Finite Group Databasebeta

← #11874308

Subgroups — #11874308

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3#10595029C212yesmaximal, complemented
4C2×#63829C212yesmaximal, complemented
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6#10590896C211yesmaximal, characteristic, complemented
7#10590880C211yesmaximal, characteristic, complemented
8#10590877C212yesmaximal, complemented
9#10590865C211yesmaximal, characteristic, complemented
10#10590864C211yesmaximal, characteristic, complemented
11#10590862C212yesmaximal, complemented
12#83903—31nomaximal
13#78467—31nomaximal
14C2×#3828C2212yes—
15C2×C3×#235C2212yes—
16C22×C32×C8C2211yescharacteristic
17C2×#3746C2211yescharacteristic
18#64113—24no—
19C2×#3745C2211yescharacteristic
20C2×#3744C2212yes—
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C3×#904—24no—
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2212yes—
27#63978—24no—
28#63911C2212yes—
29C4×#626—24no—
30#63866C2212yes—
31#63864C2212yes—
32#63860C2212yes—
33C2×#3719C2212yes—
34C2×#3717C2212yes—
35#63829—28no—
36C2×#3716C2212yes—
37C2×#3714C2212yes—
38C3×C8×Dic3C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40C3×C8×Dic3C2211yescharacteristic
41C3×C8×Dic3C2211yescharacteristic
42C2×C3×#135—31no—
43#5832—32no—
44C2×#950—32no—
45C2×#904—32no—
46C2×#904—31no—
47C2×#904—31no—
48C2×#904—61no—
49C2×#904D311yescharacteristic, complemented
50#5477—32no—
51C2×C3×C4×C8—31no—
52#5191—31no—
53#5183—31no—
54#5175—32no—
55#5168—32no—
56#5155—31no—
57#5151—31no—
58C2×C8×Dic3D311yescharacteristic, complemented
59#4699—31no—
60#4696—31no—
61#4696—31no—
62#4696—32no—
63#4695—31no—
64#4693—32no—
65C22×C32×C4C2311yescharacteristic
66C2×#638—22no—
67#3828—24no—
68#3828—24no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3—22no—
71C2×#634C2312yes—
72C2×C3×#67—22no—
73C22×C3×Dic3D412yes—
74C3×#235—24no—
75C3×#235—24no—
76C2×C3×D12C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×Dic6C2312yes—
79C2×#626—24no—
80C2×C32×C8D414yescomplemented
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83#3746—22no—
84#3745—22no—
85#3744—24no—
86C3×C4×Dic3D412yes—
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8D414yescomplemented
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×D24—22no—
94C3×#204—24no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97(C2×D3)⋊Dic3—24no—
98#3719—24no—
99#3717—24no—
100#3716—24no—
101#3714—24no—
102#3147—91noSylow
103C2×C3×#41—32no—
104C2×#235—32no—
105C2×#235—32no—
106C2×#235—62no—
107C2×#235C2×D312yes—
108C3×#135—64no—
109C2×C3×Q16—31no—
110C2×C3×SD16—32no—
111C2×C3×D8—31no—
112C22×C3×C8—21no—
113C22×C3×C8—31no—
114C22×C3×C8C2×D311yescharacteristic
115C22×C3×C8C2×D311yescharacteristic
116C2×C3×C42—31no—
117#950—68no—
118#947—32no—
119#944—32no—
120C2×#216—32no—
121C2×#215—32no—
122#940—32no—
123#939—64no—
124#936—32no—
125C2×#214—32no—
126C2×#213—32no—
127#930—64no—
128C4×#67—64no—
129C2×C4×Dic3C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131C2×Dic12—32no—
132C2×Dic12—31no—
133C2×Dic12—31no—
134C2×Dic12—61no—
135C2×Dic12C2×D311yescharacteristic
136#904—24no—
137#904—68no—
138#904—68no—
139#904—64no—
140#904—64no—
141C2×D24—32no—
142C2×D24—31no—
143C2×D24—31no—
144C2×D24—61no—
145C2×D24C2×D311yescharacteristic
146C2×#204—32no—
147C2×#204—32no—
148C2×#204—32no—
149C2×#204—32no—
150C2×#204—62no—
151C2×#204C2×D312yes—
152#875—32no—
153#875—32no—
154#874—32no—
155C4×D12—64no—
156#869—32no—
157C3×C4×C8—31no—
158C3×C4×C8—31no—
159C3×C4×C8—31no—
160C3×C4×C8—31no—
161C8×Dic3C2×D311yescharacteristic
162C8×Dic3C2×D311yescharacteristic
163C8×Dic3C2×D311yescharacteristic
164C8×Dic3C2×D311yescharacteristic
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3×D3—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2411yescharacteristic
172#638—44no—
173C2×C3⋊Dic3—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4×C3⋊D3—44no—
177#634—22no—
178#634—22no—
179C3×#67—44no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×D12—22no—
185C3×D12—22no—
186C3×C4×D3—44no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189#626—48no—
190C32×C8C2×D412yes—
191C32×C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C3×C3⋊C8C2×D412yes—
194C2×#135—31no—
195C2×#135—92no—
196C2×#135—91no—
197#532—92no—
198#495—91no—
199#495—92no—
200#495—91no—
201#494—91no—
202#493—91no—
203#492—92no—
204C2×C4×C8—31no—
205C3×#41—64no—
206C3×#41—64no—
207C2×C3×Q8—32no—
208C2×C3×D4—32no—
209C2×C3×D4—62no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4—62no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—22no—
216C2×#67—62no—
217C2×#67—62no—
218C2×#67—64no—
219C2×#67—122no—
220C22×Dic3D1212yes—
221#235—24no—
222#235—24no—
223#235—68no—
224#235—64no—
225#235—64no—
226#235—64no—
227#235—64no—
228#235—124no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—62no—
232C2×D12—64no—
233C2×D12C22×D312yes—
234C2×C4×D3—22no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—122no—
238C2×Dic6—32no—
239C2×Dic6—32no—
240C2×Dic6—62no—
241C2×Dic6C22×D312yes—
242C3×Q16—62no—
243C3×SD16—64no—
244C3×D8—62no—
245C2×C3×C8—24no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—34no—
249C2×C3×C8—31no—
250C2×C3×C8—31no—
251C2×C3×C8D1214yescomplemented
252C2×C3×C8#6714yescomplemented
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C2×C3×C8C22×D311yescharacteristic
257C3×C42—32no—
258C3×C42—31no—
259C3×C42—31no—
260#217—64no—
261#216—64no—
262#215—64no—
263#214—64no—
264#213—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268C4⋊Dic3—64no—
269Dic3⋊C4—64no—
270C4×Dic3D1212yes—
271C4×Dic3C22×D311yescharacteristic
272C4×Dic3C22×D311yescharacteristic
273C2×C3⋊C8D1214yescomplemented
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D311yescharacteristic
276Dic12—22no—
277Dic12—64no—
278Dic12—64no—
279Dic12—62no—
280Dic12—62no—
281D24—22no—
282D24—64no—
283D24—64no—
284D24—62no—
285D24—62no—
286#204—24no—
287#204—68no—
288#204—64no—
289#204—64no—
290#204—64no—
291#204—64no—
292C22×C32—22no—
293C22×C32#12712yes—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—42no—
296C2×C3⋊D3—44no—
297C2×C3×D3—42no—
298C2×C3×D3—44no—
299C32×C4#12712yes—
300C32×C4C22×D411yescharacteristic
301C32×C4C22×D411yescharacteristic
302C3⋊Dic3—42no—
303C3×Dic3—22no—
304C3×Dic3—42no—
305C3×Dic3#13514yescomplemented
306C2×#41—32no—
307C2×#41—92no—
308#135—64no—
309#135—188no—
310#135—184no—
311C2×Q16—31no—
312C2×Q16—92no—
313C2×Q16—91no—
314C2×SD16—32no—
315C2×SD16—92no—
316C2×SD16—92no—
317C2×SD16—92no—
318C2×D8—31no—
319C2×D8—92no—
320C2×D8—91no—
321C22×C8—31no—
322C22×C8D3211yescharacteristic
323C4⋊Q8—92no—
324#127—92no—
325#124—92no—
326#124—92no—
327#121—184no—
328C4×D4—184no—
329C2×C42—31no—
330C4×C8—31no—
331C4×C8—31no—
332C4×C8—31no—
333C4×C8—31no—
334C23×C3—21no—
335C23×C3—62no—
336C23×C3C2×D1211yescharacteristic
337C23×C3D3×D411yescharacteristic
338C22×D3—22no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—122no—
342C3×Q8—62no—
343C3×Q8—62no—
344C3×D4—62no—
345C3×D4—62no—
346C3×D4—124no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—64no—
354C2×C3×C4—62no—
355C2×C3×C4—124no—
356C2×C3×C4C2×D1212yes—
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×D1212yes—
359C2×C3×C4D3×D412yes—
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C2×#6712yes—
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364#67—44no—
365#67—128no—
366#67—124no—
367#67—124no—
368#67—128no—
369C2×Dic3—24no—
370C2×Dic3—22no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3C2×D1212yes—
375C2×Dic3C2×D1212yes—
376D12—22no—
377D12—22no—
378D12—64no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—62no—
383D12—122no—
384D12—128no—
385C4×D3—44no—
386C4×D3—128no—
387C4×D3—124no—
388C4×D3—124no—
389Dic6—22no—
390Dic6—22no—
391Dic6—64no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—122no—
397C3×C8—22no—
398C3×C8—22no—
399C3×C8—32no—
400C3×C8—32no—
401C3×C8C2×D1212yes—
402C3×C8C2×D1212yes—
403C3×C8C2×#6712yes—
404C3×C8C2×#6712yes—
405C3⋊C8C2×D1212yes—
406C3⋊C8C2×D1212yes—
407C2×C32—22no—
408C2×C32C2×#12711yescharacteristic
409C2×C32C2×#13512yes—
410C3⋊D3—82no—
411C3×D3—82no—
412#41—64no—
413#41—64no—
414#41—184no—
415#41—184no—
416C2×Q8—32no—
417C2×Q8—92no—
418C2×D4—32no—
419C2×D4—62no—
420C2×D4—92no—
421C2×D4—184no—
422C2×D4—182no—
423C22×C4—32no—
424C22×C4—62no—
425C22×C4—182no—
426C22×C4C2×D3211yescharacteristic
427Q16—62no—
428Q16—184no—
429Q16—182no—
430SD16—64no—
431SD16—184no—
432SD16—184no—
433SD16—184no—
434D8—62no—
435D8—184no—
436D8—182no—
437C2×C8—31no—
438C2×C8—31no—
439C2×C8—34no—
440C2×C8#62614yescomplemented
441C2×C8C2×D3211yescharacteristic
442C2×C8C2×D3211yescharacteristic
443C4⋊C4—184no—
444C22⋊C4—184no—
445C22⋊C4—184no—
446C42—31no—
447C42—31no—
448C42—32no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—42no—
454C22×C3—122no—
455C22×C3—124no—
456C22×C3#87412yes—
457C22×C3#94012yes—
458C22×C3C22×D1211yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C2×D3—44no—
461C2×D3—42no—
462C2×D3—124no—
463C2×D3—122no—
464C2×D3—124no—
465C2×D3—124no—
466C2×D3—122no—
467C2×D3—244no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—22no—
471C3×C4—34no—
472C3×C4—62no—
473C3×C4—122no—
474C3×C4#87412yes—
475C3×C4#94012yes—
476C3×C4C22×D1211yescharacteristic
477C3×C4C22×D1211yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C22×#6711yescharacteristic
480Dic3—22no—
481Dic3—42no—
482Dic3—124no—
483Dic3—122no—
484Dic3—122no—
485Dic3#90414yescomplemented
486C32#314711yescharacteristic, complemented, Sylow
487C23—62no—
488C23—182no—
489C23D3×D1211yescharacteristic
490Q8—62no—
491Q8—62no—
492Q8—182no—
493Q8—182no—
494D4—62no—
495D4—62no—
496D4—124no—
497D4—182no—
498D4—182no—
499D4—368no—
500D4—364no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—64no—
504C2×C4—62no—
505C2×C4—124no—
506C2×C4—182no—
507C2×C4—364no—
508C2×C4D3×D1212yes—
509C2×C4D3×D1211yescharacteristic
510C2×C4C2×#62612yes—
511C2×C4C22×D3211yescharacteristic
512C8—32no—
513C8—32no—
514C8C2×#62612yes—
515C8C2×#62612yes—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—42no—
521C2×C3—242no—
522C2×C3C2×#87411yescharacteristic
523C2×C3C2×#90412yes—
524C2×C3D3×#13512yes—
525C2×C3C2×#94011yescharacteristic
526D3—82no—
527D3—244no—
528D3—242no—
529D3—242no—
530C22—22no—
531C22—124no—
532C22—122no—
533C22—364no—
534C22—362no—
535C22#6391112yes—
536C22C2×D3×D1211yescharacteristic
537C4—34no—
538C4—62no—
539C4—122no—
540C4—362no—
541C4#6391112yes—
542C4C2×D3×D1211yescharacteristic
543C4C22×#62611yescharacteristic
544C3—21no—
545C3#7846711yescharacteristic, complemented
546C3#8390311yescharacteristic, complemented
547C2—22no—
548C2—242no—
549C2—722no—
550C2D3×#90412yes—
551C2C2×#6391111yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C2×C3×#904C2semidirect
3. #10595029C2semidirect
4. C2×#63829C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. #10590896C2semidirect
7. #10590880C2semidirect
8. #10590877C2semidirect
9. #10590865C2semidirect
10. #10590864C2semidirect
11. #10590862C2semidirect
49. C2×#904D3semidirect
58. C2×C8×Dic3D3semidirect
80. C2×C32×C8D4semidirect
89. C2×C3×C3⋊C8D4semidirect
251. C2×C3×C8D12semidirect
252. C2×C3×C8#67semidirect
273. C2×C3⋊C8D12semidirect
305. C3×Dic3#135semidirect
440. C2×C8#626semidirect
485. Dic3#904semidirect
486. C32#3147semidirect
545. C3#78467semidirect
546. C3#83903semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#9042
#105950292
C2×#638292
C2×C3×C8×Dic32
#105908962
#105908802
#105908772
#105908652
#105908642
#105908622
#839033
#784673