Finite Group Databasebeta

← C73×#27126 #32936530

Subgroups — C73×#27126 #32936530

Order 18688.

714 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2512C211yesmaximal, characteristic
2C73×#2365C211yesmaximal, characteristic, complemented
3C73×#2099C211yesmaximal, characteristic, complemented
4C73×#2067C211yesmaximal, characteristic
5C73×#2057C211yesmaximal, characteristic, complemented
6C73×#2023C211yesmaximal, characteristic
7C73×#1947C211yesmaximal, characteristic, complemented
8C73×#1934C211yesmaximal, characteristic
9C73×#1925C211yesmaximal, characteristic
10C73×#1925C211yesmaximal, characteristic
11C73×#1925C211yesmaximal, characteristic
12C73×#1918C211yesmaximal, characteristic, complemented
13C73×#1918C211yesmaximal, characteristic, complemented
14C73×#1916C211yesmaximal, characteristic, complemented
15C4×#107×C73C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C73C2211yescharacteristic
17C2×#126×C73—21no—
18C2×C4×Q8×C73—21no—
19C2×#107×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#107×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×C4×C8×C73C2211yescharacteristic
29#397×C73—21no—
30#396×C73—21no—
31#391×C73—21no—
32#390×C73C2211yescharacteristic
33#390×C73C2211yescharacteristic
34#390×C73C2211yescharacteristic
35#389×C73C2211yescharacteristic
36#389×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#388×C73—21no—
39#387×C73—21no—
40#387×C73—21no—
41#384×C73C2211yescharacteristic
42C4×C4⋊C4×C73C2211yescharacteristic
43C4×C4⋊C4×C73C2211yescharacteristic
44C4×C4⋊C4×C73C2211yescharacteristic
45C4×C4⋊C4×C73C2211yescharacteristic
46C4×C4⋊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#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73—21no—
60C22×D4×C73C2311yescharacteristic
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C4⋊Q8×C73—22no—
66C4⋊Q8×C73—22no—
67#126×C73—44no—
68C4×Q8×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×C73D411yescharacteristic
76C2×C4⋊C4×C73D411yescharacteristic
77C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73—21no—
89C2×C22⋊C4×C73—21no—
90C2×C42×C73—21no—
91C2×C42×C73—21no—
92C2×C42×C73—21no—
93C2×C42×C73—21no—
94C2×C42×C73C2311yescharacteristic
95C2×C42×C73C2311yescharacteristic
96C2×C42×C73C2311yescharacteristic
97#107×C73—22no—
98#107×C73—22no—
99#107×C73—22no—
100#107×C73—22no—
101C4⋊C8×C73—22no—
102#102×C73—22no—
103#102×C73—22no—
104#102×C73—22no—
105#102×C73—22no—
106C4×C8×C73—22no—
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×C73D411yescharacteristic
115#95×C73D411yescharacteristic
116C24×C73—21no—
117C2×Q8×C73—24no—
118C2×Q8×C73—42no—
119C2×Q8×C73—42no—
120C2×D4×C73—21no—
121C2×D4×C73—21no—
122C2×D4×C73—21no—
123C2×D4×C73—21no—
124C2×D4×C73—21no—
125C2×D4×C73—21no—
126C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
134C22×C4×C73C2×D411yescharacteristic
135C22×C4×C73C2×D411yescharacteristic
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2×D411yescharacteristic
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2411yescharacteristic
140C2×C8×C73—21no—
141C2×C8×C73—21no—
142C2×C8×C73—21no—
143C2×C8×C73—21no—
144C2×C8×C73—21no—
145C2×C8×C73—21no—
146C2×C8×C73—21no—
147C2×C8×C73—21no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73#4112yes—
152C4⋊C4×C73—24no—
153C4⋊C4×C73—21no—
154C4⋊C4×C73—21no—
155C4⋊C4×C73—21no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—21no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—41no—
165C4⋊C4×C73—42no—
166C4⋊C4×C73—42no—
167C4⋊C4×C73—42no—
168C4⋊C4×C73—42no—
169C4⋊C4×C73—81no—
170C4⋊C4×C73D814yes—
171C4⋊C4×C73#4112yes—
172C4⋊C4×C73#4112yes—
173C4⋊C4×C73#4112yes—
174C22⋊C4×C73—42no—
175C22⋊C4×C73—42no—
176C22⋊C4×C73—42no—
177C22⋊C4×C73—42no—
178C22⋊C4×C73—81no—
179C22⋊C4×C73—81no—
180C42×C73—21no—
181C42×C73—21no—
182C42×C73—21no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—42no—
187C42×C73—42no—
188C42×C73—42no—
189C42×C73—42no—
190C23×C73—41no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73C22×D411yescharacteristic
198Q8×C73—48no—
199D4×C73—41no—
200D4×C73—41no—
201D4×C73—41no—
202D4×C73—41no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—22no—
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—41no—
222C2×C4×C73—41no—
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×C73C2×D812yes—
240C2×C4×C73C2×D812yes—
241C2×C4×C73C2×D812yes—
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C732−1+411yescharacteristic
247C2×C4×C732−1+411yescharacteristic
248C8×C73—22no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C22×C73—81no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73—81no—
256C22×C73—81no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73#52511yescharacteristic
260C22×C73#54711yescharacteristic
261C22×C73#54811yescharacteristic
262C22×C73C22×D811yescharacteristic
263C22×C73#57511yescharacteristic
264C22×C73#57711yescharacteristic
265C22×C73#57811yescharacteristic
266C4×C73—22no—
267C4×C73—22no—
268C4×C73—22no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—42no—
272C4×C73—42no—
273C4×C73—42no—
274C4×C73—41no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73#52911yescharacteristic
280C4×C73#54111yescharacteristic
281C4×C73#55611yescharacteristic
282C4×C73#55611yescharacteristic
283#27126C7311yesmaximal, characteristic, direct product factor, Sylow
284C2×C73—161no—
285C2×C73#246911yescharacteristic
286C2×C73#310011yescharacteristic
287C2×C73#312111yescharacteristic
288C2×C73#333411yescharacteristic
289C2×C73#335011yescharacteristic
290C2×C73#335811yescharacteristic
291C2×C73#337711yescharacteristic
292#2512C2×C7311yescharacteristic
293#2365C2×C7311yescharacteristic, complemented
294#2099C2×C7311yescharacteristic, complemented
295#2067C2×C7311yescharacteristic
296#2057C2×C7311yescharacteristic, complemented
297#2023C2×C7311yescharacteristic
298#1947C2×C7311yescharacteristic, complemented
299#1934C2×C7311yescharacteristic
300#1925C2×C7311yescharacteristic
301#1925C2×C7311yescharacteristic
302#1925C2×C7311yescharacteristic
303#1918C2×C7311yescharacteristic, complemented
304#1918C2×C7311yescharacteristic, complemented
305#1916C2×C7311yescharacteristic, complemented
306C4×#107C2×C7311yescharacteristic, complemented
307C73#2712611yescharacteristic, direct product factor, Sylow
308C2×C4⋊Q8C22×C7311yescharacteristic
309C2×#126—21no—
310C2×C4×Q8—21no—
311C2×#107C22×C7311yescharacteristic
312C2×#107C22×C7311yescharacteristic
313C2×#107C22×C7311yescharacteristic
314C2×#107C22×C7311yescharacteristic
315C2×C4⋊C8C22×C7311yescharacteristic
316C2×#102C22×C7311yescharacteristic
317C2×#102C22×C7311yescharacteristic
318C2×#102C22×C7311yescharacteristic
319C2×#102C22×C7311yescharacteristic
320C2×C4×C8C22×C7311yescharacteristic
321#397—21no—
322#396—21no—
323#391—21no—
324#390C22×C7311yescharacteristic
325#390C22×C7311yescharacteristic
326#390C22×C7311yescharacteristic
327#389C22×C7311yescharacteristic
328#389C22×C7311yescharacteristic
329#389C22×C7311yescharacteristic
330#388—21no—
331#387—21no—
332#387—21no—
333#384C22×C7311yescharacteristic
334C4×C4⋊C4C22×C7311yescharacteristic
335C4×C4⋊C4C22×C7311yescharacteristic
336C4×C4⋊C4C22×C7311yescharacteristic
337C4×C4⋊C4C22×C7311yescharacteristic
338C4×C4⋊C4C22×C7311yescharacteristic
339#340C22×C7311yescharacteristic
340#340C22×C7311yescharacteristic
341#340C22×C7311yescharacteristic
342#340C22×C7311yescharacteristic
343#340C22×C7311yescharacteristic
344#340C22×C7311yescharacteristic
345#340C22×C7311yescharacteristic
346#340C22×C7311yescharacteristic
347#336C22×C7311yescharacteristic
348#336C22×C7311yescharacteristic
349#336C22×C7311yescharacteristic
350#336C22×C7311yescharacteristic
351C22×Q8—21no—
352C22×D4C23×C7311yescharacteristic
353C22×C8C23×C7311yescharacteristic
354C22×C8C23×C7311yescharacteristic
355C22×C8C23×C7311yescharacteristic
356C22×C8C23×C7311yescharacteristic
357C4⋊Q8—22no—
358C4⋊Q8—22no—
359#126—44no—
360C4×Q8—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C7311yescharacteristic
368C2×C4⋊C4D4×C7311yescharacteristic
369C2×C4⋊C4C23×C7311yescharacteristic
370C2×C4⋊C4C23×C7311yescharacteristic
371C2×C4⋊C4C23×C7311yescharacteristic
372C2×C4⋊C4C23×C7311yescharacteristic
373C2×C4⋊C4C23×C7311yescharacteristic
374C2×C4⋊C4C23×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C7311yescharacteristic
387C2×C42C23×C7311yescharacteristic
388C2×C42C23×C7311yescharacteristic
389#107—22no—
390#107—22no—
391#107—22no—
392#107—22no—
393C4⋊C8—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398C4×C8—22no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95D4×C7311yescharacteristic
407#95D4×C7311yescharacteristic
408C24—21no—
409C2×Q8—24no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4C2×D4×C7311yescharacteristic
426C22×C4C2×D4×C7311yescharacteristic
427C22×C4C2×D4×C7311yescharacteristic
428C22×C4C2×D4×C7311yescharacteristic
429C22×C4C2×D4×C7311yescharacteristic
430C22×C4C2×D4×C7311yescharacteristic
431C22×C4C24×C7311yescharacteristic
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8#41×C7312yes—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—81no—
462C4⋊C4D8×C7314yes—
463C4⋊C4#41×C7312yes—
464C4⋊C4#41×C7312yes—
465C4⋊C4#41×C7312yes—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—42no—
480C42—42no—
481C42—42no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23C22×D4×C7311yescharacteristic
490Q8—48no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
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×C4C2×D8×C7312yes—
532C2×C4C2×D8×C7312yes—
533C2×C4C2×D8×C7312yes—
534C2×C4C2×#41×C7311yescharacteristic
535C2×C4C2×#41×C7311yescharacteristic
536C2×C4C2×#41×C7311yescharacteristic
537C2×C4C2×#41×C7311yescharacteristic
538C2×C42−1+4×C7311yescharacteristic
539C2×C42−1+4×C7311yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22#525×C7311yescharacteristic
552C22#547×C7311yescharacteristic
553C22#548×C7311yescharacteristic
554C22C22×D8×C7311yescharacteristic
555C22#575×C7311yescharacteristic
556C22#577×C7311yescharacteristic
557C22#578×C7311yescharacteristic
558C4—22no—
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4#529×C7311yescharacteristic
572C4#541×C7311yescharacteristic
573C4#556×C7311yescharacteristic
574C4#556×C7311yescharacteristic
575C2—161no—
576C2C73×#246911yescharacteristic
577C2C73×#310011yescharacteristic
578C2C73×#312111yescharacteristic
579C2C73×#333411yescharacteristic
580C2C73×#335011yescharacteristic
581C2C73×#335811yescharacteristic
582C2C73×#337711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2365C2semidirect
3. C73×#2099C2semidirect
5. C73×#2057C2semidirect
7. C73×#1947C2semidirect
12. C73×#1918C2semidirect
13. C73×#1918C2semidirect
14. C73×#1916C2semidirect
15. C4×#107×C73C2semidirect
283. #27126C73direct (N × H)
293. #2365C2×C73semidirect
294. #2099C2×C73semidirect
296. #2057C2×C73semidirect
298. #1947C2×C73semidirect
303. #1918C2×C73semidirect
304. #1918C2×C73semidirect
305. #1916C2×C73semidirect
306. C4×#107C2×C73semidirect
307. C73#27126direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25122
C73×#23652
C73×#20992
C73×#20672
C73×#20572
C73×#20232
C73×#19472
C73×#19342
C73×#19252
C73×#19182
C73×#19162
C4×#107×C732
#2712673