Finite Group Databasebeta

← C73×#25636 #32935040

Subgroups — C73×#25636 #32935040

Order 18688.

1140 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C73C211yesmaximal, characteristic, complemented
2C2×#495×C73C211yesmaximal, characteristic
3C2×#464×C73C211yesmaximal, characteristic, complemented
4C73×#2592C211yesmaximal, characteristic, complemented
5C73×#2016C211yesmaximal, characteristic, complemented
6C73×#2015C211yesmaximal, characteristic, complemented
7C73×#2013C211yesmaximal, characteristic, complemented
8C73×#2012C211yesmaximal, characteristic
9C73×#1984C211yesmaximal, characteristic, complemented
10C73×#1983C211yesmaximal, characteristic, complemented
11C73×#1880C211yesmaximal, characteristic, complemented
12C73×#1879C211yesmaximal, characteristic
13C73×#1878C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C4×#103×C73C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C22×D8×C73C2211yescharacteristic
22#556×C73—24no—
23#556×C73—24no—
24C2×C4⋊Q8×C73C2211yescharacteristic
25C2×#126×C73—21no—
26C2×#126×C73—21no—
27C2×#124×C73C2211yescharacteristic
28C2×#124×C73C2211yescharacteristic
29C2×#124×C73C2211yescharacteristic
30C2×C22⋊Q8×C73—21no—
31C2×C4×Q8×C73C2211yescharacteristic
32C2×C4×Q8×C73C2211yescharacteristic
33C2×C4×Q8×C73C2211yescharacteristic
34C2×C4×D4×C73C2211yescharacteristic
35C2×#117×C73—21no—
36#495×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×C4×C8×C73C2211yescharacteristic
48#397×C73—21no—
49#393×C73—21no—
50#391×C73C2211yescharacteristic
51#391×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#390×C73C2211yescharacteristic
54#388×C73—21no—
55#388×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73D411yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×Q8×C73C2311yescharacteristic
66C22×Q8×C73C2311yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C2×Q16×C73—22no—
71C2×Q16×C73—22no—
72C2×Q16×C73—22no—
73C2×Q16×C73—41no—
74C2×Q16×C73—41no—
75C2×Q16×C73—41no—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×SD16×C73—41no—
82C2×SD16×C73—41no—
83C2×SD16×C73—41no—
84C2×SD16×C73—41no—
85C2×D8×C73—22no—
86C2×D8×C73—22no—
87C2×D8×C73—41no—
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C4⋊Q8×C73—22no—
93C4⋊Q8×C73—22no—
94#126×C73—28no—
95#126×C73—28no—
96#124×C73—22no—
97#124×C73—22no—
98#124×C73—22no—
99#124×C73—22no—
100#124×C73—22no—
101#124×C73D414yes—
102C22⋊Q8×C73—28no—
103C4×Q8×C73—22no—
104C4×Q8×C73—22no—
105C4×Q8×C73—22no—
106C4×Q8×C73—22no—
107C4×Q8×C73—22no—
108C4×Q8×C73D414yes—
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111#117×C73—28no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73D411yescharacteristic
117C2×C4⋊C4×C73D411yescharacteristic
118C2×C4⋊C4×C73D411yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
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×C42×C73—21no—
134C2×C42×C73—21no—
135C2×C42×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C2×C42×C73C2311yescharacteristic
139C4⋊C8×C73—22no—
140#103×C73—22no—
141#103×C73—22no—
142#103×C73—22no—
143#103×C73—41no—
144#103×C73—41no—
145#102×C73—22no—
146#102×C73—41no—
147#102×C73—41no—
148C4×C8×C73—22no—
149#95×C73—21no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C2×Q8×C73—22no—
157C2×Q8×C73—22no—
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×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73—21no—
173C2×Q8×C73—21no—
174C2×Q8×C73—41no—
175C2×Q8×C73C2×D412yes—
176C2×Q8×C73C2×D412yes—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73C2×D412yes—
189C22×C4×C73—24no—
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—42no—
197C22×C4×C73—42no—
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205Q16×C73—44no—
206Q16×C73—44no—
207SD16×C73—44no—
208SD16×C73—44no—
209SD16×C73—44no—
210D8×C73—44no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
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#4112yes—
222C2×C8×C73#4112yes—
223C4⋊C4×C73—24no—
224C4⋊C4×C73—24no—
225C4⋊C4×C73—24no—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—22no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—22no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73C2×D412yes—
236C22⋊C4×C73—24no—
237C22⋊C4×C73—24no—
238C22⋊C4×C73—24no—
239C22⋊C4×C73—24no—
240C22⋊C4×C73—24no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—81no—
246C22⋊C4×C73—81no—
247C42×C73—24no—
248C42×C73—24no—
249C42×C73—21no—
250C42×C73—21no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—81no—
254C42×C73C2×D412yes—
255C42×C73C2×D412yes—
256C23×C73—22no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73C22×D411yescharacteristic
271Q8×C73—22no—
272Q8×C73—22no—
273Q8×C73—22no—
274Q8×C73—22no—
275Q8×C73—44no—
276Q8×C73—41no—
277Q8×C73—41no—
278Q8×C73—41no—
279Q8×C73—41no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73—41no—
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—21no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—48no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
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#12012yes—
327C2×C4×C73#12012yes—
328C2×C4×C73#13512yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C2×#4111yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73H(5,𝔽2)11yescharacteristic
334C2×C4×C73H(5,𝔽2)11yescharacteristic
335C8×C73—22no—
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73—81no—
353C22×C73C2×#12011yescharacteristic
354C22×C73#55011yescharacteristic
355C22×C73#55011yescharacteristic
356C22×C73C2×#13511yescharacteristic
357C22×C73#57511yescharacteristic
358C22×C73#57711yescharacteristic
359C22×C73#57811yescharacteristic
360C4×C73—22no—
361C4×C73—22no—
362C4×C73—22no—
363C4×C73—42no—
364C4×C73—42no—
365C4×C73—41no—
366C4×C73—42no—
367C4×C73—41no—
368C4×C73—41no—
369C4×C73—81no—
370C4×C73—81no—
371C4×C73—81no—
372C4×C73#53211yescharacteristic
373C4×C73#53511yescharacteristic
374C4×C73#54611yescharacteristic
375C4×C73#54611yescharacteristic
376#25636C7311yesmaximal, characteristic, direct product factor, Sylow
377C2×C73—82no—
378C2×C73—161no—
379C2×C73#243111yescharacteristic
380C2×C73#300211yescharacteristic
381C2×C73#301311yescharacteristic
382C2×C73#339311yescharacteristic
383C2×C73#339411yescharacteristic
384C2×C73#340111yescharacteristic
385C2×C73#340211yescharacteristic
386C2×#556C2×C7311yescharacteristic, complemented
387C2×#495C2×C7311yescharacteristic
388C2×#464C2×C7311yescharacteristic, complemented
389#2592C2×C7311yescharacteristic, complemented
390#2016C2×C7311yescharacteristic, complemented
391#2015C2×C7311yescharacteristic, complemented
392#2013C2×C7311yescharacteristic, complemented
393#2012C2×C7311yescharacteristic
394#1984C2×C7311yescharacteristic, complemented
395#1983C2×C7311yescharacteristic, complemented
396#1880C2×C7311yescharacteristic, complemented
397#1879C2×C7311yescharacteristic
398#1878C2×C7311yescharacteristic, complemented
399#1877C2×C7311yescharacteristic, complemented
400C4×#103C2×C7311yescharacteristic, complemented
401C73#2563611yescharacteristic, direct product factor, Sylow
402C22×Q16C22×C7311yescharacteristic
403C22×Q16C22×C7311yescharacteristic
404C22×SD16C22×C7311yescharacteristic
405C22×SD16C22×C7311yescharacteristic
406C22×SD16C22×C7311yescharacteristic
407C22×D8C22×C7311yescharacteristic
408#556—24no—
409#556—24no—
410C2×C4⋊Q8C22×C7311yescharacteristic
411C2×#126—21no—
412C2×#126—21no—
413C2×#124C22×C7311yescharacteristic
414C2×#124C22×C7311yescharacteristic
415C2×#124C22×C7311yescharacteristic
416C2×C22⋊Q8—21no—
417C2×C4×Q8C22×C7311yescharacteristic
418C2×C4×Q8C22×C7311yescharacteristic
419C2×C4×Q8C22×C7311yescharacteristic
420C2×C4×D4C22×C7311yescharacteristic
421C2×#117—21no—
422#495—24no—
423#464—24no—
424C2×C4⋊C8C22×C7311yescharacteristic
425C2×#103C22×C7311yescharacteristic
426C2×#103C22×C7311yescharacteristic
427C2×#103C22×C7311yescharacteristic
428C2×#103C22×C7311yescharacteristic
429C2×#103C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433C2×C4×C8C22×C7311yescharacteristic
434#397—21no—
435#393—21no—
436#391C22×C7311yescharacteristic
437#391C22×C7311yescharacteristic
438#390C22×C7311yescharacteristic
439#390C22×C7311yescharacteristic
440#388—21no—
441#388—21no—
442C4×C4⋊C4C22×C7311yescharacteristic
443#340C22×C7311yescharacteristic
444#340C22×C7311yescharacteristic
445#336C22×C7311yescharacteristic
446#336C22×C7311yescharacteristic
447#336C22×C7311yescharacteristic
448#336C22×C7311yescharacteristic
449C22×Q8D4×C7311yescharacteristic
450C22×Q8C23×C7311yescharacteristic
451C22×Q8C23×C7311yescharacteristic
452C22×Q8C23×C7311yescharacteristic
453C22×D4C23×C7311yescharacteristic
454C22×D4C23×C7311yescharacteristic
455C23×C4—21no—
456C2×Q16—22no—
457C2×Q16—22no—
458C2×Q16—22no—
459C2×Q16—41no—
460C2×Q16—41no—
461C2×Q16—41no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—41no—
468C2×SD16—41no—
469C2×SD16—41no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—41no—
474C22×C8C23×C7311yescharacteristic
475C22×C8C23×C7311yescharacteristic
476C22×C8C23×C7311yescharacteristic
477C22×C8C23×C7311yescharacteristic
478C4⋊Q8—22no—
479C4⋊Q8—22no—
480#126—28no—
481#126—28no—
482#124—22no—
483#124—22no—
484#124—22no—
485#124—22no—
486#124—22no—
487#124D4×C7314yes—
488C22⋊Q8—28no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8D4×C7314yes—
495C4×D4—22no—
496C4×D4—22no—
497#117—28no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C7311yescharacteristic
503C2×C4⋊C4D4×C7311yescharacteristic
504C2×C4⋊C4D4×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—21no—
522C2×C42C23×C7311yescharacteristic
523C2×C42C23×C7311yescharacteristic
524C2×C42C23×C7311yescharacteristic
525C4⋊C8—22no—
526#103—22no—
527#103—22no—
528#103—22no—
529#103—41no—
530#103—41no—
531#102—22no—
532#102—41no—
533#102—41no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540C24—21no—
541C24—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—41no—
561C2×Q8C2×D4×C7312yes—
562C2×Q8C2×D4×C7312yes—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4C2×D4×C7312yes—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587C22×C4C2×D4×C7311yescharacteristic
588C22×C4C2×D4×C7311yescharacteristic
589C22×C4C2×D4×C7311yescharacteristic
590C22×C4C24×C7311yescharacteristic
591Q16—44no—
592Q16—44no—
593SD16—44no—
594SD16—44no—
595SD16—44no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8#41×C7312yes—
608C2×C8#41×C7312yes—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C2×D4×C7312yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—24no—
634C42—24no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—81no—
640C42C2×D4×C7312yes—
641C42C2×D4×C7312yes—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C22×D4×C7311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4#120×C7312yes—
713C2×C4#120×C7312yes—
714C2×C4#135×C7312yes—
715C2×C4C22×D4×C7311yescharacteristic
716C2×C4C22×D4×C7311yescharacteristic
717C2×C4C2×#41×C7311yescharacteristic
718C2×C4C2×#41×C7311yescharacteristic
719C2×C4H(5,𝔽2)×C7311yescharacteristic
720C2×C4H(5,𝔽2)×C7311yescharacteristic
721C8—22no—
722C8—22no—
723C8—41no—
724C8—41no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22C2×#120×C7311yescharacteristic
740C22#550×C7311yescharacteristic
741C22#550×C7311yescharacteristic
742C22C2×#135×C7311yescharacteristic
743C22#575×C7311yescharacteristic
744C22#577×C7311yescharacteristic
745C22#578×C7311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—42no—
754C4—42no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4#532×C7311yescharacteristic
759C4#535×C7311yescharacteristic
760C4#546×C7311yescharacteristic
761C4#546×C7311yescharacteristic
762C2—82no—
763C2—161no—
764C2C73×#243111yescharacteristic
765C2C73×#300211yescharacteristic
766C2C73×#301311yescharacteristic
767C2C73×#339311yescharacteristic
768C2C73×#339411yescharacteristic
769C2C73×#340111yescharacteristic
770C2C73×#340211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D8×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#556×C73C2semidirect
3. C2×#464×C73C2semidirect
4. C73×#2592C2semidirect
5. C73×#2016C2semidirect
6. C73×#2015C2semidirect
7. C73×#2013C2semidirect
9. C73×#1984C2semidirect
10. C73×#1983C2semidirect
11. C73×#1880C2semidirect
13. C73×#1878C2semidirect
14. C73×#1877C2semidirect
15. C4×#103×C73C2semidirect
376. #25636C73direct (N × H)
386. C2×#556C2×C73semidirect
388. C2×#464C2×C73semidirect
389. #2592C2×C73semidirect
390. #2016C2×C73semidirect
391. #2015C2×C73semidirect
392. #2013C2×C73semidirect
394. #1984C2×C73semidirect
395. #1983C2×C73semidirect
396. #1880C2×C73semidirect
398. #1878C2×C73semidirect
399. #1877C2×C73semidirect
400. C4×#103C2×C73semidirect
401. C73#25636direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C732
C2×#495×C732
C2×#464×C732
C73×#25922
C73×#20162
C73×#20152
C73×#20132
C73×#20122
C73×#19842
C73×#19832
C73×#18802
C73×#18792
C73×#18782
C73×#18772
C4×#103×C732
#2563673