Finite Group Databasebeta

← #33057429

Subgroups — #33057429

Order 18688.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618951C211yesmaximal, characteristic, complemented
2#22618943C211yesmaximal, characteristic, complemented
3C4×#14556611C211yesmaximal, characteristic
4#22608824C212yesmaximal, complemented
5#22608778C212yesmaximal, complemented
6#22608763C212yesmaximal, complemented
7#22608728C212yesmaximal, complemented
8#22608692C211yesmaximal, characteristic, complemented
9#22608366C211yesmaximal, characteristic, complemented
10#22608212C211yesmaximal, characteristic, complemented
11C73×#1488C211yesmaximal, characteristic, complemented
12C2×#14556611C411yescharacteristic
13C4×#11924028C2211yescharacteristic
14#17988714C2212yes—
15Q8×#10596831C2212yes—
16C4×#11924018C411yescharacteristic
17C4×#11924018C2211yescharacteristic
18C4×#11924015C411yescharacteristic
19C4×#11924015C2211yescharacteristic
20C4×#11924016C411yescharacteristic
21C4×#11924016C2211yescharacteristic
22C4×#11924013C411yescharacteristic
23C4×#11924013C2211yescharacteristic
24#17988665—22no—
25#17988665C2212yes—
26#17988661—22no—
27#17988652C2212yes—
28#17988644—21no—
29#17988644C2211yescharacteristic
30#17988642—21no—
31#17988623C411yescharacteristic
32#17988583C411yescharacteristic
33#17988581C411yescharacteristic
34C4×#11924012—21no—
35C4×#11924012C2211yescharacteristic
36#97×D73—21no—
37C2×C4×#10596831C2211yescharacteristic
38#17988339C2212yes—
39#17988337C2212yes—
40#17988319C2212yes—
41#17988316C2212yes—
42#17988309C2212yes—
43C8×#10596831C2212yes—
44C4×#41×C73C2211yescharacteristic
45#432×C73C2211yescharacteristic
46#431×C73C2211yescharacteristic
47Q8⋊C8×C73C2212yes—
48D4⋊C8×C73C2212yes—
49C2×#11924028C2×C411yescharacteristic
50#14556611—24no—
51C2×#11924018C2×C411yescharacteristic
52C2×#11924016C2×C411yescharacteristic
53C2×#11924015C2×C411yescharacteristic
54C2×#11924013C2×C411yescharacteristic
55C2×#11924012—22no—
56C2×#11924012D412yes—
57C22×#10596831C2×C411yescharacteristic
58C22×#10596831C2×C411yescharacteristic
59C2×C8×D73—22no—
60C4×Dic146C2×C411yescharacteristic
61C4×Dic146C2311yescharacteristic
62C4×D292C2×C411yescharacteristic
63C4×D292C2311yescharacteristic
64C4×C22⋊D73—21no—
65C4×C22⋊D73—21no—
66#14556550C2×C411yescharacteristic
67#14556548—21no—
68C42×D73—21no—
69#14556524C2×C411yescharacteristic
70#14556524C2×C411yescharacteristic
71#14556522C2×C411yescharacteristic
72#14556522C2×C411yescharacteristic
73C4⋊#10596831—22no—
74C4⋊#10596831C2312yes—
75#14556520—22no—
76#14556515C2×C411yescharacteristic
77#14556515C2×C411yescharacteristic
78#14556514C2×C411yescharacteristic
79#14556514C2×C411yescharacteristic
80#14556512C2×C411yescharacteristic
81#14556512C2×C411yescharacteristic
82#14556511C2×C411yescharacteristic
83#14556511C2×C411yescharacteristic
84C22⋊#10596831—22no—
85C22⋊#10596831—21no—
86#14556503—22no—
87#14556502—21no—
88#14556502D411yescharacteristic
89#14556502D411yescharacteristic
90#14556501—22no—
91C4×#10596831—22no—
92C4×#10596831C2×C411yescharacteristic
93C4×#10596831C2×C411yescharacteristic
94C4×#10596831C2311yescharacteristic
95C4×#10596831C2311yescharacteristic
96C4×#10596831C2312yes—
97C2×#41×C73C2×C411yescharacteristic
98C4×Q8×C73C2×C411yescharacteristic
99C4×Q8×C73C2311yescharacteristic
100C4×D4×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73C2×C411yescharacteristic
103C4×D4×C73C2311yescharacteristic
104#117×C73—21no—
105#117×C73C2×C411yescharacteristic
106C2×C42×C73—21no—
107C2×C42×C73C2311yescharacteristic
108C4⋊C8×C73—21no—
109C4⋊C8×C73C2312yes—
110C22⋊C8×C73—21no—
111C22⋊C8×C73—21no—
112#97×C73—21no—
113C4×C8×C73C2312yes—
114#11924028—22no—
115#11924028—41no—
116C2×Dic146C22×C411yescharacteristic
117C2×D292C22×C411yescharacteristic
118C2×C22⋊D73—21no—
119C2×C4×D73—21no—
120C2×C4×D73—21no—
121C2×C4×D73—21no—
122#11924018—22no—
123#11924016—22no—
124#11924015M1614yescomplemented
125#11924013—22no—
126#11924012—24no—
127#11924012—44no—
128C2×#10596831—22no—
129C2×#10596831—22no—
130C2×#10596831—41no—
131C2×#10596831C22×C411yescharacteristic
132C2×#10596831C22×C411yescharacteristic
133C2×#10596831C22×C411yescharacteristic
134C2×#10596831C22×C411yescharacteristic
135C2×#10596831C2×D412yes—
136C2×#10596831C2×D412yes—
137C8×D73—44no—
138C4⋊Dic73C22×C411yescharacteristic
139C4⋊Dic73C22×C411yescharacteristic
140#11924007—21no—
141#11924007—21no—
142C22⋊Dic73—21no—
143#11924005—21no—
144#11924005—21no—
145C4×Dic73—21no—
146C4×Dic73—21no—
147C4×Dic73—21no—
148#41×C73—22no—
149#41×C73—41no—
150C2×Q8×C73C22×C411yescharacteristic
151C2×D4×C73—21no—
152C2×D4×C73C22×C411yescharacteristic
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73C22×C411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73#4111yescharacteristic
159C2×C8×C73—22no—
160C2×C8×C73—22no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73C22×C411yescharacteristic
164C4⋊C4×C73C22×C411yescharacteristic
165C22⋊C4×C73—21no—
166C22⋊C4×C73—21no—
167C22⋊C4×C73—21no—
168C42×C73—21no—
169C42×C73—21no—
170C42×C73—21no—
171C42×C73C22×C411yescharacteristic
172C42×C73C2×D411yescharacteristic
173C42×C73#4111yescharacteristic
174C42×C73C2411yescharacteristic
175C23×C73—21no—
176C23×C73C4×D411yescharacteristic
177C22×D73—21no—
178Q8×C73—21no—
179Q8×C73C2×M1612yes—
180D4×C73—21no—
181D4×C73—21no—
182D4×C73—42no—
183C2×C4×C73—21no—
184C2×C4×C73—21no—
185C2×C4×C73—21no—
186C2×C4×C73—22no—
187C2×C4×C73—21no—
188C2×C4×C73—21no—
189C2×C4×C73—41no—
190C2×C4×C73—42no—
191C2×C4×C73—42no—
192C2×C4×C73—81no—
193C2×C4×C73C4×D411yescharacteristic
194C2×C4×C73C4×D411yescharacteristic
195C2×C4×C73C4×D411yescharacteristic
196C2×C4×C73C23×C411yescharacteristic
197C2×C4×C73C22×D411yescharacteristic
198C2×C4×C73C2×#4111yescharacteristic
199C22⋊D73—42no—
200C2×Dic73—21no—
201C2×Dic73—21no—
202C2×Dic73—21no—
203D292—21no—
204D292C2×M1612yes—
205C4×D73—42no—
206C4×D73—42no—
207C4×D73—81no—
208Dic146—21no—
209Dic146—21no—
210C8×C73—42no—
211C8×C73—42no—
212#10596831—21no—
213#10596831—21no—
214#10596831—21no—
215#10596831—22no—
216#10596831—42no—
217#10596831C2×M1612yes—
218#10596831#13514yescomplemented
219C22×C73—21no—
220C22×C73—21no—
221C22×C73—21no—
222C22×C73—41no—
223C22×C73—41no—
224C22×C73—41no—
225C22×C73C2×C4×D411yescharacteristic
226C2×D73—22no—
227C2×D73—41no—
228C2×D73—41no—
229C4×C73—21no—
230C4×C73—22no—
231C4×C73—21no—
232C4×C73—21no—
233C4×C73—21no—
234C4×C73—41no—
235C4×C73—41no—
236C4×C73C22×M1611yescharacteristic
237C4×C73#56811yescharacteristic
238C4×C73C2×#13512yes—
239Dic73—41no—
240Dic73—41no—
241Dic73—41no—
242#18037—731nomaximal, Sylow
243C2×C73—41no—
244C2×C73—81no—
245C2×C73D4×M1611yescharacteristic
246C2×C73C4×#13511yescharacteristic
247C2×C73#295711yescharacteristic
248D73—42no—
249#2971—731no—
250#2970—731no—
251C4×#135—731no—
252#1590—732no—
253#1584—732no—
254#1581—732no—
255C8×SD16—732no—
256#1568—731no—
257#1488—731no—
258#1488D7311yescharacteristic, complemented
259C8×M16—731no—
260C73#1803711yescharacteristic, complemented, Sylow
261C2×#135—731no—
262C4×#41—731no—
263C4×#41C2×D7311yescharacteristic
264#446—732no—
265C8×Q8—732no—
266C4×Q16—731no—
267C4×Q16—731no—
268C4×SD16—731no—
269C4×SD16—731no—
270C4×SD16—731no—
271C4×SD16—731no—
272C4×D8—731no—
273C4×D8—731no—
274#436—732no—
275#436—1462no—
276#435—1462no—
277C8×D4—732no—
278#432—731no—
279#432—1461no—
280#432—1461no—
281#432C2×D7311yescharacteristic
282#431C2×D7311yescharacteristic
283#427—731no—
284#416—731no—
285#416—731no—
286C4×M16—731no—
287C4×M16—1461no—
288C2×#97—1461no—
289C2×C4×C8—731no—
290#335—732no—
291#334—732no—
292Q8⋊C8—732no—
293Q8⋊C8C2×D7312yes—
294D4⋊C8—732no—
295D4⋊C8C2×D7312yes—
296#322—732no—
297C82—732no—
298C2×#41—731no—
299C2×#41C4×D7311yescharacteristic
300#135—1464no—
301C2×Q16—731no—
302C2×SD16—731no—
303C2×SD16—731no—
304C2×D8—731no—
305C2×M16—732no—
306C2×M16—1462no—
307C22×C8—731no—
308C22×C8—731no—
309C22×C8—1462no—
310C4×Q8—731no—
311C4×Q8—731no—
312C4×Q8C4×D7311yescharacteristic
313C4×Q8C22×D7311yescharacteristic
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—731no—
317C4×D4—731no—
318C4×D4—1461no—
319C4×D4—1461no—
320C4×D4C4×D7311yescharacteristic
321C4×D4C22×D7311yescharacteristic
322#117—21no—
323#117—731no—
324#117—1461no—
325#117C4×D7311yescharacteristic
326C2×C42—21no—
327C2×C42—1461no—
328C2×C42C22×D7311yescharacteristic
329#107—731no—
330#107—731no—
331#106—731no—
332#106—731no—
333C4⋊C8—21no—
334C4⋊C8—732no—
335C4⋊C8—1462no—
336C4⋊C8—1462no—
337C4⋊C8C22×D7312yes—
338#103—731no—
339#103—731no—
340#103—731no—
341#103—731no—
342#102—731no—
343#102—731no—
344#102—731no—
345#102—731no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—1462no—
349C22⋊C8—1462no—
350C22⋊C8—1461no—
351#97—21no—
352#97—731no—
353#97—731no—
354#97—1462no—
355#97—1461no—
356C4×C8—731no—
357C4×C8—731no—
358C4×C8—731no—
359C4×C8—732no—
360C4×C8—731no—
361C4×C8—1462no—
362C4×C8C22×D7312yes—
363#41—22no—
364#41—41no—
365#41—2921no—
366#41—1462no—
367C2×Q8—731no—
368C2×Q8C2×C4×D7311yescharacteristic
369C2×D4—21no—
370C2×D4—731no—
371C2×D4—1461no—
372C2×D4C2×C4×D7311yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—1461no—
377C22×C4—1461no—
378C22×C4—1461no—
379C22×C4C2×C4×D7311yescharacteristic
380C22×C4D4×D7311yescharacteristic
381C22×C4#1192402711yescharacteristic
382Q16—1462no—
383SD16—734no—
384SD16—1462no—
385D8—1462no—
386M16—2924no—
387M16—1464no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—2924no—
391C2×C8—2921no—
392C2×C8—731no—
393C2×C8—732no—
394C2×C8—731no—
395C2×C8—731no—
396C2×C8—731no—
397C2×C8—732no—
398C2×C8—1462no—
399C2×C8—1462no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—731no—
403C4⋊C4—731no—
404C4⋊C4—1461no—
405C4⋊C4—1461no—
406C4⋊C4C2×C4×D7311yescharacteristic
407C4⋊C4C2×C4×D7311yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—1461no—
412C22⋊C4—1461no—
413C22⋊C4—1461no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—1461no—
418C42—1461no—
419C42—1461no—
420C42C2×C4×D7311yescharacteristic
421C42D4×D7311yescharacteristic
422C42#1192402711yescharacteristic
423C42C23×D7311yescharacteristic
424C23—21no—
425C23—1461no—
426C23#1455655111yescharacteristic
427Q8—21no—
428Q8—1461no—
429Q8—1461no—
430Q8M16×D7312yes—
431D4—21no—
432D4—21no—
433D4—42no—
434D4—2922no—
435D4—732no—
436D4—1461no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—2922no—
448C2×C4—2922no—
449C2×C4—5841no—
450C2×C4—1461no—
451C2×C4—1461no—
452C2×C4—1461no—
453C2×C4#1455655111yescharacteristic
454C2×C4#1455655111yescharacteristic
455C2×C4#1455655111yescharacteristic
456C2×C4C22×C4×D7311yescharacteristic
457C2×C4C2×D4×D7311yescharacteristic
458C2×C4C2×#1192402711yescharacteristic
459C8—42no—
460C8—42no—
461C8—2922no—
462C8—732no—
463C8—734no—
464C8—1461no—
465C8—1461no—
466C8—1461no—
467C8—1462no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—2921no—
475C22—2921no—
476C22—1462no—
477C22C2×#1455655111yescharacteristic
478C4—21no—
479C4—22no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—2921no—
486C4—2921no—
487C4—2921no—
488C4C2×M16×D7311yescharacteristic
489C4#1798935311yescharacteristic
490C4#135×D7312yes—
491C2—41no—
492C2—81no—
493C2—2922no—
494C2#2261866311yescharacteristic
495C2#2261869911yescharacteristic
496C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1488C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556611C4
cosocleC42×C73C24
hypercenter#1488D73
hypocenterC73#18037
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
1. #22618951C2semidirect
2. #22618943C2semidirect
4. #22608824C2semidirect
5. #22608778C2semidirect
6. #22608763C2semidirect
7. #22608728C2semidirect
8. #22608692C2semidirect
9. #22608366C2semidirect
10. #22608212C2semidirect
11. C73×#1488C2semidirect
124. #11924015M16semidirect
218. #10596831#135semidirect
258. #1488D73semidirect
260. C73#18037semidirect

Maximal subgroups

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

subgroupindex
#226189512
#226189432
C4×#145566112
#226088242
#226087782
#226087632
#226087282
#226086922
#226083662
#226082122
C73×#14882
#1803773