Finite Group Databasebeta

← C73×#24404 #32933808

Subgroups — C73×#24404 #32933808

Order 18688.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C73C211yesmaximal, characteristic, complemented
3C22×#99×C73C211yesmaximal, characteristic, complemented
4C73×#2410C212yesmaximal, complemented
5C73×#2403C211yesmaximal, characteristic, complemented
6C73×#2044C212yesmaximal, complemented
7C73×#2021C212yesmaximal, complemented
8C73×#1898C212yesmaximal, complemented
9C73×#1889C211yesmaximal, characteristic, complemented
10C73×#1867C211yesmaximal, characteristic, complemented
11C73×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C73C2211yescharacteristic
13C23×D4×C73C2211yescharacteristic
14C23×D4×C73C2211yescharacteristic, complemented
15#546×C73—22no—
16#546×C73—22no—
17D42×C73—22no—
18D42×C73—22no—
19#535×C73—21no—
20#534×C73—21no—
21#534×C73C2212yes—
22#525×C73—21no—
23C2×#121×C73—22no—
24C2×#120×C73—21no—
25C2×#120×C73—21no—
26C2×#120×C73C2211yescharacteristic
27C2×#120×C73C2212yes—
28C2×#120×C73C2212yescomplemented
29C2×#120×C73C2211yescharacteristic, complemented
30#518×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2212yescomplemented
32B(4,𝔽2)×C73—24no—
33C2×#99×C73—24no—
34C2×#99×C73C2211yescharacteristic
35C2×#99×C73C2211yescharacteristic
36C2×#99×C73C2212yescomplemented
37C2×#99×C73C2212yescomplemented
38C2×#99×C73C2212yescomplemented
39#394×C73—22no—
40#392×C73—21no—
41#392×C73—21no—
42#392×C73—22no—
43#386×C73—21no—
44#386×C73—22no—
45#386×C73C2211yescharacteristic
46#386×C73C2211yescharacteristic, complemented
47#386×C73C2212yescomplemented
48#385×C73C2212yescomplemented
49#379×C73C2212yescomplemented
50#379×C73C2211yescharacteristic, complemented
51#342×C73C2212yescomplemented
52#342×C73C2212yescomplemented
53C25×C73D411yescharacteristic, complemented
54C25×C73C2311yescharacteristic
55C25×C73C2311yescharacteristic
56H(5,𝔽2)×C73—22no—
57H(5,𝔽2)×C73—22no—
58H(5,𝔽2)×C73—42no—
59C2×#41×C73—21no—
60C2×#41×C73—22no—
61C22×D4×C73—21no—
62C22×D4×C73—22no—
63C22×D4×C73—21no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—22no—
70C22×D4×C73—22no—
71C22×D4×C73—21no—
72C22×D4×C73—22no—
73C22×D4×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73—22no—
76C22×D4×C73—44no—
77C22×D4×C73—42no—
78C22×D4×C73D411yescharacteristic, complemented
79C22×D4×C73D411yescharacteristic, complemented
80C22×D4×C73D412yescomplemented
81C22×D4×C73D412yescomplemented
82C22×D4×C73C2312yes—
83C22×D4×C73C2311yescharacteristic
84C22×D4×C73C2311yescharacteristic
85C23×C4×C73—22no—
86C23×C4×C73D411yescharacteristic, complemented
87C23×C4×C73C2311yescharacteristic
88#127×C73—22no—
89#124×C73—22no—
90#123×C73—22no—
91#123×C73—22no—
92#123×C73—22no—
93C22⋊Q8×C73—21no—
94C22⋊Q8×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—48no—
104#120×C73—22no—
105#120×C73—22no—
106#120×C73—22no—
107#120×C73—22no—
108#120×C73—22no—
109#120×C73—22no—
110#120×C73—22no—
111#120×C73—22no—
112#120×C73—22no—
113#120×C73—22no—
114#120×C73—22no—
115#120×C73—24no—
116#120×C73—42no—
117#120×C73—42no—
118#120×C73—44no—
119C4×D4×C73—22no—
120C4×D4×C73—22no—
121C4×D4×C73—22no—
122C4×D4×C73—22no—
123#117×C73—21no—
124C2×C4⋊C4×C73—22no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—24no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—22no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—21no—
137C2×C22⋊C4×C73—22no—
138C2×C22⋊C4×C73—21no—
139C2×C22⋊C4×C73—22no—
140C2×C22⋊C4×C73—42no—
141C2×C22⋊C4×C73D412yescomplemented
142C2×C22⋊C4×C73D412yescomplemented
143C2×C22⋊C4×C73C2311yescharacteristic
144C2×C22⋊C4×C73C2312yes—
145C2×C22⋊C4×C73C2311yescharacteristic
146C2×C22⋊C4×C73C2312yes—
147C2×C22⋊C4×C73C2312yes—
148#99×C73—22no—
149#99×C73—24no—
150#99×C73—24no—
151#99×C73—42no—
152#99×C73D414yescomplemented
153#95×C73—22no—
154#95×C73—21no—
155#95×C73—21no—
156#95×C73—22no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—22no—
160C24×C73—21no—
161C24×C73—22no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73—21no—
165C24×C73—22no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73—22no—
169C24×C73—41no—
170C24×C73—42no—
171C24×C73—42no—
172C24×C73—42no—
173C24×C73—81no—
174C24×C73—81no—
175C24×C73—81no—
176C24×C73C2×D411yescharacteristic
177C24×C73C2×D412yes—
178C24×C73C2×D411yescharacteristic
179C24×C73C2×D412yes—
180C24×C73C2×D412yes—
181C24×C73C2×D411yescharacteristic
182C24×C73C2×D411yescharacteristic
183C24×C73C2411yescharacteristic
184#41×C73—44no—
185#41×C73—44no—
186#41×C73—42no—
187#41×C73—42no—
188C2×Q8×C73—21no—
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—24no—
193C2×D4×C73—21no—
194C2×D4×C73—28no—
195C2×D4×C73—22no—
196C2×D4×C73—22no—
197C2×D4×C73—22no—
198C2×D4×C73—22no—
199C2×D4×C73—22no—
200C2×D4×C73—21no—
201C2×D4×C73—22no—
202C2×D4×C73—22no—
203C2×D4×C73—22no—
204C2×D4×C73—22no—
205C2×D4×C73—21no—
206C2×D4×C73—22no—
207C2×D4×C73—22no—
208C2×D4×C73—22no—
209C2×D4×C73—22no—
210C2×D4×C73—22no—
211C2×D4×C73—22no—
212C2×D4×C73—22no—
213C2×D4×C73—22no—
214C2×D4×C73—22no—
215C2×D4×C73—41no—
216C2×D4×C73—41no—
217C2×D4×C73—42no—
218C2×D4×C73—44no—
219C2×D4×C73—44no—
220C2×D4×C73—44no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
226C2×D4×C73—44no—
227C2×D4×C73—42no—
228C2×D4×C73—42no—
229C2×D4×C73—44no—
230C2×D4×C73—42no—
231C2×D4×C73—41no—
232C2×D4×C73—42no—
233C2×D4×C73—41no—
234C2×D4×C73—42no—
235C2×D4×C73—44no—
236C2×D4×C73—42no—
237C2×D4×C73—42no—
238C2×D4×C73—42no—
239C2×D4×C73—44no—
240C2×D4×C73—42no—
241C2×D4×C73—82no—
242C2×D4×C73—82no—
243C2×D4×C73—81no—
244C2×D4×C73—81no—
245C2×D4×C73—82no—
246C2×D4×C73—82no—
247C2×D4×C73C2×D412yes—
248C2×D4×C73#4112yes—
249C22×C4×C73—21no—
250C22×C4×C73—22no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—22no—
255C22×C4×C73—22no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—22no—
259C22×C4×C73—22no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—42no—
263C22×C4×C73—41no—
264C22×C4×C73—44no—
265C22×C4×C73—44no—
266C22×C4×C73—82no—
267C22×C4×C73C2×D412yes—
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2×D412yes—
271C22×C4×C73C2×D412yes—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—22no—
275C4⋊C4×C73—22no—
276C4⋊C4×C73—44no—
277C22⋊C4×C73—22no—
278C22⋊C4×C73—22no—
279C22⋊C4×C73—22no—
280C22⋊C4×C73—22no—
281C22⋊C4×C73—22no—
282C22⋊C4×C73—22no—
283C22⋊C4×C73—22no—
284C22⋊C4×C73—22no—
285C22⋊C4×C73—22no—
286C22⋊C4×C73—22no—
287C22⋊C4×C73—22no—
288C22⋊C4×C73—22no—
289C22⋊C4×C73—22no—
290C22⋊C4×C73—21no—
291C22⋊C4×C73—21no—
292C22⋊C4×C73—22no—
293C22⋊C4×C73—22no—
294C22⋊C4×C73—44no—
295C22⋊C4×C73—44no—
296C22⋊C4×C73—42no—
297C22⋊C4×C73—42no—
298C22⋊C4×C73—42no—
299C22⋊C4×C73—44no—
300C22⋊C4×C73—42no—
301C22⋊C4×C73—44no—
302C22⋊C4×C73—42no—
303C22⋊C4×C73—82no—
304C22⋊C4×C73—81no—
305C22⋊C4×C73C2×D414yescomplemented
306C42×C73—22no—
307C23×C73—21no—
308C23×C73—21no—
309C23×C73—21no—
310C23×C73—22no—
311C23×C73—22no—
312C23×C73—22no—
313C23×C73—24no—
314C23×C73—21no—
315C23×C73—21no—
316C23×C73—21no—
317C23×C73—22no—
318C23×C73—22no—
319C23×C73—24no—
320C23×C73—22no—
321C23×C73—21no—
322C23×C73—22no—
323C23×C73—21no—
324C23×C73—21no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—41no—
328C23×C73—42no—
329C23×C73—41no—
330C23×C73—41no—
331C23×C73—41no—
332C23×C73—42no—
333C23×C73—41no—
334C23×C73—42no—
335C23×C73—42no—
336C23×C73—42no—
337C23×C73—41no—
338C23×C73—41no—
339C23×C73—41no—
340C23×C73—41no—
341C23×C73—42no—
342C23×C73—42no—
343C23×C73—41no—
344C23×C73—42no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—42no—
348C23×C73—42no—
349C23×C73—42no—
350C23×C73—42no—
351C23×C73—41no—
352C23×C73—41no—
353C23×C73—41no—
354C23×C73—42no—
355C23×C73—42no—
356C23×C73—42no—
357C23×C73—81no—
358C23×C73—81no—
359C23×C73—82no—
360C23×C73—82no—
361C23×C73—82no—
362C23×C73—82no—
363C23×C73—84no—
364C23×C73—84no—
365C23×C73—81no—
366C23×C73—81no—
367C23×C73—84no—
368C23×C73—84no—
369C23×C73#12011yescharacteristic
370C23×C73#12012yes—
371C23×C73#12011yescharacteristic
372C23×C73#12112yescomplemented
373C23×C73C22×D411yescharacteristic
374C23×C73C22×D412yes—
375C23×C73C22×D411yescharacteristic
376C23×C73C2×#4111yescharacteristic
377C23×C73H(5,𝔽2)12yes—
378Q8×C73—42no—
379D4×C73—24no—
380D4×C73—24no—
381D4×C73—44no—
382D4×C73—42no—
383D4×C73—44no—
384D4×C73—48no—
385D4×C73—44no—
386D4×C73—44no—
387D4×C73—44no—
388D4×C73—42no—
389D4×C73—42no—
390D4×C73—42no—
391D4×C73—42no—
392D4×C73—42no—
393D4×C73—42no—
394D4×C73—44no—
395D4×C73—44no—
396D4×C73—82no—
397D4×C73—82no—
398D4×C73—82no—
399D4×C73—82no—
400D4×C73—88no—
401D4×C73—84no—
402D4×C73—84no—
403C2×C4×C73—21no—
404C2×C4×C73—21no—
405C2×C4×C73—22no—
406C2×C4×C73—24no—
407C2×C4×C73—22no—
408C2×C4×C73—22no—
409C2×C4×C73—22no—
410C2×C4×C73—21no—
411C2×C4×C73—21no—
412C2×C4×C73—21no—
413C2×C4×C73—24no—
414C2×C4×C73—22no—
415C2×C4×C73—22no—
416C2×C4×C73—42no—
417C2×C4×C73—42no—
418C2×C4×C73—44no—
419C2×C4×C73—42no—
420C2×C4×C73—42no—
421C2×C4×C73—41no—
422C2×C4×C73—42no—
423C2×C4×C73—42no—
424C2×C4×C73—41no—
425C2×C4×C73—42no—
426C2×C4×C73—42no—
427C2×C4×C73—42no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73—42no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73—41no—
435C2×C4×C73—42no—
436C2×C4×C73—81no—
437C2×C4×C73—81no—
438C2×C4×C73—88no—
439C2×C4×C73#12112yescomplemented
440C22×C73—21no—
441C22×C73—22no—
442C22×C73—21no—
443C22×C73—22no—
444C22×C73—21no—
445C22×C73—21no—
446C22×C73—21no—
447C22×C73—22no—
448C22×C73—22no—
449C22×C73—22no—
450C22×C73—21no—
451C22×C73—21no—
452C22×C73—22no—
453C22×C73—41no—
454C22×C73—41no—
455C22×C73—42no—
456C22×C73—44no—
457C22×C73—44no—
458C22×C73—42no—
459C22×C73—42no—
460C22×C73—42no—
461C22×C73—44no—
462C22×C73—42no—
463C22×C73—42no—
464C22×C73—42no—
465C22×C73—44no—
466C22×C73—41no—
467C22×C73—41no—
468C22×C73—42no—
469C22×C73—41no—
470C22×C73—42no—
471C22×C73—42no—
472C22×C73—41no—
473C22×C73—42no—
474C22×C73—41no—
475C22×C73—82no—
476C22×C73—81no—
477C22×C73—81no—
478C22×C73—81no—
479C22×C73—82no—
480C22×C73—84no—
481C22×C73—82no—
482C22×C73—82no—
483C22×C73—81no—
484C22×C73—82no—
485C22×C73—81no—
486C22×C73—81no—
487C22×C73—82no—
488C22×C73—84no—
489C22×C73—81no—
490C22×C73—81no—
491C22×C73—162no—
492C22×C73B(4,𝔽2)12yescomplemented
493C22×C73C2×#12011yescharacteristic
494C22×C73C2×#12111yescharacteristic
495C22×C73#53411yescharacteristic
496C22×C73D4212yes—
497C22×C73#54612yes—
498C4×C73—22no—
499C4×C73—44no—
500C4×C73—41no—
501C4×C73—42no—
502C4×C73—42no—
503C4×C73—42no—
504C4×C73—42no—
505C4×C73—82no—
506C4×C73—81no—
507C4×C73—81no—
508#24404C7311yesmaximal, characteristic, direct product factor, Sylow
509C2×C73—22no—
510C2×C73—21no—
511C2×C73—21no—
512C2×C73—22no—
513C2×C73—22no—
514C2×C73—42no—
515C2×C73—41no—
516C2×C73—42no—
517C2×C73—82no—
518C2×C73—81no—
519C2×C73—82no—
520C2×C73#241011yescharacteristic
521C2×C73C2×B(4,𝔽2)11yescharacteristic
522C2×C73#302611yescharacteristic
523#3484C2×C7311yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C7311yescharacteristic, complemented
525C22×#99C2×C7311yescharacteristic, complemented
526#2410C2×C7312yescomplemented
527#2403C2×C7311yescharacteristic, complemented
528#2044C2×C7312yescomplemented
529#2021C2×C7312yescomplemented
530#1898C2×C7312yescomplemented
531#1889C2×C7311yescharacteristic, complemented
532#1867C2×C7311yescharacteristic, complemented
533#1790C2×C7311yescharacteristic, complemented
534C73#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C7311yescharacteristic
536C23×D4C22×C7311yescharacteristic
537C23×D4C22×C7311yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C7312yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C7311yescharacteristic
550C2×#120C22×C7312yes—
551C2×#120C22×C7312yescomplemented
552C2×#120C22×C7311yescharacteristic, complemented
553#518C22×C7311yescharacteristic
554C22×C22⋊C4C22×C7312yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C7311yescharacteristic
558C2×#99C22×C7311yescharacteristic
559C2×#99C22×C7312yescomplemented
560C2×#99C22×C7312yescomplemented
561C2×#99C22×C7312yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C7311yescharacteristic
569#386C22×C7311yescharacteristic, complemented
570#386C22×C7312yescomplemented
571#385C22×C7312yescomplemented
572#379C22×C7312yescomplemented
573#379C22×C7311yescharacteristic, complemented
574#342C22×C7312yescomplemented
575#342C22×C7312yescomplemented
576C25D4×C7311yescharacteristic, complemented
577C25C23×C7311yescharacteristic
578C25C23×C7311yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C7311yescharacteristic, complemented
602C22×D4D4×C7311yescharacteristic, complemented
603C22×D4D4×C7312yescomplemented
604C22×D4D4×C7312yescomplemented
605C22×D4C23×C7312yes—
606C22×D4C23×C7311yescharacteristic
607C22×D4C23×C7311yescharacteristic
608C23×C4—22no—
609C23×C4D4×C7311yescharacteristic, complemented
610C23×C4C23×C7311yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C7312yescomplemented
665C2×C22⋊C4D4×C7312yescomplemented
666C2×C22⋊C4C23×C7312yes—
667C2×C22⋊C4C23×C7311yescharacteristic
668C2×C22⋊C4C23×C7311yescharacteristic
669C2×C22⋊C4C23×C7312yes—
670C2×C22⋊C4C23×C7312yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C7314yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C7311yescharacteristic
700C24C2×D4×C7312yes—
701C24C2×D4×C7311yescharacteristic
702C24C2×D4×C7312yes—
703C24C2×D4×C7312yes—
704C24C2×D4×C7311yescharacteristic
705C24C2×D4×C7311yescharacteristic
706C24C24×C7311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C7312yes—
771C2×D4#41×C7312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C7312yes—
791C22×C4C2×D4×C7311yescharacteristic
792C22×C4C2×D4×C7311yescharacteristic
793C22×C4C2×D4×C7312yes—
794C22×C4C2×D4×C7312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C7314yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C7311yescharacteristic
893C23#120×C7312yes—
894C23#120×C7311yescharacteristic
895C23#121×C7312yescomplemented
896C23C22×D4×C7311yescharacteristic
897C23C22×D4×C7312yes—
898C23C22×D4×C7311yescharacteristic
899C23C2×#41×C7311yescharacteristic
900C23H(5,𝔽2)×C7312yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C7312yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C7312yescomplemented
1016C22C2×#120×C7311yescharacteristic
1017C22C2×#121×C7311yescharacteristic
1018C22#534×C7311yescharacteristic
1019C22D42×C7312yes—
1020C22#546×C7312yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C73×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C7311yescharacteristic
1044C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C25×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3484C2semidirect
2. C2×B(4,𝔽2)×C73C2semidirect
3. C22×#99×C73C2semidirect
4. C73×#2410C2semidirect
5. C73×#2403C2semidirect
6. C73×#2044C2semidirect
7. C73×#2021C2semidirect
8. C73×#1898C2semidirect
9. C73×#1889C2semidirect
10. C73×#1867C2semidirect
11. C73×#1790C2semidirect
14. C23×D4×C73C22semidirect
28. C2×#120×C73C22semidirect
29. C2×#120×C73C22semidirect
31. C22×C22⋊C4×C73C22semidirect
36. C2×#99×C73C22semidirect
37. C2×#99×C73C22semidirect
38. C2×#99×C73C22semidirect
46. #386×C73C22semidirect
47. #386×C73C22semidirect
48. #385×C73C22semidirect
49. #379×C73C22semidirect
50. #379×C73C22semidirect
51. #342×C73C22semidirect
52. #342×C73C22semidirect
53. C25×C73D4semidirect
78. C22×D4×C73D4semidirect
79. C22×D4×C73D4semidirect
80. C22×D4×C73D4semidirect
81. C22×D4×C73D4semidirect
86. C23×C4×C73D4semidirect
141. C2×C22⋊C4×C73D4semidirect
142. C2×C22⋊C4×C73D4semidirect
152. #99×C73D4semidirect
305. C22⋊C4×C73C2×D4semidirect
372. C23×C73#121semidirect
439. C2×C4×C73#121semidirect
492. C22×C73B(4,𝔽2)semidirect
508. #24404C73direct (N × H)
523. #3484C2×C73semidirect
524. C2×B(4,𝔽2)C2×C73semidirect
525. C22×#99C2×C73semidirect
526. #2410C2×C73semidirect
527. #2403C2×C73semidirect
528. #2044C2×C73semidirect
529. #2021C2×C73semidirect
530. #1898C2×C73semidirect
531. #1889C2×C73semidirect
532. #1867C2×C73semidirect
533. #1790C2×C73semidirect
534. C73#24404direct (N × H)
537. C23×D4C22×C73semidirect
551. C2×#120C22×C73semidirect
552. C2×#120C22×C73semidirect
554. C22×C22⋊C4C22×C73semidirect
559. C2×#99C22×C73semidirect
560. C2×#99C22×C73semidirect
561. C2×#99C22×C73semidirect
569. #386C22×C73semidirect
570. #386C22×C73semidirect
571. #385C22×C73semidirect
572. #379C22×C73semidirect
573. #379C22×C73semidirect
574. #342C22×C73semidirect
575. #342C22×C73semidirect
576. C25D4×C73semidirect
601. C22×D4D4×C73semidirect
602. C22×D4D4×C73semidirect
603. C22×D4D4×C73semidirect
604. C22×D4D4×C73semidirect
609. C23×C4D4×C73semidirect
664. C2×C22⋊C4D4×C73semidirect
665. C2×C22⋊C4D4×C73semidirect
675. #99D4×C73semidirect
828. C22⋊C4C2×D4×C73semidirect
895. C23#121×C73semidirect
962. C2×C4#121×C73semidirect
1015. C22B(4,𝔽2)×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34842
C2×B(4,𝔽2)×C732
C22×#99×C732
C73×#24102
C73×#24032
C73×#20442
C73×#20212
C73×#18982
C73×#18892
C73×#18672
C73×#17902
#2440473