Finite Group Databasebeta

← C73×#23126 #32932530

Subgroups — C73×#23126 #32932530

Order 18688.

994 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C73C211yesmaximal, characteristic
2C73×#2361C211yesmaximal, characteristic
3C73×#2360C211yesmaximal, characteristic, complemented
4C73×#1934C211yesmaximal, characteristic, complemented
5C73×#1933C211yesmaximal, characteristic, complemented
6C73×#1920C211yesmaximal, characteristic, complemented
7C73×#1919C211yesmaximal, characteristic, complemented
8C73×#1880C211yesmaximal, characteristic, complemented
9C73×#1877C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic
11C73×#1872C211yesmaximal, characteristic, complemented
12C4×#103×C73C211yesmaximal, characteristic, complemented
13C4×#102×C73C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, 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
26C2×#106×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×C22⋊C8×C73C2211yescharacteristic
34C2×C4×C8×C73C2211yescharacteristic
35C2×C4×C8×C73C2211yescharacteristic
36#391×C73C2211yescharacteristic
37#390×C73C2211yescharacteristic
38#389×C73—21no—
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#388×C73—21no—
42#387×C73—21no—
43#386×C73—21no—
44#385×C73—21no—
45#385×C73—21no—
46C4×C4⋊C4×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C22⋊C4×C73—21no—
49C4×C22⋊C4×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×Q8×C73C2311yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×SD16×C73—41no—
68C2×SD16×C73—41no—
69C2×SD16×C73C2×C414yescomplemented
70C22×C8×C73—41no—
71C22×C8×C73—41no—
72C22×C8×C73C2×C414yescomplemented
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22⋊Q8×C73—22no—
78C22⋊Q8×C73C2×C414yescomplemented
79#121×C73—22no—
80#121×C73C2×C414yes—
81C4×Q8×C73—22no—
82C4×Q8×C73—41no—
83C4×D4×C73—22no—
84C4×D4×C73—41no—
85C4×D4×C73—44no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73—41no—
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×C73D411yescharacteristic
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114#106×C73C2×C414yescomplemented
115#103×C73—22no—
116#103×C73—41no—
117#103×C73C2×C414yescomplemented
118#102×C73—22no—
119#102×C73—41no—
120#102×C73C2×C414yescomplemented
121C22⋊C8×C73—22no—
122C4×C8×C73—41no—
123C4×C8×C73—41no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C24×C73—21no—
133C24×C73C2×D411yescharacteristic
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73C22×C412yes—
140C2×D4×C73—24no—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—42no—
147C2×D4×C73—42no—
148C2×D4×C73C22×C412yes—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—42no—
161C22×C4×C73—42no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—81no—
167C22×C4×C73—81no—
168C22×C4×C73—81no—
169C22×C4×C73C22×C412yes—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73#4112yes—
176C22×C4×C73C2411yescharacteristic
177SD16×C73—44no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—44no—
189C2×C8×C73C22×C412yes—
190C2×C8×C73C22×C412yes—
191C4⋊C4×C73—24no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73C22×C412yes—
206C4⋊C4×C73C22×C412yes—
207C4⋊C4×C73#4112yes—
208C4⋊C4×C73#4112yes—
209C22⋊C4×C73—24no—
210C22⋊C4×C73—22no—
211C22⋊C4×C73—24no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73SD1614yescomplemented
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—42no—
221C42×C73—42no—
222C42×C73—81no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—22no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73C4×D412yes—
235C23×C73C2×SD1612yes—
236C23×C73#13512yes—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—41no—
241Q8×C73—41no—
242D4×C73—22no—
243D4×C73—22no—
244D4×C73—48no—
245D4×C73—41no—
246D4×C73—41no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
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—84no—
285C2×C4×C73—84no—
286C2×C4×C73—84no—
287C2×C4×C73C4×D412yes—
288C2×C4×C73C2×SD1612yes—
289C2×C4×C73C2×SD1612yes—
290C2×C4×C73C23×C411yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C8×C73—22no—
297C8×C73—22no—
298C8×C73—41no—
299C8×C73—41no—
300C22×C73—22no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—42no—
307C22×C73—42no—
308C22×C73—42no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73C4×SD1614yes—
314C22×C73C2×C4×D411yescharacteristic
315C22×C73#54611yescharacteristic
316C22×C73#54611yescharacteristic
317C22×C73C22×SD1611yescharacteristic
318C22×C73C2×#13511yescharacteristic
319C22×C73#57611yescharacteristic
320C22×C73#57811yescharacteristic
321C4×C73—22no—
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—42no—
325C4×C73—42no—
326C4×C73—42no—
327C4×C73—42no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—41no—
331C4×C73—81no—
332C4×C73—81no—
333C4×C73C4×#4111yescharacteristic
334C4×C73#51811yescharacteristic
335C4×C73#55311yescharacteristic
336C4×C73#55311yescharacteristic
337#23126C7311yesmaximal, characteristic, direct product factor, Sylow
338C2×C73—24no—
339C2×C73—82no—
340C2×C73#236411yescharacteristic
341C2×C73C2×C4×SD1611yescharacteristic
342C2×C73#295111yescharacteristic
343C2×C73#329511yescharacteristic
344C2×C73#329711yescharacteristic
345C2×C73#329811yescharacteristic
346C2×C73#330011yescharacteristic
347C2×#465C2×C7311yescharacteristic
348#2361C2×C7311yescharacteristic
349#2360C2×C7311yescharacteristic, complemented
350#1934C2×C7311yescharacteristic, complemented
351#1933C2×C7311yescharacteristic, complemented
352#1920C2×C7311yescharacteristic, complemented
353#1919C2×C7311yescharacteristic, complemented
354#1880C2×C7311yescharacteristic, complemented
355#1877C2×C7311yescharacteristic, complemented
356#1874C2×C7311yescharacteristic
357#1872C2×C7311yescharacteristic, complemented
358C4×#103C2×C7311yescharacteristic, complemented
359C4×#102C2×C7311yescharacteristic, complemented
360C8×C22⋊C4C2×C7311yescharacteristic, complemented
361C2×#340C2×C7311yescharacteristic, complemented
362C73#2312611yescharacteristic, direct product factor, Sylow
363C22×SD16C22×C7311yescharacteristic
364C23×C8C22×C7311yescharacteristic
365C2×C22⋊Q8C22×C7311yescharacteristic
366C2×#121C22×C7311yescharacteristic
367C2×C4×Q8C22×C7311yescharacteristic
368C2×C4×D4—21no—
369C2×C4×D4C22×C7311yescharacteristic
370C22×C4⋊C4C22×C7311yescharacteristic
371C22×C4⋊C4C22×C7311yescharacteristic
372#465C4×C7318yescomplemented
373C2×#106C22×C7311yescharacteristic
374C2×#103C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#103C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#102C22×C7311yescharacteristic
380C2×C22⋊C8C22×C7311yescharacteristic
381C2×C4×C8C22×C7311yescharacteristic
382C2×C4×C8C22×C7311yescharacteristic
383#391C22×C7311yescharacteristic
384#390C22×C7311yescharacteristic
385#389—21no—
386#389C22×C7311yescharacteristic
387#389C22×C7311yescharacteristic
388#388—21no—
389#387—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393C4×C4⋊C4C22×C7311yescharacteristic
394C4×C4⋊C4C22×C7311yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#336C22×C7311yescharacteristic
406#336C22×C7311yescharacteristic
407C22×Q8C23×C7311yescharacteristic
408C22×D4—21no—
409C22×D4C23×C7311yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4C23×C7311yescharacteristic
414C2×SD16—41no—
415C2×SD16—41no—
416C2×SD16C2×C4×C7314yescomplemented
417C22×C8—41no—
418C22×C8—41no—
419C22×C8C2×C4×C7314yescomplemented
420C22×C8C23×C7311yescharacteristic
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22⋊Q8—22no—
425C22⋊Q8C2×C4×C7314yescomplemented
426#121—22no—
427#121C2×C4×C7314yes—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—44no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4D4×C7311yescharacteristic
455C2×C22⋊C4D4×C7311yescharacteristic
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C7311yescharacteristic
460C2×C42C23×C7311yescharacteristic
461#106C2×C4×C7314yescomplemented
462#103—22no—
463#103—41no—
464#103C2×C4×C7314yescomplemented
465#102—22no—
466#102—41no—
467#102C2×C4×C7314yescomplemented
468C22⋊C8—22no—
469C4×C8—41no—
470C4×C8—41no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C7311yescharacteristic
478#95D4×C7311yescharacteristic
479C24—21no—
480C24C2×D4×C7311yescharacteristic
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C22×C4×C7312yes—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4C22×C4×C7312yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4C22×C4×C7312yes—
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4#41×C7312yes—
523C22×C4C24×C7311yescharacteristic
524SD16—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—44no—
536C2×C8C22×C4×C7312yes—
537C2×C8C22×C4×C7312yes—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—81no—
552C4⋊C4C22×C4×C7312yes—
553C4⋊C4C22×C4×C7312yes—
554C4⋊C4#41×C7312yes—
555C4⋊C4#41×C7312yes—
556C22⋊C4—24no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4SD16×C7314yescomplemented
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—42no—
569C42—81no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C4×D4×C7312yes—
582C23C2×SD16×C7312yes—
583C23#135×C7312yes—
584C23C22×D4×C7311yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—48no—
592D4—41no—
593D4—41no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—84no—
634C2×C4C4×D4×C7312yes—
635C2×C4C2×SD16×C7312yes—
636C2×C4C2×SD16×C7312yes—
637C2×C4C23×C4×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4C2×#41×C7311yescharacteristic
640C2×C4C2×#41×C7311yescharacteristic
641C2×C4H(5,𝔽2)×C7311yescharacteristic
642C2×C4H(5,𝔽2)×C7311yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22C4×SD16×C7314yes—
661C22C2×C4×D4×C7311yescharacteristic
662C22#546×C7311yescharacteristic
663C22#546×C7311yescharacteristic
664C22C22×SD16×C7311yescharacteristic
665C22C2×#135×C7311yescharacteristic
666C22#576×C7311yescharacteristic
667C22#578×C7311yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—42no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4C4×#41×C7311yescharacteristic
681C4#518×C7311yescharacteristic
682C4#553×C7311yescharacteristic
683C4#553×C7311yescharacteristic
684C2—24no—
685C2—82no—
686C2C73×#236411yescharacteristic
687C2C2×C4×SD16×C7311yescharacteristic
688C2C73×#295111yescharacteristic
689C2C73×#329511yescharacteristic
690C2C73×#329711yescharacteristic
691C2C73×#329811yescharacteristic
692C2C73×#330011yescharacteristic
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
3. C73×#2360C2semidirect
4. C73×#1934C2semidirect
5. C73×#1933C2semidirect
6. C73×#1920C2semidirect
7. C73×#1919C2semidirect
8. C73×#1880C2semidirect
9. C73×#1877C2semidirect
11. C73×#1872C2semidirect
12. C4×#103×C73C2semidirect
13. C4×#102×C73C2semidirect
14. C8×C22⋊C4×C73C2semidirect
15. C2×#340×C73C2semidirect
25. #465×C73C4semidirect
69. C2×SD16×C73C2×C4semidirect
72. C22×C8×C73C2×C4semidirect
78. C22⋊Q8×C73C2×C4semidirect
114. #106×C73C2×C4semidirect
117. #103×C73C2×C4semidirect
120. #102×C73C2×C4semidirect
215. C22⋊C4×C73SD16semidirect
337. #23126C73direct (N × H)
349. #2360C2×C73semidirect
350. #1934C2×C73semidirect
351. #1933C2×C73semidirect
352. #1920C2×C73semidirect
353. #1919C2×C73semidirect
354. #1880C2×C73semidirect
355. #1877C2×C73semidirect
357. #1872C2×C73semidirect
358. C4×#103C2×C73semidirect
359. C4×#102C2×C73semidirect
360. C8×C22⋊C4C2×C73semidirect
361. C2×#340C2×C73semidirect
362. C73#23126direct (N × H)
372. #465C4×C73semidirect
416. C2×SD16C2×C4×C73semidirect
419. C22×C8C2×C4×C73semidirect
425. C22⋊Q8C2×C4×C73semidirect
461. #106C2×C4×C73semidirect
464. #103C2×C4×C73semidirect
467. #102C2×C4×C73semidirect
562. C22⋊C4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C732
C73×#23612
C73×#23602
C73×#19342
C73×#19332
C73×#19202
C73×#19192
C73×#18802
C73×#18772
C73×#18742
C73×#18722
C4×#103×C732
C4×#102×C732
C8×C22⋊C4×C732
C2×#340×C732
#2312673