Finite Group Databasebeta

← C73×#16294 #32925698

Subgroups — C73×#16294 #32925698

Order 18688.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C73C211yesmaximal, characteristic
2C2×#394×C73C211yesmaximal, characteristic
3C2×#393×C73C211yesmaximal, characteristic, complemented
4C2×#393×C73C211yesmaximal, characteristic, complemented
5C2×#391×C73C211yesmaximal, characteristic, complemented
6C2×#388×C73C211yesmaximal, characteristic, complemented
7C73×#1444C211yesmaximal, characteristic, complemented
8C73×#1443C211yesmaximal, characteristic, complemented
9C73×#1441C211yesmaximal, characteristic, complemented
10C73×#1440C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic, complemented
12C73×#1439C211yesmaximal, characteristic, complemented
13C73×#1439C211yesmaximal, characteristic, complemented
14C73×#1438C211yesmaximal, characteristic
15C73×#1437C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C22⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊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×C42×C73C2211yescharacteristic
35#394×C73—24no—
36#394×C73—24no—
37#393×C73—24no—
38#393×C73—24no—
39#391×C73—24no—
40#388×C73—24no—
41C2×#95×C73C2211yescharacteristic
42C2×#95×C73C2211yescharacteristic
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
57C25×C73C2311yescharacteristic
58C25×C73C2311yescharacteristic
59C22×Q8×C73—22no—
60C22×Q8×C73—22no—
61C22×Q8×C73—22no—
62C22×Q8×C73—22no—
63C22×Q8×C73—22no—
64C22×Q8×C73—41no—
65C22×Q8×C73—41no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
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
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—41no—
92C2×C4⋊C4×C73—41no—
93C2×C4⋊C4×C73—41no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73—41no—
96C2×C4⋊C4×C73—41no—
97C2×C4⋊C4×C73—41no—
98C2×C22⋊C4×C73—22no—
99C2×C22⋊C4×C73—22no—
100C2×C22⋊C4×C73—22no—
101C2×C22⋊C4×C73—22no—
102C2×C22⋊C4×C73—22no—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73—22no—
105C2×C22⋊C4×C73—22no—
106C2×C22⋊C4×C73—22no—
107C2×C22⋊C4×C73—22no—
108C2×C22⋊C4×C73—22no—
109C2×C22⋊C4×C73—22no—
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—41no—
122C2×C22⋊C4×C73—41no—
123C2×C22⋊C4×C73—41no—
124C2×C22⋊C4×C73—41no—
125C2×C22⋊C4×C73—41no—
126C2×C22⋊C4×C73—41no—
127C2×C22⋊C4×C73—41no—
128C2×C22⋊C4×C73—41no—
129C2×C22⋊C4×C73—41no—
130C2×C22⋊C4×C73—41no—
131C2×C22⋊C4×C73—41no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73D414yes—
134C2×C42×C73—22no—
135C2×C42×C73—22no—
136C2×C42×C73—41no—
137#95×C73—22no—
138#95×C73—22no—
139#95×C73—22no—
140#95×C73—22no—
141#95×C73—22no—
142#95×C73—22no—
143#95×C73—22no—
144#95×C73—22no—
145#95×C73—22no—
146#95×C73—22no—
147#95×C73—41no—
148#95×C73—41no—
149#95×C73—41no—
150#95×C73—41no—
151#95×C73D414yes—
152#95×C73D414yescomplemented
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—21no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—21no—
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×C73C2×D412yes—
182C24×C73#4112yes—
183C24×C73C2411yescharacteristic
184C2×Q8×C73—28no—
185C2×Q8×C73—44no—
186C2×Q8×C73—44no—
187C2×Q8×C73—44no—
188C2×Q8×C73—44no—
189C2×Q8×C73—44no—
190C2×Q8×C73—44no—
191C2×D4×C73—44no—
192C2×D4×C73—44no—
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—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×C73C2×D412yes—
279C22×C4×C73C2×D412yes—
280C22×C4×C73C2×D412yes—
281C22×C4×C73C2×D412yes—
282C22×C4×C73C2×D412yes—
283C22×C4×C73C2×D412yes—
284C22×C4×C73C2×D412yes—
285C22×C4×C73C2×D412yes—
286C22×C4×C73#4112yes—
287C22×C4×C73#4112yes—
288C22×C4×C73#4112yes—
289C4⋊C4×C73—44no—
290C4⋊C4×C73—44no—
291C4⋊C4×C73—44no—
292C4⋊C4×C73—44no—
293C22⋊C4×C73—28no—
294C22⋊C4×C73—44no—
295C22⋊C4×C73—44no—
296C22⋊C4×C73—44no—
297C22⋊C4×C73—44no—
298C22⋊C4×C73—44no—
299C22⋊C4×C73—44no—
300C22⋊C4×C73—44no—
301C22⋊C4×C73—44no—
302C22⋊C4×C73—44no—
303C22⋊C4×C73—44no—
304C22⋊C4×C73—44no—
305C42×C73—44no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73—22no—
311C23×C73—22no—
312C23×C73—22no—
313C23×C73—22no—
314C23×C73—22no—
315C23×C73—22no—
316C23×C73—22no—
317C23×C73—22no—
318C23×C73—22no—
319C23×C73—22no—
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—41no—
334C23×C73—41no—
335C23×C73—41no—
336C23×C73—41no—
337C23×C73—41no—
338C23×C73—41no—
339C23×C73—41no—
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×C73C22×D411yescharacteristic
377C23×C73C22×D411yescharacteristic
378C23×C73C22×D411yescharacteristic
379C23×C73C2×#4111yescharacteristic
380C23×C73C2×#4111yescharacteristic
381C23×C73C2×#4111yescharacteristic
382C23×C73C2×#4111yescharacteristic
383C23×C73H(5,𝔽2)11yescharacteristic
384C23×C73H(5,𝔽2)11yescharacteristic
385C23×C73H(5,𝔽2)11yescharacteristic
386C23×C73H(5,𝔽2)11yescharacteristic
387C23×C73H(5,𝔽2)11yescharacteristic
388C23×C732−1+411yescharacteristic
389C23×C732−1+411yescharacteristic
390C23×C732−1+411yescharacteristic
391Q8×C73—416no—
392D4×C73—416no—
393C2×C4×C73—22no—
394C2×C4×C73—22no—
395C2×C4×C73—22no—
396C2×C4×C73—22no—
397C2×C4×C73—22no—
398C2×C4×C73—22no—
399C2×C4×C73—22no—
400C2×C4×C73—22no—
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—41no—
424C2×C4×C73—41no—
425C2×C4×C73—41no—
426C2×C4×C73—41no—
427C2×C4×C73—41no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73—41no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73—41no—
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#12114yes—
484C22×C73—42no—
485C22×C73—42no—
486C22×C73—42no—
487C22×C73—42no—
488C22×C73—42no—
489C22×C73—42no—
490C22×C73—42no—
491C22×C73—42no—
492C22×C73—42no—
493C22×C73—42no—
494C22×C73—42no—
495C22×C73—42no—
496C22×C73—42no—
497C22×C73—42no—
498C22×C73—81no—
499C22×C73—81no—
500C22×C73—81no—
501C22×C73—81no—
502C22×C73—81no—
503C22×C73—81no—
504C22×C73—81no—
505C22×C73—81no—
506C22×C73—81no—
507C22×C73—81no—
508C22×C73—81no—
509C22×C73—81no—
510C22×C73—81no—
511C22×C73—81no—
512C22×C73—81no—
513C22×C73—81no—
514C22×C73C2×#12111yescharacteristic
515C22×C73#52511yescharacteristic
516C22×C73#52911yescharacteristic
517C22×C73#53511yescharacteristic
518C22×C73#53511yescharacteristic
519C22×C73#53611yescharacteristic
520C22×C73#53611yescharacteristic
521C22×C73#53711yescharacteristic
522C22×C73#53711yescharacteristic
523C22×C73#53811yescharacteristic
524C22×C73#53811yescharacteristic
525C22×C73#53811yescharacteristic
526C22×C73#53911yescharacteristic
527C22×C73#54211yescharacteristic
528C22×C73#54211yescharacteristic
529C22×C73#54211yescharacteristic
530C22×C73#54211yescharacteristic
531C22×C73#54211yescharacteristic
532C22×C73#54211yescharacteristic
533C22×C73D4211yescharacteristic
534C22×C73D4211yescharacteristic
535C22×C73#54611yescharacteristic
536C22×C73#54611yescharacteristic
537C22×C73#54611yescharacteristic
538C22×C73#54611yescharacteristic
539C22×C73#54611yescharacteristic
540C22×C73#54711yescharacteristic
541C22×C73#54811yescharacteristic
542C22×C73#54811yescharacteristic
543C22×C73#55211yescharacteristic
544C22×C73#55911yescharacteristic
545C22×C73H(3,𝔽4)11yescharacteristic
546C22×C73#56211yescharacteristic
547C22×C73#56211yescharacteristic
548C22×C73#56311yescharacteristic
549C4×C73—24no—
550C4×C73—42no—
551C4×C73—42no—
552C4×C73—42no—
553C4×C73—42no—
554C4×C73—42no—
555C4×C73—42no—
556C4×C73—42no—
557C4×C73—42no—
558C4×C73—81no—
559C4×C73—81no—
560C4×C73—81no—
561C4×C73—81no—
562#16294C7311yesmaximal, characteristic, direct product factor, Sylow
563C2×C73—82no—
564C2×C73—82no—
565C2×C73#242411yescharacteristic
566C2×C73#242711yescharacteristic
567C2×C73#245811yescharacteristic
568C2×C73#262011yescharacteristic
569C2×C73#263211yescharacteristic
570C2×C73#265311yescharacteristic
571C2×C73#267011yescharacteristic
572C2×C73#267411yescharacteristic
573C2×C73#267611yescharacteristic
574C2×C73#268111yescharacteristic
575C2×C73#268711yescharacteristic
576C2×C73#270211yescharacteristic
577C2×C73#271011yescharacteristic
578C2×C73#271211yescharacteristic
579C2×C73#283211yescharacteristic
580C2×#394C2×C7311yescharacteristic
581C2×#394C2×C7311yescharacteristic
582C2×#393C2×C7311yescharacteristic, complemented
583C2×#393C2×C7311yescharacteristic, complemented
584C2×#391C2×C7311yescharacteristic, complemented
585C2×#388C2×C7311yescharacteristic, complemented
586#1444C2×C7311yescharacteristic, complemented
587#1443C2×C7311yescharacteristic, complemented
588#1441C2×C7311yescharacteristic, complemented
589#1440C2×C7311yescharacteristic, complemented
590#1439C2×C7311yescharacteristic, complemented
591#1439C2×C7311yescharacteristic, complemented
592#1439C2×C7311yescharacteristic, complemented
593#1438C2×C7311yescharacteristic
594#1437C2×C7311yescharacteristic, complemented
595C73#1629411yescharacteristic, direct product factor, Sylow
596C23×Q8C22×C7311yescharacteristic
597C23×D4C22×C7311yescharacteristic
598C22×C4⋊C4C22×C7311yescharacteristic
599C22×C4⋊C4C22×C7311yescharacteristic
600C22×C4⋊C4C22×C7311yescharacteristic
601C22×C4⋊C4C22×C7311yescharacteristic
602C22×C22⋊C4C22×C7311yescharacteristic
603C22×C22⋊C4C22×C7311yescharacteristic
604C22×C22⋊C4C22×C7311yescharacteristic
605C22×C22⋊C4C22×C7311yescharacteristic
606C22×C22⋊C4C22×C7311yescharacteristic
607C22×C22⋊C4C22×C7311yescharacteristic
608C22×C22⋊C4C22×C7311yescharacteristic
609C22×C22⋊C4C22×C7311yescharacteristic
610C22×C22⋊C4C22×C7311yescharacteristic
611C22×C22⋊C4C22×C7311yescharacteristic
612C22×C22⋊C4C22×C7311yescharacteristic
613C22×C22⋊C4C22×C7311yescharacteristic
614C22×C42C22×C7311yescharacteristic
615#394—24no—
616#394—24no—
617#393—24no—
618#393—24no—
619#391—24no—
620#388—24no—
621C2×#95C22×C7311yescharacteristic
622C2×#95C22×C7311yescharacteristic
623C2×#95C22×C7311yescharacteristic
624C2×#95C22×C7311yescharacteristic
625C2×#95C22×C7311yescharacteristic
626C2×#95C22×C7311yescharacteristic
627C2×#95C22×C7311yescharacteristic
628C2×#95C22×C7311yescharacteristic
629C2×#95C22×C7311yescharacteristic
630C2×#95C22×C7311yescharacteristic
631C2×#95C22×C7311yescharacteristic
632C2×#95C22×C7311yescharacteristic
633C2×#95C22×C7311yescharacteristic
634C2×#95C22×C7311yescharacteristic
635C2×#95C22×C7311yescharacteristic
636C2×#95C22×C7311yescharacteristic
637C25C23×C7311yescharacteristic
638C25C23×C7311yescharacteristic
639C22×Q8—22no—
640C22×Q8—22no—
641C22×Q8—22no—
642C22×Q8—22no—
643C22×Q8—22no—
644C22×Q8—41no—
645C22×Q8—41no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—41no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4—41no—
653C23×C4C23×C7311yescharacteristic
654C23×C4C23×C7311yescharacteristic
655C23×C4C23×C7311yescharacteristic
656C23×C4C23×C7311yescharacteristic
657C23×C4C23×C7311yescharacteristic
658C23×C4C23×C7311yescharacteristic
659C23×C4C23×C7311yescharacteristic
660C23×C4C23×C7311yescharacteristic
661C23×C4C23×C7311yescharacteristic
662C23×C4C23×C7311yescharacteristic
663C23×C4C23×C7311yescharacteristic
664C23×C4C23×C7311yescharacteristic
665C23×C4C23×C7311yescharacteristic
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4D4×C7314yes—
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—41no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95D4×C7314yes—
732#95D4×C7314yescomplemented
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24C2×D4×C7312yes—
762C24#41×C7312yes—
763C24C24×C7311yescharacteristic
764C2×Q8—28no—
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
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—21no—
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×C4C2×D4×C7312yes—
859C22×C4C2×D4×C7312yes—
860C22×C4C2×D4×C7312yes—
861C22×C4C2×D4×C7312yes—
862C22×C4C2×D4×C7312yes—
863C22×C4C2×D4×C7312yes—
864C22×C4C2×D4×C7312yes—
865C22×C4C2×D4×C7312yes—
866C22×C4#41×C7312yes—
867C22×C4#41×C7312yes—
868C22×C4#41×C7312yes—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C22⋊C4—28no—
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—
885C42—44no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
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—
956C23C22×D4×C7311yescharacteristic
957C23C22×D4×C7311yescharacteristic
958C23C22×D4×C7311yescharacteristic
959C23C2×#41×C7311yescharacteristic
960C23C2×#41×C7311yescharacteristic
961C23C2×#41×C7311yescharacteristic
962C23C2×#41×C7311yescharacteristic
963C23H(5,𝔽2)×C7311yescharacteristic
964C23H(5,𝔽2)×C7311yescharacteristic
965C23H(5,𝔽2)×C7311yescharacteristic
966C23H(5,𝔽2)×C7311yescharacteristic
967C23H(5,𝔽2)×C7311yescharacteristic
968C232−1+4×C7311yescharacteristic
969C232−1+4×C7311yescharacteristic
970C232−1+4×C7311yescharacteristic
971Q8—416no—
972D4—416no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
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—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
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#121×C7314yes—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×#121×C7311yescharacteristic
1095C22#525×C7311yescharacteristic
1096C22#529×C7311yescharacteristic
1097C22#535×C7311yescharacteristic
1098C22#535×C7311yescharacteristic
1099C22#536×C7311yescharacteristic
1100C22#536×C7311yescharacteristic
1101C22#537×C7311yescharacteristic
1102C22#537×C7311yescharacteristic
1103C22#538×C7311yescharacteristic
1104C22#538×C7311yescharacteristic
1105C22#538×C7311yescharacteristic
1106C22#539×C7311yescharacteristic
1107C22#542×C7311yescharacteristic
1108C22#542×C7311yescharacteristic
1109C22#542×C7311yescharacteristic
1110C22#542×C7311yescharacteristic
1111C22#542×C7311yescharacteristic
1112C22#542×C7311yescharacteristic
1113C22D42×C7311yescharacteristic
1114C22D42×C7311yescharacteristic
1115C22#546×C7311yescharacteristic
1116C22#546×C7311yescharacteristic
1117C22#546×C7311yescharacteristic
1118C22#546×C7311yescharacteristic
1119C22#546×C7311yescharacteristic
1120C22#547×C7311yescharacteristic
1121C22#548×C7311yescharacteristic
1122C22#548×C7311yescharacteristic
1123C22#552×C7311yescharacteristic
1124C22#559×C7311yescharacteristic
1125C22H(3,𝔽4)×C7311yescharacteristic
1126C22#562×C7311yescharacteristic
1127C22#562×C7311yescharacteristic
1128C22#563×C7311yescharacteristic
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—82no—
1143C2—82no—
1144C2C73×#242411yescharacteristic
1145C2C73×#242711yescharacteristic
1146C2C73×#245811yescharacteristic
1147C2C73×#262011yescharacteristic
1148C2C73×#263211yescharacteristic
1149C2C73×#265311yescharacteristic
1150C2C73×#267011yescharacteristic
1151C2C73×#267411yescharacteristic
1152C2C73×#267611yescharacteristic
1153C2C73×#268111yescharacteristic
1154C2C73×#268711yescharacteristic
1155C2C73×#270211yescharacteristic
1156C2C73×#271011yescharacteristic
1157C2C73×#271211yescharacteristic
1158C2C73×#283211yescharacteristic
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
3. C2×#393×C73C2semidirect
4. C2×#393×C73C2semidirect
5. C2×#391×C73C2semidirect
6. C2×#388×C73C2semidirect
7. C73×#1444C2semidirect
8. C73×#1443C2semidirect
9. C73×#1441C2semidirect
10. C73×#1440C2semidirect
11. C73×#1439C2semidirect
12. C73×#1439C2semidirect
13. C73×#1439C2semidirect
15. C73×#1437C2semidirect
152. #95×C73D4semidirect
562. #16294C73direct (N × H)
582. C2×#393C2×C73semidirect
583. C2×#393C2×C73semidirect
584. C2×#391C2×C73semidirect
585. C2×#388C2×C73semidirect
586. #1444C2×C73semidirect
587. #1443C2×C73semidirect
588. #1441C2×C73semidirect
589. #1440C2×C73semidirect
590. #1439C2×C73semidirect
591. #1439C2×C73semidirect
592. #1439C2×C73semidirect
594. #1437C2×C73semidirect
595. C73#16294direct (N × H)
732. #95D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C732
C2×#393×C732
C2×#391×C732
C2×#388×C732
C73×#14442
C73×#14432
C73×#14412
C73×#14402
C73×#14392
C73×#14382
C73×#14372
#1629473