Finite Group Databasebeta

← C73×#25575 #32934979

Subgroups — C73×#25575 #32934979

Order 18688.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C73C211yesmaximal, characteristic, complemented
2C2×#488×C73C211yesmaximal, characteristic, complemented
3C2×#463×C73C211yesmaximal, characteristic, complemented
4C73×#2540C211yesmaximal, characteristic, complemented
5C73×#2000C211yesmaximal, characteristic, complemented
6C73×#2000C211yesmaximal, characteristic, complemented
7C73×#1999C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, 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×#102×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18#553×C73—24no—
19#553×C73—24no—
20C2×#126×C73—21no—
21C2×#125×C73C2211yescharacteristic
22C2×#124×C73C2211yescharacteristic
23C2×#123×C73—21no—
24C2×C22⋊Q8×C73C2211yescharacteristic
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73—21no—
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×#121×C73C2211yescharacteristic
31C2×C4×D4×C73—21no—
32C2×C4×D4×C73C2211yescharacteristic
33C2×C4×D4×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36#488×C73—24no—
37#463×C73—24no—
38C2×C4⋊C8×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×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×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73D411yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C2×SD16×C73—22no—
76C2×SD16×C73—41no—
77C2×SD16×C73—41no—
78C2×D8×C73—22no—
79C2×D8×C73—41no—
80C2×D8×C73—41no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85#126×C73—28no—
86#125×C73—22no—
87#125×C73D414yescomplemented
88#124×C73—22no—
89#124×C73—22no—
90#123×C73—28no—
91C22⋊Q8×C73—22no—
92C22⋊Q8×C73—22no—
93C22⋊Q8×C73—41no—
94C22⋊Q8×C73—41no—
95#121×C73—28no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—41no—
103#121×C73—41no—
104C4×D4×C73—28no—
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108C4×D4×C73D414yescomplemented
109#117×C73—22no—
110#117×C73—22no—
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×C73—21no—
134C2×C22⋊C4×C73D411yescharacteristic
135C2×C22⋊C4×C73D411yescharacteristic
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#102×C73—22no—
144#102×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×C73—21no—
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D411yescharacteristic
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×D4×C73—24no—
165C2×D4×C73—22no—
166C2×D4×C73—24no—
167C2×D4×C73—22no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
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—21no—
178C2×D4×C73—21no—
179C2×D4×C73—41no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—81no—
187C2×D4×C73—81no—
188C2×D4×C73—81no—
189C2×D4×C73—81no—
190C2×D4×C73C2×D412yes—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—24no—
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—24no—
210C22×C4×C73—21no—
211C22×C4×C73—81no—
212C22×C4×C73—81no—
213C22×C4×C73—81no—
214C22×C4×C73—81no—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2411yescharacteristic
220SD16×C73—44no—
221D8×C73—44no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C4⋊C4×C73—24no—
235C4⋊C4×C73—24no—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—22no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—42no—
244C4⋊C4×C73—42no—
245C4⋊C4×C73C2×D412yes—
246C4⋊C4×C73C2×D412yes—
247C4⋊C4×C73C2×D412yes—
248C4⋊C4×C73#4112yes—
249C4⋊C4×C73#4112yes—
250C22⋊C4×C73—24no—
251C22⋊C4×C73—24no—
252C22⋊C4×C73—24no—
253C22⋊C4×C73—24no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C42×C73—24no—
263C42×C73—81no—
264C42×C73C2×D412yes—
265C42×C73C2×D412yes—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73#13512yes—
294C23×C73C22×D411yescharacteristic
295Q8×C73—41no—
296Q8×C73—41no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—44no—
302D4×C73—48no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—84no—
310D4×C73—84no—
311D4×C73—84no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
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—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—84no—
349C2×C4×C73—84no—
350C2×C4×C73#12012yes—
351C2×C4×C73#12012yes—
352C2×C4×C73C22×D411yescharacteristic
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C2×#4111yescharacteristic
355C2×C4×C73C2×#4111yescharacteristic
356C2×C4×C73H(5,𝔽2)11yescharacteristic
357C2×C4×C73H(5,𝔽2)11yescharacteristic
358C8×C73—41no—
359C8×C73—41no—
360C8×C73—41no—
361C8×C73—41no—
362C22×C73—22no—
363C22×C73—22no—
364C22×C73—22no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—42no—
371C22×C73—41no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—41no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73C2×#12011yescharacteristic
391C22×C73#54611yescharacteristic
392C22×C73#54611yescharacteristic
393C22×C73C2×#13511yescharacteristic
394C22×C73#57511yescharacteristic
395C22×C73#57611yescharacteristic
396C22×C73#57711yescharacteristic
397C4×C73—22no—
398C4×C73—22no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—42no—
402C4×C73—42no—
403C4×C73—42no—
404C4×C73—42no—
405C4×C73—42no—
406C4×C73—81no—
407C4×C73#53211yescharacteristic
408C4×C73#53511yescharacteristic
409C4×C73#55011yescharacteristic
410C4×C73#55011yescharacteristic
411#25575C7311yesmaximal, characteristic, direct product factor, Sylow
412C2×C73—42no—
413C2×C73—81no—
414C2×C73—82no—
415C2×C73—161no—
416C2×C73#243111yescharacteristic
417C2×C73#300211yescharacteristic
418C2×C73#301211yescharacteristic
419C2×C73#329711yescharacteristic
420C2×C73#330111yescharacteristic
421C2×C73#332211yescharacteristic
422C2×C73#332611yescharacteristic
423C2×#553C2×C7311yescharacteristic, complemented
424C2×#488C2×C7311yescharacteristic, complemented
425C2×#463C2×C7311yescharacteristic, complemented
426#2540C2×C7311yescharacteristic, complemented
427#2000C2×C7311yescharacteristic, complemented
428#2000C2×C7311yescharacteristic, complemented
429#1999C2×C7311yescharacteristic, complemented
430#1999C2×C7311yescharacteristic, complemented
431#1989C2×C7311yescharacteristic, complemented
432#1954C2×C7311yescharacteristic, complemented
433#1875C2×C7311yescharacteristic, complemented
434#1874C2×C7311yescharacteristic, complemented
435#1873C2×C7311yescharacteristic, complemented
436#1872C2×C7311yescharacteristic, complemented
437C4×#102C2×C7311yescharacteristic, complemented
438C73#2557511yescharacteristic, direct product factor, Sylow
439C22×SD16C22×C7311yescharacteristic
440C22×D8C22×C7311yescharacteristic
441#553—24no—
442#553—24no—
443C2×#126—21no—
444C2×#125C22×C7311yescharacteristic
445C2×#124C22×C7311yescharacteristic
446C2×#123—21no—
447C2×C22⋊Q8C22×C7311yescharacteristic
448C2×C22⋊Q8C22×C7311yescharacteristic
449C2×#121—21no—
450C2×#121C22×C7311yescharacteristic
451C2×#121C22×C7311yescharacteristic
452C2×#121C22×C7311yescharacteristic
453C2×#121C22×C7311yescharacteristic
454C2×C4×D4—21no—
455C2×C4×D4C22×C7311yescharacteristic
456C2×C4×D4C22×C7311yescharacteristic
457C2×#117C22×C7311yescharacteristic
458C22×C4⋊C4C22×C7311yescharacteristic
459#488—24no—
460#463—24no—
461C2×C4⋊C8C22×C7311yescharacteristic
462C2×#103C22×C7311yescharacteristic
463C2×#103C22×C7311yescharacteristic
464C2×#103C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×#102C22×C7311yescharacteristic
467C2×#102C22×C7311yescharacteristic
468C2×#102C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×C22⋊C8C22×C7311yescharacteristic
471C2×C22⋊C8C22×C7311yescharacteristic
472C2×C22⋊C8C22×C7311yescharacteristic
473C2×C22⋊C8C22×C7311yescharacteristic
474C2×C4×C8C22×C7311yescharacteristic
475#399—21no—
476#392—21no—
477#390—21no—
478#390—21no—
479C4×C4⋊C4C22×C7311yescharacteristic
480#340C22×C7311yescharacteristic
481#340C22×C7311yescharacteristic
482#340C22×C7311yescharacteristic
483#340C22×C7311yescharacteristic
484#340C22×C7311yescharacteristic
485#340C22×C7311yescharacteristic
486C22×Q8C23×C7311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C7311yescharacteristic
492C22×D4C23×C7311yescharacteristic
493C22×D4C23×C7311yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C7311yescharacteristic
497C23×C4C23×C7311yescharacteristic
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C22×C8C23×C7311yescharacteristic
505C22×C8C23×C7311yescharacteristic
506C22×C8C23×C7311yescharacteristic
507C22×C8C23×C7311yescharacteristic
508#126—28no—
509#125—22no—
510#125D4×C7314yescomplemented
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4D4×C7314yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C7311yescharacteristic
542C2×C4⋊C4C23×C7311yescharacteristic
543C2×C4⋊C4C23×C7311yescharacteristic
544C2×C4⋊C4C23×C7311yescharacteristic
545C2×C4⋊C4C23×C7311yescharacteristic
546C2×C4⋊C4C23×C7311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C7311yescharacteristic
558C2×C22⋊C4D4×C7311yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C7311yescharacteristic
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C22⋊C8—41no—
575C4×C8—22no—
576#95—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C7311yescharacteristic
580C24C2×D4×C7311yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C7312yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C7311yescharacteristic
639C22×C4C2×D4×C7311yescharacteristic
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C2×D4×C7311yescharacteristic
642C22×C4C24×C7311yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C7312yes—
669C4⋊C4C2×D4×C7312yes—
670C4⋊C4C2×D4×C7312yes—
671C4⋊C4#41×C7312yes—
672C4⋊C4#41×C7312yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C7312yes—
688C42C2×D4×C7312yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23#135×C7312yes—
717C23C22×D4×C7311yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#120×C7312yes—
774C2×C4#120×C7312yes—
775C2×C4C22×D4×C7311yescharacteristic
776C2×C4C22×D4×C7311yescharacteristic
777C2×C4C2×#41×C7311yescharacteristic
778C2×C4C2×#41×C7311yescharacteristic
779C2×C4H(5,𝔽2)×C7311yescharacteristic
780C2×C4H(5,𝔽2)×C7311yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×#120×C7311yescharacteristic
814C22#546×C7311yescharacteristic
815C22#546×C7311yescharacteristic
816C22C2×#135×C7311yescharacteristic
817C22#575×C7311yescharacteristic
818C22#576×C7311yescharacteristic
819C22#577×C7311yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4#532×C7311yescharacteristic
831C4#535×C7311yescharacteristic
832C4#550×C7311yescharacteristic
833C4#550×C7311yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C73×#243111yescharacteristic
839C2C73×#300211yescharacteristic
840C2C73×#301211yescharacteristic
841C2C73×#329711yescharacteristic
842C2C73×#330111yescharacteristic
843C2C73×#332211yescharacteristic
844C2C73×#332611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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×#553×C73C2semidirect
2. C2×#488×C73C2semidirect
3. C2×#463×C73C2semidirect
4. C73×#2540C2semidirect
5. C73×#2000C2semidirect
6. C73×#2000C2semidirect
7. C73×#1999C2semidirect
8. C73×#1999C2semidirect
9. C73×#1989C2semidirect
10. C73×#1954C2semidirect
11. C73×#1875C2semidirect
12. C73×#1874C2semidirect
13. C73×#1873C2semidirect
14. C73×#1872C2semidirect
15. C4×#102×C73C2semidirect
87. #125×C73D4semidirect
108. C4×D4×C73D4semidirect
411. #25575C73direct (N × H)
423. C2×#553C2×C73semidirect
424. C2×#488C2×C73semidirect
425. C2×#463C2×C73semidirect
426. #2540C2×C73semidirect
427. #2000C2×C73semidirect
428. #2000C2×C73semidirect
429. #1999C2×C73semidirect
430. #1999C2×C73semidirect
431. #1989C2×C73semidirect
432. #1954C2×C73semidirect
433. #1875C2×C73semidirect
434. #1874C2×C73semidirect
435. #1873C2×C73semidirect
436. #1872C2×C73semidirect
437. C4×#102C2×C73semidirect
438. C73#25575direct (N × H)
510. #125D4×C73semidirect
531. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C732
C2×#488×C732
C2×#463×C732
C73×#25402
C73×#20002
C73×#19992
C73×#19892
C73×#19542
C73×#18752
C73×#18742
C73×#18732
C73×#18722
C4×#102×C732
#2557573