Finite Group Databasebeta

← C73×#24767 #32934171

Subgroups — C73×#24767 #32934171

Order 18688.

1002 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic
2C2×#465×C73C211yesmaximal, characteristic, complemented
3C2×#463×C73C211yesmaximal, characteristic, complemented
4C2×#424×C73C211yesmaximal, characteristic, complemented
5C73×#2620C211yesmaximal, characteristic, complemented
6C73×#2324C211yesmaximal, characteristic, complemented
7C73×#2066C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2055C211yesmaximal, characteristic, complemented
10C73×#2054C211yesmaximal, characteristic, complemented
11C73×#1983C211yesmaximal, characteristic, complemented
12C73×#1948C211yesmaximal, characteristic, complemented
13C73×#1894C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1802C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#124×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#469×C73—24no—
27#465×C73—24no—
28#463×C73—24no—
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31#424×C73—24no—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44#396×C73—21no—
45#396×C73—21no—
46#394×C73—21no—
47#394×C73—21no—
48#391×C73C2211yescharacteristic
49#390×C73—21no—
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#386×C73—21no—
55#385×C73—21no—
56#384×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73C2311yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C23×C4×C73—21no—
69C23×C4×C73C2311yescharacteristic
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—41no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—41no—
76C2×M16×C73—22no—
77C2×M16×C73—22no—
78C2×M16×C73—41no—
79C22×C8×C73—22no—
80C22×C8×C73—22no—
81C22×C8×C73—41no—
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86#124×C73—22no—
87#124×C73—22no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73D414yes—
94C4×D4×C73—22no—
95C4×D4×C73—22no—
96#117×C73—22no—
97#117×C73—22no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73D411yescharacteristic
121C2×C22⋊C4×C73D411yescharacteristic
122C2×C42×C73—21no—
123C2×C42×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125#106×C73—22no—
126#106×C73—22no—
127C4⋊C8×C73—22no—
128C4⋊C8×C73—22no—
129C4⋊C8×C73—22no—
130C4⋊C8×C73D414yescomplemented
131#103×C73—22no—
132#103×C73—22no—
133#103×C73—41no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—41no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144C24×C73—21no—
145C24×C73—21no—
146C24×C73C2×D411yescharacteristic
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×D4×C73—24no—
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—21no—
165C2×D4×C73—42no—
166C2×D4×C73—81no—
167C2×D4×C73—81no—
168C2×D4×C73—81no—
169C2×D4×C73—81no—
170C2×D4×C73C2×D412yes—
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—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
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×C73C2×D412yes—
190C22×C4×C73#4112yes—
191C22×C4×C73C2411yescharacteristic
192SD16×C73—44no—
193D8×C73—44no—
194M16×C73—44no—
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×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—44no—
206C2×C8×C73C2×D412yes—
207C2×C8×C73C2×D412yes—
208C4⋊C4×C73—22no—
209C4⋊C4×C73—22no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73—81no—
221C4⋊C4×C73—81no—
222C4⋊C4×C73—81no—
223C4⋊C4×C73C2×D412yes—
224C22⋊C4×C73—24no—
225C22⋊C4×C73—22no—
226C22⋊C4×C73—22no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—81no—
233C22⋊C4×C73—81no—
234C22⋊C4×C73—81no—
235C22⋊C4×C73—81no—
236C22⋊C4×C73—81no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—81no—
240C42×C73C2×D412yes—
241C42×C73#4112yes—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
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×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73#12112yes—
263C23×C73C22×D411yescharacteristic
264Q8×C73—41no—
265Q8×C73—41no—
266Q8×C73—41no—
267Q8×C73—41no—
268D4×C73—22no—
269D4×C73—22no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—84no—
277D4×C73—84no—
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—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—22no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
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—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—84no—
313C2×C4×C73#12112yes—
314C2×C4×C73#12112yes—
315C2×C4×C73#12112yes—
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C2×#4111yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73H(5,𝔽2)11yescharacteristic
321C2×C4×C732−1+411yescharacteristic
322C8×C73—22no—
323C8×C73—22no—
324C8×C73—41no—
325C8×C73—41no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—22no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—42no—
334C22×C73—42no—
335C22×C73—42no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73C2×#12111yescharacteristic
348C22×C73C2×#12111yescharacteristic
349C22×C73#53711yescharacteristic
350C22×C73#57611yescharacteristic
351C22×C73#57711yescharacteristic
352C22×C73#57711yescharacteristic
353C22×C73#57711yescharacteristic
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—22no—
357C4×C73—42no—
358C4×C73—41no—
359C4×C73—41no—
360C4×C73—81no—
361C4×C73—81no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73D4211yescharacteristic
366C4×C73#54711yescharacteristic
367C4×C73#54811yescharacteristic
368C4×C73#55311yescharacteristic
369#24767C7311yesmaximal, characteristic, direct product factor, Sylow
370C2×C73—42no—
371C2×C73—82no—
372C2×C73—161no—
373C2×C73#241611yescharacteristic
374C2×C73#304211yescharacteristic
375C2×C73#304511yescharacteristic
376C2×C73#306011yescharacteristic
377C2×C73#306211yescharacteristic
378C2×C73#325711yescharacteristic
379C2×C73#326311yescharacteristic
380C2×#469C2×C7311yescharacteristic
381C2×#465C2×C7311yescharacteristic, complemented
382C2×#463C2×C7311yescharacteristic, complemented
383C2×#424C2×C7311yescharacteristic, complemented
384#2620C2×C7311yescharacteristic, complemented
385#2324C2×C7311yescharacteristic, complemented
386#2066C2×C7311yescharacteristic, complemented
387#2065C2×C7311yescharacteristic, complemented
388#2055C2×C7311yescharacteristic, complemented
389#2054C2×C7311yescharacteristic, complemented
390#1983C2×C7311yescharacteristic, complemented
391#1948C2×C7311yescharacteristic, complemented
392#1894C2×C7311yescharacteristic, complemented
393#1893C2×C7311yescharacteristic, complemented
394#1802C2×C7311yescharacteristic, complemented
395C73#2476711yescharacteristic, direct product factor, Sylow
396C22×SD16C22×C7311yescharacteristic
397C22×D8C22×C7311yescharacteristic
398C22×M16C22×C7311yescharacteristic
399C23×C8C22×C7311yescharacteristic
400C2×#124C22×C7311yescharacteristic
401C2×C22⋊Q8C22×C7311yescharacteristic
402C2×#121C22×C7311yescharacteristic
403C2×#121C22×C7311yescharacteristic
404C2×C4×D4C22×C7311yescharacteristic
405C2×#117C22×C7311yescharacteristic
406#469—24no—
407#465—24no—
408#463—24no—
409C2×#106C22×C7311yescharacteristic
410C2×#106C22×C7311yescharacteristic
411#424—24no—
412C2×C4⋊C8C22×C7311yescharacteristic
413C2×C4⋊C8C22×C7311yescharacteristic
414C2×C4⋊C8C22×C7311yescharacteristic
415C2×C4⋊C8C22×C7311yescharacteristic
416C2×#103C22×C7311yescharacteristic
417C2×#103C22×C7311yescharacteristic
418C2×#103C22×C7311yescharacteristic
419C2×#102C22×C7311yescharacteristic
420C2×#102C22×C7311yescharacteristic
421C2×#102C22×C7311yescharacteristic
422C2×#102C22×C7311yescharacteristic
423C2×#102C22×C7311yescharacteristic
424#396—21no—
425#396—21no—
426#394—21no—
427#394—21no—
428#391C22×C7311yescharacteristic
429#390—21no—
430#390C22×C7311yescharacteristic
431#390C22×C7311yescharacteristic
432#389C22×C7311yescharacteristic
433#388—21no—
434#386—21no—
435#385—21no—
436#384C22×C7311yescharacteristic
437#380C22×C7311yescharacteristic
438C4×C4⋊C4C22×C7311yescharacteristic
439#340C22×C7311yescharacteristic
440#340C22×C7311yescharacteristic
441#340C22×C7311yescharacteristic
442#340C22×C7311yescharacteristic
443C22×Q8C23×C7311yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C23×C7311yescharacteristic
447C22×D4C23×C7311yescharacteristic
448C23×C4—21no—
449C23×C4C23×C7311yescharacteristic
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—41no—
453C2×D8—22no—
454C2×D8—22no—
455C2×D8—41no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16—41no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—41no—
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464C22×C8C23×C7311yescharacteristic
465C22×C8C23×C7311yescharacteristic
466#124—22no—
467#124—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121D4×C7314yes—
474C4×D4—22no—
475C4×D4—22no—
476#117—22no—
477#117—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4D4×C7311yescharacteristic
483C2×C4⋊C4D4×C7311yescharacteristic
484C2×C4⋊C4C23×C7311yescharacteristic
485C2×C4⋊C4C23×C7311yescharacteristic
486C2×C4⋊C4C23×C7311yescharacteristic
487C2×C4⋊C4C23×C7311yescharacteristic
488C2×C4⋊C4C23×C7311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4D4×C7311yescharacteristic
501C2×C22⋊C4D4×C7311yescharacteristic
502C2×C42—21no—
503C2×C42C23×C7311yescharacteristic
504C2×C42C23×C7311yescharacteristic
505#106—22no—
506#106—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8D4×C7314yescomplemented
511#103—22no—
512#103—22no—
513#103—41no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—22no—
518#102—41no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—21no—
525C24—21no—
526C24C2×D4×C7311yescharacteristic
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×D4—24no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4C2×D4×C7312yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4C2×D4×C7311yescharacteristic
565C22×C4C2×D4×C7311yescharacteristic
566C22×C4C2×D4×C7311yescharacteristic
567C22×C4C2×D4×C7311yescharacteristic
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7312yes—
570C22×C4#41×C7312yes—
571C22×C4C24×C7311yescharacteristic
572SD16—44no—
573D8—44no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—44no—
586C2×C8C2×D4×C7312yes—
587C2×C8C2×D4×C7312yes—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4—81no—
602C4⋊C4—81no—
603C4⋊C4C2×D4×C7312yes—
604C22⋊C4—24no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—21no—
618C42—21no—
619C42—81no—
620C42C2×D4×C7312yes—
621C42#41×C7312yes—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23#121×C7312yes—
643C23C22×D4×C7311yescharacteristic
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648D4—22no—
649D4—22no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
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—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4#121×C7312yes—
694C2×C4#121×C7312yes—
695C2×C4#121×C7312yes—
696C2×C4C22×D4×C7311yescharacteristic
697C2×C4C22×D4×C7311yescharacteristic
698C2×C4C2×#41×C7311yescharacteristic
699C2×C4C2×#41×C7311yescharacteristic
700C2×C4H(5,𝔽2)×C7311yescharacteristic
701C2×C42−1+4×C7311yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×#121×C7311yescharacteristic
728C22C2×#121×C7311yescharacteristic
729C22#537×C7311yescharacteristic
730C22#576×C7311yescharacteristic
731C22#577×C7311yescharacteristic
732C22#577×C7311yescharacteristic
733C22#577×C7311yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4D42×C7311yescharacteristic
746C4#547×C7311yescharacteristic
747C4#548×C7311yescharacteristic
748C4#553×C7311yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2C73×#241611yescharacteristic
753C2C73×#304211yescharacteristic
754C2C73×#304511yescharacteristic
755C2C73×#306011yescharacteristic
756C2C73×#306211yescharacteristic
757C2C73×#325711yescharacteristic
758C2C73×#326311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#469×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#465×C73C2semidirect
3. C2×#463×C73C2semidirect
4. C2×#424×C73C2semidirect
5. C73×#2620C2semidirect
6. C73×#2324C2semidirect
7. C73×#2066C2semidirect
8. C73×#2065C2semidirect
9. C73×#2055C2semidirect
10. C73×#2054C2semidirect
11. C73×#1983C2semidirect
12. C73×#1948C2semidirect
13. C73×#1894C2semidirect
14. C73×#1893C2semidirect
15. C73×#1802C2semidirect
130. C4⋊C8×C73D4semidirect
369. #24767C73direct (N × H)
381. C2×#465C2×C73semidirect
382. C2×#463C2×C73semidirect
383. C2×#424C2×C73semidirect
384. #2620C2×C73semidirect
385. #2324C2×C73semidirect
386. #2066C2×C73semidirect
387. #2065C2×C73semidirect
388. #2055C2×C73semidirect
389. #2054C2×C73semidirect
390. #1983C2×C73semidirect
391. #1948C2×C73semidirect
392. #1894C2×C73semidirect
393. #1893C2×C73semidirect
394. #1802C2×C73semidirect
395. C73#24767direct (N × H)
510. C4⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#465×C732
C2×#463×C732
C2×#424×C732
C73×#26202
C73×#23242
C73×#20662
C73×#20652
C73×#20552
C73×#20542
C73×#19832
C73×#19482
C73×#18942
C73×#18932
C73×#18022
#2476773