Finite Group Databasebeta

← C73×#24895 #32934299

Subgroups — C73×#24895 #32934299

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C73C211yesmaximal, characteristic
2C2×C4×D8×C73C211yesmaximal, characteristic, complemented
3C73×#2420C211yesmaximal, characteristic, complemented
4C73×#2339C211yesmaximal, characteristic, complemented
5C73×#2097C211yesmaximal, characteristic, complemented
6C73×#2075C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#1933C211yesmaximal, characteristic, complemented
10C73×#1923C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1877C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1804C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23#449×C73—24no—
24C4×D8×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39#397×C73—21no—
40#394×C73—21no—
41#391×C73C2211yescharacteristic
42#391×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#386×C73—21no—
46#386×C73—21no—
47#386×C73—21no—
48#382×C73C2211yescharacteristic
49#381×C73—21no—
50#381×C73—21no—
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C22⋊C4×C73C2211yescharacteristic
54C2×#95×C73—21no—
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×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73C2311yescharacteristic
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—41no—
80C2×D8×C73—22no—
81C2×D8×C73—22no—
82C2×D8×C73D414yes—
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87#121×C73—22no—
88#121×C73—41no—
89C4×D4×C73—22no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—41no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
110C2×C22⋊C4×C73D411yescharacteristic
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#107×C73—22no—
114#106×C73—41no—
115C4⋊C8×C73—41no—
116#103×C73—22no—
117#103×C73—22no—
118#103×C73—41no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—41no—
124C22⋊C8×C73—22no—
125C22⋊C8×C73—41no—
126C4×C8×C73—22no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73D411yescharacteristic
137#95×C73D411yescharacteristic
138C24×C73—21no—
139C24×C73—21no—
140C24×C73C2×D411yescharacteristic
141#41×C73—44no—
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—24no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73—81no—
165C2×D4×C73C2×D412yes—
166C2×D4×C73C2×D412yes—
167C2×D4×C73#4112yes—
168C2×D4×C73#4112yes—
169C22×C4×C73—24no—
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—42no—
183C22×C4×C73—42no—
184C22×C4×C73—42no—
185C22×C4×C73—42no—
186C22×C4×C73—42no—
187C22×C4×C73—42no—
188C22×C4×C73—42no—
189C22×C4×C73—42no—
190C22×C4×C73—81no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2411yescharacteristic
199SD16×C73—44no—
200D8×C73—28no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73C2×D412yes—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—81no—
224C22⋊C4×C73—22no—
225C22⋊C4×C73—41no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—81no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73—81no—
233C22⋊C4×C73—81no—
234C42×C73—21no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—21no—
238C23×C73—22no—
239C23×C73—22no—
240C23×C73—22no—
241C23×C73—21no—
242C23×C73—22no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73C22×D411yescharacteristic
260Q8×C73—22no—
261Q8×C73—22no—
262Q8×C73—41no—
263Q8×C73—41no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—22no—
267D4×C73—22no—
268D4×C73—22no—
269D4×C73—48no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—84no—
273D4×C73#12314yes—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—22no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—48no—
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—84no—
312C2×C4×C73—84no—
313C2×C4×C73—84no—
314C2×C4×C73#13512yes—
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73C2×#4111yescharacteristic
319C2×C4×C73H(5,𝔽2)11yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C8×C73—22no—
322C8×C73—41no—
323C8×C73—41no—
324C8×C73—41no—
325C22×C73—24no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—42no—
336C22×C73—41no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73#52511yescharacteristic
347C22×C73D4211yescharacteristic
348C22×C73#54611yescharacteristic
349C22×C73C2×#13511yescharacteristic
350C22×C73#57511yescharacteristic
351C22×C73#57611yescharacteristic
352C22×C73#57711yescharacteristic
353C4×C73—22no—
354C4×C73—41no—
355C4×C73—42no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73—81no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73C2×#12311yescharacteristic
365C4×C73#53811yescharacteristic
366C4×C73#54611yescharacteristic
367C4×C73#55111yescharacteristic
368#24895C7311yesmaximal, characteristic, direct product factor, Sylow
369C2×C73—44no—
370C2×C73—81no—
371C2×C73—82no—
372C2×C73#241811yescharacteristic
373C2×C73#310211yescharacteristic
374C2×C73#311911yescharacteristic
375C2×C73#326711yescharacteristic
376C2×C73#328011yescharacteristic
377C2×C73#330311yescharacteristic
378C2×C73#332211yescharacteristic
379C2×#449C2×C7311yescharacteristic
380C2×C4×D8C2×C7311yescharacteristic, complemented
381#2420C2×C7311yescharacteristic, complemented
382#2339C2×C7311yescharacteristic, complemented
383#2097C2×C7311yescharacteristic, complemented
384#2075C2×C7311yescharacteristic, complemented
385#2055C2×C7311yescharacteristic, complemented
386#2034C2×C7311yescharacteristic, complemented
387#1933C2×C7311yescharacteristic, complemented
388#1923C2×C7311yescharacteristic, complemented
389#1879C2×C7311yescharacteristic, complemented
390#1877C2×C7311yescharacteristic, complemented
391#1864C2×C7311yescharacteristic, complemented
392#1804C2×C7311yescharacteristic, complemented
393#1788C2×C7311yescharacteristic, complemented
394C73#2489511yescharacteristic, direct product factor, Sylow
395C22×#41C22×C7311yescharacteristic
396C22×SD16C22×C7311yescharacteristic
397C22×D8C22×C7311yescharacteristic
398C2×#121C22×C7311yescharacteristic
399C2×C4×D4C22×C7311yescharacteristic
400C2×C4×D4C22×C7311yescharacteristic
401C2×C4×D4C22×C7311yescharacteristic
402#449—24no—
403C4×D8—24no—
404C2×#107C22×C7311yescharacteristic
405C2×#106C22×C7311yescharacteristic
406C2×C4⋊C8C22×C7311yescharacteristic
407C2×#103C22×C7311yescharacteristic
408C2×#103C22×C7311yescharacteristic
409C2×#103C22×C7311yescharacteristic
410C2×#102C22×C7311yescharacteristic
411C2×#102C22×C7311yescharacteristic
412C2×#102C22×C7311yescharacteristic
413C2×#102C22×C7311yescharacteristic
414C2×#102C22×C7311yescharacteristic
415C2×C22⋊C8C22×C7311yescharacteristic
416C2×C22⋊C8C22×C7311yescharacteristic
417C2×C4×C8C22×C7311yescharacteristic
418#397—21no—
419#394—21no—
420#391C22×C7311yescharacteristic
421#391C22×C7311yescharacteristic
422#390C22×C7311yescharacteristic
423#389C22×C7311yescharacteristic
424#386—21no—
425#386—21no—
426#386—21no—
427#382C22×C7311yescharacteristic
428#381—21no—
429#381—21no—
430#380C22×C7311yescharacteristic
431#380C22×C7311yescharacteristic
432C4×C22⋊C4C22×C7311yescharacteristic
433C2×#95—21no—
434#340C22×C7311yescharacteristic
435#340C22×C7311yescharacteristic
436#340C22×C7311yescharacteristic
437#340C22×C7311yescharacteristic
438#336C22×C7311yescharacteristic
439#336C22×C7311yescharacteristic
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C22×Q8C23×C7311yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C7311yescharacteristic
450C22×D4C23×C7311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4—21no—
455C23×C4C23×C7311yescharacteristic
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×D8—22no—
460C2×D8—22no—
461C2×D8D4×C7314yes—
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464C22×C8C23×C7311yescharacteristic
465C22×C8C23×C7311yescharacteristic
466#121—22no—
467#121—41no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4C23×C7311yescharacteristic
476C2×C4⋊C4C23×C7311yescharacteristic
477C2×C4⋊C4C23×C7311yescharacteristic
478C2×C4⋊C4C23×C7311yescharacteristic
479C2×C4⋊C4C23×C7311yescharacteristic
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×C42C23×C7311yescharacteristic
491C2×C42C23×C7311yescharacteristic
492#107—22no—
493#106—41no—
494C4⋊C8—41no—
495#103—22no—
496#103—22no—
497#103—41no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—22no—
502#102—41no—
503C22⋊C8—22no—
504C22⋊C8—41no—
505C4×C8—22no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95D4×C7311yescharacteristic
516#95D4×C7311yescharacteristic
517C24—21no—
518C24—21no—
519C24C2×D4×C7311yescharacteristic
520#41—44no—
521#41—44no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8#41×C7312yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4C2×D4×C7312yes—
545C2×D4C2×D4×C7312yes—
546C2×D4#41×C7312yes—
547C2×D4#41×C7312yes—
548C22×C4—24no—
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—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—81no—
570C22×C4—81no—
571C22×C4—81no—
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C2×D4×C7311yescharacteristic
574C22×C4C2×D4×C7311yescharacteristic
575C22×C4C2×D4×C7311yescharacteristic
576C22×C4C2×D4×C7311yescharacteristic
577C22×C4C24×C7311yescharacteristic
578SD16—44no—
579D8—28no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8C2×D4×C7312yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—81no—
603C22⋊C4—22no—
604C22⋊C4—41no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—21no—
621C23—22no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23C22×D4×C7311yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—84no—
652D4#123×C7314yes—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—48no—
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—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4#135×C7312yes—
694C2×C4C22×D4×C7311yescharacteristic
695C2×C4C2×#41×C7311yescharacteristic
696C2×C4C2×#41×C7311yescharacteristic
697C2×C4C2×#41×C7311yescharacteristic
698C2×C4H(5,𝔽2)×C7311yescharacteristic
699C2×C4H(5,𝔽2)×C7311yescharacteristic
700C8—22no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22#525×C7311yescharacteristic
726C22D42×C7311yescharacteristic
727C22#546×C7311yescharacteristic
728C22C2×#135×C7311yescharacteristic
729C22#575×C7311yescharacteristic
730C22#576×C7311yescharacteristic
731C22#577×C7311yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4C2×#123×C7311yescharacteristic
744C4#538×C7311yescharacteristic
745C4#546×C7311yescharacteristic
746C4#551×C7311yescharacteristic
747C2—44no—
748C2—81no—
749C2—82no—
750C2C73×#241811yescharacteristic
751C2C73×#310211yescharacteristic
752C2C73×#311911yescharacteristic
753C2C73×#326711yescharacteristic
754C2C73×#328011yescharacteristic
755C2C73×#330311yescharacteristic
756C2C73×#332211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#449×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C73C2semidirect
3. C73×#2420C2semidirect
4. C73×#2339C2semidirect
5. C73×#2097C2semidirect
6. C73×#2075C2semidirect
7. C73×#2055C2semidirect
8. C73×#2034C2semidirect
9. C73×#1933C2semidirect
10. C73×#1923C2semidirect
11. C73×#1879C2semidirect
12. C73×#1877C2semidirect
13. C73×#1864C2semidirect
14. C73×#1804C2semidirect
15. C73×#1788C2semidirect
368. #24895C73direct (N × H)
380. C2×C4×D8C2×C73semidirect
381. #2420C2×C73semidirect
382. #2339C2×C73semidirect
383. #2097C2×C73semidirect
384. #2075C2×C73semidirect
385. #2055C2×C73semidirect
386. #2034C2×C73semidirect
387. #1933C2×C73semidirect
388. #1923C2×C73semidirect
389. #1879C2×C73semidirect
390. #1877C2×C73semidirect
391. #1864C2×C73semidirect
392. #1804C2×C73semidirect
393. #1788C2×C73semidirect
394. C73#24895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#449×C732
C2×C4×D8×C732
C73×#24202
C73×#23392
C73×#20972
C73×#20752
C73×#20552
C73×#20342
C73×#19332
C73×#19232
C73×#18792
C73×#18772
C73×#18642
C73×#18042
C73×#17882
#2489573