Finite Group Databasebeta

← C73×#27035 #32936439

Subgroups — C73×#27035 #32936439

Order 18688.

700 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×#2495C211yesmaximal, characteristic
2C73×#2360C211yesmaximal, characteristic
3C73×#2074C211yesmaximal, characteristic, complemented
4C73×#2068C211yesmaximal, characteristic, complemented
5C73×#2036C211yesmaximal, characteristic
6C73×#2035C211yesmaximal, characteristic
7C73×#1949C211yesmaximal, characteristic, complemented
8C73×#1942C211yesmaximal, characteristic, complemented
9C73×#1923C211yesmaximal, characteristic
10C73×#1920C211yesmaximal, characteristic, complemented
11C73×#1918C211yesmaximal, characteristic, complemented
12C73×#1863C211yesmaximal, characteristic, complemented
13C73×#1852C211yesmaximal, characteristic
14C73×#1823C211yesmaximal, characteristic
15C4×#103×C73C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C73C2211yescharacteristic
17C2×C4×Q8×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C2×#107×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×#103×C73C2211yescharacteristic
25C2×#103×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×C22⋊C8×C73C2211yescharacteristic
29C2×C22⋊C8×C73C2211yescharacteristic
30C2×C4×C8×C73C2211yescharacteristic
31#400×C73—21no—
32#397×C73—21no—
33#391×C73C2211yescharacteristic
34#389×C73—21no—
35#389×C73C2211yescharacteristic
36#389×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#388×C73—21no—
39#387×C73—21no—
40#385×C73—21no—
41#383×C73—21no—
42#382×C73C2211yescharacteristic
43#380×C73C2211yescharacteristic
44#380×C73C2211yescharacteristic
45C4×C4⋊C4×C73C2211yescharacteristic
46C4×C4⋊C4×C73C2211yescharacteristic
47C4×C22⋊C4×C73—21no—
48C4×C22⋊C4×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
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22⋊Q8×C73—22no—
67C22⋊Q8×C73—22no—
68C4×Q8×C73—22no—
69C4×Q8×C73—41no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73—22no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73—41no—
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
83C2×C4⋊C4×C73C2311yescharacteristic
84C2×C4⋊C4×C73C2311yescharacteristic
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73D411yescharacteristic
89C2×C22⋊C4×C73D411yescharacteristic
90C2×C42×C73—21no—
91C2×C42×C73—21no—
92C2×C42×C73—21no—
93C2×C42×C73C2311yescharacteristic
94C2×C42×C73C2311yescharacteristic
95#107×C73—22no—
96#107×C73—22no—
97#107×C73—41no—
98#106×C73—22no—
99C4⋊C8×C73—22no—
100#103×C73—22no—
101#103×C73—22no—
102#103×C73—22no—
103#103×C73—41no—
104C22⋊C8×C73—22no—
105C22⋊C8×C73—41no—
106C4×C8×C73—41no—
107#95×C73—21no—
108#95×C73—21no—
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×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C24×C73C2×D411yescharacteristic
121C2×Q8×C73—21no—
122C2×Q8×C73—21no—
123C2×Q8×C73—21no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73#4112yes—
127C22×C4×C73—21no—
128C22×C4×C73—21no—
129C22×C4×C73—21no—
130C22×C4×C73—21no—
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—42no—
142C22×C4×C73—42no—
143C22×C4×C73—81no—
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148C22×C4×C73C2×D411yescharacteristic
149C22×C4×C73C2411yescharacteristic
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—
161C2×C8×C73#4112yes—
162C4⋊C4×C73—24no—
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—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—42no—
176C4⋊C4×C73—42no—
177C4⋊C4×C73—81no—
178C4⋊C4×C73—81no—
179C4⋊C4×C73—81no—
180C4⋊C4×C73#4112yes—
181C4⋊C4×C73#4112yes—
182C22⋊C4×C73—24no—
183C22⋊C4×C73—22no—
184C22⋊C4×C73—22no—
185C22⋊C4×C73—42no—
186C22⋊C4×C73—81no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—42no—
192C42×C73—42no—
193C42×C73—81no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73—21no—
197C23×C73—21no—
198C23×C73—21no—
199C23×C73—21no—
200C23×C73#13512yes—
201C23×C73C22×D411yescharacteristic
202Q8×C73—22no—
203Q8×C73—22no—
204Q8×C73—41no—
205Q8×C73—41no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—22no—
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—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
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—41no—
248C2×C4×C73—84no—
249C2×C4×C73#13712yes—
250C2×C4×C73C2×#4111yescharacteristic
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73H(5,𝔽2)11yescharacteristic
255C2×C4×C732−1+411yescharacteristic
256C8×C73—22no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260C22×C73—22no—
261C22×C73—22no—
262C22×C73—22no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73#52511yescharacteristic
268C22×C73#54611yescharacteristic
269C22×C73#54711yescharacteristic
270C22×C73C2×#13511yescharacteristic
271C22×C73C2×#13711yescharacteristic
272C22×C73#57611yescharacteristic
273C22×C73#57811yescharacteristic
274C4×C73—22no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—42no—
278C4×C73—41no—
279C4×C73—42no—
280C4×C73—41no—
281C4×C73—42no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73—81no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73#52911yescharacteristic
288C4×C73#53911yescharacteristic
289C4×C73#55311yescharacteristic
290C4×C73#55611yescharacteristic
291#27035C7311yesmaximal, characteristic, direct product factor, Sylow
292C2×C73—42no—
293C2×C73#246611yescharacteristic
294C2×C73#310811yescharacteristic
295C2×C73#312411yescharacteristic
296C2×C73#329711yescharacteristic
297C2×C73#331211yescharacteristic
298C2×C73#333611yescharacteristic
299C2×C73#335711yescharacteristic
300#2495C2×C7311yescharacteristic
301#2360C2×C7311yescharacteristic
302#2074C2×C7311yescharacteristic, complemented
303#2068C2×C7311yescharacteristic, complemented
304#2036C2×C7311yescharacteristic
305#2035C2×C7311yescharacteristic
306#1949C2×C7311yescharacteristic, complemented
307#1942C2×C7311yescharacteristic, complemented
308#1923C2×C7311yescharacteristic
309#1920C2×C7311yescharacteristic, complemented
310#1918C2×C7311yescharacteristic, complemented
311#1863C2×C7311yescharacteristic, complemented
312#1852C2×C7311yescharacteristic
313#1823C2×C7311yescharacteristic
314C4×#103C2×C7311yescharacteristic, complemented
315C73#2703511yescharacteristic, direct product factor, Sylow
316C2×C22⋊Q8C22×C7311yescharacteristic
317C2×C4×Q8C22×C7311yescharacteristic
318C22×C4⋊C4C22×C7311yescharacteristic
319C2×#107C22×C7311yescharacteristic
320C2×#107C22×C7311yescharacteristic
321C2×#107C22×C7311yescharacteristic
322C2×#106C22×C7311yescharacteristic
323C2×C4⋊C8C22×C7311yescharacteristic
324C2×#103C22×C7311yescharacteristic
325C2×#103C22×C7311yescharacteristic
326C2×#103C22×C7311yescharacteristic
327C2×#103C22×C7311yescharacteristic
328C2×C22⋊C8C22×C7311yescharacteristic
329C2×C22⋊C8C22×C7311yescharacteristic
330C2×C4×C8C22×C7311yescharacteristic
331#400—21no—
332#397—21no—
333#391C22×C7311yescharacteristic
334#389—21no—
335#389C22×C7311yescharacteristic
336#389C22×C7311yescharacteristic
337#389C22×C7311yescharacteristic
338#388—21no—
339#387—21no—
340#385—21no—
341#383—21no—
342#382C22×C7311yescharacteristic
343#380C22×C7311yescharacteristic
344#380C22×C7311yescharacteristic
345C4×C4⋊C4C22×C7311yescharacteristic
346C4×C4⋊C4C22×C7311yescharacteristic
347C4×C22⋊C4—21no—
348C4×C22⋊C4C22×C7311yescharacteristic
349#340C22×C7311yescharacteristic
350#340C22×C7311yescharacteristic
351#340C22×C7311yescharacteristic
352#340C22×C7311yescharacteristic
353#340C22×C7311yescharacteristic
354#340C22×C7311yescharacteristic
355#340C22×C7311yescharacteristic
356#340C22×C7311yescharacteristic
357#336C22×C7311yescharacteristic
358#336C22×C7311yescharacteristic
359C22×Q8C23×C7311yescharacteristic
360C23×C4—21no—
361C23×C4C23×C7311yescharacteristic
362C22×C8C23×C7311yescharacteristic
363C22×C8C23×C7311yescharacteristic
364C22×C8C23×C7311yescharacteristic
365C22×C8C23×C7311yescharacteristic
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C4×Q8—22no—
369C4×Q8—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C4⋊C4C23×C7311yescharacteristic
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C4⋊C4C23×C7311yescharacteristic
382C2×C4⋊C4C23×C7311yescharacteristic
383C2×C4⋊C4C23×C7311yescharacteristic
384C2×C4⋊C4C23×C7311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4D4×C7311yescharacteristic
389C2×C22⋊C4D4×C7311yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C7311yescharacteristic
394C2×C42C23×C7311yescharacteristic
395#107—22no—
396#107—22no—
397#107—41no—
398#106—22no—
399C4⋊C8—22no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—41no—
404C22⋊C8—22no—
405C22⋊C8—41no—
406C4×C8—41no—
407#95—21no—
408#95—21no—
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#95D4×C7311yescharacteristic
419#95D4×C7311yescharacteristic
420C24C2×D4×C7311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#41×C7312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4C2×D4×C7311yescharacteristic
445C22×C4C2×D4×C7311yescharacteristic
446C22×C4C2×D4×C7311yescharacteristic
447C22×C4C2×D4×C7311yescharacteristic
448C22×C4C2×D4×C7311yescharacteristic
449C22×C4C24×C7311yescharacteristic
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—
461C2×C8#41×C7312yes—
462C4⋊C4—24no—
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—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4#41×C7312yes—
481C4⋊C4#41×C7312yes—
482C22⋊C4—24no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—42no—
492C42—42no—
493C42—81no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23#135×C7312yes—
501C23C22×D4×C7311yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
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—41no—
524C2×C4—41no—
525C2×C4—41no—
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—41no—
548C2×C4—84no—
549C2×C4#137×C7312yes—
550C2×C4C2×#41×C7311yescharacteristic
551C2×C4C2×#41×C7311yescharacteristic
552C2×C4C2×#41×C7311yescharacteristic
553C2×C4C2×#41×C7311yescharacteristic
554C2×C4H(5,𝔽2)×C7311yescharacteristic
555C2×C42−1+4×C7311yescharacteristic
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#525×C7311yescharacteristic
568C22#546×C7311yescharacteristic
569C22#547×C7311yescharacteristic
570C22C2×#135×C7311yescharacteristic
571C22C2×#137×C7311yescharacteristic
572C22#576×C7311yescharacteristic
573C22#578×C7311yescharacteristic
574C4—22no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4#529×C7311yescharacteristic
588C4#539×C7311yescharacteristic
589C4#553×C7311yescharacteristic
590C4#556×C7311yescharacteristic
591C2—42no—
592C2C73×#246611yescharacteristic
593C2C73×#310811yescharacteristic
594C2C73×#312411yescharacteristic
595C2C73×#329711yescharacteristic
596C2C73×#331211yescharacteristic
597C2C73×#333611yescharacteristic
598C2C73×#335711yescharacteristic
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×#2074C2semidirect
4. C73×#2068C2semidirect
7. C73×#1949C2semidirect
8. C73×#1942C2semidirect
10. C73×#1920C2semidirect
11. C73×#1918C2semidirect
12. C73×#1863C2semidirect
15. C4×#103×C73C2semidirect
291. #27035C73direct (N × H)
302. #2074C2×C73semidirect
303. #2068C2×C73semidirect
306. #1949C2×C73semidirect
307. #1942C2×C73semidirect
309. #1920C2×C73semidirect
310. #1918C2×C73semidirect
311. #1863C2×C73semidirect
314. C4×#103C2×C73semidirect
315. C73#27035direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24952
C73×#23602
C73×#20742
C73×#20682
C73×#20362
C73×#20352
C73×#19492
C73×#19422
C73×#19232
C73×#19202
C73×#19182
C73×#18632
C73×#18522
C73×#18232
C4×#103×C732
#2703573