Finite Group Databasebeta

← C73×#26969 #32936373

Subgroups — C73×#26969 #32936373

Order 18688.

964 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×C4×D8×C73C211yesmaximal, characteristic, complemented
3C73×#2427C211yesmaximal, characteristic, complemented
4C73×#2422C211yesmaximal, characteristic, complemented
5C73×#2083C211yesmaximal, characteristic, complemented
6C73×#2036C211yesmaximal, characteristic, complemented
7C73×#2012C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1959C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1933C211yesmaximal, characteristic, complemented
12C73×#1895C211yesmaximal, characteristic, complemented
13C73×#1877C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C2×#124×C73C2211yescharacteristic
20C2×#123×C73—21no—
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26#468×C73—24no—
27C4×D8×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#397×C73—21no—
42#397×C73—21no—
43#394×C73—21no—
44#394×C73—21no—
45#391×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#386×C73—21no—
50#385×C73—21no—
51#384×C73C2211yescharacteristic
52#380×C73—21no—
53#380×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—41no—
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—22no—
77C2×M16×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#124×C73—22no—
83#124×C73—41no—
84#123×C73—44no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—41no—
87#121×C73—22no—
88#121×C73—22no—
89#121×C73—41no—
90#121×C73—41no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
116C2×C22⋊C4×C73D411yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119#107×C73—22no—
120#107×C73—22no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—41no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—41no—
127#102×C73—41no—
128#102×C73D414yescomplemented
129C22⋊C8×C73—22no—
130#97×C73—41no—
131C4×C8×C73—22no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C24×C73C2×D411yescharacteristic
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
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—21no—
157C2×D4×C73—21no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—81no—
163C2×D4×C73—81no—
164C2×D4×C73C2×D412yes—
165C2×D4×C73#4112yes—
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—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—42no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73—42no—
182C22×C4×C73—81no—
183C22×C4×C73—81no—
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2411yescharacteristic
190SD16×C73—44no—
191D8×C73—28no—
192M16×C73—44no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73C2×D412yes—
203C2×C8×C73#4112yes—
204C2×C8×C73#4112yes—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73—81no—
219C4⋊C4×C73C2×D412yes—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—41no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C42×C73—21no—
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—22no—
239C23×C73—22no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73C22×D411yescharacteristic
258Q8×C73—41no—
259Q8×C73—41no—
260Q8×C73—41no—
261Q8×C73—41no—
262D4×C73—22no—
263D4×C73—22no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—41no—
267D4×C73—41no—
268D4×C73—41no—
269D4×C73—41no—
270D4×C73—84no—
271D4×C73—84no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—84no—
309C2×C4×C73—84no—
310C2×C4×C73AGL(1,ℤ/8)12yes—
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C2×#4111yescharacteristic
313C2×C4×C73C2×#4111yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C2×C4×C73H(5,𝔽2)11yescharacteristic
316C2×C4×C73H(5,𝔽2)11yescharacteristic
317C8×C73—22no—
318C8×C73—22no—
319C8×C73—22no—
320C8×C73—41no—
321C22×C73—41no—
322C22×C73—42no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—42no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—42no—
332C22×C73—41no—
333C22×C73—42no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73#53211yescharacteristic
343C22×C73D4211yescharacteristic
344C22×C73#54611yescharacteristic
345C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C73#57511yescharacteristic
347C22×C73#57611yescharacteristic
348C22×C73#57811yescharacteristic
349C4×C73—22no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73—42no—
353C4×C73—41no—
354C4×C73—41no—
355C4×C73—81no—
356C4×C73—81no—
357C4×C73—81no—
358C4×C73—81no—
359C4×C73—81no—
360C4×C73#52511yescharacteristic
361C4×C73#54011yescharacteristic
362C4×C73#54611yescharacteristic
363C4×C73#55311yescharacteristic
364#26969C7311yesmaximal, characteristic, direct product factor, Sylow
365C2×C73—81no—
366C2×C73—82no—
367C2×C73—82no—
368C2×C73#246411yescharacteristic
369C2×C73#317111yescharacteristic
370C2×C73#317511yescharacteristic
371C2×C73#326411yescharacteristic
372C2×C73#326911yescharacteristic
373C2×C73#332211yescharacteristic
374C2×C73#333011yescharacteristic
375C2×#468C2×C7311yescharacteristic, complemented
376C2×C4×D8C2×C7311yescharacteristic, complemented
377#2427C2×C7311yescharacteristic, complemented
378#2422C2×C7311yescharacteristic, complemented
379#2083C2×C7311yescharacteristic, complemented
380#2036C2×C7311yescharacteristic, complemented
381#2012C2×C7311yescharacteristic, complemented
382#1999C2×C7311yescharacteristic
383#1959C2×C7311yescharacteristic, complemented
384#1936C2×C7311yescharacteristic, complemented
385#1933C2×C7311yescharacteristic, complemented
386#1895C2×C7311yescharacteristic, complemented
387#1877C2×C7311yescharacteristic, complemented
388#1862C2×C7311yescharacteristic, complemented
389#1753C2×C7311yescharacteristic, complemented
390C73#2696911yescharacteristic, direct product factor, Sylow
391C22×SD16C22×C7311yescharacteristic
392C22×D8C22×C7311yescharacteristic
393C22×M16C22×C7311yescharacteristic
394C2×#124C22×C7311yescharacteristic
395C2×#123—21no—
396C2×C22⋊Q8C22×C7311yescharacteristic
397C2×#121C22×C7311yescharacteristic
398C2×#121C22×C7311yescharacteristic
399C2×C4×D4C22×C7311yescharacteristic
400C2×C4×D4C22×C7311yescharacteristic
401#468—24no—
402C4×D8—24no—
403C2×#107C22×C7311yescharacteristic
404C2×#107C22×C7311yescharacteristic
405C2×#103C22×C7311yescharacteristic
406C2×#103C22×C7311yescharacteristic
407C2×#103C22×C7311yescharacteristic
408C2×#102C22×C7311yescharacteristic
409C2×#102C22×C7311yescharacteristic
410C2×#102C22×C7311yescharacteristic
411C2×#102C22×C7311yescharacteristic
412C2×#102C22×C7311yescharacteristic
413C2×C22⋊C8C22×C7311yescharacteristic
414C2×#97C22×C7311yescharacteristic
415C2×C4×C8C22×C7311yescharacteristic
416#397—21no—
417#397—21no—
418#394—21no—
419#394—21no—
420#391C22×C7311yescharacteristic
421#390C22×C7311yescharacteristic
422#389C22×C7311yescharacteristic
423#389C22×C7311yescharacteristic
424#386—21no—
425#385—21no—
426#384C22×C7311yescharacteristic
427#380—21no—
428#380C22×C7311yescharacteristic
429C4×C22⋊C4C22×C7311yescharacteristic
430#340C22×C7311yescharacteristic
431#340C22×C7311yescharacteristic
432#340C22×C7311yescharacteristic
433#340C22×C7311yescharacteristic
434#336C22×C7311yescharacteristic
435#336C22×C7311yescharacteristic
436C22×Q8C23×C7311yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C23×C7311yescharacteristic
440C22×D4C23×C7311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C23×C7311yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—41no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8C23×C7311yescharacteristic
454C22×C8C23×C7311yescharacteristic
455C22×C8C23×C7311yescharacteristic
456C22×C8C23×C7311yescharacteristic
457#124—22no—
458#124—41no—
459#123—44no—
460C22⋊Q8—22no—
461C22⋊Q8—41no—
462#121—22no—
463#121—22no—
464#121—41no—
465#121—41no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—41no—
469C4×D4—41no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4C23×C7311yescharacteristic
476C2×C4⋊C4C23×C7311yescharacteristic
477C2×C4⋊C4C23×C7311yescharacteristic
478C2×C4⋊C4C23×C7311yescharacteristic
479C2×C4⋊C4C23×C7311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C7311yescharacteristic
491C2×C22⋊C4D4×C7311yescharacteristic
492C2×C42C23×C7311yescharacteristic
493C2×C42C23×C7311yescharacteristic
494#107—22no—
495#107—22no—
496#103—22no—
497#103—22no—
498#103—41no—
499#102—22no—
500#102—22no—
501#102—41no—
502#102—41no—
503#102D4×C7314yescomplemented
504C22⋊C8—22no—
505#97—41no—
506C4×C8—22no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95D4×C7311yescharacteristic
513#95D4×C7311yescharacteristic
514C24—21no—
515C24—21no—
516C24C2×D4×C7311yescharacteristic
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4C2×D4×C7312yes—
540C2×D4#41×C7312yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×D4×C7311yescharacteristic
560C22×C4C2×D4×C7311yescharacteristic
561C22×C4C2×D4×C7311yescharacteristic
562C22×C4C2×D4×C7311yescharacteristic
563C22×C4C2×D4×C7311yescharacteristic
564C22×C4C24×C7311yescharacteristic
565SD16—44no—
566D8—28no—
567M16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8C2×D4×C7312yes—
578C2×C8#41×C7312yes—
579C2×C8#41×C7312yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4—81no—
594C4⋊C4C2×D4×C7312yes—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23C22×D4×C7311yescharacteristic
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637D4—22no—
638D4—22no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—84no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4AGL(1,ℤ/8)×C7312yes—
686C2×C4C22×D4×C7311yescharacteristic
687C2×C4C2×#41×C7311yescharacteristic
688C2×C4C2×#41×C7311yescharacteristic
689C2×C4C2×#41×C7311yescharacteristic
690C2×C4H(5,𝔽2)×C7311yescharacteristic
691C2×C4H(5,𝔽2)×C7311yescharacteristic
692C8—22no—
693C8—22no—
694C8—22no—
695C8—41no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22#532×C7311yescharacteristic
718C22D42×C7311yescharacteristic
719C22#546×C7311yescharacteristic
720C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
721C22#575×C7311yescharacteristic
722C22#576×C7311yescharacteristic
723C22#578×C7311yescharacteristic
724C4—22no—
725C4—41no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4#525×C7311yescharacteristic
736C4#540×C7311yescharacteristic
737C4#546×C7311yescharacteristic
738C4#553×C7311yescharacteristic
739C2—81no—
740C2—82no—
741C2—82no—
742C2C73×#246411yescharacteristic
743C2C73×#317111yescharacteristic
744C2C73×#317511yescharacteristic
745C2C73×#326411yescharacteristic
746C2C73×#326911yescharacteristic
747C2C73×#332211yescharacteristic
748C2C73×#333011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C73C2semidirect
2. C2×C4×D8×C73C2semidirect
3. C73×#2427C2semidirect
4. C73×#2422C2semidirect
5. C73×#2083C2semidirect
6. C73×#2036C2semidirect
7. C73×#2012C2semidirect
9. C73×#1959C2semidirect
10. C73×#1936C2semidirect
11. C73×#1933C2semidirect
12. C73×#1895C2semidirect
13. C73×#1877C2semidirect
14. C73×#1862C2semidirect
15. C73×#1753C2semidirect
128. #102×C73D4semidirect
364. #26969C73direct (N × H)
375. C2×#468C2×C73semidirect
376. C2×C4×D8C2×C73semidirect
377. #2427C2×C73semidirect
378. #2422C2×C73semidirect
379. #2083C2×C73semidirect
380. #2036C2×C73semidirect
381. #2012C2×C73semidirect
383. #1959C2×C73semidirect
384. #1936C2×C73semidirect
385. #1933C2×C73semidirect
386. #1895C2×C73semidirect
387. #1877C2×C73semidirect
388. #1862C2×C73semidirect
389. #1753C2×C73semidirect
390. C73#26969direct (N × H)
503. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×C4×D8×C732
C73×#24272
C73×#24222
C73×#20832
C73×#20362
C73×#20122
C73×#19992
C73×#19592
C73×#19362
C73×#19332
C73×#18952
C73×#18772
C73×#18622
C73×#17532
#2696973