Finite Group Databasebeta

← C73×#25549 #32934953

Subgroups — C73×#25549 #32934953

Order 18688.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C73C211yesmaximal, characteristic, complemented
2C2×#481×C73C211yesmaximal, characteristic, complemented
3C2×#469×C73C211yesmaximal, characteristic, complemented
4C73×#2414C211yesmaximal, characteristic, complemented
5C73×#2058C211yesmaximal, characteristic, complemented
6C73×#2034C211yesmaximal, characteristic, complemented
7C73×#2023C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1879C211yesmaximal, characteristic, complemented
10C73×#1875C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C73—21no—
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19#547×C73—24no—
20#547×C73—24no—
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×#123×C73—21no—
24C2×C22⋊Q8×C73—21no—
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#481×C73—24no—
35#469×C73—24no—
36C2×#106×C73C2211yescharacteristic
37C2×#106×C73C2211yescharacteristic
38C2×#106×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48#394×C73—21no—
49#392×C73—21no—
50#390×C73—21no—
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—28no—
64C2×#41×C73—44no—
65C2×#41×C73—44no—
66C22×Q8×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73—21no—
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—41no—
82C2×M16×C73—22no—
83C2×M16×C73—22no—
84C2×M16×C73—41no—
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C4⋊Q8×C73—22no—
90C4⋊Q8×C73—22no—
91#123×C73—28no—
92#123×C73—28no—
93C22⋊Q8×C73—28no—
94#121×C73—22no—
95#121×C73—22no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—41no—
101#121×C73D414yescomplemented
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104C4×D4×C73—22no—
105C4×D4×C73—22no—
106#117×C73—22no—
107#117×C73—41no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—22no—
113C2×C4⋊C4×C73—22no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73D411yescharacteristic
116C2×C4⋊C4×C73D414yescomplemented
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73D411yescharacteristic
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
136#106×C73—22no—
137#106×C73—22no—
138#106×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—22no—
144#102×C73—41no—
145C22⋊C8×C73—22no—
146C22⋊C8×C73—22no—
147C22⋊C8×C73—41no—
148#95×C73—21no—
149#95×C73—21no—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73C2×D411yescharacteristic
153C24×C73C2×D411yescharacteristic
154#41×C73—432no—
155C2×Q8×C73—24no—
156C2×Q8×C73—42no—
157C2×Q8×C73—42no—
158C2×D4×C73—22no—
159C2×D4×C73—22no—
160C2×D4×C73—24no—
161C2×D4×C73—24no—
162C2×D4×C73—22no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—42no—
175C2×D4×C73—42no—
176C2×D4×C73—42no—
177C2×D4×C73—42no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—42no—
181C2×D4×C73—81no—
182C2×D4×C73—81no—
183C2×D4×C73—81no—
184C2×D4×C73C2×D412yes—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—24no—
190C22×C4×C73—24no—
191C22×C4×C73—24no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—42no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D412yes—
214C22×C4×C73C2×D412yes—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2411yescharacteristic
217D8×C73—44no—
218M16×C73—44no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73#4112yescomplemented
231C4⋊C4×C73—24no—
232C4⋊C4×C73—24no—
233C4⋊C4×C73—24no—
234C4⋊C4×C73—22no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—81no—
244C4⋊C4×C73C2×D412yes—
245C4⋊C4×C73C2×D412yes—
246C4⋊C4×C73C2×D412yes—
247C4⋊C4×C73#4112yescomplemented
248C22⋊C4×C73—24no—
249C22⋊C4×C73—24no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—24no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—81no—
258C22⋊C4×C73—81no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—42no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—22no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73#12012yes—
289C23×C73AGL(1,ℤ/8)12yes—
290C23×C73C22×D411yescharacteristic
291Q8×C73—48no—
292D4×C73—28no—
293D4×C73—22no—
294D4×C73—22no—
295D4×C73—48no—
296D4×C73—48no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—84no—
304D4×C73—84no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—48no—
324C2×C4×C73—48no—
325C2×C4×C73—48no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73#12012yes—
345C2×C4×C73AGL(1,ℤ/8)12yes—
346C2×C4×C73C22×D411yescharacteristic
347C2×C4×C73C22×D411yescharacteristic
348C2×C4×C73C2×#4111yescharacteristic
349C2×C4×C73C2×#4111yescharacteristic
350C2×C4×C73H(5,𝔽2)11yescharacteristic
351C2×C4×C732−1+411yescharacteristic
352C8×C73—22no—
353C8×C73—41no—
354C8×C73—41no—
355C8×C73—41no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—22no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—42no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73C2×#12011yescharacteristic
385C22×C73#54611yescharacteristic
386C22×C73#54711yescharacteristic
387C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C73#57711yescharacteristic
390C22×C73#57711yescharacteristic
391C4×C73—22no—
392C4×C73—22no—
393C4×C73—41no—
394C4×C73—42no—
395C4×C73—42no—
396C4×C73—42no—
397C4×C73—41no—
398C4×C73—42no—
399C4×C73—81no—
400C4×C73—81no—
401C4×C73#53211yescharacteristic
402C4×C73#53711yescharacteristic
403C4×C73#54611yescharacteristic
404C4×C73#54711yescharacteristic
405#25549C7311yesmaximal, characteristic, direct product factor, Sylow
406C2×C73—42no—
407C2×C73—42no—
408C2×C73—82no—
409C2×C73—161no—
410C2×C73#243011yescharacteristic
411C2×C73#300311yescharacteristic
412C2×C73#301011yescharacteristic
413C2×C73#330611yescharacteristic
414C2×C73#333211yescharacteristic
415C2×C73#334511yescharacteristic
416C2×C73#335411yescharacteristic
417C2×#547C2×C7311yescharacteristic, complemented
418C2×#481C2×C7311yescharacteristic, complemented
419C2×#469C2×C7311yescharacteristic, complemented
420#2414C2×C7311yescharacteristic, complemented
421#2058C2×C7311yescharacteristic, complemented
422#2034C2×C7311yescharacteristic, complemented
423#2023C2×C7311yescharacteristic, complemented
424#1999C2×C7311yescharacteristic, complemented
425#1879C2×C7311yescharacteristic, complemented
426#1875C2×C7311yescharacteristic, complemented
427#1874C2×C7311yescharacteristic, complemented
428#1870C2×C7311yescharacteristic, complemented
429#1864C2×C7311yescharacteristic, complemented
430#1853C2×C7311yescharacteristic, complemented
431#1736C2×C7311yescharacteristic, complemented
432C73#2554911yescharacteristic, direct product factor, Sylow
433C22×#41—21no—
434C22×D8C22×C7311yescharacteristic
435C22×M16C22×C7311yescharacteristic
436#547—24no—
437#547—24no—
438C2×C4⋊Q8C22×C7311yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×C22⋊Q8—21no—
442C2×#121C22×C7311yescharacteristic
443C2×#121C22×C7311yescharacteristic
444C2×#121C22×C7311yescharacteristic
445C2×#121C22×C7311yescharacteristic
446C2×C4×D4C22×C7311yescharacteristic
447C2×C4×D4C22×C7311yescharacteristic
448C2×#117C22×C7311yescharacteristic
449C22×C4⋊C4C22×C7311yescharacteristic
450C22×C4⋊C4C22×C7311yescharacteristic
451#481—24no—
452#469—24no—
453C2×#106C22×C7311yescharacteristic
454C2×#106C22×C7311yescharacteristic
455C2×#106C22×C7311yescharacteristic
456C2×#102C22×C7311yescharacteristic
457C2×#102C22×C7311yescharacteristic
458C2×#102C22×C7311yescharacteristic
459C2×#102C22×C7311yescharacteristic
460C2×#102C22×C7311yescharacteristic
461C2×#102C22×C7311yescharacteristic
462C2×C22⋊C8C22×C7311yescharacteristic
463C2×C22⋊C8C22×C7311yescharacteristic
464C2×C22⋊C8C22×C7311yescharacteristic
465#394—21no—
466#392—21no—
467#390—21no—
468#390C22×C7311yescharacteristic
469#389C22×C7311yescharacteristic
470#388—21no—
471#380C22×C7311yescharacteristic
472#340C22×C7311yescharacteristic
473#340C22×C7311yescharacteristic
474#340C22×C7311yescharacteristic
475#340C22×C7311yescharacteristic
476#340C22×C7311yescharacteristic
477#340C22×C7311yescharacteristic
478#336C22×C7311yescharacteristic
479#336C22×C7311yescharacteristic
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C7311yescharacteristic
489C22×D4C23×C7311yescharacteristic
490C22×D4C23×C7311yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C7311yescharacteristic
495C23×C4C23×C7311yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C7311yescharacteristic
503C22×C8C23×C7311yescharacteristic
504C22×C8C23×C7311yescharacteristic
505C22×C8C23×C7311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C7314yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C7311yescharacteristic
533C2×C4⋊C4D4×C7314yescomplemented
534C2×C4⋊C4C23×C7311yescharacteristic
535C2×C4⋊C4C23×C7311yescharacteristic
536C2×C4⋊C4C23×C7311yescharacteristic
537C2×C4⋊C4C23×C7311yescharacteristic
538C2×C4⋊C4C23×C7311yescharacteristic
539C2×C4⋊C4C23×C7311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C7311yescharacteristic
550C2×C22⋊C4D4×C7311yescharacteristic
551C2×C42—21no—
552C2×C42C23×C7311yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C7311yescharacteristic
570C24C2×D4×C7311yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C7312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C7311yescharacteristic
628C22×C4C2×D4×C7311yescharacteristic
629C22×C4C2×D4×C7311yescharacteristic
630C22×C4C2×D4×C7312yes—
631C22×C4C2×D4×C7312yes—
632C22×C4C2×D4×C7311yescharacteristic
633C22×C4C24×C7311yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C7312yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C7312yes—
662C4⋊C4C2×D4×C7312yes—
663C4⋊C4C2×D4×C7312yes—
664C4⋊C4#41×C7312yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C7312yes—
706C23AGL(1,ℤ/8)×C7312yes—
707C23C22×D4×C7311yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4#120×C7312yes—
762C2×C4AGL(1,ℤ/8)×C7312yes—
763C2×C4C22×D4×C7311yescharacteristic
764C2×C4C22×D4×C7311yescharacteristic
765C2×C4C2×#41×C7311yescharacteristic
766C2×C4C2×#41×C7311yescharacteristic
767C2×C4H(5,𝔽2)×C7311yescharacteristic
768C2×C42−1+4×C7311yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C7311yescharacteristic
802C22#546×C7311yescharacteristic
803C22#547×C7311yescharacteristic
804C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
805C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
806C22#577×C7311yescharacteristic
807C22#577×C7311yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—42no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4#532×C7311yescharacteristic
819C4#537×C7311yescharacteristic
820C4#546×C7311yescharacteristic
821C4#547×C7311yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C73×#243011yescharacteristic
827C2C73×#300311yescharacteristic
828C2C73×#301011yescharacteristic
829C2C73×#330611yescharacteristic
830C2C73×#333211yescharacteristic
831C2C73×#334511yescharacteristic
832C2C73×#335411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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
1. C2×#547×C73C2semidirect
2. C2×#481×C73C2semidirect
3. C2×#469×C73C2semidirect
4. C73×#2414C2semidirect
5. C73×#2058C2semidirect
6. C73×#2034C2semidirect
7. C73×#2023C2semidirect
8. C73×#1999C2semidirect
9. C73×#1879C2semidirect
10. C73×#1875C2semidirect
11. C73×#1874C2semidirect
12. C73×#1870C2semidirect
13. C73×#1864C2semidirect
14. C73×#1853C2semidirect
15. C73×#1736C2semidirect
101. #121×C73D4semidirect
116. C2×C4⋊C4×C73D4semidirect
230. C2×C8×C73#41semidirect
247. C4⋊C4×C73#41semidirect
405. #25549C73direct (N × H)
417. C2×#547C2×C73semidirect
418. C2×#481C2×C73semidirect
419. C2×#469C2×C73semidirect
420. #2414C2×C73semidirect
421. #2058C2×C73semidirect
422. #2034C2×C73semidirect
423. #2023C2×C73semidirect
424. #1999C2×C73semidirect
425. #1879C2×C73semidirect
426. #1875C2×C73semidirect
427. #1874C2×C73semidirect
428. #1870C2×C73semidirect
429. #1864C2×C73semidirect
430. #1853C2×C73semidirect
431. #1736C2×C73semidirect
432. C73#25549direct (N × H)
518. #121D4×C73semidirect
533. C2×C4⋊C4D4×C73semidirect
647. C2×C8#41×C73semidirect
664. C4⋊C4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C732
C2×#481×C732
C2×#469×C732
C73×#24142
C73×#20582
C73×#20342
C73×#20232
C73×#19992
C73×#18792
C73×#18752
C73×#18742
C73×#18702
C73×#18642
C73×#18532
C73×#17362
#2554973