Finite Group Databasebeta

← #11895166

Subgroups — #11895166

Order 1152.

840 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic
3C3×C4×#215C211yesmaximal, characteristic
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591569C212yesmaximal
6#10591538C212yesmaximal, complemented
7#10590460C212yesmaximal
8#10590431C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic
10#10590288C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81037—31nomaximal
13#79619—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4×Q8C2211yescharacteristic
16#64153C2212yes—
17#64098—22no—
18#64096C2212yes—
19#64079—21no—
20#64078C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63919C2212yes—
27#63899—22no—
28#63898C2212yes—
29#63856—21no—
30C2×#3716C2212yes—
31C3×#835C2211yescharacteristic
32C3×#835C2212yes—
33C3×#809C2211yescharacteristic
34C3×#808C2212yes—
35C3×#808C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63553C2212yes—
43#5727—31no—
44#5567—31no—
45#5567—31no—
46#5567—61no—
47D4×Dic6—31no—
48C3×#475—31no—
49C3×C4×SD16—31no—
50#5162—32no—
51#5093—31no—
52C4×#215D311yescharacteristic
53#5020D311yescharacteristic, complemented
54#5019—31no—
55#4854—32no—
56#4854—32no—
57#4852—32no—
58#4841—31no—
59#4830—31no—
60#4818—32no—
61#4792—32no—
62#4792—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634D411yescharacteristic
68C2×#634C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×#627—22no—
73C2×D3×Dic3—22no—
74D3×Dic6—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C42—21no—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82#3750—22no—
83#3750—22no—
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3C2312yes—
88C3×#215—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3716—24no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—31no—
104C3×C4×Q8—21no—
105C3×C4×Q8C2×D311yescharacteristic
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×D4—31no—
108#946—61no—
109#944—32no—
110#944—32no—
111#944—62no—
112C2×#215C2×D311yescharacteristic
113D4×Dic3—32no—
114C2×#214—32no—
115#924—61no—
116C2×#204—32no—
117#896—62no—
118#893—32no—
119#889—62no—
120#889—62no—
121#889—64no—
122#888—32no—
123#888—32no—
124#887—32no—
125#887—32no—
126#887—62no—
127#878—62no—
128C4×D12C2×D311yescharacteristic
129#870—61no—
130#870—61no—
131#870—62no—
132#869—31no—
133#869—31no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6—62no—
142C3×#106—31no—
143C3×#106—32no—
144C3×C4⋊C8—31no—
145C3×#103—31no—
146C3×#103—32no—
147C3×#102—31no—
148C3×C4×C8—31no—
149#835C2×D312yes—
150#835C2×D311yescharacteristic
151#816—32no—
152#816—32no—
153#816—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156C8×Dic3—32no—
157C8×Dic3—32no—
158#810—32no—
159#810—32no—
160#810—32no—
161#809C2×D311yescharacteristic
162#808C2×D312yes—
163#808C2×D311yescharacteristic
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—21no—
167C32×Q8—21no—
168C32×Q8—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177#634—22no—
178#634—22no—
179#634SD1614yescomplemented
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12#4112yes—
184C3×C4×D3—42no—
185C3×Dic6—42no—
186#627—44no—
187D3×Dic3—44no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192D4×Q8—91no—
193#487—91no—
194#487—92no—
195#475—31no—
196#475—92no—
197#461—92no—
198#461—91no—
199C8×Q8—91no—
200C4×SD16—31no—
201C4×SD16—92no—
202C2×C3×Q8—21no—
203C2×C3×Q8—61no—
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×Q8C22×D311yescharacteristic
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—124no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—61no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—124no—
223C3×SD16—62no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—61no—
237C3×C42—22no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#215—22no—
245#214—64no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—21no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—61no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3C22×D312yes—
259C4⋊Dic3C22×D311yescharacteristic
260Dic3⋊C4—32no—
261Dic3⋊C4—32no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—32no—
275C4×Dic3—32no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—64no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D312yes—
283#204—64no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×SD1612yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—42no—
296C3⋊Dic3C2×SD1614yes—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C22×Q8—181no—
300C2×SD16—31no—
301C2×SD16—92no—
302C4⋊Q8—31no—
303C4⋊Q8—92no—
304C4⋊Q8—92no—
305C4⋊Q8—91no—
306#125—181no—
307#125—182no—
308C22⋊Q8—182no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×Q8—92no—
312C4×Q8—181no—
313C4×Q8D3211yescharacteristic
314C4×D4—31no—
315C4×D4—92no—
316#106—31no—
317#106—32no—
318C4⋊C8—31no—
319C4⋊C8—92no—
320#103—31no—
321#103—32no—
322#103—92no—
323#103—92no—
324#103—92no—
325#102—31no—
326C4×C8—31no—
327C4×C8—92no—
328C23×C3—61no—
329C22×D3—21no—
330C3×Q8—21no—
331C3×Q8—21no—
332C3×Q8—21no—
333C3×Q8—21no—
334C3×Q8—41no—
335C3×Q8—41no—
336C3×Q8—122no—
337C3×D4—32no—
338C3×D4—61no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—122no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—124no—
369D12—21no—
370D12#23512yes—
371C4×D3—42no—
372C4×D3—124no—
373Dic6—34no—
374Dic6—34no—
375Dic6—42no—
376Dic6—64no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—124no—
384Dic6—124no—
385C3×C8—62no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C22×SD1611yescharacteristic
393C2×C32#57811yescharacteristic
394C3×D3—42no—
395C2×Q8—61no—
396C2×Q8—91no—
397C2×Q8—92no—
398C2×Q8—182no—
399C2×Q8—364no—
400C2×Q8C2×D3211yescharacteristic
401C2×D4—31no—
402C22×C4—61no—
403C22×C4—182no—
404SD16—62no—
405SD16—184no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—32no—
409C4⋊C4—21no—
410C4⋊C4—31no—
411C4⋊C4—32no—
412C4⋊C4—61no—
413C4⋊C4—92no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C2×D3211yescharacteristic
422C22⋊C4—61no—
423C22⋊C4—182no—
424C42—21no—
425C42—92no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—62no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—22no—
435C2×D3—41no—
436C2×D3—41no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—41no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—121no—
450C3×C4—122no—
451C3×C4D3×SD1612yes—
452C3×C4D3×SD1612yes—
453C3×C4C2×#23511yescharacteristic
454C3×C4#100711yescharacteristic
455C3×C4D3×#4111yescharacteristic
456C3×C4#101011yescharacteristic
457Dic3—34no—
458Dic3—34no—
459Dic3—42no—
460Dic3—41no—
461Dic3—64no—
462Dic3—62no—
463Dic3—62no—
464Dic3—122no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468C32#335911yescharacteristic, complemented, Sylow
469C23—61no—
470Q8—21no—
471Q8—21no—
472Q8—94no—
473Q8—122no—
474Q8—182no—
475Q8—182no—
476Q8—364no—
477D4—32no—
478D4—61no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—122no—
486C2×C4—182no—
487C2×C4—364no—
488C2×C4#381111yescharacteristic
489C2×C4#381111yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—61no—
492C8—61no—
493C8—62no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—122no—
498C2×C3#555211yescharacteristic
499C2×C3#563311yescharacteristic
500C2×C3C2×D3×SD1611yescharacteristic
501C2×C3C2×D3×SD1611yescharacteristic
502C2×C3#577111yescharacteristic
503C2×C3#577911yescharacteristic
504D3—42no—
505C22—62no—
506C22—121no—
507C22—121no—
508C22C2×#381111yescharacteristic
509C4—21no—
510C4—41no—
511C4—41no—
512C4—94no—
513C4—121no—
514C4—122no—
515C4—182no—
516C4—362no—
517C4#6394012yes—
518C4#6429711yescharacteristic
519C4D3×#23511yescharacteristic
520C3—21no—
521C3#7961911yescharacteristic, complemented
522C3#8103711yescharacteristic, complemented
523C2—122no—
524C2#1059491611yescharacteristic
525C2C2×#6394011yescharacteristic
526C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
4. C3×#5020C2semidirect
6. #10591538C2semidirect
8. #10590431C2semidirect
10. #10590288C2semidirect
11. #10590254C2semidirect
53. #5020D3semidirect
179. #634SD16semidirect
468. C32#3359semidirect
521. C3#79619semidirect
522. C3#81037semidirect

Maximal subgroups

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

subgroupindex
#105960382
#105939042
C3×C4×#2152
C3×#50202
#105915692
#105915382
#105904602
#105904312
#105903652
#105902882
#105902542
#810373
#796193