Finite Group Databasebeta

← #33240787

Subgroups — #33240787

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619513C211yesmaximal, characteristic
2#427×D73C211yesmaximal, characteristic, complemented
3#22612142C211yesmaximal, characteristic, complemented
4#22612141C211yesmaximal, characteristic, complemented
5#22612135C211yesmaximal, characteristic, complemented
6#22612130C211yesmaximal, characteristic, complemented
7#22612125C211yesmaximal, characteristic, complemented
8#22612124C211yesmaximal, characteristic, complemented
9#22612118C211yesmaximal, characteristic, complemented
10#22612113C211yesmaximal, characteristic, complemented
11#22611713C211yesmaximal, characteristic, complemented
12#22611639C211yesmaximal, characteristic, complemented
13#22611636C211yesmaximal, characteristic, complemented
14C2×#17988366C211yesmaximal, characteristic, complemented
15C73×#2158C211yesmaximal, characteristic, complemented
16C2×#14556613C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#17989099—21no—
19#117×D73—21no—
20C22×#11924003C2211yescharacteristic
21#17988829C2211yescharacteristic
22#17988829C2211yescharacteristic
23#17988824C2211yescharacteristic
24#17988824C2211yescharacteristic
25#17988817—21no—
26#17988817—21no—
27#17988625C2211yescharacteristic
28#17988624C2211yescharacteristic
29#17988624C2211yescharacteristic
30#17988623—21no—
31#17988622—21no—
32#107×D73C2211yescharacteristic
33#107×D73C2211yescharacteristic
34#106×D73—21no—
35#17988581—21no—
36#17988414C2211yescharacteristic, complemented
37#17988414C2211yescharacteristic, complemented
38#17988412C2211yescharacteristic, complemented
39#17988412C2211yescharacteristic, complemented
40#17988392C2211yescharacteristic, complemented
41#17988392C2211yescharacteristic, complemented
42#17988390C2211yescharacteristic, complemented
43#17988390C2211yescharacteristic, complemented
44#17988389C2211yescharacteristic, complemented
45#17988389C2211yescharacteristic, complemented
46#17988387C2211yescharacteristic, complemented
47#17988387C2211yescharacteristic, complemented
48#17988366C2211yescharacteristic
49#17988366C2211yescharacteristic
50#17988366C2211yescharacteristic
51#17988366C2211yescharacteristic
52C22×C16×C73C2211yescharacteristic
53#427×C73C2211yescharacteristic
54#427×C73C2211yescharacteristic
55#367×C73C2211yescharacteristic, complemented
56#367×C73C2211yescharacteristic, complemented
57#366×C73C2211yescharacteristic, complemented
58#366×C73C2211yescharacteristic, complemented
59C2×#11924028—21no—
60C22×C4×D73D411yescharacteristic
61#14556613—22no—
62#14556613—22no—
63C2×Dic292C2311yescharacteristic
64C2×#11924017—21no—
65C2×D584C2311yescharacteristic
66C22×#10596831D411yescharacteristic
67C2×C8×D73—22no—
68C2×C8×D73—22no—
69C2×C8×D73D411yescharacteristic
70C2×C8×D73D411yescharacteristic
71C2×C8×D73C2311yescharacteristic
72C2×C8×D73C2311yescharacteristic
73#14556575—41no—
74#14556571—21no—
75#14556571—21no—
76#14556566—21no—
77#14556566—21no—
78#14556561—41no—
79C4×D292—41no—
80C4×D292—41no—
81#14556550—21no—
82#14556549—21no—
83#14556549—21no—
84#14556548—41no—
85#14556547—41no—
86C4⋊C4×D73—21no—
87C4⋊C4×D73—21no—
88C22⋊C4×D73—41no—
89C42×D73—41no—
90C2×#11924003—22no—
91C2×#11924003C2311yescharacteristic
92C2×#11924003C2311yescharacteristic
93#14556525C2311yescharacteristic
94#14556525C2311yescharacteristic
95#14556524—21no—
96#14556524—21no—
97#14556523—21no—
98#14556522—21no—
99#14556522—21no—
100#14556514—21no—
101#14556514—21no—
102#14556511—21no—
103#14556511—21no—
104C22×C8×C73C2311yescharacteristic
105#117×C73—21no—
106#117×C73—21no—
107C2×C16×C73—22no—
108C2×C16×C73C2311yescharacteristic
109C2×C16×C73C2311yescharacteristic
110#107×C73C2311yescharacteristic
111#107×C73C2311yescharacteristic
112#107×C73C2311yescharacteristic
113#107×C73C2311yescharacteristic
114#106×C73—21no—
115#106×C73—21no—
116C23×D73D811yescharacteristic
117#11924028—42no—
118#11924028—42no—
119C2×Dic146—21no—
120C2×D292—21no—
121C2×D292—41no—
122C2×D292—41no—
123C2×C22⋊D73—41no—
124C22×Dic73D811yescharacteristic
125C2×C4×D73—22no—
126C2×C4×D73—22no—
127C2×C4×D73—41no—
128C2×C4×D73—41no—
129C2×C4×D73—41no—
130C2×C4×D73D811yescharacteristic
131C2×C4×D73D811yescharacteristic
132C2×C4×D73C2×D411yescharacteristic
133C2×C4×D73C2×D411yescharacteristic
134Dic292—21no—
135Dic292—21no—
136#11924017—42no—
137D584—21no—
138D584—21no—
139C2×#10596831—22no—
140C2×#10596831C2×D411yescharacteristic
141C2×#10596831C2×D411yescharacteristic
142C8×D73—22no—
143C8×D73—22no—
144C8×D73—21no—
145C8×D73—21no—
146C8×D73—21no—
147C8×D73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—41no—
151C4⋊Dic73—41no—
152#11924007—41no—
153#11924007—41no—
154C22⋊Dic73—41no—
155#11924005—41no—
156#11924005—41no—
157#11924005—41no—
158#11924005—41no—
159#11924005—41no—
160#11924005—41no—
161C4×Dic73—41no—
162C4×Dic73—41no—
163C4×Dic73—41no—
164#11924003—21no—
165#11924003—21no—
166C22×C4×C73C2×D411yescharacteristic
167C2×C8×C73C2×D411yescharacteristic
168C2×C8×C73#4112yes—
169C2×C8×C73#4112yes—
170C2×C8×C73C2411yescharacteristic
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C22⋊C4×C73—41no—
176C22⋊C4×C73—41no—
177C42×C73—41no—
178C42×C73—41no—
179C16×C73—21no—
180C16×C73—21no—
181C23×C73C2×D811yescharacteristic
182C22×D73—22no—
183C22×D73—22no—
184C22×D73—41no—
185C22×D73—41no—
186C22×D73C2×D811yescharacteristic
187C22×D73C2×D811yescharacteristic
188C2×C4×C73—41no—
189C2×C4×C73—41no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73#12312yes—
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73#13712yes—
195C2×C4×C73C22×D411yescharacteristic
196C22⋊D73—82no—
197C2×Dic73—22no—
198C2×Dic73—41no—
199C2×Dic73—41no—
200C2×Dic73—41no—
201C2×Dic73C2×D811yescharacteristic
202C2×Dic73C2×D811yescharacteristic
203D292—41no—
204D292—41no—
205D292—82no—
206D292—82no—
207C4×D73—21no—
208C4×D73—21no—
209C4×D73—21no—
210C4×D73—21no—
211C4×D73—22no—
212C4×D73—22no—
213C4×D73—82no—
214C4×D73—82no—
215C4×D73—82no—
216Dic146—41no—
217Dic146—41no—
218C8×C73#12312yes—
219C8×C73C2×#4111yescharacteristic
220C8×C73C2×#4111yescharacteristic
221#10596831—21no—
222#10596831—21no—
223C22×C73—21no—
224C22×C73—21no—
225C22×C73#48012yes—
226C22×C73C22×D811yescharacteristic
227C2×D73—21no—
228C2×D73—21no—
229C2×D73—21no—
230C2×D73—21no—
231C2×D73—21no—
232C2×D73—44no—
233C2×D73—81no—
234C2×D73—81no—
235C2×D73—81no—
236C2×D73#50812yes—
237C4×C73—81no—
238C4×C73—81no—
239C4×C73—81no—
240C4×C73—81no—
241C4×C73#48012yes—
242C4×C73C2×#12311yescharacteristic
243C4×C73C2×#13711yescharacteristic
244Dic73—21no—
245Dic73—21no—
246Dic73—81no—
247Dic73—81no—
248Dic73—81no—
249#33645—731nomaximal, Sylow
250C2×C73—22no—
251C2×C73C2×#48011yescharacteristic
252C2×C73C2×#50811yescharacteristic
253C2×C73#341411yescharacteristic
254D73—22no—
255D73—41no—
256D73—161no—
257#3050—731no—
258C2×#427—731no—
259#2237—731no—
260#2237—731no—
261#2236—731no—
262#2235—731no—
263#2234—731no—
264#2234—731no—
265#2233—731no—
266#2232—731no—
267#2158—731no—
268#2158D7311yescharacteristic, complemented
269#2138—731no—
270#2138—731no—
271C2×C22⋊C16—731no—
272C73#3364511yescharacteristic, complemented, Sylow
273C2×#135—731no—
274C23×C8—731no—
275#525—1461no—
276C2×#117—1461no—
277C22×C16—731no—
278C22×C16C2×D7311yescharacteristic
279#467—731no—
280#467—731no—
281#466—731no—
282#466—731no—
283#465—1461no—
284#465—1461no—
285#427—731no—
286#427—731no—
287#427—731no—
288#427—1461no—
289#427—1461no—
290#427C2×D7311yescharacteristic
291#427C2×D7311yescharacteristic
292C2×#107—731no—
293C2×#107—731no—
294C2×#106—1461no—
295#416—1461no—
296#367—731no—
297#367—731no—
298#367C2×D7311yescharacteristic, complemented
299#367C2×D7311yescharacteristic, complemented
300#366—731no—
301#366—731no—
302#366C2×D7311yescharacteristic, complemented
303#366C2×D7311yescharacteristic, complemented
304#358—731no—
305#358—731no—
306#358—731no—
307#358—731no—
308#357—731no—
309#357—731no—
310#357—731no—
311#357—731no—
312C22⋊C16—731no—
313C22⋊C16—731no—
314C22⋊C16—731no—
315C22⋊C16—731no—
316C2×#41—1461no—
317C23×C4—731no—
318#135—1462no—
319#135—1462no—
320C2×Q16—731no—
321C2×SD16—1461no—
322C2×D8—731no—
323C22×C8—731no—
324C22×C8—731no—
325C22×C8—731no—
326C22×C8—731no—
327C22×C8—731no—
328C22×C8—1462no—
329C22×C8—1462no—
330C22×C8C22×D7311yescharacteristic
331#123—2921no—
332C22⋊Q8—1461no—
333C22⋊Q8—1461no—
334#121—1461no—
335#121—1461no—
336#120—2921no—
337C4×D4—2921no—
338C4×D4—2921no—
339#117—21no—
340#117—21no—
341#117—2921no—
342#117—2921no—
343#117—1461no—
344#117—1461no—
345#117—1461no—
346C2×C4⋊C4—1461no—
347C2×C4⋊C4—1461no—
348C2×C22⋊C4—2921no—
349C2×C42—2921no—
350C2×C16—22no—
351C2×C16—731no—
352C2×C16—731no—
353C2×C16—1462no—
354C2×C16C22×D7311yescharacteristic
355C2×C16C22×D7311yescharacteristic
356#107—731no—
357#107—731no—
358#107—1461no—
359#107—1461no—
360#107C22×D7311yescharacteristic
361#107C22×D7311yescharacteristic
362#107C22×D7311yescharacteristic
363#107C22×D7311yescharacteristic
364#106—21no—
365#106—21no—
366#106—1461no—
367#106—1461no—
368#106—1461no—
369#103—1461no—
370#103—1461no—
371#102—1461no—
372#102—1461no—
373C24—731no—
374#41—2922no—
375#41—2922no—
376C2×Q8—1461no—
377C2×D4—2921no—
378C2×D4—2921no—
379C2×D4—2921no—
380C2×D4—1461no—
381C22×C4—2921no—
382C22×C4—2921no—
383C22×C4—2921no—
384C22×C4—731no—
385C22×C4—731no—
386C22×C4—731no—
387C22×C4—731no—
388C22×C4—731no—
389C22×C4—1462no—
390C22×C4—1462no—
391C22×C4D4×D7311yescharacteristic
392Q16—1461no—
393Q16—1461no—
394SD16—2922no—
395D8—1461no—
396D8—1461no—
397C2×C8—731no—
398C2×C8—731no—
399C2×C8—1462no—
400C2×C8—1462no—
401C2×C8—1462no—
402C2×C8—1461no—
403C2×C8—1461no—
404C2×C8—1461no—
405C2×C8—1461no—
406C2×C8D4×D7311yescharacteristic
407C2×C8#1192402812yes—
408C2×C8#1192402912yes—
409C2×C8C23×D7311yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—2921no—
415C4⋊C4—2921no—
416C4⋊C4—2921no—
417C4⋊C4—2921no—
418C4⋊C4—1461no—
419C4⋊C4—1461no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—2921no—
423C22⋊C4—2921no—
424C22⋊C4—2921no—
425C22⋊C4—2921no—
426C22⋊C4—2921no—
427C22⋊C4—2921no—
428C22⋊C4—2921no—
429C42—41no—
430C42—41no—
431C42—2921no—
432C42—2921no—
433C42—2921no—
434C16—21no—
435C16—21no—
436C16—1461no—
437C16—1461no—
438C23—2921no—
439C23—2921no—
440C23—731no—
441C23—731no—
442C23—1462no—
443C23—1462no—
444C23D8×D7311yescharacteristic
445Q8—2921no—
446Q8—2921no—
447D4—2921no—
448D4—2921no—
449D4—5842no—
450D4—5842no—
451D4—5842no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—2921no—
457C2×C4—2921no—
458C2×C4—2921no—
459C2×C4—5842no—
460C2×C4—5842no—
461C2×C4—5842no—
462C2×C4—731no—
463C2×C4—731no—
464C2×C4—1462no—
465C2×C4—1461no—
466C2×C4—1461no—
467C2×C4—1462no—
468C2×C4—1462no—
469C2×C4—1461no—
470C2×C4—1461no—
471C2×C4#1455657612yes—
472C2×C4D8×D7311yescharacteristic
473C2×C4#1455662312yes—
474C2×C4C2×D4×D7311yescharacteristic
475C8—1461no—
476C8—1461no—
477C8#1455657612yes—
478C8C2×#1192402811yescharacteristic
479C8C2×#1192402911yescharacteristic
480C22—21no—
481C22—21no—
482C22—2924no—
483C22—5841no—
484C22—5841no—
485C22—5841no—
486C22—732no—
487C22—1461no—
488C22—1461no—
489C22—1461no—
490C22—1461no—
491C22—1461no—
492C22#1798890212yes—
493C22C2×D8×D7311yescharacteristic
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—5841no—
499C4—5841no—
500C4—5841no—
501C4—1461no—
502C4—1461no—
503C4#1798890212yes—
504C4C2×#1455657611yescharacteristic
505C4C2×#1455662311yescharacteristic
506C2—22no—
507C2—2921no—
508C2—11681no—
509C2—1462no—
510C2C2×#1798890211yescharacteristic
511C2#508×D7311yescharacteristic
512C2#2262306411yescharacteristic
subgroupG/H
centerC2×C4D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2158C2
socleC22×C73C22×D8
prime radical#22619513C2
hypercenter#2158D73
hypocenterC73#33645
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
2. #427×D73C2semidirect
3. #22612142C2semidirect
4. #22612141C2semidirect
5. #22612135C2semidirect
6. #22612130C2semidirect
7. #22612125C2semidirect
8. #22612124C2semidirect
9. #22612118C2semidirect
10. #22612113C2semidirect
11. #22611713C2semidirect
12. #22611639C2semidirect
13. #22611636C2semidirect
14. C2×#17988366C2semidirect
15. C73×#2158C2semidirect
36. #17988414C22semidirect
37. #17988414C22semidirect
38. #17988412C22semidirect
39. #17988412C22semidirect
40. #17988392C22semidirect
41. #17988392C22semidirect
42. #17988390C22semidirect
43. #17988390C22semidirect
44. #17988389C22semidirect
45. #17988389C22semidirect
46. #17988387C22semidirect
47. #17988387C22semidirect
55. #367×C73C22semidirect
56. #367×C73C22semidirect
57. #366×C73C22semidirect
58. #366×C73C22semidirect
268. #2158D73semidirect
272. C73#33645semidirect
298. #367C2×D73semidirect
299. #367C2×D73semidirect
302. #366C2×D73semidirect
303. #366C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226195132
#427×D732
#226121422
#226121412
#226121352
#226121302
#226121252
#226121242
#226121182
#226121132
#226117132
#226116392
#226116362
C2×#179883662
C73×#21582
#3364573