Finite Group Databasebeta

← C73×#15269 #32924673

Subgroups — C73×#15269 #32924673

Order 18688.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C73C211yesmaximal, characteristic
2C2×#397×C73C211yesmaximal, characteristic, complemented
3C2×#394×C73C211yesmaximal, characteristic
4C2×#386×C73C211yesmaximal, characteristic
5C2×#385×C73C211yesmaximal, characteristic, complemented
6C2×#380×C73C211yesmaximal, characteristic, complemented
7C73×#1444C211yesmaximal, characteristic, complemented
8C73×#1444C211yesmaximal, characteristic, complemented
9C73×#1442C211yesmaximal, characteristic, complemented
10C73×#1441C211yesmaximal, characteristic, complemented
11C73×#1440C211yesmaximal, characteristic, complemented
12C73×#1440C211yesmaximal, characteristic, complemented
13C73×#1439C211yesmaximal, characteristic, complemented
14C73×C22⋊#95C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C24×C4×C73C2211yescharacteristic
18C24×C4×C73C2211yescharacteristic
19C2×#123×C73—24no—
20C2×#123×C73—24no—
21C2×#123×C73—24no—
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
38#397×C73—24no—
39#394×C73—24no—
40#386×C73—24no—
41#385×C73—24no—
42#380×C73—24no—
43C2×#95×C73C2211yescharacteristic
44C2×#95×C73C2211yescharacteristic
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—22no—
74C23×C4×C73—22no—
75C23×C4×C73—22no—
76C23×C4×C73—22no—
77C23×C4×C73—22no—
78C23×C4×C73—41no—
79C23×C4×C73—41no—
80C23×C4×C73—41no—
81C23×C4×C73—41no—
82C23×C4×C73C2311yescharacteristic
83C23×C4×C73C2311yescharacteristic
84C23×C4×C73C2311yescharacteristic
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95#123×C73—232no—
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—22no—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—41no—
110C2×C4⋊C4×C73—41no—
111C2×C4⋊C4×C73—41no—
112C2×C4⋊C4×C73—41no—
113C2×C4⋊C4×C73—41no—
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—22no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73—41no—
139C2×C22⋊C4×C73—41no—
140C2×C22⋊C4×C73—41no—
141C2×C22⋊C4×C73D414yes—
142C2×C22⋊C4×C73D414yes—
143C2×C22⋊C4×C73D414yes—
144#95×C73—22no—
145#95×C73—22no—
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—22no—
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×C73C2×D412yes—
185C24×C73C2×D412yes—
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—28no—
203C22×C4×C73—28no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
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—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—44no—
281C22×C4×C73—44no—
282C22×C4×C73—44no—
283C22×C4×C73—44no—
284C22×C4×C73—44no—
285C22×C4×C73—44no—
286C22×C4×C73—44no—
287C22×C4×C73—44no—
288C22×C4×C73—44no—
289C22×C4×C73—44no—
290C22×C4×C73—44no—
291C22×C4×C73—44no—
292C22×C4×C73C2×D412yes—
293C22×C4×C73C2×D412yes—
294C22×C4×C73C2×D412yes—
295C22×C4×C73C2×D412yes—
296C22×C4×C73C2×D412yes—
297C22×C4×C73C2×D412yes—
298C22×C4×C73C2×D412yes—
299C22×C4×C73#4112yes—
300C22×C4×C73#4112yes—
301C22×C4×C73#4112yes—
302C22×C4×C73#4112yes—
303C4⋊C4×C73—28no—
304C4⋊C4×C73—28no—
305C4⋊C4×C73—44no—
306C4⋊C4×C73—44no—
307C4⋊C4×C73—44no—
308C4⋊C4×C73—44no—
309C22⋊C4×C73—28no—
310C22⋊C4×C73—28no—
311C22⋊C4×C73—28no—
312C22⋊C4×C73—28no—
313C22⋊C4×C73—44no—
314C22⋊C4×C73—44no—
315C22⋊C4×C73—44no—
316C22⋊C4×C73—44no—
317C22⋊C4×C73—44no—
318C22⋊C4×C73—44no—
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—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—22no—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—22no—
354C23×C73—22no—
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—41no—
385C23×C73—41no—
386C23×C73—41no—
387C23×C73#12014yes—
388C23×C73#12114yes—
389C23×C73C22×D411yescharacteristic
390C23×C73C22×D411yescharacteristic
391C23×C73C22×D411yescharacteristic
392C23×C73C22×D411yescharacteristic
393C23×C73C2×#4111yescharacteristic
394C23×C73C2×#4111yescharacteristic
395C23×C73C2×#4111yescharacteristic
396C23×C73C2×#4111yescharacteristic
397C23×C73C2×#4111yescharacteristic
398C23×C73H(5,𝔽2)11yescharacteristic
399C23×C73H(5,𝔽2)11yescharacteristic
400C23×C73H(5,𝔽2)11yescharacteristic
401C23×C732−1+411yescharacteristic
402C23×C732−1+411yescharacteristic
403C23×C732−1+411yescharacteristic
404D4×C73—416no—
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—22no—
435C2×C4×C73—416no—
436C2×C4×C73—416no—
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—41no—
492C2×C4×C73—41no—
493C2×C4×C73—41no—
494C2×C4×C73—41no—
495C2×C4×C73—41no—
496C2×C4×C73—41no—
497C2×C4×C73#12314yescomplemented
498C22×C73—24no—
499C22×C73—24no—
500C22×C73—24no—
501C22×C73—24no—
502C22×C73—24no—
503C22×C73—24no—
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—42no—
516C22×C73—42no—
517C22×C73—42no—
518C22×C73—42no—
519C22×C73—42no—
520C22×C73—42no—
521C22×C73—42no—
522C22×C73—42no—
523C22×C73—42no—
524C22×C73—42no—
525C22×C73—42no—
526C22×C73—42no—
527C22×C73—42no—
528C22×C73C2×#12011yescharacteristic
529C22×C73C2×#12111yescharacteristic
530C22×C73C2×#12311yescharacteristic
531C22×C73#52511yescharacteristic
532C22×C73#52911yescharacteristic
533C22×C73#53211yescharacteristic
534C22×C73#53411yescharacteristic
535C22×C73#53611yescharacteristic
536C22×C73#53611yescharacteristic
537C22×C73#53711yescharacteristic
538C22×C73#53811yescharacteristic
539C22×C73#53911yescharacteristic
540C22×C73#53911yescharacteristic
541C22×C73#54211yescharacteristic
542C22×C73#54211yescharacteristic
543C22×C73D4211yescharacteristic
544C22×C73D4211yescharacteristic
545C22×C73#54611yescharacteristic
546C22×C73#54611yescharacteristic
547C22×C73#54611yescharacteristic
548C22×C73#54611yescharacteristic
549C22×C73#54611yescharacteristic
550C22×C73#54711yescharacteristic
551C22×C73#54711yescharacteristic
552C22×C73#54711yescharacteristic
553C22×C73#54711yescharacteristic
554C22×C73#54711yescharacteristic
555C22×C73#54711yescharacteristic
556C22×C73#54711yescharacteristic
557C22×C73#55111yescharacteristic
558C22×C73#55211yescharacteristic
559C22×C73#55211yescharacteristic
560C22×C73#55311yescharacteristic
561C22×C73#56211yescharacteristic
562C22×C73#56311yescharacteristic
563C4×C73—24no—
564C4×C73—42no—
565C4×C73—42no—
566C4×C73—42no—
567C4×C73—42no—
568C4×C73—42no—
569C4×C73—42no—
570C4×C73—42no—
571C4×C73—42no—
572C4×C73—81no—
573C4×C73—81no—
574C4×C73—81no—
575C4×C73—81no—
576#15269C7311yesmaximal, characteristic, direct product factor, Sylow
577C2×C73—44no—
578C2×C73—44no—
579C2×C73#240611yescharacteristic
580C2×C73#241011yescharacteristic
581C2×C73#241811yescharacteristic
582C2×C73#242211yescharacteristic
583C2×C73#242511yescharacteristic
584C2×C73#243011yescharacteristic
585C2×C73#247011yescharacteristic
586C2×C73#248611yescharacteristic
587C2×C73#255311yescharacteristic
588C2×C73#267211yescharacteristic
589C2×C73#268011yescharacteristic
590C2×C73#268711yescharacteristic
591C2×C73#269511yescharacteristic
592C2×C73#270811yescharacteristic
593C2×C73#271711yescharacteristic
594C22×#123C2×C7311yescharacteristic
595C2×#397C2×C7311yescharacteristic, complemented
596C2×#394C2×C7311yescharacteristic
597C2×#386C2×C7311yescharacteristic
598C2×#385C2×C7311yescharacteristic, complemented
599C2×#380C2×C7311yescharacteristic, complemented
600#1444C2×C7311yescharacteristic, complemented
601#1444C2×C7311yescharacteristic, complemented
602#1442C2×C7311yescharacteristic, complemented
603#1441C2×C7311yescharacteristic, complemented
604#1440C2×C7311yescharacteristic, complemented
605#1440C2×C7311yescharacteristic, complemented
606#1439C2×C7311yescharacteristic, complemented
607C22⋊#95C2×C7311yescharacteristic, complemented
608C22⋊#95C2×C7311yescharacteristic, complemented
609C73#1526911yescharacteristic, direct product factor, Sylow
610C23×D4C22×C7311yescharacteristic
611C24×C4C22×C7311yescharacteristic
612C24×C4C22×C7311yescharacteristic
613C2×#123—24no—
614C2×#123—24no—
615C2×#123—24no—
616C22×C4⋊C4C22×C7311yescharacteristic
617C22×C4⋊C4C22×C7311yescharacteristic
618C22×C4⋊C4C22×C7311yescharacteristic
619C22×C4⋊C4C22×C7311yescharacteristic
620C22×C4⋊C4C22×C7311yescharacteristic
621C22×C4⋊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×C22⋊C4C22×C7311yescharacteristic
629C22×C22⋊C4C22×C7311yescharacteristic
630C22×C22⋊C4C22×C7311yescharacteristic
631C22×C22⋊C4C22×C7311yescharacteristic
632#397—24no—
633#394—24no—
634#386—24no—
635#385—24no—
636#380—24no—
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
648C2×#95C22×C7311yescharacteristic
649C2×#95C22×C7311yescharacteristic
650C2×#95C22×C7311yescharacteristic
651C2×#95C22×C7311yescharacteristic
652C2×#95C22×C7311yescharacteristic
653C25C23×C7311yescharacteristic
654C25C23×C7311yescharacteristic
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—41no—
660C22×D4—41no—
661C22×D4D4×C7314yes—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4—41no—
676C23×C4C23×C7311yescharacteristic
677C23×C4C23×C7311yescharacteristic
678C23×C4C23×C7311yescharacteristic
679C23×C4C23×C7311yescharacteristic
680C23×C4C23×C7311yescharacteristic
681C23×C4C23×C7311yescharacteristic
682C23×C4C23×C7311yescharacteristic
683C23×C4C23×C7311yescharacteristic
684C23×C4C23×C7311yescharacteristic
685C23×C4C23×C7311yescharacteristic
686C23×C4C23×C7311yescharacteristic
687C23×C4C23×C7311yescharacteristic
688C23×C4C23×C7311yescharacteristic
689#123—232no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—41no—
704C2×C4⋊C4—41no—
705C2×C4⋊C4—41no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
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—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4D4×C7314yes—
736C2×C22⋊C4D4×C7314yes—
737C2×C22⋊C4D4×C7314yes—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—22no—
750#95—22no—
751#95—41no—
752#95—41no—
753#95—41no—
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—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C2×D4×C7312yes—
779C24C2×D4×C7312yes—
780C24C2×D4×C7312yes—
781C24C2×D4×C7312yes—
782C24C2×D4×C7312yes—
783C24#41×C7312yes—
784C24C24×C7311yescharacteristic
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—28no—
797C22×C4—28no—
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—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4C2×D4×C7312yes—
887C22×C4C2×D4×C7312yes—
888C22×C4C2×D4×C7312yes—
889C22×C4C2×D4×C7312yes—
890C22×C4C2×D4×C7312yes—
891C22×C4C2×D4×C7312yes—
892C22×C4C2×D4×C7312yes—
893C22×C4#41×C7312yes—
894C22×C4#41×C7312yes—
895C22×C4#41×C7312yes—
896C22×C4#41×C7312yes—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
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—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23#120×C7314yes—
982C23#121×C7314yes—
983C23C22×D4×C7311yescharacteristic
984C23C22×D4×C7311yescharacteristic
985C23C22×D4×C7311yescharacteristic
986C23C22×D4×C7311yescharacteristic
987C23C2×#41×C7311yescharacteristic
988C23C2×#41×C7311yescharacteristic
989C23C2×#41×C7311yescharacteristic
990C23C2×#41×C7311yescharacteristic
991C23C2×#41×C7311yescharacteristic
992C23H(5,𝔽2)×C7311yescharacteristic
993C23H(5,𝔽2)×C7311yescharacteristic
994C23H(5,𝔽2)×C7311yescharacteristic
995C232−1+4×C7311yescharacteristic
996C232−1+4×C7311yescharacteristic
997C232−1+4×C7311yescharacteristic
998D4—416no—
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—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
1030C2×C4—416no—
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—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4#123×C7314yescomplemented
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22C2×#120×C7311yescharacteristic
1123C22C2×#121×C7311yescharacteristic
1124C22C2×#123×C7311yescharacteristic
1125C22#525×C7311yescharacteristic
1126C22#529×C7311yescharacteristic
1127C22#532×C7311yescharacteristic
1128C22#534×C7311yescharacteristic
1129C22#536×C7311yescharacteristic
1130C22#536×C7311yescharacteristic
1131C22#537×C7311yescharacteristic
1132C22#538×C7311yescharacteristic
1133C22#539×C7311yescharacteristic
1134C22#539×C7311yescharacteristic
1135C22#542×C7311yescharacteristic
1136C22#542×C7311yescharacteristic
1137C22D42×C7311yescharacteristic
1138C22D42×C7311yescharacteristic
1139C22#546×C7311yescharacteristic
1140C22#546×C7311yescharacteristic
1141C22#546×C7311yescharacteristic
1142C22#546×C7311yescharacteristic
1143C22#546×C7311yescharacteristic
1144C22#547×C7311yescharacteristic
1145C22#547×C7311yescharacteristic
1146C22#547×C7311yescharacteristic
1147C22#547×C7311yescharacteristic
1148C22#547×C7311yescharacteristic
1149C22#547×C7311yescharacteristic
1150C22#547×C7311yescharacteristic
1151C22#551×C7311yescharacteristic
1152C22#552×C7311yescharacteristic
1153C22#552×C7311yescharacteristic
1154C22#553×C7311yescharacteristic
1155C22#562×C7311yescharacteristic
1156C22#563×C7311yescharacteristic
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—44no—
1172C2C73×#240611yescharacteristic
1173C2C73×#241011yescharacteristic
1174C2C73×#241811yescharacteristic
1175C2C73×#242211yescharacteristic
1176C2C73×#242511yescharacteristic
1177C2C73×#243011yescharacteristic
1178C2C73×#247011yescharacteristic
1179C2C73×#248611yescharacteristic
1180C2C73×#255311yescharacteristic
1181C2C73×#267211yescharacteristic
1182C2C73×#268011yescharacteristic
1183C2C73×#268711yescharacteristic
1184C2C73×#269511yescharacteristic
1185C2C73×#270811yescharacteristic
1186C2C73×#271711yescharacteristic
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×#397×C73C2semidirect
5. C2×#385×C73C2semidirect
6. C2×#380×C73C2semidirect
7. C73×#1444C2semidirect
8. C73×#1444C2semidirect
9. C73×#1442C2semidirect
10. C73×#1441C2semidirect
11. C73×#1440C2semidirect
12. C73×#1440C2semidirect
13. C73×#1439C2semidirect
14. C73×C22⋊#95C2semidirect
15. C73×C22⋊#95C2semidirect
497. C2×C4×C73#123semidirect
576. #15269C73direct (N × H)
595. C2×#397C2×C73semidirect
598. C2×#385C2×C73semidirect
599. C2×#380C2×C73semidirect
600. #1444C2×C73semidirect
601. #1444C2×C73semidirect
602. #1442C2×C73semidirect
603. #1441C2×C73semidirect
604. #1440C2×C73semidirect
605. #1440C2×C73semidirect
606. #1439C2×C73semidirect
607. C22⋊#95C2×C73semidirect
608. C22⋊#95C2×C73semidirect
609. C73#15269direct (N × H)
1091. 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×#397×C732
C2×#394×C732
C2×#386×C732
C2×#385×C732
C2×#380×C732
C73×#14442
C73×#14422
C73×#14412
C73×#14402
C73×#14392
C73×C22⋊#952
#1526973