Finite Group Databasebeta

← C73×#24136 #32933540

Subgroups — C73×#24136 #32933540

Order 18688.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C73C211yesmaximal, characteristic, complemented
2C2×#478×C73C211yesmaximal, characteristic, complemented
3C2×#442×C73C211yesmaximal, characteristic, complemented
4C73×#2537C211yesmaximal, characteristic, complemented
5C73×#2034C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#1999C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1992C211yesmaximal, characteristic, complemented
10C73×#1955C211yesmaximal, characteristic, complemented
11C73×#1875C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1802C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17#553×C73—24no—
18#553×C73—24no—
19C2×#126×C73—21no—
20C2×#125×C73C2211yescharacteristic
21C2×#123×C73—21no—
22C2×#121×C73—21no—
23C2×#121×C73—21no—
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×C4×D4×C73—21no—
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×C4×D4×C73C2211yescharacteristic
32C2×#117×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#478×C73—24no—
35#442×C73—24no—
36C2×#107×C73C2211yescharacteristic
37C2×#106×C73C2211yescharacteristic
38C2×#106×C73C2211yescharacteristic
39C2×C4⋊C8×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C22⋊C8×C73C2211yescharacteristic
50C2×#97×C73C2211yescharacteristic
51#394×C73—21no—
52#394×C73—21no—
53#384×C73C2211yescharacteristic
54#380×C73—21no—
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#126×C73—28no—
83#125×C73—22no—
84#125×C73D414yescomplemented
85#123×C73—28no—
86#121×C73—28no—
87#121×C73—22no—
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—41no—
94#121×C73—41no—
95#121×C73—44no—
96C4×D4×C73—28no—
97C4×D4×C73—22no—
98C4×D4×C73—22no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73D414yescomplemented
103#117×C73—22no—
104#117×C73—22no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73D411yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—22no—
134#106×C73—22no—
135C4⋊C8×C73—22no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—41no—
141#102×C73—41no—
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144C22⋊C8×C73—41no—
145C22⋊C8×C73—41no—
146#97×C73—22no—
147#95×C73—21no—
148#95×C73—21no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73C2×D411yescharacteristic
152C24×C73C2×D411yescharacteristic
153C2×D4×C73—24no—
154C2×D4×C73—22no—
155C2×D4×C73—24no—
156C2×D4×C73—22no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—41no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—42no—
173C2×D4×C73—42no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
177C2×D4×C73—81no—
178C2×D4×C73C2×D412yes—
179C2×D4×C73#4112yes—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—24no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—24no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—42no—
201C22×C4×C73—42no—
202C22×C4×C73—42no—
203C22×C4×C73—81no—
204C22×C4×C73—81no—
205C22×C4×C73—81no—
206C22×C4×C73—81no—
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2411yescharacteristic
212D8×C73—28no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73#4112yes—
225C4⋊C4×C73—24no—
226C4⋊C4×C73—24no—
227C4⋊C4×C73—24no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—42no—
239C4⋊C4×C73—81no—
240C4⋊C4×C73C2×D412yes—
241C4⋊C4×C73C2×D412yes—
242C4⋊C4×C73C2×D412yes—
243C22⋊C4×C73—24no—
244C22⋊C4×C73—24no—
245C22⋊C4×C73—24no—
246C22⋊C4×C73—24no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C42×C73—24no—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
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×C73AGL(1,ℤ/8)12yes—
285C23×C73C22×D411yescharacteristic
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—44no—
291D4×C73—48no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—84no—
297D4×C73—84no—
298D4×C73—84no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—21no—
307C2×C4×C73—22no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
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—84no—
336C2×C4×C73—84no—
337C2×C4×C73—84no—
338C2×C4×C73#12012yes—
339C2×C4×C73#12012yes—
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C22×D411yescharacteristic
342C2×C4×C73C2×#4111yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73H(5,𝔽2)11yescharacteristic
345C2×C4×C732−1+411yescharacteristic
346C8×C73—22no—
347C8×C73—41no—
348C8×C73—41no—
349C8×C73—41no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—42no—
368C22×C73—41no—
369C22×C73—42no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73C2×#12011yescharacteristic
379C22×C73#54611yescharacteristic
380C22×C73#54711yescharacteristic
381C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C73#57511yescharacteristic
383C22×C73#57611yescharacteristic
384C22×C73#57711yescharacteristic
385C4×C73—22no—
386C4×C73—22no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73—42no—
390C4×C73—42no—
391C4×C73—42no—
392C4×C73—81no—
393C4×C73—81no—
394C4×C73—81no—
395C4×C73#52511yescharacteristic
396C4×C73#53711yescharacteristic
397C4×C73#54811yescharacteristic
398C4×C73#55011yescharacteristic
399#24136C7311yesmaximal, characteristic, direct product factor, Sylow
400C2×C73—42no—
401C2×C73—81no—
402C2×C73—82no—
403C2×C73—82no—
404C2×C73#240711yescharacteristic
405C2×C73#300611yescharacteristic
406C2×C73#301211yescharacteristic
407C2×C73#330711yescharacteristic
408C2×C73#331811yescharacteristic
409C2×C73#334511yescharacteristic
410C2×C73#334711yescharacteristic
411C2×#553C2×C7311yescharacteristic, complemented
412C2×#478C2×C7311yescharacteristic, complemented
413C2×#442C2×C7311yescharacteristic, complemented
414#2537C2×C7311yescharacteristic, complemented
415#2034C2×C7311yescharacteristic, complemented
416#2033C2×C7311yescharacteristic, complemented
417#1999C2×C7311yescharacteristic, complemented
418#1999C2×C7311yescharacteristic, complemented
419#1992C2×C7311yescharacteristic, complemented
420#1955C2×C7311yescharacteristic, complemented
421#1875C2×C7311yescharacteristic, complemented
422#1874C2×C7311yescharacteristic, complemented
423#1854C2×C7311yescharacteristic, complemented
424#1853C2×C7311yescharacteristic, complemented
425#1802C2×C7311yescharacteristic, complemented
426C73#2413611yescharacteristic, direct product factor, Sylow
427C22×D8C22×C7311yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C7311yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C7311yescharacteristic
436C2×#121C22×C7311yescharacteristic
437C2×#121C22×C7311yescharacteristic
438C2×#121C22×C7311yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C7311yescharacteristic
441C2×C4×D4C22×C7311yescharacteristic
442C2×C4×D4C22×C7311yescharacteristic
443C2×#117C22×C7311yescharacteristic
444C22×C4⋊C4C22×C7311yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C7311yescharacteristic
448C2×#106C22×C7311yescharacteristic
449C2×#106C22×C7311yescharacteristic
450C2×C4⋊C8C22×C7311yescharacteristic
451C2×#102C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×#102C22×C7311yescharacteristic
454C2×#102C22×C7311yescharacteristic
455C2×#102C22×C7311yescharacteristic
456C2×#102C22×C7311yescharacteristic
457C2×C22⋊C8C22×C7311yescharacteristic
458C2×C22⋊C8C22×C7311yescharacteristic
459C2×C22⋊C8C22×C7311yescharacteristic
460C2×C22⋊C8C22×C7311yescharacteristic
461C2×#97C22×C7311yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C7311yescharacteristic
465#380—21no—
466#380C22×C7311yescharacteristic
467#380C22×C7311yescharacteristic
468#340C22×C7311yescharacteristic
469#340C22×C7311yescharacteristic
470#340C22×C7311yescharacteristic
471#340C22×C7311yescharacteristic
472#340C22×C7311yescharacteristic
473#340C22×C7311yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C7311yescharacteristic
479C22×D4C23×C7311yescharacteristic
480C22×D4C23×C7311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C7311yescharacteristic
485C23×C4C23×C7311yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C7311yescharacteristic
490C22×C8C23×C7311yescharacteristic
491C22×C8C23×C7311yescharacteristic
492C22×C8C23×C7311yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C7314yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C7314yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C7311yescharacteristic
524C2×C4⋊C4C23×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C4⋊C4C23×C7311yescharacteristic
528C2×C4⋊C4C23×C7311yescharacteristic
529C2×C4⋊C4C23×C7311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C7311yescharacteristic
540C2×C22⋊C4D4×C7311yescharacteristic
541C2×C42—21no—
542C2×C42C23×C7311yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C7311yescharacteristic
563C24C2×D4×C7311yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C7312yes—
590C2×D4#41×C7312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C7311yescharacteristic
619C22×C4C2×D4×C7311yescharacteristic
620C22×C4C2×D4×C7311yescharacteristic
621C22×C4C2×D4×C7311yescharacteristic
622C22×C4C24×C7311yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C7312yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C7312yes—
652C4⋊C4C2×D4×C7312yes—
653C4⋊C4C2×D4×C7312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C7312yes—
667C42C2×D4×C7312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C7312yes—
696C23C22×D4×C7311yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C7312yes—
750C2×C4#120×C7312yes—
751C2×C4C22×D4×C7311yescharacteristic
752C2×C4C22×D4×C7311yescharacteristic
753C2×C4C2×#41×C7311yescharacteristic
754C2×C4C2×#41×C7311yescharacteristic
755C2×C4H(5,𝔽2)×C7311yescharacteristic
756C2×C42−1+4×C7311yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C7311yescharacteristic
790C22#546×C7311yescharacteristic
791C22#547×C7311yescharacteristic
792C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
793C22#575×C7311yescharacteristic
794C22#576×C7311yescharacteristic
795C22#577×C7311yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C7311yescharacteristic
807C4#537×C7311yescharacteristic
808C4#548×C7311yescharacteristic
809C4#550×C7311yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C73×#240711yescharacteristic
815C2C73×#300611yescharacteristic
816C2C73×#301211yescharacteristic
817C2C73×#330711yescharacteristic
818C2C73×#331811yescharacteristic
819C2C73×#334511yescharacteristic
820C2C73×#334711yescharacteristic
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×#553×C73C2semidirect
2. C2×#478×C73C2semidirect
3. C2×#442×C73C2semidirect
4. C73×#2537C2semidirect
5. C73×#2034C2semidirect
6. C73×#2033C2semidirect
7. C73×#1999C2semidirect
8. C73×#1999C2semidirect
9. C73×#1992C2semidirect
10. C73×#1955C2semidirect
11. C73×#1875C2semidirect
12. C73×#1874C2semidirect
13. C73×#1854C2semidirect
14. C73×#1853C2semidirect
15. C73×#1802C2semidirect
84. #125×C73D4semidirect
102. C4×D4×C73D4semidirect
399. #24136C73direct (N × H)
411. C2×#553C2×C73semidirect
412. C2×#478C2×C73semidirect
413. C2×#442C2×C73semidirect
414. #2537C2×C73semidirect
415. #2034C2×C73semidirect
416. #2033C2×C73semidirect
417. #1999C2×C73semidirect
418. #1999C2×C73semidirect
419. #1992C2×C73semidirect
420. #1955C2×C73semidirect
421. #1875C2×C73semidirect
422. #1874C2×C73semidirect
423. #1854C2×C73semidirect
424. #1853C2×C73semidirect
425. #1802C2×C73semidirect
426. C73#24136direct (N × H)
495. #125D4×C73semidirect
513. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C732
C2×#478×C732
C2×#442×C732
C73×#25372
C73×#20342
C73×#20332
C73×#19992
C73×#19922
C73×#19552
C73×#18752
C73×#18742
C73×#18542
C73×#18532
C73×#18022
#2413673