Finite Group Databasebeta

← C73×#10229 #32919633

Subgroups — C73×#10229 #32919633

Order 18688.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C73C211yesmaximal, characteristic, complemented
2C2×#459×C73C211yesmaximal, characteristic
3C73×#2538C211yesmaximal, characteristic, complemented
4C73×#1957C211yesmaximal, characteristic, complemented
5C2×Q8⋊C8×C73C211yesmaximal, characteristic, complemented
6C2×D4⋊C8×C73C211yesmaximal, characteristic, complemented
7C73×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C73—21no—
9C22×D8×C73—21no—
10C2×#127×C73C2211yescharacteristic
11C2×C22⋊Q8×C73—21no—
12C2×C4×Q8×C73C2211yescharacteristic
13C2×C4×D4×C73C2211yescharacteristic
14#460×C73—22no—
15#460×C73—22no—
16#459×C73—22no—
17#459×C73—22no—
18C2×C4⋊C8×C73C2211yescharacteristic
19C2×C4⋊C8×C73C2211yescharacteristic
20C2×#102×C73—21no—
21C2×#102×C73—21no—
22C2×#102×C73—22no—
23C2×C4×C8×C73C2211yescharacteristic
24#396×C73—22no—
25#390×C73—21no—
26#389×C73—21no—
27#384×C73C2211yescharacteristic
28#380×C73—21no—
29Q8⋊C8×C73—22no—
30D4⋊C8×C73—22no—
31C22×Q8×C73D411yescharacteristic
32C22×D4×C73—21no—
33C22×D4×C73—21no—
34C22×D4×C73—21no—
35C22×D4×C73D411yescharacteristic
36C23×C4×C73—21no—
37C2×SD16×C73—24no—
38C2×SD16×C73—42no—
39C2×SD16×C73—42no—
40C2×D8×C73—24no—
41C2×D8×C73—42no—
42C2×D8×C73—42no—
43C22×C8×C73—21no—
44C22×C8×C73—21no—
45C22×C8×C73—21no—
46#127×C73—21no—
47#127×C73—21no—
48#127×C73—21no—
49#127×C73D412yes—
50C22⋊Q8×C73—42no—
51C22⋊Q8×C73—42no—
52C4×Q8×C73—21no—
53C4×Q8×C73—21no—
54C4×Q8×C73—21no—
55C4×Q8×C73—21no—
56C4×D4×C73—21no—
57C4×D4×C73—21no—
58C4×D4×C73—21no—
59C4×D4×C73—21no—
60C2×C4⋊C4×C73—22no—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73D411yescharacteristic
65C2×C4⋊C4×C73D411yescharacteristic
66C2×C4⋊C4×C73D412yes—
67C2×C22⋊C4×C73—22no—
68C2×C22⋊C4×C73—21no—
69C2×C22⋊C4×C73—22no—
70C2×C42×C73—21no—
71C2×C42×C73C2311yescharacteristic
72C4⋊C8×C73—21no—
73C4⋊C8×C73—21no—
74C4⋊C8×C73D412yes—
75C4⋊C8×C73D412yes—
76#102×C73—24no—
77#102×C73—24no—
78#102×C73—44no—
79C4×C8×C73—21no—
80C4×C8×C73—21no—
81#95×C73—22no—
82C24×C73—21no—
83C24×C73—41no—
84C2×Q8×C73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73—21no—
87C2×Q8×C73—21no—
88C2×Q8×C73—21no—
89C2×Q8×C73D812yescomplemented
90C2×D4×C73—21no—
91C2×D4×C73—22no—
92C2×D4×C73—22no—
93C2×D4×C73—21no—
94C2×D4×C73—22no—
95C2×D4×C73—21no—
96C2×D4×C73—21no—
97C2×D4×C73—21no—
98C2×D4×C73—42no—
99C2×D4×C73—42no—
100C2×D4×C73—41no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73—41no—
105C2×D4×C73—41no—
106C2×D4×C73—41no—
107C2×D4×C73—41no—
108C2×D4×C73—41no—
109C2×D4×C73—41no—
110C2×D4×C73—41no—
111C2×D4×C73SD1612yescomplemented
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—22no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73C2×D411yescharacteristic
123C22×C4×C73C2×D411yescharacteristic
124C22×C4×C73C2×D411yescharacteristic
125SD16×C73—48no—
126D8×C73—48no—
127C2×C8×C73—22no—
128C2×C8×C73—22no—
129C2×C8×C73—22no—
130C2×C8×C73—41no—
131C2×C8×C73—41no—
132C2×C8×C73—41no—
133C2×C8×C73—41no—
134C2×C8×C73—41no—
135C2×C8×C73—41no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—21no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73—42no—
141C4⋊C4×C73—44no—
142C4⋊C4×C73—41no—
143C4⋊C4×C73—41no—
144C4⋊C4×C73—41no—
145C4⋊C4×C73—41no—
146C4⋊C4×C73—41no—
147C4⋊C4×C73—41no—
148C22⋊C4×C73—44no—
149C22⋊C4×C73—41no—
150C22⋊C4×C73—41no—
151C22⋊C4×C73—82no—
152C42×C73—41no—
153C42×C73—41no—
154C42×C73C2×D411yescharacteristic
155C42×C73C2×D411yescharacteristic
156C42×C73C2×D411yescharacteristic
157C42×C73#4111yescharacteristic
158C23×C73—22no—
159C23×C73—41no—
160C23×C73—41no—
161C23×C73—41no—
162C23×C73—41no—
163C23×C73—41no—
164C23×C73—41no—
165C23×C73—42no—
166C23×C73—81no—
167C23×C73—81no—
168C23×C73—81no—
169C23×C73—81no—
170C23×C73—81no—
171C23×C73—81no—
172C23×C73#12011yescharacteristic
173Q8×C73—22no—
174Q8×C73—22no—
175Q8×C73—41no—
176Q8×C73—41no—
177D4×C73—22no—
178D4×C73—22no—
179D4×C73—44no—
180D4×C73—42no—
181D4×C73—42no—
182D4×C73—42no—
183D4×C73—41no—
184D4×C73—42no—
185D4×C73—41no—
186D4×C73—82no—
187D4×C73—81no—
188D4×C73—81no—
189D4×C73—81no—
190D4×C73—81no—
191C2×C4×C73—21no—
192C2×C4×C73—21no—
193C2×C4×C73—22no—
194C2×C4×C73—41no—
195C2×C4×C73—41no—
196C2×C4×C73—41no—
197C2×C4×C73—41no—
198C2×C4×C73—42no—
199C2×C4×C73—41no—
200C2×C4×C73—42no—
201C2×C4×C73—41no—
202C2×C4×C73—41no—
203C2×C4×C73—42no—
204C2×C4×C73—41no—
205C2×C4×C73—81no—
206C2×C4×C73—81no—
207C2×C4×C73—81no—
208C2×C4×C73—81no—
209C2×C4×C73#12011yescharacteristic
210C2×C4×C73#12011yescharacteristic
211C2×C4×C73#12111yescharacteristic
212C2×C4×C73#12111yescharacteristic
213C2×C4×C73#12111yescharacteristic
214C2×C4×C73#12711yescharacteristic
215C2×C4×C73C2×D811yescharacteristic
216C2×C4×C73C2×SD1611yescharacteristic
217C2×C4×C73#13511yescharacteristic
218C2×C4×C73#13511yescharacteristic
219C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C73#13711yescharacteristic
223C8×C73—42no—
224C8×C73—42no—
225C8×C73—42no—
226C22×C73—42no—
227C22×C73—42no—
228C22×C73—42no—
229C22×C73—81no—
230C22×C73—81no—
231C22×C73—81no—
232C22×C73—81no—
233C22×C73—82no—
234C22×C73—82no—
235C22×C73—82no—
236C22×C73—161no—
237C22×C73—161no—
238C22×C73—161no—
239C22×C73—161no—
240C22×C73#39211yescharacteristic
241C22×C73#44711yescharacteristic
242C22×C73#44811yescharacteristic
243C22×C73#44911yescharacteristic
244C22×C73#44911yescharacteristic
245C22×C73#45311yescharacteristic
246C22×C73#45411yescharacteristic
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—42no—
250C4×C73—82no—
251C4×C73—81no—
252C4×C73—81no—
253C4×C73#44711yescharacteristic
254C4×C73#44911yescharacteristic
255C4×C73#45011yescharacteristic
256C4×C73#45211yescharacteristic
257C4×C73#46511yescharacteristic
258C4×C73#46611yescharacteristic
259C4×C73#46811yescharacteristic
260C4×C73#46911yescharacteristic
261#10229C7311yesmaximal, characteristic, direct product factor, Sylow
262C2×C73—82no—
263C2×C73—162no—
264C2×C73#162111yescharacteristic
265C2×C73#162211yescharacteristic
266C2×C73#162711yescharacteristic
267C2×C73#162811yescharacteristic
268C2×C73#199911yescharacteristic
269C2×C73#200011yescharacteristic
270C2×C73#200611yescharacteristic
271C2×#460C2×C7311yescharacteristic, complemented
272C2×#459C2×C7311yescharacteristic
273#2538C2×C7311yescharacteristic, complemented
274#1957C2×C7311yescharacteristic, complemented
275C2×Q8⋊C8C2×C7311yescharacteristic, complemented
276C2×D4⋊C8C2×C7311yescharacteristic, complemented
277#1296C2×C7311yescharacteristic, complemented
278C73#1022911yescharacteristic, direct product factor, Sylow
279C22×SD16—21no—
280C22×D8—21no—
281C2×#127C22×C7311yescharacteristic
282C2×C22⋊Q8—21no—
283C2×C4×Q8C22×C7311yescharacteristic
284C2×C4×D4C22×C7311yescharacteristic
285#460—22no—
286#460—22no—
287#459—22no—
288#459—22no—
289C2×C4⋊C8C22×C7311yescharacteristic
290C2×C4⋊C8C22×C7311yescharacteristic
291C2×#102—21no—
292C2×#102—21no—
293C2×#102—22no—
294C2×C4×C8C22×C7311yescharacteristic
295#396—22no—
296#390—21no—
297#389—21no—
298#384C22×C7311yescharacteristic
299#380—21no—
300Q8⋊C8—22no—
301D4⋊C8—22no—
302C22×Q8D4×C7311yescharacteristic
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4D4×C7311yescharacteristic
307C23×C4—21no—
308C2×SD16—24no—
309C2×SD16—42no—
310C2×SD16—42no—
311C2×D8—24no—
312C2×D8—42no—
313C2×D8—42no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127D4×C7312yes—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C7311yescharacteristic
336C2×C4⋊C4D4×C7311yescharacteristic
337C2×C4⋊C4D4×C7312yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C42—21no—
342C2×C42C23×C7311yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—21no—
345C4⋊C8D4×C7312yes—
346C4⋊C8D4×C7312yes—
347#102—24no—
348#102—24no—
349#102—44no—
350C4×C8—21no—
351C4×C8—21no—
352#95—22no—
353C24—21no—
354C24—41no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8D8×C7312yescomplemented
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4SD16×C7312yescomplemented
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4C2×D4×C7311yescharacteristic
394C22×C4C2×D4×C7311yescharacteristic
395C22×C4C2×D4×C7311yescharacteristic
396SD16—48no—
397D8—48no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—42no—
412C4⋊C4—44no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—44no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—82no—
423C42—41no—
424C42—41no—
425C42C2×D4×C7311yescharacteristic
426C42C2×D4×C7311yescharacteristic
427C42C2×D4×C7311yescharacteristic
428C42#41×C7311yescharacteristic
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23#120×C7311yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—22no—
450D4—44no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—41no—
455D4—42no—
456D4—41no—
457D4—82no—
458D4—81no—
459D4—81no—
460D4—81no—
461D4—81no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4#120×C7311yescharacteristic
481C2×C4#120×C7311yescharacteristic
482C2×C4#121×C7311yescharacteristic
483C2×C4#121×C7311yescharacteristic
484C2×C4#121×C7311yescharacteristic
485C2×C4#127×C7311yescharacteristic
486C2×C4C2×D8×C7311yescharacteristic
487C2×C4C2×SD16×C7311yescharacteristic
488C2×C4#135×C7311yescharacteristic
489C2×C4#135×C7311yescharacteristic
490C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
491C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
492C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
493C2×C4#137×C7311yescharacteristic
494C8—42no—
495C8—42no—
496C8—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—161no—
508C22—161no—
509C22—161no—
510C22—161no—
511C22#392×C7311yescharacteristic
512C22#447×C7311yescharacteristic
513C22#448×C7311yescharacteristic
514C22#449×C7311yescharacteristic
515C22#449×C7311yescharacteristic
516C22#453×C7311yescharacteristic
517C22#454×C7311yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—81no—
523C4—82no—
524C4#447×C7311yescharacteristic
525C4#449×C7311yescharacteristic
526C4#450×C7311yescharacteristic
527C4#452×C7311yescharacteristic
528C4#465×C7311yescharacteristic
529C4#466×C7311yescharacteristic
530C4#468×C7311yescharacteristic
531C4#469×C7311yescharacteristic
532C2—82no—
533C2—162no—
534C2C73×#162111yescharacteristic
535C2C73×#162211yescharacteristic
536C2C73×#162711yescharacteristic
537C2C73×#162811yescharacteristic
538C2C73×#199911yescharacteristic
539C2C73×#200011yescharacteristic
540C2C73×#200611yescharacteristic
subgroupG/H
center, socleC23×C73#120
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC2×#459×C73C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C73C2semidirect
3. C73×#2538C2semidirect
4. C73×#1957C2semidirect
5. C2×Q8⋊C8×C73C2semidirect
6. C2×D4⋊C8×C73C2semidirect
7. C73×#1296C2semidirect
89. C2×Q8×C73D8semidirect
111. C2×D4×C73SD16semidirect
261. #10229C73direct (N × H)
271. C2×#460C2×C73semidirect
273. #2538C2×C73semidirect
274. #1957C2×C73semidirect
275. C2×Q8⋊C8C2×C73semidirect
276. C2×D4⋊C8C2×C73semidirect
277. #1296C2×C73semidirect
278. C73#10229direct (N × H)
360. C2×Q8D8×C73semidirect
382. C2×D4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C732
C2×#459×C732
C73×#25382
C73×#19572
C2×Q8⋊C8×C732
C2×D4⋊C8×C732
C73×#12962
#1022973