Finite Group Databasebeta

← C73×#13080 #32922484

Subgroups — C73×#13080 #32922484

Order 18688.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C73C211yesmaximal, characteristic
2C73×#2405C211yesmaximal, characteristic
3C2×#352×C73C212yesmaximal, complemented
4C73×#1781C211yesmaximal, characteristic
5C73×#1390C212yesmaximal, complemented
6C23×D4×C73C2211yescharacteristic
7C22×M16×C73—21no—
8C2×#123×C73C411yescharacteristic, complemented
9C2×#123×C73C2211yescharacteristic
10C22×C22⋊C4×C73C411yescharacteristic, complemented
11C2×#100×C73—21no—
12C2×#100×C73—24no—
13C2×#100×C73C2212yes—
14C2×#99×C73—21no—
15C2×#99×C73C2212yes—
16#394×C73—21no—
17#394×C73—21no—
18#386×C73C411yescharacteristic, complemented
19#386×C73C2211yescharacteristic
20#385×C73—21no—
21#379×C73—21no—
22#379×C73—21no—
23#379×C73C411yescharacteristic, complemented
24#352×C73—24no—
25C25×C73C2×C411yescharacteristic
26C25×C73D411yescharacteristic
27C22×D4×C73—22no—
28C22×D4×C73—22no—
29C22×D4×C73—42no—
30C22×D4×C73—41no—
31C22×D4×C73—41no—
32C22×D4×C73C2×C411yescharacteristic
33C22×D4×C73D411yescharacteristic
34C22×D4×C73D411yescharacteristic
35C22×D4×C73C2311yescharacteristic
36C23×C4×C73C2×C411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73D411yescharacteristic
39C2×M16×C73—24no—
40C2×M16×C73—22no—
41C2×M16×C73—41no—
42C2×M16×C73—42no—
43C22×C8×C73—41no—
44#123×C73—22no—
45#123×C73—22no—
46#123×C73—42no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—21no—
49C2×C22⋊C4×C73—21no—
50C2×C22⋊C4×C73—21no—
51C2×C22⋊C4×C73—21no—
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73—22no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—21no—
58C2×C22⋊C4×C73—41no—
59C2×C22⋊C4×C73—41no—
60C2×C22⋊C4×C73—41no—
61C2×C22⋊C4×C73—41no—
62C2×C22⋊C4×C73C2×C411yescharacteristic
63C2×C22⋊C4×C73C2×C411yescharacteristic
64#100×C73—24no—
65#100×C73—22no—
66#100×C73D414yes—
67#99×C73—22no—
68#99×C73—22no—
69#99×C73—42no—
70#95×C73—21no—
71#95×C73—21no—
72C24×C73—21no—
73C24×C73—21no—
74C24×C73—21no—
75C24×C73—21no—
76C24×C73—22no—
77C24×C73—22no—
78C24×C73—41no—
79C24×C73—41no—
80C24×C73—42no—
81C24×C73—42no—
82C24×C73—81no—
83C24×C73—81no—
84C24×C73C22⋊C411yescharacteristic
85C24×C73C22⋊C411yescharacteristic
86C24×C73C22⋊C411yescharacteristic
87C24×C73C22×C411yescharacteristic
88C24×C73C2×D411yescharacteristic
89C2×D4×C73—22no—
90C2×D4×C73—22no—
91C2×D4×C73—22no—
92C2×D4×C73—22no—
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—41no—
96C2×D4×C73—41no—
97C2×D4×C73—41no—
98C2×D4×C73—41no—
99C2×D4×C73—41no—
100C2×D4×C73—41no—
101C2×D4×C73—44no—
102C2×D4×C73—44no—
103C2×D4×C73—44no—
104C2×D4×C73—44no—
105C2×D4×C73C2×D412yes—
106C2×D4×C73#4112yes—
107C22×C4×C73—21no—
108C22×C4×C73—21no—
109C22×C4×C73—22no—
110C22×C4×C73—21no—
111C22×C4×C73—21no—
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—42no—
121C22×C4×C73—81no—
122C22×C4×C73C22⋊C411yescharacteristic
123C22×C4×C73C2×D411yescharacteristic
124M16×C73—24no—
125M16×C73—44no—
126M16×C73—42no—
127C2×C8×C73—44no—
128C2×C8×C73—42no—
129C4⋊C4×C73—42no—
130C4⋊C4×C73—41no—
131C4⋊C4×C73—41no—
132C22⋊C4×C73—22no—
133C22⋊C4×C73—42no—
134C22⋊C4×C73—42no—
135C22⋊C4×C73—42no—
136C22⋊C4×C73—41no—
137C22⋊C4×C73—41no—
138C22⋊C4×C73—42no—
139C22⋊C4×C73—41no—
140C22⋊C4×C73—42no—
141C22⋊C4×C73—42no—
142C22⋊C4×C73—81no—
143C22⋊C4×C73—81no—
144C22⋊C4×C73—81no—
145C22⋊C4×C73—82no—
146C22⋊C4×C73—82no—
147C23×C73—22no—
148C23×C73—21no—
149C23×C73—21no—
150C23×C73—21no—
151C23×C73—21no—
152C23×C73—21no—
153C23×C73—21no—
154C23×C73—21no—
155C23×C73—21no—
156C23×C73—21no—
157C23×C73—21no—
158C23×C73—21no—
159C23×C73—21no—
160C23×C73—41no—
161C23×C73—42no—
162C23×C73—42no—
163C23×C73—42no—
164C23×C73—42no—
165C23×C73—41no—
166C23×C73—41no—
167C23×C73—41no—
168C23×C73—41no—
169C23×C73—41no—
170C23×C73—41no—
171C23×C73—42no—
172C23×C73—42no—
173C23×C73—41no—
174C23×C73—41no—
175C23×C73—42no—
176C23×C73—42no—
177C23×C73—81no—
178C23×C73—81no—
179C23×C73—81no—
180C23×C73—81no—
181C23×C73—84no—
182C23×C73—84no—
183C23×C73—84no—
184C23×C73—84no—
185C23×C73#9911yescharacteristic
186C23×C73#9911yescharacteristic
187C23×C73C2×C22⋊C411yescharacteristic
188C23×C73C4×D412yes—
189C23×C73#12112yes—
190D4×C73—42no—
191D4×C73—42no—
192D4×C73—44no—
193D4×C73—44no—
194D4×C73—42no—
195D4×C73—42no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—41no—
205C2×C4×C73—41no—
206C2×C4×C73—41no—
207C2×C4×C73—41no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—82no—
217C2×C4×C73—82no—
218C2×C4×C73—82no—
219C2×C4×C73—82no—
220C2×C4×C73—82no—
221C2×C4×C73#9912yes—
222C2×C4×C73#12011yescharacteristic
223C2×C4×C73#12311yescharacteristic
224C8×C73—44no—
225C22×C73—21no—
226C22×C73—21no—
227C22×C73—21no—
228C22×C73—21no—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—21no—
232C22×C73—22no—
233C22×C73—22no—
234C22×C73—42no—
235C22×C73—42no—
236C22×C73—42no—
237C22×C73—42no—
238C22×C73—42no—
239C22×C73—42no—
240C22×C73—41no—
241C22×C73—41no—
242C22×C73—41no—
243C22×C73—41no—
244C22×C73—41no—
245C22×C73—41no—
246C22×C73—41no—
247C22×C73—41no—
248C22×C73—41no—
249C22×C73—41no—
250C22×C73—81no—
251C22×C73—84no—
252C22×C73—84no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73—81no—
256C22×C73—84no—
257C22×C73—84no—
258C22×C73#35212yescomplemented
259C22×C73#38611yescharacteristic
260C22×C73C2×#9911yescharacteristic
261C22×C73C2×#9911yescharacteristic
262C4×C73—21no—
263C4×C73—22no—
264C4×C73—21no—
265C4×C73—81no—
266C4×C73—81no—
267C4×C73—81no—
268C4×C73—81no—
269C4×C73—162no—
270#13080C7311yesmaximal, characteristic, direct product factor, Sylow
271C2×C73—21no—
272C2×C73—21no—
273C2×C73—22no—
274C2×C73—42no—
275C2×C73—41no—
276C2×C73—42no—
277C2×C73—81no—
278C2×C73—81no—
279C2×C73#189811yescharacteristic
280C2×C73C2×#35211yescharacteristic
281C2×C73#212111yescharacteristic
282C22×#100C2×C7311yescharacteristic
283#2405C2×C7311yescharacteristic
284C2×#352C2×C7312yescomplemented
285#1781C2×C7311yescharacteristic
286#1390C2×C7312yescomplemented
287C73#1308011yescharacteristic, direct product factor, Sylow
288C23×D4C22×C7311yescharacteristic
289C22×M16—21no—
290C2×#123C4×C7311yescharacteristic, complemented
291C2×#123C22×C7311yescharacteristic
292C22×C22⋊C4C4×C7311yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C7312yes—
296C2×#99—21no—
297C2×#99C22×C7312yes—
298#394—21no—
299#394—21no—
300#386C4×C7311yescharacteristic, complemented
301#386C22×C7311yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C7311yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C7311yescharacteristic
308C25D4×C7311yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C7311yescharacteristic
315C22×D4D4×C7311yescharacteristic
316C22×D4D4×C7311yescharacteristic
317C22×D4C23×C7311yescharacteristic
318C23×C4C2×C4×C7311yescharacteristic
319C23×C4C2×C4×C7311yescharacteristic
320C23×C4D4×C7311yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C7311yescharacteristic
345C2×C22⋊C4C2×C4×C7311yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C7314yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C7311yescharacteristic
367C24C22⋊C4×C7311yescharacteristic
368C24C22⋊C4×C7311yescharacteristic
369C24C22×C4×C7311yescharacteristic
370C24C2×D4×C7311yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C7312yes—
388C2×D4#41×C7312yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C7311yescharacteristic
405C22×C4C2×D4×C7311yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C7311yescharacteristic
468C23#99×C7311yescharacteristic
469C23C2×C22⋊C4×C7311yescharacteristic
470C23C4×D4×C7312yes—
471C23#121×C7312yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C7312yes—
504C2×C4#120×C7311yescharacteristic
505C2×C4#123×C7311yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C7312yescomplemented
541C22#386×C7311yescharacteristic
542C22C2×#99×C7311yescharacteristic
543C22C2×#99×C7311yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C73×#189811yescharacteristic
561C2C2×#352×C7311yescharacteristic
562C2C73×#212111yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC24C22×C4×C73
Frattini, cosocleC22×D4C23×C73
prime radicalC23×D4×C73C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C24×C73 ◁ C23×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C73C2semidirect
5. C73×#1390C2semidirect
8. C2×#123×C73C4semidirect
10. C22×C22⋊C4×C73C4semidirect
18. #386×C73C4semidirect
23. #379×C73C4semidirect
258. C22×C73#352semidirect
270. #13080C73direct (N × H)
284. C2×#352C2×C73semidirect
286. #1390C2×C73semidirect
287. C73#13080direct (N × H)
290. C2×#123C4×C73semidirect
292. C22×C22⋊C4C4×C73semidirect
300. #386C4×C73semidirect
305. #379C4×C73semidirect
540. C22#352×C73semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C732
C73×#24052
C2×#352×C732
C73×#17812
C73×#13902
#1308073