Finite Group Databasebeta

← C73×#24762 #32934166

Subgroups — C73×#24762 #32934166

Order 18688.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#466×C73C211yesmaximal, characteristic, complemented
3C2×#459×C73C211yesmaximal, characteristic, complemented
4C2×#424×C73C211yesmaximal, characteristic, complemented
5C73×#2619C211yesmaximal, characteristic, complemented
6C73×#2324C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2054C211yesmaximal, characteristic, complemented
10C73×#2054C211yesmaximal, characteristic, complemented
11C73×#1982C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#127×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#469×C73—24no—
27#466×C73—24no—
28#459×C73—24no—
29C2×#107×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×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44#394×C73—21no—
45#394×C73—21no—
46#392×C73—21no—
47#392×C73—21no—
48#390×C73—21no—
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#386×C73—21no—
55#385×C73—21no—
56#382×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×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×C73—21no—
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73C2311yescharacteristic
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—41no—
78C2×D8×C73—41no—
79C2×M16×C73—22no—
80C2×M16×C73—22no—
81C2×M16×C73—41no—
82C22×C8×C73—22no—
83C22×C8×C73—22no—
84C22×C8×C73—41no—
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89#127×C73—22no—
90#127×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—22no—
94#121×C73—22no—
95#121×C73—22no—
96#121×C73D414yescomplemented
97C4×D4×C73—22no—
98C4×D4×C73—22no—
99#117×C73—22no—
100#117×C73—22no—
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#107×C73—22no—
126#106×C73—22no—
127C4⋊C8×C73—22no—
128C4⋊C8×C73—22no—
129C4⋊C8×C73—22no—
130C4⋊C8×C73D414yescomplemented
131#102×C73—22no—
132#102×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—22no—
137#102×C73—41no—
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×C73—21no—
147C24×C73C2×D411yescharacteristic
148C2×D4×C73—24no—
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—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—42no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—81no—
171C2×D4×C73—81no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
177C2×D4×C73—81no—
178C2×D4×C73—81no—
179C2×D4×C73—81no—
180C2×D4×C73C2×D412yes—
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—42no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D412yes—
199C22×C4×C73#4112yes—
200C22×C4×C73C2411yescharacteristic
201D8×C73—44no—
202D8×C73—44no—
203M16×C73—44no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
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—44no—
215C2×C8×C73C2×D412yes—
216C2×C8×C73C2×D412yes—
217C4⋊C4×C73—22no—
218C4⋊C4×C73—22no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
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—81no—
229C4⋊C4×C73C2×D412yes—
230C22⋊C4×C73—24no—
231C22⋊C4×C73—22no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—81no—
237C22⋊C4×C73—81no—
238C22⋊C4×C73—81no—
239C22⋊C4×C73—81no—
240C22⋊C4×C73—81no—
241C22⋊C4×C73—81no—
242C22⋊C4×C73—81no—
243C42×C73—21no—
244C42×C73—21no—
245C42×C73—81no—
246C42×C73C2×D412yes—
247C42×C73#4112yes—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—22no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
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#12112yes—
276C23×C73C22×D411yescharacteristic
277D4×C73—22no—
278D4×C73—22no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—84no—
290D4×C73—84no—
291D4×C73—84no—
292D4×C73—84no—
293D4×C73—84no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
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—22no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
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—84no—
326C2×C4×C73#12112yes—
327C2×C4×C73#12112yes—
328C2×C4×C73#12112yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C2×#4111yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73H(5,𝔽2)11yescharacteristic
334C2×C4×C732−1+411yescharacteristic
335C8×C73—22no—
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—42no—
347C22×C73—42no—
348C22×C73—42no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73—81no—
358C22×C73—81no—
359C22×C73—81no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73—81no—
363C22×C73—81no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73C2×#12111yescharacteristic
368C22×C73C2×#12111yescharacteristic
369C22×C73#53711yescharacteristic
370C22×C73#57611yescharacteristic
371C22×C73#57611yescharacteristic
372C22×C73#57611yescharacteristic
373C22×C73#57711yescharacteristic
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—42no—
378C4×C73—41no—
379C4×C73—41no—
380C4×C73—81no—
381C4×C73—81no—
382C4×C73—81no—
383C4×C73—81no—
384C4×C73D4211yescharacteristic
385C4×C73#54711yescharacteristic
386C4×C73#54811yescharacteristic
387C4×C73#55311yescharacteristic
388#24762C7311yesmaximal, characteristic, direct product factor, Sylow
389C2×C73—42no—
390C2×C73—82no—
391C2×C73—161no—
392C2×C73—161no—
393C2×C73#241611yescharacteristic
394C2×C73#304111yescharacteristic
395C2×C73#304511yescharacteristic
396C2×C73#305811yescharacteristic
397C2×C73#306211yescharacteristic
398C2×C73#325711yescharacteristic
399C2×C73#325911yescharacteristic
400C2×#469C2×C7311yescharacteristic, complemented
401C2×#466C2×C7311yescharacteristic, complemented
402C2×#459C2×C7311yescharacteristic, complemented
403C2×#424C2×C7311yescharacteristic, complemented
404#2619C2×C7311yescharacteristic, complemented
405#2324C2×C7311yescharacteristic, complemented
406#2067C2×C7311yescharacteristic, complemented
407#2065C2×C7311yescharacteristic, complemented
408#2054C2×C7311yescharacteristic, complemented
409#2054C2×C7311yescharacteristic, complemented
410#1982C2×C7311yescharacteristic, complemented
411#1949C2×C7311yescharacteristic, complemented
412#1895C2×C7311yescharacteristic, complemented
413#1893C2×C7311yescharacteristic, complemented
414#1804C2×C7311yescharacteristic, complemented
415C73#2476211yescharacteristic, direct product factor, Sylow
416C22×D8C22×C7311yescharacteristic
417C22×D8C22×C7311yescharacteristic
418C22×M16C22×C7311yescharacteristic
419C23×C8C22×C7311yescharacteristic
420C2×#127C22×C7311yescharacteristic
421C2×#121C22×C7311yescharacteristic
422C2×#121C22×C7311yescharacteristic
423C2×#121C22×C7311yescharacteristic
424C2×C4×D4C22×C7311yescharacteristic
425C2×#117C22×C7311yescharacteristic
426#469—24no—
427#466—24no—
428#459—24no—
429C2×#107C22×C7311yescharacteristic
430C2×#106C22×C7311yescharacteristic
431#424—24no—
432C2×C4⋊C8C22×C7311yescharacteristic
433C2×C4⋊C8C22×C7311yescharacteristic
434C2×C4⋊C8C22×C7311yescharacteristic
435C2×C4⋊C8C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×#102C22×C7311yescharacteristic
438C2×#102C22×C7311yescharacteristic
439C2×#102C22×C7311yescharacteristic
440C2×#102C22×C7311yescharacteristic
441C2×#102C22×C7311yescharacteristic
442C2×#102C22×C7311yescharacteristic
443C2×#102C22×C7311yescharacteristic
444#394—21no—
445#394—21no—
446#392—21no—
447#392—21no—
448#390—21no—
449#390C22×C7311yescharacteristic
450#390C22×C7311yescharacteristic
451#390C22×C7311yescharacteristic
452#389C22×C7311yescharacteristic
453#388—21no—
454#386—21no—
455#385—21no—
456#382C22×C7311yescharacteristic
457#380C22×C7311yescharacteristic
458C4×C4⋊C4C22×C7311yescharacteristic
459#340C22×C7311yescharacteristic
460#340C22×C7311yescharacteristic
461#340C22×C7311yescharacteristic
462#340C22×C7311yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C23×C7311yescharacteristic
469C22×D4C23×C7311yescharacteristic
470C22×D4C23×C7311yescharacteristic
471C23×C4—21no—
472C23×C4C23×C7311yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487C22×C8C23×C7311yescharacteristic
488C22×C8C23×C7311yescharacteristic
489#127—22no—
490#127—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121D4×C7314yescomplemented
497C4×D4—22no—
498C4×D4—22no—
499#117—22no—
500#117—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C7311yescharacteristic
503C2×C4⋊C4D4×C7311yescharacteristic
504C2×C4⋊C4C23×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C4⋊C4C23×C7311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C7311yescharacteristic
521C2×C22⋊C4D4×C7311yescharacteristic
522C2×C42—21no—
523C2×C42C23×C7311yescharacteristic
524C2×C42C23×C7311yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8D4×C7314yescomplemented
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C2×D4×C7311yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C7312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C2×D4×C7312yes—
599C22×C4#41×C7312yes—
600C22×C4C24×C7311yescharacteristic
601D8—44no—
602D8—44no—
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—44no—
615C2×C8C2×D4×C7312yes—
616C2×C8C2×D4×C7312yes—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—81no—
629C4⋊C4C2×D4×C7312yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42C2×D4×C7312yes—
647C42#41×C7312yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#121×C7312yes—
676C23C22×D4×C7311yescharacteristic
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4#121×C7312yes—
727C2×C4#121×C7312yes—
728C2×C4#121×C7312yes—
729C2×C4C22×D4×C7311yescharacteristic
730C2×C4C22×D4×C7311yescharacteristic
731C2×C4C2×#41×C7311yescharacteristic
732C2×C4C2×#41×C7311yescharacteristic
733C2×C4H(5,𝔽2)×C7311yescharacteristic
734C2×C42−1+4×C7311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C7311yescharacteristic
768C22C2×#121×C7311yescharacteristic
769C22#537×C7311yescharacteristic
770C22#576×C7311yescharacteristic
771C22#576×C7311yescharacteristic
772C22#576×C7311yescharacteristic
773C22#577×C7311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4D42×C7311yescharacteristic
785C4#547×C7311yescharacteristic
786C4#548×C7311yescharacteristic
787C4#553×C7311yescharacteristic
788C2—42no—
789C2—82no—
790C2—161no—
791C2—161no—
792C2C73×#241611yescharacteristic
793C2C73×#304111yescharacteristic
794C2C73×#304511yescharacteristic
795C2C73×#305811yescharacteristic
796C2C73×#306211yescharacteristic
797C2C73×#325711yescharacteristic
798C2C73×#325911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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
1. C2×#469×C73C2semidirect
2. C2×#466×C73C2semidirect
3. C2×#459×C73C2semidirect
4. C2×#424×C73C2semidirect
5. C73×#2619C2semidirect
6. C73×#2324C2semidirect
7. C73×#2067C2semidirect
8. C73×#2065C2semidirect
9. C73×#2054C2semidirect
10. C73×#2054C2semidirect
11. C73×#1982C2semidirect
12. C73×#1949C2semidirect
13. C73×#1895C2semidirect
14. C73×#1893C2semidirect
15. C73×#1804C2semidirect
96. #121×C73D4semidirect
130. C4⋊C8×C73D4semidirect
388. #24762C73direct (N × H)
400. C2×#469C2×C73semidirect
401. C2×#466C2×C73semidirect
402. C2×#459C2×C73semidirect
403. C2×#424C2×C73semidirect
404. #2619C2×C73semidirect
405. #2324C2×C73semidirect
406. #2067C2×C73semidirect
407. #2065C2×C73semidirect
408. #2054C2×C73semidirect
409. #2054C2×C73semidirect
410. #1982C2×C73semidirect
411. #1949C2×C73semidirect
412. #1895C2×C73semidirect
413. #1893C2×C73semidirect
414. #1804C2×C73semidirect
415. C73#24762direct (N × H)
496. #121D4×C73semidirect
530. 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×#466×C732
C2×#459×C732
C2×#424×C732
C73×#26192
C73×#23242
C73×#20672
C73×#20652
C73×#20542
C73×#19822
C73×#19492
C73×#18952
C73×#18932
C73×#18042
#2476273