Finite Group Databasebeta

← #11884045

Subgroups — #11884045

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#611C211yesmaximal, characteristic, complemented
2C22×#3675C211yesmaximal, characteristic, complemented
3C2×#63480C211yesmaximal, characteristic, complemented
4#10589732C211yesmaximal, characteristic
5C9×#451C211yesmaximal, characteristic, complemented
6#10588870C211yesmaximal, characteristic, complemented
7#10588867C211yesmaximal, characteristic, complemented
8#10588865C211yesmaximal, characteristic, complemented
9#10588727C211yesmaximal, characteristic, complemented
10#10588498C211yesmaximal, characteristic, complemented
11#10588497C211yesmaximal, characteristic, complemented
12#10588492C211yesmaximal, characteristic, complemented
13#10588486C211yesmaximal, characteristic, complemented
14#10588413C211yesmaximal, characteristic, complemented
15#10588412C211yesmaximal, characteristic, complemented
16#80204—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic, complemented
20C22×D36C2211yescharacteristic
21C2×C9×Q16C2211yescharacteristic, complemented
22C2×C9×Q16C2211yescharacteristic, complemented
23C9×C22⋊Q8C2211yescharacteristic
24#63509C2211yescharacteristic
25#63508—21no—
26#63508C2211yescharacteristic, complemented
27Q8×Dic9C2211yescharacteristic, complemented
28#63506—21no—
29#63506C2211yescharacteristic, complemented
30C2×#3675—24no—
31C2×#3675C2211yescharacteristic
32C2×#3675C2211yescharacteristic
33C2×#3675C2211yescharacteristic
34C2×#3675C2211yescharacteristic
35C2×#3674C2211yescharacteristic, complemented
36C4×#611—21no—
37C4×#611C2211yescharacteristic
38#63486—21no—
39#63486C2211yescharacteristic
40C22×C9⋊C8C2211yescharacteristic
41#63480—24no—
42C2×#3664C2211yescharacteristic
43C2×#3664C2211yescharacteristic
44C2×#3663C2211yescharacteristic, complemented
45#63457—21no—
46#63457C2211yescharacteristic
47#63456—21no—
48#63455C2211yescharacteristic
49#63444—21no—
50C22⋊C4×D9—21no—
51C9×#103C2211yescharacteristic, complemented
52C9×#103C2211yescharacteristic, complemented
53C9×C22⋊C8C2211yescharacteristic
54#63395C2211yescharacteristic, complemented
55#63380C2211yescharacteristic
56#63380C2211yescharacteristic
57(C2×D9)⋊C8C2211yescharacteristic, complemented
58#63375C2211yescharacteristic, complemented
59Dic9⋊C8C2211yescharacteristic, complemented
60#63368C2211yescharacteristic, complemented
61#63366C2211yescharacteristic, complemented
62Q8×#67—31no—
63C22×#215—31no—
64C2×#918—31no—
65#5630—31no—
66C3×#451D311yescharacteristic
67#5190—31no—
68#5187—31no—
69#5185—31no—
70#5051—31no—
71#4818—31no—
72#4817—31no—
73#4812—31no—
74#4806—31no—
75#4731—31no—
76#4730—31no—
77C23×D9—21no—
78C2×Q8×C9—21no—
79C2×Q8×C9—22no—
80C2×Q8×C9—41no—
81C2×Q8×C9C2311yescharacteristic
82C2×Q8×C9C2311yescharacteristic
83C2×Q8×C9C2311yescharacteristic
84C22×C4×C9—21no—
85C22×C4×C9C2311yescharacteristic
86C2×#611D411yescharacteristic
87#3701—22no—
88#3701—41no—
89Q8×D9—22no—
90Q8×D9—41no—
91C2×D36—22no—
92C2×D36—21no—
93C2×D36—21no—
94C2×D36—21no—
95C2×D36—41no—
96C2×D36C2311yescharacteristic
97C2×D36C2311yescharacteristic
98C2×C4×D9—21no—
99C2×C4×D9—21no—
100C2×C4×D9—21no—
101C2×C4×D9C2311yescharacteristic
102C2×Dic18—21no—
103C2×Dic18C2311yescharacteristic
104C9×Q16—22no—
105C9×Q16—41no—
106C2×C8×C9C2311yescharacteristic
107C2×C8×C9C2311yescharacteristic
108C9×C4⋊C4—21no—
109C9×C4⋊C4C2311yescharacteristic
110C9×C22⋊C4—21no—
111#3676—21no—
112#3676D411yescharacteristic
113#3675—22no—
114#3675—22no—
115#3675—22no—
116#3675D414yescomplemented
117#3674—22no—
118(C2×D9)⋊C4—21no—
119(C2×D9)⋊C4—21no—
120(C2×D9)⋊C4—21no—
121(C2×D9)⋊C4—21no—
122(C2×D9)⋊C4—21no—
123(C2×D9)⋊C4D411yescharacteristic
124C4⋊Dic9—21no—
125C4⋊Dic9C2311yescharacteristic
126Dic9⋊C4—21no—
127Dic9⋊C4—21no—
128Dic9⋊C4—21no—
129Dic9⋊C4—21no—
130Dic9⋊C4D411yescharacteristic
131C4×Dic9—21no—
132C4×Dic9C2311yescharacteristic
133C2×C9⋊C8—22no—
134C2×C9⋊C8C2311yescharacteristic
135C2×C9⋊C8C2311yescharacteristic
136#3664—22no—
137#3664—41no—
138#3663—22no—
139#3266—91noSylow
140C22×C3×Q8C2×D311yescharacteristic
141C2×#239—31no—
142C2×D3×Q8—31no—
143C22×D12—31no—
144C2×C3×Q16C2×D311yescharacteristic
145C2×C3×Q16C2×D311yescharacteristic
146C3×C22⋊Q8C2×D311yescharacteristic
147#947—31no—
148#946—31no—
149#946—61no—
150Q8×Dic3—31no—
151#944—31no—
152#944—61no—
153C2×#216—31no—
154C2×#215—31no—
155C2×#215—31no—
156C2×#215—31no—
157C2×#215—31no—
158C2×#215—64no—
159C4×#67—31no—
160C4×#67—61no—
161#924—31no—
162#924—61no—
163C22×C3⋊C8—31no—
164#918—64no—
165C2×#204—31no—
166C2×#204—31no—
167C2×ΓL(1,𝔽25)—31no—
168#895—31no—
169#895—61no—
170#894—61no—
171#893—31no—
172#882—61no—
173D3×C22⋊C4—61no—
174C3×#103C2×D311yescharacteristic
175C3×#103C2×D311yescharacteristic
176C3×C22⋊C8C2×D311yescharacteristic
177#835—31no—
178#821—31no—
179#821—31no—
180(C2×D3)⋊C8—31no—
181#815—31no—
182Dic3⋊C8—31no—
183#810—31no—
184#807—31no—
185C23×C9C2×D411yescharacteristic
186C22×D9—21no—
187C22×D9—21no—
188C22×D9—42no—
189C22×D9—42no—
190C22×D9—81no—
191C22×D9C2×D411yescharacteristic
192Q8×C9—21no—
193Q8×C9—21no—
194Q8×C9—21no—
195Q8×C9—21no—
196Q8×C9—21no—
197Q8×C9—42no—
198Q8×C9C2×D412yes—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—21no—
203C2×C4×C9—21no—
204C2×C4×C9—21no—
205C2×C4×C9—42no—
206C2×C4×C9C2×D411yescharacteristic
207C2×C4×C9C2411yescharacteristic
208#611—22no—
209C2×Dic9—21no—
210C2×Dic9—21no—
211C2×Dic9C2×D411yescharacteristic
212C2×Dic9C2×D411yescharacteristic
213C2×Dic9C2×D411yescharacteristic
214D36—21no—
215D36—21no—
216D36—21no—
217D36—42no—
218D36—42no—
219D36—81no—
220D36C2×D412yes—
221C4×D9—21no—
222C4×D9—21no—
223C4×D9—42no—
224C4×D9—42no—
225C4×D9—81no—
226Dic18—21no—
227Dic18—21no—
228Dic18—42no—
229C8×C9—21no—
230C8×C9—21no—
231C9⋊C8—21no—
232C9⋊C8C2×D412yes—
233C2×#137—91no—
234C22×SD16—91no—
235D4×Q8—91no—
236#546—91no—
237#497—91no—
238#468—91no—
239#467—91no—
240#464—91no—
241#461—91no—
242#452—91no—
243#451D911yescharacteristic, complemented
244#450—91no—
245#448—91no—
246#440—91no—
247#435—91no—
248C23×D3—61no—
249C2×C3×Q8—21no—
250C2×C3×Q8—22no—
251C2×C3×Q8—41no—
252C2×C3×Q8C22×D311yescharacteristic
253C2×C3×Q8C22×D311yescharacteristic
254C2×C3×Q8C22×D311yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—31no—
258#239—62no—
259#239—121no—
260D3×Q8—62no—
261D3×Q8—121no—
262C2×D12—31no—
263C2×D12—31no—
264C2×D12—62no—
265C2×D12—61no—
266C2×D12—61no—
267C2×D12—61no—
268C2×D12—121no—
269C2×C4×D3—31no—
270C2×C4×D3—61no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×Dic6—31no—
274C2×Dic6—61no—
275C3×Q16—22no—
276C3×Q16—41no—
277C2×C3×C8C22×D311yescharacteristic
278C2×C3×C8C22×D311yescharacteristic
279C3×C4⋊C4—21no—
280C3×C4⋊C4C22×D311yescharacteristic
281C3×C22⋊C4—21no—
282#217—31no—
283#217—61no—
284#216—62no—
285#215—34no—
286#215—62no—
287#215—62no—
288#215—62no—
289(C2×D3)⋊C4—31no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—61no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—61no—
294(C2×D3)⋊C4—61no—
295C4⋊Dic3—31no—
296C4⋊Dic3—61no—
297Dic3⋊C4—31no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302C4×Dic3—31no—
303C4×Dic3—61no—
304C2×C3⋊C8—31no—
305C2×C3⋊C8—31no—
306C2×C3⋊C8—62no—
307#204—62no—
308#204—121no—
309ΓL(1,𝔽25)—62no—
310C22×C9—21no—
311C22×C9—21no—
312C22×C9#13712yescomplemented
313C22×C9C22×D411yescharacteristic
314C2×D9—21no—
315C2×D9—22no—
316C2×D9—21no—
317C2×D9—21no—
318C2×D9—41no—
319C2×D9—41no—
320C2×D9—41no—
321C2×D9—41no—
322C2×D9—41no—
323C2×D9—84no—
324C4×C9—22no—
325C4×C9—21no—
326C4×C9—41no—
327C4×C9—41no—
328C4×C9—41no—
329C4×C9C22×D411yescharacteristic
330C4×C9H(5,𝔽2)11yescharacteristic
331Dic9—21no—
332Dic9—21no—
333Dic9—21no—
334Dic9—41no—
335Dic9—41no—
336C2×#41—91no—
337C22×Q8—91no—
338C22×Q8C2×D911yescharacteristic
339C22×D4—91no—
340#137—184no—
341C2×Q16—91no—
342C2×Q16C2×D911yescharacteristic, complemented
343C2×Q16C2×D911yescharacteristic, complemented
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—184no—
351C2×M16—91no—
352C22×C8—91no—
353C4⋊Q8—91no—
354C4⋊Q8—181no—
355#124—91no—
356#123—181no—
357C22⋊Q8—91no—
358C22⋊Q8—91no—
359C22⋊Q8—181no—
360C22⋊Q8—181no—
361C22⋊Q8C2×D911yescharacteristic
362#121—91no—
363#121—181no—
364#120—181no—
365C4×Q8—91no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C2×C22⋊C4—181no—
370#107—91no—
371C4⋊C8—91no—
372#103—91no—
373#103—91no—
374#103C2×D911yescharacteristic, complemented
375#103C2×D911yescharacteristic, complemented
376#102—91no—
377#102—91no—
378C22⋊C8—91no—
379C22⋊C8C2×D911yescharacteristic
380#97—91no—
381C23×C3D3×D411yescharacteristic
382C22×D3—31no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—241no—
388C3×Q8—21no—
389C3×Q8—21no—
390C3×Q8—21no—
391C3×Q8—21no—
392C3×Q8—21no—
393C3×Q8—42no—
394C3×Q8D3×D412yes—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—42no—
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—62no—
405C2×Dic3—31no—
406C2×Dic3—31no—
407C2×Dic3—31no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410D12—32no—
411D12—61no—
412D12—61no—
413D12—61no—
414D12—122no—
415D12—122no—
416D12—241no—
417C4×D3—61no—
418C4×D3—61no—
419C4×D3—122no—
420C4×D3—122no—
421C4×D3—241no—
422Dic6—61no—
423Dic6—61no—
424Dic6—122no—
425C3×C8—21no—
426C3×C8—21no—
427C3⋊C8—32no—
428C3⋊C8—61no—
429C2×C9—22no—
430C2×C9D4211yescharacteristic
431C2×C9C2×#13711yescharacteristic
432C2×C9#57711yescharacteristic
433D9—41no—
434D9—42no—
435D9—81no—
436C24—181no—
437#41—182no—
438#41—361no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8—91no—
443C2×Q8—181no—
444C2×Q8—182no—
445C2×Q8—361no—
446C2×Q8C22×D911yescharacteristic
447C2×Q8C22×D911yescharacteristic
448C2×Q8C22×D911yescharacteristic
449C2×D4—91no—
450C2×D4—91no—
451C2×D4—91no—
452C2×D4—182no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—361no—
457C22×C4—21no—
458C22×C4—91no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4C22×D911yescharacteristic
463Q16—22no—
464Q16—41no—
465Q16—182no—
466SD16—94no—
467SD16—182no—
468SD16—182no—
469SD16—182no—
470SD16—182no—
471SD16—361no—
472M16—182no—
473C2×C8—91no—
474C2×C8—91no—
475C2×C8—182no—
476C2×C8C22×D911yescharacteristic
477C2×C8C22×D911yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—91no—
480C4⋊C4—91no—
481C4⋊C4—181no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C4⋊C4C22×D911yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—91no—
489C22⋊C4—91no—
490C22⋊C4—181no—
491C22⋊C4—181no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C42—91no—
497C42—181no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3#91812yes—
501C22×C3C2×D3×D411yescharacteristic
502C2×D3—61no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—62no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—244no—
512C3×C4—22no—
513C3×C4—21no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—41no—
517C3×C4C2×D3×D411yescharacteristic
518C3×C4#100411yescharacteristic
519Dic3—61no—
520Dic3—61no—
521Dic3—61no—
522Dic3—121no—
523Dic3—121no—
524C9#326611yescharacteristic, complemented, Sylow
525C23—91no—
526C23—181no—
527C23—181no—
528C23—362no—
529C23—362no—
530C23—721no—
531C23D4×D911yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—42no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8D4×D912yes—
542D4—92no—
543D4—182no—
544D4—181no—
545D4—181no—
546D4—181no—
547D4—362no—
548D4—362no—
549D4—721no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—42no—
557C2×C4—91no—
558C2×C4—91no—
559C2×C4—91no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4—721no—
567C2×C4D4×D911yescharacteristic
568C2×C4C23×D911yescharacteristic
569C8—21no—
570C8—21no—
571C8—92no—
572C8—181no—
573C2×C3—22no—
574C2×C3#559011yescharacteristic
575C2×C3C2×#91811yescharacteristic
576C2×C3#577811yescharacteristic
577D3—121no—
578D3—122no—
579D3—241no—
580C22—21no—
581C22—21no—
582C22—181no—
583C22—181no—
584C22—181no—
585C22—182no—
586C22—361no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22—361no—
591C22—724no—
592C22#6348012yescomplemented
593C22C2×D4×D911yescharacteristic
594C4—21no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—181no—
600C4—181no—
601C4—181no—
602C4—361no—
603C4—361no—
604C4C2×D4×D911yescharacteristic
605C4#6371011yescharacteristic
606C3#8020411yescharacteristic
607C2—22no—
608C2—361no—
609C2—362no—
610C2—721no—
611C2#1058969211yescharacteristic
612C2C2×#6348011yescharacteristic
613C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#451C2
socleC22×C3C2×D3×D4
prime radical#10589732C2
hypercenter#451D9
hypocenterC9#3266
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. Q8×#611C2semidirect
2. C22×#3675C2semidirect
3. C2×#63480C2semidirect
5. C9×#451C2semidirect
6. #10588870C2semidirect
7. #10588867C2semidirect
8. #10588865C2semidirect
9. #10588727C2semidirect
10. #10588498C2semidirect
11. #10588497C2semidirect
12. #10588492C2semidirect
13. #10588486C2semidirect
14. #10588413C2semidirect
15. #10588412C2semidirect
19. C2×Q8×D9C22semidirect
21. C2×C9×Q16C22semidirect
22. C2×C9×Q16C22semidirect
26. #63508C22semidirect
27. Q8×Dic9C22semidirect
29. #63506C22semidirect
35. C2×#3674C22semidirect
44. C2×#3663C22semidirect
51. C9×#103C22semidirect
52. C9×#103C22semidirect
54. #63395C22semidirect
57. (C2×D9)⋊C8C22semidirect
58. #63375C22semidirect
59. Dic9⋊C8C22semidirect
60. #63368C22semidirect
61. #63366C22semidirect
116. #3675D4semidirect
243. #451D9semidirect
312. C22×C9#137semidirect
342. C2×Q16C2×D9semidirect
343. C2×Q16C2×D9semidirect
374. #103C2×D9semidirect
375. #103C2×D9semidirect
524. C9#3266semidirect
592. C22#63480semidirect

Maximal subgroups

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

subgroupindex
Q8×#6112
C22×#36752
C2×#634802
#105897322
C9×#4512
#105888702
#105888672
#105888652
#105887272
#105884982
#105884972
#105884922
#105884862
#105884132
#105884122
#802043