Finite Group Databasebeta

← #33950526

Subgroups — #33950526

Order 18688.

1962 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
1#22623226C211yesmaximal, characteristic
2#22618941C218yesmaximal, complemented
3#22618922C218yesmaximal, complemented
4#22618871C211yesmaximal, characteristic, complemented
5#22618868C211yesmaximal, characteristic, complemented
6#22618649C211yesmaximal, characteristic, complemented
7#22618628C212yesmaximal, complemented
8#22618623C212yesmaximal, complemented
9#22618578C212yesmaximal, complemented
10#22618563C211yesmaximal, characteristic, complemented
11#22618357C212yesmaximal, complemented
12C2×#97×D73C211yesmaximal, characteristic, complemented
13C73×#2932C211yesmaximal, characteristic, complemented
14C2×#14556598C2212yes—
15C22×C8×D73C2211yescharacteristic
16C22×C8×D73C2211yescharacteristic
17#17989144C2211yescharacteristic
18#17989142C412yes—
19#17989135C412yes—
20#17989119C2214yes—
21#17989118C414yes—
22#17989116C414yes—
23#17989097C414yes—
24#17989094C2212yes—
25#41×Dic73C2212yes—
26C4×#11924027C2214yes—
27C2×C42×D73C2211yescharacteristic
28#17988716C2218yescomplemented
29#17988715C2218yescomplemented
30#17988661C2218yes—
31#17988659C2218yescomplemented
32#17988656C2218yes—
33C8×C22⋊D73C2218yes—
34#17988650C2218yes—
35#17988645C2218yescomplemented
36#17988643C2214yes—
37#17988641C2218yescomplemented
38#17988639C2214yes—
39#17988615C2212yes—
40#17988613C2212yes—
41#17988611C2211yescharacteristic
42#17988554C2212yes—
43#17988550C2212yes—
44#17988545C2212yes—
45#17988545C2214yescomplemented
46#17988542C2212yes—
47#17988542C2214yescomplemented
48M16×Dic73C2212yes—
49M16×Dic73C2214yescomplemented
50C2×#14556502C2211yescharacteristic
51C2×#14556501C2211yescharacteristic
52C2×#14556501C2211yescharacteristic
53C2×#14556501C2214yescomplemented
54#97×D73C2214yes—
55#97×D73C2214yes—
56C2×#131×C73C2212yes—
57#532×C73C2211yescharacteristic
58#435×C73C2218yescomplemented
59#423×C73C2211yescharacteristic
60#408×C73C2212yes—
61C2×#97×C73C2211yescharacteristic
62C2×#11924027C2×C414yes—
63C22×C4×D73C2×C412yes—
64C22×C4×D73C2311yescharacteristic
65#14556598—28no—
66C2×#11924012C2312yes—
67C2×#11924012C2314yes—
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2314yes—
70C22×#10596831C2311yescharacteristic
71C2×C8×D73—24no—
72C2×C8×D73—24no—
73C2×C8×D73C2314yes—
74C2×C8×D73C2314yes—
75#14556591C2×C412yes—
76#14556584C2×C418yes—
77#14556583C2×C412yes—
78#14556582C2×C414yes—
79#14556578C2×C414yes—
80#14556573C2×C418yes—
81#14556572C2×C414yes—
82#14556571C2×C414yes—
83#14556570C2×C414yes—
84#14556567C2×C414yes—
85#14556562C2×C414yes—
86#14556562C2×C414yes—
87#14556559C2×C414yes—
88Q8×Dic73C2×C414yes—
89C4×Dic146C2314yes—
90#14556556C2×C414yes—
91D4×Dic73C2×C414yes—
92D4×Dic73C2×C414yes—
93D4×Dic73C2×C418yes—
94C4×C22⋊D73C2318yes—
95#14556551C2×C418yes—
96#14556550C2312yes—
97#14556550C2314yes—
98#14556549C2×C414yes—
99#14556547C2×C418yes—
100C2×C4×Dic73C2×C412yes—
101C2×C4×Dic73C2314yes—
102C2×C4×Dic73C2311yescharacteristic
103C42×D73C2×C412yes—
104C42×D73C2×C412yes—
105C42×D73C2312yes—
106C42×D73C2312yes—
107C4⋊#10596831C2314yes—
108#14556520C2318yes—
109#14556520C2318yes—
110C22⋊#10596831C2318yes—
111#14556503C2318yes—
112#14556502C2314yes—
113#14556501C2312yes—
114#14556501C2314yes—
115#14556501C2312yes—
116#14556501C2314yes—
117#14556501C2314yes—
118#14556501C2312yes—
119#14556501C2312yes—
120C8×Dic73C2314yes—
121C8×Dic73C2314yes—
122C8×Dic73C2314yes—
123C2×#41×C73C2312yes—
124#131×C73—28no—
125C2×M16×C73C2312yes—
126C2×M16×C73C2314yes—
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2314yes—
129C22×C8×C73C2311yescharacteristic
130C4⋊Q8×C73C2×C411yescharacteristic
131#127×C73C2×C411yescharacteristic
132#124×C73C2×C412yes—
133#121×C73C2×C414yes—
134C4×D4×C73C2314yes—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73C2314yes—
137C22⋊C8×C73C2318yes—
138#97×C73C2314yes—
139C23×D73C22×C411yescharacteristic
140#11924027—48no—
141C2×Dic146C22×C414yes—
142C2×C22⋊D73C22×C418yes—
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C412yes—
145C22×Dic73C22×C418yes—
146C2×C4×D73—22no—
147C2×C4×D73—22no—
148C2×C4×D73—44no—
149C2×C4×D73C22×C412yes—
150C2×C4×D73C22×C412yes—
151C2×C4×D73C22×C412yes—
152C2×C4×D73C22×C412yes—
153C2×C4×D73C22×C412yes—
154C2×C4×D73C2412yes—
155#11924012—24no—
156#11924012—28no—
157C2×#10596831—22no—
158C2×#10596831—28no—
159C2×#10596831#4114yescomplemented
160C2×#10596831C2414yes—
161C2×#10596831C2412yes—
162C2×#10596831C2412yes—
163C8×D73—28no—
164C8×D73—28no—
165C4⋊Dic73C22×C414yes—
166C4⋊Dic73C22×C414yes—
167C4⋊Dic73C22×C418yes—
168#11924007C22×C418yes—
169#11924007C22×C418yes—
170C22⋊Dic73C22×C418yes—
171C22⋊Dic73C22×C414yes—
172C22⋊Dic73C22×C418yes—
173#11924005C22×C418yes—
174C4×Dic73C22×C412yes—
175C4×Dic73C22×C412yes—
176C4×Dic73C22×C412yes—
177C4×Dic73C22×C412yes—
178C4×Dic73C22×C412yes—
179C4×Dic73C22×C418yes—
180C4×Dic73C2411yescharacteristic
181C4×Dic73C2414yes—
182C4×Dic73C2411yescharacteristic
183#41×C73—24no—
184#41×C73—24no—
185C2×Q8×C73C22×C412yes—
186C2×D4×C73C22×C414yes—
187C2×D4×C73C22×C412yes—
188C2×D4×C73C22×C414yes—
189C22×C4×C73C22×C412yes—
190C22×C4×C73C2414yes—
191C22×C4×C73C2411yescharacteristic
192M16×C73—24no—
193M16×C73—28no—
194C2×C8×C73—22no—
195C2×C8×C73—28no—
196C2×C8×C73#4114yescomplemented
197C2×C8×C73C2412yes—
198C2×C8×C73C2414yes—
199C2×C8×C73C2412yes—
200C4⋊C4×C73C22×C414yes—
201C22⋊C4×C73C22×C418yes—
202C42×C73C22×C411yescharacteristic
203C42×C73C22×C411yescharacteristic
204C42×C73C2412yes—
205C23×C73C23×C414yes—
206C23×C73C23×C411yescharacteristic
207C22×D73—22no—
208C22×D73—24no—
209C22×D73C23×C412yes—
210Q8×C73—24no—
211D4×C73—28no—
212D4×C73—24no—
213D4×C73—44no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—42no—
217C2×C4×C73C23×C412yes—
218C2×C4×C73C23×C412yes—
219C2×C4×C73C23×C414yes—
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C2×#4112yes—
222C2×C4×C73C2×#4112yes—
223C2×C4×C73C2511yescharacteristic
224C22⋊D73—216no—
225C2×Dic73—22no—
226C2×Dic73—42no—
227C2×Dic73—48no—
228C2×Dic73C23×C412yes—
229C2×Dic73C23×C412yes—
230C2×Dic73C23×C412yes—
231C2×Dic73C23×C418yes—
232C4×D73—24no—
233C4×D73—24no—
234C4×D73—24no—
235C4×D73—22no—
236C4×D73—22no—
237C4×D73—42no—
238C4×D73—42no—
239Dic146—44no—
240C8×C73—24no—
241C8×C73—22no—
242C8×C73C2×#4114yes—
243#10596831—22no—
244#10596831—24no—
245#10596831C2×#4114yes—
246C22×C73—22no—
247C22×C73—24no—
248C22×C73—28no—
249C22×C73C4×#4112yes—
250C22×C73C24×C411yescharacteristic
251C2×D73—28no—
252C2×D73—22no—
253C2×D73—22no—
254C2×D73#56814yes—
255C4×C73—24no—
256C4×C73—22no—
257C4×C73—22no—
258C4×C73C4×#4112yes—
259C4×C73C22×#4111yescharacteristic
260C4×C73C22×#4111yescharacteristic
261Dic73—22no—
262Dic73—28no—
263Dic73—22no—
264Dic73—22no—
265#60207—731nomaximal, Sylow
266C2×C73—22no—
267C2×C73—44no—
268C2×C73C2×C4×#4111yescharacteristic
269C2×C73C2×#56812yes—
270D73—24no—
271#3444—731no—
272#2970—738no—
273#2968—738no—
274#2961—731no—
275#2961—731no—
276#2932—731no—
277#2932D7311yescharacteristic, complemented
278#2929—732no—
279#2929—732no—
280#2923—732no—
281#2920—731no—
282#2875—732no—
283C22×#97—731no—
284C73#6020711yescharacteristic, complemented, Sylow
285C2×#131—732no—
286C2×#131C2×D7312yes—
287C23×C8—731no—
288C23×C8—731no—
289#533—732no—
290#533—731no—
291#532—732no—
292#532C2×D7311yescharacteristic
293#529—734no—
294#529—734no—
295#529—734no—
296#525—732no—
297#525—734no—
298C4×#41—732no—
299C4×#41—734no—
300C22×C42—731no—
301#446—738no—
302#446—738no—
303#435—738no—
304#435—738no—
305#435—738no—
306#435C2×D7318yescomplemented
307C8×D4—738no—
308C8×D4—738no—
309#433—738no—
310#432—734no—
311#432—738no—
312#431—734no—
313#424—732no—
314#424—732no—
315#423—731no—
316#423C2×D7311yescharacteristic
317#408—732no—
318#408C2×D7312yes—
319#407—732no—
320#405—732no—
321#405—734no—
322#405—732no—
323#405—734no—
324C4×M16—732no—
325C4×M16—734no—
326C2×#97—731no—
327C2×#97—731no—
328C2×#97—734no—
329C2×#97—731no—
330C2×#97—734no—
331C2×#97—734no—
332C2×#97C2×D7311yescharacteristic
333C2×#41—734no—
334C2×#41C22×D7312yes—
335C23×C4—732no—
336C23×C4—731no—
337#131—28no—
338#131—1468no—
339C2×M16—732no—
340C2×M16—734no—
341C2×M16C22×D7312yes—
342C2×M16C22×D7314yes—
343C22×C8—731no—
344C22×C8—731no—
345C22×C8—734no—
346C22×C8—734no—
347C22×C8—734no—
348C22×C8—1464no—
349C22×C8—1464no—
350C22×C8C22×D7311yescharacteristic
351C22×C8C22×D7314yes—
352C22×C8C22×D7311yescharacteristic
353C4⋊Q8—732no—
354C4⋊Q8C4×D7311yescharacteristic
355#127C4×D7311yescharacteristic
356#126—738no—
357#125—734no—
358#125—732no—
359#124—734no—
360#124C4×D7312yes—
361#123—734no—
362#123—738no—
363C22⋊Q8—734no—
364C22⋊Q8—734no—
365C22⋊Q8—734no—
366#121—734no—
367#121—734no—
368#121C4×D7314yes—
369#120—734no—
370C4×Q8—734no—
371C4×Q8—734no—
372C4×Q8—734no—
373C4×D4—738no—
374C4×D4—734no—
375C4×D4—734no—
376C4×D4—738no—
377C4×D4—738no—
378C4×D4C22×D7314yes—
379#117—732no—
380#117—734no—
381#117—734no—
382#117—738no—
383C2×C42—732no—
384C2×C42—734no—
385C2×C42—731no—
386C2×C42—732no—
387C2×C42—732no—
388C2×C42—732no—
389C2×C42—732no—
390C2×C42C22×D7311yescharacteristic
391C4⋊C8—738no—
392C4⋊C8—738no—
393C4⋊C8—734no—
394C4⋊C8C22×D7314yes—
395C22⋊C8—738no—
396C22⋊C8—738no—
397C22⋊C8C22×D7318yes—
398#97—732no—
399#97—732no—
400#97—732no—
401#97—732no—
402#97—734no—
403#97—734no—
404#97—734no—
405#97—734no—
406#97C22×D7314yes—
407C4×C8—734no—
408C4×C8—734no—
409C4×C8—734no—
410C24—731no—
411#41—24no—
412#41—24no—
413#41—2928no—
414C2×Q8—734no—
415C2×Q8C2×C4×D7312yes—
416C2×D4—738no—
417C2×D4C2×C4×D7314yes—
418C2×D4C2×C4×D7312yes—
419C2×D4C2×C4×D7314yes—
420C22×C4—2924no—
421C22×C4—732no—
422C22×C4—738no—
423C22×C4—732no—
424C22×C4—732no—
425C22×C4—731no—
426C22×C4—732no—
427C22×C4—732no—
428C22×C4—732no—
429C22×C4—732no—
430C22×C4—1462no—
431C22×C4—1462no—
432C22×C4C2×C4×D7312yes—
433C22×C4C23×D7314yes—
434C22×C4C23×D7311yescharacteristic
435M16—24no—
436M16—28no—
437M16—1468no—
438M16—1464no—
439C2×C8—22no—
440C2×C8—28no—
441C2×C8—734no—
442C2×C8—732no—
443C2×C8—734no—
444C2×C8—732no—
445C2×C8—1468no—
446C2×C8—1468no—
447C2×C8—1462no—
448C2×C8—1468no—
449C2×C8#1192402714yescomplemented
450C2×C8C23×D7314yes—
451C2×C8C23×D7312yes—
452C2×C8C23×D7312yes—
453C4⋊C4—738no—
454C4⋊C4—738no—
455C4⋊C4—734no—
456C4⋊C4—734no—
457C4⋊C4—738no—
458C4⋊C4C2×C4×D7314yes—
459C22⋊C4—734no—
460C22⋊C4—738no—
461C22⋊C4—738no—
462C22⋊C4—738no—
463C22⋊C4C2×C4×D7318yes—
464C42—732no—
465C42—732no—
466C42—732no—
467C42—732no—
468C42—732no—
469C42—738no—
470C42—731no—
471C42—734no—
472C42—731no—
473C42C2×C4×D7311yescharacteristic
474C42C2×C4×D7311yescharacteristic
475C42C23×D7312yes—
476C23—732no—
477C23—1464no—
478C23—1462no—
479C23C22×C4×D7314yes—
480C23C22×C4×D7311yescharacteristic
481Q8—24no—
482Q8—2924no—
483D4—28no—
484D4—24no—
485D4—44no—
486D4—14616no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—2922no—
491C2×C4—2922no—
492C2×C4—2922no—
493C2×C4—2928no—
494C2×C4—732no—
495C2×C4—732no—
496C2×C4—732no—
497C2×C4—738no—
498C2×C4—1464no—
499C2×C4—1464no—
500C2×C4—1462no—
501C2×C4—1462no—
502C2×C4—1462no—
503C2×C4—1464no—
504C2×C4C22×C4×D7312yes—
505C2×C4C22×C4×D7312yes—
506C2×C4C22×C4×D7314yes—
507C2×C4C22×C4×D7311yescharacteristic
508C2×C4#41×D7312yes—
509C2×C4C2×#1192402712yes—
510C2×C4C24×D7311yescharacteristic
511C8—22no—
512C8—24no—
513C8—734no—
514C8—1464no—
515C8—1462no—
516C8C2×#1192402714yes—
517C22—22no—
518C22—28no—
519C22—24no—
520C22—734no—
521C22—1468no—
522C22—1462no—
523C22—1462no—
524C22C4×#1192402712yes—
525C22C23×C4×D7311yescharacteristic
526C4—22no—
527C4—22no—
528C4—24no—
529C4—1462no—
530C4—1462no—
531C4—1468no—
532C4—1462no—
533C4C4×#1192402712yes—
534C4C2×#41×D7311yescharacteristic
535C4C22×#1192402711yescharacteristic
536C2—22no—
537C2—44no—
538C2—1464no—
539C2C2×C4×#1192402711yescharacteristic
540C2#568×D7312yes—
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2932C2
prime radical#22623226C2
cosocleC2×C4×C73C25
hypercenter#2932D73
hypocenterC73#60207
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #22618941C2semidirect
3. #22618922C2semidirect
4. #22618871C2semidirect
5. #22618868C2semidirect
6. #22618649C2semidirect
7. #22618628C2semidirect
8. #22618623C2semidirect
9. #22618578C2semidirect
10. #22618563C2semidirect
11. #22618357C2semidirect
12. C2×#97×D73C2semidirect
13. C73×#2932C2semidirect
28. #17988716C22semidirect
29. #17988715C22semidirect
31. #17988659C22semidirect
35. #17988645C22semidirect
37. #17988641C22semidirect
45. #17988545C22semidirect
47. #17988542C22semidirect
49. M16×Dic73C22semidirect
53. C2×#14556501C22semidirect
58. #435×C73C22semidirect
159. C2×#10596831#41semidirect
196. C2×C8×C73#41semidirect
277. #2932D73semidirect
284. C73#60207semidirect
306. #435C2×D73semidirect
449. C2×C8#11924027semidirect

Maximal subgroups

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

subgroupindex
#226232262
#226189412
#226189222
#226188712
#226188682
#226186492
#226186282
#226186232
#226185782
#226185632
#226183572
C2×#97×D732
C73×#29322
#6020773