Finite Group Databasebeta

← C73×#24874 #32934278

Subgroups — C73×#24874 #32934278

Order 18688.

1004 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×#416×C73C211yesmaximal, characteristic, complemented
3C73×#2407C211yesmaximal, characteristic
4C73×#2354C211yesmaximal, characteristic, complemented
5C73×#2095C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1927C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1869C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1808C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23#482×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28#416×C73—24no—
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40#394×C73—21no—
41#392×C73—21no—
42#391×C73C2211yescharacteristic
43#390×C73—21no—
44#390×C73C2211yescharacteristic
45#388×C73—21no—
46#388×C73—21no—
47#386×C73—21no—
48#385×C73—21no—
49#384×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C4⋊C4×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—41no—
66C2×#41×C73—41no—
67C22×Q8×C73C2311yescharacteristic
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73D411yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C22×C8×C73—22no—
76C22×C8×C73—22no—
77C22×C8×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—41no—
84#121×C73—22no—
85#121×C73—41no—
86C4×D4×C73—22no—
87C4×D4×C73—22no—
88#117×C73—22no—
89#117×C73—22no—
90#117×C73—41no—
91#117×C73—41no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73D411yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C42×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117#107×C73—22no—
118#107×C73—41no—
119#107×C73—41no—
120#106×C73—22no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—22no—
124#103×C73—41no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—41no—
128#102×C73D414yescomplemented
129C22⋊C8×C73—22no—
130C22⋊C8×C73—22no—
131C22⋊C8×C73—41no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138C24×C73—21no—
139C24×C73C2×D411yescharacteristic
140C24×C73C2×D411yescharacteristic
141#41×C73—28no—
142#41×C73—44no—
143#41×C73—44no—
144#41×C73—44no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73#4112yes—
151C2×D4×C73—22no—
152C2×D4×C73—22no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—41no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73—81no—
165C2×D4×C73C2×D412yes—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—42no—
184C22×C4×C73—42no—
185C22×C4×C73—42no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73#4112yes—
191C22×C4×C73#4112yes—
192C22×C4×C73C2411yescharacteristic
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—44no—
205C2×C8×C73C2×D412yes—
206C4⋊C4×C73—22no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—42no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73—81no—
221C4⋊C4×C73C2×D412yes—
222C22⋊C4×C73—22no—
223C22⋊C4×C73—22no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—81no—
230C22⋊C4×C73—81no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73—81no—
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—42no—
236C42×C73—42no—
237C42×C73—42no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73#12312yes—
259C23×C73C22×D411yescharacteristic
260Q8×C73—22no—
261Q8×C73—22no—
262Q8×C73—41no—
263Q8×C73—41no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—44no—
267D4×C73—48no—
268D4×C73—41no—
269D4×C73—41no—
270D4×C73—84no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—22no—
282C2×C4×C73—21no—
283C2×C4×C73—22no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—48no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73#12312yes—
312C2×C4×C73#13512yes—
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73H(5,𝔽2)11yescharacteristic
318C2×C4×C73H(5,𝔽2)11yescharacteristic
319C8×C73—22no—
320C8×C73—41no—
321C8×C73—41no—
322C8×C73—41no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—42no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—42no—
336C22×C73—41no—
337C22×C73—42no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73C2×#12311yescharacteristic
345C22×C73D4211yescharacteristic
346C22×C73#54611yescharacteristic
347C22×C73C2×#13511yescharacteristic
348C22×C73#57511yescharacteristic
349C22×C73#57611yescharacteristic
350C22×C73#57811yescharacteristic
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—41no—
354C4×C73—41no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73—81no—
358C4×C73—81no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73—81no—
362C4×C73#52511yescharacteristic
363C4×C73#53811yescharacteristic
364C4×C73#54611yescharacteristic
365C4×C73#55111yescharacteristic
366#24874C7311yesmaximal, characteristic, direct product factor, Sylow
367C2×C73—42no—
368C2×C73—81no—
369C2×C73—82no—
370C2×C73#241811yescharacteristic
371C2×C73#309111yescharacteristic
372C2×C73#309811yescharacteristic
373C2×C73#326811yescharacteristic
374C2×C73#328311yescharacteristic
375C2×C73#330511yescharacteristic
376C2×C73#331311yescharacteristic
377C2×#482C2×C7311yescharacteristic, complemented
378C2×#416C2×C7311yescharacteristic, complemented
379#2407C2×C7311yescharacteristic
380#2354C2×C7311yescharacteristic, complemented
381#2095C2×C7311yescharacteristic, complemented
382#2071C2×C7311yescharacteristic, complemented
383#2036C2×C7311yescharacteristic, complemented
384#2033C2×C7311yescharacteristic, complemented
385#1927C2×C7311yescharacteristic, complemented
386#1925C2×C7311yescharacteristic, complemented
387#1873C2×C7311yescharacteristic, complemented
388#1869C2×C7311yescharacteristic, complemented
389#1854C2×C7311yescharacteristic, complemented
390#1808C2×C7311yescharacteristic, complemented
391#1788C2×C7311yescharacteristic, complemented
392C73#2487411yescharacteristic, direct product factor, Sylow
393C22×#41C22×C7311yescharacteristic
394C23×C8C22×C7311yescharacteristic
395C2×C22⋊Q8C22×C7311yescharacteristic
396C2×#121C22×C7311yescharacteristic
397C2×C4×D4C22×C7311yescharacteristic
398C2×#117C22×C7311yescharacteristic
399C2×#117C22×C7311yescharacteristic
400#482—24no—
401C2×#107C22×C7311yescharacteristic
402C2×#107C22×C7311yescharacteristic
403C2×#107C22×C7311yescharacteristic
404C2×#106C22×C7311yescharacteristic
405#416—24no—
406C2×#103C22×C7311yescharacteristic
407C2×#103C22×C7311yescharacteristic
408C2×#103C22×C7311yescharacteristic
409C2×#103C22×C7311yescharacteristic
410C2×#102C22×C7311yescharacteristic
411C2×#102C22×C7311yescharacteristic
412C2×#102C22×C7311yescharacteristic
413C2×#102C22×C7311yescharacteristic
414C2×C22⋊C8C22×C7311yescharacteristic
415C2×C22⋊C8C22×C7311yescharacteristic
416C2×C22⋊C8C22×C7311yescharacteristic
417#394—21no—
418#392—21no—
419#391C22×C7311yescharacteristic
420#390—21no—
421#390C22×C7311yescharacteristic
422#388—21no—
423#388—21no—
424#386—21no—
425#385—21no—
426#384C22×C7311yescharacteristic
427#380C22×C7311yescharacteristic
428#380C22×C7311yescharacteristic
429#380C22×C7311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4C22×C7311yescharacteristic
432#340C22×C7311yescharacteristic
433#340C22×C7311yescharacteristic
434#340C22×C7311yescharacteristic
435#340C22×C7311yescharacteristic
436#336C22×C7311yescharacteristic
437#336C22×C7311yescharacteristic
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C23×C7311yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4D4×C7311yescharacteristic
448C22×D4C23×C7311yescharacteristic
449C23×C4—21no—
450C23×C4C23×C7311yescharacteristic
451C23×C4C23×C7311yescharacteristic
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—41no—
455C22×C8C23×C7311yescharacteristic
456C22×C8C23×C7311yescharacteristic
457C22×C8C23×C7311yescharacteristic
458C22×C8C23×C7311yescharacteristic
459C22⋊Q8—22no—
460C22⋊Q8—41no—
461#121—22no—
462#121—41no—
463C4×D4—22no—
464C4×D4—22no—
465#117—22no—
466#117—22no—
467#117—41no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4D4×C7311yescharacteristic
473C2×C4⋊C4C23×C7311yescharacteristic
474C2×C4⋊C4C23×C7311yescharacteristic
475C2×C4⋊C4C23×C7311yescharacteristic
476C2×C4⋊C4C23×C7311yescharacteristic
477C2×C4⋊C4C23×C7311yescharacteristic
478C2×C4⋊C4C23×C7311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4D4×C7311yescharacteristic
489C2×C22⋊C4D4×C7311yescharacteristic
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C23×C7311yescharacteristic
494#107—22no—
495#107—41no—
496#107—41no—
497#106—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—41no—
502#102—22no—
503#102—22no—
504#102—41no—
505#102D4×C7314yescomplemented
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—41no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24C2×D4×C7311yescharacteristic
517C24C2×D4×C7311yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#41×C7312yes—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4C2×D4×C7312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4C2×D4×C7311yescharacteristic
564C22×C4C2×D4×C7311yescharacteristic
565C22×C4C2×D4×C7311yescharacteristic
566C22×C4C2×D4×C7311yescharacteristic
567C22×C4#41×C7312yes—
568C22×C4#41×C7312yes—
569C22×C4C24×C7311yescharacteristic
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—44no—
582C2×C8C2×D4×C7312yes—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—81no—
598C4⋊C4C2×D4×C7312yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C42—21no—
611C42—21no—
612C42—42no—
613C42—42no—
614C42—42no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#123×C7312yes—
636C23C22×D4×C7311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641D4—22no—
642D4—22no—
643D4—44no—
644D4—48no—
645D4—41no—
646D4—41no—
647D4—84no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4#123×C7312yes—
689C2×C4#135×C7312yes—
690C2×C4C22×D4×C7311yescharacteristic
691C2×C4C2×#41×C7311yescharacteristic
692C2×C4C2×#41×C7311yescharacteristic
693C2×C4C2×#41×C7311yescharacteristic
694C2×C4H(5,𝔽2)×C7311yescharacteristic
695C2×C4H(5,𝔽2)×C7311yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—41no—
710C22—42no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#123×C7311yescharacteristic
722C22D42×C7311yescharacteristic
723C22#546×C7311yescharacteristic
724C22C2×#135×C7311yescharacteristic
725C22#575×C7311yescharacteristic
726C22#576×C7311yescharacteristic
727C22#578×C7311yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—81no—
739C4#525×C7311yescharacteristic
740C4#538×C7311yescharacteristic
741C4#546×C7311yescharacteristic
742C4#551×C7311yescharacteristic
743C2—42no—
744C2—81no—
745C2—82no—
746C2C73×#241811yescharacteristic
747C2C73×#309111yescharacteristic
748C2C73×#309811yescharacteristic
749C2C73×#326811yescharacteristic
750C2C73×#328311yescharacteristic
751C2C73×#330511yescharacteristic
752C2C73×#331311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2407C2
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×#482×C73C2semidirect
2. C2×#416×C73C2semidirect
4. C73×#2354C2semidirect
5. C73×#2095C2semidirect
6. C73×#2071C2semidirect
7. C73×#2036C2semidirect
8. C73×#2033C2semidirect
9. C73×#1927C2semidirect
10. C73×#1925C2semidirect
11. C73×#1873C2semidirect
12. C73×#1869C2semidirect
13. C73×#1854C2semidirect
14. C73×#1808C2semidirect
15. C73×#1788C2semidirect
128. #102×C73D4semidirect
366. #24874C73direct (N × H)
377. C2×#482C2×C73semidirect
378. C2×#416C2×C73semidirect
380. #2354C2×C73semidirect
381. #2095C2×C73semidirect
382. #2071C2×C73semidirect
383. #2036C2×C73semidirect
384. #2033C2×C73semidirect
385. #1927C2×C73semidirect
386. #1925C2×C73semidirect
387. #1873C2×C73semidirect
388. #1869C2×C73semidirect
389. #1854C2×C73semidirect
390. #1808C2×C73semidirect
391. #1788C2×C73semidirect
392. C73#24874direct (N × H)
505. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C2×#416×C732
C73×#24072
C73×#23542
C73×#20952
C73×#20712
C73×#20362
C73×#20332
C73×#19272
C73×#19252
C73×#18732
C73×#18692
C73×#18542
C73×#18082
C73×#17882
#2487473