Finite Group Databasebeta

← C73×#15280 #32924684

Subgroups — C73×#15280 #32924684

Order 18688.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
2C2×#396×C73C211yesmaximal, characteristic, complemented
3C2×#393×C73C211yesmaximal, characteristic, complemented
4C2×#391×C73C211yesmaximal, characteristic, complemented
5C2×#390×C73C211yesmaximal, characteristic
6C2×#386×C73C211yesmaximal, characteristic
7C73×#1444C211yesmaximal, characteristic, complemented
8C73×#1441C211yesmaximal, characteristic, complemented
9C73×#1439C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic, complemented
12C73×#1439C211yesmaximal, characteristic, complemented
13C73×#1438C211yesmaximal, characteristic
14C73×#1436C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C24×C4×C73C2211yescharacteristic
19C2×C22⋊Q8×C73—24no—
20C2×C22⋊Q8×C73—24no—
21C2×C22⋊Q8×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
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C42×C73C2211yescharacteristic
40#396×C73—24no—
41#393×C73—24no—
42#391×C73—24no—
43#390×C73—24no—
44#386×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×Q8×C73—22no—
62C22×Q8×C73—22no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—41no—
66C22×Q8×C73—41no—
67C22×Q8×C73D414yescomplemented
68C22×D4×C73—22no—
69C22×D4×C73—22no—
70C22×D4×C73—22no—
71C22×D4×C73—22no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73Q814yescomplemented
75C23×C4×C73—22no—
76C23×C4×C73—22no—
77C23×C4×C73—22no—
78C23×C4×C73—22no—
79C23×C4×C73—22no—
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
95C22⋊Q8×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×C73D414yescomplemented
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×C73—41no—
143C2×C22⋊C4×C73—41no—
144C2×C22⋊C4×C73—41no—
145C2×C22⋊C4×C73—41no—
146C2×C22⋊C4×C73D414yes—
147C2×C42×C73—22no—
148C2×C42×C73—22no—
149C2×C42×C73—41no—
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—22no—
158#95×C73—22no—
159#95×C73—22no—
160#95×C73—41no—
161#95×C73—41no—
162#95×C73—41no—
163#95×C73D414yes—
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×C73—21no—
187C24×C73—21no—
188C24×C73—21no—
189C24×C73—21no—
190C24×C73C2×D412yes—
191C24×C73C2×Q812yes—
192C24×C73C2×Q812yes—
193C24×C73#4112yes—
194C24×C73C2411yescharacteristic
195C2×Q8×C73—28no—
196C2×Q8×C73—28no—
197C2×Q8×C73—44no—
198C2×Q8×C73—44no—
199C2×Q8×C73—44no—
200C2×Q8×C73—44no—
201C2×Q8×C73—44no—
202C2×D4×C73—28no—
203C2×D4×C73—28no—
204C2×D4×C73—44no—
205C2×D4×C73—44no—
206C2×D4×C73—44no—
207C2×D4×C73—44no—
208C2×D4×C73—44no—
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—28no—
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—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
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×C73C2×D412yes—
300C22×C4×C73C2×D412yes—
301C22×C4×C73C2×D412yes—
302C22×C4×C73C2×D412yes—
303C22×C4×C73C2×Q812yes—
304C22×C4×C73#4112yes—
305C22×C4×C73#4112yes—
306C22×C4×C73#4112yes—
307C4⋊C4×C73—28no—
308C4⋊C4×C73—28no—
309C4⋊C4×C73—28no—
310C4⋊C4×C73—44no—
311C4⋊C4×C73—44no—
312C4⋊C4×C73—44no—
313C22⋊C4×C73—28no—
314C22⋊C4×C73—28no—
315C22⋊C4×C73—44no—
316C22⋊C4×C73—44no—
317C22⋊C4×C73—44no—
318C22⋊C4×C73—44no—
319C22⋊C4×C73—44no—
320C22⋊C4×C73—44no—
321C22⋊C4×C73—44no—
322C22⋊C4×C73—44no—
323C22⋊C4×C73—44no—
324C42×C73—44no—
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—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—41no—
385C23×C73—41no—
386C23×C73—41no—
387C23×C73—41no—
388C23×C73—41no—
389C23×C73—41no—
390C23×C73—41no—
391C23×C73—41no—
392C23×C73—41no—
393C23×C73—41no—
394C23×C73C22⋊Q814yes—
395C23×C73C22×D411yescharacteristic
396C23×C73C22×D411yescharacteristic
397C23×C73C22×D411yescharacteristic
398C23×C73C22×D411yescharacteristic
399C23×C73C22×Q811yescharacteristic
400C23×C73C2×#4111yescharacteristic
401C23×C73C2×#4111yescharacteristic
402C23×C73C2×#4111yescharacteristic
403C23×C73C2×#4111yescharacteristic
404C23×C73H(5,𝔽2)11yescharacteristic
405C23×C73H(5,𝔽2)11yescharacteristic
406C23×C73H(5,𝔽2)11yescharacteristic
407C23×C73H(5,𝔽2)11yescharacteristic
408C23×C732−1+411yescharacteristic
409C23×C732−1+411yescharacteristic
410Q8×C73—416no—
411D4×C73—416no—
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—22no—
436C2×C4×C73—22no—
437C2×C4×C73—22no—
438C2×C4×C73—22no—
439C2×C4×C73—22no—
440C2×C4×C73—22no—
441C2×C4×C73—22no—
442C2×C4×C73—22no—
443C2×C4×C73—22no—
444C2×C4×C73—22no—
445C2×C4×C73—22no—
446C2×C4×C73—22no—
447C2×C4×C73—22no—
448C2×C4×C73—416no—
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—41no—
498C2×C4×C73—41no—
499C2×C4×C73—41no—
500C2×C4×C73—41no—
501C2×C4×C73#12014yes—
502C2×C4×C73#12114yes—
503C2×C4×C73C22⋊Q814yescomplemented
504C22×C73—24no—
505C22×C73—24no—
506C22×C73—24no—
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—81no—
527C22×C73—81no—
528C22×C73—81no—
529C22×C73—81no—
530C22×C73—81no—
531C22×C73—81no—
532C22×C73—81no—
533C22×C73—81no—
534C22×C73C2×#12011yescharacteristic
535C22×C73C2×#12111yescharacteristic
536C22×C73C2×C22⋊Q811yescharacteristic
537C22×C73C2×C22⋊Q811yescharacteristic
538C22×C73#52911yescharacteristic
539C22×C73#53211yescharacteristic
540C22×C73#53411yescharacteristic
541C22×C73#53511yescharacteristic
542C22×C73#53611yescharacteristic
543C22×C73#53711yescharacteristic
544C22×C73#53811yescharacteristic
545C22×C73#53911yescharacteristic
546C22×C73#54211yescharacteristic
547C22×C73#54211yescharacteristic
548C22×C73#54311yescharacteristic
549C22×C73D4211yescharacteristic
550C22×C73D4211yescharacteristic
551C22×C73#54611yescharacteristic
552C22×C73#54611yescharacteristic
553C22×C73#54611yescharacteristic
554C22×C73#54611yescharacteristic
555C22×C73#54611yescharacteristic
556C22×C73#54811yescharacteristic
557C22×C73#54811yescharacteristic
558C22×C73#54811yescharacteristic
559C22×C73D4×Q811yescharacteristic
560C22×C73D4×Q811yescharacteristic
561C22×C73#55011yescharacteristic
562C22×C73#55011yescharacteristic
563C22×C73#55111yescharacteristic
564C22×C73#55411yescharacteristic
565C22×C73#55411yescharacteristic
566C22×C73#55611yescharacteristic
567C22×C73#56211yescharacteristic
568C22×C73#56211yescharacteristic
569C4×C73—24no—
570C4×C73—24no—
571C4×C73—24no—
572C4×C73—42no—
573C4×C73—42no—
574C4×C73—42no—
575C4×C73—42no—
576C4×C73—42no—
577C4×C73—42no—
578C4×C73—81no—
579C4×C73—81no—
580C4×C73—81no—
581C4×C73—81no—
582#15280C7311yesmaximal, characteristic, direct product factor, Sylow
583C2×C73—44no—
584C2×C73—82no—
585C2×C73#240911yescharacteristic
586C2×C73#241011yescharacteristic
587C2×C73#242611yescharacteristic
588C2×C73#243111yescharacteristic
589C2×C73#243711yescharacteristic
590C2×C73#245011yescharacteristic
591C2×C73#245211yescharacteristic
592C2×C73#253811yescharacteristic
593C2×C73#256011yescharacteristic
594C2×C73#267611yescharacteristic
595C2×C73#268111yescharacteristic
596C2×C73#269211yescharacteristic
597C2×C73#270011yescharacteristic
598C2×C73#273011yescharacteristic
599C2×C73#273211yescharacteristic
600C22×C22⋊Q8C2×C7311yescharacteristic, complemented
601C2×#396C2×C7311yescharacteristic, complemented
602C2×#393C2×C7311yescharacteristic, complemented
603C2×#391C2×C7311yescharacteristic, complemented
604C2×#390C2×C7311yescharacteristic
605C2×#386C2×C7311yescharacteristic
606#1444C2×C7311yescharacteristic, complemented
607#1441C2×C7311yescharacteristic, complemented
608#1439C2×C7311yescharacteristic, complemented
609#1439C2×C7311yescharacteristic, complemented
610#1439C2×C7311yescharacteristic, complemented
611#1439C2×C7311yescharacteristic, complemented
612#1438C2×C7311yescharacteristic
613#1436C2×C7311yescharacteristic, complemented
614C22⋊#95C2×C7311yescharacteristic, complemented
615C73#1528011yescharacteristic, direct product factor, Sylow
616C23×Q8C22×C7311yescharacteristic
617C23×D4C22×C7311yescharacteristic
618C24×C4C22×C7311yescharacteristic
619C2×C22⋊Q8—24no—
620C2×C22⋊Q8—24no—
621C2×C22⋊Q8—24no—
622C22×C4⋊C4C22×C7311yescharacteristic
623C22×C4⋊C4C22×C7311yescharacteristic
624C22×C4⋊C4C22×C7311yescharacteristic
625C22×C4⋊C4C22×C7311yescharacteristic
626C22×C4⋊C4C22×C7311yescharacteristic
627C22×C4⋊C4C22×C7311yescharacteristic
628C22×C22⋊C4C22×C7311yescharacteristic
629C22×C22⋊C4C22×C7311yescharacteristic
630C22×C22⋊C4C22×C7311yescharacteristic
631C22×C22⋊C4C22×C7311yescharacteristic
632C22×C22⋊C4C22×C7311yescharacteristic
633C22×C22⋊C4C22×C7311yescharacteristic
634C22×C22⋊C4C22×C7311yescharacteristic
635C22×C22⋊C4C22×C7311yescharacteristic
636C22×C22⋊C4C22×C7311yescharacteristic
637C22×C22⋊C4C22×C7311yescharacteristic
638C22×C22⋊C4C22×C7311yescharacteristic
639C22×C42C22×C7311yescharacteristic
640#396—24no—
641#393—24no—
642#391—24no—
643#390—24no—
644#386—24no—
645C2×#95C22×C7311yescharacteristic
646C2×#95C22×C7311yescharacteristic
647C2×#95C22×C7311yescharacteristic
648C2×#95C22×C7311yescharacteristic
649C2×#95C22×C7311yescharacteristic
650C2×#95C22×C7311yescharacteristic
651C2×#95C22×C7311yescharacteristic
652C2×#95C22×C7311yescharacteristic
653C2×#95C22×C7311yescharacteristic
654C2×#95C22×C7311yescharacteristic
655C2×#95C22×C7311yescharacteristic
656C2×#95C22×C7311yescharacteristic
657C2×#95C22×C7311yescharacteristic
658C2×#95C22×C7311yescharacteristic
659C25C23×C7311yescharacteristic
660C25C23×C7311yescharacteristic
661C22×Q8—22no—
662C22×Q8—22no—
663C22×Q8—22no—
664C22×Q8—22no—
665C22×Q8—41no—
666C22×Q8—41no—
667C22×Q8D4×C7314yescomplemented
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—22no—
672C22×D4—41no—
673C22×D4—41no—
674C22×D4Q8×C7314yescomplemented
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4C23×C7311yescharacteristic
683C23×C4C23×C7311yescharacteristic
684C23×C4C23×C7311yescharacteristic
685C23×C4C23×C7311yescharacteristic
686C23×C4C23×C7311yescharacteristic
687C23×C4C23×C7311yescharacteristic
688C23×C4C23×C7311yescharacteristic
689C23×C4C23×C7311yescharacteristic
690C23×C4C23×C7311yescharacteristic
691C23×C4C23×C7311yescharacteristic
692C23×C4C23×C7311yescharacteristic
693C23×C4C23×C7311yescharacteristic
694C23×C4C23×C7311yescharacteristic
695C22⋊Q8—232no—
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—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4D4×C7314yescomplemented
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—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4D4×C7314yes—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—41no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—41no—
762#95—41no—
763#95D4×C7314yes—
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—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C2×D4×C7312yes—
791C24C2×Q8×C7312yes—
792C24C2×Q8×C7312yes—
793C24#41×C7312yes—
794C24C24×C7311yescharacteristic
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
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—28no—
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—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C7312yes—
893C22×C4C2×D4×C7312yes—
894C22×C4C2×D4×C7312yes—
895C22×C4C2×D4×C7312yes—
896C22×C4C2×D4×C7312yes—
897C22×C4C2×D4×C7312yes—
898C22×C4C2×D4×C7312yes—
899C22×C4C2×D4×C7312yes—
900C22×C4C2×D4×C7312yes—
901C22×C4C2×D4×C7312yes—
902C22×C4C2×D4×C7312yes—
903C22×C4C2×Q8×C7312yes—
904C22×C4#41×C7312yes—
905C22×C4#41×C7312yes—
906C22×C4#41×C7312yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—44no—
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—22no—
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—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C22⋊Q8×C7314yes—
995C23C22×D4×C7311yescharacteristic
996C23C22×D4×C7311yescharacteristic
997C23C22×D4×C7311yescharacteristic
998C23C22×D4×C7311yescharacteristic
999C23C22×Q8×C7311yescharacteristic
1000C23C2×#41×C7311yescharacteristic
1001C23C2×#41×C7311yescharacteristic
1002C23C2×#41×C7311yescharacteristic
1003C23C2×#41×C7311yescharacteristic
1004C23H(5,𝔽2)×C7311yescharacteristic
1005C23H(5,𝔽2)×C7311yescharacteristic
1006C23H(5,𝔽2)×C7311yescharacteristic
1007C23H(5,𝔽2)×C7311yescharacteristic
1008C232−1+4×C7311yescharacteristic
1009C232−1+4×C7311yescharacteristic
1010Q8—416no—
1011D4—416no—
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—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—416no—
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—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4#120×C7314yes—
1102C2×C4#121×C7314yes—
1103C2×C4C22⋊Q8×C7314yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
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—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×#120×C7311yescharacteristic
1135C22C2×#121×C7311yescharacteristic
1136C22C2×C22⋊Q8×C7311yescharacteristic
1137C22C2×C22⋊Q8×C7311yescharacteristic
1138C22#529×C7311yescharacteristic
1139C22#532×C7311yescharacteristic
1140C22#534×C7311yescharacteristic
1141C22#535×C7311yescharacteristic
1142C22#536×C7311yescharacteristic
1143C22#537×C7311yescharacteristic
1144C22#538×C7311yescharacteristic
1145C22#539×C7311yescharacteristic
1146C22#542×C7311yescharacteristic
1147C22#542×C7311yescharacteristic
1148C22#543×C7311yescharacteristic
1149C22D42×C7311yescharacteristic
1150C22D42×C7311yescharacteristic
1151C22#546×C7311yescharacteristic
1152C22#546×C7311yescharacteristic
1153C22#546×C7311yescharacteristic
1154C22#546×C7311yescharacteristic
1155C22#546×C7311yescharacteristic
1156C22#548×C7311yescharacteristic
1157C22#548×C7311yescharacteristic
1158C22#548×C7311yescharacteristic
1159C22D4×Q8×C7311yescharacteristic
1160C22D4×Q8×C7311yescharacteristic
1161C22#550×C7311yescharacteristic
1162C22#550×C7311yescharacteristic
1163C22#551×C7311yescharacteristic
1164C22#554×C7311yescharacteristic
1165C22#554×C7311yescharacteristic
1166C22#556×C7311yescharacteristic
1167C22#562×C7311yescharacteristic
1168C22#562×C7311yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—82no—
1184C2C73×#240911yescharacteristic
1185C2C73×#241011yescharacteristic
1186C2C73×#242611yescharacteristic
1187C2C73×#243111yescharacteristic
1188C2C73×#243711yescharacteristic
1189C2C73×#245011yescharacteristic
1190C2C73×#245211yescharacteristic
1191C2C73×#253811yescharacteristic
1192C2C73×#256011yescharacteristic
1193C2C73×#267611yescharacteristic
1194C2C73×#268111yescharacteristic
1195C2C73×#269211yescharacteristic
1196C2C73×#270011yescharacteristic
1197C2C73×#273011yescharacteristic
1198C2C73×#273211yescharacteristic
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
1. C22×C22⋊Q8×C73C2semidirect
2. C2×#396×C73C2semidirect
3. C2×#393×C73C2semidirect
4. C2×#391×C73C2semidirect
7. C73×#1444C2semidirect
8. C73×#1441C2semidirect
9. C73×#1439C2semidirect
10. C73×#1439C2semidirect
11. C73×#1439C2semidirect
12. C73×#1439C2semidirect
14. C73×#1436C2semidirect
15. C73×C22⋊#95C2semidirect
67. C22×Q8×C73D4semidirect
74. C22×D4×C73Q8semidirect
113. C2×C4⋊C4×C73D4semidirect
503. C2×C4×C73C22⋊Q8semidirect
582. #15280C73direct (N × H)
600. C22×C22⋊Q8C2×C73semidirect
601. C2×#396C2×C73semidirect
602. C2×#393C2×C73semidirect
603. C2×#391C2×C73semidirect
606. #1444C2×C73semidirect
607. #1441C2×C73semidirect
608. #1439C2×C73semidirect
609. #1439C2×C73semidirect
610. #1439C2×C73semidirect
611. #1439C2×C73semidirect
613. #1436C2×C73semidirect
614. C22⋊#95C2×C73semidirect
615. C73#15280direct (N × H)
667. C22×Q8D4×C73semidirect
674. C22×D4Q8×C73semidirect
713. C2×C4⋊C4D4×C73semidirect
1103. C2×C4C22⋊Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C732
C2×#396×C732
C2×#393×C732
C2×#391×C732
C2×#390×C732
C2×#386×C732
C73×#14442
C73×#14412
C73×#14392
C73×#14382
C73×#14362
C73×C22⋊#952
#1528073