Finite Group Databasebeta

← C73×#26251 #32935655

Subgroups — C73×#26251 #32935655

Order 18688.

880 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#495×C73C211yesmaximal, characteristic
2C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
3C73×#2448C211yesmaximal, characteristic, complemented
4C73×#2447C211yesmaximal, characteristic, complemented
5C73×#2056C211yesmaximal, characteristic, complemented
6C73×#2054C211yesmaximal, characteristic
7C73×#2042C211yesmaximal, characteristic, complemented
8C73×#2042C211yesmaximal, characteristic, complemented
9C73×#1968C211yesmaximal, characteristic, complemented
10C73×#1968C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1941C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic
14C73×#1878C211yesmaximal, characteristic, complemented
15C8×C4⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C2×#124×C73C2211yescharacteristic
21C2×#124×C73C2211yescharacteristic
22C2×C4×Q8×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24#495×C73—24no—
25C4×SD16×C73—24no—
26C2×#106×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
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×C4×C8×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#399×C73—21no—
41#397×C73—21no—
42#397×C73—21no—
43#397×C73—21no—
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#391×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#390×C73C2211yescharacteristic
50#389×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#388×C73—21no—
53#388×C73—21no—
54#385×C73—21no—
55#381×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73C2311yescharacteristic
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C2×Q16×C73—22no—
67C2×Q16×C73—22no—
68C2×Q16×C73—41no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×SD16×C73D414yes—
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#124×C73—22no—
83#124×C73—22no—
84#124×C73—41no—
85#124×C73—41no—
86C4×Q8×C73—22no—
87C4×Q8×C73—41no—
88C4×D4×C73—22no—
89C4×D4×C73—41no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73D411yescharacteristic
94C2×C4⋊C4×C73D411yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
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×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#106×C73—22no—
115#106×C73—22no—
116C4⋊C8×C73—22no—
117#103×C73—22no—
118#103×C73—41no—
119#103×C73—41no—
120#103×C73—41no—
121#102×C73—22no—
122#102×C73—41no—
123#102×C73—41no—
124#102×C73—41no—
125C4×C8×C73—22no—
126C4×C8×C73—22no—
127C4×C8×C73—22no—
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—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73C2×D412yes—
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—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73C2×D412yes—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—81no—
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180Q16×C73—44no—
181SD16×C73—28no—
182SD16×C73—44no—
183D8×C73—44no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73C2×D412yes—
193C2×C8×C73#4112yes—
194C2×C8×C73#4112yes—
195C2×C8×C73#4112yes—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—22no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—81no—
208C4⋊C4×C73—81no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—81no—
218C22⋊C4×C73—81no—
219C22⋊C4×C73—81no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—42no—
227C23×C73—22no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73C22×D411yescharacteristic
242Q8×C73—22no—
243Q8×C73—22no—
244Q8×C73—41no—
245Q8×C73—41no—
246Q8×C73—41no—
247Q8×C73—41no—
248Q8×C73—41no—
249Q8×C73—41no—
250D4×C73—22no—
251D4×C73—22no—
252D4×C73—41no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—41no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—22no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—84no—
293C2×C4×C73#13512yes—
294C2×C4×C73#13512yes—
295C2×C4×C73C22×D411yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C8×C73—22no—
302C8×C73—41no—
303C8×C73—41no—
304C8×C73#12314yes—
305C22×C73—42no—
306C22×C73—42no—
307C22×C73—42no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73#53211yescharacteristic
320C22×C73D4211yescharacteristic
321C22×C73#55011yescharacteristic
322C22×C73C2×#13511yescharacteristic
323C22×C73C2×#13511yescharacteristic
324C22×C73#57711yescharacteristic
325C22×C73#57711yescharacteristic
326C4×C73—22no—
327C4×C73—22no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—41no—
331C4×C73—41no—
332C4×C73—41no—
333C4×C73—81no—
334C4×C73—81no—
335C4×C73—81no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73C2×#12311yescharacteristic
339C4×C73#54011yescharacteristic
340C4×C73#54611yescharacteristic
341C4×C73#55911yescharacteristic
342#26251C7311yesmaximal, characteristic, direct product factor, Sylow
343C2×C73—82no—
344C2×C73—161no—
345C2×C73#244511yescharacteristic
346C2×C73#316811yescharacteristic
347C2×C73#317311yescharacteristic
348C2×C73#328211yescharacteristic
349C2×C73#328411yescharacteristic
350C2×C73#339411yescharacteristic
351C2×C73#339411yescharacteristic
352C2×#495C2×C7311yescharacteristic
353C2×C4×SD16C2×C7311yescharacteristic, complemented
354#2448C2×C7311yescharacteristic, complemented
355#2447C2×C7311yescharacteristic, complemented
356#2056C2×C7311yescharacteristic, complemented
357#2054C2×C7311yescharacteristic
358#2042C2×C7311yescharacteristic, complemented
359#2042C2×C7311yescharacteristic, complemented
360#1968C2×C7311yescharacteristic, complemented
361#1968C2×C7311yescharacteristic, complemented
362#1968C2×C7311yescharacteristic, complemented
363#1941C2×C7311yescharacteristic, complemented
364#1879C2×C7311yescharacteristic
365#1878C2×C7311yescharacteristic, complemented
366C8×C4⋊C4C2×C7311yescharacteristic, complemented
367C73#2625111yescharacteristic, direct product factor, Sylow
368C22×Q16C22×C7311yescharacteristic
369C22×SD16C22×C7311yescharacteristic
370C22×SD16C22×C7311yescharacteristic
371C22×D8C22×C7311yescharacteristic
372C2×#124C22×C7311yescharacteristic
373C2×#124C22×C7311yescharacteristic
374C2×C4×Q8C22×C7311yescharacteristic
375C2×C4×D4C22×C7311yescharacteristic
376#495—24no—
377C4×SD16—24no—
378C2×#106C22×C7311yescharacteristic
379C2×#106C22×C7311yescharacteristic
380C2×C4⋊C8C22×C7311yescharacteristic
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×C4×C8C22×C7311yescharacteristic
390C2×C4×C8C22×C7311yescharacteristic
391C2×C4×C8C22×C7311yescharacteristic
392#399—21no—
393#397—21no—
394#397—21no—
395#397—21no—
396#391C22×C7311yescharacteristic
397#391C22×C7311yescharacteristic
398#391C22×C7311yescharacteristic
399#390C22×C7311yescharacteristic
400#390C22×C7311yescharacteristic
401#390C22×C7311yescharacteristic
402#389C22×C7311yescharacteristic
403#389C22×C7311yescharacteristic
404#388—21no—
405#388—21no—
406#385—21no—
407#381—21no—
408C4×C4⋊C4C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#336C22×C7311yescharacteristic
412#336C22×C7311yescharacteristic
413C22×Q8C23×C7311yescharacteristic
414C22×Q8C23×C7311yescharacteristic
415C22×D4C23×C7311yescharacteristic
416C22×D4C23×C7311yescharacteristic
417C23×C4—21no—
418C2×Q16—22no—
419C2×Q16—22no—
420C2×Q16—41no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16D4×C7314yes—
427C2×D8—22no—
428C2×D8—22no—
429C2×D8—41no—
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432C22×C8C23×C7311yescharacteristic
433C22×C8C23×C7311yescharacteristic
434#124—22no—
435#124—22no—
436#124—41no—
437#124—41no—
438C4×Q8—22no—
439C4×Q8—41no—
440C4×D4—22no—
441C4×D4—41no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C7311yescharacteristic
446C2×C4⋊C4D4×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42C23×C7311yescharacteristic
464C2×C42C23×C7311yescharacteristic
465C2×C42C23×C7311yescharacteristic
466#106—22no—
467#106—22no—
468C4⋊C8—22no—
469#103—22no—
470#103—41no—
471#103—41no—
472#103—41no—
473#102—22no—
474#102—41no—
475#102—41no—
476#102—41no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95D4×C7311yescharacteristic
489#95D4×C7311yescharacteristic
490C24—21no—
491C24—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×D4×C7312yes—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4C2×D4×C7312yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4C2×D4×C7311yescharacteristic
531C22×C4C24×C7311yescharacteristic
532Q16—44no—
533SD16—28no—
534SD16—44no—
535D8—44no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×D4×C7312yes—
545C2×C8#41×C7312yes—
546C2×C8#41×C7312yes—
547C2×C8#41×C7312yes—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
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—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—42no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×D4×C7311yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4#135×C7312yes—
646C2×C4#135×C7312yes—
647C2×C4C22×D4×C7311yescharacteristic
648C2×C4C2×#41×C7311yescharacteristic
649C2×C4C2×#41×C7311yescharacteristic
650C2×C4C2×#41×C7311yescharacteristic
651C2×C4H(5,𝔽2)×C7311yescharacteristic
652C2×C4H(5,𝔽2)×C7311yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8#123×C7314yes—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22#532×C7311yescharacteristic
672C22D42×C7311yescharacteristic
673C22#550×C7311yescharacteristic
674C22C2×#135×C7311yescharacteristic
675C22C2×#135×C7311yescharacteristic
676C22#577×C7311yescharacteristic
677C22#577×C7311yescharacteristic
678C4—22no—
679C4—22no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4C2×#123×C7311yescharacteristic
691C4#540×C7311yescharacteristic
692C4#546×C7311yescharacteristic
693C4#559×C7311yescharacteristic
694C2—82no—
695C2—161no—
696C2C73×#244511yescharacteristic
697C2C73×#316811yescharacteristic
698C2C73×#317311yescharacteristic
699C2C73×#328211yescharacteristic
700C2C73×#328411yescharacteristic
701C2C73×#339411yescharacteristic
702C2C73×#339411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D8×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C73C2semidirect
3. C73×#2448C2semidirect
4. C73×#2447C2semidirect
5. C73×#2056C2semidirect
7. C73×#2042C2semidirect
8. C73×#2042C2semidirect
9. C73×#1968C2semidirect
10. C73×#1968C2semidirect
11. C73×#1968C2semidirect
12. C73×#1941C2semidirect
14. C73×#1878C2semidirect
15. C8×C4⋊C4×C73C2semidirect
342. #26251C73direct (N × H)
353. C2×C4×SD16C2×C73semidirect
354. #2448C2×C73semidirect
355. #2447C2×C73semidirect
356. #2056C2×C73semidirect
358. #2042C2×C73semidirect
359. #2042C2×C73semidirect
360. #1968C2×C73semidirect
361. #1968C2×C73semidirect
362. #1968C2×C73semidirect
363. #1941C2×C73semidirect
365. #1878C2×C73semidirect
366. C8×C4⋊C4C2×C73semidirect
367. C73#26251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#495×C732
C2×C4×SD16×C732
C73×#24482
C73×#24472
C73×#20562
C73×#20542
C73×#20422
C73×#19682
C73×#19412
C73×#18792
C73×#18782
C8×C4⋊C4×C732
#2625173