Finite Group Databasebeta

← C73×#24865 #32934269

Subgroups — C73×#24865 #32934269

Order 18688.

1238 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic, complemented
2C22×#102×C73C211yesmaximal, characteristic, complemented
3C73×#2408C211yesmaximal, characteristic
4D4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
5C73×#2094C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#1926C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, characteristic, complemented
11C73×#1874C211yesmaximal, characteristic, complemented
12C73×#1869C211yesmaximal, characteristic, complemented
13C73×#1853C211yesmaximal, characteristic, complemented
14C73×#1807C211yesmaximal, characteristic, complemented
15C73×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×#120×C73—21no—
21C2×C4×D4×C73—21no—
22C2×C4×D4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic, complemented
25#481×C73—24no—
26C2×#106×C73C2211yescharacteristic, complemented
27C2×#106×C73C2211yescharacteristic, complemented
28C2×#106×C73C2211yescharacteristic, complemented
29C2×#106×C73C2211yescharacteristic, complemented
30C2×#102×C73—24no—
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic, complemented
41C2×C22⋊C8×C73C2211yescharacteristic, complemented
42#394×C73—21no—
43#392×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73—21no—
47#385×C73—21no—
48#385×C73—21no—
49#384×C73C2211yescharacteristic, complemented
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic, complemented
53#379×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic, complemented
55#340×C73C2211yescharacteristic, complemented
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C25×C73—21no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73D411yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C22×C8×C73—22no—
79C22×C8×C73—22no—
80C22×C8×C73—41no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85#121×C73—22no—
86#121×C73—22no—
87#121×C73—41no—
88#121×C73—41no—
89#120×C73—44no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—44no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—41no—
100C2×C4⋊C4×C73—41no—
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121#106×C73—22no—
122#106×C73—22no—
123#106×C73—41no—
124#106×C73—41no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—41no—
131#102×C73—41no—
132#102×C73D414yescomplemented
133C22⋊C8×C73—22no—
134C22⋊C8×C73—22no—
135C22⋊C8×C73—41no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140C24×C73—21no—
141C24×C73—21no—
142C24×C73—42no—
143C24×C73—42no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73—42no—
147C24×C73—81no—
148C24×C73—81no—
149C24×C73C2×D411yescharacteristic
150C24×C73C2×D411yescharacteristic
151C2×D4×C73—22no—
152C2×D4×C73—22no—
153C2×D4×C73—28no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
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—44no—
165C2×D4×C73—44no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—44no—
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×C73SD1614yes—
177C2×D4×C73C2×D412yes—
178C2×D4×C73#4112yes—
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—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—42no—
196C22×C4×C73—42no—
197C22×C4×C73—42no—
198C22×C4×C73—42no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73#4112yes—
206C22×C4×C73#4112yes—
207C22×C4×C73C2411yescharacteristic
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—21no—
218C2×C8×C73—21no—
219C2×C8×C73—44no—
220C2×C8×C73C2×D412yes—
221C4⋊C4×C73—22no—
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—42no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73—42no—
236C4⋊C4×C73—81no—
237C4⋊C4×C73C2×D412yes—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—22no—
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—
247C22⋊C4×C73—81no—
248C22⋊C4×C73—81no—
249C42×C73—21no—
250C42×C73—21no—
251C42×C73—42no—
252C23×C73—21no—
253C23×C73—21no—
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—22no—
263C23×C73—22no—
264C23×C73—48no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—84no—
278C23×C73—84no—
279C23×C73—84no—
280C23×C73—84no—
281C23×C73—84no—
282C23×C73—84no—
283C23×C73#12312yes—
284C23×C73C2×SD1612yes—
285C23×C73C2×SD1612yes—
286C23×C73AGL(1,ℤ/8)12yes—
287C23×C73C22×D411yescharacteristic
288D4×C73—28no—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—48no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—84no—
299D4×C73—84no—
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—22no—
307C2×C4×C73—22no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—22no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
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—41no—
336C2×C4×C73—84no—
337C2×C4×C73—84no—
338C2×C4×C73#12312yes—
339C2×C4×C73C2×SD1612yes—
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C2×#4111yescharacteristic
342C2×C4×C73C2×#4111yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73H(5,𝔽2)11yescharacteristic
345C2×C4×C73H(5,𝔽2)11yescharacteristic
346C8×C73—22no—
347C8×C73—41no—
348C8×C73—41no—
349C8×C73—41no—
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—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—816no—
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×C73#48114yescomplemented
379C22×C73C2×#12311yescharacteristic
380C22×C73D4211yescharacteristic
381C22×C73#54611yescharacteristic
382C22×C73C22×SD1611yescharacteristic
383C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C73#57611yescharacteristic
385C22×C73#57711yescharacteristic
386C4×C73—22no—
387C4×C73—22no—
388C4×C73—41no—
389C4×C73—41no—
390C4×C73—42no—
391C4×C73—81no—
392C4×C73—81no—
393C4×C73—81no—
394C4×C73—81no—
395C4×C73—81no—
396C4×C73#52511yescharacteristic
397C4×C73#53811yescharacteristic
398C4×C73#54611yescharacteristic
399C4×C73#55111yescharacteristic
400#24865C7311yesmaximal, characteristic, direct product factor, Sylow
401C2×C73—24no—
402C2×C73—42no—
403C2×C73—82no—
404C2×C73—82no—
405C2×C73#241811yescharacteristic
406C2×C73C2×#48111yescharacteristic
407C2×C73#309611yescharacteristic
408C2×C73#326411yescharacteristic
409C2×C73D4×SD1611yescharacteristic
410C2×C73#329511yescharacteristic
411C2×C73#330611yescharacteristic
412C2×#481C2×C7311yescharacteristic, complemented
413C22×#102C2×C7311yescharacteristic, complemented
414#2408C2×C7311yescharacteristic
415D4×C4⋊C4C2×C7311yescharacteristic, complemented
416#2094C2×C7311yescharacteristic, complemented
417#2071C2×C7311yescharacteristic, complemented
418#2034C2×C7311yescharacteristic, complemented
419#2034C2×C7311yescharacteristic, complemented
420#1926C2×C7311yescharacteristic, complemented
421#1926C2×C7311yescharacteristic, complemented
422#1874C2×C7311yescharacteristic, complemented
423#1869C2×C7311yescharacteristic, complemented
424#1853C2×C7311yescharacteristic, complemented
425#1807C2×C7311yescharacteristic, complemented
426#1786C2×C7311yescharacteristic, complemented
427C73#2486511yescharacteristic, direct product factor, Sylow
428C23×D4C22×C7311yescharacteristic
429C23×C8C22×C7311yescharacteristic
430C2×#121C22×C7311yescharacteristic
431C2×#121C22×C7311yescharacteristic
432C2×#120—21no—
433C2×C4×D4—21no—
434C2×C4×D4C22×C7311yescharacteristic
435C22×C4⋊C4C22×C7311yescharacteristic
436C22×C4⋊C4C22×C7311yescharacteristic, complemented
437#481—24no—
438C2×#106C22×C7311yescharacteristic, complemented
439C2×#106C22×C7311yescharacteristic, complemented
440C2×#106C22×C7311yescharacteristic, complemented
441C2×#106C22×C7311yescharacteristic, complemented
442C2×#102—24no—
443C2×#102C22×C7311yescharacteristic
444C2×#102C22×C7311yescharacteristic
445C2×#102C22×C7311yescharacteristic
446C2×#102C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×#102C22×C7311yescharacteristic
449C2×#102C22×C7311yescharacteristic
450C2×#102C22×C7311yescharacteristic
451C2×C22⋊C8C22×C7311yescharacteristic
452C2×C22⋊C8C22×C7311yescharacteristic, complemented
453C2×C22⋊C8C22×C7311yescharacteristic, complemented
454#394—21no—
455#392—21no—
456#390C22×C7311yescharacteristic
457#390C22×C7311yescharacteristic
458#389—21no—
459#385—21no—
460#385—21no—
461#384C22×C7311yescharacteristic, complemented
462#380C22×C7311yescharacteristic
463#380C22×C7311yescharacteristic
464#380C22×C7311yescharacteristic, complemented
465#379—21no—
466C4×C4⋊C4C22×C7311yescharacteristic, complemented
467#340C22×C7311yescharacteristic, complemented
468#340C22×C7311yescharacteristic, complemented
469#340C22×C7311yescharacteristic, complemented
470#340C22×C7311yescharacteristic, complemented
471#336C22×C7311yescharacteristic, complemented
472#336C22×C7311yescharacteristic, complemented
473C25—21no—
474C22×D4—22no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4D4×C7311yescharacteristic
484C22×D4C23×C7311yescharacteristic
485C22×D4C23×C7311yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C7311yescharacteristic
489C23×C4C23×C7311yescharacteristic
490C22×C8—22no—
491C22×C8—22no—
492C22×C8—41no—
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495C22×C8C23×C7311yescharacteristic
496C22×C8C23×C7311yescharacteristic
497#121—22no—
498#121—22no—
499#121—41no—
500#121—41no—
501#120—44no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—44no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4D4×C7311yescharacteristic
514C2×C4⋊C4C23×C7311yescharacteristic
515C2×C4⋊C4C23×C7311yescharacteristic
516C2×C4⋊C4C23×C7311yescharacteristic
517C2×C4⋊C4C23×C7311yescharacteristic
518C2×C4⋊C4C23×C7311yescharacteristic
519C2×C4⋊C4C23×C7311yescharacteristic
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×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4D4×C7311yescharacteristic
530C2×C22⋊C4D4×C7311yescharacteristic
531C2×C42—21no—
532C2×C42C23×C7311yescharacteristic
533#106—22no—
534#106—22no—
535#106—41no—
536#106—41no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543#102—41no—
544#102D4×C7314yescomplemented
545C22⋊C8—22no—
546C22⋊C8—22no—
547C22⋊C8—41no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—81no—
560C24—81no—
561C24C2×D4×C7311yescharacteristic
562C24C2×D4×C7311yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—28no—
566C2×D4—21no—
567C2×D4—21no—
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—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4SD16×C7314yes—
589C2×D4C2×D4×C7312yes—
590C2×D4#41×C7312yes—
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—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C7311yescharacteristic
614C22×C4C2×D4×C7311yescharacteristic
615C22×C4C2×D4×C7311yescharacteristic
616C22×C4C2×D4×C7311yescharacteristic
617C22×C4#41×C7312yes—
618C22×C4#41×C7312yes—
619C22×C4C24×C7311yescharacteristic
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8C2×D4×C7312yes—
633C4⋊C4—22no—
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—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—81no—
649C4⋊C4C2×D4×C7312yes—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—48no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23#123×C7312yes—
696C23C2×SD16×C7312yes—
697C23C2×SD16×C7312yes—
698C23AGL(1,ℤ/8)×C7312yes—
699C23C22×D4×C7311yescharacteristic
700D4—28no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—48no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
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—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4#123×C7312yes—
751C2×C4C2×SD16×C7312yes—
752C2×C4C22×D4×C7311yescharacteristic
753C2×C4C2×#41×C7311yescharacteristic
754C2×C4C2×#41×C7311yescharacteristic
755C2×C4C2×#41×C7311yescharacteristic
756C2×C4H(5,𝔽2)×C7311yescharacteristic
757C2×C4H(5,𝔽2)×C7311yescharacteristic
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—816no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22#481×C7314yescomplemented
791C22C2×#123×C7311yescharacteristic
792C22D42×C7311yescharacteristic
793C22#546×C7311yescharacteristic
794C22C22×SD16×C7311yescharacteristic
795C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
796C22#576×C7311yescharacteristic
797C22#577×C7311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4#525×C7311yescharacteristic
809C4#538×C7311yescharacteristic
810C4#546×C7311yescharacteristic
811C4#551×C7311yescharacteristic
812C2—24no—
813C2—42no—
814C2—82no—
815C2—82no—
816C2C73×#241811yescharacteristic
817C2C2×#481×C7311yescharacteristic
818C2C73×#309611yescharacteristic
819C2C73×#326411yescharacteristic
820C2D4×SD16×C7311yescharacteristic
821C2C73×#329511yescharacteristic
822C2C73×#330611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2408C2
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×#481×C73C2semidirect
2. C22×#102×C73C2semidirect
4. D4×C4⋊C4×C73C2semidirect
5. C73×#2094C2semidirect
6. C73×#2071C2semidirect
7. C73×#2034C2semidirect
8. C73×#2034C2semidirect
9. C73×#1926C2semidirect
10. C73×#1926C2semidirect
11. C73×#1874C2semidirect
12. C73×#1869C2semidirect
13. C73×#1853C2semidirect
14. C73×#1807C2semidirect
15. C73×#1786C2semidirect
24. C22×C4⋊C4×C73C22semidirect
26. C2×#106×C73C22semidirect
27. C2×#106×C73C22semidirect
28. C2×#106×C73C22semidirect
29. C2×#106×C73C22semidirect
40. C2×C22⋊C8×C73C22semidirect
41. C2×C22⋊C8×C73C22semidirect
49. #384×C73C22semidirect
52. #380×C73C22semidirect
54. C4×C4⋊C4×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
132. #102×C73D4semidirect
378. C22×C73#481semidirect
400. #24865C73direct (N × H)
412. C2×#481C2×C73semidirect
413. C22×#102C2×C73semidirect
415. D4×C4⋊C4C2×C73semidirect
416. #2094C2×C73semidirect
417. #2071C2×C73semidirect
418. #2034C2×C73semidirect
419. #2034C2×C73semidirect
420. #1926C2×C73semidirect
421. #1926C2×C73semidirect
422. #1874C2×C73semidirect
423. #1869C2×C73semidirect
424. #1853C2×C73semidirect
425. #1807C2×C73semidirect
426. #1786C2×C73semidirect
427. C73#24865direct (N × H)
436. C22×C4⋊C4C22×C73semidirect
438. C2×#106C22×C73semidirect
439. C2×#106C22×C73semidirect
440. C2×#106C22×C73semidirect
441. C2×#106C22×C73semidirect
452. C2×C22⋊C8C22×C73semidirect
453. C2×C22⋊C8C22×C73semidirect
461. #384C22×C73semidirect
464. #380C22×C73semidirect
466. C4×C4⋊C4C22×C73semidirect
467. #340C22×C73semidirect
468. #340C22×C73semidirect
469. #340C22×C73semidirect
470. #340C22×C73semidirect
471. #336C22×C73semidirect
472. #336C22×C73semidirect
544. #102D4×C73semidirect
790. C22#481×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C732
C22×#102×C732
C73×#24082
D4×C4⋊C4×C732
C73×#20942
C73×#20712
C73×#20342
C73×#19262
C73×#18742
C73×#18692
C73×#18532
C73×#18072
C73×#17862
#2486573