Finite Group Databasebeta

← #33950553

Subgroups — #33950553

Order 18688.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623323C211yesmaximal, characteristic
2#22618937C218yesmaximal, complemented
3#22618924C218yesmaximal, complemented
4#22618866C211yesmaximal, characteristic, complemented
5#22618650C211yesmaximal, characteristic, complemented
6#22618642C211yesmaximal, characteristic, complemented
7#22618633C212yesmaximal, complemented
8#22618627C212yesmaximal, complemented
9#22618574C212yesmaximal, complemented
10#22618568C211yesmaximal, characteristic, complemented
11#22618358C212yesmaximal, complemented
12C2×#17988544C211yesmaximal, characteristic, complemented
13C73×#2961C211yesmaximal, characteristic, complemented
14C2×#14556599C2212yes—
15C2×#14556597C2212yes—
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#17989211C414yes—
19#17989200C412yes—
20#17989193C412yes—
21#17989186C414yes—
22#17989177C414yes—
23#17989137C2211yescharacteristic
24#17989124C2218yes—
25#17989099C2212yes—
26#17989055C2212yes—
27C2×#14556548C2211yescharacteristic
28#17988718C2214yescomplemented
29Q8×#10596831C2214yescomplemented
30#17988664C2218yes—
31#17988664C2214yescomplemented
32#17988660C2218yes—
33#17988660C2218yescomplemented
34#17988657C2218yes—
35C8×D292C2218yes—
36#17988652C2214yescomplemented
37#17988647C2218yes—
38#17988647C2218yescomplemented
39#17988639C2218yescomplemented
40#17988614C2212yes—
41#17988611C2211yescharacteristic
42#17988555C2212yes—
43#17988553C2212yes—
44#17988550C2212yes—
45#17988544C2214yes—
46#17988544C2214yes—
47#17988544C2214yescomplemented
48#17988543C2212yes—
49#17988541C2214yescomplemented
50M16×Dic73C2212yes—
51C4×#11924011C2214yescomplemented
52C2×#14556501C2211yescharacteristic
53#97×D73C2214yescomplemented
54C2×C4×#10596831C2211yescharacteristic
55C2×C8×Dic73C2211yescharacteristic
56#533×C73C2211yescharacteristic
57#446×C73C2218yescomplemented
58#424×C73C2212yes—
59#423×C73C2211yescharacteristic
60#405×C73C2212yes—
61C2×#97×C73C2211yescharacteristic
62C2×#11924028C2312yes—
63C22×C4×D73C2311yescharacteristic
64#14556599—28no—
65#14556597—28no—
66C2×#11924012C2312yes—
67C2×#11924011—24no—
68C2×#11924011C2312yes—
69C2×#11924011C2314yes—
70C2×#11924011C2312yes—
71C2×#11924011C2314yes—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C2×C8×D73—24no—
75C2×C8×D73C2314yes—
76C2×C8×D73C2314yes—
77C2×C8×D73C2314yes—
78#14556591C2×C411yescharacteristic
79#14556588C2×C411yescharacteristic
80#14556586C2×C418yes—
81#14556586C2×C418yes—
82#14556582C2×C418yes—
83#14556580C2×C418yes—
84#14556579C2×C412yes—
85#14556576C2×C418yes—
86#14556576C2×C418yes—
87#14556575C2×C414yes—
88#14556571C2×C414yes—
89#14556567C2×C418yes—
90#14556566C2×C418yes—
91#14556566C2×C414yes—
92#14556565C2×C414yes—
93#14556561C2×C414yes—
94#14556556C2×C414yes—
95C4×D292C2314yes—
96C4×D292C2318yes—
97#14556553C2×C414yes—
98#14556551C2×C418yes—
99#14556548C2×C412yes—
100#14556548C2×C412yes—
101#14556548C2314yes—
102#14556548C2314yes—
103C2×#11924007C2×C412yes—
104C2×#11924005C2×C412yes—
105C2×C4×Dic73C2311yescharacteristic
106C42×D73C2314yes—
107C4⋊#10596831C2314yes—
108C4⋊#10596831C2318yes—
109#14556503C2318yes—
110#14556503C2318yes—
111#14556503C2318yes—
112#14556502C2314yes—
113#14556501C2314yes—
114#14556501C2312yes—
115#14556501C2312yes—
116C4×#10596831C2312yes—
117C4×#10596831C2314yes—
118C4×#10596831C2312yes—
119C8×Dic73C2314yes—
120C8×Dic73C2314yes—
121C2×M16×C73C2312yes—
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C4⋊Q8×C73C2×C412yes—
125#125×C73C2×C412yes—
126C22⋊Q8×C73C2×C414yes—
127C4×Q8×C73C2314yes—
128#117×C73C2312yes—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73C2318yes—
131C4⋊C8×C73C2314yes—
132#97×C73C2314yes—
133#97×C73C2314yes—
134C4×C8×C73C2314yes—
135C23×D73C22×C411yescharacteristic
136#11924028—24no—
137#11924028—24no—
138C2×Dic146C22×C412yes—
139C2×D292C22×C412yes—
140C2×D292C22×C418yes—
141C2×D292C22×C414yes—
142C2×C22⋊D73C22×C414yes—
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C412yes—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73C22×C412yes—
148C2×C4×D73C22×C418yes—
149C2×C4×D73C2414yes—
150C2×C4×D73C2412yes—
151#11924012—24no—
152#11924011—28no—
153#11924011—24no—
154#11924011—24no—
155#11924011—28no—
156C2×#10596831—22no—
157C2×#10596831#4114yes—
158C2×#10596831C2412yes—
159C2×#10596831C2414yes—
160C2×#10596831C2411yescharacteristic
161C2×#10596831C2411yescharacteristic
162C8×D73—28no—
163C8×D73—28no—
164C8×D73—28no—
165C4⋊Dic73C22×C414yes—
166C4⋊Dic73C22×C418yes—
167#11924007C22×C414yes—
168#11924007C22×C414yes—
169#11924007C22×C418yes—
170#11924005C22×C414yes—
171#11924005C22×C414yes—
172#11924005C22×C418yes—
173#11924005C22×C418yes—
174#11924005C22×C418yes—
175#11924005C22×C418yes—
176C4×Dic73C22×C418yes—
177C4×Dic73C22×C412yes—
178C4×Dic73C2412yes—
179C2×Q8×C73C22×C414yes—
180C22×C4×C73C22×C412yes—
181C22×C4×C73C2411yescharacteristic
182M16×C73—24no—
183C2×C8×C73—22no—
184C2×C8×C73#4114yes—
185C2×C8×C73C2414yes—
186C2×C8×C73C2412yes—
187C2×C8×C73C2412yes—
188C4⋊C4×C73C22×C414yes—
189C4⋊C4×C73C22×C418yes—
190C4⋊C4×C73C22×C414yes—
191C22⋊C4×C73C22×C414yes—
192C42×C73C22×C411yescharacteristic
193C42×C73C22×C411yescharacteristic
194C42×C73C2414yes—
195C42×C73C2412yes—
196C23×C73C23×C411yescharacteristic
197C22×D73—22no—
198C22×D73—42no—
199C22×D73C23×C412yes—
200C22×D73C23×C414yes—
201Q8×C73—44no—
202C2×C4×C73—42no—
203C2×C4×C73C23×C412yes—
204C2×C4×C73C23×C412yes—
205C2×C4×C73C23×C418yes—
206C2×C4×C73C23×C411yescharacteristic
207C2×C4×C73C2×#4112yes—
208C2×C4×C73C2×#4112yes—
209C2×C4×C73C2511yescharacteristic
210C22⋊D73—28no—
211C2×Dic73—22no—
212C2×Dic73—42no—
213C2×Dic73C23×C414yes—
214C2×Dic73C23×C414yes—
215C2×Dic73C23×C412yes—
216D292—24no—
217D292—48no—
218D292—44no—
219C4×D73—24no—
220C4×D73—22no—
221C4×D73—24no—
222C4×D73—24no—
223C4×D73—22no—
224C4×D73—48no—
225Dic146—24no—
226C8×C73—22no—
227C8×C73—24no—
228C8×C73C2×#4114yes—
229#10596831—22no—
230#10596831—24no—
231#10596831C2×#4112yes—
232#10596831C2×#4112yes—
233C22×C73—22no—
234C22×C73C4×#4112yes—
235C22×C73C24×C411yescharacteristic
236C2×D73—22no—
237C2×D73—24no—
238C2×D73—28no—
239C2×D73—24no—
240C2×D73—44no—
241C4×C73—28no—
242C4×C73—22no—
243C4×C73—22no—
244C4×C73C4×#4112yes—
245C4×C73C22×#4111yescharacteristic
246C4×C73C22×#4111yescharacteristic
247Dic73—24no—
248Dic73—22no—
249Dic73—24no—
250#60209—731nomaximal, Sylow
251C2×C73—22no—
252C2×C73C2×C4×#4111yescharacteristic
253C2×C73#357312yes—
254D73—44no—
255D73—42no—
256#3455—731no—
257#2969—738no—
258#2968—738no—
259#2961D7311yescharacteristic, complemented
260#2960—731no—
261#2932—731no—
262#2931—731no—
263#2930—732no—
264#2929—732no—
265#2922—732no—
266#2921—731no—
267#2875—732no—
268C2×#405—731no—
269C73#6020911yescharacteristic, complemented, Sylow
270C2×#131—732no—
271C2×#131—732no—
272C22×M16—731no—
273C23×C8—731no—
274#542—734no—
275#541—732no—
276#540—732no—
277#539—734no—
278#538—734no—
279#533C2×D7311yescharacteristic
280#532—731no—
281#529—738no—
282#525—732no—
283C4×#41—732no—
284C2×#117—731no—
285#446—734no—
286#446C2×D7318yescomplemented
287C8×Q8—734no—
288#436—738no—
289#436—734no—
290#435—738no—
291#435—738no—
292#435—738no—
293C8×D4—734no—
294C8×D4—738no—
295#433—738no—
296#433—738no—
297#431—738no—
298#424—732no—
299#424C2×D7312yes—
300#423—731no—
301#423C2×D7311yescharacteristic
302#408—732no—
303#408—732no—
304#407—732no—
305#405—732no—
306#405—734no—
307#405—734no—
308#405—734no—
309#405—734no—
310#405C2×D7312yes—
311C4×M16—732no—
312C4×M16—734no—
313C2×#97—731no—
314C2×#97—734no—
315C2×#97C2×D7311yescharacteristic
316C2×C4×C8—731no—
317C2×C4×C8—731no—
318C2×#41—732no—
319C23×C4—731no—
320#131—1468no—
321#131—1468no—
322C2×M16—732no—
323C2×M16—732no—
324C2×M16—732no—
325C2×M16—734no—
326C2×M16—734no—
327C2×M16—1464no—
328C2×M16C22×D7312yes—
329C22×C8—731no—
330C22×C8—731no—
331C22×C8—734no—
332C22×C8—734no—
333C22×C8—734no—
334C22×C8—1464no—
335C22×C8C22×D7311yescharacteristic
336C22×C8C22×D7311yescharacteristic
337C4⋊Q8—731no—
338C4⋊Q8C4×D7312yes—
339#127—731no—
340#126—738no—
341#126—738no—
342#125—738no—
343#125C4×D7312yes—
344#124—738no—
345#124—732no—
346#123—738no—
347#123—738no—
348#123—734no—
349C22⋊Q8—738no—
350C22⋊Q8—734no—
351C22⋊Q8C4×D7314yes—
352#121—734no—
353#121—734no—
354#121—738no—
355#120—734no—
356C4×Q8—734no—
357C4×Q8C22×D7314yes—
358C4×D4—734no—
359C4×D4—738no—
360C4×D4—738no—
361C4×D4—734no—
362#117—732no—
363#117—732no—
364#117—734no—
365#117—734no—
366#117C22×D7312yes—
367C2×C4⋊C4—732no—
368C2×C22⋊C4—732no—
369C2×C42—731no—
370C2×C42—734no—
371C2×C42C22×D7311yescharacteristic
372C4⋊C8—734no—
373C4⋊C8—738no—
374C4⋊C8C22×D7314yes—
375C4⋊C8C22×D7318yes—
376C22⋊C8—738no—
377C22⋊C8—738no—
378C22⋊C8—738no—
379#97—732no—
380#97—732no—
381#97—734no—
382#97—734no—
383#97C22×D7314yes—
384#97C22×D7314yes—
385C4×C8—734no—
386C4×C8—734no—
387C4×C8—732no—
388C4×C8—732no—
389C4×C8—734no—
390C4×C8C22×D7314yes—
391C24—731no—
392#41—1464no—
393#41—1464no—
394C2×Q8—732no—
395C2×Q8C2×C4×D7314yes—
396C2×D4—734no—
397C2×D4—738no—
398C2×D4—734no—
399C2×D4—732no—
400C22×C4—732no—
401C22×C4—738no—
402C22×C4—731no—
403C22×C4—732no—
404C22×C4—734no—
405C22×C4—732no—
406C22×C4—1462no—
407C22×C4—1462no—
408C22×C4C2×C4×D7312yes—
409C22×C4C23×D7311yescharacteristic
410M16—24no—
411M16—1464no—
412M16—1464no—
413M16—1468no—
414M16—1464no—
415M16—1468no—
416C2×C8—22no—
417C2×C8—734no—
418C2×C8—731no—
419C2×C8—731no—
420C2×C8—732no—
421C2×C8—734no—
422C2×C8—1468no—
423C2×C8—1462no—
424C2×C8—1468no—
425C2×C8—1468no—
426C2×C8#1192402914yes—
427C2×C8C23×D7312yes—
428C2×C8C23×D7314yes—
429C2×C8C23×D7312yes—
430C4⋊C4—734no—
431C4⋊C4—734no—
432C4⋊C4—738no—
433C4⋊C4—734no—
434C4⋊C4—738no—
435C4⋊C4C2×C4×D7314yes—
436C4⋊C4C2×C4×D7318yes—
437C4⋊C4C2×C4×D7314yes—
438C22⋊C4—734no—
439C22⋊C4—734no—
440C22⋊C4—738no—
441C22⋊C4—738no—
442C22⋊C4—738no—
443C22⋊C4—738no—
444C22⋊C4C2×C4×D7314yes—
445C42—732no—
446C42—738no—
447C42—732no—
448C42C2×C4×D7311yescharacteristic
449C42C2×C4×D7311yescharacteristic
450C42C23×D7312yes—
451C42C23×D7314yes—
452C23—2922no—
453C23—732no—
454C23—734no—
455C23—1462no—
456C23C22×C4×D7311yescharacteristic
457Q8—44no—
458Q8—1464no—
459D4—2924no—
460D4—2928no—
461D4—1468no—
462D4—1464no—
463C2×C4—42no—
464C2×C4—2928no—
465C2×C4—2922no—
466C2×C4—734no—
467C2×C4—734no—
468C2×C4—732no—
469C2×C4—1462no—
470C2×C4—1464no—
471C2×C4—1462no—
472C2×C4—1462no—
473C2×C4—1464no—
474C2×C4—1464no—
475C2×C4C22×C4×D7318yes—
476C2×C4C22×C4×D7312yes—
477C2×C4C22×C4×D7312yes—
478C2×C4C22×C4×D7311yescharacteristic
479C2×C4#41×D7312yes—
480C2×C4C2×#1192402912yes—
481C2×C4C24×D7311yescharacteristic
482C8—22no—
483C8—24no—
484C8—732no—
485C8—732no—
486C8—1462no—
487C8—1464no—
488C8C2×#1192402914yes—
489C22—22no—
490C22—2924no—
491C22—1468no—
492C22—1464no—
493C22—1462no—
494C22—1464no—
495C22C4×#1192402912yes—
496C22C23×C4×D7311yescharacteristic
497C4—22no—
498C4—22no—
499C4—28no—
500C4—1464no—
501C4—1462no—
502C4—1464no—
503C4C4×#1192402912yes—
504C4C2×#41×D7311yescharacteristic
505C4C22×#1192402911yescharacteristic
506C2—22no—
507C2—2922no—
508C2—2924no—
509C2C2×C4×#1192402911yescharacteristic
510C2#2262464412yes—
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2961C2
prime radical#22623323C2
cosocleC2×C4×C73C25
hypercenter#2961D73
hypocenterC73#60209
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #22618937C2semidirect
3. #22618924C2semidirect
4. #22618866C2semidirect
5. #22618650C2semidirect
6. #22618642C2semidirect
7. #22618633C2semidirect
8. #22618627C2semidirect
9. #22618574C2semidirect
10. #22618568C2semidirect
11. #22618358C2semidirect
12. C2×#17988544C2semidirect
13. C73×#2961C2semidirect
28. #17988718C22semidirect
29. Q8×#10596831C22semidirect
31. #17988664C22semidirect
33. #17988660C22semidirect
36. #17988652C22semidirect
38. #17988647C22semidirect
39. #17988639C22semidirect
47. #17988544C22semidirect
49. #17988541C22semidirect
51. C4×#11924011C22semidirect
53. #97×D73C22semidirect
57. #446×C73C22semidirect
259. #2961D73semidirect
269. C73#60209semidirect
286. #446C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226233232
#226189372
#226189242
#226188662
#226186502
#226186422
#226186332
#226186272
#226185742
#226185682
#226183582
C2×#179885442
C73×#29612
#6020973