Finite Group Databasebeta

← C73×#26785 #32936189

Subgroups — C73×#26785 #32936189

Order 18688.

888 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C73C211yesmaximal, characteristic, complemented
2C2×#478×C73C211yesmaximal, characteristic, complemented
3C73×#2489C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic
5C73×#2068C211yesmaximal, characteristic, complemented
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic
8C73×#2000C211yesmaximal, characteristic
9C73×#1968C211yesmaximal, characteristic, complemented
10C73×#1927C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1877C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C4×#107×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73—21no—
21C2×C4×D4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#484×C73—24no—
24#478×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#400×C73—21no—
41#397×C73—21no—
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#388×C73—21no—
48#386×C73—21no—
49#385×C73—21no—
50#382×C73—21no—
51#380×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×SD16×C73—22no—
68C2×SD16×C73—22no—
69C2×SD16×C73—41no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74#125×C73—22no—
75#125×C73—41no—
76C22⋊Q8×C73—22no—
77C22⋊Q8×C73—41no—
78#121×C73—22no—
79#121×C73—22no—
80C4×D4×C73—22no—
81C4×D4×C73—41no—
82C4×D4×C73—44no—
83C2×C4⋊C4×C73—22no—
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×C73—41no—
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×C73D411yescharacteristic
103C2×C22⋊C4×C73D411yescharacteristic
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73C2311yescharacteristic
107C2×C42×C73C2311yescharacteristic
108#107×C73—22no—
109#107×C73—22no—
110#107×C73D414yescomplemented
111#106×C73—22no—
112#106×C73—41no—
113C4⋊C8×C73—22no—
114#103×C73—22no—
115#103×C73—22no—
116#103×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120C22⋊C8×C73—22no—
121C22⋊C8×C73—22no—
122C4×C8×C73—22no—
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—
131#95×C73D411yescharacteristic
132#95×C73D411yescharacteristic
133C24×C73—21no—
134C24×C73C2×D411yescharacteristic
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×D4×C73—24no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—42no—
148C2×D4×C73—42no—
149C2×D4×C73#4112yes—
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—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—81no—
168C22×C4×C73—81no—
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2411yescharacteristic
175SD16×C73—44no—
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×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73C2×D412yes—
187C2×C8×C73#4112yes—
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×D412yes—
203C4⋊C4×C73C2×D412yes—
204C4⋊C4×C73#4112yes—
205C22⋊C4×C73—24no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—81no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—42no—
218C42×C73—42no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—22no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73#13512yes—
233C23×C73C22×D411yescharacteristic
234Q8×C73—41no—
235Q8×C73—41no—
236Q8×C73—41no—
237Q8×C73—41no—
238D4×C73—22no—
239D4×C73—22no—
240D4×C73—48no—
241D4×C73—41no—
242D4×C73—41no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—22no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
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—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—84no—
283C2×C4×C73—84no—
284C2×C4×C73AGL(1,ℤ/8)12yes—
285C2×C4×C73C22×D411yescharacteristic
286C2×C4×C73C2×#4111yescharacteristic
287C2×C4×C73C2×#4111yescharacteristic
288C2×C4×C73C2×#4111yescharacteristic
289C2×C4×C73H(5,𝔽2)11yescharacteristic
290C2×C4×C732−1+411yescharacteristic
291C8×C73—22no—
292C8×C73—22no—
293C8×C73—41no—
294C8×C73—41no—
295C22×C73—22no—
296C22×C73—22no—
297C22×C73—22no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—42no—
303C22×C73—42no—
304C22×C73—42no—
305C22×C73—81no—
306C22×C73—81no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73#52511yescharacteristic
310C22×C73D4211yescharacteristic
311C22×C73#54711yescharacteristic
312C22×C73C2×#13511yescharacteristic
313C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C73#57711yescharacteristic
315C22×C73#57811yescharacteristic
316C4×C73—22no—
317C4×C73—41no—
318C4×C73—42no—
319C4×C73—41no—
320C4×C73—41no—
321C4×C73—42no—
322C4×C73—42no—
323C4×C73—41no—
324C4×C73—81no—
325C4×C73—81no—
326C4×C73—81no—
327C4×C73—81no—
328C4×C73#53211yescharacteristic
329C4×C73#54211yescharacteristic
330C4×C73#54811yescharacteristic
331C4×C73#55111yescharacteristic
332#26785C7311yesmaximal, characteristic, direct product factor, Sylow
333C2×C73—42no—
334C2×C73—82no—
335C2×C73#246111yescharacteristic
336C2×C73#310511yescharacteristic
337C2×C73#312011yescharacteristic
338C2×C73#327211yescharacteristic
339C2×C73#328511yescharacteristic
340C2×C73#333711yescharacteristic
341C2×C73#334311yescharacteristic
342C2×#484C2×C7311yescharacteristic, complemented
343C2×#478C2×C7311yescharacteristic, complemented
344#2489C2×C7311yescharacteristic, complemented
345#2361C2×C7311yescharacteristic
346#2068C2×C7311yescharacteristic, complemented
347#2059C2×C7311yescharacteristic, complemented
348#2033C2×C7311yescharacteristic
349#2000C2×C7311yescharacteristic
350#1968C2×C7311yescharacteristic, complemented
351#1927C2×C7311yescharacteristic, complemented
352#1925C2×C7311yescharacteristic, complemented
353#1923C2×C7311yescharacteristic, complemented
354#1877C2×C7311yescharacteristic, complemented
355#1853C2×C7311yescharacteristic, complemented
356C4×#107C2×C7311yescharacteristic, complemented
357C73#2678511yescharacteristic, direct product factor, Sylow
358C22×SD16C22×C7311yescharacteristic
359C2×#125C22×C7311yescharacteristic
360C2×C22⋊Q8C22×C7311yescharacteristic
361C2×#121C22×C7311yescharacteristic
362C2×C4×D4—21no—
363C2×C4×D4C22×C7311yescharacteristic
364C22×C4⋊C4C22×C7311yescharacteristic
365#484—24no—
366#478—24no—
367C2×#107C22×C7311yescharacteristic
368C2×#107C22×C7311yescharacteristic
369C2×#107C22×C7311yescharacteristic
370C2×#106C22×C7311yescharacteristic
371C2×#106C22×C7311yescharacteristic
372C2×C4⋊C8C22×C7311yescharacteristic
373C2×#103C22×C7311yescharacteristic
374C2×#103C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#102C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×C22⋊C8C22×C7311yescharacteristic
380C2×C22⋊C8C22×C7311yescharacteristic
381C2×C4×C8C22×C7311yescharacteristic
382#400—21no—
383#397—21no—
384#391C22×C7311yescharacteristic
385#391C22×C7311yescharacteristic
386#390C22×C7311yescharacteristic
387#389C22×C7311yescharacteristic
388#388—21no—
389#388—21no—
390#386—21no—
391#385—21no—
392#382—21no—
393#380C22×C7311yescharacteristic
394C4×C4⋊C4C22×C7311yescharacteristic
395C4×C4⋊C4C22×C7311yescharacteristic
396C4×C22⋊C4C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#336C22×C7311yescharacteristic
402#336C22×C7311yescharacteristic
403C22×Q8C23×C7311yescharacteristic
404C22×D4—21no—
405C22×D4C23×C7311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4C23×C7311yescharacteristic
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16—41no—
412C22×C8C23×C7311yescharacteristic
413C22×C8C23×C7311yescharacteristic
414C22×C8C23×C7311yescharacteristic
415C22×C8C23×C7311yescharacteristic
416#125—22no—
417#125—41no—
418C22⋊Q8—22no—
419C22⋊Q8—41no—
420#121—22no—
421#121—22no—
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—44no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C4⋊C4C23×C7311yescharacteristic
434C2×C4⋊C4C23×C7311yescharacteristic
435C2×C4⋊C4C23×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4D4×C7311yescharacteristic
445C2×C22⋊C4D4×C7311yescharacteristic
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C7311yescharacteristic
449C2×C42C23×C7311yescharacteristic
450#107—22no—
451#107—22no—
452#107D4×C7314yescomplemented
453#106—22no—
454#106—41no—
455C4⋊C8—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#102—22no—
460#102—22no—
461#102—22no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464C4×C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95D4×C7311yescharacteristic
474#95D4×C7311yescharacteristic
475C24—21no—
476C24C2×D4×C7311yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4#41×C7312yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4C2×D4×C7311yescharacteristic
512C22×C4C2×D4×C7311yescharacteristic
513C22×C4C2×D4×C7311yescharacteristic
514C22×C4C2×D4×C7311yescharacteristic
515C22×C4C2×D4×C7311yescharacteristic
516C22×C4C24×C7311yescharacteristic
517SD16—44no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×D4×C7312yes—
529C2×C8#41×C7312yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4C2×D4×C7312yes—
545C4⋊C4C2×D4×C7312yes—
546C4⋊C4#41×C7312yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—42no—
560C42—42no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23#135×C7312yes—
575C23C22×D4×C7311yescharacteristic
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580D4—22no—
581D4—22no—
582D4—48no—
583D4—41no—
584D4—41no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
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—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—84no—
625C2×C4—84no—
626C2×C4AGL(1,ℤ/8)×C7312yes—
627C2×C4C22×D4×C7311yescharacteristic
628C2×C4C2×#41×C7311yescharacteristic
629C2×C4C2×#41×C7311yescharacteristic
630C2×C4C2×#41×C7311yescharacteristic
631C2×C4H(5,𝔽2)×C7311yescharacteristic
632C2×C42−1+4×C7311yescharacteristic
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22#525×C7311yescharacteristic
652C22D42×C7311yescharacteristic
653C22#547×C7311yescharacteristic
654C22C2×#135×C7311yescharacteristic
655C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
656C22#577×C7311yescharacteristic
657C22#578×C7311yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4#532×C7311yescharacteristic
671C4#542×C7311yescharacteristic
672C4#548×C7311yescharacteristic
673C4#551×C7311yescharacteristic
674C2—42no—
675C2—82no—
676C2C73×#246111yescharacteristic
677C2C73×#310511yescharacteristic
678C2C73×#312011yescharacteristic
679C2C73×#327211yescharacteristic
680C2C73×#328511yescharacteristic
681C2C73×#333711yescharacteristic
682C2C73×#334311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C73C2semidirect
2. C2×#478×C73C2semidirect
3. C73×#2489C2semidirect
5. C73×#2068C2semidirect
6. C73×#2059C2semidirect
9. C73×#1968C2semidirect
10. C73×#1927C2semidirect
11. C73×#1925C2semidirect
12. C73×#1923C2semidirect
13. C73×#1877C2semidirect
14. C73×#1853C2semidirect
15. C4×#107×C73C2semidirect
110. #107×C73D4semidirect
332. #26785C73direct (N × H)
342. C2×#484C2×C73semidirect
343. C2×#478C2×C73semidirect
344. #2489C2×C73semidirect
346. #2068C2×C73semidirect
347. #2059C2×C73semidirect
350. #1968C2×C73semidirect
351. #1927C2×C73semidirect
352. #1925C2×C73semidirect
353. #1923C2×C73semidirect
354. #1877C2×C73semidirect
355. #1853C2×C73semidirect
356. C4×#107C2×C73semidirect
357. C73#26785direct (N × H)
452. #107D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C732
C2×#478×C732
C73×#24892
C73×#23612
C73×#20682
C73×#20592
C73×#20332
C73×#20002
C73×#19682
C73×#19272
C73×#19252
C73×#19232
C73×#18772
C73×#18532
C4×#107×C732
#2678573