Finite Group Databasebeta

← C73×#26434 #32935838

Subgroups — C73×#26434 #32935838

Order 18688.

748 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2441C211yesmaximal, characteristic
2C73×#2360C211yesmaximal, characteristic
3C73×#2100C211yesmaximal, characteristic, complemented
4C73×#2088C211yesmaximal, characteristic, complemented
5C73×#2066C211yesmaximal, characteristic, complemented
6C73×#2026C211yesmaximal, characteristic, complemented
7C73×#1989C211yesmaximal, characteristic, complemented
8C73×#1920C211yesmaximal, characteristic, complemented
9C73×#1894C211yesmaximal, characteristic
10C73×#1873C211yesmaximal, characteristic
11C73×#1865C211yesmaximal, characteristic, complemented
12C73×#1853C211yesmaximal, characteristic
13C73×#1851C211yesmaximal, characteristic
14C73×#1803C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic
16C22×M16×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C2×#117×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23C2×#106×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×C22⋊C8×C73C2211yescharacteristic
31#399×C73—21no—
32#396×C73—21no—
33#391×C73C2211yescharacteristic
34#389×C73—21no—
35#389×C73—21no—
36#389×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#387×C73—21no—
40#387×C73—21no—
41#385×C73—21no—
42#384×C73C2211yescharacteristic
43#380×C73C2211yescharacteristic
44C4×C4⋊C4×C73C2211yescharacteristic
45C4×C22⋊C4×C73—21no—
46C4×C22⋊C4×C73C2211yescharacteristic
47#340×C73C2211yescharacteristic
48#340×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73C2311yescharacteristic
60C23×C4×C73—21no—
61C23×C4×C73C2311yescharacteristic
62C2×M16×C73—22no—
63C2×M16×C73—41no—
64C2×M16×C73—41no—
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69#125×C73—22no—
70#125×C73—41no—
71C22⋊Q8×C73—22no—
72C22⋊Q8×C73Q814yes—
73C4×Q8×C73—22no—
74C4×Q8×C73—41no—
75#117×C73—22no—
76#117×C73—41no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—22no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C4⋊C4×C73—21no—
82C2×C4⋊C4×C73—21no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—41no—
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×C73D411yescharacteristic
100C2×C22⋊C4×C73D411yescharacteristic
101C2×C42×C73—21no—
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106#106×C73—22no—
107#106×C73—41no—
108C4⋊C8×C73—41no—
109C4⋊C8×C73—41no—
110#103×C73—22no—
111#103×C73—41no—
112#103×C73—41no—
113#103×C73—41no—
114C22⋊C8×C73—22no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73D411yescharacteristic
123#95×C73D411yescharacteristic
124C24×C73C2×D411yescharacteristic
125C2×Q8×C73—21no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×Q8×C73—21no—
129C2×Q8×C73—21no—
130C2×Q8×C73C2×Q812yes—
131C22×C4×C73—21no—
132C22×C4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—42no—
144C22×C4×C73—42no—
145C22×C4×C73—81no—
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148C22×C4×C73C2×D411yescharacteristic
149C22×C4×C73C2×D411yescharacteristic
150C22×C4×C73C2×D411yescharacteristic
151C22×C4×C73C2×Q812yes—
152C22×C4×C73#4112yes—
153C22×C4×C73C2411yescharacteristic
154M16×C73—44no—
155C2×C8×C73—21no—
156C2×C8×C73—21no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C4⋊C4×C73—24no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—42no—
180C4⋊C4×C73—42no—
181C4⋊C4×C73—42no—
182C4⋊C4×C73—42no—
183C4⋊C4×C73—42no—
184C4⋊C4×C73—42no—
185C4⋊C4×C73—81no—
186C4⋊C4×C73—81no—
187C4⋊C4×C73—81no—
188C4⋊C4×C73C2×Q812yes—
189C4⋊C4×C73#4112yes—
190C4⋊C4×C73#4112yes—
191C22⋊C4×C73—24no—
192C22⋊C4×C73—22no—
193C22⋊C4×C73—41no—
194C22⋊C4×C73—42no—
195C22⋊C4×C73—81no—
196C42×C73—21no—
197C42×C73—21no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—42no—
201C42×C73—42no—
202C42×C73—81no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73C22⋊Q812yes—
210C23×C73C22×D411yescharacteristic
211Q8×C73—22no—
212Q8×C73—22no—
213Q8×C73—41no—
214Q8×C73—41no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—22no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—22no—
224C2×C4×C73—22no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—22no—
229C2×C4×C73—22no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—84no—
257C2×C4×C73C22⋊Q812yes—
258C2×C4×C73#13712yes—
259C2×C4×C73C22×Q811yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C2×C4×C73C2×#4111yescharacteristic
262C2×C4×C73C2×#4111yescharacteristic
263C2×C4×C73H(5,𝔽2)11yescharacteristic
264C2×C4×C73H(5,𝔽2)11yescharacteristic
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268C8×C73—41no—
269C22×C73—22no—
270C22×C73—22no—
271C22×C73—22no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73C2×C22⋊Q811yescharacteristic
277C22×C73#54611yescharacteristic
278C22×C73#54611yescharacteristic
279C22×C73C2×#13711yescharacteristic
280C22×C73#57511yescharacteristic
281C22×C73#57711yescharacteristic
282C22×C73#57711yescharacteristic
283C4×C73—22no—
284C4×C73—22no—
285C4×C73—41no—
286C4×C73—42no—
287C4×C73—42no—
288C4×C73—42no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—42no—
292C4×C73—81no—
293C4×C73—81no—
294C4×C73—81no—
295C4×C73—81no—
296C4×C73#52911yescharacteristic
297C4×C73#53811yescharacteristic
298C4×C73#55411yescharacteristic
299C4×C73#55411yescharacteristic
300#26434C7311yesmaximal, characteristic, direct product factor, Sylow
301C2×C73—42no—
302C2×C73#245011yescharacteristic
303C2×C73#307811yescharacteristic
304C2×C73#308411yescharacteristic
305C2×C73#331711yescharacteristic
306C2×C73#332011yescharacteristic
307C2×C73#332311yescharacteristic
308C2×C73#333111yescharacteristic
309#2441C2×C7311yescharacteristic
310#2360C2×C7311yescharacteristic
311#2100C2×C7311yescharacteristic, complemented
312#2088C2×C7311yescharacteristic, complemented
313#2066C2×C7311yescharacteristic, complemented
314#2026C2×C7311yescharacteristic, complemented
315#1989C2×C7311yescharacteristic, complemented
316#1920C2×C7311yescharacteristic, complemented
317#1894C2×C7311yescharacteristic
318#1873C2×C7311yescharacteristic
319#1865C2×C7311yescharacteristic, complemented
320#1853C2×C7311yescharacteristic
321#1851C2×C7311yescharacteristic
322#1803C2×C7311yescharacteristic, complemented
323#1736C2×C7311yescharacteristic
324C73#2643411yescharacteristic, direct product factor, Sylow
325C22×M16C22×C7311yescharacteristic
326C2×#125C22×C7311yescharacteristic
327C2×C22⋊Q8C22×C7311yescharacteristic
328C2×C4×Q8C22×C7311yescharacteristic
329C2×#117C22×C7311yescharacteristic
330C22×C4⋊C4C22×C7311yescharacteristic
331C2×#106C22×C7311yescharacteristic
332C2×#106C22×C7311yescharacteristic
333C2×C4⋊C8C22×C7311yescharacteristic
334C2×C4⋊C8C22×C7311yescharacteristic
335C2×#103C22×C7311yescharacteristic
336C2×#103C22×C7311yescharacteristic
337C2×#103C22×C7311yescharacteristic
338C2×#103C22×C7311yescharacteristic
339C2×C22⋊C8C22×C7311yescharacteristic
340#399—21no—
341#396—21no—
342#391C22×C7311yescharacteristic
343#389—21no—
344#389—21no—
345#389C22×C7311yescharacteristic
346#389C22×C7311yescharacteristic
347#389C22×C7311yescharacteristic
348#387—21no—
349#387—21no—
350#385—21no—
351#384C22×C7311yescharacteristic
352#380C22×C7311yescharacteristic
353C4×C4⋊C4C22×C7311yescharacteristic
354C4×C22⋊C4—21no—
355C4×C22⋊C4C22×C7311yescharacteristic
356#340C22×C7311yescharacteristic
357#340C22×C7311yescharacteristic
358#340C22×C7311yescharacteristic
359#340C22×C7311yescharacteristic
360#340C22×C7311yescharacteristic
361#340C22×C7311yescharacteristic
362#340C22×C7311yescharacteristic
363#340C22×C7311yescharacteristic
364#340C22×C7311yescharacteristic
365#340C22×C7311yescharacteristic
366#336C22×C7311yescharacteristic
367#336C22×C7311yescharacteristic
368C22×Q8C23×C7311yescharacteristic
369C23×C4—21no—
370C23×C4C23×C7311yescharacteristic
371C2×M16—22no—
372C2×M16—41no—
373C2×M16—41no—
374C22×C8C23×C7311yescharacteristic
375C22×C8C23×C7311yescharacteristic
376C22×C8C23×C7311yescharacteristic
377C22×C8C23×C7311yescharacteristic
378#125—22no—
379#125—41no—
380C22⋊Q8—22no—
381C22⋊Q8Q8×C7314yes—
382C4×Q8—22no—
383C4×Q8—41no—
384#117—22no—
385#117—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4C23×C7311yescharacteristic
399C2×C4⋊C4C23×C7311yescharacteristic
400C2×C4⋊C4C23×C7311yescharacteristic
401C2×C4⋊C4C23×C7311yescharacteristic
402C2×C4⋊C4C23×C7311yescharacteristic
403C2×C4⋊C4C23×C7311yescharacteristic
404C2×C4⋊C4C23×C7311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4D4×C7311yescharacteristic
409C2×C22⋊C4D4×C7311yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C23×C7311yescharacteristic
414C2×C42C23×C7311yescharacteristic
415#106—22no—
416#106—41no—
417C4⋊C8—41no—
418C4⋊C8—41no—
419#103—22no—
420#103—41no—
421#103—41no—
422#103—41no—
423C22⋊C8—22no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95D4×C7311yescharacteristic
432#95D4×C7311yescharacteristic
433C24C2×D4×C7311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×Q8×C7312yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4C2×D4×C7311yescharacteristic
456C22×C4C2×D4×C7311yescharacteristic
457C22×C4C2×D4×C7311yescharacteristic
458C22×C4C2×D4×C7311yescharacteristic
459C22×C4C2×D4×C7311yescharacteristic
460C22×C4C2×Q8×C7312yes—
461C22×C4#41×C7312yes—
462C22×C4C24×C7311yescharacteristic
463M16—44no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4C2×Q8×C7312yes—
498C4⋊C4#41×C7312yes—
499C4⋊C4#41×C7312yes—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—41no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—42no—
511C42—81no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C22⋊Q8×C7312yes—
519C23C22×D4×C7311yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4C22⋊Q8×C7312yes—
567C2×C4#137×C7312yes—
568C2×C4C22×Q8×C7311yescharacteristic
569C2×C4C2×#41×C7311yescharacteristic
570C2×C4C2×#41×C7311yescharacteristic
571C2×C4C2×#41×C7311yescharacteristic
572C2×C4H(5,𝔽2)×C7311yescharacteristic
573C2×C4H(5,𝔽2)×C7311yescharacteristic
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C22⋊Q8×C7311yescharacteristic
586C22#546×C7311yescharacteristic
587C22#546×C7311yescharacteristic
588C22C2×#137×C7311yescharacteristic
589C22#575×C7311yescharacteristic
590C22#577×C7311yescharacteristic
591C22#577×C7311yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4#529×C7311yescharacteristic
606C4#538×C7311yescharacteristic
607C4#554×C7311yescharacteristic
608C4#554×C7311yescharacteristic
609C2—42no—
610C2C73×#245011yescharacteristic
611C2C73×#307811yescharacteristic
612C2C73×#308411yescharacteristic
613C2C73×#331711yescharacteristic
614C2C73×#332011yescharacteristic
615C2C73×#332311yescharacteristic
616C2C73×#333111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
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
3. C73×#2100C2semidirect
4. C73×#2088C2semidirect
5. C73×#2066C2semidirect
6. C73×#2026C2semidirect
7. C73×#1989C2semidirect
8. C73×#1920C2semidirect
11. C73×#1865C2semidirect
14. C73×#1803C2semidirect
300. #26434C73direct (N × H)
311. #2100C2×C73semidirect
312. #2088C2×C73semidirect
313. #2066C2×C73semidirect
314. #2026C2×C73semidirect
315. #1989C2×C73semidirect
316. #1920C2×C73semidirect
319. #1865C2×C73semidirect
322. #1803C2×C73semidirect
324. C73#26434direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24412
C73×#23602
C73×#21002
C73×#20882
C73×#20662
C73×#20262
C73×#19892
C73×#19202
C73×#18942
C73×#18732
C73×#18652
C73×#18532
C73×#18512
C73×#18032
C73×#17362
#2643473