Finite Group Databasebeta

← #33950528

Subgroups — #33950528

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#22623228C211yesmaximal, characteristic
2#22618944C218yesmaximal, complemented
3#22618924C218yesmaximal, complemented
4#22618872C211yesmaximal, characteristic, complemented
5#22618650C211yesmaximal, characteristic, complemented
6#22618648C211yesmaximal, characteristic, complemented
7#22618627C212yesmaximal, complemented
8#22618624C212yesmaximal, complemented
9#22618581C212yesmaximal, complemented
10#22618563C211yesmaximal, characteristic, complemented
11#22618358C212yesmaximal, complemented
12C2×#97×D73C211yesmaximal, characteristic, complemented
13C73×#2961C211yesmaximal, characteristic, complemented
14C2×#14556599C2212yes—
15C2×#14556597C2212yes—
16C22×C8×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#17989142C412yes—
19#17989138C412yes—
20#17989137C2211yescharacteristic
21#17989124C2214yes—
22#17989123C414yes—
23#17989122C414yes—
24#17989100C414yes—
25#17989099C2212yes—
26C4×#11924029C2214yes—
27#17989055C2212yes—
28C2×C42×D73C2211yescharacteristic
29#17988718C2218yescomplemented
30#17988660C2218yes—
31#17988660C2218yescomplemented
32#17988657C2218yes—
33#17988657C2218yescomplemented
34C8×D292C2218yes—
35#17988652C2218yes—
36#17988647C2218yescomplemented
37#17988643C2214yes—
38#17988643C2218yescomplemented
39#17988639C2214yes—
40#17988614C2212yes—
41#17988611C2211yescharacteristic
42#17988555C2212yes—
43#17988553C2212yes—
44#17988550C2212yes—
45#17988544C2214yescomplemented
46#17988543C2212yes—
47#17988541C2214yescomplemented
48M16×Dic73C2212yes—
49C4×#11924011C2214yescomplemented
50C2×#14556502C2211yescharacteristic
51C2×#14556501C2211yescharacteristic
52C2×#14556501C2211yescharacteristic
53#97×D73C2214yes—
54#97×D73C2214yes—
55#97×D73C2214yescomplemented
56#533×C73C2211yescharacteristic
57#446×C73C2218yescomplemented
58#424×C73C2212yes—
59#423×C73C2211yescharacteristic
60#405×C73C2212yes—
61C2×#97×C73C2211yescharacteristic
62C2×#11924029C2×C414yes—
63C2×#11924028C2312yes—
64C22×C4×D73C2×C412yes—
65C22×C4×D73C2311yescharacteristic
66#14556599—28no—
67#14556597—28no—
68C2×#11924012C2312yes—
69C2×#11924011C2314yes—
70C2×#11924011C2314yes—
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C2×C8×D73—24no—
74C2×C8×D73—24no—
75C2×C8×D73C2314yes—
76C2×C8×D73C2314yes—
77C2×C8×D73C2314yes—
78C2×C8×D73C2314yes—
79#14556591C2×C411yescharacteristic
80#14556588C2×C411yescharacteristic
81#14556586C2×C418yes—
82#14556582C2×C414yes—
83#14556580C2×C414yes—
84#14556579C2×C412yes—
85#14556576C2×C418yes—
86#14556575C2×C414yes—
87#14556571C2×C414yes—
88#14556567C2×C414yes—
89#14556566C2×C414yes—
90#14556566C2×C414yes—
91#14556565C2×C414yes—
92#14556561C2×C414yes—
93Q8×Dic73C2×C414yes—
94#14556556C2×C414yes—
95C4×D292C2314yes—
96C4×D292C2318yes—
97#14556553C2×C414yes—
98#14556553C2×C418yes—
99#14556553C2×C414yes—
100#14556551C2×C418yes—
101#14556549C2×C418yes—
102#14556549C2×C414yes—
103#14556548C2314yes—
104C2×C4×Dic73C2×C412yes—
105C2×C4×Dic73C2311yescharacteristic
106C42×D73C2×C412yes—
107C42×D73C2×C412yes—
108C42×D73C2312yes—
109C42×D73C2312yes—
110C42×D73C2314yes—
111C4⋊#10596831C2314yes—
112C4⋊#10596831C2318yes—
113#14556503C2318yes—
114#14556503C2318yes—
115#14556503C2318yes—
116#14556502C2314yes—
117#14556502C2314yes—
118#14556501C2314yes—
119#14556501C2312yes—
120#14556501C2312yes—
121#14556501C2312yes—
122#14556501C2312yes—
123C4×#10596831C2314yes—
124C8×Dic73C2314yes—
125C2×M16×C73C2312yes—
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C4⋊Q8×C73C2×C412yes—
129#125×C73C2×C412yes—
130C22⋊Q8×C73C2×C414yes—
131C4×Q8×C73C2314yes—
132#117×C73C2312yes—
133C2×C42×C73C2311yescharacteristic
134C4⋊C8×C73C2314yes—
135C4⋊C8×C73C2318yes—
136#97×C73C2314yes—
137#97×C73C2314yes—
138C4×C8×C73C2314yes—
139C23×D73C22×C411yescharacteristic
140#11924029—48no—
141#11924028—24no—
142#11924028—24no—
143C2×Dic146C22×C412yes—
144C2×D292C22×C412yes—
145C2×D292C22×C418yes—
146C2×D292C22×C414yes—
147C2×C22⋊D73C22×C414yes—
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C412yes—
150C2×C4×D73—22no—
151C2×C4×D73—22no—
152C2×C4×D73—44no—
153C2×C4×D73C22×C412yes—
154C2×C4×D73C22×C412yes—
155C2×C4×D73C22×C412yes—
156C2×C4×D73C22×C412yes—
157C2×C4×D73C22×C412yes—
158C2×C4×D73C22×C418yes—
159C2×C4×D73C2412yes—
160C2×C4×D73C2414yes—
161#11924012—24no—
162#11924011—28no—
163#11924011—28no—
164C2×#10596831—22no—
165C2×#10596831#4114yescomplemented
166C2×#10596831C2414yes—
167C2×#10596831C2412yes—
168C2×#10596831C2412yes—
169C8×D73—28no—
170C8×D73—28no—
171C8×D73—28no—
172C8×D73—28no—
173C4⋊Dic73C22×C414yes—
174C4⋊Dic73C22×C418yes—
175#11924007C22×C418yes—
176#11924005C22×C418yes—
177#11924005C22×C418yes—
178#11924005C22×C418yes—
179#11924005C22×C418yes—
180C4×Dic73C22×C412yes—
181C4×Dic73C22×C412yes—
182C4×Dic73C22×C412yes—
183C4×Dic73C22×C412yes—
184C4×Dic73C22×C412yes—
185C4×Dic73C22×C418yes—
186C4×Dic73C2411yescharacteristic
187C4×Dic73C2411yescharacteristic
188C2×Q8×C73C22×C414yes—
189C22×C4×C73C22×C412yes—
190C22×C4×C73C2411yescharacteristic
191M16×C73—24no—
192C2×C8×C73—22no—
193C2×C8×C73#4114yescomplemented
194C2×C8×C73C2414yes—
195C2×C8×C73C2412yes—
196C2×C8×C73C2412yes—
197C4⋊C4×C73C22×C414yes—
198C4⋊C4×C73C22×C418yes—
199C4⋊C4×C73C22×C414yes—
200C22⋊C4×C73C22×C414yes—
201C42×C73C22×C411yescharacteristic
202C42×C73C22×C411yescharacteristic
203C42×C73C2414yes—
204C42×C73C2412yes—
205C23×C73C23×C411yescharacteristic
206C22×D73—22no—
207C22×D73—24no—
208C22×D73C23×C414yes—
209C22×D73C23×C412yes—
210Q8×C73—44no—
211C2×C4×C73—42no—
212C2×C4×C73C23×C412yes—
213C2×C4×C73C23×C412yes—
214C2×C4×C73C23×C418yes—
215C2×C4×C73C23×C411yescharacteristic
216C2×C4×C73C2×#4112yes—
217C2×C4×C73C2×#4112yes—
218C2×C4×C73C2511yescharacteristic
219C22⋊D73—28no—
220C2×Dic73—22no—
221C2×Dic73—42no—
222C2×Dic73C23×C412yes—
223C2×Dic73C23×C412yes—
224C2×Dic73C23×C412yes—
225C2×Dic73C23×C414yes—
226D292—216no—
227D292—24no—
228D292—44no—
229C4×D73—24no—
230C4×D73—24no—
231C4×D73—24no—
232C4×D73—22no—
233C4×D73—22no—
234C4×D73—24no—
235C4×D73—24no—
236C4×D73—42no—
237C4×D73—42no—
238C4×D73—48no—
239Dic146—24no—
240C8×C73—22no—
241C8×C73—24no—
242C8×C73C2×#4114yes—
243#10596831—22no—
244#10596831—24no—
245#10596831C2×#4114yes—
246C22×C73—22no—
247C22×C73C4×#4112yes—
248C22×C73C24×C411yescharacteristic
249C2×D73—28no—
250C2×D73—22no—
251C2×D73—22no—
252C2×D73—24no—
253C2×D73—28no—
254C2×D73#56814yes—
255C4×C73—22no—
256C4×C73—22no—
257C4×C73—28no—
258C4×C73C4×#4112yes—
259C4×C73C22×#4111yescharacteristic
260C4×C73C22×#4111yescharacteristic
261Dic73—24no—
262Dic73—22no—
263Dic73—22no—
264Dic73—22no—
265#60207—731nomaximal, Sylow
266C2×C73—22no—
267C2×C73C2×C4×#4111yescharacteristic
268C2×C73C2×#56812yes—
269D73—24no—
270D73—44no—
271#3444—731no—
272#2970—738no—
273#2968—738no—
274#2961—731no—
275#2961D7311yescharacteristic, complemented
276#2932—731no—
277#2932—731no—
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×#131—732no—
287C23×C8—731no—
288C23×C8—731no—
289#533—732no—
290#533C2×D7311yescharacteristic
291#532—732no—
292#532—731no—
293#529—734no—
294#529—734no—
295#529—734no—
296#525—734no—
297#525—732no—
298C4×#41—734no—
299C4×#41—732no—
300C22×C42—731no—
301#446—738no—
302#446C2×D7318yescomplemented
303#435—738no—
304#435—738no—
305#435—738no—
306#435—738no—
307C8×D4—738no—
308C8×D4—738no—
309#433—738no—
310#432—734no—
311#432—738no—
312#431—734no—
313#424—732no—
314#424C2×D7312yes—
315#423—731no—
316#423C2×D7311yescharacteristic
317#408—732no—
318#408—732no—
319#407—732no—
320#405—732no—
321#405—734no—
322#405—734no—
323#405C2×D7312yes—
324C4×M16—732no—
325C4×M16—734no—
326C2×#97—731no—
327C2×#97—731no—
328C2×#97—731no—
329C2×#97—734no—
330C2×#97—734no—
331C2×#97—734no—
332C2×#97C2×D7311yescharacteristic
333C2×#41—734no—
334C2×#41—732no—
335C23×C4—732no—
336C23×C4—731no—
337#131—1468no—
338#131—1468no—
339C2×M16—732no—
340C2×M16—734no—
341C2×M16—734no—
342C2×M16C22×D7312yes—
343C22×C8—731no—
344C22×C8—731no—
345C22×C8—734no—
346C22×C8—734no—
347C22×C8—734no—
348C22×C8—734no—
349C22×C8—1464no—
350C22×C8—1464no—
351C22×C8C22×D7311yescharacteristic
352C22×C8C22×D7311yescharacteristic
353C4⋊Q8—731no—
354C4⋊Q8C4×D7312yes—
355#127—731no—
356#126—738no—
357#125—734no—
358#125C4×D7312yes—
359#124—734no—
360#124—732no—
361#123—738no—
362#123—734no—
363C22⋊Q8—734no—
364C22⋊Q8—734no—
365C22⋊Q8C4×D7314yes—
366#121—734no—
367#121—734no—
368#121—734no—
369#120—734no—
370C4×Q8—734no—
371C4×Q8—734no—
372C4×Q8C22×D7314yes—
373C4×D4—738no—
374C4×D4—734no—
375C4×D4—734no—
376C4×D4—738no—
377C4×D4—738no—
378C4×D4—734no—
379#117—734no—
380#117—738no—
381#117—734no—
382#117C22×D7312yes—
383C2×C42—732no—
384C2×C42—731no—
385C2×C42—732no—
386C2×C42—732no—
387C2×C42—734no—
388C2×C42—732no—
389C2×C42—732no—
390C2×C42C22×D7311yescharacteristic
391C4⋊C8—734no—
392C4⋊C8—738no—
393C4⋊C8C22×D7314yes—
394C4⋊C8C22×D7318yes—
395C22⋊C8—738no—
396C22⋊C8—738no—
397C22⋊C8—738no—
398#97—732no—
399#97—732no—
400#97—732no—
401#97—732no—
402#97—734no—
403#97—734no—
404#97—734no—
405#97C22×D7314yes—
406#97C22×D7314yes—
407C4×C8—734no—
408C4×C8—734no—
409C4×C8C22×D7314yes—
410C24—731no—
411#41—2928no—
412#41—1464no—
413#41—1464no—
414C2×Q8—732no—
415C2×Q8C2×C4×D7314yes—
416C2×D4—734no—
417C2×D4—734no—
418C2×D4—738no—
419C2×D4—732no—
420C22×C4—2924no—
421C22×C4—732no—
422C22×C4—732no—
423C22×C4—732no—
424C22×C4—738no—
425C22×C4—731no—
426C22×C4—732no—
427C22×C4—732no—
428C22×C4—732no—
429C22×C4—732no—
430C22×C4—734no—
431C22×C4—1462no—
432C22×C4—1462no—
433C22×C4C2×C4×D7312yes—
434C22×C4C23×D7311yescharacteristic
435M16—24no—
436M16—1468no—
437M16—1464no—
438M16—1468no—
439C2×C8—22no—
440C2×C8—734no—
441C2×C8—732no—
442C2×C8—734no—
443C2×C8—732no—
444C2×C8—1468no—
445C2×C8—1468no—
446C2×C8—1462no—
447C2×C8—1468no—
448C2×C8—1468no—
449C2×C8#1192402914yescomplemented
450C2×C8C23×D7314yes—
451C2×C8C23×D7312yes—
452C2×C8C23×D7312yes—
453C4⋊C4—738no—
454C4⋊C4—734no—
455C4⋊C4—738no—
456C4⋊C4C2×C4×D7314yes—
457C4⋊C4C2×C4×D7318yes—
458C4⋊C4C2×C4×D7314yes—
459C22⋊C4—738no—
460C22⋊C4—738no—
461C22⋊C4—738no—
462C22⋊C4—738no—
463C22⋊C4C2×C4×D7314yes—
464C42—732no—
465C42—732no—
466C42—732no—
467C42—732no—
468C42—732no—
469C42—738no—
470C42—731no—
471C42—731no—
472C42C2×C4×D7311yescharacteristic
473C42C2×C4×D7311yescharacteristic
474C42C23×D7314yes—
475C42C23×D7312yes—
476C23—732no—
477C23—734no—
478C23—1464no—
479C23—1462no—
480C23C22×C4×D7311yescharacteristic
481Q8—44no—
482Q8—1464no—
483D4—2924no—
484D4—14616no—
485D4—1468no—
486D4—1464no—
487C2×C4—42no—
488C2×C4—2922no—
489C2×C4—2922no—
490C2×C4—2928no—
491C2×C4—2922no—
492C2×C4—732no—
493C2×C4—732no—
494C2×C4—732no—
495C2×C4—734no—
496C2×C4—1464no—
497C2×C4—1464no—
498C2×C4—1462no—
499C2×C4—1462no—
500C2×C4—1464no—
501C2×C4—1462no—
502C2×C4—1464no—
503C2×C4—1464no—
504C2×C4C22×C4×D7312yes—
505C2×C4C22×C4×D7312yes—
506C2×C4C22×C4×D7318yes—
507C2×C4C22×C4×D7311yescharacteristic
508C2×C4#41×D7312yes—
509C2×C4C2×#1192402912yes—
510C2×C4C24×D7311yescharacteristic
511C8—22no—
512C8—24no—
513C8—734no—
514C8—1462no—
515C8—1464no—
516C8C2×#1192402914yes—
517C22—22no—
518C22—734no—
519C22—1468no—
520C22—1468no—
521C22—1464no—
522C22—1462no—
523C22—1462no—
524C22C4×#1192402912yes—
525C22C23×C4×D7311yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—1462no—
530C4—1462no—
531C4—1462no—
532C4—1464no—
533C4C4×#1192402912yes—
534C4C2×#41×D7311yescharacteristic
535C4C22×#1192402911yescharacteristic
536C2—22no—
537C2—2924no—
538C2—1464no—
539C2C2×C4×#1192402911yescharacteristic
540C2#568×D7312yes—
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2961C2
prime radical#22623228C2
cosocleC2×C4×C73C25
hypercenter#2961D73
hypocenterC73#60207
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #22618944C2semidirect
3. #22618924C2semidirect
4. #22618872C2semidirect
5. #22618650C2semidirect
6. #22618648C2semidirect
7. #22618627C2semidirect
8. #22618624C2semidirect
9. #22618581C2semidirect
10. #22618563C2semidirect
11. #22618358C2semidirect
12. C2×#97×D73C2semidirect
13. C73×#2961C2semidirect
29. #17988718C22semidirect
31. #17988660C22semidirect
33. #17988657C22semidirect
36. #17988647C22semidirect
38. #17988643C22semidirect
45. #17988544C22semidirect
47. #17988541C22semidirect
49. C4×#11924011C22semidirect
55. #97×D73C22semidirect
57. #446×C73C22semidirect
165. C2×#10596831#41semidirect
193. C2×C8×C73#41semidirect
275. #2961D73semidirect
284. C73#60207semidirect
302. #446C2×D73semidirect
449. C2×C8#11924029semidirect

Maximal subgroups

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

subgroupindex
#226232282
#226189442
#226189242
#226188722
#226186502
#226186482
#226186272
#226186242
#226185812
#226185632
#226183582
C2×#97×D732
C73×#29612
#6020773