Finite Group Databasebeta

← #2647×D73 #33253087

Subgroups — #2647×D73 #33253087

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615911C211yesmaximal, characteristic, complemented
2#22615910C211yesmaximal, characteristic, complemented
3#22615909C214yesmaximal, complemented
4#22615908C212yesmaximal, complemented
5#22615907C212yesmaximal, complemented
6#22615906C211yesmaximal, characteristic, complemented
7#22615905C214yesmaximal, complemented
8#400×D73C214yesmaximal
9#398×D73C214yesmaximal
10#389×D73C212yesmaximal
11#389×D73C212yesmaximal
12#384×D73C211yesmaximal, characteristic
13#382×D73C211yesmaximal, characteristic
14#376×D73C211yesmaximal, characteristic
15C73×#2647C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D73C2212yes—
17C2×C4⋊C4×D73C2212yes—
18C2×C4⋊C4×D73C2214yes—
19C2×C4⋊C4×D73C2214yes—
20C2×C4⋊C4×D73C2214yes—
21C2×C42×D73C2211yescharacteristic
22C2×C42×D73C2211yescharacteristic
23C2×C42×D73C2211yescharacteristic
24#17988529C2214yes—
25#17988529C2214yes—
26#17988528C2214yes—
27#17988528C2214yes—
28#17988527C2214yes—
29#17988526C2214yes—
30#17988525C2214yes—
31#17988521C2214yes—
32#17988521C2214yes—
33#17988520C2214yes—
34#17988520C2214yes—
35#17988519C2214yes—
36#17988518C2214yes—
37#17988517C2214yes—
38#17988486C2212yes—
39#17988486C2212yes—
40#17988485C2212yes—
41#17988485C2212yes—
42#17988484C2214yes—
43#17988484C2214yes—
44#17988483C2212yes—
45#17988483C2212yes—
46#17988482C2214yes—
47#17988482C2214yes—
48#17988457C2211yescharacteristic
49#17988456C2214yes—
50#17988456C2212yes—
51#17988453C2211yescharacteristic
52#17988452C2212yes—
53#17988451C2214yes—
54#17988433C2211yescharacteristic
55#17988433C2211yescharacteristic
56#17988433C2211yescharacteristic
57#17988432C2212yes—
58#17988432C2212yes—
59#95×D73C2212yes—
60#95×D73C2212yes—
61#95×D73C2214yes—
62#95×D73C2214yes—
63#95×D73C2214yes—
64#400×C73C2214yes—
65#398×C73C2214yes—
66#389×C73C2212yes—
67#389×C73C2212yes—
68#384×C73C2211yescharacteristic
69#382×C73C2211yescharacteristic
70#376×C73C2211yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2312yes—
73C22×C4×D73C2314yes—
74C22×C4×D73C2311yescharacteristic
75C22×C4×D73C2314yes—
76C22×C4×D73C2312yes—
77C22×C4×D73C2311yescharacteristic
78C2×C4⋊Dic73C2312yes—
79C2×C4⋊Dic73C2312yes—
80C2×C4⋊Dic73C2314yes—
81C2×C4⋊Dic73C2314yes—
82C2×C4⋊Dic73C2314yes—
83C2×#11924007C2314yes—
84C2×#11924007C2314yes—
85C2×#11924007C2314yes—
86C2×#11924007C2314yes—
87C2×#11924007C2314yes—
88C2×#11924007C2314yes—
89C2×#11924007C2314yes—
90C2×#11924007C2314yes—
91C4⋊C4×D73—28no—
92C4⋊C4×D73—28no—
93C4⋊C4×D73—48no—
94C4⋊C4×D73—48no—
95C4⋊C4×D73—48no—
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2312yes—
98C2×C4×Dic73C2311yescharacteristic
99C2×C4×Dic73C2311yescharacteristic
100C2×C4×Dic73C2311yescharacteristic
101C2×C4×Dic73C2312yes—
102C2×C4×Dic73C2311yescharacteristic
103C42×D73—24no—
104C42×D73—24no—
105C42×D73Q818yes—
106#14556498C2312yes—
107#14556498C2312yes—
108#14556498C2312yes—
109#14556498C2312yes—
110#14556498C2312yes—
111#14556498C2312yes—
112#14556498C2314yes—
113#14556498C2314yes—
114#14556498C2314yes—
115#14556498C2314yes—
116#14556498C2314yes—
117#14556498C2314yes—
118#14556498C2314yes—
119#14556498C2314yes—
120#14556498C2314yes—
121C2×C4⋊C4×C73C2312yes—
122C2×C4⋊C4×C73C2312yes—
123C2×C4⋊C4×C73C2314yes—
124C2×C4⋊C4×C73C2314yes—
125C2×C4⋊C4×C73C2314yes—
126C2×C42×C73C2311yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129#95×C73C2314yes—
130#95×C73C2314yes—
131#95×C73C2314yes—
132#95×C73C2312yes—
133#95×C73C2312yes—
134C23×D73C2411yescharacteristic
135C22×Dic73C2411yescharacteristic
136C22×Dic73C2412yes—
137C22×Dic73C2414yes—
138C22×Dic73C2411yescharacteristic
139C22×Dic73C2414yes—
140C22×Dic73C2412yes—
141C22×Dic73C2411yescharacteristic
142C2×C4×D73—24no—
143C2×C4×D73—24no—
144C2×C4×D73—22no—
145C2×C4×D73—22no—
146C2×C4×D73—24no—
147C2×C4×D73—28no—
148C2×C4×D73—28no—
149C2×C4×D73—28no—
150C2×C4×D73—24no—
151C2×C4×D73—28no—
152C2×C4×D73—28no—
153C2×C4×D73—24no—
154C2×C4×D73—24no—
155C2×C4×D73—24no—
156C2×C4×D73—28no—
157C2×C4×D73C2×Q818yes—
158C2×C4×D73C2×Q814yes—
159C2×C4×D73#4114yes—
160C2×C4×D73#4114yes—
161C4⋊Dic73—24no—
162C4⋊Dic73—24no—
163C4⋊Dic73—44no—
164C4⋊Dic73—44no—
165C4⋊Dic73—44no—
166#11924007—28no—
167#11924007—28no—
168#11924007—44no—
169#11924007—44no—
170#11924007—44no—
171#11924007—44no—
172#11924007—44no—
173#11924007—44no—
174C4×Dic73—22no—
175C4×Dic73—22no—
176C4×Dic73—22no—
177C4×Dic73—24no—
178C4×Dic73—22no—
179C4×Dic73C2×Q814yes—
180C4×Dic73C2×Q818yes—
181C22×C4×C73C2411yescharacteristic
182C22×C4×C73C2412yes—
183C22×C4×C73C2414yes—
184C22×C4×C73C2411yescharacteristic
185C22×C4×C73C2414yes—
186C22×C4×C73C2412yes—
187C22×C4×C73C2411yescharacteristic
188C4⋊C4×C73—24no—
189C4⋊C4×C73—24no—
190C4⋊C4×C73—44no—
191C4⋊C4×C73—44no—
192C4⋊C4×C73—44no—
193C42×C73—22no—
194C42×C73—22no—
195C42×C73C2×Q814yes—
196C23×C73C2511yescharacteristic
197C22×D73C22×Q812yes—
198C22×D73C2×#4112yes—
199C22×D73C2×#4112yes—
200C22×D73H(5,𝔽2)14yes—
201C22×D732−1+414yes—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—22no—
207C2×C4×C73—24no—
208C2×C4×C73—24no—
209C2×C4×C73—22no—
210C2×C4×C73—24no—
211C2×C4×C73—22no—
212C2×C4×C73—24no—
213C2×C4×C73—24no—
214C2×C4×C73—22no—
215C2×C4×C73—22no—
216C2×C4×C73—24no—
217C2×C4×C73C22×Q814yes—
218C2×C4×C73C22×Q812yes—
219C2×C4×C73C2×#4112yes—
220C2×C4×C73C2×#4112yes—
221C2×Dic73—22no—
222C2×Dic73—22no—
223C2×Dic73—21no—
224C2×Dic73—21no—
225C2×Dic73—22no—
226C2×Dic73—24no—
227C2×Dic73—24no—
228C2×Dic73—24no—
229C2×Dic73—24no—
230C2×Dic73—22no—
231C2×Dic73—24no—
232C2×Dic73—22no—
233C2×Dic73—22no—
234C2×Dic73—22no—
235C2×Dic73—24no—
236C2×Dic73C22×Q814yes—
237C2×Dic73C22×Q812yes—
238C2×Dic73C2×#4112yes—
239C2×Dic73C2×#4112yes—
240C4×D73—216no—
241C4×D73—44no—
242C4×D73—416no—
243C4×D73—44no—
244C4×D73—48no—
245C4×D73—416no—
246C4×D73#125116yes—
247C22×C73C23×Q811yescharacteristic
248C22×C73C22×#4111yescharacteristic
249C22×C73C22×#4111yescharacteristic
250C22×C73C2×H(5,𝔽2)12yes—
251C22×C73C2×2−1+412yes—
252C2×D73C2×#12514yes—
253C2×D73#54014yes—
254C2×D73#54114yes—
255C2×D73#54218yes—
256C2×D73#54418yes—
257C4×C73—24no—
258C4×C73—41no—
259C4×C73—44no—
260C4×C73—41no—
261C4×C73—42no—
262C4×C73—44no—
263C4×C73C2×#12514yes—
264Dic73—24no—
265Dic73—41no—
266Dic73—44no—
267Dic73—41no—
268Dic73—42no—
269Dic73—44no—
270Dic73C2×#12514yes—
271C2×#2647—731nomaximal, Sylow
272C2×C73C22×#12511yescharacteristic
273C2×C73C2×#54011yescharacteristic
274C2×C73C2×#54111yescharacteristic
275C2×C73C2×#54212yes—
276C2×C73C2×#54412yes—
277D73#264718yesdirect product factor
278#2647—734no—
279#2647—734no—
280#2647—732no—
281#2647—732no—
282#2647—731no—
283#2647—731no—
284#2647—731no—
285#2647D7311yescharacteristic, direct product factor
286C2×#400—734no—
287C2×#398—734no—
288C2×#389—732no—
289C2×#389—732no—
290C2×#384—731no—
291C2×#382—731no—
292C2×#376—731no—
293C73C2×#264711yescharacteristic, complemented, Sylow
294C22×C4⋊C4—734no—
295C22×C4⋊C4—734no—
296C22×C4⋊C4—734no—
297C22×C4⋊C4—732no—
298C22×C4⋊C4—732no—
299C22×C42—731no—
300C22×C42—731no—
301C22×C42—731no—
302#400—734no—
303#400—734no—
304#400—734no—
305#400—734no—
306#400—734no—
307#400—734no—
308#400—734no—
309#400C2×D7314yes—
310#398—734no—
311#398—734no—
312#398—734no—
313#398—734no—
314#398—734no—
315#398—734no—
316#398—734no—
317#398C2×D7314yes—
318#389—734no—
319#389—734no—
320#389—732no—
321#389—732no—
322#389—732no—
323#389—732no—
324#389—732no—
325#389—732no—
326#389—734no—
327#389—734no—
328#389C2×D7312yes—
329#389C2×D7312yes—
330#384—732no—
331#384—734no—
332#384—731no—
333#384C2×D7311yescharacteristic
334#382—732no—
335#382—731no—
336#382—734no—
337#382C2×D7311yescharacteristic
338#376—731no—
339#376—731no—
340#376—731no—
341#376—732no—
342#376—732no—
343#376C2×D7311yescharacteristic
344C2×#95—732no—
345C2×#95—734no—
346C2×#95—734no—
347C2×#95—732no—
348C2×#95—734no—
349C23×C4—731no—
350C23×C4—732no—
351C23×C4—734no—
352C23×C4—731no—
353C23×C4—734no—
354C23×C4—732no—
355C23×C4—731no—
356C2×C4⋊C4—2928no—
357C2×C4⋊C4—2928no—
358C2×C4⋊C4—2928no—
359C2×C4⋊C4—734no—
360C2×C4⋊C4—734no—
361C2×C4⋊C4—734no—
362C2×C4⋊C4—734no—
363C2×C4⋊C4—734no—
364C2×C4⋊C4—734no—
365C2×C4⋊C4—734no—
366C2×C4⋊C4—734no—
367C2×C4⋊C4—734no—
368C2×C4⋊C4—734no—
369C2×C4⋊C4—732no—
370C2×C4⋊C4—734no—
371C2×C4⋊C4—732no—
372C2×C4⋊C4—1468no—
373C2×C4⋊C4—1468no—
374C2×C4⋊C4C22×D7312yes—
375C2×C4⋊C4C22×D7312yes—
376C2×C4⋊C4C22×D7314yes—
377C2×C4⋊C4C22×D7314yes—
378C2×C4⋊C4C22×D7314yes—
379C2×C42—732no—
380C2×C42—731no—
381C2×C42—738no—
382C2×C42—731no—
383C2×C42—732no—
384C2×C42—731no—
385C2×C42—731no—
386C2×C42—731no—
387C2×C42—1464no—
388C2×C42—1464no—
389C2×C42C22×D7311yescharacteristic
390C2×C42C22×D7311yescharacteristic
391C2×C42C22×D7311yescharacteristic
392#95—732no—
393#95—732no—
394#95—732no—
395#95—732no—
396#95—732no—
397#95—732no—
398#95—734no—
399#95—734no—
400#95—734no—
401#95—734no—
402#95—734no—
403#95—734no—
404#95—734no—
405#95—734no—
406#95—734no—
407#95C22×D7312yes—
408#95C22×D7312yes—
409#95C22×D7314yes—
410#95C22×D7314yes—
411#95C22×D7314yes—
412C24—731no—
413C22×C4—731no—
414C22×C4—734no—
415C22×C4—734no—
416C22×C4—734no—
417C22×C4—732no—
418C22×C4—738no—
419C22×C4—731no—
420C22×C4—732no—
421C22×C4—734no—
422C22×C4—731no—
423C22×C4—734no—
424C22×C4—1462no—
425C22×C4—1464no—
426C22×C4—1462no—
427C22×C4—1468no—
428C22×C4—1468no—
429C22×C4—1464no—
430C22×C4—1468no—
431C22×C4—1464no—
432C22×C4—1468no—
433C22×C4—1468no—
434C22×C4—1468no—
435C22×C4—1464no—
436C22×C4—1464no—
437C22×C4—1464no—
438C22×C4—1464no—
439C22×C4C23×D7311yescharacteristic
440C22×C4C23×D7312yes—
441C22×C4C23×D7314yes—
442C22×C4C23×D7311yescharacteristic
443C22×C4C23×D7314yes—
444C22×C4C23×D7312yes—
445C22×C4C23×D7311yescharacteristic
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—2924no—
452C4⋊C4—2924no—
453C4⋊C4—2924no—
454C4⋊C4—2924no—
455C4⋊C4—2924no—
456C4⋊C4—2924no—
457C4⋊C4—2924no—
458C4⋊C4—2924no—
459C4⋊C4—2924no—
460C4⋊C4—1468no—
461C4⋊C4—1468no—
462C4⋊C4—1464no—
463C4⋊C4—1464no—
464C42—22no—
465C42—22no—
466C42—738no—
467C42—734no—
468C42—1462no—
469C42—1462no—
470C42—1464no—
471C42—1462no—
472C42—1462no—
473C42Q8×D7314yes—
474C23—732no—
475C23—732no—
476C23—732no—
477C23—734no—
478C23—734no—
479C23C24×D7311yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—2924no—
496C2×C4—29216no—
497C2×C4—2924no—
498C2×C4—2928no—
499C2×C4—29216no—
500C2×C4—732no—
501C2×C4—732no—
502C2×C4—732no—
503C2×C4—7316no—
504C2×C4—734no—
505C2×C4—14616no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1462no—
509C2×C4—1464no—
510C2×C4—1464no—
511C2×C4—1464no—
512C2×C4—1462no—
513C2×C4—1464no—
514C2×C4—1464no—
515C2×C4—1462no—
516C2×C4—1462no—
517C2×C4—1462no—
518C2×C4—1464no—
519C2×C4—1462no—
520C2×C4—1462no—
521C2×C4C2×Q8×D7314yes—
522C2×C4C2×Q8×D7312yes—
523C2×C4#41×D7312yes—
524C2×C4#41×D7312yes—
525C22—734no—
526C22—734no—
527C22—738no—
528C22—738no—
529C22—734no—
530C22C22×Q8×D7311yescharacteristic
531C22C2×#41×D7311yescharacteristic
532C22C2×#41×D7311yescharacteristic
533C22H(5,𝔽2)×D7312yes—
534C222−1+4×D7312yes—
535C4—24no—
536C4—41no—
537C4—44no—
538C4—41no—
539C4—42no—
540C4—44no—
541C4—2921no—
542C4—2924no—
543C4—2921no—
544C4—2922no—
545C4—2924no—
546C4—734no—
547C4—1464no—
548C4#125×D7314yes—
549C2—738no—
550C2C2×#125×D7311yescharacteristic
551C2#540×D7311yescharacteristic
552C2#541×D7311yescharacteristic
553C2#542×D7312yes—
554C2#544×D7312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2647C2
prime radicalC23×D73C24
hypercenter#2647D73
hypocenterC73C2×#2647
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2647

Complements

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

NH ≅ G/Ntype
1. #22615911C2semidirect
2. #22615910C2semidirect
3. #22615909C2semidirect
4. #22615908C2semidirect
5. #22615907C2semidirect
6. #22615906C2semidirect
7. #22615905C2semidirect
15. C73×#2647C2semidirect
277. D73#2647direct (N × H)
285. #2647D73direct (N × H)
293. C73C2×#2647semidirect

Maximal subgroups

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

subgroupindex
#226159112
#226159102
#226159092
#226159082
#226159072
#226159062
#226159052
#400×D732
#398×D732
#389×D732
#384×D732
#382×D732
#376×D732
C73×#26472
C2×#264773