Finite Group Databasebeta

← #33240628

Subgroups — #33240628

Order 18688.

546 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620443C211yesmaximal, characteristic, complemented
2#22618702C211yesmaximal, characteristic
3#22612098C211yesmaximal, characteristic, complemented
4#22612094C211yesmaximal, characteristic, complemented
5#22612091C211yesmaximal, characteristic, complemented
6#22612087C211yesmaximal, characteristic, complemented
7#22612082C211yesmaximal, characteristic, complemented
8#22612077C211yesmaximal, characteristic, complemented
9#22612072C211yesmaximal, characteristic, complemented
10#22612067C211yesmaximal, characteristic, complemented
11#22611713C211yesmaximal, characteristic, complemented
12C2×#17988405C211yesmaximal, characteristic, complemented
13#22611639C211yesmaximal, characteristic
14#22611636C211yesmaximal, characteristic
15C73×#2158C211yesmaximal, characteristic, complemented
16C2×#14556613C2211yescharacteristic
17#17989140—21no—
18#17989055—21no—
19C22×#11924003C2211yescharacteristic
20#17988991C2211yescharacteristic
21#17988991C2211yescharacteristic
22#17988988C2211yescharacteristic
23#17988988C2211yescharacteristic
24#17988987—21no—
25#17988984—21no—
26#17988681C2211yescharacteristic
27#17988681C2211yescharacteristic
28#17988674—21no—
29#17988674—21no—
30#17988669C2211yescharacteristic
31#17988669C2211yescharacteristic
32#17988625C2211yescharacteristic
33#17988623—21no—
34#17988581—21no—
35C2×C8×Dic73C2211yescharacteristic
36#17988414C2211yescharacteristic
37#17988414C2211yescharacteristic
38#17988412C2211yescharacteristic
39#17988412C2211yescharacteristic
40#17988405C2211yescharacteristic
41#17988405C2211yescharacteristic
42#17988405C2211yescharacteristic
43#17988405C2211yescharacteristic
44#17988392C2211yescharacteristic
45#17988392C2211yescharacteristic
46#17988390C2211yescharacteristic
47#17988390C2211yescharacteristic
48#17988389C2211yescharacteristic
49#17988389C2211yescharacteristic
50#17988387C2211yescharacteristic
51#17988387C2211yescharacteristic
52C22×C16×C73C2211yescharacteristic
53#427×C73C2211yescharacteristic
54#427×C73C2211yescharacteristic
55#367×C73C2211yescharacteristic
56#367×C73C2211yescharacteristic
57#366×C73C2211yescharacteristic
58#366×C73C2211yescharacteristic
59C2×#11924028—21no—
60#14556613—22no—
61#14556613Q814yescomplemented
62C2×Dic292C2311yescharacteristic
63C2×#11924017—21no—
64C2×D584C2311yescharacteristic
65C22×#10596831D411yescharacteristic
66#14556590—21no—
67#14556590—21no—
68#14556582—21no—
69#14556582—21no—
70#14556568—41no—
71#14556568—41no—
72C4×Dic146—41no—
73C4×Dic146—41no—
74#14556556—21no—
75#14556556—21no—
76#14556553—21no—
77#14556553—21no—
78#14556551—41no—
79#14556551—41no—
80#14556550—21no—
81#14556548—41no—
82C2×C4×Dic73D411yescharacteristic
83C42×D73—41no—
84C2×#11924003—22no—
85C2×#11924003C2311yescharacteristic
86C2×#11924003C2311yescharacteristic
87#14556525C2311yescharacteristic
88#14556525C2311yescharacteristic
89#14556524—21no—
90#14556524—21no—
91#14556523—21no—
92#14556522—21no—
93#14556522—21no—
94#14556514—21no—
95#14556514—21no—
96#14556511—21no—
97#14556511—21no—
98C8×Dic73D411yescharacteristic
99C8×Dic73D411yescharacteristic
100C8×Dic73C2311yescharacteristic
101C8×Dic73C2311yescharacteristic
102C22×C8×C73C2311yescharacteristic
103#117×C73—21no—
104#117×C73—21no—
105C2×C16×C73—22no—
106C2×C16×C73C2311yescharacteristic
107C2×C16×C73C2311yescharacteristic
108#107×C73C2311yescharacteristic
109#107×C73C2311yescharacteristic
110#107×C73C2311yescharacteristic
111#107×C73C2311yescharacteristic
112#106×C73—21no—
113#106×C73—21no—
114#11924028—24no—
115#11924028—42no—
116C2×Dic146—21no—
117C2×Dic146—41no—
118C2×Dic146—41no—
119C2×D292—21no—
120C2×C22⋊D73—41no—
121C22×Dic73D811yescharacteristic
122C22×Dic73D811yescharacteristic
123C2×C4×D73—41no—
124C2×C4×D73—41no—
125C2×C4×D73—41no—
126Dic292—21no—
127Dic292C2×Q812yes—
128#11924017—24no—
129D584—21no—
130D584C2×Q812yes—
131C2×#10596831—22no—
132C2×#10596831C2×D411yescharacteristic
133C2×#10596831C2×D411yescharacteristic
134C4⋊Dic73—21no—
135C4⋊Dic73—21no—
136C4⋊Dic73—41no—
137C4⋊Dic73—41no—
138#11924007—41no—
139#11924007—41no—
140#11924007—41no—
141#11924007—41no—
142#11924007—41no—
143#11924007—41no—
144C22⋊Dic73—41no—
145#11924005—41no—
146#11924005—41no—
147C4×Dic73—41no—
148C4×Dic73—41no—
149C4×Dic73—41no—
150C4×Dic73D811yescharacteristic
151C4×Dic73D811yescharacteristic
152C4×Dic73C2×D411yescharacteristic
153C4×Dic73C2×D411yescharacteristic
154#11924003—21no—
155#11924003—21no—
156C22×C4×C73C2×D411yescharacteristic
157C2×C8×C73C2×D411yescharacteristic
158C2×C8×C73C2×Q812yes—
159C2×C8×C73#4112yes—
160C2×C8×C73C2411yescharacteristic
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C22⋊C4×C73—41no—
166C22⋊C4×C73—41no—
167C42×C73—41no—
168C42×C73—41no—
169C16×C73—21no—
170C16×C73—21no—
171C23×C73C2×D811yescharacteristic
172C22×D73—41no—
173C2×C4×C73—41no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—41no—
177C2×C4×C73C22⋊Q812yes—
178C2×C4×C73C2×D811yescharacteristic
179C2×C4×C73#13712yes—
180C2×C4×C73C22×D411yescharacteristic
181C22⋊D73—44no—
182C2×Dic73—22no—
183C2×Dic73—41no—
184C2×Dic73—41no—
185C2×Dic73—41no—
186C2×Dic73—41no—
187C2×Dic73C2×D811yescharacteristic
188C2×Dic73C2×D811yescharacteristic
189C2×Dic73C2×D811yescharacteristic
190C2×Dic73C2×D811yescharacteristic
191D292—22no—
192D292—41no—
193C4×D73—44no—
194C4×D73—82no—
195C4×D73—82no—
196Dic146—22no—
197Dic146—41no—
198Dic146—82no—
199Dic146—82no—
200C8×C73C22⋊Q812yes—
201C8×C73C22×Q811yescharacteristic
202C8×C73C2×#4111yescharacteristic
203#10596831—21no—
204#10596831—21no—
205C22×C73—21no—
206C22×C73—21no—
207C22×C73#47412yes—
208C22×C73C22×D811yescharacteristic
209C2×D73—42no—
210C2×D73—81no—
211C2×D73—81no—
212C4×C73—81no—
213C4×C73—81no—
214C4×C73—81no—
215C4×C73—81no—
216C4×C73#47412yes—
217C4×C73C2×C22⋊Q811yescharacteristic
218C4×C73C2×#13711yescharacteristic
219Dic73—21no—
220Dic73—21no—
221Dic73—21no—
222Dic73—42no—
223Dic73—81no—
224Dic73—81no—
225Dic73#50812yes—
226#33626—731nomaximal, Sylow
227C2×C73—22no—
228C2×C73C2×#47411yescharacteristic
229C2×C73C2×#50811yescharacteristic
230C2×C73#341411yescharacteristic
231D73—82no—
232#3160—731no—
233C4×#135—731no—
234#2229—731no—
235#2229—731no—
236#2228—731no—
237#2228—731no—
238#2227—731no—
239#2226—731no—
240#2225—731no—
241#2224—731no—
242#2158—731no—
243#2158D7311yescharacteristic, complemented
244C2×C4⋊C16—731no—
245#2138—731no—
246#2138—731no—
247C73#3362611yescharacteristic, complemented, Sylow
248C2×#135—731no—
249#533—1461no—
250C4×#41—1461no—
251C22×C16—731no—
252C22×C16C2×D7311yescharacteristic
253#500—731no—
254#500—731no—
255#499—731no—
256#499—731no—
257#499—1461no—
258#498—1461no—
259C4×Q16—731no—
260C4×Q16—731no—
261C4×SD16—1461no—
262C4×SD16—1461no—
263C4×D8—731no—
264C4×D8—731no—
265#427—731no—
266#427—1461no—
267#427C2×D7311yescharacteristic
268#427C2×D7311yescharacteristic
269#416—1461no—
270C2×C4×C8—731no—
271#367—731no—
272#367—731no—
273#367C2×D7311yescharacteristic
274#367C2×D7311yescharacteristic
275#366—731no—
276#366—731no—
277#366C2×D7311yescharacteristic
278#366C2×D7311yescharacteristic
279C4⋊C16—731no—
280C4⋊C16—731no—
281C4⋊C16—731no—
282C4⋊C16—731no—
283#358—731no—
284#358—731no—
285#358—731no—
286#358—731no—
287#357—731no—
288#357—731no—
289#357—731no—
290#357—731no—
291C2×#41—1461no—
292#135—734no—
293#135—1462no—
294C2×Q16—731no—
295C2×SD16—1461no—
296C2×D8—731no—
297C22×C8—731no—
298C22×C8C22×D7311yescharacteristic
299C4⋊Q8—1461no—
300C4⋊Q8—1461no—
301#125—1461no—
302#125—1461no—
303C22⋊Q8—2921no—
304C22⋊Q8—2921no—
305C4×Q8—2921no—
306C4×Q8—2921no—
307C4×Q8—1461no—
308C4×Q8—1461no—
309C4×D4—2921no—
310C4×D4—2921no—
311C4×D4—1461no—
312C4×D4—1461no—
313#117—21no—
314#117—21no—
315#117—2921no—
316#117—1461no—
317C2×C42—2921no—
318C2×C42—731no—
319C2×C16—22no—
320C2×C16—731no—
321C2×C16—731no—
322C2×C16—1462no—
323C2×C16C22×D7311yescharacteristic
324C2×C16C22×D7311yescharacteristic
325#107—731no—
326#107—731no—
327#107—1461no—
328#107—1461no—
329#107C22×D7311yescharacteristic
330#107C22×D7311yescharacteristic
331#107C22×D7311yescharacteristic
332#107C22×D7311yescharacteristic
333#106—21no—
334#106—21no—
335#106—1461no—
336#106—1461no—
337#106—1461no—
338#103—1461no—
339#103—1461no—
340#102—1461no—
341#102—1461no—
342C4×C8—731no—
343C4×C8—731no—
344C4×C8—731no—
345C4×C8—731no—
346#41—2922no—
347#41—1464no—
348C2×Q8—2921no—
349C2×Q8—2921no—
350C2×Q8—1461no—
351C2×D4—2921no—
352C2×D4—1461no—
353C22×C4—2921no—
354C22×C4—2921no—
355C22×C4—2921no—
356C22×C4—731no—
357C22×C4—731no—
358C22×C4D4×D7311yescharacteristic
359Q16—732no—
360Q16—1461no—
361SD16—1464no—
362D8—732no—
363D8—1461no—
364C2×C8—731no—
365C2×C8—731no—
366C2×C8—1462no—
367C2×C8D4×D7311yescharacteristic
368C2×C8Q8×D7312yes—
369C2×C8#1192402812yes—
370C2×C8C23×D7311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—2921no—
376C4⋊C4—2921no—
377C4⋊C4—2921no—
378C4⋊C4—2921no—
379C4⋊C4—2921no—
380C4⋊C4—2921no—
381C4⋊C4—2921no—
382C4⋊C4—2921no—
383C4⋊C4—1461no—
384C4⋊C4—1461no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—2921no—
388C22⋊C4—2921no—
389C22⋊C4—2921no—
390C42—41no—
391C42—41no—
392C42—2921no—
393C42—2921no—
394C42—2921no—
395C42—731no—
396C42—731no—
397C42—731no—
398C42—731no—
399C16—21no—
400C16—21no—
401C16—1461no—
402C16—1461no—
403C23—2921no—
404C23D8×D7311yescharacteristic
405Q8—2921no—
406Q8—5842no—
407Q8—5842no—
408Q8—1462no—
409D4—2924no—
410D4—2921no—
411D4—1462no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—2921no—
417C2×C4—2924no—
418C2×C4—2921no—
419C2×C4—2921no—
420C2×C4—2921no—
421C2×C4—5842no—
422C2×C4—5842no—
423C2×C4—731no—
424C2×C4—731no—
425C2×C4—731no—
426C2×C4—731no—
427C2×C4—1462no—
428C2×C4#1455656912yes—
429C2×C4D8×D7311yescharacteristic
430C2×C4#1455662312yes—
431C2×C4C2×D4×D7311yescharacteristic
432C8—1461no—
433C8—1461no—
434C8#1455656912yes—
435C8C2×Q8×D7311yescharacteristic
436C8C2×#1192402811yescharacteristic
437C22—21no—
438C22—21no—
439C22—2922no—
440C22—5841no—
441C22—5841no—
442C22#1798886612yes—
443C22C2×D8×D7311yescharacteristic
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—2922no—
449C4—5841no—
450C4—5841no—
451C4—732no—
452C4—1461no—
453C4—1461no—
454C4—1461no—
455C4#1798886612yes—
456C4C2×#1455656911yescharacteristic
457C4C2×#1455662311yescharacteristic
458C2—22no—
459C2—5842no—
460C2C2×#1798886611yescharacteristic
461C2#508×D7311yescharacteristic
462C2#2262306411yescharacteristic
subgroupG/H
centerC2×C4D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2158C2
socleC22×C73C22×D8
prime radicalC2×#14556613C22
hypercenter#2158D73
hypocenterC73#33626
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

Complements

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

NH ≅ G/Ntype
1. #22620443C2semidirect
3. #22612098C2semidirect
4. #22612094C2semidirect
5. #22612091C2semidirect
6. #22612087C2semidirect
7. #22612082C2semidirect
8. #22612077C2semidirect
9. #22612072C2semidirect
10. #22612067C2semidirect
11. #22611713C2semidirect
12. C2×#17988405C2semidirect
15. C73×#2158C2semidirect
61. #14556613Q8semidirect
243. #2158D73semidirect
247. C73#33626semidirect

Maximal subgroups

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

subgroupindex
#226204432
#226187022
#226120982
#226120942
#226120912
#226120872
#226120822
#226120772
#226120722
#226120672
#226117132
C2×#179884052
#226116392
#226116362
C73×#21582
#3362673