Finite Group Databasebeta

← C73×#24841 #32934245

Subgroups — C73×#24841 #32934245

Order 18688.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C73C211yesmaximal, characteristic, complemented
2C2×#423×C73C211yesmaximal, characteristic, complemented
3C73×#2851C211yesmaximal, characteristic, complemented
4C4×#121×C73C211yesmaximal, characteristic
5C73×#2088C211yesmaximal, characteristic, complemented
6C73×#2086C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#1989C211yesmaximal, characteristic, complemented
10C73×#1949C211yesmaximal, characteristic, complemented
11C73×#1895C211yesmaximal, characteristic
12C73×#1895C211yesmaximal, characteristic
13C73×#1809C211yesmaximal, characteristic, complemented
14C73×#1809C211yesmaximal, characteristic, complemented
15C73×#1804C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×#125×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73—21no—
21C2×C4×D4×C73C2211yescharacteristic
22C22×C42×C73C2211yescharacteristic
23#478×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28#423×C73—24no—
29C2×C4⋊C8×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37#390×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#388×C73—21no—
42#387×C73—21no—
43#387×C73—21no—
44#386×C73—21no—
45#385×C73—21no—
46#385×C73—21no—
47#382×C73C2211yescharacteristic
48#380×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C22⋊C4×C73—21no—
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73D411yescharacteristic
65C23×C4×C73D411yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C2×M16×C73—22no—
68C2×M16×C73—22no—
69C2×M16×C73—22no—
70C2×M16×C73—22no—
71C2×M16×C73—41no—
72C2×M16×C73—41no—
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77#125×C73—22no—
78#125×C73—22no—
79#121×C73—22no—
80#121×C73Q814yes—
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83C4×D4×C73—44no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C42×C73—22no—
104C2×C42×C73—22no—
105C2×C42×C73—21no—
106C2×C42×C73D411yescharacteristic
107C2×C42×C73D411yescharacteristic
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110#107×C73—22no—
111#107×C73—41no—
112#106×C73—22no—
113#106×C73—41no—
114C4⋊C8×C73—22no—
115C4⋊C8×C73—22no—
116C4⋊C8×C73—22no—
117C4⋊C8×C73D414yescomplemented
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—41no—
121#102×C73—41no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131C24×C73—21no—
132C24×C73C2×D411yescharacteristic
133C2×D4×C73—24no—
134C2×D4×C73—21no—
135C2×D4×C73—21no—
136C2×D4×C73—21no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—42no—
140C2×D4×C73—42no—
141C2×D4×C73C2×Q812yes—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—22no—
148C22×C4×C73—22no—
149C22×C4×C73—22no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—41no—
157C22×C4×C73—41no—
158C22×C4×C73—41no—
159C22×C4×C73—42no—
160C22×C4×C73—42no—
161C22×C4×C73—42no—
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×Q812yes—
168C22×C4×C73#4112yes—
169C22×C4×C73C2411yescharacteristic
170M16×C73—44no—
171M16×C73—44no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73C2×D412yes—
183C2×C8×C73C2×D412yes—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73C2×Q812yes—
203C22⋊C4×C73—24no—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C42×C73—22no—
211C42×C73—22no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—42no—
215C42×C73C2×D412yes—
216C42×C73#4112yes—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—22no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73C22⋊Q812yes—
231C23×C73C22×D411yescharacteristic
232D4×C73—22no—
233D4×C73—22no—
234D4×C73—48no—
235D4×C73—41no—
236D4×C73—41no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—21no—
250C2×C4×C73—22no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—44no—
254C2×C4×C73—44no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—84no—
276C2×C4×C73#12112yes—
277C2×C4×C73#12112yes—
278C2×C4×C73C22⋊Q812yes—
279C2×C4×C73AGL(1,ℤ/8)12yes—
280C2×C4×C73C22×D411yescharacteristic
281C2×C4×C73C22×Q811yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73H(5,𝔽2)11yescharacteristic
285C2×C4×C732−1+411yescharacteristic
286C8×C73—22no—
287C8×C73—22no—
288C8×C73—41no—
289C8×C73—41no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—81no—
301C22×C73—81no—
302C22×C73—81no—
303C22×C73—81no—
304C22×C73C2×#12111yescharacteristic
305C22×C73C2×C22⋊Q811yescharacteristic
306C22×C73#53711yescharacteristic
307C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C73#57511yescharacteristic
309C22×C73#57511yescharacteristic
310C22×C73#57511yescharacteristic
311C4×C73—22no—
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—22no—
315C4×C73—42no—
316C4×C73—41no—
317C4×C73—81no—
318C4×C73—81no—
319C4×C73—81no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73—81no—
323C4×C73#54611yescharacteristic
324C4×C73D4×Q811yescharacteristic
325C4×C73#55211yescharacteristic
326C4×C73#55411yescharacteristic
327#24841C7311yesmaximal, characteristic, direct product factor, Sylow
328C2×C73—42no—
329C2×C73—82no—
330C2×C73#241711yescharacteristic
331C2×C73#305411yescharacteristic
332C2×C73#305511yescharacteristic
333C2×C73#307711yescharacteristic
334C2×C73#308011yescharacteristic
335C2×C73#325111yescharacteristic
336C2×C73#325611yescharacteristic
337C2×#478C2×C7311yescharacteristic, complemented
338C2×#423C2×C7311yescharacteristic, complemented
339#2851C2×C7311yescharacteristic, complemented
340C4×#121C2×C7311yescharacteristic
341#2088C2×C7311yescharacteristic, complemented
342#2086C2×C7311yescharacteristic, complemented
343#2067C2×C7311yescharacteristic, complemented
344#2065C2×C7311yescharacteristic, complemented
345#1989C2×C7311yescharacteristic, complemented
346#1949C2×C7311yescharacteristic, complemented
347#1895C2×C7311yescharacteristic
348#1895C2×C7311yescharacteristic
349#1809C2×C7311yescharacteristic, complemented
350#1809C2×C7311yescharacteristic, complemented
351#1804C2×C7311yescharacteristic, complemented
352C73#2484111yescharacteristic, direct product factor, Sylow
353C22×M16C22×C7311yescharacteristic
354C22×M16C22×C7311yescharacteristic
355C2×#125C22×C7311yescharacteristic
356C2×#121C22×C7311yescharacteristic
357C2×C4×D4—21no—
358C2×C4×D4C22×C7311yescharacteristic
359C22×C42C22×C7311yescharacteristic
360#478—24no—
361C2×#107C22×C7311yescharacteristic
362C2×#107C22×C7311yescharacteristic
363C2×#106C22×C7311yescharacteristic
364C2×#106C22×C7311yescharacteristic
365#423—24no—
366C2×C4⋊C8C22×C7311yescharacteristic
367C2×C4⋊C8C22×C7311yescharacteristic
368C2×C4⋊C8C22×C7311yescharacteristic
369C2×C4⋊C8C22×C7311yescharacteristic
370C2×#102C22×C7311yescharacteristic
371C2×#102C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×#102C22×C7311yescharacteristic
374#390C22×C7311yescharacteristic
375#389C22×C7311yescharacteristic
376#389C22×C7311yescharacteristic
377#389C22×C7311yescharacteristic
378#388—21no—
379#387—21no—
380#387—21no—
381#386—21no—
382#385—21no—
383#385—21no—
384#382C22×C7311yescharacteristic
385#380C22×C7311yescharacteristic
386#380C22×C7311yescharacteristic
387#380C22×C7311yescharacteristic
388C4×C4⋊C4C22×C7311yescharacteristic
389C4×C22⋊C4—21no—
390#340C22×C7311yescharacteristic
391#340C22×C7311yescharacteristic
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398C22×D4—21no—
399C22×D4C23×C7311yescharacteristic
400C23×C4—21no—
401C23×C4D4×C7311yescharacteristic
402C23×C4D4×C7311yescharacteristic
403C23×C4C23×C7311yescharacteristic
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—41no—
409C2×M16—41no—
410C22×C8C23×C7311yescharacteristic
411C22×C8C23×C7311yescharacteristic
412C22×C8C23×C7311yescharacteristic
413C22×C8C23×C7311yescharacteristic
414#125—22no—
415#125—22no—
416#121—22no—
417#121Q8×C7314yes—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—44no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—21no—
443C2×C42D4×C7311yescharacteristic
444C2×C42D4×C7311yescharacteristic
445C2×C42C23×C7311yescharacteristic
446C2×C42C23×C7311yescharacteristic
447#107—22no—
448#107—41no—
449#106—22no—
450#106—41no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454C4⋊C8D4×C7314yescomplemented
455#102—22no—
456#102—22no—
457#102—41no—
458#102—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468C24—21no—
469C24C2×D4×C7311yescharacteristic
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4C2×Q8×C7312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4C2×D4×C7311yescharacteristic
500C22×C4C2×D4×C7311yescharacteristic
501C22×C4C2×D4×C7311yescharacteristic
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×D4×C7311yescharacteristic
504C22×C4C2×Q8×C7312yes—
505C22×C4#41×C7312yes—
506C22×C4C24×C7311yescharacteristic
507M16—44no—
508M16—44no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8C2×D4×C7312yes—
520C2×C8C2×D4×C7312yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×Q8×C7312yes—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C42—22no—
548C42—22no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42C2×D4×C7312yes—
553C42#41×C7312yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C22⋊Q8×C7312yes—
568C23C22×D4×C7311yescharacteristic
569D4—22no—
570D4—22no—
571D4—48no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4#121×C7312yes—
614C2×C4#121×C7312yes—
615C2×C4C22⋊Q8×C7312yes—
616C2×C4AGL(1,ℤ/8)×C7312yes—
617C2×C4C22×D4×C7311yescharacteristic
618C2×C4C22×Q8×C7311yescharacteristic
619C2×C4C2×#41×C7311yescharacteristic
620C2×C4C2×#41×C7311yescharacteristic
621C2×C4H(5,𝔽2)×C7311yescharacteristic
622C2×C42−1+4×C7311yescharacteristic
623C8—22no—
624C8—22no—
625C8—41no—
626C8—41no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22C2×#121×C7311yescharacteristic
642C22C2×C22⋊Q8×C7311yescharacteristic
643C22#537×C7311yescharacteristic
644C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
645C22#575×C7311yescharacteristic
646C22#575×C7311yescharacteristic
647C22#575×C7311yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—22no—
652C4—41no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4#546×C7311yescharacteristic
661C4D4×Q8×C7311yescharacteristic
662C4#552×C7311yescharacteristic
663C4#554×C7311yescharacteristic
664C2—42no—
665C2—82no—
666C2C73×#241711yescharacteristic
667C2C73×#305411yescharacteristic
668C2C73×#305511yescharacteristic
669C2C73×#307711yescharacteristic
670C2C73×#308011yescharacteristic
671C2C73×#325111yescharacteristic
672C2C73×#325611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#478×C73C2semidirect
2. C2×#423×C73C2semidirect
3. C73×#2851C2semidirect
5. C73×#2088C2semidirect
6. C73×#2086C2semidirect
7. C73×#2067C2semidirect
8. C73×#2065C2semidirect
9. C73×#1989C2semidirect
10. C73×#1949C2semidirect
13. C73×#1809C2semidirect
14. C73×#1809C2semidirect
15. C73×#1804C2semidirect
117. C4⋊C8×C73D4semidirect
327. #24841C73direct (N × H)
337. C2×#478C2×C73semidirect
338. C2×#423C2×C73semidirect
339. #2851C2×C73semidirect
341. #2088C2×C73semidirect
342. #2086C2×C73semidirect
343. #2067C2×C73semidirect
344. #2065C2×C73semidirect
345. #1989C2×C73semidirect
346. #1949C2×C73semidirect
349. #1809C2×C73semidirect
350. #1809C2×C73semidirect
351. #1804C2×C73semidirect
352. C73#24841direct (N × H)
454. C4⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C732
C2×#423×C732
C73×#28512
C4×#121×C732
C73×#20882
C73×#20862
C73×#20672
C73×#20652
C73×#19892
C73×#19492
C73×#18952
C73×#18092
C73×#18042
#2484173