Finite Group Databasebeta

← C73×#32861 #32942265

Subgroups — C73×#32861 #32942265

Order 18688.

654 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2863C211yesmaximal, characteristic, complemented
2C73×#2860C211yesmaximal, characteristic
3C73×#2088C211yesmaximal, characteristic, complemented
4C73×#2087C211yesmaximal, characteristic, complemented
5C73×#2086C211yesmaximal, characteristic, complemented
6C73×#2068C211yesmaximal, characteristic, complemented
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2067C211yesmaximal, characteristic
9C73×#2067C211yesmaximal, characteristic
10C73×#2066C211yesmaximal, characteristic, complemented
11C73×#2065C211yesmaximal, characteristic
12C73×#2055C211yesmaximal, characteristic
13C73×#2055C211yesmaximal, characteristic
14C73×#2055C211yesmaximal, characteristic
15C73×#1842C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C2×#126×C73—21no—
18C2×#107×C73C2211yescharacteristic
19C2×#107×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33#391×C73C2211yescharacteristic
34#391×C73C2211yescharacteristic
35#391×C73C2211yescharacteristic
36#390×C73C2211yescharacteristic
37#390×C73C2211yescharacteristic
38#390×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#388×C73—21no—
46#388×C73—21no—
47#388×C73—21no—
48#387×C73—21no—
49#387×C73—21no—
50#387×C73—21no—
51#383×C73—21no—
52C43×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59C22×Q8×C73C2311yescharacteristic
60C22×D4×C73C2311yescharacteristic
61C2×SD16×C73—41no—
62C2×SD16×C73—41no—
63C2×SD16×C73—41no—
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68#126×C73—44no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73C2311yescharacteristic
76C2×C4⋊C4×C73C2311yescharacteristic
77C2×C4⋊C4×C73C2311yescharacteristic
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C22⋊C4×C73—21no—
82C2×C22⋊C4×C73—21no—
83C2×C22⋊C4×C73—21no—
84C2×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C42×C73D411yescharacteristic
88C2×C42×C73D411yescharacteristic
89C2×C42×C73D411yescharacteristic
90C2×C42×C73D411yescharacteristic
91C2×C42×C73C2311yescharacteristic
92C2×C42×C73C2311yescharacteristic
93C2×C42×C73C2311yescharacteristic
94#107×C73—41no—
95#107×C73—41no—
96#106×C73—41no—
97C4⋊C8×C73—41no—
98C4⋊C8×C73—41no—
99C4⋊C8×C73—41no—
100C4⋊C8×C73—41no—
101C4⋊C8×C73—41no—
102C4⋊C8×C73—41no—
103#103×C73—41no—
104#103×C73—41no—
105#103×C73—41no—
106#102×C73—41no—
107#102×C73—41no—
108#102×C73—41no—
109#95×C73—21no—
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121C24×C73—21no—
122C2×Q8×C73—21no—
123C2×Q8×C73—21no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×D4×C73—21no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×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×C73C2×D411yescharacteristic
142C22×C4×C73C2×D411yescharacteristic
143C22×C4×C73C2×D411yescharacteristic
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2411yescharacteristic
148SD16×C73—44no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73—21no—
152C2×C8×C73—21no—
153C2×C8×C73—21no—
154C2×C8×C73—21no—
155C2×C8×C73—21no—
156C2×C8×C73—21no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—21no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—42no—
174C4⋊C4×C73—42no—
175C4⋊C4×C73—42no—
176C4⋊C4×C73—42no—
177C4⋊C4×C73—42no—
178C4⋊C4×C73—42no—
179C22⋊C4×C73—42no—
180C22⋊C4×C73—42no—
181C22⋊C4×C73—42no—
182C22⋊C4×C73—42no—
183C22⋊C4×C73—42no—
184C22⋊C4×C73—42no—
185C42×C73—22no—
186C42×C73—22no—
187C42×C73—22no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—41no—
201C23×C73—41no—
202C23×C73C22×D411yescharacteristic
203Q8×C73—41no—
204Q8×C73—41no—
205Q8×C73—41no—
206Q8×C73—41no—
207D4×C73—41no—
208D4×C73—41no—
209D4×C73—41no—
210D4×C73—41no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
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#13512yes—
248C2×C4×C73AGL(1,ℤ/8)12yes—
249C2×C4×C73#13712yes—
250C2×C4×C73H(5,𝔽2)11yescharacteristic
251C2×C4×C73H(5,𝔽2)11yescharacteristic
252C2×C4×C73H(5,𝔽2)11yescharacteristic
253C2×C4×C732−1+411yescharacteristic
254C2×C4×C732−1+411yescharacteristic
255C2×C4×C732−1+411yescharacteristic
256C8×C73—41no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260C22×C73—81no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73—81no—
265C22×C73—81no—
266C22×C73—81no—
267C22×C73#53711yescharacteristic
268C22×C73#53711yescharacteristic
269C22×C73#53711yescharacteristic
270C22×C73C2×#13511yescharacteristic
271C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C73C2×#13711yescharacteristic
273C22×C73#57511yescharacteristic
274C4×C73—22no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73#56011yescharacteristic
288C4×C73#56311yescharacteristic
289C4×C73#56311yescharacteristic
290C4×C73#56311yescharacteristic
291#32861C7311yesmaximal, characteristic, direct product factor, Sylow
292C2×C73—161no—
293C2×C73#282311yescharacteristic
294C2×C73#324711yescharacteristic
295C2×C73#324811yescharacteristic
296C2×C73#325011yescharacteristic
297C2×C73#325111yescharacteristic
298C2×C73#325211yescharacteristic
299C2×C73#325411yescharacteristic
300#2863C2×C7311yescharacteristic, complemented
301#2860C2×C7311yescharacteristic
302#2088C2×C7311yescharacteristic, complemented
303#2087C2×C7311yescharacteristic, complemented
304#2086C2×C7311yescharacteristic, complemented
305#2068C2×C7311yescharacteristic, complemented
306#2068C2×C7311yescharacteristic, complemented
307#2067C2×C7311yescharacteristic
308#2067C2×C7311yescharacteristic
309#2066C2×C7311yescharacteristic, complemented
310#2065C2×C7311yescharacteristic
311#2055C2×C7311yescharacteristic
312#2055C2×C7311yescharacteristic
313#2055C2×C7311yescharacteristic
314#1842C2×C7311yescharacteristic, complemented
315C73#3286111yescharacteristic, direct product factor, Sylow
316C22×SD16C22×C7311yescharacteristic
317C2×#126—21no—
318C2×#107C22×C7311yescharacteristic
319C2×#107C22×C7311yescharacteristic
320C2×#106C22×C7311yescharacteristic
321C2×C4⋊C8C22×C7311yescharacteristic
322C2×C4⋊C8C22×C7311yescharacteristic
323C2×C4⋊C8C22×C7311yescharacteristic
324C2×C4⋊C8C22×C7311yescharacteristic
325C2×C4⋊C8C22×C7311yescharacteristic
326C2×C4⋊C8C22×C7311yescharacteristic
327C2×#103C22×C7311yescharacteristic
328C2×#103C22×C7311yescharacteristic
329C2×#103C22×C7311yescharacteristic
330C2×#102C22×C7311yescharacteristic
331C2×#102C22×C7311yescharacteristic
332C2×#102C22×C7311yescharacteristic
333#391C22×C7311yescharacteristic
334#391C22×C7311yescharacteristic
335#391C22×C7311yescharacteristic
336#390C22×C7311yescharacteristic
337#390C22×C7311yescharacteristic
338#390C22×C7311yescharacteristic
339#389C22×C7311yescharacteristic
340#389C22×C7311yescharacteristic
341#389C22×C7311yescharacteristic
342#389C22×C7311yescharacteristic
343#389C22×C7311yescharacteristic
344#389C22×C7311yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#383—21no—
352C43C22×C7311yescharacteristic
353#340C22×C7311yescharacteristic
354#340C22×C7311yescharacteristic
355#340C22×C7311yescharacteristic
356#340C22×C7311yescharacteristic
357#340C22×C7311yescharacteristic
358#340C22×C7311yescharacteristic
359C22×Q8C23×C7311yescharacteristic
360C22×D4C23×C7311yescharacteristic
361C2×SD16—41no—
362C2×SD16—41no—
363C2×SD16—41no—
364C22×C8C23×C7311yescharacteristic
365C22×C8C23×C7311yescharacteristic
366C22×C8C23×C7311yescharacteristic
367C22×C8C23×C7311yescharacteristic
368#126—44no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C4⋊C4C23×C7311yescharacteristic
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42D4×C7311yescharacteristic
388C2×C42D4×C7311yescharacteristic
389C2×C42D4×C7311yescharacteristic
390C2×C42D4×C7311yescharacteristic
391C2×C42C23×C7311yescharacteristic
392C2×C42C23×C7311yescharacteristic
393C2×C42C23×C7311yescharacteristic
394#107—41no—
395#107—41no—
396#106—41no—
397C4⋊C8—41no—
398C4⋊C8—41no—
399C4⋊C8—41no—
400C4⋊C8—41no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#103—41no—
404#103—41no—
405#103—41no—
406#102—41no—
407#102—41no—
408#102—41no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C24—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C2×D4×C7311yescharacteristic
442C22×C4C2×D4×C7311yescharacteristic
443C22×C4C2×D4×C7311yescharacteristic
444C22×C4C2×D4×C7311yescharacteristic
445C22×C4C2×D4×C7311yescharacteristic
446C22×C4C2×D4×C7311yescharacteristic
447C22×C4C24×C7311yescharacteristic
448SD16—44no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C42—22no—
486C42—22no—
487C42—22no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C22×D4×C7311yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4#135×C7312yes—
548C2×C4AGL(1,ℤ/8)×C7312yes—
549C2×C4#137×C7312yes—
550C2×C4H(5,𝔽2)×C7311yescharacteristic
551C2×C4H(5,𝔽2)×C7311yescharacteristic
552C2×C4H(5,𝔽2)×C7311yescharacteristic
553C2×C42−1+4×C7311yescharacteristic
554C2×C42−1+4×C7311yescharacteristic
555C2×C42−1+4×C7311yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#537×C7311yescharacteristic
568C22#537×C7311yescharacteristic
569C22#537×C7311yescharacteristic
570C22C2×#135×C7311yescharacteristic
571C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
572C22C2×#137×C7311yescharacteristic
573C22#575×C7311yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4#560×C7311yescharacteristic
588C4#563×C7311yescharacteristic
589C4#563×C7311yescharacteristic
590C4#563×C7311yescharacteristic
591C2—161no—
592C2C73×#282311yescharacteristic
593C2C73×#324711yescharacteristic
594C2C73×#324811yescharacteristic
595C2C73×#325011yescharacteristic
596C2C73×#325111yescharacteristic
597C2C73×#325211yescharacteristic
598C2C73×#325411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C43×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2863C2semidirect
3. C73×#2088C2semidirect
4. C73×#2087C2semidirect
5. C73×#2086C2semidirect
6. C73×#2068C2semidirect
7. C73×#2068C2semidirect
10. C73×#2066C2semidirect
15. C73×#1842C2semidirect
291. #32861C73direct (N × H)
300. #2863C2×C73semidirect
302. #2088C2×C73semidirect
303. #2087C2×C73semidirect
304. #2086C2×C73semidirect
305. #2068C2×C73semidirect
306. #2068C2×C73semidirect
309. #2066C2×C73semidirect
314. #1842C2×C73semidirect
315. C73#32861direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28632
C73×#28602
C73×#20882
C73×#20872
C73×#20862
C73×#20682
C73×#20672
C73×#20662
C73×#20652
C73×#20552
C73×#18422
#3286173