Finite Group Databasebeta

← C73×#22876 #32932280

Subgroups — C73×#22876 #32932280

Order 18688.

1130 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C73C211yesmaximal, characteristic
2C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
3C2×#416×C73C211yesmaximal, characteristic
4C73×#2362C211yesmaximal, characteristic, complemented
5C73×#2339C211yesmaximal, characteristic
6C73×#1969C211yesmaximal, characteristic, complemented
7C73×#1933C211yesmaximal, characteristic, complemented
8C73×#1927C211yesmaximal, characteristic, complemented
9C73×#1892C211yesmaximal, characteristic, complemented
10C73×#1878C211yesmaximal, characteristic, complemented
11C73×#1877C211yesmaximal, characteristic, complemented
12C73×#1862C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×C4×Q8×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24C2×#117×C73C2211yescharacteristic
25#452×C73C418yescomplemented
26C4×SD16×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29#416×C73—24no—
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#391×C73C2211yescharacteristic
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#388×C73—21no—
46#388×C73—21no—
47#387×C73—21no—
48#386×C73—21no—
49#386×C73—21no—
50#381×C73—21no—
51#380×C73C2211yescharacteristic
52C4×C4⋊C4×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55C2×#95×C73—21no—
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—41no—
66C2×#41×C73—41no—
67C2×#41×C73C2×C414yes—
68C22×Q8×C73C2311yescharacteristic
69C22×Q8×C73C2311yescharacteristic
70C22×D4×C73—21no—
71C22×D4×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73—21no—
75C23×C4×C73C2311yescharacteristic
76C2×Q16×C73—41no—
77C2×Q16×C73—41no—
78C2×Q16×C73C2×C414yescomplemented
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×SD16×C73C2×C414yes—
82C22×C8×C73—22no—
83C22×C8×C73—22no—
84C22×C8×C73—41no—
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73C2×C414yescomplemented
91C4×Q8×C73—22no—
92C4×Q8×C73—41no—
93C4×D4×C73—22no—
94C4×D4×C73—22no—
95C4×D4×C73—41no—
96C4×D4×C73—41no—
97#117×C73—22no—
98#117×C73—41no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73—21no—
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
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#103×C73C2×C414yescomplemented
126#102×C73—22no—
127#102×C73C2×C414yes—
128#102×C73D414yes—
129C22⋊C8×C73C2×C414yescomplemented
130C4×C8×C73—22no—
131C4×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—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73D411yescharacteristic
142#95×C73D411yescharacteristic
143C24×C73—21no—
144C24×C73C2×D411yescharacteristic
145#41×C73—28no—
146#41×C73—44no—
147#41×C73—44no—
148#41×C73—44no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73C22×C412yes—
160C2×Q8×C73C22×C412yes—
161C2×D4×C73—24no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73C22×C412yes—
168C2×D4×C73C2×D412yes—
169C2×D4×C73#4112yes—
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—24no—
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—81no—
189C22×C4×C73—81no—
190C22×C4×C73C22×C412yes—
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73#4112yes—
197C22×C4×C73C2411yescharacteristic
198Q16×C73—44no—
199SD16×C73—28no—
200C2×C8×C73—21no—
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—44no—
210C2×C8×C73C22×C412yes—
211C2×C8×C73C22×C412yes—
212C2×C8×C73C2×D412yes—
213C4⋊C4×C73—24no—
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—42no—
223C4⋊C4×C73—42no—
224C4⋊C4×C73C22×C412yes—
225C4⋊C4×C73C2×D412yes—
226C22⋊C4×C73—24no—
227C22⋊C4×C73—22no—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—81no—
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—42no—
238C42×C73—42no—
239C42×C73—42no—
240C23×C73—22no—
241C23×C73—21no—
242C23×C73—22no—
243C23×C73—22no—
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×C73C4×D412yes—
254C23×C73C22×D411yescharacteristic
255Q8×C73—22no—
256Q8×C73—22no—
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—41no—
260Q8×C73—41no—
261Q8×C73—41no—
262Q8×C73—41no—
263D4×C73—22no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—48no—
267D4×C73C4×D414yes—
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—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—21no—
282C2×C4×C73—22no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—48no—
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—84no—
307C2×C4×C73—84no—
308C2×C4×C73C4×D412yes—
309C2×C4×C73#13512yes—
310C2×C4×C73#13512yes—
311C2×C4×C73C23×C411yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C2×#4111yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C2×C4×C73H(5,𝔽2)11yescharacteristic
316C2×C4×C73H(5,𝔽2)11yescharacteristic
317C8×C73—22no—
318C8×C73—22no—
319C8×C73—22no—
320C8×C73—41no—
321C22×C73—22no—
322C22×C73—24no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—42no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—42no—
335C22×C73C2×C4×D411yescharacteristic
336C22×C73D4211yescharacteristic
337C22×C73#54611yescharacteristic
338C22×C73C2×#13511yescharacteristic
339C22×C73C2×#13511yescharacteristic
340C22×C73#57711yescharacteristic
341C22×C73#57811yescharacteristic
342C4×C73—22no—
343C4×C73—22no—
344C4×C73—22no—
345C4×C73—42no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73—41no—
349C4×C73—42no—
350C4×C73—41no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73C2×C4×D411yescharacteristic
355C4×C73#51811yescharacteristic
356C4×C73#54611yescharacteristic
357C4×C73#55111yescharacteristic
358#22876C7311yesmaximal, characteristic, direct product factor, Sylow
359C2×C73—42no—
360C2×C73—44no—
361C2×C73#235811yescharacteristic
362C2×C73C4×#13511yescharacteristic
363C2×C73#294711yescharacteristic
364C2×C73#328211yescharacteristic
365C2×C73#328311yescharacteristic
366C2×C73#329611yescharacteristic
367C2×C73#330211yescharacteristic
368C2×#452C2×C7311yescharacteristic
369C2×C4×SD16C2×C7311yescharacteristic, complemented
370C2×#416C2×C7311yescharacteristic
371#2362C2×C7311yescharacteristic, complemented
372#2339C2×C7311yescharacteristic
373#1969C2×C7311yescharacteristic, complemented
374#1933C2×C7311yescharacteristic, complemented
375#1927C2×C7311yescharacteristic, complemented
376#1892C2×C7311yescharacteristic, complemented
377#1878C2×C7311yescharacteristic, complemented
378#1877C2×C7311yescharacteristic, complemented
379#1862C2×C7311yescharacteristic, complemented
380#1854C2×C7311yescharacteristic, complemented
381C4×#102C2×C7311yescharacteristic, complemented
382C8×C22⋊C4C2×C7311yescharacteristic, complemented
383C73#2287611yescharacteristic, direct product factor, Sylow
384C22×#41C22×C7311yescharacteristic
385C22×Q16C22×C7311yescharacteristic
386C22×SD16C22×C7311yescharacteristic
387C23×C8C22×C7311yescharacteristic
388C2×C22⋊Q8C22×C7311yescharacteristic
389C2×C4×Q8C22×C7311yescharacteristic
390C2×C4×D4C22×C7311yescharacteristic
391C2×C4×D4C22×C7311yescharacteristic
392C2×#117C22×C7311yescharacteristic
393#452C4×C7318yescomplemented
394C4×SD16—24no—
395C2×#107C22×C7311yescharacteristic
396C2×#106C22×C7311yescharacteristic
397#416—24no—
398C2×#103C22×C7311yescharacteristic
399C2×#103C22×C7311yescharacteristic
400C2×#103C22×C7311yescharacteristic
401C2×#103C22×C7311yescharacteristic
402C2×#103C22×C7311yescharacteristic
403C2×#102C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405C2×#102C22×C7311yescharacteristic
406C2×C22⋊C8C22×C7311yescharacteristic
407C2×C4×C8C22×C7311yescharacteristic
408C2×C4×C8C22×C7311yescharacteristic
409#391C22×C7311yescharacteristic
410#391C22×C7311yescharacteristic
411#391C22×C7311yescharacteristic
412#389C22×C7311yescharacteristic
413#388—21no—
414#388—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#381—21no—
419#380C22×C7311yescharacteristic
420C4×C4⋊C4—21no—
421C4×C4⋊C4C22×C7311yescharacteristic
422C4×C22⋊C4C22×C7311yescharacteristic
423C2×#95—21no—
424#340C22×C7311yescharacteristic
425#340C22×C7311yescharacteristic
426#340C22×C7311yescharacteristic
427#340C22×C7311yescharacteristic
428#336C22×C7311yescharacteristic
429#336C22×C7311yescharacteristic
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C2×C4×C7314yes—
436C22×Q8C23×C7311yescharacteristic
437C22×Q8C23×C7311yescharacteristic
438C22×D4—21no—
439C22×D4C23×C7311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C7311yescharacteristic
444C2×Q16—41no—
445C2×Q16—41no—
446C2×Q16C2×C4×C7314yescomplemented
447C2×SD16—22no—
448C2×SD16—22no—
449C2×SD16C2×C4×C7314yes—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C23×C7311yescharacteristic
454C22×C8C23×C7311yescharacteristic
455C22×C8C23×C7311yescharacteristic
456C22×C8C23×C7311yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8C2×C4×C7314yescomplemented
459C4×Q8—22no—
460C4×Q8—41no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465#117—22no—
466#117—41no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C4⋊C4C23×C7311yescharacteristic
472C2×C4⋊C4C23×C7311yescharacteristic
473C2×C4⋊C4C23×C7311yescharacteristic
474C2×C4⋊C4C23×C7311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C7311yescharacteristic
481C2×C22⋊C4D4×C7311yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C23×C7311yescharacteristic
486C2×C42C23×C7311yescharacteristic
487#107—41no—
488#106—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—41no—
493#103C2×C4×C7314yescomplemented
494#102—22no—
495#102C2×C4×C7314yes—
496#102D4×C7314yes—
497C22⋊C8C2×C4×C7314yescomplemented
498C4×C8—22no—
499C4×C8—41no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95D4×C7311yescharacteristic
510#95D4×C7311yescharacteristic
511C24—21no—
512C24C2×D4×C7311yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8C22×C4×C7312yes—
528C2×Q8C22×C4×C7312yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C22×C4×C7312yes—
536C2×D4C2×D4×C7312yes—
537C2×D4#41×C7312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4C22×C4×C7312yes—
559C22×C4C2×D4×C7311yescharacteristic
560C22×C4C2×D4×C7311yescharacteristic
561C22×C4C2×D4×C7311yescharacteristic
562C22×C4C2×D4×C7311yescharacteristic
563C22×C4C2×D4×C7311yescharacteristic
564C22×C4#41×C7312yes—
565C22×C4C24×C7311yescharacteristic
566Q16—44no—
567SD16—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—44no—
578C2×C8C22×C4×C7312yes—
579C2×C8C22×C4×C7312yes—
580C2×C8C2×D4×C7312yes—
581C4⋊C4—24no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4C22×C4×C7312yes—
593C4⋊C4C2×D4×C7312yes—
594C22⋊C4—24no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—42no—
607C42—42no—
608C23—22no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C4×D4×C7312yes—
622C23C22×D4×C7311yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4C4×D4×C7314yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—48no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
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—84no—
675C2×C4—84no—
676C2×C4C4×D4×C7312yes—
677C2×C4#135×C7312yes—
678C2×C4#135×C7312yes—
679C2×C4C23×C4×C7311yescharacteristic
680C2×C4C22×D4×C7311yescharacteristic
681C2×C4C2×#41×C7311yescharacteristic
682C2×C4C2×#41×C7311yescharacteristic
683C2×C4H(5,𝔽2)×C7311yescharacteristic
684C2×C4H(5,𝔽2)×C7311yescharacteristic
685C8—22no—
686C8—22no—
687C8—22no—
688C8—41no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—42no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—42no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C2×C4×D4×C7311yescharacteristic
704C22D42×C7311yescharacteristic
705C22#546×C7311yescharacteristic
706C22C2×#135×C7311yescharacteristic
707C22C2×#135×C7311yescharacteristic
708C22#577×C7311yescharacteristic
709C22#578×C7311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4C2×C4×D4×C7311yescharacteristic
723C4#518×C7311yescharacteristic
724C4#546×C7311yescharacteristic
725C4#551×C7311yescharacteristic
726C2—42no—
727C2—44no—
728C2C73×#235811yescharacteristic
729C2C4×#135×C7311yescharacteristic
730C2C73×#294711yescharacteristic
731C2C73×#328211yescharacteristic
732C2C73×#328311yescharacteristic
733C2C73×#329611yescharacteristic
734C2C73×#330211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
LCSG ▷ C2×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×SD16×C73C2semidirect
4. C73×#2362C2semidirect
6. C73×#1969C2semidirect
7. C73×#1933C2semidirect
8. C73×#1927C2semidirect
9. C73×#1892C2semidirect
10. C73×#1878C2semidirect
11. C73×#1877C2semidirect
12. C73×#1862C2semidirect
13. C73×#1854C2semidirect
14. C4×#102×C73C2semidirect
15. C8×C22⋊C4×C73C2semidirect
25. #452×C73C4semidirect
78. C2×Q16×C73C2×C4semidirect
90. C22⋊Q8×C73C2×C4semidirect
125. #103×C73C2×C4semidirect
129. C22⋊C8×C73C2×C4semidirect
358. #22876C73direct (N × H)
369. C2×C4×SD16C2×C73semidirect
371. #2362C2×C73semidirect
373. #1969C2×C73semidirect
374. #1933C2×C73semidirect
375. #1927C2×C73semidirect
376. #1892C2×C73semidirect
377. #1878C2×C73semidirect
378. #1877C2×C73semidirect
379. #1862C2×C73semidirect
380. #1854C2×C73semidirect
381. C4×#102C2×C73semidirect
382. C8×C22⋊C4C2×C73semidirect
383. C73#22876direct (N × H)
393. #452C4×C73semidirect
446. C2×Q16C2×C4×C73semidirect
458. C22⋊Q8C2×C4×C73semidirect
493. #103C2×C4×C73semidirect
497. C22⋊C8C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C732
C2×C4×SD16×C732
C2×#416×C732
C73×#23622
C73×#23392
C73×#19692
C73×#19332
C73×#19272
C73×#18922
C73×#18782
C73×#18772
C73×#18622
C73×#18542
C4×#102×C732
C8×C22⋊C4×C732
#2287673