Finite Group Databasebeta

← C73×#16535 #32925939

Subgroups — C73×#16535 #32925939

Order 18688.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C73C211yesmaximal, characteristic, complemented
2C2×#394×C73C211yesmaximal, characteristic, complemented
3C2×#392×C73C211yesmaximal, characteristic
4C2×#388×C73C211yesmaximal, characteristic, complemented
5C73×#1443C211yesmaximal, characteristic, complemented
6C73×#1442C211yesmaximal, characteristic, complemented
7C73×#1439C211yesmaximal, characteristic, complemented
8C73×#1439C211yesmaximal, characteristic, complemented
9C73×#1438C211yesmaximal, characteristic, complemented
10C73×#1438C211yesmaximal, characteristic, complemented
11C73×#1438C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1438C211yesmaximal, characteristic, complemented
14C73×#1437C211yesmaximal, characteristic, complemented
15C73×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C22⋊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×C22⋊C4×C73C2211yescharacteristic
35C22×C22⋊C4×C73C2211yescharacteristic
36C22×C42×C73C2211yescharacteristic
37#397×C73—24no—
38#394×C73—24no—
39#392×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
55C25×C73C2311yescharacteristic
56C25×C73C2311yescharacteristic
57C25×C73C2311yescharacteristic
58C22×D4×C73—22no—
59C22×D4×C73—22no—
60C22×D4×C73—22no—
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—41no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73—41no—
76C22×D4×C73—41no—
77C22×D4×C73—41no—
78C22×D4×C73—41no—
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
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73—41no—
96C2×C4⋊C4×C73—41no—
97C2×C22⋊C4×C73—22no—
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—41no—
118C2×C22⋊C4×C73—41no—
119C2×C22⋊C4×C73—41no—
120C2×C22⋊C4×C73—41no—
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×C73—41no—
134C2×C22⋊C4×C73—41no—
135C2×C22⋊C4×C73—41no—
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×C73D414yes—
142C2×C42×C73—22no—
143C2×C42×C73—41no—
144C2×C42×C73—41no—
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—41no—
152#95×C73—41no—
153#95×C73—41no—
154#95×C73—41no—
155#95×C73—41no—
156#95×C73—41no—
157#95×C73—41no—
158#95×C73D414yescomplemented
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×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×C73—21no—
191C24×C73—21no—
192C24×C73—21no—
193C24×C73—21no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73—21no—
197C24×C73—21no—
198C24×C73—21no—
199C24×C73—21no—
200C24×C73—21no—
201C24×C73C2×D412yes—
202C24×C73#4112yes—
203C24×C73#4112yes—
204C24×C73C2411yescharacteristic
205C2×D4×C73—44no—
206C2×D4×C73—44no—
207C2×D4×C73—44no—
208C2×D4×C73—44no—
209C2×D4×C73—44no—
210C2×D4×C73—44no—
211C2×D4×C73—44no—
212C2×D4×C73—44no—
213C2×D4×C73—44no—
214C2×D4×C73—44no—
215C2×D4×C73—44no—
216C2×D4×C73—44no—
217C2×D4×C73—44no—
218C2×D4×C73—44no—
219C2×D4×C73—44no—
220C2×D4×C73—44no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
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—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
298C22×C4×C73—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73C2×D412yes—
303C22×C4×C73C2×D412yes—
304C22×C4×C73C2×D412yes—
305C22×C4×C73C2×D412yes—
306C22×C4×C73C2×D412yes—
307C22×C4×C73#4112yes—
308C22×C4×C73#4112yes—
309C22×C4×C73#4112yes—
310C4⋊C4×C73—44no—
311C4⋊C4×C73—44no—
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—
319C22⋊C4×C73—44no—
320C22⋊C4×C73—44no—
321C22⋊C4×C73—44no—
322C22⋊C4×C73—44no—
323C22⋊C4×C73—44no—
324C22⋊C4×C73—44no—
325C22⋊C4×C73—44no—
326C22⋊C4×C73—44no—
327C42×C73—44no—
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—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—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×C73—41no—
395C23×C73—41no—
396C23×C73—41no—
397C23×C73—41no—
398C23×C73—41no—
399C23×C73—41no—
400C23×C73—41no—
401C23×C73—41no—
402C23×C73—41no—
403C23×C73—41no—
404C23×C73—41no—
405C23×C73—41no—
406C23×C73—41no—
407C23×C73—41no—
408C23×C73—41no—
409C23×C73—41no—
410C23×C73—41no—
411C23×C73—41no—
412C23×C73—41no—
413C23×C73—41no—
414C23×C73—41no—
415C23×C73—41no—
416C23×C73—41no—
417C23×C73—41no—
418C23×C73—41no—
419C23×C73—41no—
420C23×C73—41no—
421C23×C73—41no—
422C23×C73—41no—
423C23×C73—41no—
424C23×C73—41no—
425C23×C73—41no—
426C23×C73—41no—
427C23×C73—41no—
428C23×C73—41no—
429C23×C73—41no—
430C23×C73—41no—
431C23×C73—41no—
432C23×C73—41no—
433C23×C73C22×D411yescharacteristic
434C23×C73C22×D411yescharacteristic
435C23×C73C2×#4111yescharacteristic
436C23×C73C2×#4111yescharacteristic
437C23×C73C2×#4111yescharacteristic
438C23×C73C2×#4111yescharacteristic
439C23×C73C2×#4111yescharacteristic
440C23×C73H(5,𝔽2)11yescharacteristic
441C23×C73H(5,𝔽2)11yescharacteristic
442C23×C73H(5,𝔽2)11yescharacteristic
443C23×C73H(5,𝔽2)11yescharacteristic
444C23×C73H(5,𝔽2)11yescharacteristic
445C23×C73H(5,𝔽2)11yescharacteristic
446C23×C73H(5,𝔽2)11yescharacteristic
447C23×C73H(5,𝔽2)11yescharacteristic
448D4×C73—416no—
449D4×C73—416no—
450D4×C73—416no—
451C2×C4×C73—22no—
452C2×C4×C73—22no—
453C2×C4×C73—22no—
454C2×C4×C73—22no—
455C2×C4×C73—22no—
456C2×C4×C73—22no—
457C2×C4×C73—22no—
458C2×C4×C73—22no—
459C2×C4×C73—22no—
460C2×C4×C73—22no—
461C2×C4×C73—22no—
462C2×C4×C73—22no—
463C2×C4×C73—22no—
464C2×C4×C73—22no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—22no—
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—41no—
502C2×C4×C73—41no—
503C2×C4×C73—41no—
504C2×C4×C73—41no—
505C2×C4×C73—41no—
506C2×C4×C73—41no—
507C2×C4×C73—41no—
508C2×C4×C73—41no—
509C2×C4×C73—41no—
510C2×C4×C73—41no—
511C2×C4×C73—41no—
512C2×C4×C73—41no—
513C2×C4×C73—41no—
514C2×C4×C73—41no—
515C2×C4×C73—41no—
516C2×C4×C73—41no—
517C2×C4×C73—41no—
518C2×C4×C73—41no—
519C2×C4×C73—41no—
520C2×C4×C73—41no—
521C2×C4×C73—41no—
522C2×C4×C73—41no—
523C2×C4×C73—41no—
524C2×C4×C73—41no—
525C2×C4×C73—41no—
526C2×C4×C73—41no—
527C2×C4×C73—41no—
528C2×C4×C73—41no—
529C2×C4×C73—41no—
530C2×C4×C73—41no—
531C2×C4×C73—41no—
532C2×C4×C73—41no—
533C2×C4×C73—41no—
534C2×C4×C73—41no—
535C22×C73—42no—
536C22×C73—42no—
537C22×C73—42no—
538C22×C73—42no—
539C22×C73—42no—
540C22×C73—42no—
541C22×C73—42no—
542C22×C73—42no—
543C22×C73—42no—
544C22×C73—42no—
545C22×C73—42no—
546C22×C73—42no—
547C22×C73—42no—
548C22×C73—42no—
549C22×C73—42no—
550C22×C73—42no—
551C22×C73—42no—
552C22×C73—42no—
553C22×C73—42no—
554C22×C73—42no—
555C22×C73—42no—
556C22×C73—81no—
557C22×C73—81no—
558C22×C73—81no—
559C22×C73—81no—
560C22×C73—81no—
561C22×C73—81no—
562C22×C73—81no—
563C22×C73—81no—
564C22×C73—81no—
565C22×C73—81no—
566C22×C73—81no—
567C22×C73—81no—
568C22×C73—81no—
569C22×C73—81no—
570C22×C73—81no—
571C22×C73—81no—
572C22×C73—81no—
573C22×C73—81no—
574C22×C73—81no—
575C22×C73—81no—
576C22×C73—81no—
577C22×C73—81no—
578C22×C73—81no—
579C22×C73—81no—
580C22×C73#52511yescharacteristic
581C22×C73#52911yescharacteristic
582C22×C73#53211yescharacteristic
583C22×C73#53411yescharacteristic
584C22×C73#53511yescharacteristic
585C22×C73#53511yescharacteristic
586C22×C73#53511yescharacteristic
587C22×C73#53811yescharacteristic
588C22×C73#53811yescharacteristic
589C22×C73#53811yescharacteristic
590C22×C73#53811yescharacteristic
591C22×C73#53811yescharacteristic
592C22×C73#53811yescharacteristic
593C22×C73#53811yescharacteristic
594C22×C73#53811yescharacteristic
595C22×C73#54011yescharacteristic
596C22×C73#54011yescharacteristic
597C22×C73#54011yescharacteristic
598C22×C73#54011yescharacteristic
599C22×C73D4211yescharacteristic
600C22×C73#54611yescharacteristic
601C22×C73#54611yescharacteristic
602C22×C73#54611yescharacteristic
603C22×C73#54611yescharacteristic
604C22×C73#54611yescharacteristic
605C22×C73#55011yescharacteristic
606C22×C73#55111yescharacteristic
607C22×C73#55111yescharacteristic
608C22×C73#55311yescharacteristic
609C22×C73#55311yescharacteristic
610C22×C73#55311yescharacteristic
611C22×C73#56011yescharacteristic
612C22×C73#56011yescharacteristic
613C22×C73#56011yescharacteristic
614C22×C73H(3,𝔽4)11yescharacteristic
615C4×C73—42no—
616C4×C73—42no—
617C4×C73—42no—
618C4×C73—42no—
619C4×C73—42no—
620C4×C73—42no—
621C4×C73—42no—
622C4×C73—42no—
623C4×C73—81no—
624C4×C73—81no—
625C4×C73—81no—
626C4×C73—81no—
627#16535C7311yesmaximal, characteristic, direct product factor, Sylow
628C2×C73—82no—
629C2×C73—82no—
630C2×C73—82no—
631C2×C73#246411yescharacteristic
632C2×C73#247111yescharacteristic
633C2×C73#255911yescharacteristic
634C2×C73#263111yescharacteristic
635C2×C73#264811yescharacteristic
636C2×C73#266111yescharacteristic
637C2×C73#267011yescharacteristic
638C2×C73#267311yescharacteristic
639C2×C73#268511yescharacteristic
640C2×C73#269711yescharacteristic
641C2×C73#270311yescharacteristic
642C2×C73#271411yescharacteristic
643C2×C73#275311yescharacteristic
644C2×C73#277811yescharacteristic
645C2×C73#282811yescharacteristic
646C2×#397C2×C7311yescharacteristic, complemented
647C2×#394C2×C7311yescharacteristic, complemented
648C2×#392C2×C7311yescharacteristic
649C2×#388C2×C7311yescharacteristic, complemented
650#1443C2×C7311yescharacteristic, complemented
651#1442C2×C7311yescharacteristic, complemented
652#1439C2×C7311yescharacteristic, complemented
653#1439C2×C7311yescharacteristic, complemented
654#1438C2×C7311yescharacteristic, complemented
655#1438C2×C7311yescharacteristic, complemented
656#1438C2×C7311yescharacteristic, complemented
657#1438C2×C7311yescharacteristic, complemented
658#1438C2×C7311yescharacteristic, complemented
659#1437C2×C7311yescharacteristic, complemented
660#1437C2×C7311yescharacteristic, complemented
661C73#1653511yescharacteristic, direct product factor, Sylow
662C23×D4C22×C7311yescharacteristic
663C23×D4C22×C7311yescharacteristic
664C23×D4C22×C7311yescharacteristic
665C22×C4⋊C4C22×C7311yescharacteristic
666C22×C4⋊C4C22×C7311yescharacteristic
667C22×C22⋊C4C22×C7311yescharacteristic
668C22×C22⋊C4C22×C7311yescharacteristic
669C22×C22⋊C4C22×C7311yescharacteristic
670C22×C22⋊C4C22×C7311yescharacteristic
671C22×C22⋊C4C22×C7311yescharacteristic
672C22×C22⋊C4C22×C7311yescharacteristic
673C22×C22⋊C4C22×C7311yescharacteristic
674C22×C22⋊C4C22×C7311yescharacteristic
675C22×C22⋊C4C22×C7311yescharacteristic
676C22×C22⋊C4C22×C7311yescharacteristic
677C22×C22⋊C4C22×C7311yescharacteristic
678C22×C22⋊C4C22×C7311yescharacteristic
679C22×C22⋊C4C22×C7311yescharacteristic
680C22×C22⋊C4C22×C7311yescharacteristic
681C22×C22⋊C4C22×C7311yescharacteristic
682C22×C42C22×C7311yescharacteristic
683#397—24no—
684#394—24no—
685#392—24no—
686#388—24no—
687C2×#95C22×C7311yescharacteristic
688C2×#95C22×C7311yescharacteristic
689C2×#95C22×C7311yescharacteristic
690C2×#95C22×C7311yescharacteristic
691C2×#95C22×C7311yescharacteristic
692C2×#95C22×C7311yescharacteristic
693C2×#95C22×C7311yescharacteristic
694C2×#95C22×C7311yescharacteristic
695C2×#95C22×C7311yescharacteristic
696C2×#95C22×C7311yescharacteristic
697C2×#95C22×C7311yescharacteristic
698C2×#95C22×C7311yescharacteristic
699C2×#95C22×C7311yescharacteristic
700C2×#95C22×C7311yescharacteristic
701C25C23×C7311yescharacteristic
702C25C23×C7311yescharacteristic
703C25C23×C7311yescharacteristic
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C23×C4C23×C7311yescharacteristic
726C23×C4C23×C7311yescharacteristic
727C23×C4C23×C7311yescharacteristic
728C23×C4C23×C7311yescharacteristic
729C23×C4C23×C7311yescharacteristic
730C23×C4C23×C7311yescharacteristic
731C23×C4C23×C7311yescharacteristic
732C23×C4C23×C7311yescharacteristic
733C23×C4C23×C7311yescharacteristic
734C23×C4C23×C7311yescharacteristic
735C23×C4C23×C7311yescharacteristic
736C23×C4C23×C7311yescharacteristic
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4—41no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4D4×C7314yes—
788C2×C42—22no—
789C2×C42—41no—
790C2×C42—41no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95D4×C7314yescomplemented
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C7312yes—
848C24#41×C7312yes—
849C24#41×C7312yes—
850C24C24×C7311yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
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—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4C2×D4×C7312yes—
949C22×C4C2×D4×C7312yes—
950C22×C4C2×D4×C7312yes—
951C22×C4C2×D4×C7312yes—
952C22×C4C2×D4×C7312yes—
953C22×C4#41×C7312yes—
954C22×C4#41×C7312yes—
955C22×C4#41×C7312yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—28no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C7311yescharacteristic
1080C23C22×D4×C7311yescharacteristic
1081C23C2×#41×C7311yescharacteristic
1082C23C2×#41×C7311yescharacteristic
1083C23C2×#41×C7311yescharacteristic
1084C23C2×#41×C7311yescharacteristic
1085C23C2×#41×C7311yescharacteristic
1086C23H(5,𝔽2)×C7311yescharacteristic
1087C23H(5,𝔽2)×C7311yescharacteristic
1088C23H(5,𝔽2)×C7311yescharacteristic
1089C23H(5,𝔽2)×C7311yescharacteristic
1090C23H(5,𝔽2)×C7311yescharacteristic
1091C23H(5,𝔽2)×C7311yescharacteristic
1092C23H(5,𝔽2)×C7311yescharacteristic
1093C23H(5,𝔽2)×C7311yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22#525×C7311yescharacteristic
1227C22#529×C7311yescharacteristic
1228C22#532×C7311yescharacteristic
1229C22#534×C7311yescharacteristic
1230C22#535×C7311yescharacteristic
1231C22#535×C7311yescharacteristic
1232C22#535×C7311yescharacteristic
1233C22#538×C7311yescharacteristic
1234C22#538×C7311yescharacteristic
1235C22#538×C7311yescharacteristic
1236C22#538×C7311yescharacteristic
1237C22#538×C7311yescharacteristic
1238C22#538×C7311yescharacteristic
1239C22#538×C7311yescharacteristic
1240C22#538×C7311yescharacteristic
1241C22#540×C7311yescharacteristic
1242C22#540×C7311yescharacteristic
1243C22#540×C7311yescharacteristic
1244C22#540×C7311yescharacteristic
1245C22D42×C7311yescharacteristic
1246C22#546×C7311yescharacteristic
1247C22#546×C7311yescharacteristic
1248C22#546×C7311yescharacteristic
1249C22#546×C7311yescharacteristic
1250C22#546×C7311yescharacteristic
1251C22#550×C7311yescharacteristic
1252C22#551×C7311yescharacteristic
1253C22#551×C7311yescharacteristic
1254C22#553×C7311yescharacteristic
1255C22#553×C7311yescharacteristic
1256C22#553×C7311yescharacteristic
1257C22#560×C7311yescharacteristic
1258C22#560×C7311yescharacteristic
1259C22#560×C7311yescharacteristic
1260C22H(3,𝔽4)×C7311yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C73×#246411yescharacteristic
1277C2C73×#247111yescharacteristic
1278C2C73×#255911yescharacteristic
1279C2C73×#263111yescharacteristic
1280C2C73×#264811yescharacteristic
1281C2C73×#266111yescharacteristic
1282C2C73×#267011yescharacteristic
1283C2C73×#267311yescharacteristic
1284C2C73×#268511yescharacteristic
1285C2C73×#269711yescharacteristic
1286C2C73×#270311yescharacteristic
1287C2C73×#271411yescharacteristic
1288C2C73×#275311yescharacteristic
1289C2C73×#277811yescharacteristic
1290C2C73×#282811yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC2×#392×C73C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C73C2semidirect
2. C2×#394×C73C2semidirect
4. C2×#388×C73C2semidirect
5. C73×#1443C2semidirect
6. C73×#1442C2semidirect
7. C73×#1439C2semidirect
8. C73×#1439C2semidirect
9. C73×#1438C2semidirect
10. C73×#1438C2semidirect
11. C73×#1438C2semidirect
12. C73×#1438C2semidirect
13. C73×#1438C2semidirect
14. C73×#1437C2semidirect
15. C73×#1437C2semidirect
158. #95×C73D4semidirect
627. #16535C73direct (N × H)
646. C2×#397C2×C73semidirect
647. C2×#394C2×C73semidirect
649. C2×#388C2×C73semidirect
650. #1443C2×C73semidirect
651. #1442C2×C73semidirect
652. #1439C2×C73semidirect
653. #1439C2×C73semidirect
654. #1438C2×C73semidirect
655. #1438C2×C73semidirect
656. #1438C2×C73semidirect
657. #1438C2×C73semidirect
658. #1438C2×C73semidirect
659. #1437C2×C73semidirect
660. #1437C2×C73semidirect
661. C73#16535direct (N × H)
804. #95D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C732
C2×#394×C732
C2×#392×C732
C2×#388×C732
C73×#14432
C73×#14422
C73×#14392
C73×#14382
C73×#14372
#1653573