Finite Group Databasebeta

← C73×#15271 #32924675

Subgroups — C73×#15271 #32924675

Order 18688.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C73C211yesmaximal, characteristic
2C2×#398×C73C211yesmaximal, characteristic, complemented
3C2×#394×C73C211yesmaximal, characteristic
4C2×#390×C73C211yesmaximal, characteristic
5C2×#389×C73C211yesmaximal, characteristic, complemented
6C2×#385×C73C211yesmaximal, characteristic, complemented
7C73×#1441C211yesmaximal, characteristic, complemented
8C73×#1440C211yesmaximal, characteristic, complemented
9C73×#1440C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic, complemented
12C73×#1439C211yesmaximal, characteristic, complemented
13C73×#1439C211yesmaximal, characteristic, complemented
14C73×#1436C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C24×C4×C73C2211yescharacteristic
18C2×#123×C73—24no—
19C2×#123×C73—24no—
20C2×#123×C73—24no—
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C22×C4⋊C4×C73C2211yescharacteristic
27C22×C4⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C22×C22⋊C4×C73C2211yescharacteristic
33C22×C22⋊C4×C73C2211yescharacteristic
34C22×C22⋊C4×C73C2211yescharacteristic
35C22×C22⋊C4×C73C2211yescharacteristic
36C22×C22⋊C4×C73C2211yescharacteristic
37C22×C22⋊C4×C73C2211yescharacteristic
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C42×C73C2211yescharacteristic
40#398×C73—24no—
41#394×C73—24no—
42#390×C73—24no—
43#389×C73—24no—
44#385×C73—24no—
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C2×#95×C73C2211yescharacteristic
59C25×C73C2311yescharacteristic
60C25×C73C2311yescharacteristic
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—41no—
66C22×D4×C73—41no—
67C22×D4×C73D414yes—
68C23×C4×C73—22no—
69C23×C4×C73—22no—
70C23×C4×C73—22no—
71C23×C4×C73—22no—
72C23×C4×C73—22no—
73C23×C4×C73—41no—
74C23×C4×C73—41no—
75C23×C4×C73C2311yescharacteristic
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2311yescharacteristic
84C23×C4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2311yescharacteristic
88#123×C73—232no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—22no—
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73—22no—
99C2×C4⋊C4×C73—22no—
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—22no—
102C2×C4⋊C4×C73—22no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73—22no—
105C2×C4⋊C4×C73—41no—
106C2×C4⋊C4×C73—41no—
107C2×C4⋊C4×C73—41no—
108C2×C4⋊C4×C73D414yes—
109C2×C4⋊C4×C73D414yes—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—22no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—22no—
119C2×C22⋊C4×C73—22no—
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—22no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊C4×C73—22no—
136C2×C22⋊C4×C73—41no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73—41no—
139C2×C22⋊C4×C73—41no—
140C2×C22⋊C4×C73—41no—
141C2×C22⋊C4×C73—41no—
142C2×C22⋊C4×C73D414yes—
143C2×C42×C73—22no—
144C2×C42×C73—22no—
145C2×C42×C73—41no—
146#95×C73—22no—
147#95×C73—22no—
148#95×C73—22no—
149#95×C73—22no—
150#95×C73—22no—
151#95×C73—22no—
152#95×C73—22no—
153#95×C73—22no—
154#95×C73—22no—
155#95×C73—22no—
156#95×C73—41no—
157#95×C73—41no—
158#95×C73—41no—
159#95×C73—41no—
160C24×C73—21no—
161C24×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73—21no—
165C24×C73—21no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73—21no—
169C24×C73—21no—
170C24×C73—21no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—21no—
175C24×C73—21no—
176C24×C73—21no—
177C24×C73—21no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—21no—
181C24×C73—21no—
182C24×C73—21no—
183C24×C73—21no—
184C24×C73—21no—
185C24×C73—21no—
186C24×C73C2×D412yes—
187C24×C73C2×D412yes—
188C24×C73C2×D412yes—
189C24×C73#4112yes—
190C24×C73C2411yescharacteristic
191C2×D4×C73—28no—
192C2×D4×C73—28no—
193C2×D4×C73—44no—
194C2×D4×C73—44no—
195C2×D4×C73—44no—
196C2×D4×C73—44no—
197C2×D4×C73—44no—
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—28no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
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—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
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—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
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—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—44no—
278C22×C4×C73—44no—
279C22×C4×C73—44no—
280C22×C4×C73—44no—
281C22×C4×C73—44no—
282C22×C4×C73—44no—
283C22×C4×C73C2×D412yes—
284C22×C4×C73C2×D412yes—
285C22×C4×C73C2×D412yes—
286C22×C4×C73C2×D412yes—
287C22×C4×C73C2×D412yes—
288C22×C4×C73C2×D412yes—
289C22×C4×C73C2×D412yes—
290C22×C4×C73C2×D412yes—
291C22×C4×C73C2×D412yes—
292C22×C4×C73#4112yes—
293C22×C4×C73#4112yes—
294C22×C4×C73#4112yes—
295C22×C4×C73#4112yes—
296C4⋊C4×C73—28no—
297C4⋊C4×C73—28no—
298C4⋊C4×C73—28no—
299C4⋊C4×C73—44no—
300C4⋊C4×C73—44no—
301C4⋊C4×C73—44no—
302C4⋊C4×C73—44no—
303C22⋊C4×C73—28no—
304C22⋊C4×C73—28no—
305C22⋊C4×C73—28no—
306C22⋊C4×C73—28no—
307C22⋊C4×C73—44no—
308C22⋊C4×C73—44no—
309C22⋊C4×C73—44no—
310C22⋊C4×C73—44no—
311C22⋊C4×C73—44no—
312C22⋊C4×C73—44no—
313C22⋊C4×C73—44no—
314C42×C73—44no—
315C23×C73—22no—
316C23×C73—22no—
317C23×C73—22no—
318C23×C73—22no—
319C23×C73—22no—
320C23×C73—22no—
321C23×C73—22no—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—22no—
328C23×C73—22no—
329C23×C73—22no—
330C23×C73—22no—
331C23×C73—22no—
332C23×C73—22no—
333C23×C73—22no—
334C23×C73—22no—
335C23×C73—22no—
336C23×C73—22no—
337C23×C73—22no—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—41no—
341C23×C73—41no—
342C23×C73—41no—
343C23×C73—41no—
344C23×C73—41no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—41no—
348C23×C73—41no—
349C23×C73—41no—
350C23×C73—41no—
351C23×C73—41no—
352C23×C73—41no—
353C23×C73—41no—
354C23×C73—41no—
355C23×C73—41no—
356C23×C73—41no—
357C23×C73—41no—
358C23×C73—41no—
359C23×C73—41no—
360C23×C73—41no—
361C23×C73—41no—
362C23×C73—41no—
363C23×C73—41no—
364C23×C73—41no—
365C23×C73—41no—
366C23×C73—41no—
367C23×C73—41no—
368C23×C73—41no—
369C23×C73—41no—
370C23×C73—41no—
371C23×C73—41no—
372C23×C73—41no—
373C23×C73—41no—
374C23×C73—41no—
375C23×C73—41no—
376C23×C73—41no—
377C23×C73—41no—
378C23×C73—41no—
379C23×C73—41no—
380C23×C73—41no—
381C23×C73—41no—
382C23×C73—41no—
383C23×C73—41no—
384C23×C73#12114yes—
385C23×C73C22×D411yescharacteristic
386C23×C73C22×D411yescharacteristic
387C23×C73C22×D411yescharacteristic
388C23×C73C22×D411yescharacteristic
389C23×C73C2×#4111yescharacteristic
390C23×C73C2×#4111yescharacteristic
391C23×C73C2×#4111yescharacteristic
392C23×C73C2×#4111yescharacteristic
393C23×C73C2×#4111yescharacteristic
394C23×C73H(5,𝔽2)11yescharacteristic
395C23×C73H(5,𝔽2)11yescharacteristic
396C23×C73H(5,𝔽2)11yescharacteristic
397C23×C732−1+411yescharacteristic
398C23×C732−1+411yescharacteristic
399C23×C732−1+411yescharacteristic
400D4×C73—416no—
401C2×C4×C73—22no—
402C2×C4×C73—22no—
403C2×C4×C73—22no—
404C2×C4×C73—22no—
405C2×C4×C73—22no—
406C2×C4×C73—22no—
407C2×C4×C73—22no—
408C2×C4×C73—22no—
409C2×C4×C73—22no—
410C2×C4×C73—22no—
411C2×C4×C73—22no—
412C2×C4×C73—22no—
413C2×C4×C73—22no—
414C2×C4×C73—22no—
415C2×C4×C73—22no—
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—22no—
419C2×C4×C73—22no—
420C2×C4×C73—22no—
421C2×C4×C73—22no—
422C2×C4×C73—22no—
423C2×C4×C73—22no—
424C2×C4×C73—22no—
425C2×C4×C73—22no—
426C2×C4×C73—22no—
427C2×C4×C73—22no—
428C2×C4×C73—22no—
429C2×C4×C73—22no—
430C2×C4×C73—22no—
431C2×C4×C73—22no—
432C2×C4×C73—22no—
433C2×C4×C73—22no—
434C2×C4×C73—416no—
435C2×C4×C73—41no—
436C2×C4×C73—41no—
437C2×C4×C73—41no—
438C2×C4×C73—41no—
439C2×C4×C73—41no—
440C2×C4×C73—41no—
441C2×C4×C73—41no—
442C2×C4×C73—41no—
443C2×C4×C73—41no—
444C2×C4×C73—41no—
445C2×C4×C73—41no—
446C2×C4×C73—41no—
447C2×C4×C73—41no—
448C2×C4×C73—41no—
449C2×C4×C73—41no—
450C2×C4×C73—41no—
451C2×C4×C73—41no—
452C2×C4×C73—41no—
453C2×C4×C73—41no—
454C2×C4×C73—41no—
455C2×C4×C73—41no—
456C2×C4×C73—41no—
457C2×C4×C73—41no—
458C2×C4×C73—41no—
459C2×C4×C73—41no—
460C2×C4×C73—41no—
461C2×C4×C73—41no—
462C2×C4×C73—41no—
463C2×C4×C73—41no—
464C2×C4×C73—41no—
465C2×C4×C73—41no—
466C2×C4×C73—41no—
467C2×C4×C73—41no—
468C2×C4×C73—41no—
469C2×C4×C73—41no—
470C2×C4×C73—41no—
471C2×C4×C73—41no—
472C2×C4×C73—41no—
473C2×C4×C73—41no—
474C2×C4×C73—41no—
475C2×C4×C73—41no—
476C2×C4×C73—41no—
477C2×C4×C73—41no—
478C2×C4×C73—41no—
479C2×C4×C73—41no—
480C2×C4×C73—41no—
481C2×C4×C73—41no—
482C2×C4×C73—41no—
483C2×C4×C73—41no—
484C2×C4×C73—41no—
485C2×C4×C73—41no—
486C2×C4×C73—41no—
487C2×C4×C73—41no—
488C2×C4×C73—41no—
489C2×C4×C73—41no—
490C2×C4×C73—41no—
491C2×C4×C73#12014yes—
492C2×C4×C73#12314yescomplemented
493C22×C73—24no—
494C22×C73—24no—
495C22×C73—24no—
496C22×C73—42no—
497C22×C73—42no—
498C22×C73—42no—
499C22×C73—42no—
500C22×C73—42no—
501C22×C73—42no—
502C22×C73—42no—
503C22×C73—42no—
504C22×C73—42no—
505C22×C73—42no—
506C22×C73—42no—
507C22×C73—42no—
508C22×C73—42no—
509C22×C73—42no—
510C22×C73—42no—
511C22×C73—42no—
512C22×C73—42no—
513C22×C73—42no—
514C22×C73—42no—
515C22×C73—81no—
516C22×C73—81no—
517C22×C73—81no—
518C22×C73—81no—
519C22×C73—81no—
520C22×C73—81no—
521C22×C73—81no—
522C22×C73—81no—
523C22×C73C2×#12011yescharacteristic
524C22×C73C2×#12111yescharacteristic
525C22×C73C2×#12311yescharacteristic
526C22×C73#52511yescharacteristic
527C22×C73#52911yescharacteristic
528C22×C73#53211yescharacteristic
529C22×C73#53411yescharacteristic
530C22×C73#53611yescharacteristic
531C22×C73#53611yescharacteristic
532C22×C73#53711yescharacteristic
533C22×C73#53911yescharacteristic
534C22×C73#53911yescharacteristic
535C22×C73#53911yescharacteristic
536C22×C73#54011yescharacteristic
537C22×C73#54211yescharacteristic
538C22×C73D4211yescharacteristic
539C22×C73D4211yescharacteristic
540C22×C73#54611yescharacteristic
541C22×C73#54611yescharacteristic
542C22×C73#54611yescharacteristic
543C22×C73#54611yescharacteristic
544C22×C73#54711yescharacteristic
545C22×C73#54711yescharacteristic
546C22×C73#54711yescharacteristic
547C22×C73#54711yescharacteristic
548C22×C73#54811yescharacteristic
549C22×C73#54811yescharacteristic
550C22×C73#54811yescharacteristic
551C22×C73#55011yescharacteristic
552C22×C73#55211yescharacteristic
553C22×C73#55211yescharacteristic
554C22×C73#55311yescharacteristic
555C22×C73#55911yescharacteristic
556C22×C73#56211yescharacteristic
557C22×C73#56311yescharacteristic
558C4×C73—24no—
559C4×C73—24no—
560C4×C73—42no—
561C4×C73—42no—
562C4×C73—42no—
563C4×C73—42no—
564C4×C73—42no—
565C4×C73—42no—
566C4×C73—42no—
567C4×C73—81no—
568C4×C73—81no—
569C4×C73—81no—
570C4×C73—81no—
571#15271C7311yesmaximal, characteristic, direct product factor, Sylow
572C2×C73—44no—
573C2×C73—82no—
574C2×C73#240711yescharacteristic
575C2×C73#241011yescharacteristic
576C2×C73#242511yescharacteristic
577C2×C73#243211yescharacteristic
578C2×C73#244311yescharacteristic
579C2×C73#244511yescharacteristic
580C2×C73#245811yescharacteristic
581C2×C73#248611yescharacteristic
582C2×C73#255811yescharacteristic
583C2×C73#267411yescharacteristic
584C2×C73#268111yescharacteristic
585C2×C73#269411yescharacteristic
586C2×C73#270111yescharacteristic
587C2×C73#270711yescharacteristic
588C2×C73#272411yescharacteristic
589C22×#123C2×C7311yescharacteristic
590C2×#398C2×C7311yescharacteristic, complemented
591C2×#394C2×C7311yescharacteristic
592C2×#390C2×C7311yescharacteristic
593C2×#389C2×C7311yescharacteristic, complemented
594C2×#385C2×C7311yescharacteristic, complemented
595#1441C2×C7311yescharacteristic, complemented
596#1440C2×C7311yescharacteristic, complemented
597#1440C2×C7311yescharacteristic, complemented
598#1439C2×C7311yescharacteristic, complemented
599#1439C2×C7311yescharacteristic, complemented
600#1439C2×C7311yescharacteristic, complemented
601#1439C2×C7311yescharacteristic, complemented
602#1436C2×C7311yescharacteristic, complemented
603C22⋊#95C2×C7311yescharacteristic, complemented
604C73#1527111yescharacteristic, direct product factor, Sylow
605C23×D4C22×C7311yescharacteristic
606C24×C4C22×C7311yescharacteristic
607C2×#123—24no—
608C2×#123—24no—
609C2×#123—24no—
610C22×C4⋊C4C22×C7311yescharacteristic
611C22×C4⋊C4C22×C7311yescharacteristic
612C22×C4⋊C4C22×C7311yescharacteristic
613C22×C4⋊C4C22×C7311yescharacteristic
614C22×C4⋊C4C22×C7311yescharacteristic
615C22×C4⋊C4C22×C7311yescharacteristic
616C22×C4⋊C4C22×C7311yescharacteristic
617C22×C22⋊C4C22×C7311yescharacteristic
618C22×C22⋊C4C22×C7311yescharacteristic
619C22×C22⋊C4C22×C7311yescharacteristic
620C22×C22⋊C4C22×C7311yescharacteristic
621C22×C22⋊C4C22×C7311yescharacteristic
622C22×C22⋊C4C22×C7311yescharacteristic
623C22×C22⋊C4C22×C7311yescharacteristic
624C22×C22⋊C4C22×C7311yescharacteristic
625C22×C22⋊C4C22×C7311yescharacteristic
626C22×C22⋊C4C22×C7311yescharacteristic
627C22×C22⋊C4C22×C7311yescharacteristic
628C22×C42C22×C7311yescharacteristic
629#398—24no—
630#394—24no—
631#390—24no—
632#389—24no—
633#385—24no—
634C2×#95C22×C7311yescharacteristic
635C2×#95C22×C7311yescharacteristic
636C2×#95C22×C7311yescharacteristic
637C2×#95C22×C7311yescharacteristic
638C2×#95C22×C7311yescharacteristic
639C2×#95C22×C7311yescharacteristic
640C2×#95C22×C7311yescharacteristic
641C2×#95C22×C7311yescharacteristic
642C2×#95C22×C7311yescharacteristic
643C2×#95C22×C7311yescharacteristic
644C2×#95C22×C7311yescharacteristic
645C2×#95C22×C7311yescharacteristic
646C2×#95C22×C7311yescharacteristic
647C2×#95C22×C7311yescharacteristic
648C25C23×C7311yescharacteristic
649C25C23×C7311yescharacteristic
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—41no—
655C22×D4—41no—
656C22×D4D4×C7314yes—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—41no—
663C23×C4—41no—
664C23×C4C23×C7311yescharacteristic
665C23×C4C23×C7311yescharacteristic
666C23×C4C23×C7311yescharacteristic
667C23×C4C23×C7311yescharacteristic
668C23×C4C23×C7311yescharacteristic
669C23×C4C23×C7311yescharacteristic
670C23×C4C23×C7311yescharacteristic
671C23×C4C23×C7311yescharacteristic
672C23×C4C23×C7311yescharacteristic
673C23×C4C23×C7311yescharacteristic
674C23×C4C23×C7311yescharacteristic
675C23×C4C23×C7311yescharacteristic
676C23×C4C23×C7311yescharacteristic
677#123—232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C4⋊C4D4×C7314yes—
698C2×C4⋊C4D4×C7314yes—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4D4×C7314yes—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C7312yes—
776C24C2×D4×C7312yes—
777C24C2×D4×C7312yes—
778C24#41×C7312yes—
779C24C24×C7311yescharacteristic
780C2×D4—28no—
781C2×D4—28no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4C2×D4×C7312yes—
873C22×C4C2×D4×C7312yes—
874C22×C4C2×D4×C7312yes—
875C22×C4C2×D4×C7312yes—
876C22×C4C2×D4×C7312yes—
877C22×C4C2×D4×C7312yes—
878C22×C4C2×D4×C7312yes—
879C22×C4C2×D4×C7312yes—
880C22×C4C2×D4×C7312yes—
881C22×C4#41×C7312yes—
882C22×C4#41×C7312yes—
883C22×C4#41×C7312yes—
884C22×C4#41×C7312yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23#121×C7314yes—
974C23C22×D4×C7311yescharacteristic
975C23C22×D4×C7311yescharacteristic
976C23C22×D4×C7311yescharacteristic
977C23C22×D4×C7311yescharacteristic
978C23C2×#41×C7311yescharacteristic
979C23C2×#41×C7311yescharacteristic
980C23C2×#41×C7311yescharacteristic
981C23C2×#41×C7311yescharacteristic
982C23C2×#41×C7311yescharacteristic
983C23H(5,𝔽2)×C7311yescharacteristic
984C23H(5,𝔽2)×C7311yescharacteristic
985C23H(5,𝔽2)×C7311yescharacteristic
986C232−1+4×C7311yescharacteristic
987C232−1+4×C7311yescharacteristic
988C232−1+4×C7311yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—416no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4#120×C7314yes—
1081C2×C4#123×C7314yescomplemented
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×#120×C7311yescharacteristic
1113C22C2×#121×C7311yescharacteristic
1114C22C2×#123×C7311yescharacteristic
1115C22#525×C7311yescharacteristic
1116C22#529×C7311yescharacteristic
1117C22#532×C7311yescharacteristic
1118C22#534×C7311yescharacteristic
1119C22#536×C7311yescharacteristic
1120C22#536×C7311yescharacteristic
1121C22#537×C7311yescharacteristic
1122C22#539×C7311yescharacteristic
1123C22#539×C7311yescharacteristic
1124C22#539×C7311yescharacteristic
1125C22#540×C7311yescharacteristic
1126C22#542×C7311yescharacteristic
1127C22D42×C7311yescharacteristic
1128C22D42×C7311yescharacteristic
1129C22#546×C7311yescharacteristic
1130C22#546×C7311yescharacteristic
1131C22#546×C7311yescharacteristic
1132C22#546×C7311yescharacteristic
1133C22#547×C7311yescharacteristic
1134C22#547×C7311yescharacteristic
1135C22#547×C7311yescharacteristic
1136C22#547×C7311yescharacteristic
1137C22#548×C7311yescharacteristic
1138C22#548×C7311yescharacteristic
1139C22#548×C7311yescharacteristic
1140C22#550×C7311yescharacteristic
1141C22#552×C7311yescharacteristic
1142C22#552×C7311yescharacteristic
1143C22#553×C7311yescharacteristic
1144C22#559×C7311yescharacteristic
1145C22#562×C7311yescharacteristic
1146C22#563×C7311yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C73×#240711yescharacteristic
1163C2C73×#241011yescharacteristic
1164C2C73×#242511yescharacteristic
1165C2C73×#243211yescharacteristic
1166C2C73×#244311yescharacteristic
1167C2C73×#244511yescharacteristic
1168C2C73×#245811yescharacteristic
1169C2C73×#248611yescharacteristic
1170C2C73×#255811yescharacteristic
1171C2C73×#267411yescharacteristic
1172C2C73×#268111yescharacteristic
1173C2C73×#269411yescharacteristic
1174C2C73×#270111yescharacteristic
1175C2C73×#270711yescharacteristic
1176C2C73×#272411yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC23×D4×C73C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#398×C73C2semidirect
5. C2×#389×C73C2semidirect
6. C2×#385×C73C2semidirect
7. C73×#1441C2semidirect
8. C73×#1440C2semidirect
9. C73×#1440C2semidirect
10. C73×#1439C2semidirect
11. C73×#1439C2semidirect
12. C73×#1439C2semidirect
13. C73×#1439C2semidirect
14. C73×#1436C2semidirect
15. C73×C22⋊#95C2semidirect
492. C2×C4×C73#123semidirect
571. #15271C73direct (N × H)
590. C2×#398C2×C73semidirect
593. C2×#389C2×C73semidirect
594. C2×#385C2×C73semidirect
595. #1441C2×C73semidirect
596. #1440C2×C73semidirect
597. #1440C2×C73semidirect
598. #1439C2×C73semidirect
599. #1439C2×C73semidirect
600. #1439C2×C73semidirect
601. #1439C2×C73semidirect
602. #1436C2×C73semidirect
603. C22⋊#95C2×C73semidirect
604. C73#15271direct (N × H)
1081. C2×C4#123×C73semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C732
C2×#398×C732
C2×#394×C732
C2×#390×C732
C2×#389×C732
C2×#385×C732
C73×#14412
C73×#14402
C73×#14392
C73×#14362
C73×C22⋊#952
#1527173