Finite Group Databasebeta

← C73×#26214 #32935618

Subgroups — C73×#26214 #32935618

Order 18688.

890 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2414C211yesmaximal, characteristic
2D4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
3C73×#2100C211yesmaximal, characteristic, complemented
4C73×#2077C211yesmaximal, characteristic, complemented
5C73×#2071C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#1926C211yesmaximal, characteristic, complemented
8C73×#1921C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1874C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1823C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17C2×#121×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×C4×D4×C73—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×C22⋊C8×C73C2211yescharacteristic
31C2×C22⋊C8×C73C2211yescharacteristic
32C2×C22⋊C8×C73C2211yescharacteristic
33#394×C73—21no—
34#392×C73—21no—
35#390×C73—21no—
36#390×C73C2211yescharacteristic
37#389×C73—21no—
38#389×C73C2211yescharacteristic
39#388×C73—21no—
40#385×C73—21no—
41#385×C73—21no—
42#384×C73C2211yescharacteristic
43#380×C73C2211yescharacteristic
44#380×C73C2211yescharacteristic
45#380×C73C2211yescharacteristic
46C4×C4⋊C4×C73C2211yescharacteristic
47#340×C73C2211yescharacteristic
48#340×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D4×C73—21no—
60C22×D4×C73—21no—
61C22×D4×C73D411yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C2×M16×C73—22no—
68C2×M16×C73—41no—
69C2×M16×C73—41no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74#121×C73—22no—
75#121×C73—22no—
76#121×C73—22no—
77#121×C73—41no—
78C4×D4×C73—22no—
79C4×D4×C73—22no—
80C4×D4×C73—44no—
81#117×C73—22no—
82#117×C73—41no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—41no—
91C2×C4⋊C4×C73—41no—
92C2×C4⋊C4×C73D411yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
109C2×C22⋊C4×C73D411yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113#107×C73—22no—
114#106×C73—41no—
115#102×C73—22no—
116#102×C73—41no—
117#102×C73—41no—
118#102×C73—41no—
119C22⋊C8×C73—22no—
120C22⋊C8×C73—41no—
121C22⋊C8×C73—41no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127C24×C73—21no—
128C24×C73C2×D411yescharacteristic
129C24×C73C2×D411yescharacteristic
130C2×D4×C73—22no—
131C2×D4×C73—22no—
132C2×D4×C73—22no—
133C2×D4×C73—21no—
134C2×D4×C73—21no—
135C2×D4×C73—21no—
136C2×D4×C73—21no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—42no—
140C2×D4×C73—42no—
141C2×D4×C73—42no—
142C2×D4×C73—81no—
143C2×D4×C73—81no—
144C2×D4×C73—81no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
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—21no—
161C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73#4112yes—
173C22×C4×C73#4112yes—
174C22×C4×C73C2411yescharacteristic
175M16×C73—44no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
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—
188C4⋊C4×C73—22no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
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—21no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73#4112yes—
207C4⋊C4×C73#4112yes—
208C22⋊C4×C73—22no—
209C22⋊C4×C73—22no—
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—81no—
217C22⋊C4×C73—81no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—42no—
221C42×C73—42no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73#12312yes—
242C23×C73AGL(1,ℤ/8)12yes—
243C23×C73C22×D411yescharacteristic
244D4×C73—28no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73—84no—
250D4×C73—84no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
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—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—41no—
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—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—84no—
291C2×C4×C73—84no—
292C2×C4×C73#12312yes—
293C2×C4×C73#13712yes—
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C8×C73—41no—
301C8×C73—41no—
302C8×C73—41no—
303C8×C73—41no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73C2×#12311yescharacteristic
326C22×C73#54611yescharacteristic
327C22×C73#54611yescharacteristic
328C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C73C2×#13711yescharacteristic
330C22×C73#57611yescharacteristic
331C22×C73#57711yescharacteristic
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—41no—
335C4×C73—41no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73—81no—
342C4×C73—81no—
343C4×C73#52911yescharacteristic
344C4×C73#53811yescharacteristic
345C4×C73#55311yescharacteristic
346C4×C73#55311yescharacteristic
347#26214C7311yesmaximal, characteristic, direct product factor, Sylow
348C2×C73—42no—
349C2×C73—42no—
350C2×C73—161no—
351C2×C73#244411yescharacteristic
352C2×C73#309211yescharacteristic
353C2×C73#309611yescharacteristic
354C2×C73#330611yescharacteristic
355C2×C73#331811yescharacteristic
356C2×C73#332911yescharacteristic
357C2×C73#333311yescharacteristic
358#2414C2×C7311yescharacteristic
359D4×C4⋊C4C2×C7311yescharacteristic, complemented
360#2100C2×C7311yescharacteristic, complemented
361#2077C2×C7311yescharacteristic, complemented
362#2071C2×C7311yescharacteristic, complemented
363#2033C2×C7311yescharacteristic, complemented
364#1926C2×C7311yescharacteristic, complemented
365#1921C2×C7311yescharacteristic, complemented
366#1895C2×C7311yescharacteristic, complemented
367#1874C2×C7311yescharacteristic, complemented
368#1874C2×C7311yescharacteristic, complemented
369#1870C2×C7311yescharacteristic, complemented
370#1854C2×C7311yescharacteristic, complemented
371#1823C2×C7311yescharacteristic, complemented
372#1736C2×C7311yescharacteristic, complemented
373C73#2621411yescharacteristic, direct product factor, Sylow
374C22×M16C22×C7311yescharacteristic
375C2×#121C22×C7311yescharacteristic
376C2×#121C22×C7311yescharacteristic
377C2×C4×D4—21no—
378C2×C4×D4C22×C7311yescharacteristic
379C2×#117C22×C7311yescharacteristic
380C22×C4⋊C4C22×C7311yescharacteristic
381C22×C4⋊C4C22×C7311yescharacteristic
382C2×#107C22×C7311yescharacteristic
383C2×#106C22×C7311yescharacteristic
384C2×#102C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×C22⋊C8C22×C7311yescharacteristic
389C2×C22⋊C8C22×C7311yescharacteristic
390C2×C22⋊C8C22×C7311yescharacteristic
391#394—21no—
392#392—21no—
393#390—21no—
394#390C22×C7311yescharacteristic
395#389—21no—
396#389C22×C7311yescharacteristic
397#388—21no—
398#385—21no—
399#385—21no—
400#384C22×C7311yescharacteristic
401#380C22×C7311yescharacteristic
402#380C22×C7311yescharacteristic
403#380C22×C7311yescharacteristic
404C4×C4⋊C4C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#336C22×C7311yescharacteristic
416#336C22×C7311yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4D4×C7311yescharacteristic
420C22×D4C23×C7311yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4C23×C7311yescharacteristic
424C23×C4C23×C7311yescharacteristic
425C2×M16—22no—
426C2×M16—41no—
427C2×M16—41no—
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432#121—22no—
433#121—22no—
434#121—22no—
435#121—41no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—44no—
439#117—22no—
440#117—41no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4D4×C7311yescharacteristic
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×C4⋊C4C23×C7311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4D4×C7311yescharacteristic
467C2×C22⋊C4D4×C7311yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C7311yescharacteristic
471#107—22no—
472#106—41no—
473#102—22no—
474#102—41no—
475#102—41no—
476#102—41no—
477C22⋊C8—22no—
478C22⋊C8—41no—
479C22⋊C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485C24—21no—
486C24C2×D4×C7311yescharacteristic
487C24C2×D4×C7311yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—81no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
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—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4#41×C7312yes—
531C22×C4#41×C7312yes—
532C22×C4C24×C7311yescharacteristic
533M16—44no—
534C2×C8—21no—
535C2×C8—21no—
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×C8—21no—
545C2×C8—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
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—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4#41×C7312yes—
565C4⋊C4#41×C7312yes—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—42no—
579C42—42no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23#123×C7312yes—
600C23AGL(1,ℤ/8)×C7312yes—
601C23C22×D4×C7311yescharacteristic
602D4—28no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—84no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
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—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4#123×C7312yes—
651C2×C4#137×C7312yes—
652C2×C4C2×#41×C7311yescharacteristic
653C2×C4C2×#41×C7311yescharacteristic
654C2×C4C2×#41×C7311yescharacteristic
655C2×C4C2×#41×C7311yescharacteristic
656C2×C4H(5,𝔽2)×C7311yescharacteristic
657C2×C4H(5,𝔽2)×C7311yescharacteristic
658C8—41no—
659C8—41no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C2×#123×C7311yescharacteristic
684C22#546×C7311yescharacteristic
685C22#546×C7311yescharacteristic
686C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
687C22C2×#137×C7311yescharacteristic
688C22#576×C7311yescharacteristic
689C22#577×C7311yescharacteristic
690C4—22no—
691C4—22no—
692C4—41no—
693C4—42no—
694C4—42no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4#529×C7311yescharacteristic
702C4#538×C7311yescharacteristic
703C4#553×C7311yescharacteristic
704C4#553×C7311yescharacteristic
705C2—42no—
706C2—42no—
707C2—161no—
708C2C73×#244411yescharacteristic
709C2C73×#309211yescharacteristic
710C2C73×#309611yescharacteristic
711C2C73×#330611yescharacteristic
712C2C73×#331811yescharacteristic
713C2C73×#332911yescharacteristic
714C2C73×#333311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊C4×C73C2semidirect
3. C73×#2100C2semidirect
4. C73×#2077C2semidirect
5. C73×#2071C2semidirect
6. C73×#2033C2semidirect
7. C73×#1926C2semidirect
8. C73×#1921C2semidirect
9. C73×#1895C2semidirect
10. C73×#1874C2semidirect
11. C73×#1874C2semidirect
12. C73×#1870C2semidirect
13. C73×#1854C2semidirect
14. C73×#1823C2semidirect
15. C73×#1736C2semidirect
347. #26214C73direct (N × H)
359. D4×C4⋊C4C2×C73semidirect
360. #2100C2×C73semidirect
361. #2077C2×C73semidirect
362. #2071C2×C73semidirect
363. #2033C2×C73semidirect
364. #1926C2×C73semidirect
365. #1921C2×C73semidirect
366. #1895C2×C73semidirect
367. #1874C2×C73semidirect
368. #1874C2×C73semidirect
369. #1870C2×C73semidirect
370. #1854C2×C73semidirect
371. #1823C2×C73semidirect
372. #1736C2×C73semidirect
373. C73#26214direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24142
D4×C4⋊C4×C732
C73×#21002
C73×#20772
C73×#20712
C73×#20332
C73×#19262
C73×#19212
C73×#18952
C73×#18742
C73×#18702
C73×#18542
C73×#18232
C73×#17362
#2621473