Finite Group Databasebeta

← C73×#15317 #32924721

Subgroups — C73×#15317 #32924721

Order 18688.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C73C211yesmaximal, characteristic, complemented
2C2×#394×C73C211yesmaximal, characteristic, complemented
3C2×#393×C73C211yesmaximal, characteristic, complemented
4C2×#392×C73C211yesmaximal, characteristic
5C2×#391×C73C211yesmaximal, characteristic, complemented
6C2×#390×C73C211yesmaximal, characteristic, complemented
7C73×#1440C211yesmaximal, characteristic, complemented
8C73×#1439C211yesmaximal, characteristic, complemented
9C73×#1439C211yesmaximal, characteristic, complemented
10C73×#1438C211yesmaximal, characteristic, complemented
11C73×#1438C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1437C211yesmaximal, characteristic, complemented
14C73×#1437C211yesmaximal, characteristic, complemented
15C73×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C23×D4×C73C2211yescharacteristic
20C2×#124×C73—24no—
21C2×#124×C73—24no—
22C2×#124×C73—24no—
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C73C2211yescharacteristic
38C22×C22⋊C4×C73C2211yescharacteristic
39C22×C22⋊C4×C73C2211yescharacteristic
40C22×C42×C73C2211yescharacteristic
41C22×C42×C73C2211yescharacteristic
42#394×C73—24no—
43#393×C73—24no—
44#392×C73—24no—
45#391×C73—24no—
46#390×C73—24no—
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
61C25×C73C2311yescharacteristic
62C22×Q8×C73—22no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—41no—
67C22×Q8×C73—41no—
68C22×Q8×C73D414yescomplemented
69C22×D4×C73—22no—
70C22×D4×C73—22no—
71C22×D4×C73—22no—
72C22×D4×C73—22no—
73C22×D4×C73—22no—
74C22×D4×C73—22no—
75C22×D4×C73—22no—
76C22×D4×C73—22no—
77C22×D4×C73—22no—
78C22×D4×C73—22no—
79C22×D4×C73—22no—
80C22×D4×C73—22no—
81C22×D4×C73—22no—
82C22×D4×C73—41no—
83C22×D4×C73—41no—
84C22×D4×C73—41no—
85C22×D4×C73—41no—
86C22×D4×C73—41no—
87C22×D4×C73—41no—
88C22×D4×C73—41no—
89C22×D4×C73—41no—
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
101C23×C4×C73C2311yescharacteristic
102#124×C73—232no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73—22no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—41no—
108C2×C4⋊C4×C73—41no—
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—22no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—22no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—22no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73—22no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊C4×C73—22no—
136C2×C22⋊C4×C73—22no—
137C2×C22⋊C4×C73—22no—
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×C73—41no—
149C2×C22⋊C4×C73—41no—
150C2×C22⋊C4×C73—41no—
151C2×C22⋊C4×C73—41no—
152C2×C22⋊C4×C73D414yescomplemented
153C2×C22⋊C4×C73D414yescomplemented
154C2×C42×C73—22no—
155C2×C42×C73—22no—
156C2×C42×C73—22no—
157C2×C42×C73—22no—
158C2×C42×C73—22no—
159C2×C42×C73—41no—
160#95×C73—22no—
161#95×C73—22no—
162#95×C73—22no—
163#95×C73—22no—
164#95×C73—22no—
165#95×C73—22no—
166#95×C73—22no—
167#95×C73—22no—
168#95×C73—41no—
169#95×C73—41no—
170#95×C73—41no—
171#95×C73D414yes—
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×C73—21no—
211C24×C73—21no—
212C24×C73—21no—
213C24×C73—21no—
214C24×C73C2×D412yes—
215C24×C73C2×D412yes—
216C24×C73#4112yes—
217C24×C73C2411yescharacteristic
218C2×Q8×C73—28no—
219C2×Q8×C73—28no—
220C2×Q8×C73—44no—
221C2×Q8×C73—44no—
222C2×Q8×C73—44no—
223C2×Q8×C73—44no—
224C2×Q8×C73—44no—
225C2×D4×C73—28no—
226C2×D4×C73—28no—
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—
237C2×D4×C73—44no—
238C2×D4×C73—44no—
239C2×D4×C73—44no—
240C2×D4×C73—44no—
241C2×D4×C73—44no—
242C2×D4×C73—44no—
243C2×D4×C73—44no—
244C2×D4×C73—44no—
245C2×D4×C73—44no—
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—21no—
308C22×C4×C73—21no—
309C22×C4×C73—21no—
310C22×C4×C73—21no—
311C22×C4×C73—21no—
312C22×C4×C73—21no—
313C22×C4×C73—21no—
314C22×C4×C73—21no—
315C22×C4×C73—21no—
316C22×C4×C73C2×D412yes—
317C22×C4×C73C2×D412yes—
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—
328C22×C4×C73#4112yes—
329C22×C4×C73#4112yes—
330C4⋊C4×C73—44no—
331C4⋊C4×C73—44no—
332C22⋊C4×C73—28no—
333C22⋊C4×C73—28no—
334C22⋊C4×C73—28no—
335C22⋊C4×C73—28no—
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—
345C22⋊C4×C73—44no—
346C22⋊C4×C73—44no—
347C42×C73—28no—
348C42×C73—44no—
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—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×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×C73—41no—
452C23×C73—41no—
453C23×C73—41no—
454C23×C73C22×D411yescharacteristic
455C23×C73C22×D411yescharacteristic
456C23×C73C22×D411yescharacteristic
457C23×C73C22×D411yescharacteristic
458C23×C73C2×#4111yescharacteristic
459C23×C73C2×#4111yescharacteristic
460C23×C73C2×#4111yescharacteristic
461C23×C73C2×#4111yescharacteristic
462C23×C73C2×#4111yescharacteristic
463C23×C73H(5,𝔽2)11yescharacteristic
464C23×C73H(5,𝔽2)11yescharacteristic
465C23×C73H(5,𝔽2)11yescharacteristic
466C23×C73H(5,𝔽2)11yescharacteristic
467C23×C73H(5,𝔽2)11yescharacteristic
468C23×C732−1+411yescharacteristic
469Q8×C73—416no—
470D4×C73—416no—
471D4×C73—416no—
472D4×C73—416no—
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—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—
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×C73—41no—
554C2×C4×C73#12014yes—
555C2×C4×C73#12114yes—
556C2×C4×C73#12414yescomplemented
557C22×C73—42no—
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—81no—
579C22×C73—81no—
580C22×C73—81no—
581C22×C73—81no—
582C22×C73—81no—
583C22×C73—81no—
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×C73—81no—
601C22×C73—81no—
602C22×C73C2×#12011yescharacteristic
603C22×C73C2×#12111yescharacteristic
604C22×C73#52511yescharacteristic
605C22×C73C2×#12411yescharacteristic
606C22×C73#52911yescharacteristic
607C22×C73#53211yescharacteristic
608C22×C73#53411yescharacteristic
609C22×C73#53511yescharacteristic
610C22×C73#53511yescharacteristic
611C22×C73#53711yescharacteristic
612C22×C73#53811yescharacteristic
613C22×C73#53811yescharacteristic
614C22×C73#53811yescharacteristic
615C22×C73#54211yescharacteristic
616C22×C73#54211yescharacteristic
617C22×C73D4211yescharacteristic
618C22×C73D4211yescharacteristic
619C22×C73#54611yescharacteristic
620C22×C73#54611yescharacteristic
621C22×C73#54611yescharacteristic
622C22×C73#54611yescharacteristic
623C22×C73#54611yescharacteristic
624C22×C73#54611yescharacteristic
625C22×C73#54711yescharacteristic
626C22×C73#54811yescharacteristic
627C22×C73#54811yescharacteristic
628C22×C73#55011yescharacteristic
629C22×C73#55011yescharacteristic
630C22×C73#55011yescharacteristic
631C22×C73#55111yescharacteristic
632C22×C73#55511yescharacteristic
633C22×C73#55911yescharacteristic
634C22×C73#55911yescharacteristic
635C22×C73H(3,𝔽4)11yescharacteristic
636C22×C73#56211yescharacteristic
637C4×C73—24no—
638C4×C73—24no—
639C4×C73—24no—
640C4×C73—42no—
641C4×C73—42no—
642C4×C73—42no—
643C4×C73—42no—
644C4×C73—42no—
645C4×C73—81no—
646C4×C73—81no—
647C4×C73—81no—
648C4×C73—81no—
649#15317C7311yesmaximal, characteristic, direct product factor, Sylow
650C2×C73—82no—
651C2×C73—82no—
652C2×C73—82no—
653C2×C73#240711yescharacteristic
654C2×C73#241011yescharacteristic
655C2×C73#242611yescharacteristic
656C2×C73#243111yescharacteristic
657C2×C73#245911yescharacteristic
658C2×C73#247211yescharacteristic
659C2×C73#249111yescharacteristic
660C2×C73#254811yescharacteristic
661C2×C73#255711yescharacteristic
662C2×C73#267011yescharacteristic
663C2×C73#267611yescharacteristic
664C2×C73#271011yescharacteristic
665C2×C73#271211yescharacteristic
666C2×C73#273011yescharacteristic
667C2×C73#273311yescharacteristic
668C22×#124C2×C7311yescharacteristic, complemented
669C2×#394C2×C7311yescharacteristic, complemented
670C2×#393C2×C7311yescharacteristic, complemented
671C2×#392C2×C7311yescharacteristic
672C2×#391C2×C7311yescharacteristic, complemented
673C2×#390C2×C7311yescharacteristic, complemented
674#1440C2×C7311yescharacteristic, complemented
675#1439C2×C7311yescharacteristic, complemented
676#1439C2×C7311yescharacteristic, complemented
677#1438C2×C7311yescharacteristic, complemented
678#1438C2×C7311yescharacteristic, complemented
679#1438C2×C7311yescharacteristic, complemented
680#1437C2×C7311yescharacteristic, complemented
681#1437C2×C7311yescharacteristic, complemented
682#1436C2×C7311yescharacteristic, complemented
683C73#1531711yescharacteristic, direct product factor, Sylow
684C23×Q8C22×C7311yescharacteristic
685C23×D4C22×C7311yescharacteristic
686C23×D4C22×C7311yescharacteristic
687C23×D4C22×C7311yescharacteristic
688C2×#124—24no—
689C2×#124—24no—
690C2×#124—24no—
691C22×C4⋊C4C22×C7311yescharacteristic
692C22×C4⋊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×C22⋊C4C22×C7311yescharacteristic
704C22×C22⋊C4C22×C7311yescharacteristic
705C22×C22⋊C4C22×C7311yescharacteristic
706C22×C22⋊C4C22×C7311yescharacteristic
707C22×C22⋊C4C22×C7311yescharacteristic
708C22×C42C22×C7311yescharacteristic
709C22×C42C22×C7311yescharacteristic
710#394—24no—
711#393—24no—
712#392—24no—
713#391—24no—
714#390—24no—
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
724C2×#95C22×C7311yescharacteristic
725C2×#95C22×C7311yescharacteristic
726C2×#95C22×C7311yescharacteristic
727C25C23×C7311yescharacteristic
728C25C23×C7311yescharacteristic
729C25C23×C7311yescharacteristic
730C22×Q8—22no—
731C22×Q8—22no—
732C22×Q8—22no—
733C22×Q8—22no—
734C22×Q8—41no—
735C22×Q8—41no—
736C22×Q8D4×C7314yescomplemented
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
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
767C23×C4C23×C7311yescharacteristic
768C23×C4C23×C7311yescharacteristic
769C23×C4C23×C7311yescharacteristic
770#124—232no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
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—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
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⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4D4×C7314yescomplemented
821C2×C22⋊C4D4×C7314yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—22no—
827C2×C42—41no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95D4×C7314yes—
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24C2×D4×C7312yes—
883C24C2×D4×C7312yes—
884C24#41×C7312yes—
885C24C24×C7311yescharacteristic
886C2×Q8—28no—
887C2×Q8—28no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
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—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
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×C4C2×D4×C7312yes—
993C22×C4C2×D4×C7312yes—
994C22×C4#41×C7312yes—
995C22×C4#41×C7312yes—
996C22×C4#41×C7312yes—
997C22×C4#41×C7312yes—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—28no—
1016C42—44no—
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—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—
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—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23C22×D4×C7311yescharacteristic
1123C23C22×D4×C7311yescharacteristic
1124C23C22×D4×C7311yescharacteristic
1125C23C22×D4×C7311yescharacteristic
1126C23C2×#41×C7311yescharacteristic
1127C23C2×#41×C7311yescharacteristic
1128C23C2×#41×C7311yescharacteristic
1129C23C2×#41×C7311yescharacteristic
1130C23C2×#41×C7311yescharacteristic
1131C23H(5,𝔽2)×C7311yescharacteristic
1132C23H(5,𝔽2)×C7311yescharacteristic
1133C23H(5,𝔽2)×C7311yescharacteristic
1134C23H(5,𝔽2)×C7311yescharacteristic
1135C23H(5,𝔽2)×C7311yescharacteristic
1136C232−1+4×C7311yescharacteristic
1137Q8—416no—
1138D4—416no—
1139D4—416no—
1140D4—416no—
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—22no—
1173C2×C4—22no—
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×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4#120×C7314yes—
1223C2×C4#121×C7314yes—
1224C2×C4#124×C7314yescomplemented
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—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
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—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C7311yescharacteristic
1271C22C2×#121×C7311yescharacteristic
1272C22#525×C7311yescharacteristic
1273C22C2×#124×C7311yescharacteristic
1274C22#529×C7311yescharacteristic
1275C22#532×C7311yescharacteristic
1276C22#534×C7311yescharacteristic
1277C22#535×C7311yescharacteristic
1278C22#535×C7311yescharacteristic
1279C22#537×C7311yescharacteristic
1280C22#538×C7311yescharacteristic
1281C22#538×C7311yescharacteristic
1282C22#538×C7311yescharacteristic
1283C22#542×C7311yescharacteristic
1284C22#542×C7311yescharacteristic
1285C22D42×C7311yescharacteristic
1286C22D42×C7311yescharacteristic
1287C22#546×C7311yescharacteristic
1288C22#546×C7311yescharacteristic
1289C22#546×C7311yescharacteristic
1290C22#546×C7311yescharacteristic
1291C22#546×C7311yescharacteristic
1292C22#546×C7311yescharacteristic
1293C22#547×C7311yescharacteristic
1294C22#548×C7311yescharacteristic
1295C22#548×C7311yescharacteristic
1296C22#550×C7311yescharacteristic
1297C22#550×C7311yescharacteristic
1298C22#550×C7311yescharacteristic
1299C22#551×C7311yescharacteristic
1300C22#555×C7311yescharacteristic
1301C22#559×C7311yescharacteristic
1302C22#559×C7311yescharacteristic
1303C22H(3,𝔽4)×C7311yescharacteristic
1304C22#562×C7311yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—24no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2C73×#240711yescharacteristic
1321C2C73×#241011yescharacteristic
1322C2C73×#242611yescharacteristic
1323C2C73×#243111yescharacteristic
1324C2C73×#245911yescharacteristic
1325C2C73×#247211yescharacteristic
1326C2C73×#249111yescharacteristic
1327C2C73×#254811yescharacteristic
1328C2C73×#255711yescharacteristic
1329C2C73×#267011yescharacteristic
1330C2C73×#267611yescharacteristic
1331C2C73×#271011yescharacteristic
1332C2C73×#271211yescharacteristic
1333C2C73×#273011yescharacteristic
1334C2C73×#273311yescharacteristic
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. C22×#124×C73C2semidirect
2. C2×#394×C73C2semidirect
3. C2×#393×C73C2semidirect
5. C2×#391×C73C2semidirect
6. C2×#390×C73C2semidirect
7. C73×#1440C2semidirect
8. C73×#1439C2semidirect
9. C73×#1439C2semidirect
10. C73×#1438C2semidirect
11. C73×#1438C2semidirect
12. C73×#1438C2semidirect
13. C73×#1437C2semidirect
14. C73×#1437C2semidirect
15. C73×#1436C2semidirect
68. C22×Q8×C73D4semidirect
152. C2×C22⋊C4×C73D4semidirect
153. C2×C22⋊C4×C73D4semidirect
556. C2×C4×C73#124semidirect
649. #15317C73direct (N × H)
668. C22×#124C2×C73semidirect
669. C2×#394C2×C73semidirect
670. C2×#393C2×C73semidirect
672. C2×#391C2×C73semidirect
673. C2×#390C2×C73semidirect
674. #1440C2×C73semidirect
675. #1439C2×C73semidirect
676. #1439C2×C73semidirect
677. #1438C2×C73semidirect
678. #1438C2×C73semidirect
679. #1438C2×C73semidirect
680. #1437C2×C73semidirect
681. #1437C2×C73semidirect
682. #1436C2×C73semidirect
683. C73#15317direct (N × H)
736. C22×Q8D4×C73semidirect
820. C2×C22⋊C4D4×C73semidirect
821. C2×C22⋊C4D4×C73semidirect
1224. C2×C4#124×C73semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C732
C2×#394×C732
C2×#393×C732
C2×#392×C732
C2×#391×C732
C2×#390×C732
C73×#14402
C73×#14392
C73×#14382
C73×#14372
C73×#14362
#1531773