Finite Group Databasebeta

← C73×#14534 #32923938

Subgroups — C73×#14534 #32923938

Order 18688.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C73C211yesmaximal, characteristic
2C2×#390×C73C211yesmaximal, characteristic, complemented
3C2×#390×C73C211yesmaximal, characteristic, complemented
4C2×#388×C73C211yesmaximal, characteristic, complemented
5C2×#386×C73C211yesmaximal, characteristic, complemented
6C2×#386×C73C211yesmaximal, characteristic, complemented
7C2×#385×C73C211yesmaximal, characteristic, complemented
8C73×#1440C211yesmaximal, characteristic, complemented
9C73×#1439C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1438C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1437C211yesmaximal, characteristic, complemented
14C73×#1436C211yesmaximal, characteristic, complemented
15C73×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C24×C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C73C2211yescharacteristic
37C22×C42×C73C2211yescharacteristic
38C22×C42×C73C2211yescharacteristic
39#392×C73C418yescomplemented
40#390×C73—24no—
41#390×C73—24no—
42#388×C73—24no—
43#386×C73—24no—
44#386×C73—24no—
45#385×C73—24no—
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
58C25×C73C2311yescharacteristic
59C25×C73C2311yescharacteristic
60C25×C73C2311yescharacteristic
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—22no—
68C22×D4×C73—22no—
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—
79C22×D4×C73C2×C414yes—
80C22×D4×C73C2×C414yes—
81C22×D4×C73C2×C414yescomplemented
82C23×C4×C73—22no—
83C23×C4×C73—22no—
84C23×C4×C73—22no—
85C23×C4×C73—41no—
86C23×C4×C73—41no—
87C23×C4×C73—41no—
88C23×C4×C73—41no—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C23×C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73—22no—
102C2×C4⋊C4×C73—22no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73—22no—
105C2×C4⋊C4×C73—41no—
106C2×C4⋊C4×C73—41no—
107C2×C4⋊C4×C73—41no—
108C2×C4⋊C4×C73—41no—
109C2×C4⋊C4×C73D414yescomplemented
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—22no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—22no—
119C2×C22⋊C4×C73—22no—
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—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×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×C73—41no—
147C2×C22⋊C4×C73—41no—
148C2×C22⋊C4×C73C2×C414yes—
149C2×C22⋊C4×C73C2×C414yescomplemented
150C2×C22⋊C4×C73C2×C414yescomplemented
151C2×C22⋊C4×C73D414yescomplemented
152C2×C42×C73—22no—
153C2×C42×C73—22no—
154C2×C42×C73—22no—
155C2×C42×C73—41no—
156C2×C42×C73—41no—
157C2×C42×C73—41no—
158#95×C73—22no—
159#95×C73—22no—
160#95×C73—22no—
161#95×C73—22no—
162#95×C73—22no—
163#95×C73—22no—
164#95×C73—22no—
165#95×C73—41no—
166#95×C73—41no—
167#95×C73—41no—
168#95×C73C2×C414yescomplemented
169#95×C73D414yescomplemented
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×C73—21no—
202C24×C73—21no—
203C24×C73—21no—
204C24×C73—21no—
205C24×C73—21no—
206C24×C73—21no—
207C24×C73—21no—
208C24×C73—21no—
209C24×C73—21no—
210C24×C73C22×C412yes—
211C24×C73C22×C412yes—
212C24×C73C22×C412yes—
213C24×C73C2×D412yes—
214C24×C73#4112yes—
215C24×C73C2411yescharacteristic
216C2×D4×C73—28no—
217C2×D4×C73—28no—
218C2×D4×C73—28no—
219C2×D4×C73—28no—
220C2×D4×C73—44no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
226C2×D4×C73—44no—
227C2×D4×C73—44no—
228C2×D4×C73—44no—
229C2×D4×C73—44no—
230C2×D4×C73—44no—
231C2×D4×C73—44no—
232C2×D4×C73—44no—
233C2×D4×C73—44no—
234C2×D4×C73—44no—
235C2×D4×C73—44no—
236C2×D4×C73—44no—
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×C73—21no—
303C22×C4×C73—21no—
304C22×C4×C73—21no—
305C22×C4×C73—21no—
306C22×C4×C73—21no—
307C22×C4×C73—44no—
308C22×C4×C73—44no—
309C22×C4×C73—44no—
310C22×C4×C73—44no—
311C22×C4×C73—44no—
312C22×C4×C73—44no—
313C22×C4×C73—44no—
314C22×C4×C73C22×C412yes—
315C22×C4×C73C22×C412yes—
316C22×C4×C73C22×C412yes—
317C22×C4×C73C22×C412yes—
318C22×C4×C73C2×D412yes—
319C22×C4×C73C2×D412yes—
320C22×C4×C73C2×D412yes—
321C22×C4×C73C2×D412yes—
322C22×C4×C73C2×D412yes—
323C22×C4×C73C2×D412yes—
324C22×C4×C73C2×D412yes—
325C22×C4×C73C2×D412yes—
326C22×C4×C73#4112yes—
327C22×C4×C73#4112yes—
328C4⋊C4×C73—44no—
329C4⋊C4×C73—44no—
330C4⋊C4×C73—44no—
331C22⋊C4×C73—28no—
332C22⋊C4×C73—28no—
333C22⋊C4×C73—44no—
334C22⋊C4×C73—44no—
335C22⋊C4×C73—44no—
336C22⋊C4×C73—44no—
337C22⋊C4×C73—44no—
338C22⋊C4×C73—44no—
339C22⋊C4×C73—44no—
340C22⋊C4×C73—44no—
341C22⋊C4×C73—44no—
342C22⋊C4×C73—44no—
343C22⋊C4×C73—44no—
344C22⋊C4×C73—44no—
345C42×C73—44no—
346C42×C73—44no—
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—22no—
356C23×C73—22no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—22no—
365C23×C73—22no—
366C23×C73—22no—
367C23×C73—22no—
368C23×C73—22no—
369C23×C73—22no—
370C23×C73—22no—
371C23×C73—22no—
372C23×C73—22no—
373C23×C73—22no—
374C23×C73—22no—
375C23×C73—22no—
376C23×C73—22no—
377C23×C73—22no—
378C23×C73—22no—
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×C73—41no—
434C23×C73—41no—
435C23×C73—41no—
436C23×C73—41no—
437C23×C73—41no—
438C23×C73—41no—
439C23×C73—41no—
440C23×C73—41no—
441C23×C73—41no—
442C23×C73—41no—
443C23×C73—41no—
444C23×C73—41no—
445C23×C73—41no—
446C23×C73—41no—
447C23×C73—41no—
448C23×C73—41no—
449C23×C73—41no—
450C23×C73—41no—
451C23×C73C4×D414yes—
452C23×C73C23×C411yescharacteristic
453C23×C73C22×D411yescharacteristic
454C23×C73C22×D411yescharacteristic
455C23×C73C22×D411yescharacteristic
456C23×C73C2×#4111yescharacteristic
457C23×C73C2×#4111yescharacteristic
458C23×C73C2×#4111yescharacteristic
459C23×C73H(5,𝔽2)11yescharacteristic
460C23×C73H(5,𝔽2)11yescharacteristic
461C23×C73H(5,𝔽2)11yescharacteristic
462C23×C73H(5,𝔽2)11yescharacteristic
463C23×C73H(5,𝔽2)11yescharacteristic
464C23×C73H(5,𝔽2)11yescharacteristic
465C23×C73H(5,𝔽2)11yescharacteristic
466C23×C732−1+411yescharacteristic
467D4×C73—416no—
468D4×C73—416no—
469D4×C73—416no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—22no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—22no—
480C2×C4×C73—22no—
481C2×C4×C73—22no—
482C2×C4×C73—22no—
483C2×C4×C73—22no—
484C2×C4×C73—22no—
485C2×C4×C73—22no—
486C2×C4×C73—22no—
487C2×C4×C73—22no—
488C2×C4×C73—22no—
489C2×C4×C73—22no—
490C2×C4×C73—22no—
491C2×C4×C73—22no—
492C2×C4×C73—22no—
493C2×C4×C73—22no—
494C2×C4×C73—22no—
495C2×C4×C73—22no—
496C2×C4×C73—22no—
497C2×C4×C73—22no—
498C2×C4×C73—22no—
499C2×C4×C73—22no—
500C2×C4×C73—22no—
501C2×C4×C73—22no—
502C2×C4×C73—22no—
503C2×C4×C73—22no—
504C2×C4×C73—22no—
505C2×C4×C73—22no—
506C2×C4×C73—416no—
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—
535C2×C4×C73—41no—
536C2×C4×C73—41no—
537C2×C4×C73—41no—
538C2×C4×C73—41no—
539C2×C4×C73—41no—
540C2×C4×C73—41no—
541C2×C4×C73—41no—
542C2×C4×C73—41no—
543C2×C4×C73—41no—
544C2×C4×C73—41no—
545C2×C4×C73—41no—
546C2×C4×C73—41no—
547C2×C4×C73—41no—
548C2×C4×C73—41no—
549C2×C4×C73—41no—
550C2×C4×C73—41no—
551C2×C4×C73—41no—
552C2×C4×C73—41no—
553C2×C4×C73C4×D414yes—
554C2×C4×C73C4×D414yes—
555C22×C73—24no—
556C22×C73—24no—
557C22×C73—24no—
558C22×C73—42no—
559C22×C73—42no—
560C22×C73—42no—
561C22×C73—42no—
562C22×C73—42no—
563C22×C73—42no—
564C22×C73—42no—
565C22×C73—42no—
566C22×C73—42no—
567C22×C73—42no—
568C22×C73—42no—
569C22×C73—42no—
570C22×C73—42no—
571C22×C73—42no—
572C22×C73—42no—
573C22×C73—42no—
574C22×C73—42no—
575C22×C73—42no—
576C22×C73—42no—
577C22×C73—42no—
578C22×C73—42no—
579C22×C73—42no—
580C22×C73—42no—
581C22×C73—42no—
582C22×C73—42no—
583C22×C73—42no—
584C22×C73—81no—
585C22×C73—81no—
586C22×C73—81no—
587C22×C73—81no—
588C22×C73—81no—
589C22×C73—81no—
590C22×C73—81no—
591C22×C73—81no—
592C22×C73—81no—
593C22×C73—81no—
594C22×C73—81no—
595C22×C73—81no—
596C22×C73—81no—
597C22×C73—81no—
598C22×C73—81no—
599C22×C73—81no—
600C22×C73C2×C4×D411yescharacteristic
601C22×C73C2×C4×D411yescharacteristic
602C22×C73C2×C4×D411yescharacteristic
603C22×C73#51811yescharacteristic
604C22×C73#51811yescharacteristic
605C22×C73#51811yescharacteristic
606C22×C73#52011yescharacteristic
607C22×C73#53411yescharacteristic
608C22×C73#53411yescharacteristic
609C22×C73#53511yescharacteristic
610C22×C73#53511yescharacteristic
611C22×C73#53511yescharacteristic
612C22×C73#53711yescharacteristic
613C22×C73#53811yescharacteristic
614C22×C73#53811yescharacteristic
615C22×C73#53811yescharacteristic
616C22×C73#53811yescharacteristic
617C22×C73#54011yescharacteristic
618C22×C73#54211yescharacteristic
619C22×C73D4211yescharacteristic
620C22×C73D4211yescharacteristic
621C22×C73D4211yescharacteristic
622C22×C73#54611yescharacteristic
623C22×C73#54611yescharacteristic
624C22×C73#54711yescharacteristic
625C22×C73#54811yescharacteristic
626C22×C73#55011yescharacteristic
627C22×C73#55011yescharacteristic
628C22×C73#55111yescharacteristic
629C22×C73#55311yescharacteristic
630C22×C73#55911yescharacteristic
631C22×C73#56011yescharacteristic
632C22×C73#56011yescharacteristic
633C22×C73#56211yescharacteristic
634C22×C73#56211yescharacteristic
635C4×C73—24no—
636C4×C73—24no—
637C4×C73—42no—
638C4×C73—42no—
639C4×C73—42no—
640C4×C73—42no—
641C4×C73—42no—
642C4×C73—42no—
643C4×C73—42no—
644C4×C73—42no—
645C4×C73—81no—
646C4×C73—81no—
647#14534C7311yesmaximal, characteristic, direct product factor, Sylow
648C2×C73—44no—
649C2×C73—82no—
650C2×C73—82no—
651C2×C73#232111yescharacteristic
652C2×C73#232111yescharacteristic
653C2×C73#232411yescharacteristic
654C2×C73#235811yescharacteristic
655C2×C73#236111yescharacteristic
656C2×C73#236611yescharacteristic
657C2×C73#237711yescharacteristic
658C2×C73#266911yescharacteristic
659C2×C73#267311yescharacteristic
660C2×C73#267611yescharacteristic
661C2×C73#268211yescharacteristic
662C2×C73#271011yescharacteristic
663C2×C73#271411yescharacteristic
664C2×C73#273011yescharacteristic
665C2×C73#279711yescharacteristic
666C2×#392C2×C7311yescharacteristic
667C2×#390C2×C7311yescharacteristic, complemented
668C2×#390C2×C7311yescharacteristic, complemented
669C2×#388C2×C7311yescharacteristic, complemented
670C2×#386C2×C7311yescharacteristic, complemented
671C2×#386C2×C7311yescharacteristic, complemented
672C2×#385C2×C7311yescharacteristic, complemented
673#1440C2×C7311yescharacteristic, complemented
674#1439C2×C7311yescharacteristic, complemented
675#1439C2×C7311yescharacteristic, complemented
676#1438C2×C7311yescharacteristic, complemented
677#1438C2×C7311yescharacteristic, complemented
678#1437C2×C7311yescharacteristic, complemented
679#1436C2×C7311yescharacteristic, complemented
680#1436C2×C7311yescharacteristic, complemented
681C73#1453411yescharacteristic, direct product factor, Sylow
682C23×D4C22×C7311yescharacteristic
683C23×D4C22×C7311yescharacteristic
684C23×D4C22×C7311yescharacteristic
685C24×C4C22×C7311yescharacteristic
686C22×C4⋊C4C22×C7311yescharacteristic
687C22×C4⋊C4C22×C7311yescharacteristic
688C22×C4⋊C4C22×C7311yescharacteristic
689C22×C22⋊C4C22×C7311yescharacteristic
690C22×C22⋊C4C22×C7311yescharacteristic
691C22×C22⋊C4C22×C7311yescharacteristic
692C22×C22⋊C4C22×C7311yescharacteristic
693C22×C22⋊C4C22×C7311yescharacteristic
694C22×C22⋊C4C22×C7311yescharacteristic
695C22×C22⋊C4C22×C7311yescharacteristic
696C22×C22⋊C4C22×C7311yescharacteristic
697C22×C22⋊C4C22×C7311yescharacteristic
698C22×C22⋊C4C22×C7311yescharacteristic
699C22×C22⋊C4C22×C7311yescharacteristic
700C22×C22⋊C4C22×C7311yescharacteristic
701C22×C22⋊C4C22×C7311yescharacteristic
702C22×C22⋊C4C22×C7311yescharacteristic
703C22×C42C22×C7311yescharacteristic
704C22×C42C22×C7311yescharacteristic
705#392C4×C7318yescomplemented
706#390—24no—
707#390—24no—
708#388—24no—
709#386—24no—
710#386—24no—
711#385—24no—
712C2×#95C22×C7311yescharacteristic
713C2×#95C22×C7311yescharacteristic
714C2×#95C22×C7311yescharacteristic
715C2×#95C22×C7311yescharacteristic
716C2×#95C22×C7311yescharacteristic
717C2×#95C22×C7311yescharacteristic
718C2×#95C22×C7311yescharacteristic
719C2×#95C22×C7311yescharacteristic
720C2×#95C22×C7311yescharacteristic
721C2×#95C22×C7311yescharacteristic
722C2×#95C22×C7311yescharacteristic
723C2×#95C22×C7311yescharacteristic
724C25C23×C7311yescharacteristic
725C25C23×C7311yescharacteristic
726C25C23×C7311yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4C2×C4×C7314yes—
746C22×D4C2×C4×C7314yes—
747C22×D4C2×C4×C7314yescomplemented
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4C23×C7311yescharacteristic
756C23×C4C23×C7311yescharacteristic
757C23×C4C23×C7311yescharacteristic
758C23×C4C23×C7311yescharacteristic
759C23×C4C23×C7311yescharacteristic
760C23×C4C23×C7311yescharacteristic
761C23×C4C23×C7311yescharacteristic
762C23×C4C23×C7311yescharacteristic
763C23×C4C23×C7311yescharacteristic
764C23×C4C23×C7311yescharacteristic
765C23×C4C23×C7311yescharacteristic
766C23×C4C23×C7311yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4D4×C7314yescomplemented
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4C2×C4×C7314yes—
815C2×C22⋊C4C2×C4×C7314yescomplemented
816C2×C22⋊C4C2×C4×C7314yescomplemented
817C2×C22⋊C4D4×C7314yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823C2×C42—41no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—41no—
832#95—41no—
833#95—41no—
834#95C2×C4×C7314yescomplemented
835#95D4×C7314yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24C22×C4×C7312yes—
877C24C22×C4×C7312yes—
878C24C22×C4×C7312yes—
879C24C2×D4×C7312yes—
880C24#41×C7312yes—
881C24C24×C7311yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
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×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C7312yes—
981C22×C4C22×C4×C7312yes—
982C22×C4C22×C4×C7312yes—
983C22×C4C22×C4×C7312yes—
984C22×C4C2×D4×C7312yes—
985C22×C4C2×D4×C7312yes—
986C22×C4C2×D4×C7312yes—
987C22×C4C2×D4×C7312yes—
988C22×C4C2×D4×C7312yes—
989C22×C4C2×D4×C7312yes—
990C22×C4C2×D4×C7312yes—
991C22×C4C2×D4×C7312yes—
992C22×C4#41×C7312yes—
993C22×C4#41×C7312yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
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—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C4×D4×C7314yes—
1118C23C23×C4×C7311yescharacteristic
1119C23C22×D4×C7311yescharacteristic
1120C23C22×D4×C7311yescharacteristic
1121C23C22×D4×C7311yescharacteristic
1122C23C2×#41×C7311yescharacteristic
1123C23C2×#41×C7311yescharacteristic
1124C23C2×#41×C7311yescharacteristic
1125C23H(5,𝔽2)×C7311yescharacteristic
1126C23H(5,𝔽2)×C7311yescharacteristic
1127C23H(5,𝔽2)×C7311yescharacteristic
1128C23H(5,𝔽2)×C7311yescharacteristic
1129C23H(5,𝔽2)×C7311yescharacteristic
1130C23H(5,𝔽2)×C7311yescharacteristic
1131C23H(5,𝔽2)×C7311yescharacteristic
1132C232−1+4×C7311yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4C4×D4×C7314yes—
1220C2×C4C4×D4×C7314yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×D4×C7311yescharacteristic
1267C22C2×C4×D4×C7311yescharacteristic
1268C22C2×C4×D4×C7311yescharacteristic
1269C22#518×C7311yescharacteristic
1270C22#518×C7311yescharacteristic
1271C22#518×C7311yescharacteristic
1272C22#520×C7311yescharacteristic
1273C22#534×C7311yescharacteristic
1274C22#534×C7311yescharacteristic
1275C22#535×C7311yescharacteristic
1276C22#535×C7311yescharacteristic
1277C22#535×C7311yescharacteristic
1278C22#537×C7311yescharacteristic
1279C22#538×C7311yescharacteristic
1280C22#538×C7311yescharacteristic
1281C22#538×C7311yescharacteristic
1282C22#538×C7311yescharacteristic
1283C22#540×C7311yescharacteristic
1284C22#542×C7311yescharacteristic
1285C22D42×C7311yescharacteristic
1286C22D42×C7311yescharacteristic
1287C22D42×C7311yescharacteristic
1288C22#546×C7311yescharacteristic
1289C22#546×C7311yescharacteristic
1290C22#547×C7311yescharacteristic
1291C22#548×C7311yescharacteristic
1292C22#550×C7311yescharacteristic
1293C22#550×C7311yescharacteristic
1294C22#551×C7311yescharacteristic
1295C22#553×C7311yescharacteristic
1296C22#559×C7311yescharacteristic
1297C22#560×C7311yescharacteristic
1298C22#560×C7311yescharacteristic
1299C22#562×C7311yescharacteristic
1300C22#562×C7311yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C73×#232111yescharacteristic
1317C2C73×#232111yescharacteristic
1318C2C73×#232411yescharacteristic
1319C2C73×#235811yescharacteristic
1320C2C73×#236111yescharacteristic
1321C2C73×#236611yescharacteristic
1322C2C73×#237711yescharacteristic
1323C2C73×#266911yescharacteristic
1324C2C73×#267311yescharacteristic
1325C2C73×#267611yescharacteristic
1326C2C73×#268211yescharacteristic
1327C2C73×#271011yescharacteristic
1328C2C73×#271411yescharacteristic
1329C2C73×#273011yescharacteristic
1330C2C73×#279711yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC24C24×C73
prime radicalC2×#392×C73C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C73C2semidirect
3. C2×#390×C73C2semidirect
4. C2×#388×C73C2semidirect
5. C2×#386×C73C2semidirect
6. C2×#386×C73C2semidirect
7. C2×#385×C73C2semidirect
8. C73×#1440C2semidirect
9. C73×#1439C2semidirect
10. C73×#1439C2semidirect
11. C73×#1438C2semidirect
12. C73×#1438C2semidirect
13. C73×#1437C2semidirect
14. C73×#1436C2semidirect
15. C73×#1436C2semidirect
39. #392×C73C4semidirect
81. C22×D4×C73C2×C4semidirect
109. C2×C4⋊C4×C73D4semidirect
149. C2×C22⋊C4×C73C2×C4semidirect
150. C2×C22⋊C4×C73C2×C4semidirect
151. C2×C22⋊C4×C73D4semidirect
168. #95×C73C2×C4semidirect
169. #95×C73D4semidirect
647. #14534C73direct (N × H)
667. C2×#390C2×C73semidirect
668. C2×#390C2×C73semidirect
669. C2×#388C2×C73semidirect
670. C2×#386C2×C73semidirect
671. C2×#386C2×C73semidirect
672. C2×#385C2×C73semidirect
673. #1440C2×C73semidirect
674. #1439C2×C73semidirect
675. #1439C2×C73semidirect
676. #1438C2×C73semidirect
677. #1438C2×C73semidirect
678. #1437C2×C73semidirect
679. #1436C2×C73semidirect
680. #1436C2×C73semidirect
681. C73#14534direct (N × H)
705. #392C4×C73semidirect
747. C22×D4C2×C4×C73semidirect
775. C2×C4⋊C4D4×C73semidirect
815. C2×C22⋊C4C2×C4×C73semidirect
816. C2×C22⋊C4C2×C4×C73semidirect
817. C2×C22⋊C4D4×C73semidirect
834. #95C2×C4×C73semidirect
835. #95D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C732
C2×#390×C732
C2×#388×C732
C2×#386×C732
C2×#385×C732
C73×#14402
C73×#14392
C73×#14382
C73×#14372
C73×#14362
#1453473