Finite Group Databasebeta

← C73×#24555 #32933959

Subgroups — C73×#24555 #32933959

Order 18688.

1194 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C73C211yesmaximal, characteristic, complemented
3C73×#2847C211yesmaximal, characteristic
4C73×#2280C211yesmaximal, characteristic, complemented
5C73×#2077C211yesmaximal, characteristic, complemented
6C73×#2076C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1893C211yesmaximal, characteristic, complemented
10C73×#1893C211yesmaximal, characteristic, complemented
11C73×#1875C211yesmaximal, characteristic, complemented
12C73×#1854C211yesmaximal, characteristic, complemented
13C73×#1825C211yesmaximal, characteristic, complemented
14C73×#1808C211yesmaximal, characteristic, complemented
15C73×#1807C211yesmaximal, characteristic, complemented
16C24×C4×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#120×C73—21no—
23C2×#117×C73C2211yescharacteristic
24C2×#117×C73C2211yescharacteristic
25#482×C73—24no—
26C2×#107×C73C2211yescharacteristic, complemented
27C2×#107×C73C2211yescharacteristic, complemented
28C2×#106×C73C2211yescharacteristic, complemented
29C2×#106×C73C2211yescharacteristic, complemented
30C2×#102×C73C2211yescharacteristic, complemented
31C2×#102×C73C2211yescharacteristic, complemented
32C2×#102×C73C2211yescharacteristic, complemented
33C2×#102×C73C2211yescharacteristic, complemented
34C2×C22⋊C8×C73—24no—
35C2×C22⋊C8×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#386×C73—21no—
40#386×C73—21no—
41#386×C73—21no—
42#381×C73—21no—
43#380×C73C2211yescharacteristic
44#380×C73C2211yescharacteristic
45#380×C73C2211yescharacteristic
46#380×C73C2211yescharacteristic
47#380×C73C2211yescharacteristic
48#380×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50#379×C73—21no—
51C4×C22⋊C4×C73—21no—
52C4×C22⋊C4×C73—21no—
53#340×C73C2211yescharacteristic, complemented
54#340×C73C2211yescharacteristic, complemented
55#340×C73C2211yescharacteristic, complemented
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61C25×C73D411yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—22no—
67C23×C4×C73—22no—
68C23×C4×C73—22no—
69C23×C4×C73—22no—
70C23×C4×C73—41no—
71C23×C4×C73—41no—
72C23×C4×C73D411yescharacteristic
73C23×C4×C73D411yescharacteristic
74C23×C4×C73D411yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C22×C8×C73—22no—
79C22×C8×C73—22no—
80C22×C8×C73—22no—
81C22×C8×C73—22no—
82C22×C8×C73—41no—
83C22×C8×C73—41no—
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—41no—
93#121×C73—41no—
94#120×C73—44no—
95#117×C73—22no—
96#117×C73—22no—
97#117×C73—41no—
98#117×C73—41no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C42×C73—21no—
119C2×C42×C73—21no—
120#107×C73—22no—
121#107×C73—41no—
122#106×C73—22no—
123#106×C73—41no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—41no—
127#102×C73—41no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73—22no—
131C22⋊C8×C73D414yescomplemented
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139C24×C73—22no—
140C24×C73—22no—
141C24×C73—22no—
142C24×C73—22no—
143C24×C73—22no—
144C24×C73—21no—
145C24×C73—41no—
146C24×C73—41no—
147C24×C73C2×D411yescharacteristic
148C24×C73C2×D411yescharacteristic
149C24×C73C2×D411yescharacteristic
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—42no—
157C2×D4×C73—42no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73—42no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—22no—
174C22×C4×C73—22no—
175C22×C4×C73—22no—
176C22×C4×C73—22no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
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—41no—
193C22×C4×C73—41no—
194C22×C4×C73—41no—
195C22×C4×C73—44no—
196C22×C4×C73—44no—
197C22×C4×C73—44no—
198C22×C4×C73—44no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73#4112yes—
204C22×C4×C73#4112yes—
205C22×C4×C73#4112yes—
206C22×C4×C73C2411yescharacteristic
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—44no—
218C2×C8×C73—44no—
219C2×C8×C73C2×D412yes—
220C2×C8×C73C2×D412yes—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—42no—
247C42×C73—42no—
248C42×C73—42no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—28no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—44no—
267C23×C73—44no—
268C23×C73—44no—
269C23×C73—44no—
270C23×C73—44no—
271C23×C73—44no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73#12112yes—
280C23×C73#12312yes—
281C23×C73#13512yes—
282C23×C73#13512yes—
283C23×C73AGL(1,ℤ/8)12yes—
284C23×C73C22×D411yescharacteristic
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—84no—
290D4×C73—84no—
291D4×C73—84no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—44no—
308C2×C4×C73—44no—
309C2×C4×C73—44no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
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#12112yes—
336C2×C4×C73#12312yes—
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73C2×#4111yescharacteristic
339C2×C4×C73C2×#4111yescharacteristic
340C2×C4×C73C2×#4111yescharacteristic
341C2×C4×C73H(5,𝔽2)11yescharacteristic
342C2×C4×C73H(5,𝔽2)11yescharacteristic
343C8×C73—22no—
344C8×C73—22no—
345C8×C73—41no—
346C8×C73—41no—
347C22×C73—22no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—416no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73#48214yescomplemented
376C22×C73C2×#12111yescharacteristic
377C22×C73C2×#12311yescharacteristic
378C22×C73#53411yescharacteristic
379C22×C73C2×#13511yescharacteristic
380C22×C73C2×#13511yescharacteristic
381C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C73#57511yescharacteristic
383C4×C73—22no—
384C4×C73—22no—
385C4×C73—41no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73—81no—
389C4×C73—81no—
390C4×C73—81no—
391C4×C73—81no—
392C4×C73—81no—
393C4×C73#54611yescharacteristic
394C4×C73#54611yescharacteristic
395C4×C73#55111yescharacteristic
396C4×C73#55111yescharacteristic
397#24555C7311yesmaximal, characteristic, direct product factor, Sylow
398C2×C73—24no—
399C2×C73—42no—
400C2×C73—42no—
401C2×C73—161no—
402C2×C73#241211yescharacteristic
403C2×C73#305011yescharacteristic
404C2×C73#305511yescharacteristic
405C2×C73C2×#48211yescharacteristic
406C2×C73#309111yescharacteristic
407C2×C73#318811yescharacteristic
408C2×C73#319111yescharacteristic
409C2×#482C2×C7311yescharacteristic, complemented
410C22×C22⋊C8C2×C7311yescharacteristic, complemented
411#2847C2×C7311yescharacteristic
412#2280C2×C7311yescharacteristic, complemented
413#2077C2×C7311yescharacteristic, complemented
414#2076C2×C7311yescharacteristic, complemented
415#2034C2×C7311yescharacteristic, complemented
416#2033C2×C7311yescharacteristic, complemented
417#1893C2×C7311yescharacteristic, complemented
418#1893C2×C7311yescharacteristic, complemented
419#1875C2×C7311yescharacteristic, complemented
420#1854C2×C7311yescharacteristic, complemented
421#1825C2×C7311yescharacteristic, complemented
422#1808C2×C7311yescharacteristic, complemented
423#1807C2×C7311yescharacteristic, complemented
424C73#2455511yescharacteristic, direct product factor, Sylow
425C24×C4C22×C7311yescharacteristic
426C23×C8C22×C7311yescharacteristic
427C23×C8C22×C7311yescharacteristic
428C2×#121C22×C7311yescharacteristic
429C2×#121C22×C7311yescharacteristic
430C2×#121C22×C7311yescharacteristic
431C2×#120—21no—
432C2×#117C22×C7311yescharacteristic
433C2×#117C22×C7311yescharacteristic
434#482—24no—
435C2×#107C22×C7311yescharacteristic, complemented
436C2×#107C22×C7311yescharacteristic, complemented
437C2×#106C22×C7311yescharacteristic, complemented
438C2×#106C22×C7311yescharacteristic, complemented
439C2×#102C22×C7311yescharacteristic, complemented
440C2×#102C22×C7311yescharacteristic, complemented
441C2×#102C22×C7311yescharacteristic, complemented
442C2×#102C22×C7311yescharacteristic, complemented
443C2×C22⋊C8—24no—
444C2×C22⋊C8C22×C7311yescharacteristic
445C2×C22⋊C8C22×C7311yescharacteristic
446C2×C22⋊C8C22×C7311yescharacteristic
447C2×C22⋊C8C22×C7311yescharacteristic
448#386—21no—
449#386—21no—
450#386—21no—
451#381—21no—
452#380C22×C7311yescharacteristic
453#380C22×C7311yescharacteristic
454#380C22×C7311yescharacteristic
455#380C22×C7311yescharacteristic
456#380C22×C7311yescharacteristic
457#380C22×C7311yescharacteristic
458#380C22×C7311yescharacteristic
459#379—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462#340C22×C7311yescharacteristic, complemented
463#340C22×C7311yescharacteristic, complemented
464#340C22×C7311yescharacteristic, complemented
465#340C22×C7311yescharacteristic, complemented
466#340C22×C7311yescharacteristic, complemented
467#340C22×C7311yescharacteristic, complemented
468#340C22×C7311yescharacteristic, complemented
469#340C22×C7311yescharacteristic, complemented
470C25D4×C7311yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C7311yescharacteristic
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4D4×C7311yescharacteristic
482C23×C4D4×C7311yescharacteristic
483C23×C4D4×C7311yescharacteristic
484C23×C4C23×C7311yescharacteristic
485C23×C4C23×C7311yescharacteristic
486C23×C4C23×C7311yescharacteristic
487C22×C8—22no—
488C22×C8—22no—
489C22×C8—22no—
490C22×C8—22no—
491C22×C8—41no—
492C22×C8—41no—
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495C22×C8C23×C7311yescharacteristic
496C22×C8C23×C7311yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503#120—44no—
504#117—22no—
505#117—22no—
506#117—41no—
507#117—41no—
508C2×C4⋊C4C23×C7311yescharacteristic
509C2×C4⋊C4C23×C7311yescharacteristic
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C4⋊C4C23×C7311yescharacteristic
512C2×C4⋊C4C23×C7311yescharacteristic
513C2×C4⋊C4C23×C7311yescharacteristic
514C2×C4⋊C4C23×C7311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C42—21no—
528C2×C42—21no—
529#107—22no—
530#107—41no—
531#106—22no—
532#106—41no—
533#102—22no—
534#102—22no—
535#102—41no—
536#102—41no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8D4×C7314yescomplemented
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—41no—
555C24—41no—
556C24C2×D4×C7311yescharacteristic
557C24C2×D4×C7311yescharacteristic
558C24C2×D4×C7311yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4C2×D4×C7311yescharacteristic
609C22×C4C2×D4×C7311yescharacteristic
610C22×C4C2×D4×C7312yes—
611C22×C4C2×D4×C7311yescharacteristic
612C22×C4#41×C7312yes—
613C22×C4#41×C7312yes—
614C22×C4#41×C7312yes—
615C22×C4C24×C7311yescharacteristic
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—44no—
627C2×C8—44no—
628C2×C8C2×D4×C7312yes—
629C2×C8C2×D4×C7312yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C42—42no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—28no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23#121×C7312yes—
689C23#123×C7312yes—
690C23#135×C7312yes—
691C23#135×C7312yes—
692C23AGL(1,ℤ/8)×C7312yes—
693C23C22×D4×C7311yescharacteristic
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
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#121×C7312yes—
745C2×C4#123×C7312yes—
746C2×C4C22×D4×C7311yescharacteristic
747C2×C4C2×#41×C7311yescharacteristic
748C2×C4C2×#41×C7311yescharacteristic
749C2×C4C2×#41×C7311yescharacteristic
750C2×C4H(5,𝔽2)×C7311yescharacteristic
751C2×C4H(5,𝔽2)×C7311yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—416no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22#482×C7314yescomplemented
785C22C2×#121×C7311yescharacteristic
786C22C2×#123×C7311yescharacteristic
787C22#534×C7311yescharacteristic
788C22C2×#135×C7311yescharacteristic
789C22C2×#135×C7311yescharacteristic
790C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
791C22#575×C7311yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C7311yescharacteristic
803C4#546×C7311yescharacteristic
804C4#551×C7311yescharacteristic
805C4#551×C7311yescharacteristic
806C2—24no—
807C2—42no—
808C2—42no—
809C2—161no—
810C2C73×#241211yescharacteristic
811C2C73×#305011yescharacteristic
812C2C73×#305511yescharacteristic
813C2C2×#482×C7311yescharacteristic
814C2C73×#309111yescharacteristic
815C2C73×#318811yescharacteristic
816C2C73×#319111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C24×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C73C2semidirect
2. C22×C22⋊C8×C73C2semidirect
4. C73×#2280C2semidirect
5. C73×#2077C2semidirect
6. C73×#2076C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1893C2semidirect
10. C73×#1893C2semidirect
11. C73×#1875C2semidirect
12. C73×#1854C2semidirect
13. C73×#1825C2semidirect
14. C73×#1808C2semidirect
15. C73×#1807C2semidirect
26. C2×#107×C73C22semidirect
27. C2×#107×C73C22semidirect
28. C2×#106×C73C22semidirect
29. C2×#106×C73C22semidirect
30. C2×#102×C73C22semidirect
31. C2×#102×C73C22semidirect
32. C2×#102×C73C22semidirect
33. C2×#102×C73C22semidirect
53. #340×C73C22semidirect
54. #340×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
131. C22⋊C8×C73D4semidirect
375. C22×C73#482semidirect
397. #24555C73direct (N × H)
409. C2×#482C2×C73semidirect
410. C22×C22⋊C8C2×C73semidirect
412. #2280C2×C73semidirect
413. #2077C2×C73semidirect
414. #2076C2×C73semidirect
415. #2034C2×C73semidirect
416. #2033C2×C73semidirect
417. #1893C2×C73semidirect
418. #1893C2×C73semidirect
419. #1875C2×C73semidirect
420. #1854C2×C73semidirect
421. #1825C2×C73semidirect
422. #1808C2×C73semidirect
423. #1807C2×C73semidirect
424. C73#24555direct (N × H)
435. C2×#107C22×C73semidirect
436. C2×#107C22×C73semidirect
437. C2×#106C22×C73semidirect
438. C2×#106C22×C73semidirect
439. C2×#102C22×C73semidirect
440. C2×#102C22×C73semidirect
441. C2×#102C22×C73semidirect
442. C2×#102C22×C73semidirect
462. #340C22×C73semidirect
463. #340C22×C73semidirect
464. #340C22×C73semidirect
465. #340C22×C73semidirect
466. #340C22×C73semidirect
467. #340C22×C73semidirect
468. #340C22×C73semidirect
469. #340C22×C73semidirect
540. C22⋊C8D4×C73semidirect
784. C22#482×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C22×C22⋊C8×C732
C73×#28472
C73×#22802
C73×#20772
C73×#20762
C73×#20342
C73×#20332
C73×#18932
C73×#18752
C73×#18542
C73×#18252
C73×#18082
C73×#18072
#2455573