Finite Group Databasebeta

← C73×#15314 #32924718

Subgroups — C73×#15314 #32924718

Order 18688.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1346 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×#386×C73C211yesmaximal, characteristic, complemented
6C2×#386×C73C211yesmaximal, characteristic, complemented
7C73×#1446C211yesmaximal, characteristic, complemented
8C73×#1440C211yesmaximal, characteristic, complemented
9C73×#1440C211yesmaximal, characteristic, complemented
10C73×#1439C211yesmaximal, characteristic, complemented
11C73×#1438C211yesmaximal, characteristic, complemented
12C73×#1438C211yesmaximal, characteristic, complemented
13C73×#1437C211yesmaximal, characteristic, complemented
14C73×#1436C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C23×D4×C73C2211yescharacteristic
20C24×C4×C73C2211yescharacteristic
21C2×#124×C73—24no—
22C2×#124×C73—24no—
23C2×#124×C73—24no—
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×C42×C73C2211yescharacteristic
40#394×C73—24no—
41#393×C73—24no—
42#392×C73—24no—
43#386×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
61C25×C73C2311yescharacteristic
62C22×Q8×C73—22no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—22no—
67C22×Q8×C73—41no—
68C22×Q8×C73—41no—
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—41no—
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×C73D414yes—
90C23×C4×C73—22no—
91C23×C4×C73—22no—
92C23×C4×C73—22no—
93C23×C4×C73—41no—
94C23×C4×C73—41no—
95C23×C4×C73—41no—
96C23×C4×C73—41no—
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C23×C4×C73C2311yescharacteristic
101C23×C4×C73C2311yescharacteristic
102C23×C4×C73C2311yescharacteristic
103C23×C4×C73C2311yescharacteristic
104C23×C4×C73C2311yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C23×C4×C73C2311yescharacteristic
107C23×C4×C73C2311yescharacteristic
108C23×C4×C73C2311yescharacteristic
109#124×C73—232no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—22no—
112C2×C4⋊C4×C73—41no—
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—22no—
139C2×C22⋊C4×C73—22no—
140C2×C22⋊C4×C73—22no—
141C2×C22⋊C4×C73—22no—
142C2×C22⋊C4×C73—22no—
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×C73—41no—
153C2×C22⋊C4×C73D414yescomplemented
154C2×C22⋊C4×C73D414yescomplemented
155C2×C42×C73—22no—
156C2×C42×C73—22no—
157C2×C42×C73—22no—
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—22no—
166#95×C73—41no—
167#95×C73—41no—
168#95×C73—41no—
169#95×C73—41no—
170#95×C73—41no—
171#95×C73D414yescomplemented
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×C73C2×D412yes—
213C24×C73C2×D412yes—
214C24×C73C2×D412yes—
215C24×C73C2×D412yes—
216C24×C73#4112yes—
217C24×C73C2411yescharacteristic
218C2×Q8×C73—28no—
219C2×Q8×C73—44no—
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—28no—
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×C73—21no—
317C22×C4×C73—21no—
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×C73C2×D412yes—
326C22×C4×C73C2×D412yes—
327C22×C4×C73C2×D412yes—
328C22×C4×C73C2×D412yes—
329C22×C4×C73C2×D412yes—
330C22×C4×C73C2×D412yes—
331C22×C4×C73C2×D412yes—
332C22×C4×C73C2×D412yes—
333C22×C4×C73#4112yes—
334C22×C4×C73#4112yes—
335C22×C4×C73#4112yes—
336C22×C4×C73#4112yes—
337C4⋊C4×C73—44no—
338C22⋊C4×C73—28no—
339C22⋊C4×C73—28no—
340C22⋊C4×C73—28no—
341C22⋊C4×C73—28no—
342C22⋊C4×C73—44no—
343C22⋊C4×C73—44no—
344C22⋊C4×C73—44no—
345C22⋊C4×C73—44no—
346C22⋊C4×C73—44no—
347C22⋊C4×C73—44no—
348C22⋊C4×C73—44no—
349C22⋊C4×C73—44no—
350C22⋊C4×C73—44no—
351C22⋊C4×C73—44no—
352C42×C73—28no—
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—22no—
380C23×C73—22no—
381C23×C73—22no—
382C23×C73—22no—
383C23×C73—22no—
384C23×C73—22no—
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×C73—41no—
455C23×C73—41no—
456C23×C73—41no—
457C23×C73#12014yes—
458C23×C73C22×D411yescharacteristic
459C23×C73C22×D411yescharacteristic
460C23×C73C22×D411yescharacteristic
461C23×C73C22×D411yescharacteristic
462C23×C73C2×#4111yescharacteristic
463C23×C73C2×#4111yescharacteristic
464C23×C73C2×#4111yescharacteristic
465C23×C73C2×#4111yescharacteristic
466C23×C73C2×#4111yescharacteristic
467C23×C73H(5,𝔽2)11yescharacteristic
468C23×C73H(5,𝔽2)11yescharacteristic
469C23×C73H(5,𝔽2)11yescharacteristic
470C23×C73H(5,𝔽2)11yescharacteristic
471C23×C73H(5,𝔽2)11yescharacteristic
472C23×C732−1+411yescharacteristic
473Q8×C73—416no—
474D4×C73—416no—
475D4×C73—416no—
476D4×C73—416no—
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—22no—
507C2×C4×C73—22no—
508C2×C4×C73—22no—
509C2×C4×C73—22no—
510C2×C4×C73—416no—
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—41no—
555C2×C4×C73—41no—
556C2×C4×C73—41no—
557C2×C4×C73—41no—
558C2×C4×C73—41no—
559C2×C4×C73—41no—
560C2×C4×C73—41no—
561C2×C4×C73#12114yes—
562C22×C73—24no—
563C22×C73—24no—
564C22×C73—24no—
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—42no—
585C22×C73—42no—
586C22×C73—42no—
587C22×C73—42no—
588C22×C73—42no—
589C22×C73—42no—
590C22×C73—42no—
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×C73—81no—
603C22×C73—81no—
604C22×C73—81no—
605C22×C73—81no—
606C22×C73—81no—
607C22×C73C2×#12011yescharacteristic
608C22×C73C2×#12111yescharacteristic
609C22×C73#52511yescharacteristic
610C22×C73#52911yescharacteristic
611C22×C73#53211yescharacteristic
612C22×C73#53211yescharacteristic
613C22×C73#53411yescharacteristic
614C22×C73#53511yescharacteristic
615C22×C73#53511yescharacteristic
616C22×C73#53711yescharacteristic
617C22×C73#53811yescharacteristic
618C22×C73#53811yescharacteristic
619C22×C73#53811yescharacteristic
620C22×C73#54211yescharacteristic
621C22×C73#54211yescharacteristic
622C22×C73D4211yescharacteristic
623C22×C73D4211yescharacteristic
624C22×C73#54611yescharacteristic
625C22×C73#54611yescharacteristic
626C22×C73#54611yescharacteristic
627C22×C73#54611yescharacteristic
628C22×C73#54611yescharacteristic
629C22×C73#54611yescharacteristic
630C22×C73#54611yescharacteristic
631C22×C73#54611yescharacteristic
632C22×C73#54611yescharacteristic
633C22×C73#54711yescharacteristic
634C22×C73#54711yescharacteristic
635C22×C73#54811yescharacteristic
636C22×C73#55111yescharacteristic
637C22×C73#55511yescharacteristic
638C22×C73#55911yescharacteristic
639C22×C73#55911yescharacteristic
640C22×C73H(3,𝔽4)11yescharacteristic
641C22×C73#56211yescharacteristic
642C4×C73—24no—
643C4×C73—42no—
644C4×C73—42no—
645C4×C73—42no—
646C4×C73—42no—
647C4×C73—42no—
648C4×C73—42no—
649C4×C73—42no—
650C4×C73—42no—
651C4×C73—42no—
652C4×C73—81no—
653C4×C73—81no—
654#15314C7311yesmaximal, characteristic, direct product factor, Sylow
655C2×C73—44no—
656C2×C73—82no—
657C2×C73—82no—
658C2×C73#240411yescharacteristic
659C2×C73#241011yescharacteristic
660C2×C73#242711yescharacteristic
661C2×C73#243011yescharacteristic
662C2×C73#245911yescharacteristic
663C2×C73#246111yescharacteristic
664C2×C73#254411yescharacteristic
665C2×C73#255511yescharacteristic
666C2×C73#255711yescharacteristic
667C2×C73#267011yescharacteristic
668C2×C73#267611yescharacteristic
669C2×C73#268411yescharacteristic
670C2×C73#268611yescharacteristic
671C2×C73#271011yescharacteristic
672C2×C73#271211yescharacteristic
673C22×#124C2×C7311yescharacteristic, complemented
674C2×#394C2×C7311yescharacteristic, complemented
675C2×#393C2×C7311yescharacteristic, complemented
676C2×#392C2×C7311yescharacteristic
677C2×#386C2×C7311yescharacteristic, complemented
678C2×#386C2×C7311yescharacteristic, complemented
679#1446C2×C7311yescharacteristic, complemented
680#1440C2×C7311yescharacteristic, complemented
681#1440C2×C7311yescharacteristic, complemented
682#1439C2×C7311yescharacteristic, complemented
683#1438C2×C7311yescharacteristic, complemented
684#1438C2×C7311yescharacteristic, complemented
685#1437C2×C7311yescharacteristic, complemented
686#1436C2×C7311yescharacteristic, complemented
687C22⋊#95C2×C7311yescharacteristic, complemented
688C73#1531411yescharacteristic, direct product factor, Sylow
689C23×Q8C22×C7311yescharacteristic
690C23×D4C22×C7311yescharacteristic
691C23×D4C22×C7311yescharacteristic
692C23×D4C22×C7311yescharacteristic
693C24×C4C22×C7311yescharacteristic
694C2×#124—24no—
695C2×#124—24no—
696C2×#124—24no—
697C22×C4⋊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×C22⋊C4C22×C7311yescharacteristic
709C22×C22⋊C4C22×C7311yescharacteristic
710C22×C22⋊C4C22×C7311yescharacteristic
711C22×C22⋊C4C22×C7311yescharacteristic
712C22×C42C22×C7311yescharacteristic
713#394—24no—
714#393—24no—
715#392—24no—
716#386—24no—
717#386—24no—
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
727C2×#95C22×C7311yescharacteristic
728C2×#95C22×C7311yescharacteristic
729C2×#95C22×C7311yescharacteristic
730C2×#95C22×C7311yescharacteristic
731C2×#95C22×C7311yescharacteristic
732C25C23×C7311yescharacteristic
733C25C23×C7311yescharacteristic
734C25C23×C7311yescharacteristic
735C22×Q8—22no—
736C22×Q8—22no—
737C22×Q8—22no—
738C22×Q8—22no—
739C22×Q8—22no—
740C22×Q8—41no—
741C22×Q8—41no—
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—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4—41no—
762C22×D4D4×C7314yes—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4C23×C7311yescharacteristic
771C23×C4C23×C7311yescharacteristic
772C23×C4C23×C7311yescharacteristic
773C23×C4C23×C7311yescharacteristic
774C23×C4C23×C7311yescharacteristic
775C23×C4C23×C7311yescharacteristic
776C23×C4C23×C7311yescharacteristic
777C23×C4C23×C7311yescharacteristic
778C23×C4C23×C7311yescharacteristic
779C23×C4C23×C7311yescharacteristic
780C23×C4C23×C7311yescharacteristic
781C23×C4C23×C7311yescharacteristic
782#124—232no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—41no—
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—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4D4×C7314yescomplemented
827C2×C22⋊C4D4×C7314yescomplemented
828C2×C42—22no—
829C2×C42—22no—
830C2×C42—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95D4×C7314yescomplemented
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—
882C24—21no—
883C24—21no—
884C24—21no—
885C24C2×D4×C7312yes—
886C24C2×D4×C7312yes—
887C24C2×D4×C7312yes—
888C24C2×D4×C7312yes—
889C24#41×C7312yes—
890C24C24×C7311yescharacteristic
891C2×Q8—28no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—28no—
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—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
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×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C7312yes—
999C22×C4C2×D4×C7312yes—
1000C22×C4C2×D4×C7312yes—
1001C22×C4C2×D4×C7312yes—
1002C22×C4C2×D4×C7312yes—
1003C22×C4C2×D4×C7312yes—
1004C22×C4C2×D4×C7312yes—
1005C22×C4C2×D4×C7312yes—
1006C22×C4#41×C7312yes—
1007C22×C4#41×C7312yes—
1008C22×C4#41×C7312yes—
1009C22×C4#41×C7312yes—
1010C4⋊C4—44no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C42—28no—
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—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
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—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23#120×C7314yes—
1131C23C22×D4×C7311yescharacteristic
1132C23C22×D4×C7311yescharacteristic
1133C23C22×D4×C7311yescharacteristic
1134C23C22×D4×C7311yescharacteristic
1135C23C2×#41×C7311yescharacteristic
1136C23C2×#41×C7311yescharacteristic
1137C23C2×#41×C7311yescharacteristic
1138C23C2×#41×C7311yescharacteristic
1139C23C2×#41×C7311yescharacteristic
1140C23H(5,𝔽2)×C7311yescharacteristic
1141C23H(5,𝔽2)×C7311yescharacteristic
1142C23H(5,𝔽2)×C7311yescharacteristic
1143C23H(5,𝔽2)×C7311yescharacteristic
1144C23H(5,𝔽2)×C7311yescharacteristic
1145C232−1+4×C7311yescharacteristic
1146Q8—416no—
1147D4—416no—
1148D4—416no—
1149D4—416no—
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—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—416no—
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—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4#121×C7314yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
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—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#120×C7311yescharacteristic
1281C22C2×#121×C7311yescharacteristic
1282C22#525×C7311yescharacteristic
1283C22#529×C7311yescharacteristic
1284C22#532×C7311yescharacteristic
1285C22#532×C7311yescharacteristic
1286C22#534×C7311yescharacteristic
1287C22#535×C7311yescharacteristic
1288C22#535×C7311yescharacteristic
1289C22#537×C7311yescharacteristic
1290C22#538×C7311yescharacteristic
1291C22#538×C7311yescharacteristic
1292C22#538×C7311yescharacteristic
1293C22#542×C7311yescharacteristic
1294C22#542×C7311yescharacteristic
1295C22D42×C7311yescharacteristic
1296C22D42×C7311yescharacteristic
1297C22#546×C7311yescharacteristic
1298C22#546×C7311yescharacteristic
1299C22#546×C7311yescharacteristic
1300C22#546×C7311yescharacteristic
1301C22#546×C7311yescharacteristic
1302C22#546×C7311yescharacteristic
1303C22#546×C7311yescharacteristic
1304C22#546×C7311yescharacteristic
1305C22#546×C7311yescharacteristic
1306C22#547×C7311yescharacteristic
1307C22#547×C7311yescharacteristic
1308C22#548×C7311yescharacteristic
1309C22#551×C7311yescharacteristic
1310C22#555×C7311yescharacteristic
1311C22#559×C7311yescharacteristic
1312C22#559×C7311yescharacteristic
1313C22H(3,𝔽4)×C7311yescharacteristic
1314C22#562×C7311yescharacteristic
1315C4—24no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—82no—
1329C2—82no—
1330C2C73×#240411yescharacteristic
1331C2C73×#241011yescharacteristic
1332C2C73×#242711yescharacteristic
1333C2C73×#243011yescharacteristic
1334C2C73×#245911yescharacteristic
1335C2C73×#246111yescharacteristic
1336C2C73×#254411yescharacteristic
1337C2C73×#255511yescharacteristic
1338C2C73×#255711yescharacteristic
1339C2C73×#267011yescharacteristic
1340C2C73×#267611yescharacteristic
1341C2C73×#268411yescharacteristic
1342C2C73×#268611yescharacteristic
1343C2C73×#271011yescharacteristic
1344C2C73×#271211yescharacteristic
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×#386×C73C2semidirect
6. C2×#386×C73C2semidirect
7. C73×#1446C2semidirect
8. C73×#1440C2semidirect
9. C73×#1440C2semidirect
10. C73×#1439C2semidirect
11. C73×#1438C2semidirect
12. C73×#1438C2semidirect
13. C73×#1437C2semidirect
14. C73×#1436C2semidirect
15. C73×C22⋊#95C2semidirect
153. C2×C22⋊C4×C73D4semidirect
154. C2×C22⋊C4×C73D4semidirect
171. #95×C73D4semidirect
654. #15314C73direct (N × H)
673. C22×#124C2×C73semidirect
674. C2×#394C2×C73semidirect
675. C2×#393C2×C73semidirect
677. C2×#386C2×C73semidirect
678. C2×#386C2×C73semidirect
679. #1446C2×C73semidirect
680. #1440C2×C73semidirect
681. #1440C2×C73semidirect
682. #1439C2×C73semidirect
683. #1438C2×C73semidirect
684. #1438C2×C73semidirect
685. #1437C2×C73semidirect
686. #1436C2×C73semidirect
687. C22⋊#95C2×C73semidirect
688. C73#15314direct (N × H)
826. C2×C22⋊C4D4×C73semidirect
827. C2×C22⋊C4D4×C73semidirect
844. #95D4×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×#386×C732
C73×#14462
C73×#14402
C73×#14392
C73×#14382
C73×#14372
C73×#14362
C73×C22⋊#952
#1531473