×C73C24116yes—
272C22×C4×C73C2418yes—
273C22×C4×C73C2418yes—
274C4⋊C4×C73C2418yes—
275C4⋊C4×C73C2418yes—
276C4⋊C4×C73C2418yes—
277C4⋊C4×C73C24116yes—
278C4⋊C4×C73C24116yes—
279C4⋊C4×C73C2418yes—
280C4⋊C4×C73C2418yes—
281C4⋊C4×C73C2418yes—
282C4⋊C4×C73C24116yes—
283C4⋊C4×C73C24116yes—
284C22⋊C4×C73C2418yes—
285C22⋊C4×C73C2414yes—
286C22⋊C4×C73C2418yes—
287C22⋊C4×C73C2414yes—
288C22⋊C4×C73C24116yes—
289C22⋊C4×C73C24116yes—
290C22⋊C4×C73C24116yes—
291C22⋊C4×C73C24116yes—
292C22⋊C4×C73C2418yes—
293C22⋊C4×C73C2418yes—
294C22⋊C4×C73C2418yes—
295C22⋊C4×C73C24116yes—
296C22⋊C4×C73C24116yes—
297C22⋊C4×C73C24116yes—
298C22⋊C4×C73C24116yes—
299C22⋊C4×C73C2418yes—
300C22⋊C4×C73C2418yes—
301C22⋊C4×C73C24116yes—
302C42×C73C2418yes—
303C42×C73C2418yes—
304C42×C73C2418yes—
305C42×C73C2418yes—
306C23×C73—24no—
307C23×C73—28no—
308C23×C73—28no—
309C23×C73—28no—
310C23×C73—42no—
311C23×C73—44no—
312C23×C73—44no—
313C23×C73—48no—
314C23×C73—44no—
315C23×C73—44no—
316C23×C73—44no—
317C23×C73—48no—
318C23×C73—416no—
319C23×C73—48no—
320C23×C73—416no—
321C23×C73—88no—
322C23×C73—816no—
323C23×C73H(5,𝔽2)14yes—
324C23×C73C2514yes—
325C23×C73C2518yes—
326C23×C73C2518yes—
327C23×C73C2511yescharacteristic
328C23×C73C2512yes—
329Q8×C73—48no—
330Q8×C73—48no—
331D4×C73—232no—
332D4×C73—216no—
333D4×C73—216no—
334D4×C73—48no—
335D4×C73—48no—
336D4×C73—48no—
337D4×C73—416no—
338D4×C73—416no—
339D4×C73—48no—
340D4×C73—416no—
341D4×C73—48no—
342D4×C73—416no—
343D4×C73—48no—
344D4×C73—416no—
345C2×C4×C73—28no—
346C2×C4×C73—28no—
347C2×C4×C73—48no—
348C2×C4×C73—44no—
349C2×C4×C73—42no—
350C2×C4×C73—44no—
351C2×C4×C73—48no—
352C2×C4×C73—44no—
353C2×C4×C73—42no—
354C2×C4×C73—48no—
355C2×C4×C73—416no—
356C2×C4×C73—48no—
357C2×C4×C73—44no—
358C2×C4×C73—416no—
359C2×C4×C73C2518yes—
360C2×C4×C73C2514yes—
361C2×C4×C73C2514yes—
362C2×C4×C73C2518yes—
363C2×C4×C73C2518yes—
364C2×C4×C73C2518yes—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—28no—
369C22×C73—24no—
370C22×C73—28no—
371C22×C73—28no—
372C22×C73—216no—
373C22×C73—28no—
374C22×C73—28no—
375C22×C73—44no—
376C22×C73—48no—
377C22×C73—88no—
378C22×C73—88no—
379C22×C73—88no—
380C22×C73—816no—
381C22×C73—168no—
382C22×C73C2×H(5,𝔽2)12yes—
383C22×C73C2×H(5,𝔽2)14yes—
384C22×C73C2611yescharacteristic
385C4×C73—28no—
386C4×C73—28no—
387C4×C73—24no—
388C4×C73—28no—
389C4×C73—24no—
390C4×C73—28no—
391#62863C7311yesmaximal, characteristic, direct product factor, Sylow
392C2×C73—22no—
393C2×C73—24no—
394C2×C73—44no—
395C2×C73—48no—
396C2×C73—48no—
397C2×C73C22×H(5,𝔽2)11yescharacteristic
398C2×C73H(7,𝔽2)12yes—
399#3560C2×C7318yescomplemented
400#3558C2×C7318yescomplemented
401#3537C2×C7318yescomplemented
402#3534C2×C7318yescomplemented
403#3533C2×C7318yescomplemented
404#3532C2×C7318yescomplemented
405#3505C2×C7314yescomplemented
406#3496C2×C7314yescomplemented
407#3484C2×C7314yescomplemented
408C2×#538C2×C7312yescomplemented
409C2×#534C2×C7311yescharacteristic, complemented
410C73#6286311yescharacteristic, direct product factor, Sylow
411C2×H(5,𝔽2)C22×C7314yescomplemented
412C23×D4C22×C7312yescomplemented
413#563C22×C7318yescomplemented
414#562C22×C73116yescomplemented
415H(3,𝔽4)C22×C7318yescomplemented
416#560C22×C73116yescomplemented
417#560C22×C7318yescomplemented
418#560C22×C7318yescomplemented
419#559C22×C7318yescomplemented
420#553C22×C73116yescomplemented
421#553C22×C7318yescomplemented
422#553C22×C73116yescomplemented
423#552C22×C7318yescomplemented
424#551C22×C73116yescomplemented
425#551C22×C7318yescomplemented
426#551C22×C7318yescomplemented
427#548C22×C7318yescomplemented
428#547C22×C7318yescomplemented
429#547C22×C7318yescomplemented
430#546C22×C7318yescomplemented
431#546C22×C73116yescomplemented
432#546C22×C73116yescomplemented
433#546C22×C73116yescomplemented
434#546C22×C73116yescomplemented
435#546C22×C73116yescomplemented
436D42C22×C7318yescomplemented
437D42C22×C73116yescomplemented
438D42C22×C73116yescomplemented
439D42C22×C7318yescomplemented
440D42C22×C7318yescomplemented
441#542C22×C73116yescomplemented
442#540C22×C73116yescomplemented
443#539C22×C73116yescomplemented
444#539C22×C7318yescomplemented
445#538C22×C73116yescomplemented
446#538C22×C7318yescomplemented
447#538C22×C7318yescomplemented
448#538C22×C73116yescomplemented
449#538C22×C73116yescomplemented
450#538C22×C73116yescomplemented
451#538C22×C7318yescomplemented
452#537C22×C7318yescomplemented
453#535C22×C7318yescomplemented
454#535C22×C73116yescomplemented
455#534C22×C7318yescomplemented
456#534C22×C7318yescomplemented
457#534C22×C7318yescomplemented
458#534C22×C7318yescomplemented
459#534C22×C73116yescomplemented
460#534C22×C7318yescomplemented
461#532C22×C7318yescomplemented
462#529C22×C7318yescomplemented
463C2×#126C22×C7314yescomplemented
464C2×#124C22×C7314yescomplemented
465#525C22×C7318yescomplemented
466#525C22×C7318yescomplemented
467C2×#123C22×C7314yescomplemented
468C2×#123C22×C7314yescomplemented
469C2×C22⋊Q8C22×C7312yescomplemented
470C2×#121C22×C7314yescomplemented
471C2×#121C22×C7314yescomplemented
472C2×#121C22×C7312yescomplemented
473C2×#121C22×C7318yescomplemented
474C2×#120C22×C7314yescomplemented
475C2×#120C22×C7314yescomplemented
476C2×#120C22×C7318yescomplemented
477#518C22×C7314yescomplemented
478C2×C4×D4C22×C7314yescomplemented
479C22×C22⋊C4C22×C7311yescharacteristic, complemented
480C25C23×C7311yescharacteristic
481C25C23×C7312yes—
482H(5,𝔽2)—416no—
483C2×#41C23×C7318yes—
484C2×#41C23×C73116yescomplemented
485C2×#41C23×C7318yescomplemented
486C22×Q8C23×C7312yescomplemented
487C22×D4—48no—
488C22×D4C23×C7314yes—
489C22×D4C23×C7314yes—
490C22×D4C23×C7314yes—
491C22×D4C23×C7318yes—
492C22×D4C23×C73116yes—
493C22×D4C23×C7314yes—
494C22×D4C23×C7314yes—
495C22×D4C23×C7314yes—
496C22×D4C23×C73116yescomplemented
497C22×D4C23×C73116yescomplemented
498C22×D4C23×C7312yescomplemented
499C22×D4C23×C7318yescomplemented
500C23×C4C23×C7312yes—
501C23×C4C23×C7312yes—
502C23×C4C23×C7314yescomplemented
503C4⋊Q8C23×C7318yescomplemented
504#127C23×C7318yes—
505#127C23×C7318yes—
506#127C23×C7318yescomplemented
507#126C23×C73116yescomplemented
508#126C23×C73116yescomplemented
509#126C23×C73116yescomplemented
510#126C23×C73116yescomplemented
511#126C23×C73116yescomplemented
512#125C23×C7318yescomplemented
513#125C23×C73116yescomplemented
514#124C23×C7318yes—
515#124C23×C7318yes—
516#124C23×C73116yescomplemented
517#124C23×C73116yescomplemented
518#124C23×C7318yescomplemented
519#124C23×C73116yescomplemented
520#124C23×C73116yescomplemented
521#123C23×C73116yes—
522#123C23×C7318yes—
523#123C23×C7318yes—
524#123C23×C73116yes—
525#123C23×C7318yes—
526#123C23×C7318yes—
527#123C23×C73116yescomplemented
528#123C23×C73116yescomplemented
529#123C23×C73116yescomplemented
530#123C23×C73116yescomplemented
531#123C23×C73116yescomplemented
532#123C23×C73116yescomplemented
533#123C23×C73116yescomplemented
534#123C23×C73116yescomplemented
535C22⋊Q8C23×C7318yes—
536C22⋊Q8C23×C7318yescomplemented
537C22⋊Q8C23×C7318yescomplemented
538C22⋊Q8C23×C73116yescomplemented
539C22⋊Q8C23×C73116yescomplemented
540C22⋊Q8C23×C73116yescomplemented
541C22⋊Q8C23×C73116yescomplemented
542#121C23×C7318yes—
543#121C23×C7318yes—
544#121C23×C7318yes—
545#121C23×C7318yes—
546#121C23×C7318yes—
547#121C23×C73116yes—
548#121C23×C73116yes—
549#121C23×C73116yes—
550#121C23×C73116yes—
551#121C23×C7318yescomplemented
552#121C23×C73116yescomplemented
553#121C23×C73116yescomplemented
554#121C23×C73116yescomplemented
555#121C23×C7318yescomplemented
556#121C23×C73116yescomplemented
557#121C23×C7318yescomplemented
558#121C23×C7318yescomplemented
559#121C23×C73116yescomplemented
560#121C23×C73116yescomplemented
561#121C23×C73116yescomplemented
562#121C23×C73116yescomplemented
563#121C23×C73116yescomplemented
564#120C23×C73116yes—
565#120C23×C73116yes—
566#120C23×C7318yes—
567#120C23×C7318yes—
568#120C23×C73116yes—
569#120C23×C73116yes—
570#120C23×C7318yes—
571#120C23×C7318yes—
572#120C23×C73116yescomplemented
573#120C23×C73116yescomplemented
574#120C23×C73116yescomplemented
575#120C23×C73116yescomplemented
576#120C23×C73116yescomplemented
577C4×Q8C23×C7318yescomplemented
578C4×D4C23×C7318yes—
579C4×D4C23×C7318yes—
580C4×D4C23×C7318yescomplemented
581C4×D4C23×C7318yescomplemented
582C4×D4C23×C73116yescomplemented
583C4×D4C23×C73116yescomplemented
584C4×D4C23×C73116yescomplemented
585C4×D4C23×C73116yescomplemented
586C4×D4C23×C73116yescomplemented
587C4×D4C23×C7318yescomplemented
588C4×D4C23×C7318yescomplemented
589C4×D4C23×C7318yescomplemented
590C4×D4C23×C73116yescomplemented
591#117C23×C7318yes—
592#117C23×C7318yescomplemented
593#117C23×C73116yescomplemented
594C2×C4⋊C4C23×C7314yes—
595C2×C4⋊C4C23×C7314yescomplemented
596C2×C4⋊C4C23×C7314yescomplemented
597C2×C4⋊C4C23×C7312yescomplemented
598C2×C4⋊C4C23×C7318yescomplemented
599C2×C4⋊C4C23×C7312yescomplemented
600C2×C22⋊C4C23×C7314yes—
601C2×C22⋊C4C23×C7314yes—
602C2×C22⋊C4C23×C7314yes—
603C2×C22⋊C4C23×C7314yes—
604C2×C22⋊C4C23×C7318yes—
605C2×C22⋊C4C23×C7318yes—
606C2×C22⋊C4C23×C7314yes—
607C2×C22⋊C4C23×C7314yes—
608C2×C22⋊C4C23×C7314yescomplemented
609C2×C22⋊C4C23×C73116yescomplemented
610C2×C22⋊C4C23×C7314yescomplemented
611C2×C22⋊C4C23×C73116yescomplemented
612C2×C42C23×C7314yescomplemented
613C24—24no—
614C24—44no—
615C24—82no—
616C24—84no—
617C24C24×C7314yes—
618C24C24×C7314yes—
619C24C24×C7312yes—
620C24C24×C7314yes—
621C24C24×C7318yes—
622C24C24×C7318yes—
623C24C24×C7311yescharacteristic
624#41—416no—
625#41—432no—
626#41—88no—
627C2×Q8—82no—
628C2×Q8C24×C7318yes—
629C2×Q8C24×C7318yes—
630C2×D4—216no—
631C2×D4—216no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—416no—
635C2×D4—432no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—84no—
639C2×D4—82no—
640C2×D4—88no—
641C2×D4—816no—
642C2×D4C24×C7318yes—
643C2×D4C24×C7318yes—
644C2×D4C24×C73116yes—
645C2×D4C24×C7318yes—
646C2×D4C24×C7318yes—
647C2×D4C24×C73116yes—
648C2×D4C24×C73116yes—
649C2×D4C24×C73116yes—
650C2×D4C24×C73116yes—
651C2×D4C24×C7318yes—
652C2×D4C24×C7318yes—
653C2×D4C24×C7318yes—
654C2×D4C24×C73116yes—
655C2×D4C24×C7318yes—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—84no—
659C22×C4C24×C7314yes—
660C22×C4C24×C7314yes—
661C22×C4C24×C7314yes—
662C22×C4C24×C7314yes—
663C22×C4C24×C7314yes—
664C22×C4C24×C7312yes—
665C22×C4C24×C7312yes—
666C22×C4C24×C7314yes—
667C22×C4C24×C73116yes—
668C22×C4C24×C7318yes—
669C22×C4C24×C7318yes—
670C22×C4C24×C73116yes—
671C22×C4C24×C7318yes—
672C22×C4C24×C7318yes—
673C4⋊C4C24×C7318yes—
674C4⋊C4C24×C7318yes—
675C4⋊C4C24×C7318yes—
676C4⋊C4C24×C73116yes—
677C4⋊C4C24×C73116yes—
678C4⋊C4C24×C7318yes—
679C4⋊C4C24×C7318yes—
680C4⋊C4C24×C7318yes—
681C4⋊C4C24×C73116yes—
682C4⋊C4C24×C73116yes—
683C22⋊C4C24×C7318yes—
684C22⋊C4C24×C7314yes—
685C22⋊C4C24×C7318yes—
686C22⋊C4C24×C7314yes—
687C22⋊C4C24×C73116yes—
688C22⋊C4C24×C73116yes—
689C22⋊C4C24×C73116yes—
690C22⋊C4C24×C73116yes—
691C22⋊C4C24×C7318yes—
692C22⋊C4C24×C7318yes—
693C22⋊C4C24×C7318yes—
694C22⋊C4C24×C73116yes—
695C22⋊C4C24×C73116yes—
696C22⋊C4C24×C73116yes—
697C22⋊C4C24×C73116yes—
698C22⋊C4C24×C7318yes—
699C22⋊C4C24×C7318yes—
700C22⋊C4C24×C73116yes—
701C42C24×C7318yes—
702C42C24×C7318yes—
703C42C24×C7318yes—
704C42C24×C7318yes—
705C23—24no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—48no—
717C23—416no—
718C23—48no—
719C23—416no—
720C23—88no—
721C23—816no—
722C23H(5,𝔽2)×C7314yes—
723C23C25×C7314yes—
724C23C25×C7318yes—
725C23C25×C7318yes—
726C23C25×C7311yescharacteristic
727C23C25×C7312yes—
728Q8—48no—
729Q8—48no—
730D4—232no—
731D4—216no—
732D4—216no—
733D4—48no—
734D4—48no—
735D4—48no—
736D4—416no—
737D4—416no—
738D4—48no—
739D4—416no—
740D4—48no—
741D4—416no—
742D4—48no—
743D4—416no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—416no—
758C2×C4C25×C7318yes—
759C2×C4C25×C7314yes—
760C2×C4C25×C7314yes—
761C2×C4C25×C7318yes—
762C2×C4C25×C7318yes—
763C2×C4C25×C7318yes—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×H(5,𝔽2)×C7312yes—
782C22C2×H(5,𝔽2)×C7314yes—
783C22C26×C7311yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×H(5,𝔽2)×C7311yescharacteristic
796C2C73×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C73C26
commutator, Frattini, cosocleC22C26×C73
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3560C2semidirect
2. C73×#3558C2semidirect
3. C73×#3537C2semidirect
4. C73×#3534C2semidirect
5. C73×#3533C2semidirect
6. C73×#3532C2semidirect
7. C73×#3505C2semidirect
8. C73×#3496C2semidirect
9. C73×#3484C2semidirect
10. C2×#538×C73C2semidirect
11. C2×#534×C73C2semidirect
12. C2×H(5,𝔽2)×C73C22semidirect
13. C23×D4×C73C22semidirect
14. #563×C73C22semidirect
15. #562×C73C22semidirect
16. H(3,𝔽4)×C73C22semidirect
17. #560×C73C22semidirect
18. #560×C73C22semidirect
19. #560×C73C22semidirect
20. #559×C73C22semidirect
21. #553×C73C22semidirect
22. #553×C73C22semidirect
23. #553×C73C22semidirect
24. #552×C73C22semidirect
25. #551×C73C22semidirect
26. #551×C73C22semidirect
27. #551×C73C22semidirect
28. #548×C73C22semidirect
29. #547×C73C22semidirect
30. #547×C73C22semidirect
31. #546×C73C22semidirect
32. #546×C73C22semidirect
33. #546×C73C22semidirect
34. #546×C73C22semidirect
35. #546×C73C22semidirect
36. #546×C73C22semidirect
37. D42×C73C22semidirect
38. D42×C73C22semidirect
39. D42×C73C22semidirect
40. D42×C73C22semidirect
41. D42×C73C22semidirect
42. #542×C73C22semidirect
43. #540×C73C22semidirect
44. #539×C73C22semidirect
45. #539×C73C22semidirect
46. #538×C73C22semidirect
47. #538×C73C22semidirect
48. #538×C73C22semidirect
49. #538×C73C22semidirect
50. #538×C73C22semidirect
51. #538×C73C22semidirect
52. #538×C73C22semidirect
53. #537×C73C22semidirect
54. #535×C73C22semidirect
55. #535×C73C22semidirect
56. #534×C73C22semidirect
57. #534×C73C22semidirect
58. #534×C73C22semidirect
59. #534×C73C22semidirect
60. #534×C73C22semidirect
61. #534×C73C22semidirect
62. #532×C73C22semidirect
63. #529×C73C22semidirect
64. C2×#126×C73C22semidirect
65. C2×#124×C73C22semidirect
66. #525×C73C22semidirect
67. #525×C73C22semidirect
68. C2×#123×C73C22semidirect
69. C2×#123×C73C22semidirect
70. C2×C22⋊Q8×C73C22semidirect
71. C2×#121×C73C22semidirect
72. C2×#121×C73C22semidirect
73. C2×#121×C73C22semidirect
74. C2×#121×C73C22semidirect
75. C2×#120×C73C22semidirect
76. C2×#120×C73C22semidirect
77. C2×#120×C73C22semidirect
78. #518×C73C22semidirect
79. C2×C4×D4×C73C22semidirect
80. C22×C22⋊C4×C73C22semidirect
85. C2×#41×C73C23semidirect
86. C2×#41×C73C23semidirect
87. C22×Q8×C73C23semidirect
97. C22×D4×C73C23semidirect
98. C22×D4×C73C23semidirect
99. C22×D4×C73C23semidirect
100. C22×D4×C73C23semidirect
103. C23×C4×C73C23semidirect
104. C4⋊Q8×C73C23semidirect
107. #127×C73C23semidirect
108. #126×C73C23semidirect
109. #126×C73C23semidirect
110. #126×C73C23semidirect
111. #126×C73C23semidirect
112. #126×C73C23semidirect
113. #125×C73C23semidirect
114. #125×C73C23semidirect
117. #124×C73C23semidirect
118. #124×C73C23semidirect
119. #124×C73C23semidirect
120. #124×C73C23semidirect
121. #124×C73C23semidirect
128. #123×C73C23semidirect
129. #123×C73C23semidirect
130. #123×C73C23semidirect
131. #123×C73C23semidirect
132. #123×C73C23semidirect
133. #123×C73C23semidirect
134. #123×C73C23semidirect
135. #123×C73C23semidirect
137. C22⋊Q8×C73C23semidirect
138. C22⋊Q8×C73C23semidirect
139. C22⋊Q8×C73C23semidirect
140. C22⋊Q8×C73C23semidirect
141. C22⋊Q8×C73C23semidirect
142. C22⋊Q8×C73C23semidirect
152. #121×C73C23semidirect
153. #121×C73C23semidirect
154. #121×C73C23semidirect
155. #121×C73C23semidirect
156. #121×C73C23semidirect
157. #121×C73C23semidirect
158. #121×C73C23semidirect
159. #121×C73C23semidirect
160. #121×C73C23semidirect
161. #121×C73C23semidirect
162. #121×C73C23semidirect
163. #121×C73C23semidirect
164. #121×C73C23semidirect
173. #120×C73C23semidirect
174. #120×C73C23semidirect
175. #120×C73C23semidirect
176. #120×C73C23semidirect
177. #120×C73C23semidirect
178. C4×Q8×C73C23semidirect
181. C4×D4×C73C23semidirect
182. C4×D4×C73C23semidirect
183. C4×D4×C73C23semidirect
184. C4×D4×C73C23semidirect
185. C4×D4×C73C23semidirect
186. C4×D4×C73C23semidirect
187. C4×D4×C73C23semidirect
188. C4×D4×C73C23semidirect
189. C4×D4×C73C23semidirect
190. C4×D4×C73C23semidirect
191. C4×D4×C73C23semidirect
193. #117×C73C23semidirect
194. #117×C73C23semidirect
196. C2×C4⋊C4×C73C23semidirect
197. C2×C4⋊C4×C73C23semidirect
198. C2×C4⋊C4×C73C23semidirect
199. C2×C4⋊C4×C73C23semidirect
200. C2×C4⋊C4×C73C23semidirect
209. C2×C22⋊C4×C73C23semidirect
210. C2×C22⋊C4×C73C23semidirect
211. C2×C22⋊C4×C73C23semidirect
212. C2×C22⋊C4×C73C23semidirect
213. C2×C42×C73C23semidirect
391. #62863C73direct (N × H)
399. #3560C2×C73semidirect
400. #3558C2×C73semidirect
401. #3537C2×C73semidirect
402. #3534C2×C73semidirect
403. #3533C2×C73semidirect
404. #3532C2×C73semidirect
405. #3505C2×C73semidirect
406. #3496C2×C73semidirect
407. #3484C2×C73semidirect
408. C2×#538C2×C73semidirect
409. C2×#534C2×C73semidirect
410. C73#62863direct (N × H)
411. C2×H(5,𝔽2)C22×C73semidirect
412. C23×D4C22×C73semidirect
413. #563C22×C73semidirect
414. #562C22×C73semidirect
415. H(3,𝔽4)C22×C73semidirect
416. #560C22×C73semidirect
417. #560C22×C73semidirect
418. #560C22×C73semidirect
419. #559C22×C73semidirect
420. #553C22×C73semidirect
421. #553C22×C73semidirect
422. #553C22×C73semidirect
423. #552C22×C73semidirect
424. #551C22×C73semidirect
425. #551C22×C73semidirect
426. #551C22×C73semidirect
427. #548C22×C73semidirect
428. #547C22×C73semidirect
429. #547C22×C73semidirect
430. #546C22×C73semidirect
431. #546C22×C73semidirect
432. #546C22×C73semidirect
433. #546C22×C73semidirect
434. #546C22×C73semidirect
435. #546C22×C73semidirect
436. D42C22×C73semidirect
437. D42C22×C73semidirect
438. D42C22×C73semidirect
439. D42C22×C73semidirect
440. D42C22×C73semidirect
441. #542C22×C73semidirect
442. #540C22×C73semidirect
443. #539C22×C73semidirect
444. #539C22×C73semidirect
445. #538C22×C73semidirect
446. #538C22×C73semidirect
447. #538C22×C73semidirect
448. #538C22×C73semidirect
449. #538C22×C73semidirect
450. #538C22×C73semidirect
451. #538C22×C73semidirect
452. #537C22×C73semidirect
453. #535C22×C73semidirect
454. #535C22×C73semidirect
455. #534C22×C73semidirect
456. #534C22×C73semidirect
457. #534C22×C73semidirect
458. #534C22×C73semidirect
459. #534C22×C73semidirect
460. #534C22×C73semidirect
461. #532C22×C73semidirect
462. #529C22×C73semidirect
463. C2×#126C22×C73semidirect
464. C2×#124C22×C73semidirect
465. #525C22×C73semidirect
466. #525C22×C73semidirect
467. C2×#123C22×C73semidirect
468. C2×#123C22×C73semidirect
469. C2×C22⋊Q8C22×C73semidirect
470. C2×#121C22×C73semidirect
471. C2×#121C22×C73semidirect
472. C2×#121C22×C73semidirect
473. C2×#121C22×C73semidirect
474. C2×#120C22×C73semidirect
475. C2×#120C22×C73semidirect
476. C2×#120C22×C73semidirect
477. #518C22×C73semidirect
478. C2×C4×D4C22×C73semidirect
479. C22×C22⋊C4C22×C73semidirect
484. C2×#41C23×C73semidirect
485. C2×#41C23×C73semidirect
486. C22×Q8C23×C73semidirect
496. C22×D4C23×C73semidirect
497. C22×D4C23×C73semidirect
498. C22×D4C23×C73semidirect
499. C22×D4C23×C73semidirect
502. C23×C4C23×C73semidirect
503. C4⋊Q8C23×C73semidirect
506. #127C23×C73semidirect
507. #126C23×C73semidirect
508. #126C23×C73semidirect
509. #126C23×C73semidirect
510. #126C23×C73semidirect
511. #126C23×C73semidirect
512. #125C23×C73semidirect
513. #125C23×C73semidirect
516. #124C23×C73semidirect
517. #124C23×C73semidirect
518. #124C23×C73semidirect
519. #124C23×C73semidirect
520. #124C23×C73semidirect
527. #123C23×C73semidirect
528. #123C23×C73semidirect
529. #123C23×C73semidirect
530. #123C23×C73semidirect
531. #123C23×C73semidirect
532. #123C23×C73semidirect
533. #123C23×C73semidirect
534. #123C23×C73semidirect
536. C22⋊Q8C23×C73semidirect
537. C22⋊Q8C23×C73semidirect
538. C22⋊Q8C23×C73semidirect
539. C22⋊Q8C23×C73semidirect
540. C22⋊Q8C23×C73semidirect
541. C22⋊Q8C23×C73semidirect
551. #121C23×C73semidirect
552. #121C23×C73semidirect
553. #121C23×C73semidirect
554. #121C23×C73semidirect
555. #121C23×C73semidirect
556. #121C23×C73semidirect
557. #121C23×C73semidirect
558. #121C23×C73semidirect
559. #121C23×C73semidirect
560. #121C23×C73semidirect
561. #121C23×C73semidirect
562. #121C23×C73semidirect
563. #121C23×C73semidirect
572. #120C23×C73semidirect
573. #120C23×C73semidirect
574. #120C23×C73semidirect
575. #120C23×C73semidirect
576. #120C23×C73semidirect
577. C4×Q8C23×C73semidirect
580. C4×D4C23×C73semidirect
581. C4×D4C23×C73semidirect
582. C4×D4C23×C73semidirect
583. C4×D4C23×C73semidirect
584. C4×D4C23×C73semidirect
585. C4×D4C23×C73semidirect
586. C4×D4C23×C73semidirect
587. C4×D4C23×C73semidirect
588. C4×D4C23×C73semidirect
589. C4×D4C23×C73semidirect
590. C4×D4C23×C73semidirect
592. #117C23×C73semidirect
593. #117C23×C73semidirect
595. C2×C4⋊C4C23×C73semidirect
596. C2×C4⋊C4C23×C73semidirect
597. C2×C4⋊C4C23×C73semidirect
598. C2×C4⋊C4C23×C73semidirect
599. C2×C4⋊C4C23×C73semidirect
608. C2×C22⋊C4C23×C73semidirect
609. C2×C22⋊C4C23×C73semidirect
610. C2×C22⋊C4C23×C73semidirect
611. C2×C22⋊C4C23×C73semidirect
612. C2×C42C23×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35602
C73×#35582
C73×#35372
C73×#35342
C73×#35332
C73×#35322
C73×#35052
C73×#34962
C73×#34842
C2×#538×C732
C2×#534×C732
#6286373