Finite Group Databasebeta

← C73×#24397 #32933801

Subgroups — C73×#24397 #32933801

Order 18688.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C73C211yesmaximal, characteristic, complemented
2C2×#469×C73C211yesmaximal, characteristic, complemented
3C2×#465×C73C211yesmaximal, characteristic, complemented
4C2×#449×C73C211yesmaximal, characteristic, complemented
5C2×#408×C73C211yesmaximal, characteristic, complemented
6C73×#2615C211yesmaximal, characteristic, complemented
7C73×#2035C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2000C211yesmaximal, characteristic, complemented
10C73×#1999C211yesmaximal, characteristic, complemented
11C73×#1894C211yesmaximal, characteristic, complemented
12C73×#1893C211yesmaximal, characteristic, complemented
13C73×#1874C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21C23×C8×C73C2211yescharacteristic
22#537×C73—24no—
23#537×C73—24no—
24C2×C22⋊Q8×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×#121×C73—21no—
28C2×#121×C73—21no—
29C2×#121×C73—21no—
30C2×#121×C73C2211yescharacteristic
31C2×#121×C73C2211yescharacteristic
32C2×#121×C73C2211yescharacteristic
33C2×#121×C73C2211yescharacteristic
34C2×#121×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36#469×C73—24no—
37#465×C73—24no—
38#449×C73—24no—
39C2×#106×C73C2211yescharacteristic
40C2×#106×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#103×C73C2211yescharacteristic
43C2×#103×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×#102×C73C2211yescharacteristic
48C2×#102×C73C2211yescharacteristic
49#408×C73—24no—
50C2×C22⋊C8×C73C2211yescharacteristic
51C2×C22⋊C8×C73C2211yescharacteristic
52C2×C22⋊C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54#393×C73—21no—
55#392×C73—21no—
56#392×C73—21no—
57#392×C73—21no—
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63#340×C73C2211yescharacteristic
64#340×C73C2211yescharacteristic
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—22no—
70C2×#41×C73—22no—
71C2×#41×C73—22no—
72C2×#41×C73—22no—
73C2×#41×C73—41no—
74C2×#41×C73—41no—
75C2×#41×C73—41no—
76C2×#41×C73—41no—
77C22×Q8×C73D411yescharacteristic
78C22×Q8×C73C2311yescharacteristic
79C22×D4×C73—21no—
80C22×D4×C73—21no—
81C22×D4×C73—21no—
82C22×D4×C73—21no—
83C22×D4×C73—21no—
84C22×D4×C73—21no—
85C22×D4×C73D411yescharacteristic
86C22×D4×C73D411yescharacteristic
87C22×D4×C73D411yescharacteristic
88C22×D4×C73C2311yescharacteristic
89C22×D4×C73C2311yescharacteristic
90C23×C4×C73—21no—
91C23×C4×C73—21no—
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C2×SD16×C73—22no—
96C2×SD16×C73—22no—
97C2×SD16×C73—41no—
98C2×D8×C73—22no—
99C2×D8×C73—22no—
100C2×D8×C73—41no—
101C2×M16×C73—22no—
102C2×M16×C73—22no—
103C2×M16×C73—41no—
104C22×C8×C73—22no—
105C22×C8×C73—22no—
106C22×C8×C73—41no—
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111C22⋊Q8×C73—28no—
112C22⋊Q8×C73—22no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73D414yescomplemented
116#121×C73—28no—
117#121×C73—28no—
118#121×C73—28no—
119#121×C73—22no—
120#121×C73—22no—
121#121×C73—22no—
122#121×C73—22no—
123#121×C73—22no—
124#121×C73—22no—
125#121×C73—22no—
126#121×C73—41no—
127#121×C73—41no—
128#121×C73D414yescomplemented
129C2×C4⋊C4×C73—21no—
130C2×C4⋊C4×C73—21no—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—22no—
133C2×C4⋊C4×C73—22no—
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140C2×C22⋊C4×C73—21no—
141C2×C22⋊C4×C73—21no—
142C2×C22⋊C4×C73—21no—
143C2×C22⋊C4×C73—21no—
144C2×C22⋊C4×C73—21no—
145C2×C22⋊C4×C73—21no—
146C2×C22⋊C4×C73—21no—
147C2×C22⋊C4×C73—21no—
148C2×C22⋊C4×C73—21no—
149#106×C73—22no—
150#106×C73—22no—
151#103×C73—22no—
152#103×C73—22no—
153#103×C73—41no—
154#102×C73—22no—
155#102×C73—22no—
156#102×C73—22no—
157#102×C73—22no—
158#102×C73—41no—
159C22⋊C8×C73—22no—
160C22⋊C8×C73—22no—
161C22⋊C8×C73—22no—
162C22⋊C8×C73D414yescomplemented
163#95×C73—21no—
164#95×C73—21no—
165#95×C73—21no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73C2×D411yescharacteristic
169C24×C73C2×D411yescharacteristic
170C24×C73C2×D411yescharacteristic
171#41×C73—44no—
172#41×C73—44no—
173#41×C73—44no—
174#41×C73—44no—
175#41×C73—44no—
176#41×C73—44no—
177#41×C73—44no—
178#41×C73—44no—
179C2×Q8×C73—22no—
180C2×Q8×C73—22no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—41no—
187C2×Q8×C73C2×D412yes—
188C2×D4×C73—24no—
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—24no—
194C2×D4×C73—24no—
195C2×D4×C73—22no—
196C2×D4×C73—22no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—41no—
209C2×D4×C73—41no—
210C2×D4×C73—41no—
211C2×D4×C73—42no—
212C2×D4×C73—42no—
213C2×D4×C73—42no—
214C2×D4×C73—42no—
215C2×D4×C73—42no—
216C2×D4×C73—81no—
217C2×D4×C73—81no—
218C2×D4×C73—81no—
219C2×D4×C73—81no—
220C2×D4×C73—81no—
221C2×D4×C73—81no—
222C2×D4×C73—81no—
223C2×D4×C73—81no—
224C2×D4×C73—81no—
225C2×D4×C73—81no—
226C2×D4×C73C2×D412yes—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—24no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—24no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—42no—
250C22×C4×C73—42no—
251C22×C4×C73—81no—
252C22×C4×C73—81no—
253C22×C4×C73C2×D411yescharacteristic
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D412yes—
259C22×C4×C73#4112yes—
260C22×C4×C73C2411yescharacteristic
261SD16×C73—44no—
262D8×C73—44no—
263M16×C73—44no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—21no—
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—21no—
272C2×C8×C73—21no—
273C2×C8×C73—21no—
274C2×C8×C73—44no—
275C2×C8×C73C2×D412yes—
276C2×C8×C73C2×D412yes—
277C4⋊C4×C73—24no—
278C4⋊C4×C73—24no—
279C4⋊C4×C73—24no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73—21no—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73—21no—
288C4⋊C4×C73C2×D412yes—
289C4⋊C4×C73C2×D412yes—
290C22⋊C4×C73—24no—
291C22⋊C4×C73—24no—
292C22⋊C4×C73—24no—
293C22⋊C4×C73—24no—
294C22⋊C4×C73—42no—
295C22⋊C4×C73—42no—
296C22⋊C4×C73—42no—
297C22⋊C4×C73—81no—
298C22⋊C4×C73—81no—
299C22⋊C4×C73—81no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—21no—
303C23×C73—21no—
304C23×C73—21no—
305C23×C73—21no—
306C23×C73—21no—
307C23×C73—21no—
308C23×C73—21no—
309C23×C73—21no—
310C23×C73—21no—
311C23×C73—21no—
312C23×C73—21no—
313C23×C73—22no—
314C23×C73—21no—
315C23×C73—21no—
316C23×C73—21no—
317C23×C73—21no—
318C23×C73—21no—
319C23×C73—21no—
320C23×C73—41no—
321C23×C73—41no—
322C23×C73—41no—
323C23×C73—41no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73—41no—
327C23×C73—41no—
328C23×C73—41no—
329C23×C73—41no—
330C23×C73—41no—
331C23×C73—41no—
332C23×C73—41no—
333C23×C73#12012yes—
334C23×C73#12112yes—
335C23×C73C22×D411yescharacteristic
336Q8×C73—22no—
337Q8×C73—22no—
338Q8×C73—44no—
339Q8×C73—41no—
340Q8×C73—41no—
341D4×C73—22no—
342D4×C73—22no—
343D4×C73—44no—
344D4×C73—44no—
345D4×C73—44no—
346D4×C73—48no—
347D4×C73—41no—
348D4×C73—41no—
349D4×C73—41no—
350D4×C73—41no—
351D4×C73—41no—
352D4×C73—41no—
353D4×C73—84no—
354D4×C73—84no—
355D4×C73—84no—
356D4×C73—84no—
357D4×C73—84no—
358C2×C4×C73—21no—
359C2×C4×C73—21no—
360C2×C4×C73—21no—
361C2×C4×C73—21no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—22no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—22no—
373C2×C4×C73—21no—
374C2×C4×C73—21no—
375C2×C4×C73—21no—
376C2×C4×C73—48no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—84no—
397C2×C4×C73#12012yes—
398C2×C4×C73#12112yes—
399C2×C4×C73C22×D411yescharacteristic
400C2×C4×C73C22×D411yescharacteristic
401C2×C4×C73C22×D411yescharacteristic
402C2×C4×C73C2×#4111yescharacteristic
403C2×C4×C73H(5,𝔽2)11yescharacteristic
404C2×C4×C73H(5,𝔽2)11yescharacteristic
405C8×C73—22no—
406C8×C73—22no—
407C8×C73—41no—
408C8×C73—41no—
409C22×C73—22no—
410C22×C73—22no—
411C22×C73—22no—
412C22×C73—22no—
413C22×C73—22no—
414C22×C73—22no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—41no—
418C22×C73—41no—
419C22×C73—41no—
420C22×C73—41no—
421C22×C73—41no—
422C22×C73—41no—
423C22×C73—42no—
424C22×C73—41no—
425C22×C73—41no—
426C22×C73—41no—
427C22×C73—41no—
428C22×C73—42no—
429C22×C73—41no—
430C22×C73—42no—
431C22×C73—41no—
432C22×C73—41no—
433C22×C73—81no—
434C22×C73—81no—
435C22×C73—81no—
436C22×C73—81no—
437C22×C73—81no—
438C22×C73—81no—
439C22×C73—81no—
440C22×C73—81no—
441C22×C73—81no—
442C22×C73—81no—
443C22×C73—81no—
444C22×C73C2×#12011yescharacteristic
445C22×C73C2×#12111yescharacteristic
446C22×C73#53411yescharacteristic
447C22×C73#57611yescharacteristic
448C22×C73#57711yescharacteristic
449C22×C73#57711yescharacteristic
450C22×C73#57711yescharacteristic
451C4×C73—22no—
452C4×C73—22no—
453C4×C73—41no—
454C4×C73—42no—
455C4×C73—42no—
456C4×C73—42no—
457C4×C73—81no—
458C4×C73—81no—
459C4×C73—81no—
460C4×C73D4211yescharacteristic
461C4×C73D4211yescharacteristic
462C4×C73#54611yescharacteristic
463C4×C73#54611yescharacteristic
464#24397C7311yesmaximal, characteristic, direct product factor, Sylow
465C2×C73—42no—
466C2×C73—42no—
467C2×C73—81no—
468C2×C73—82no—
469C2×C73—161no—
470C2×C73#241011yescharacteristic
471C2×C73#301011yescharacteristic
472C2×C73#301211yescharacteristic
473C2×C73#306011yescharacteristic
474C2×C73#306211yescharacteristic
475C2×C73#319811yescharacteristic
476C2×C73#320411yescharacteristic
477C2×#537C2×C7311yescharacteristic, complemented
478C2×#469C2×C7311yescharacteristic, complemented
479C2×#465C2×C7311yescharacteristic, complemented
480C2×#449C2×C7311yescharacteristic, complemented
481C2×#408C2×C7311yescharacteristic, complemented
482#2615C2×C7311yescharacteristic, complemented
483#2035C2×C7311yescharacteristic, complemented
484#2034C2×C7311yescharacteristic, complemented
485#2000C2×C7311yescharacteristic, complemented
486#1999C2×C7311yescharacteristic, complemented
487#1894C2×C7311yescharacteristic, complemented
488#1893C2×C7311yescharacteristic, complemented
489#1874C2×C7311yescharacteristic, complemented
490#1853C2×C7311yescharacteristic, complemented
491#1788C2×C7311yescharacteristic, complemented
492C73#2439711yescharacteristic, direct product factor, Sylow
493C22×#41C22×C7311yescharacteristic
494C22×#41C22×C7311yescharacteristic
495C22×SD16C22×C7311yescharacteristic
496C22×D8C22×C7311yescharacteristic
497C22×M16C22×C7311yescharacteristic
498C23×C8C22×C7311yescharacteristic
499#537—24no—
500#537—24no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8C22×C7311yescharacteristic
503C2×C22⋊Q8C22×C7311yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C7311yescharacteristic
508C2×#121C22×C7311yescharacteristic
509C2×#121C22×C7311yescharacteristic
510C2×#121C22×C7311yescharacteristic
511C2×#121C22×C7311yescharacteristic
512C22×C4⋊C4C22×C7311yescharacteristic
513#469—24no—
514#465—24no—
515#449—24no—
516C2×#106C22×C7311yescharacteristic
517C2×#106C22×C7311yescharacteristic
518C2×#103C22×C7311yescharacteristic
519C2×#103C22×C7311yescharacteristic
520C2×#103C22×C7311yescharacteristic
521C2×#102C22×C7311yescharacteristic
522C2×#102C22×C7311yescharacteristic
523C2×#102C22×C7311yescharacteristic
524C2×#102C22×C7311yescharacteristic
525C2×#102C22×C7311yescharacteristic
526#408—24no—
527C2×C22⋊C8C22×C7311yescharacteristic
528C2×C22⋊C8C22×C7311yescharacteristic
529C2×C22⋊C8C22×C7311yescharacteristic
530C2×C22⋊C8C22×C7311yescharacteristic
531#393—21no—
532#392—21no—
533#392—21no—
534#392—21no—
535#380C22×C7311yescharacteristic
536#380C22×C7311yescharacteristic
537#380C22×C7311yescharacteristic
538#340C22×C7311yescharacteristic
539#340C22×C7311yescharacteristic
540#340C22×C7311yescharacteristic
541#340C22×C7311yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C7311yescharacteristic
555C22×Q8C23×C7311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C7311yescharacteristic
563C22×D4D4×C7311yescharacteristic
564C22×D4D4×C7311yescharacteristic
565C22×D4C23×C7311yescharacteristic
566C22×D4C23×C7311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C7311yescharacteristic
570C23×C4C23×C7311yescharacteristic
571C23×C4C23×C7311yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C7311yescharacteristic
585C22×C8C23×C7311yescharacteristic
586C22×C8C23×C7311yescharacteristic
587C22×C8C23×C7311yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C7314yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C7314yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C7311yescharacteristic
612C2×C4⋊C4C23×C7311yescharacteristic
613C2×C4⋊C4C23×C7311yescharacteristic
614C2×C4⋊C4C23×C7311yescharacteristic
615C2×C4⋊C4C23×C7311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C7314yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C7311yescharacteristic
646C24C2×D4×C7311yescharacteristic
647C24C2×D4×C7311yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C7312yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C7312yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C7311yescharacteristic
731C22×C4C2×D4×C7311yescharacteristic
732C22×C4C2×D4×C7312yes—
733C22×C4C2×D4×C7312yes—
734C22×C4C2×D4×C7311yescharacteristic
735C22×C4C2×D4×C7312yes—
736C22×C4#41×C7312yes—
737C22×C4C24×C7311yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C7312yes—
753C2×C8C2×D4×C7312yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C7312yes—
766C4⋊C4C2×D4×C7312yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C7312yes—
811C23#121×C7312yes—
812C23C22×D4×C7311yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C7312yes—
875C2×C4#121×C7312yes—
876C2×C4C22×D4×C7311yescharacteristic
877C2×C4C22×D4×C7311yescharacteristic
878C2×C4C22×D4×C7311yescharacteristic
879C2×C4C2×#41×C7311yescharacteristic
880C2×C4H(5,𝔽2)×C7311yescharacteristic
881C2×C4H(5,𝔽2)×C7311yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C7311yescharacteristic
922C22C2×#121×C7311yescharacteristic
923C22#534×C7311yescharacteristic
924C22#576×C7311yescharacteristic
925C22#577×C7311yescharacteristic
926C22#577×C7311yescharacteristic
927C22#577×C7311yescharacteristic
928C4—22no—
929C4—22no—
930C4—42no—
931C4—42no—
932C4—41no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C7311yescharacteristic
938C4D42×C7311yescharacteristic
939C4#546×C7311yescharacteristic
940C4#546×C7311yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C73×#241011yescharacteristic
947C2C73×#301011yescharacteristic
948C2C73×#301211yescharacteristic
949C2C73×#306011yescharacteristic
950C2C73×#306211yescharacteristic
951C2C73×#319811yescharacteristic
952C2C73×#320411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#537×C73C2semidirect
2. C2×#469×C73C2semidirect
3. C2×#465×C73C2semidirect
4. C2×#449×C73C2semidirect
5. C2×#408×C73C2semidirect
6. C73×#2615C2semidirect
7. C73×#2035C2semidirect
8. C73×#2034C2semidirect
9. C73×#2000C2semidirect
10. C73×#1999C2semidirect
11. C73×#1894C2semidirect
12. C73×#1893C2semidirect
13. C73×#1874C2semidirect
14. C73×#1853C2semidirect
15. C73×#1788C2semidirect
115. C22⋊Q8×C73D4semidirect
128. #121×C73D4semidirect
162. C22⋊C8×C73D4semidirect
464. #24397C73direct (N × H)
477. C2×#537C2×C73semidirect
478. C2×#469C2×C73semidirect
479. C2×#465C2×C73semidirect
480. C2×#449C2×C73semidirect
481. C2×#408C2×C73semidirect
482. #2615C2×C73semidirect
483. #2035C2×C73semidirect
484. #2034C2×C73semidirect
485. #2000C2×C73semidirect
486. #1999C2×C73semidirect
487. #1894C2×C73semidirect
488. #1893C2×C73semidirect
489. #1874C2×C73semidirect
490. #1853C2×C73semidirect
491. #1788C2×C73semidirect
492. C73#24397direct (N × H)
592. C22⋊Q8D4×C73semidirect
605. #121D4×C73semidirect
639. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C732
C2×#469×C732
C2×#465×C732
C2×#449×C732
C2×#408×C732
C73×#26152
C73×#20352
C73×#20342
C73×#20002
C73×#19992
C73×#18942
C73×#18932
C73×#18742
C73×#18532
C73×#17882
#2439773