Finite Group Databasebeta

← #11897659

Subgroups — #11897659

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic
3C3×C4×#215C211yesmaximal, characteristic
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591615C212yesmaximal, complemented
6#10591572C212yesmaximal
7#10590546C212yesmaximal, complemented
8#10590471C212yesmaximal
9#10590311C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic
12#81137—31nomaximal
13#79634—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16#64097—22no—
17#64097C2212yes—
18#64078—21no—
19#64078C2211yescharacteristic
20C4×#634—21no—
21C4×#634C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C3×#835C2212yes—
31C3×#835C2211yescharacteristic
32C3×#809C2211yescharacteristic
33C3×#808C2211yescharacteristic
34C3×#807C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63575C2212yes—
39#63573C2212yes—
40#63572C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5730—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46Q8×Dic6—61no—
47#5543—31no—
48C3×#477—31no—
49C3×C4×SD16—31no—
50#5164—32no—
51#5078—31no—
52C4×#215D311yescharacteristic
53#5021D311yescharacteristic, complemented
54#5008—31no—
55#4890—32no—
56#4876—32no—
57#4856—32no—
58#4842—31no—
59#4831—31no—
60#4817—32no—
61#4799—32no—
62#4796—32no—
63#4759—32no—
64#4682—31no—
65#4679—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×#634—22no—
69C2×#634D411yescharacteristic
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3C2312yes—
86C3×#215Q814yescomplemented
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3385—91noSylow
98C2×C3×SD16—31no—
99C3×C4⋊Q8—31no—
100C3×C4×Q8—21no—
101C3×C4×Q8C2×D311yescharacteristic
102C3×C4×Q8C2×D311yescharacteristic
103C3×C4×D4—31no—
104#946—62no—
105Q8×Dic3—32no—
106Q8×Dic3—32no—
107Q8×Dic3—62no—
108C2×#215C2×D311yescharacteristic
109D4×Dic3—32no—
110C2×C4⋊Dic3—61no—
111#924—61no—
112#897—61no—
113#893—32no—
114D3×C4⋊C4—61no—
115#890—32no—
116#890—32no—
117#888—32no—
118#888—32no—
119#888—62no—
120#888—62no—
121#888—62no—
122#888—64no—
123#878—62no—
124C4×D12C2×D311yescharacteristic
125#869—31no—
126#869—31no—
127#869—61no—
128#869—61no—
129#869—61no—
130#869—62no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6—61no—
136C4×Dic6—61no—
137C4×Dic6—62no—
138C3×#107—32no—
139C3×#106—31no—
140C3×C4⋊C8—31no—
141C3×#103—31no—
142C3×#103—32no—
143C3×#102—31no—
144C3×C4×C8—31no—
145#835C2×D312yes—
146#835C2×D311yescharacteristic
147#832—32no—
148#821—32no—
149#818—32no—
150#818—32no—
151#817—32no—
152#815—32no—
153#815—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—32no—
156#809C2×D311yescharacteristic
157#808—32no—
158#808C2×D311yescharacteristic
159#807—32no—
160#807—32no—
161#807C2×D312yes—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3×D3—21no—
165C32×Q8—21no—
166C32×Q8C2×Q812yes—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175#634—22no—
176#634—82no—
177#634—81no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—21no—
180C3×D12—21no—
181C3×D12C2×Q812yes—
182C3×C4×D3—42no—
183C3×Dic6—81no—
184D3×Dic3—82no—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C2×Q812yes—
188Q82—91no—
189#554—91no—
190#501—92no—
191#500—91no—
192#479—92no—
193#477—31no—
194#476—91no—
195#474—92no—
196#446—91no—
197#440—92no—
198C4×SD16—31no—
199C2×C3×Q8—21no—
200C2×C3×Q8—61no—
201C2×C3×Q8C22×D311yescharacteristic
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C22×Dic3—62no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—21no—
208C2×C4×D3—62no—
209C2×Dic6—21no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—61no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—64no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C3×SD16—34no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8—32no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4C22×D311yescharacteristic
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C22⋊C4—61no—
233C3×C42—22no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—62no—
240#215Dic614yescomplemented
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3—64no—
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—64no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—64no—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D312yes—
276C2×C3⋊C8C22×D311yescharacteristic
277C22×C32C22×D411yescharacteristic
278C2×C3×D3—22no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4—22no—
282C32×C4—21no—
283C32×C4—41no—
284C32×C4#13712yes—
285C32×C4C22×Q811yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—22no—
288C3⋊Dic3—22no—
289C3⋊Dic3—42no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C2×SD16—31no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—91no—
296C4⋊Q8—181no—
297C4⋊Q8—182no—
298#125—92no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—91no—
302C4×Q8—92no—
303C4×Q8—181no—
304C4×Q8D3211yescharacteristic
305C4×D4—31no—
306C4×D4—92no—
307C2×C4⋊C4—181no—
308#107—32no—
309#107—92no—
310#107—92no—
311#106—31no—
312#106—92no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315#103—31no—
316#103—32no—
317#102—31no—
318#102—92no—
319#97—92no—
320C4×C8—31no—
321C23×C3—61no—
322C22×D3—21no—
323C3×Q8—22no—
324C3×Q8—21no—
325C3×Q8—21no—
326C3×Q8—22no—
327C3×Q8—241no—
328C3×Q8C2×Dic612yes—
329C3×Q8D3×Q812yes—
330C3×D4—32no—
331C3×D4—61no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—122no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—242no—
362D12—21no—
363D12C2×Dic612yes—
364C4×D3—42no—
365C4×D3—242no—
366Dic6—64no—
367Dic6—62no—
368Dic6—62no—
369Dic6—81no—
370Dic6—242no—
371Dic6—242no—
372Dic6—241no—
373Dic6—241no—
374Dic6—242no—
375Dic6—244no—
376C3×C8—32no—
377C3×C8—61no—
378C3×C8—62no—
379C3⋊C8—22no—
380C3⋊C8—21no—
381C3⋊C8C2×Dic612yes—
382C2×C32D4×Q811yescharacteristic
383C2×C32C2×#13711yescharacteristic
384C2×C32#57611yescharacteristic
385C3×D3—42no—
386C2×Q8—61no—
387C2×Q8—91no—
388C2×Q8—182no—
389C2×Q8—181no—
390C2×Q8C2×D3211yescharacteristic
391C2×D4—31no—
392C22×C4—61no—
393C22×C4—182no—
394SD16—34no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—32no—
398C4⋊C4—21no—
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—61no—
402C4⋊C4—91no—
403C4⋊C4—92no—
404C4⋊C4—92no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—181no—
410C4⋊C4C2×D3211yescharacteristic
411C22⋊C4—61no—
412C22⋊C4—182no—
413C42—21no—
414C42—92no—
415C42—182no—
416C42C2×D3211yescharacteristic
417C22×C3—21no—
418C22×C3—62no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—22no—
424C2×D3—41no—
425C2×D3—41no—
426C3×C4—24no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—41no—
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—121no—
439C3×C4—122no—
440C3×C4#91512yes—
441C3×C4#91812yes—
442C3×C4C22×Dic611yescharacteristic
443C3×C4C2×D3×Q811yescharacteristic
444C3×C4#101011yescharacteristic
445C3×C4#101011yescharacteristic
446Dic3—41no—
447Dic3—42no—
448Dic3—64no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—122no—
454Dic3—124no—
455Dic3—122no—
456Dic3—122no—
457C32#338511yescharacteristic, complemented, Sylow
458C23—61no—
459Q8—21no—
460Q8—182no—
461Q8—241no—
462Q8—721no—
463Q8—722no—
464Q8D3×Dic612yes—
465D4—32no—
466D4—61no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—61no—
470C2×C4—62no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—122no—
474C2×C4—182no—
475C2×C4—722no—
476C2×C4#381111yescharacteristic
477C2×C4#381111yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—32no—
480C8—61no—
481C8—62no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—122no—
486C2×C3D4×Dic611yescharacteristic
487C2×C3#563211yescharacteristic
488C2×C3C2×#91511yescharacteristic
489C2×C3C2×#91811yescharacteristic
490C2×C3#576911yescharacteristic
491C2×C3#577411yescharacteristic
492D3—42no—
493C22—62no—
494C22—121no—
495C22—121no—
496C22C2×#381111yescharacteristic
497C4—22no—
498C4—21no—
499C4—41no—
500C4—121no—
501C4—122no—
502C4—182no—
503C4—182no—
504C4—362no—
505C4#6395112yes—
506C4C2×D3×Dic611yescharacteristic
507C4#6429811yescharacteristic
508C3—21no—
509C3#7963411yescharacteristic, complemented
510C3#8113711yescharacteristic, complemented
511C2—122no—
512C2#1059491511yescharacteristic
513C2C2×#6395111yescharacteristic
514C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4×Q8D32
hypocenterC32#3385
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. Q8×#634C2semidirect
4. C3×#5021C2semidirect
5. #10591615C2semidirect
7. #10590546C2semidirect
9. #10590311C2semidirect
10. #10590296C2semidirect
53. #5021D3semidirect
86. C3×#215Q8semidirect
240. #215Dic6semidirect
457. C32#3385semidirect
509. C3#79634semidirect
510. C3#81137semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
#105939562
C3×C4×#2152
C3×#50212
#105916152
#105915722
#105905462
#105904712
#105903112
#105902962
#105902682
#811373
#796343