Finite Group Databasebeta

← C73×#24034 #32933438

Subgroups — C73×#24034 #32933438

Order 18688.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C73C211yesmaximal, characteristic
2C2×#482×C73C211yesmaximal, characteristic, complemented
3C2×#416×C73C211yesmaximal, characteristic, complemented
4C73×#2485C211yesmaximal, characteristic, complemented
5C73×#2041C211yesmaximal, characteristic, complemented
6C73×#2041C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1893C211yesmaximal, characteristic, complemented
10C73×#1869C211yesmaximal, characteristic, complemented
11C73×#1865C211yesmaximal, characteristic, complemented
12C73×#1863C211yesmaximal, characteristic, complemented
13C73×#1788C211yesmaximal, characteristic, complemented
14C73×#1788C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19#550×C73—24no—
20#550×C73—24no—
21C2×#127×C73—21no—
22C2×#127×C73C2211yescharacteristic
23C2×#121×C73—21no—
24C2×#121×C73—21no—
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×C4×Q8×C73C2211yescharacteristic
28C2×C4×D4×C73—21no—
29C2×C4×D4×C73C2211yescharacteristic
30C2×#117×C73C2211yescharacteristic
31#482×C73—24no—
32C2×#107×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34#416×C73—24no—
35C2×#103×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
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C22⋊C8×C73C2211yescharacteristic
50#397×C73—21no—
51#394×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#388×C73—21no—
55#387×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—22no—
70C2×#41×C73—41no—
71C2×#41×C73—41no—
72C2×#41×C73—41no—
73C2×#41×C73—41no—
74C2×#41×C73D414yes—
75C22×Q8×C73C2311yescharacteristic
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73—21no—
81C22×D4×C73—21no—
82C22×D4×C73D411yescharacteristic
83C22×D4×C73C2311yescharacteristic
84C22×D4×C73C2311yescharacteristic
85C23×C4×C73—21no—
86C23×C4×C73—21no—
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C22×C8×C73—22no—
90C22×C8×C73—41no—
91C22×C8×C73—41no—
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96#127×C73—28no—
97#127×C73—22no—
98#127×C73—22no—
99#121×C73—28no—
100#121×C73—28no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—22no—
104#121×C73D414yes—
105C4×Q8×C73—22no—
106C4×Q8×C73—22no—
107C4×D4×C73—28no—
108C4×D4×C73—22no—
109C4×D4×C73—22no—
110#117×C73—22no—
111#117×C73—22no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73D411yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—22no—
134#103×C73—22no—
135#103×C73—22no—
136#103×C73—22no—
137#103×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—41no—
143#102×C73—41no—
144#102×C73—41no—
145#102×C73—41no—
146C22⋊C8×C73—22no—
147C22⋊C8×C73—41no—
148C22⋊C8×C73—41no—
149#95×C73—21no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D411yescharacteristic
158#41×C73—28no—
159#41×C73—44no—
160#41×C73—44no—
161#41×C73—44no—
162#41×C73—44no—
163#41×C73—44no—
164#41×C73—44no—
165#41×C73—44no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73C2×D412yes—
170C2×Q8×C73#4112yes—
171C2×Q8×C73#4112yes—
172C2×D4×C73—24no—
173C2×D4×C73—24no—
174C2×D4×C73—22no—
175C2×D4×C73—24no—
176C2×D4×C73—24no—
177C2×D4×C73—24no—
178C2×D4×C73—24no—
179C2×D4×C73—22no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—41no—
191C2×D4×C73—42no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—42no—
197C2×D4×C73—81no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73—81no—
201C2×D4×C73—81no—
202C2×D4×C73—81no—
203C2×D4×C73C2×D412yes—
204C2×D4×C73C2×D412yes—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—24no—
211C22×C4×C73—21no—
212C22×C4×C73—24no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73—42no—
226C22×C4×C73—42no—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D412yes—
231C22×C4×C73C2×D412yes—
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2411yescharacteristic
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—44no—
247C4⋊C4×C73—24no—
248C4⋊C4×C73—22no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73—21no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—21no—
258C4⋊C4×C73—42no—
259C4⋊C4×C73—81no—
260C4⋊C4×C73C2×D412yes—
261C22⋊C4×C73—24no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—24no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—42no—
266C22⋊C4×C73—42no—
267C22⋊C4×C73—81no—
268C22⋊C4×C73—81no—
269C42×C73—24no—
270C42×C73—21no—
271C42×C73—21no—
272C42×C73—42no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73#12012yes—
301C23×C73C22×D411yescharacteristic
302Q8×C73—22no—
303Q8×C73—22no—
304Q8×C73—22no—
305Q8×C73#12314yes—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—22no—
309D4×C73—22no—
310D4×C73—44no—
311D4×C73—48no—
312D4×C73—48no—
313D4×C73—48no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—84no—
319D4×C73—84no—
320D4×C73—84no—
321C2×C4×C73—21no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—21no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—21no—
333C2×C4×C73—22no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—48no—
340C2×C4×C73—48no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73#12012yes—
360C2×C4×C73#13512yes—
361C2×C4×C73C22×D411yescharacteristic
362C2×C4×C73C22×D411yescharacteristic
363C2×C4×C73C2×#4111yescharacteristic
364C2×C4×C73C2×#4111yescharacteristic
365C2×C4×C73H(5,𝔽2)11yescharacteristic
366C2×C4×C73H(5,𝔽2)11yescharacteristic
367C8×C73—41no—
368C8×C73—41no—
369C8×C73—41no—
370C8×C73—41no—
371C22×C73—22no—
372C22×C73—22no—
373C22×C73—22no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—41no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—42no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—42no—
384C22×C73—41no—
385C22×C73—42no—
386C22×C73—42no—
387C22×C73—41no—
388C22×C73—41no—
389C22×C73—41no—
390C22×C73—41no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73—81no—
397C22×C73—81no—
398C22×C73—81no—
399C22×C73C2×#12011yescharacteristic
400C22×C73#54611yescharacteristic
401C22×C73#54611yescharacteristic
402C22×C73C2×#13511yescharacteristic
403C22×C73#57511yescharacteristic
404C22×C73#57611yescharacteristic
405C22×C73#57711yescharacteristic
406C4×C73—22no—
407C4×C73—24no—
408C4×C73—22no—
409C4×C73—41no—
410C4×C73—41no—
411C4×C73—42no—
412C4×C73—81no—
413C4×C73—81no—
414C4×C73—81no—
415C4×C73—81no—
416C4×C73C2×#12311yescharacteristic
417C4×C73#53411yescharacteristic
418C4×C73#54611yescharacteristic
419C4×C73#54611yescharacteristic
420#24034C7311yesmaximal, characteristic, direct product factor, Sylow
421C2×C73—42no—
422C2×C73—81no—
423C2×C73—82no—
424C2×C73—82no—
425C2×C73#240511yescharacteristic
426C2×C73#300211yescharacteristic
427C2×C73#301211yescharacteristic
428C2×C73#330411yescharacteristic
429C2×C73#330511yescharacteristic
430C2×C73#330911yescharacteristic
431C2×C73#331711yescharacteristic
432C2×#550C2×C7311yescharacteristic
433C2×#482C2×C7311yescharacteristic, complemented
434C2×#416C2×C7311yescharacteristic, complemented
435#2485C2×C7311yescharacteristic, complemented
436#2041C2×C7311yescharacteristic, complemented
437#2041C2×C7311yescharacteristic, complemented
438#2034C2×C7311yescharacteristic, complemented
439#2033C2×C7311yescharacteristic, complemented
440#1893C2×C7311yescharacteristic, complemented
441#1869C2×C7311yescharacteristic, complemented
442#1865C2×C7311yescharacteristic, complemented
443#1863C2×C7311yescharacteristic, complemented
444#1788C2×C7311yescharacteristic, complemented
445#1788C2×C7311yescharacteristic, complemented
446#1788C2×C7311yescharacteristic, complemented
447C73#2403411yescharacteristic, direct product factor, Sylow
448C22×#41C22×C7311yescharacteristic
449C22×#41C22×C7311yescharacteristic
450C23×C8C22×C7311yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C7311yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C7311yescharacteristic
458C2×#121C22×C7311yescharacteristic
459C2×C4×Q8C22×C7311yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C7311yescharacteristic
462C2×#117C22×C7311yescharacteristic
463#482—24no—
464C2×#107C22×C7311yescharacteristic
465C2×#106C22×C7311yescharacteristic
466#416—24no—
467C2×#103C22×C7311yescharacteristic
468C2×#103C22×C7311yescharacteristic
469C2×#103C22×C7311yescharacteristic
470C2×#103C22×C7311yescharacteristic
471C2×#102C22×C7311yescharacteristic
472C2×#102C22×C7311yescharacteristic
473C2×#102C22×C7311yescharacteristic
474C2×#102C22×C7311yescharacteristic
475C2×#102C22×C7311yescharacteristic
476C2×#102C22×C7311yescharacteristic
477C2×#102C22×C7311yescharacteristic
478C2×#102C22×C7311yescharacteristic
479C2×C22⋊C8C22×C7311yescharacteristic
480C2×C22⋊C8C22×C7311yescharacteristic
481C2×C22⋊C8C22×C7311yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C7311yescharacteristic
485#389C22×C7311yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C7311yescharacteristic
489#380C22×C7311yescharacteristic
490#380C22×C7311yescharacteristic
491#340C22×C7311yescharacteristic
492#340C22×C7311yescharacteristic
493#336C22×C7311yescharacteristic
494#336C22×C7311yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C7314yes—
507C22×Q8C23×C7311yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C7311yescharacteristic
515C22×D4C23×C7311yescharacteristic
516C22×D4C23×C7311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C7311yescharacteristic
520C23×C4C23×C7311yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C7311yescharacteristic
525C22×C8C23×C7311yescharacteristic
526C22×C8C23×C7311yescharacteristic
527C22×C8C23×C7311yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C7314yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C7311yescharacteristic
548C2×C4⋊C4C23×C7311yescharacteristic
549C2×C4⋊C4C23×C7311yescharacteristic
550C2×C4⋊C4C23×C7311yescharacteristic
551C2×C4⋊C4C23×C7311yescharacteristic
552C2×C4⋊C4C23×C7311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C7311yescharacteristic
560C2×C22⋊C4D4×C7311yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C7311yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C7311yescharacteristic
589C24C2×D4×C7311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C7312yes—
602C2×Q8#41×C7312yes—
603C2×Q8#41×C7312yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C7312yes—
636C2×D4C2×D4×C7312yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C7311yescharacteristic
660C22×C4C2×D4×C7311yescharacteristic
661C22×C4C2×D4×C7311yescharacteristic
662C22×C4C2×D4×C7312yes—
663C22×C4C2×D4×C7312yes—
664C22×C4C2×D4×C7311yescharacteristic
665C22×C4C24×C7311yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C7312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C7312yes—
733C23C22×D4×C7311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C7314yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#120×C7312yes—
792C2×C4#135×C7312yes—
793C2×C4C22×D4×C7311yescharacteristic
794C2×C4C22×D4×C7311yescharacteristic
795C2×C4C2×#41×C7311yescharacteristic
796C2×C4C2×#41×C7311yescharacteristic
797C2×C4H(5,𝔽2)×C7311yescharacteristic
798C2×C4H(5,𝔽2)×C7311yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C7311yescharacteristic
832C22#546×C7311yescharacteristic
833C22#546×C7311yescharacteristic
834C22C2×#135×C7311yescharacteristic
835C22#575×C7311yescharacteristic
836C22#576×C7311yescharacteristic
837C22#577×C7311yescharacteristic
838C4—22no—
839C4—22no—
840C4—24no—
841C4—41no—
842C4—42no—
843C4—41no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C7311yescharacteristic
849C4#534×C7311yescharacteristic
850C4#546×C7311yescharacteristic
851C4#546×C7311yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2C73×#240511yescharacteristic
857C2C73×#300211yescharacteristic
858C2C73×#301211yescharacteristic
859C2C73×#330411yescharacteristic
860C2C73×#330511yescharacteristic
861C2C73×#330911yescharacteristic
862C2C73×#331711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#550×C73C2
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
2. C2×#482×C73C2semidirect
3. C2×#416×C73C2semidirect
4. C73×#2485C2semidirect
5. C73×#2041C2semidirect
6. C73×#2041C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1893C2semidirect
10. C73×#1869C2semidirect
11. C73×#1865C2semidirect
12. C73×#1863C2semidirect
13. C73×#1788C2semidirect
14. C73×#1788C2semidirect
15. C73×#1788C2semidirect
420. #24034C73direct (N × H)
433. C2×#482C2×C73semidirect
434. C2×#416C2×C73semidirect
435. #2485C2×C73semidirect
436. #2041C2×C73semidirect
437. #2041C2×C73semidirect
438. #2034C2×C73semidirect
439. #2033C2×C73semidirect
440. #1893C2×C73semidirect
441. #1869C2×C73semidirect
442. #1865C2×C73semidirect
443. #1863C2×C73semidirect
444. #1788C2×C73semidirect
445. #1788C2×C73semidirect
446. #1788C2×C73semidirect
447. C73#24034direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C732
C2×#482×C732
C2×#416×C732
C73×#24852
C73×#20412
C73×#20342
C73×#20332
C73×#18932
C73×#18692
C73×#18652
C73×#18632
C73×#17882
#2403473