Finite Group Databasebeta

← C73×#24389 #32933793

Subgroups — C73×#24389 #32933793

Order 18688.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C73C211yesmaximal, characteristic
2C2×#470×C73C211yesmaximal, characteristic, complemented
3C2×#468×C73C211yesmaximal, characteristic, complemented
4C2×#452×C73C211yesmaximal, characteristic, complemented
5C2×#407×C73C211yesmaximal, characteristic, complemented
6C73×#2848C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2001C211yesmaximal, characteristic, complemented
10C73×#2000C211yesmaximal, characteristic, complemented
11C73×#1895C211yesmaximal, characteristic, complemented
12C73×#1894C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1854C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C24×C4×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic, complemented
19C22×SD16×C73C2211yescharacteristic, complemented
20C22×M16×C73C2211yescharacteristic
21C22×M16×C73C2211yescharacteristic
22#525×C73—24no—
23#525×C73—24no—
24C2×#123×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C22⋊Q8×C73C2211yescharacteristic
29C2×C22⋊Q8×C73C2211yescharacteristic
30C2×#121×C73C2211yescharacteristic
31C2×#121×C73C2211yescharacteristic
32C2×#120×C73—21no—
33C2×C4×D4×C73—21no—
34C2×C4×D4×C73—21no—
35C2×#117×C73C2211yescharacteristic
36#470×C73—24no—
37#468×C73—24no—
38#452×C73—24no—
39C2×#107×C73C2211yescharacteristic, complemented
40C2×#106×C73C2211yescharacteristic, complemented
41C2×#103×C73C2211yescharacteristic, complemented
42C2×#103×C73C2211yescharacteristic, complemented
43C2×#103×C73C2211yescharacteristic, complemented
44C2×#103×C73C2211yescharacteristic, complemented
45C2×#103×C73C2211yescharacteristic, complemented
46C2×#102×C73C2211yescharacteristic, complemented
47C2×#102×C73C2211yescharacteristic, complemented
48C2×#102×C73C2211yescharacteristic, complemented
49#407×C73—24no—
50C2×C22⋊C8×C73C2211yescharacteristic
51C2×C22⋊C8×C73C2211yescharacteristic
52C2×C22⋊C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54#385×C73—21no—
55#385×C73—21no—
56#385×C73—21no—
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#379×C73—21no—
61#340×C73C2211yescharacteristic, complemented
62#340×C73C2211yescharacteristic, complemented
63#340×C73C2211yescharacteristic, complemented
64#340×C73C2211yescharacteristic, complemented
65C25×C73D411yescharacteristic
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—22no—
70C2×#41×C73—41no—
71C2×#41×C73—41no—
72C22×Q8×C73C2311yescharacteristic
73C22×Q8×C73C2311yescharacteristic
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73C2311yescharacteristic
78C23×C4×C73—22no—
79C23×C4×C73—21no—
80C23×C4×C73—22no—
81C23×C4×C73—22no—
82C23×C4×C73—22no—
83C23×C4×C73—41no—
84C23×C4×C73—41no—
85C23×C4×C73D411yescharacteristic
86C23×C4×C73D411yescharacteristic
87C23×C4×C73D411yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C2×Q16×C73—22no—
92C2×Q16×C73—22no—
93C2×Q16×C73—41no—
94C2×SD16×C73—22no—
95C2×SD16×C73—22no—
96C2×SD16×C73—41no—
97C2×M16×C73—22no—
98C2×M16×C73—22no—
99C2×M16×C73—22no—
100C2×M16×C73—22no—
101C2×M16×C73—41no—
102C2×M16×C73—41no—
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107#123×C73—28no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—22no—
110C22⋊Q8×C73—22no—
111C22⋊Q8×C73—22no—
112C22⋊Q8×C73—22no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—41no—
116C22⋊Q8×C73—41no—
117C22⋊Q8×C73D414yes—
118#121×C73—22no—
119#121×C73—22no—
120#121×C73—22no—
121#121×C73D414yes—
122#120×C73—28no—
123C4×D4×C73—28no—
124C4×D4×C73—28no—
125#117×C73—22no—
126#117×C73—22no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73—21no—
129C2×C4⋊C4×C73—21no—
130C2×C4⋊C4×C73—21no—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73C2311yescharacteristic
133C2×C4⋊C4×C73C2311yescharacteristic
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C22⋊C4×C73—21no—
138C2×C22⋊C4×C73—21no—
139C2×C22⋊C4×C73—21no—
140C2×C22⋊C4×C73—21no—
141C2×C22⋊C4×C73—21no—
142C2×C22⋊C4×C73—21no—
143C2×C22⋊C4×C73—21no—
144C2×C22⋊C4×C73—21no—
145C2×C22⋊C4×C73—21no—
146C2×C22⋊C4×C73—21no—
147C2×C22⋊C4×C73—21no—
148C2×C42×C73—21no—
149#107×C73—22no—
150#106×C73—22no—
151#103×C73—22no—
152#103×C73—22no—
153#103×C73—22no—
154#103×C73—22no—
155#103×C73—41no—
156#102×C73—22no—
157#102×C73—22no—
158#102×C73—41no—
159C22⋊C8×C73—22no—
160C22⋊C8×C73—22no—
161C22⋊C8×C73—22no—
162C22⋊C8×C73D414yescomplemented
163#95×C73—21no—
164#95×C73—21no—
165#95×C73—21no—
166C24×C73—22no—
167C24×C73—22no—
168C24×C73—22no—
169C24×C73—21no—
170C24×C73—41no—
171C24×C73—41no—
172C24×C73—41no—
173C24×C73—41no—
174C24×C73C2×D411yescharacteristic
175C24×C73C2×D411yescharacteristic
176C24×C73C2×D411yescharacteristic
177#41×C73—44no—
178#41×C73—44no—
179#41×C73—44no—
180#41×C73—44no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73C2×D412yes—
193C2×D4×C73—24no—
194C2×D4×C73—24no—
195C2×D4×C73—24no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—42no—
202C2×D4×C73—42no—
203C2×D4×C73—42no—
204C2×D4×C73—42no—
205C2×D4×C73—42no—
206C2×D4×C73—42no—
207C2×D4×C73C2×D412yes—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—24no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
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—41no—
237C22×C4×C73—41no—
238C22×C4×C73—41no—
239C22×C4×C73—44no—
240C22×C4×C73—44no—
241C22×C4×C73—44no—
242C22×C4×C73—44no—
243C22×C4×C73—42no—
244C22×C4×C73—42no—
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D412yes—
248C22×C4×C73C2×D412yes—
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D412yes—
251C22×C4×C73#4112yes—
252C22×C4×C73C2411yescharacteristic
253Q16×C73—44no—
254SD16×C73—44no—
255M16×C73—44no—
256M16×C73—44no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—21no—
267C2×C8×C73C2×D412yes—
268C2×C8×C73C2×D412yes—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—42no—
280C4⋊C4×C73—42no—
281C4⋊C4×C73—42no—
282C4⋊C4×C73C2×D412yes—
283C4⋊C4×C73C2×D412yes—
284C22⋊C4×C73—24no—
285C22⋊C4×C73—24no—
286C22⋊C4×C73—24no—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—24no—
289C22⋊C4×C73—42no—
290C22⋊C4×C73—42no—
291C22⋊C4×C73—42no—
292C22⋊C4×C73—42no—
293C22⋊C4×C73—42no—
294C22⋊C4×C73—42no—
295C42×C73—24no—
296C23×C73—21no—
297C23×C73—21no—
298C23×C73—21no—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—21no—
303C23×C73—21no—
304C23×C73—21no—
305C23×C73—21no—
306C23×C73—21no—
307C23×C73—21no—
308C23×C73—21no—
309C23×C73—21no—
310C23×C73—21no—
311C23×C73—21no—
312C23×C73—21no—
313C23×C73—21no—
314C23×C73—22no—
315C23×C73—44no—
316C23×C73—44no—
317C23×C73—44no—
318C23×C73—44no—
319C23×C73—44no—
320C23×C73—44no—
321C23×C73—44no—
322C23×C73—41no—
323C23×C73—41no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73—41no—
327C23×C73—41no—
328C23×C73#12012yes—
329C23×C73#12112yes—
330C23×C73#13712yes—
331C23×C73C22×D411yescharacteristic
332Q8×C73—22no—
333Q8×C73—22no—
334Q8×C73—41no—
335Q8×C73—41no—
336Q8×C73—41no—
337Q8×C73—41no—
338Q8×C73—41no—
339Q8×C73—41no—
340D4×C73—22no—
341D4×C73—22no—
342D4×C73—48no—
343D4×C73—48no—
344D4×C73—48no—
345D4×C73—41no—
346D4×C73—41no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—21no—
362C2×C4×C73—22no—
363C2×C4×C73—21no—
364C2×C4×C73—21no—
365C2×C4×C73—44no—
366C2×C4×C73—44no—
367C2×C4×C73—44no—
368C2×C4×C73—48no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73#12012yes—
392C2×C4×C73#12112yes—
393C2×C4×C73C22×D411yescharacteristic
394C2×C4×C73C22×D411yescharacteristic
395C2×C4×C73C22×D411yescharacteristic
396C2×C4×C73C2×#4111yescharacteristic
397C2×C4×C73H(5,𝔽2)11yescharacteristic
398C2×C4×C73H(5,𝔽2)11yescharacteristic
399C8×C73—22no—
400C8×C73—22no—
401C8×C73—41no—
402C8×C73—41no—
403C22×C73—22no—
404C22×C73—22no—
405C22×C73—22no—
406C22×C73—22no—
407C22×C73—22no—
408C22×C73—22no—
409C22×C73—22no—
410C22×C73—22no—
411C22×C73—22no—
412C22×C73—416no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—41no—
418C22×C73—41no—
419C22×C73—41no—
420C22×C73—41no—
421C22×C73—41no—
422C22×C73—41no—
423C22×C73—41no—
424C22×C73—41no—
425C22×C73—42no—
426C22×C73—42no—
427C22×C73—42no—
428C22×C73—81no—
429C22×C73—81no—
430C22×C73—81no—
431C22×C73—81no—
432C22×C73C2×#12011yescharacteristic
433C22×C73C2×#12111yescharacteristic
434C22×C73#53411yescharacteristic
435C22×C73C2×#13711yescharacteristic
436C22×C73#57511yescharacteristic
437C22×C73#57511yescharacteristic
438C22×C73#57511yescharacteristic
439C4×C73—22no—
440C4×C73—22no—
441C4×C73—41no—
442C4×C73—42no—
443C4×C73—42no—
444C4×C73—42no—
445C4×C73—81no—
446C4×C73—81no—
447C4×C73—81no—
448C4×C73—81no—
449C4×C73D4211yescharacteristic
450C4×C73D4211yescharacteristic
451C4×C73#54611yescharacteristic
452C4×C73#54611yescharacteristic
453#24389C7311yesmaximal, characteristic, direct product factor, Sylow
454C2×C73—42no—
455C2×C73—42no—
456C2×C73—42no—
457C2×C73—82no—
458C2×C73#241011yescharacteristic
459C2×C73#300511yescharacteristic
460C2×C73#300711yescharacteristic
461C2×C73#305411yescharacteristic
462C2×C73#305611yescharacteristic
463C2×C73#319611yescharacteristic
464C2×C73#319711yescharacteristic
465C2×#525C2×C7311yescharacteristic
466C2×#470C2×C7311yescharacteristic, complemented
467C2×#468C2×C7311yescharacteristic, complemented
468C2×#452C2×C7311yescharacteristic, complemented
469C2×#407C2×C7311yescharacteristic, complemented
470#2848C2×C7311yescharacteristic, complemented
471#2036C2×C7311yescharacteristic, complemented
472#2034C2×C7311yescharacteristic, complemented
473#2001C2×C7311yescharacteristic, complemented
474#2000C2×C7311yescharacteristic, complemented
475#1895C2×C7311yescharacteristic, complemented
476#1894C2×C7311yescharacteristic, complemented
477#1873C2×C7311yescharacteristic, complemented
478#1854C2×C7311yescharacteristic, complemented
479#1788C2×C7311yescharacteristic, complemented
480C73#2438911yescharacteristic, direct product factor, Sylow
481C22×#41C22×C7311yescharacteristic
482C24×C4C22×C7311yescharacteristic
483C22×Q16C22×C7311yescharacteristic, complemented
484C22×SD16C22×C7311yescharacteristic, complemented
485C22×M16C22×C7311yescharacteristic
486C22×M16C22×C7311yescharacteristic
487#525—24no—
488#525—24no—
489C2×#123—21no—
490C2×C22⋊Q8C22×C7311yescharacteristic
491C2×C22⋊Q8C22×C7311yescharacteristic
492C2×C22⋊Q8C22×C7311yescharacteristic
493C2×C22⋊Q8C22×C7311yescharacteristic
494C2×C22⋊Q8C22×C7311yescharacteristic
495C2×#121C22×C7311yescharacteristic
496C2×#121C22×C7311yescharacteristic
497C2×#120—21no—
498C2×C4×D4—21no—
499C2×C4×D4—21no—
500C2×#117C22×C7311yescharacteristic
501#470—24no—
502#468—24no—
503#452—24no—
504C2×#107C22×C7311yescharacteristic, complemented
505C2×#106C22×C7311yescharacteristic, complemented
506C2×#103C22×C7311yescharacteristic, complemented
507C2×#103C22×C7311yescharacteristic, complemented
508C2×#103C22×C7311yescharacteristic, complemented
509C2×#103C22×C7311yescharacteristic, complemented
510C2×#103C22×C7311yescharacteristic, complemented
511C2×#102C22×C7311yescharacteristic, complemented
512C2×#102C22×C7311yescharacteristic, complemented
513C2×#102C22×C7311yescharacteristic, complemented
514#407—24no—
515C2×C22⋊C8C22×C7311yescharacteristic
516C2×C22⋊C8C22×C7311yescharacteristic
517C2×C22⋊C8C22×C7311yescharacteristic
518C2×C22⋊C8C22×C7311yescharacteristic
519#385—21no—
520#385—21no—
521#385—21no—
522#380C22×C7311yescharacteristic
523#380C22×C7311yescharacteristic
524#380C22×C7311yescharacteristic
525#379—21no—
526#340C22×C7311yescharacteristic, complemented
527#340C22×C7311yescharacteristic, complemented
528#340C22×C7311yescharacteristic, complemented
529#340C22×C7311yescharacteristic, complemented
530C25D4×C7311yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C7311yescharacteristic
538C22×Q8C23×C7311yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C7311yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C7311yescharacteristic
551C23×C4D4×C7311yescharacteristic
552C23×C4D4×C7311yescharacteristic
553C23×C4C23×C7311yescharacteristic
554C23×C4C23×C7311yescharacteristic
555C23×C4C23×C7311yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C7311yescharacteristic
569C22×C8C23×C7311yescharacteristic
570C22×C8C23×C7311yescharacteristic
571C22×C8C23×C7311yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C7314yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C7314yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C7311yescharacteristic
598C2×C4⋊C4C23×C7311yescharacteristic
599C2×C4⋊C4C23×C7311yescharacteristic
600C2×C4⋊C4C23×C7311yescharacteristic
601C2×C4⋊C4C23×C7311yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C7314yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C7311yescharacteristic
640C24C2×D4×C7311yescharacteristic
641C24C2×D4×C7311yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C7312yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C7312yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C7311yescharacteristic
711C22×C4C2×D4×C7311yescharacteristic
712C22×C4C2×D4×C7312yes—
713C22×C4C2×D4×C7312yes—
714C22×C4C2×D4×C7311yescharacteristic
715C22×C4C2×D4×C7312yes—
716C22×C4#41×C7312yes—
717C22×C4C24×C7311yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C7312yes—
733C2×C8C2×D4×C7312yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C7312yes—
748C4⋊C4C2×D4×C7312yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C7312yes—
794C23#121×C7312yes—
795C23#137×C7312yes—
796C23C22×D4×C7311yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C7312yes—
857C2×C4#121×C7312yes—
858C2×C4C22×D4×C7311yescharacteristic
859C2×C4C22×D4×C7311yescharacteristic
860C2×C4C22×D4×C7311yescharacteristic
861C2×C4C2×#41×C7311yescharacteristic
862C2×C4H(5,𝔽2)×C7311yescharacteristic
863C2×C4H(5,𝔽2)×C7311yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C7311yescharacteristic
898C22C2×#121×C7311yescharacteristic
899C22#534×C7311yescharacteristic
900C22C2×#137×C7311yescharacteristic
901C22#575×C7311yescharacteristic
902C22#575×C7311yescharacteristic
903C22#575×C7311yescharacteristic
904C4—22no—
905C4—22no—
906C4—42no—
907C4—42no—
908C4—41no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C7311yescharacteristic
915C4D42×C7311yescharacteristic
916C4#546×C7311yescharacteristic
917C4#546×C7311yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C73×#241011yescharacteristic
923C2C73×#300511yescharacteristic
924C2C73×#300711yescharacteristic
925C2C73×#305411yescharacteristic
926C2C73×#305611yescharacteristic
927C2C73×#319611yescharacteristic
928C2C73×#319711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#525×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C24×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C73C2semidirect
3. C2×#468×C73C2semidirect
4. C2×#452×C73C2semidirect
5. C2×#407×C73C2semidirect
6. C73×#2848C2semidirect
7. C73×#2036C2semidirect
8. C73×#2034C2semidirect
9. C73×#2001C2semidirect
10. C73×#2000C2semidirect
11. C73×#1895C2semidirect
12. C73×#1894C2semidirect
13. C73×#1873C2semidirect
14. C73×#1854C2semidirect
15. C73×#1788C2semidirect
18. C22×Q16×C73C22semidirect
19. C22×SD16×C73C22semidirect
39. C2×#107×C73C22semidirect
40. C2×#106×C73C22semidirect
41. C2×#103×C73C22semidirect
42. C2×#103×C73C22semidirect
43. C2×#103×C73C22semidirect
44. C2×#103×C73C22semidirect
45. C2×#103×C73C22semidirect
46. C2×#102×C73C22semidirect
47. C2×#102×C73C22semidirect
48. C2×#102×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
63. #340×C73C22semidirect
64. #340×C73C22semidirect
162. C22⋊C8×C73D4semidirect
453. #24389C73direct (N × H)
466. C2×#470C2×C73semidirect
467. C2×#468C2×C73semidirect
468. C2×#452C2×C73semidirect
469. C2×#407C2×C73semidirect
470. #2848C2×C73semidirect
471. #2036C2×C73semidirect
472. #2034C2×C73semidirect
473. #2001C2×C73semidirect
474. #2000C2×C73semidirect
475. #1895C2×C73semidirect
476. #1894C2×C73semidirect
477. #1873C2×C73semidirect
478. #1854C2×C73semidirect
479. #1788C2×C73semidirect
480. C73#24389direct (N × H)
483. C22×Q16C22×C73semidirect
484. C22×SD16C22×C73semidirect
504. C2×#107C22×C73semidirect
505. C2×#106C22×C73semidirect
506. C2×#103C22×C73semidirect
507. C2×#103C22×C73semidirect
508. C2×#103C22×C73semidirect
509. C2×#103C22×C73semidirect
510. C2×#103C22×C73semidirect
511. C2×#102C22×C73semidirect
512. C2×#102C22×C73semidirect
513. C2×#102C22×C73semidirect
526. #340C22×C73semidirect
527. #340C22×C73semidirect
528. #340C22×C73semidirect
529. #340C22×C73semidirect
627. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C732
C2×#470×C732
C2×#468×C732
C2×#452×C732
C2×#407×C732
C73×#28482
C73×#20362
C73×#20342
C73×#20012
C73×#20002
C73×#18952
C73×#18942
C73×#18732
C73×#18542
C73×#17882
#2438973