Finite Group Databasebeta

← C73×#23032 #32932436

Subgroups — C73×#23032 #32932436

Order 18688.

1054 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C22×#107×C73C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic
5C73×#2360C211yesmaximal, characteristic, complemented
6C73×#1973C211yesmaximal, characteristic, complemented
7C73×#1944C211yesmaximal, characteristic, complemented
8C73×#1928C211yesmaximal, characteristic, complemented
9C73×#1925C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic
11C73×#1872C211yesmaximal, characteristic, complemented
12C73×#1863C211yesmaximal, characteristic, complemented
13C73×#1862C211yesmaximal, characteristic, complemented
14C73×#1776C211yesmaximal, characteristic, complemented
15C73×#1752C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73—21no—
22C2×C4×D4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#465×C73C418yescomplemented
26#440×C73—24no—
27C2×#107×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#107×C73C2211yescharacteristic
31C2×#107×C73C2211yescharacteristic
32C2×#106×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×#97×C73C2211yescharacteristic
41C2×#97×C73C2211yescharacteristic
42#391×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#389×C73—21no—
45#389×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#388×C73—21no—
48#387×C73—21no—
49#386×C73—21no—
50#385×C73—21no—
51#385×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73C2×C414yescomplemented
72C22×C8×C73—22no—
73C22×C8×C73—22no—
74C22×C8×C73C2×C414yescomplemented
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22⋊Q8×C73—22no—
80C22⋊Q8×C73C2×C414yescomplemented
81#121×C73—22no—
82#121×C73C2×C414yes—
83C4×Q8×C73—22no—
84C4×Q8×C73—41no—
85C4×D4×C73—22no—
86C4×D4×C73—41no—
87C4×D4×C73—44no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—41no—
97C2×C4⋊C4×C73—41no—
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#107×C73—22no—
117#107×C73—22no—
118#107×C73—22no—
119#107×C73D414yescomplemented
120#106×C73C2×C414yescomplemented
121#103×C73—22no—
122#103×C73—41no—
123#103×C73C2×C414yescomplemented
124#102×C73—22no—
125#102×C73—41no—
126#102×C73C2×C414yescomplemented
127C22⋊C8×C73—22no—
128#97×C73—22no—
129#97×C73—22no—
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×C73C2×D411yescharacteristic
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73C22×C412yes—
146C2×D4×C73—24no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—42no—
153C2×D4×C73—42no—
154C2×D4×C73C22×C412yes—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—81no—
173C22×C4×C73—81no—
174C22×C4×C73—81no—
175C22×C4×C73C22×C412yes—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4112yes—
182C22×C4×C73C2411yescharacteristic
183SD16×C73—28no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—28no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73C22×C412yes—
194C2×C8×C73C22×C412yes—
195C2×C8×C73C2×D412yes—
196C2×C8×C73#4112yes—
197C4⋊C4×C73—24no—
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—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—42no—
210C4⋊C4×C73—81no—
211C4⋊C4×C73C22×C412yes—
212C4⋊C4×C73C22×C412yes—
213C4⋊C4×C73C2×D412yes—
214C4⋊C4×C73C2×D412yes—
215C22⋊C4×C73—24no—
216C22⋊C4×C73—22no—
217C22⋊C4×C73—22no—
218C22⋊C4×C73—24no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—81no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—42no—
227C42×C73—42no—
228C42×C73—81no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—22no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73C4×D412yes—
241C23×C73AGL(1,ℤ/8)12yes—
242C23×C73#13712yes—
243C23×C73C22×D411yescharacteristic
244Q8×C73—22no—
245Q8×C73—22no—
246Q8×C73—41no—
247Q8×C73—41no—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—48no—
251D4×C73—41no—
252D4×C73—41no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—21no—
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—21no—
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—84no—
294C2×C4×C73—84no—
295C2×C4×C73C4×D412yes—
296C2×C4×C73C23×C411yescharacteristic
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C732−1+411yescharacteristic
302C8×C73—22no—
303C8×C73—41no—
304C8×C73—41no—
305C8×C73C4×D414yescomplemented
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73#44014yescomplemented
320C22×C73C2×C4×D411yescharacteristic
321C22×C73D4211yescharacteristic
322C22×C73#54711yescharacteristic
323C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C73C2×#13711yescharacteristic
325C22×C73#57611yescharacteristic
326C22×C73#57811yescharacteristic
327C4×C73—22no—
328C4×C73—41no—
329C4×C73—41no—
330C4×C73—42no—
331C4×C73—42no—
332C4×C73—42no—
333C4×C73—41no—
334C4×C73—42no—
335C4×C73—42no—
336C4×C73—41no—
337C4×C73—81no—
338C4×C73—81no—
339C4×C73C2×C4×D411yescharacteristic
340C4×C73#52011yescharacteristic
341C4×C73#54811yescharacteristic
342C4×C73#55311yescharacteristic
343#23032C7311yesmaximal, characteristic, direct product factor, Sylow
344C2×C73—24no—
345C2×C73—82no—
346C2×C73#236111yescharacteristic
347C2×C73C2×#44011yescharacteristic
348C2×C73#295111yescharacteristic
349C2×C73#326411yescharacteristic
350C2×C73#327011yescharacteristic
351C2×C73#334311yescharacteristic
352C2×C73#334611yescharacteristic
353C2×#465C2×C7311yescharacteristic
354C2×#440C2×C7311yescharacteristic, complemented
355C22×#107C2×C7311yescharacteristic, complemented
356#2361C2×C7311yescharacteristic
357#2360C2×C7311yescharacteristic, complemented
358#1973C2×C7311yescharacteristic, complemented
359#1944C2×C7311yescharacteristic, complemented
360#1928C2×C7311yescharacteristic, complemented
361#1925C2×C7311yescharacteristic, complemented
362#1874C2×C7311yescharacteristic
363#1872C2×C7311yescharacteristic, complemented
364#1863C2×C7311yescharacteristic, complemented
365#1862C2×C7311yescharacteristic, complemented
366#1776C2×C7311yescharacteristic, complemented
367#1752C2×C7311yescharacteristic, complemented
368C73#2303211yescharacteristic, direct product factor, Sylow
369C22×SD16C22×C7311yescharacteristic
370C23×C8C22×C7311yescharacteristic
371C2×C22⋊Q8C22×C7311yescharacteristic
372C2×#121C22×C7311yescharacteristic
373C2×C4×Q8C22×C7311yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4C22×C7311yescharacteristic
376C22×C4⋊C4C22×C7311yescharacteristic
377C22×C4⋊C4C22×C7311yescharacteristic
378#465C4×C7318yescomplemented
379#440—24no—
380C2×#107—24no—
381C2×#107C22×C7311yescharacteristic
382C2×#107C22×C7311yescharacteristic
383C2×#107C22×C7311yescharacteristic
384C2×#107C22×C7311yescharacteristic
385C2×#106C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#103C22×C7311yescharacteristic
388C2×#103C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×C22⋊C8C22×C7311yescharacteristic
393C2×#97C22×C7311yescharacteristic
394C2×#97C22×C7311yescharacteristic
395#391C22×C7311yescharacteristic
396#390C22×C7311yescharacteristic
397#389—21no—
398#389C22×C7311yescharacteristic
399#389C22×C7311yescharacteristic
400#388—21no—
401#387—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405C4×C4⋊C4C22×C7311yescharacteristic
406C4×C4⋊C4C22×C7311yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#336C22×C7311yescharacteristic
414#336C22×C7311yescharacteristic
415C22×Q8C23×C7311yescharacteristic
416C22×D4—21no—
417C22×D4C23×C7311yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C7311yescharacteristic
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×C4×C7314yescomplemented
425C22×C8—22no—
426C22×C8—22no—
427C22×C8C2×C4×C7314yescomplemented
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432C22⋊Q8—22no—
433C22⋊Q8C2×C4×C7314yescomplemented
434#121—22no—
435#121C2×C4×C7314yes—
436C4×Q8—22no—
437C4×Q8—41no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—44no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C7311yescharacteristic
463C2×C22⋊C4D4×C7311yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C7311yescharacteristic
468C2×C42C23×C7311yescharacteristic
469#107—22no—
470#107—22no—
471#107—22no—
472#107D4×C7314yescomplemented
473#106C2×C4×C7314yescomplemented
474#103—22no—
475#103—41no—
476#103C2×C4×C7314yescomplemented
477#102—22no—
478#102—41no—
479#102C2×C4×C7314yescomplemented
480C22⋊C8—22no—
481#97—22no—
482#97—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C7311yescharacteristic
490#95D4×C7311yescharacteristic
491C24—21no—
492C24C2×D4×C7311yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×C4×C7312yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×C4×C7312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C22×C4×C7312yes—
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4C2×D4×C7311yescharacteristic
531C22×C4C2×D4×C7311yescharacteristic
532C22×C4C2×D4×C7311yescharacteristic
533C22×C4C2×D4×C7311yescharacteristic
534C22×C4#41×C7312yes—
535C22×C4C24×C7311yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C22×C4×C7312yes—
547C2×C8C22×C4×C7312yes—
548C2×C8C2×D4×C7312yes—
549C2×C8#41×C7312yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—81no—
564C4⋊C4C22×C4×C7312yes—
565C4⋊C4C22×C4×C7312yes—
566C4⋊C4C2×D4×C7312yes—
567C4⋊C4C2×D4×C7312yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—24no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—81no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×D4×C7312yes—
594C23AGL(1,ℤ/8)×C7312yes—
595C23#137×C7312yes—
596C23C22×D4×C7311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
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—21no—
628C2×C4—21no—
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—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C4×D4×C7312yes—
649C2×C4C23×C4×C7311yescharacteristic
650C2×C4C22×D4×C7311yescharacteristic
651C2×C4C2×#41×C7311yescharacteristic
652C2×C4C2×#41×C7311yescharacteristic
653C2×C4H(5,𝔽2)×C7311yescharacteristic
654C2×C42−1+4×C7311yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8C4×D4×C7314yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22#440×C7314yescomplemented
673C22C2×C4×D4×C7311yescharacteristic
674C22D42×C7311yescharacteristic
675C22#547×C7311yescharacteristic
676C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
677C22C2×#137×C7311yescharacteristic
678C22#576×C7311yescharacteristic
679C22#578×C7311yescharacteristic
680C4—22no—
681C4—42no—
682C4—41no—
683C4—42no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C2×C4×D4×C7311yescharacteristic
693C4#520×C7311yescharacteristic
694C4#548×C7311yescharacteristic
695C4#553×C7311yescharacteristic
696C2—24no—
697C2—82no—
698C2C73×#236111yescharacteristic
699C2C2×#440×C7311yescharacteristic
700C2C73×#295111yescharacteristic
701C2C73×#326411yescharacteristic
702C2C73×#327011yescharacteristic
703C2C73×#334311yescharacteristic
704C2C73×#334611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×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×#440×C73C2semidirect
3. C22×#107×C73C2semidirect
5. C73×#2360C2semidirect
6. C73×#1973C2semidirect
7. C73×#1944C2semidirect
8. C73×#1928C2semidirect
9. C73×#1925C2semidirect
11. C73×#1872C2semidirect
12. C73×#1863C2semidirect
13. C73×#1862C2semidirect
14. C73×#1776C2semidirect
15. C73×#1752C2semidirect
25. #465×C73C4semidirect
71. C2×SD16×C73C2×C4semidirect
74. C22×C8×C73C2×C4semidirect
80. C22⋊Q8×C73C2×C4semidirect
119. #107×C73D4semidirect
120. #106×C73C2×C4semidirect
123. #103×C73C2×C4semidirect
126. #102×C73C2×C4semidirect
305. C8×C73C4×D4semidirect
319. C22×C73#440semidirect
343. #23032C73direct (N × H)
354. C2×#440C2×C73semidirect
355. C22×#107C2×C73semidirect
357. #2360C2×C73semidirect
358. #1973C2×C73semidirect
359. #1944C2×C73semidirect
360. #1928C2×C73semidirect
361. #1925C2×C73semidirect
363. #1872C2×C73semidirect
364. #1863C2×C73semidirect
365. #1862C2×C73semidirect
366. #1776C2×C73semidirect
367. #1752C2×C73semidirect
368. C73#23032direct (N × H)
378. #465C4×C73semidirect
424. C2×SD16C2×C4×C73semidirect
427. C22×C8C2×C4×C73semidirect
433. C22⋊Q8C2×C4×C73semidirect
472. #107D4×C73semidirect
473. #106C2×C4×C73semidirect
476. #103C2×C4×C73semidirect
479. #102C2×C4×C73semidirect
658. C8C4×D4×C73semidirect
672. C22#440×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C732
C2×#440×C732
C22×#107×C732
C73×#23612
C73×#23602
C73×#19732
C73×#19442
C73×#19282
C73×#19252
C73×#18742
C73×#18722
C73×#18632
C73×#18622
C73×#17762
C73×#17522
#2303273