Finite Group Databasebeta

← C73×#24079 #32933483

Subgroups — C73×#24079 #32933483

Order 18688.

1030 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3492C211yesmaximal, characteristic
2C73×#3093C212yesmaximal, complemented
3C73×#2317C211yesmaximal, characteristic, complemented
4C73×#2061C211yesmaximal, characteristic, complemented
5C73×#2060C211yesmaximal, characteristic, complemented
6C73×#2040C211yesmaximal, characteristic, complemented
7C73×#2039C211yesmaximal, characteristic, complemented
8C73×#1897C212yesmaximal, complemented
9C73×#1860C212yesmaximal, complemented
10C73×#1859C212yesmaximal, complemented
11C73×#1821C211yesmaximal, characteristic, complemented
12#554×C73—22no—
13#553×C73—22no—
14#552×C73—22no—
15#547×C73—22no—
16#544×C73C2211yescharacteristic
17#539×C73—22no—
18#537×C73C2211yescharacteristic
19#525×C73—22no—
20#525×C73C2212yes—
21#520×C73C2212yes—
22C2×#117×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#485×C73—22no—
26#485×C73—22no—
27#482×C73—22no—
28#482×C73—22no—
29#428×C73C2212yes—
30#428×C73C2212yes—
31C2×#104×C73C2212yes—
32C2×#104×C73C2212yes—
33#417×C73C2212yes—
34#417×C73C2212yes—
35#407×C73C2212yes—
36#389×C73—22no—
37#385×C73—22no—
38#384×C73C2211yescharacteristic
39#384×C73C2211yescharacteristic
40#382×C73C2211yescharacteristic
41#382×C73C2211yescharacteristic
42#343×C73C2211yescharacteristic
43#343×C73C2211yescharacteristic
44#343×C73C2212yes—
45#339×C73C2212yes—
46#339×C73C2212yes—
47C2×#41×C73—22no—
48C2×#41×C73C2312yes—
49C23×C4×C73D412yes—
50C23×C4×C73C2311yescharacteristic
51C2×M16×C73C2312yes—
52C2×M16×C73C2312yes—
53C4⋊Q8×C73—22no—
54#126×C73—24no—
55#125×C73—24no—
56#125×C73—22no—
57#123×C73—24no—
58#123×C73—24no—
59#123×C73—22no—
60C22⋊Q8×C73—22no—
61C22⋊Q8×C73—24no—
62C22⋊Q8×C73—22no—
63C22⋊Q8×C73—22no—
64C22⋊Q8×C73D412yes—
65C22⋊Q8×C73D412yes—
66#121×C73—22no—
67#121×C73—22no—
68#121×C73—22no—
69#121×C73D412yes—
70#121×C73D412yes—
71#120×C73—22no—
72C4×Q8×C73—22no—
73C4×D4×C73—24no—
74C4×D4×C73—22no—
75C4×D4×C73—24no—
76C4×D4×C73—22no—
77C4×D4×C73—22no—
78#117×C73—22no—
79#117×C73—22no—
80#117×C73—22no—
81#117×C73—22no—
82#117×C73—22no—
83#117×C73—22no—
84#117×C73C2312yes—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73D412yes—
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C42×C73—21no—
99C2×C42×C73C2311yescharacteristic
100C2×C42×C73C2311yescharacteristic
101#107×C73—22no—
102#107×C73—22no—
103#106×C73—22no—
104#106×C73—22no—
105#104×C73—24no—
106#104×C73—24no—
107#103×C73—22no—
108#103×C73—22no—
109#102×C73—22no—
110#102×C73—22no—
111C22⋊C8×C73—22no—
112C22⋊C8×C73—22no—
113#95×C73—22no—
114#95×C73—22no—
115C24×C73C2×D411yescharacteristic
116#41×C73—22no—
117#41×C73—22no—
118#41×C73—22no—
119#41×C73—22no—
120#41×C73—84no—
121C2×Q8×C73—22no—
122C2×Q8×C73C2×D412yes—
123C2×D4×C73—22no—
124C2×D4×C73—22no—
125C2×D4×C73—22no—
126C2×D4×C73—22no—
127C2×D4×C73C2×D412yes—
128C22×C4×C73—21no—
129C22×C4×C73—21no—
130C22×C4×C73—22no—
131C22×C4×C73—22no—
132C22×C4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—24no—
135C22×C4×C73—22no—
136C22×C4×C73—22no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—82no—
140C22×C4×C73C2×D411yescharacteristic
141C22×C4×C73C2×D412yes—
142C22×C4×C73C2×D412yes—
143C22×C4×C73C2×D412yes—
144C22×C4×C73C2×D412yes—
145C22×C4×C73C2411yescharacteristic
146M16×C73—22no—
147M16×C73—22no—
148M16×C73—22no—
149M16×C73—22no—
150C2×C8×C73—22no—
151C2×C8×C73—22no—
152C4⋊C4×C73—24no—
153C4⋊C4×C73—24no—
154C4⋊C4×C73—22no—
155C4⋊C4×C73—22no—
156C4⋊C4×C73—24no—
157C4⋊C4×C73—24no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—22no—
160C4⋊C4×C73—22no—
161C4⋊C4×C73—22no—
162C4⋊C4×C73—22no—
163C4⋊C4×C73—22no—
164C4⋊C4×C73—82no—
165C4⋊C4×C73—82no—
166C4⋊C4×C73C2×D412yes—
167C4⋊C4×C73C2×D412yes—
168C22⋊C4×C73—24no—
169C22⋊C4×C73—24no—
170C22⋊C4×C73—24no—
171C22⋊C4×C73—22no—
172C22⋊C4×C73—22no—
173C22⋊C4×C73—22no—
174C22⋊C4×C73—22no—
175C22⋊C4×C73—22no—
176C22⋊C4×C73—41no—
177C22⋊C4×C73—41no—
178C42×C73—24no—
179C42×C73—22no—
180C42×C73—21no—
181C42×C73—21no—
182C42×C73—42no—
183C42×C73#4112yescomplemented
184C42×C73#4112yescomplemented
185C23×C73—21no—
186C23×C73—21no—
187C23×C73—22no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73#12011yescharacteristic
191C23×C73#12011yescharacteristic
192C23×C73C22×D411yescharacteristic
193Q8×C73—22no—
194Q8×C73—22no—
195Q8×C73—82no—
196D4×C73—22no—
197D4×C73—22no—
198D4×C73—44no—
199D4×C73—44no—
200D4×C73—42no—
201D4×C73—42no—
202D4×C73—82no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—22no—
206C2×C4×C73—22no—
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—44no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—82no—
230C2×C4×C73—84no—
231C2×C4×C73#12012yes—
232C2×C4×C73C22×D412yes—
233C2×C4×C73C2×#4111yescharacteristic
234C2×C4×C73C2×#4111yescharacteristic
235C2×C4×C732−1+412yes—
236C8×C73—42no—
237C8×C73—42no—
238C22×C73—21no—
239C22×C73—21no—
240C22×C73—21no—
241C22×C73—21no—
242C22×C73—21no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—42no—
247C22×C73—42no—
248C22×C73—42no—
249C22×C73—42no—
250C22×C73—42no—
251C22×C73C2×#12011yescharacteristic
252C22×C73#52511yescharacteristic
253C22×C73#53611yescharacteristic
254C4×C73—22no—
255C4×C73—42no—
256C4×C73—42no—
257C4×C73—42no—
258C4×C73—42no—
259C4×C73—42no—
260C4×C73—42no—
261C4×C73—42no—
262C4×C73—81no—
263C4×C73—81no—
264C4×C73#54712yes—
265C4×C73#54712yes—
266#24079C7311yesmaximal, characteristic, direct product factor, Sylow
267C2×C73—21no—
268C2×C73—21no—
269C2×C73—41no—
270C2×C73—41no—
271C2×C73—82no—
272C2×C73#240611yescharacteristic
273C2×C73#301911yescharacteristic
274C2×C73#302011yescharacteristic
275#3492C2×C7311yescharacteristic
276#3093C2×C7312yescomplemented
277#2317C2×C7311yescharacteristic, complemented
278#2061C2×C7311yescharacteristic, complemented
279#2060C2×C7311yescharacteristic, complemented
280#2040C2×C7311yescharacteristic, complemented
281#2039C2×C7311yescharacteristic, complemented
282#1897C2×C7312yescomplemented
283#1860C2×C7312yescomplemented
284#1859C2×C7312yescomplemented
285#1821C2×C7311yescharacteristic, complemented
286C73#2407911yescharacteristic, direct product factor, Sylow
287#554—22no—
288#553—22no—
289#552—22no—
290#547—22no—
291#544C22×C7311yescharacteristic
292#539—22no—
293#537C22×C7311yescharacteristic
294#525—22no—
295#525C22×C7312yes—
296#520C22×C7312yes—
297C2×#117C22×C7311yescharacteristic
298C2×#117C22×C7311yescharacteristic
299C22×C4⋊C4C22×C7311yescharacteristic
300#485—22no—
301#485—22no—
302#482—22no—
303#482—22no—
304#428C22×C7312yes—
305#428C22×C7312yes—
306C2×#104C22×C7312yes—
307C2×#104C22×C7312yes—
308#417C22×C7312yes—
309#417C22×C7312yes—
310#407C22×C7312yes—
311#389—22no—
312#385—22no—
313#384C22×C7311yescharacteristic
314#384C22×C7311yescharacteristic
315#382C22×C7311yescharacteristic
316#382C22×C7311yescharacteristic
317#343C22×C7311yescharacteristic
318#343C22×C7311yescharacteristic
319#343C22×C7312yes—
320#339C22×C7312yes—
321#339C22×C7312yes—
322C2×#41—22no—
323C2×#41C23×C7312yes—
324C23×C4D4×C7312yes—
325C23×C4C23×C7311yescharacteristic
326C2×M16C23×C7312yes—
327C2×M16C23×C7312yes—
328C4⋊Q8—22no—
329#126—24no—
330#125—24no—
331#125—22no—
332#123—24no—
333#123—24no—
334#123—22no—
335C22⋊Q8—22no—
336C22⋊Q8—24no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8D4×C7312yes—
340C22⋊Q8D4×C7312yes—
341#121—22no—
342#121—22no—
343#121—22no—
344#121D4×C7312yes—
345#121D4×C7312yes—
346#120—22no—
347C4×Q8—22no—
348C4×D4—24no—
349C4×D4—22no—
350C4×D4—24no—
351C4×D4—22no—
352C4×D4—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117C23×C7312yes—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4D4×C7312yes—
367C2×C4⋊C4C23×C7311yescharacteristic
368C2×C4⋊C4C23×C7311yescharacteristic
369C2×C4⋊C4C23×C7311yescharacteristic
370C2×C4⋊C4C23×C7311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—21no—
374C2×C42C23×C7311yescharacteristic
375C2×C42C23×C7311yescharacteristic
376#107—22no—
377#107—22no—
378#106—22no—
379#106—22no—
380#104—24no—
381#104—24no—
382#103—22no—
383#103—22no—
384#102—22no—
385#102—22no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388#95—22no—
389#95—22no—
390C24C2×D4×C7311yescharacteristic
391#41—22no—
392#41—22no—
393#41—22no—
394#41—22no—
395#41—84no—
396C2×Q8—22no—
397C2×Q8C2×D4×C7312yes—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4C2×D4×C7312yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—82no—
415C22×C4C2×D4×C7311yescharacteristic
416C22×C4C2×D4×C7312yes—
417C22×C4C2×D4×C7312yes—
418C22×C4C2×D4×C7312yes—
419C22×C4C2×D4×C7312yes—
420C22×C4C24×C7311yescharacteristic
421M16—22no—
422M16—22no—
423M16—22no—
424M16—22no—
425C2×C8—22no—
426C2×C8—22no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—82no—
440C4⋊C4—82no—
441C4⋊C4C2×D4×C7312yes—
442C4⋊C4C2×D4×C7312yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—24no—
454C42—22no—
455C42—21no—
456C42—21no—
457C42—42no—
458C42#41×C7312yescomplemented
459C42#41×C7312yescomplemented
460C23—21no—
461C23—21no—
462C23—22no—
463C23—41no—
464C23—41no—
465C23#120×C7311yescharacteristic
466C23#120×C7311yescharacteristic
467C23C22×D4×C7311yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—82no—
471D4—22no—
472D4—22no—
473D4—44no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—82no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—84no—
506C2×C4#120×C7312yes—
507C2×C4C22×D4×C7312yes—
508C2×C4C2×#41×C7311yescharacteristic
509C2×C4C2×#41×C7311yescharacteristic
510C2×C42−1+4×C7312yes—
511C8—42no—
512C8—42no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22C2×#120×C7311yescharacteristic
527C22#525×C7311yescharacteristic
528C22#536×C7311yescharacteristic
529C4—22no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4#547×C7312yes—
540C4#547×C7312yes—
541C2—21no—
542C2—21no—
543C2—41no—
544C2—41no—
545C2—82no—
546C2C73×#240611yescharacteristic
547C2C73×#301911yescharacteristic
548C2C73×#302011yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3093C2semidirect
3. C73×#2317C2semidirect
4. C73×#2061C2semidirect
5. C73×#2060C2semidirect
6. C73×#2040C2semidirect
7. C73×#2039C2semidirect
8. C73×#1897C2semidirect
9. C73×#1860C2semidirect
10. C73×#1859C2semidirect
11. C73×#1821C2semidirect
183. C42×C73#41semidirect
184. C42×C73#41semidirect
266. #24079C73direct (N × H)
276. #3093C2×C73semidirect
277. #2317C2×C73semidirect
278. #2061C2×C73semidirect
279. #2060C2×C73semidirect
280. #2040C2×C73semidirect
281. #2039C2×C73semidirect
282. #1897C2×C73semidirect
283. #1860C2×C73semidirect
284. #1859C2×C73semidirect
285. #1821C2×C73semidirect
286. C73#24079direct (N × H)
458. C42#41×C73semidirect
459. C42#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34922
C73×#30932
C73×#23172
C73×#20612
C73×#20602
C73×#20402
C73×#20392
C73×#18972
C73×#18602
C73×#18592
C73×#18212
#2407973