Finite Group Databasebeta

← C73×#25160 #32934564

Subgroups — C73×#25160 #32934564

Order 18688.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C73C211yesmaximal, characteristic, complemented
2C2×#450×C73C211yesmaximal, characteristic, complemented
3C2×#447×C73C211yesmaximal, characteristic
4C2×C4×D8×C73C211yesmaximal, characteristic, complemented
5C73×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2036C211yesmaximal, characteristic, complemented
9C73×#2034C211yesmaximal, characteristic, complemented
10C73×#2012C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C2×#124×C73C2211yescharacteristic, complemented
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic, complemented
27C22×C22⋊C4×C73—21no—
28#463×C73—24no—
29#450×C73—24no—
30#447×C73—24no—
31C4×D8×C73—24no—
32C2×#107×C73C2211yescharacteristic, complemented
33C2×#106×C73C2211yescharacteristic, complemented
34C2×C4⋊C8×C73C2211yescharacteristic, complemented
35C2×#103×C73C2211yescharacteristic, complemented
36C2×#103×C73C2211yescharacteristic, complemented
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic, complemented
42C2×#102×C73C2211yescharacteristic, complemented
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C4×C8×C73C2211yescharacteristic, complemented
46#397×C73—21no—
47#394×C73—21no—
48#391×C73C2211yescharacteristic, complemented
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic, complemented
52#386×C73—21no—
53#386×C73—21no—
54#386×C73—21no—
55#380×C73—21no—
56#380×C73C2211yescharacteristic
57#379×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#336×C73C2211yescharacteristic, complemented
62#336×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C22×D4×C73C2311yescharacteristic
74C22×D4×C73C2311yescharacteristic
75C22×D4×C73C2311yescharacteristic
76C23×C4×C73—21no—
77C23×C4×C73—21no—
78C23×C4×C73—21no—
79C23×C4×C73C2311yescharacteristic
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×SD16×C73—41no—
86C2×D8×C73—22no—
87C2×D8×C73—22no—
88C2×D8×C73—22no—
89C2×D8×C73—22no—
90C2×D8×C73—41no—
91C2×D8×C73D414yes—
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96#124×C73—22no—
97#124×C73—41no—
98C22⋊Q8×C73—22no—
99C22⋊Q8×C73—41no—
100#121×C73—22no—
101#121×C73—41no—
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104C4×D4×C73—22no—
105C4×D4×C73—41no—
106C4×D4×C73—41no—
107C4×D4×C73—41no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
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—44no—
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C2×C42×C73C2311yescharacteristic
131#107×C73—22no—
132#106×C73—41no—
133C4⋊C8×C73—22no—
134#103×C73—22no—
135#103×C73—41no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73D414yescomplemented
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144C4×C8×C73—22no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73D411yescharacteristic
150#95×C73D411yescharacteristic
151C24×C73—21no—
152C24×C73—24no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—42no—
159C24×C73—81no—
160C24×C73—81no—
161C24×C73C2×D411yescharacteristic
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×D4×C73—24no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—44no—
185C2×D4×C73—44no—
186C2×D4×C73—44no—
187C2×D4×C73—44no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—81no—
191C2×D4×C73C2×D412yes—
192C2×D4×C73C2×D412yes—
193C2×D4×C73C2×D412yes—
194C2×D4×C73#4112yes—
195C2×D4×C73#4112yes—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—42no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—81no—
214C22×C4×C73—81no—
215C22×C4×C73—81no—
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2411yescharacteristic
222SD16×C73—44no—
223SD16×C73—44no—
224D8×C73—28no—
225D8×C73—44no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73C2×D412yes—
237C2×C8×C73C2×D412yes—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—42no—
246C4⋊C4×C73—81no—
247C4⋊C4×C73C2×D412yes—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—81no—
261C22⋊C4×C73—81no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73—21no—
266C23×C73—21no—
267C23×C73—22no—
268C23×C73—21no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—48no—
278C23×C73—48no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—84no—
296C23×C73—84no—
297C23×C73—84no—
298C23×C73—84no—
299C23×C73—84no—
300C23×C73#13512yes—
301C23×C73C22×D411yescharacteristic
302Q8×C73—41no—
303Q8×C73—41no—
304Q8×C73—41no—
305Q8×C73—41no—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—22no—
309D4×C73—22no—
310D4×C73—22no—
311D4×C73—22no—
312D4×C73—22no—
313D4×C73—48no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—84no—
319D4×C73#12114yes—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—22no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
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—84no—
354C2×C4×C73—84no—
355C2×C4×C73—84no—
356C2×C4×C73AGL(1,ℤ/8)12yes—
357C2×C4×C73C22×D411yescharacteristic
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C2×#4111yescharacteristic
360C2×C4×C73C2×#4111yescharacteristic
361C2×C4×C73H(5,𝔽2)11yescharacteristic
362C2×C4×C73H(5,𝔽2)11yescharacteristic
363C8×C73—22no—
364C8×C73—22no—
365C8×C73—41no—
366C8×C73—41no—
367C22×C73—22no—
368C22×C73—24no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—42no—
372C22×C73—41no—
373C22×C73—42no—
374C22×C73—41no—
375C22×C73—42no—
376C22×C73—41no—
377C22×C73—42no—
378C22×C73—41no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73—42no—
382C22×C73—42no—
383C22×C73—42no—
384C22×C73—42no—
385C22×C73—42no—
386C22×C73—42no—
387C22×C73—816no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73#52511yescharacteristic
397C22×C73D4211yescharacteristic
398C22×C73D4211yescharacteristic
399C22×C73C2×#13511yescharacteristic
400C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C73#57611yescharacteristic
402C22×C73#57711yescharacteristic
403C4×C73—22no—
404C4×C73—41no—
405C4×C73—42no—
406C4×C73—41no—
407C4×C73—41no—
408C4×C73—41no—
409C4×C73—81no—
410C4×C73—81no—
411C4×C73—81no—
412C4×C73—81no—
413C4×C73C2×#12111yescharacteristic
414C4×C73#53811yescharacteristic
415C4×C73#54611yescharacteristic
416C4×C73#54611yescharacteristic
417#25160C7311yesmaximal, characteristic, direct product factor, Sylow
418C2×C73—42no—
419C2×C73—44no—
420C2×C73—82no—
421C2×C73—82no—
422C2×C73#242411yescharacteristic
423C2×C73#310511yescharacteristic
424C2×C73#311811yescharacteristic
425C2×C73#326411yescharacteristic
426C2×C73#327211yescharacteristic
427C2×C73#328011yescharacteristic
428C2×C73#328211yescharacteristic
429C2×#463C2×C7311yescharacteristic, complemented
430C2×#450C2×C7311yescharacteristic, complemented
431C2×#447C2×C7311yescharacteristic
432C2×C4×D8C2×C7311yescharacteristic, complemented
433#2427C2×C7311yescharacteristic, complemented
434D4×C22⋊C4C2×C7311yescharacteristic, complemented
435#2067C2×C7311yescharacteristic, complemented
436#2036C2×C7311yescharacteristic, complemented
437#2034C2×C7311yescharacteristic, complemented
438#2012C2×C7311yescharacteristic, complemented
439#1968C2×C7311yescharacteristic, complemented
440#1923C2×C7311yescharacteristic, complemented
441#1879C2×C7311yescharacteristic, complemented
442#1877C2×C7311yescharacteristic, complemented
443#1864C2×C7311yescharacteristic, complemented
444C73#2516011yescharacteristic, direct product factor, Sylow
445C23×D4C22×C7311yescharacteristic
446C22×SD16C22×C7311yescharacteristic
447C22×SD16C22×C7311yescharacteristic
448C22×D8C22×C7311yescharacteristic
449C22×D8C22×C7311yescharacteristic
450C2×#124C22×C7311yescharacteristic, complemented
451C2×C22⋊Q8C22×C7311yescharacteristic
452C2×#121C22×C7311yescharacteristic
453C2×C4×D4C22×C7311yescharacteristic
454C2×C4×D4C22×C7311yescharacteristic
455C2×C4×D4C22×C7311yescharacteristic, complemented
456C22×C22⋊C4—21no—
457#463—24no—
458#450—24no—
459#447—24no—
460C4×D8—24no—
461C2×#107C22×C7311yescharacteristic, complemented
462C2×#106C22×C7311yescharacteristic, complemented
463C2×C4⋊C8C22×C7311yescharacteristic, complemented
464C2×#103C22×C7311yescharacteristic, complemented
465C2×#103C22×C7311yescharacteristic, complemented
466C2×#102C22×C7311yescharacteristic
467C2×#102C22×C7311yescharacteristic
468C2×#102C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×#102C22×C7311yescharacteristic, complemented
471C2×#102C22×C7311yescharacteristic, complemented
472C2×C22⋊C8C22×C7311yescharacteristic
473C2×C22⋊C8C22×C7311yescharacteristic
474C2×C4×C8C22×C7311yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#391C22×C7311yescharacteristic, complemented
478#390C22×C7311yescharacteristic
479#390C22×C7311yescharacteristic
480#389C22×C7311yescharacteristic, complemented
481#386—21no—
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C7311yescharacteristic
486#379—21no—
487C4×C22⋊C4C22×C7311yescharacteristic
488#340C22×C7311yescharacteristic, complemented
489#340C22×C7311yescharacteristic, complemented
490#336C22×C7311yescharacteristic, complemented
491#336C22×C7311yescharacteristic, complemented
492C25—21no—
493C22×Q8C23×C7311yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C7311yescharacteristic
503C22×D4C23×C7311yescharacteristic
504C22×D4C23×C7311yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C7311yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C7314yes—
521C22×C8C23×C7311yescharacteristic
522C22×C8C23×C7311yescharacteristic
523C22×C8C23×C7311yescharacteristic
524C22×C8C23×C7311yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C7311yescharacteristic
540C2×C4⋊C4C23×C7311yescharacteristic
541C2×C4⋊C4C23×C7311yescharacteristic
542C2×C4⋊C4C23×C7311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C7311yescharacteristic
557C2×C22⋊C4D4×C7311yescharacteristic
558C2×C42C23×C7311yescharacteristic
559C2×C42C23×C7311yescharacteristic
560#107—22no—
561#106—41no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C7314yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573C4×C8—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C7311yescharacteristic
579#95D4×C7311yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C7311yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C7312yes—
621C2×D4C2×D4×C7312yes—
622C2×D4C2×D4×C7312yes—
623C2×D4#41×C7312yes—
624C2×D4#41×C7312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C7311yescharacteristic
646C22×C4C2×D4×C7311yescharacteristic
647C22×C4C2×D4×C7311yescharacteristic
648C22×C4C2×D4×C7311yescharacteristic
649C22×C4C2×D4×C7311yescharacteristic
650C22×C4C24×C7311yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C7312yes—
666C2×C8C2×D4×C7312yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C7312yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#135×C7312yes—
730C23C22×D4×C7311yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C7314yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
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—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4AGL(1,ℤ/8)×C7312yes—
786C2×C4C22×D4×C7311yescharacteristic
787C2×C4C22×D4×C7311yescharacteristic
788C2×C4C2×#41×C7311yescharacteristic
789C2×C4C2×#41×C7311yescharacteristic
790C2×C4H(5,𝔽2)×C7311yescharacteristic
791C2×C4H(5,𝔽2)×C7311yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—24no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22#525×C7311yescharacteristic
826C22D42×C7311yescharacteristic
827C22D42×C7311yescharacteristic
828C22C2×#135×C7311yescharacteristic
829C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
830C22#576×C7311yescharacteristic
831C22#577×C7311yescharacteristic
832C4—22no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C7311yescharacteristic
843C4#538×C7311yescharacteristic
844C4#546×C7311yescharacteristic
845C4#546×C7311yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C73×#242411yescharacteristic
851C2C73×#310511yescharacteristic
852C2C73×#311811yescharacteristic
853C2C73×#326411yescharacteristic
854C2C73×#327211yescharacteristic
855C2C73×#328011yescharacteristic
856C2C73×#328211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#447×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C73C2semidirect
2. C2×#450×C73C2semidirect
4. C2×C4×D8×C73C2semidirect
5. C73×#2427C2semidirect
6. D4×C22⋊C4×C73C2semidirect
7. C73×#2067C2semidirect
8. C73×#2036C2semidirect
9. C73×#2034C2semidirect
10. C73×#2012C2semidirect
11. C73×#1968C2semidirect
12. C73×#1923C2semidirect
13. C73×#1879C2semidirect
14. C73×#1877C2semidirect
15. C73×#1864C2semidirect
21. C2×#124×C73C22semidirect
26. C2×C4×D4×C73C22semidirect
32. C2×#107×C73C22semidirect
33. C2×#106×C73C22semidirect
34. C2×C4⋊C8×C73C22semidirect
35. C2×#103×C73C22semidirect
36. C2×#103×C73C22semidirect
41. C2×#102×C73C22semidirect
42. C2×#102×C73C22semidirect
45. C2×C4×C8×C73C22semidirect
48. #391×C73C22semidirect
51. #389×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #336×C73C22semidirect
62. #336×C73C22semidirect
141. #102×C73D4semidirect
417. #25160C73direct (N × H)
429. C2×#463C2×C73semidirect
430. C2×#450C2×C73semidirect
432. C2×C4×D8C2×C73semidirect
433. #2427C2×C73semidirect
434. D4×C22⋊C4C2×C73semidirect
435. #2067C2×C73semidirect
436. #2036C2×C73semidirect
437. #2034C2×C73semidirect
438. #2012C2×C73semidirect
439. #1968C2×C73semidirect
440. #1923C2×C73semidirect
441. #1879C2×C73semidirect
442. #1877C2×C73semidirect
443. #1864C2×C73semidirect
444. C73#25160direct (N × H)
450. C2×#124C22×C73semidirect
455. C2×C4×D4C22×C73semidirect
461. C2×#107C22×C73semidirect
462. C2×#106C22×C73semidirect
463. C2×C4⋊C8C22×C73semidirect
464. C2×#103C22×C73semidirect
465. C2×#103C22×C73semidirect
470. C2×#102C22×C73semidirect
471. C2×#102C22×C73semidirect
474. C2×C4×C8C22×C73semidirect
477. #391C22×C73semidirect
480. #389C22×C73semidirect
488. #340C22×C73semidirect
489. #340C22×C73semidirect
490. #336C22×C73semidirect
491. #336C22×C73semidirect
570. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C732
C2×#450×C732
C2×#447×C732
C2×C4×D8×C732
C73×#24272
D4×C22⋊C4×C732
C73×#20672
C73×#20362
C73×#20342
C73×#20122
C73×#19682
C73×#19232
C73×#18792
C73×#18772
C73×#18642
#2516073