Finite Group Databasebeta

← #11887663

Subgroups — #11887663

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic
2#10593903C211yesmaximal, characteristic
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5#10590605C212yesmaximal, complemented
6#10590601C212yesmaximal, complemented
7#10590528C212yesmaximal, complemented
8#10590525C212yesmaximal, complemented
9#10590388C211yesmaximal, characteristic, complemented
10C4×#3719C211yesmaximal, characteristic, complemented
11#10590327C211yesmaximal, characteristic
12#81613—31nomaximal
13#81119—31nomaximal
14C2×#3797C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16#64155—22no—
17#64106C2212yes—
18#64102—21no—
19C4⋊C4×C3⋊D3C2212yes—
20#64099—21no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63895—22no—
27#63894—21no—
28#63871C2212yes—
29C2×#3719C2211yescharacteristic
30C2×#3719C2212yes—
31C2×#3710C2212yes—
32C3×#810C2212yes—
33C3×#810C2212yes—
34C3×#810C2212yes—
35C3×#807C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2212yes—
41#63566C2211yescharacteristic
42#63557C2212yes—
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5727—31no—
47Q8×D12—31no—
48C3×#487—31no—
49C3×#477—31no—
50#5093D311yescharacteristic, complemented
51#5091D311yescharacteristic, complemented
52#5090—31no—
53C4×#216—31no—
54#4887—32no—
55#4884—32no—
56#4849—31no—
57#4834—31no—
58#4813—32no—
59#4811—32no—
60#4809—32no—
61#4809—32no—
62D3×#103—32no—
63D3×#103—32no—
64C4×Dic12—31no—
65C8×D12—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75#3797—24no—
76#3797—42no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80#3752—22no—
81#3752D412yes—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86#3750—22no—
87C4×C3⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3719—22no—
99#3719—42no—
100#3710—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C2×D3×Q8—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8—31no—
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×C4⋊Q8C2×D311yescharacteristic
108C3×C4×Q8—31no—
109#946—32no—
110#946—62no—
111#946—62no—
112#946—64no—
113C2×#216—31no—
114C2×#216—32no—
115C2×Dic12—31no—
116C2×Dic12—32no—
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119#897—32no—
120#897—32no—
121#897—32no—
122#897—62no—
123#897—62no—
124#896—62no—
125#893—61no—
126#893—61no—
127#893—61no—
128#893—62no—
129D3×C4⋊C4—32no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—62no—
132#890—61no—
133#890—61no—
134#890—62no—
135#888—61no—
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—61no—
139C4×D12—61no—
140#869—61no—
141#869C2×D311yescharacteristic
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C3×#107—32no—
147C3×C4⋊C8—31no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×C4×C8—31no—
152#835—31no—
153#835—32no—
154(C2×D3)⋊C8—32no—
155(C2×D3)⋊C8—32no—
156#818—31no—
157#816—32no—
158#816—31no—
159#816—31no—
160#810—31no—
161#810C2×D312yes—
162#810C2×D312yes—
163#810C2×D312yes—
164#807—31no—
165#807C2×D312yes—
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C4×C3⋊C8C2×D311yescharacteristic
168C22×C3⋊D3C2×D412yes—
169C32×Q8—81no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3C2×D412yes—
177C4⋊(C3⋊D3)Q1614yescomplemented
178C4×C3⋊D3—22no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3—82no—
181#634—21no—
182#634—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×Dic6#4112yes—
190#627—44no—
191#624—44no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195#554—91no—
196D4×Q8—91no—
197#487—31no—
198#484—92no—
199#477—31no—
200#467—92no—
201#462—91no—
202#451—92no—
203C4×Q16—91no—
204C8×D4—91no—
205C2×#103—92no—
206C2×C3×Q8—22no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211D3×Q8—64no—
212D3×Q8—64no—
213D3×Q8—122no—
214D3×Q8—122no—
215C2×D12—31no—
216C2×D12—31no—
217C2×D12—61no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—64no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6C22×D312yes—
232C2×Dic6C22×D311yescharacteristic
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C2×C3×C8—31no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C22×D312yes—
246C3×C42—21no—
247C3×C42—61no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#216—62no—
251#216—122no—
252(C2×D3)⋊C4—32no—
253(C2×D3)⋊C4—32no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—64no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3—64no—
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—21no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278Dic3⋊C4—64no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281C4×Dic3—21no—
282C4×Dic3—62no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D312yes—
288Dic12—62no—
289Dic12—122no—
290D3×C8—122no—
291D3×C8—122no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—22no—
294C2×C3⋊D3—22no—
295C2×C3⋊D3C2×Q1614yes—
296C32×C4—21no—
297C32×C4—42no—
298C32×C4C2×Q1612yes—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3×Dic3—22no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C22×Q8—92no—
308C2×Q16—91no—
309C2×Q16—92no—
310C22×C8—92no—
311C4⋊Q8—31no—
312C4⋊Q8—181no—
313C4⋊Q8D3211yescharacteristic
314#125—181no—
315C22⋊Q8—92no—
316C22⋊Q8—92no—
317C22⋊Q8—182no—
318C22⋊Q8—182no—
319C4×Q8—31no—
320C4×Q8—91no—
321C4×D4—91no—
322C4×D4—181no—
323C4×D4—181no—
324C2×C4⋊C4—92no—
325#107—32no—
326#107—91no—
327C4⋊C8—31no—
328#103—32no—
329#103—32no—
330#103—32no—
331#103—91no—
332#103—91no—
333#103—92no—
334C22⋊C8—92no—
335C4×C8—31no—
336C22×D3—32no—
337C22×D3—32no—
338C22×D3—62no—
339C3×Q8—32no—
340C3×Q8—61no—
341C3×Q8—62no—
342C3×Q8—62no—
343C3×Q8—81no—
344C3×Q8—81no—
345C3×Q8—82no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—61no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373D12—34no—
374D12—34no—
375D12—64no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—124no—
383C4×D3—124no—
384C4×D3—242no—
385C4×D3—242no—
386C4×D3—244no—
387Dic6—21no—
388Dic6—22no—
389Dic6—22no—
390Dic6—61no—
391Dic6—61no—
392Dic6—61no—
393Dic6—61no—
394Dic6—121no—
395Dic6—121no—
396Dic6—124no—
397Dic6—124no—
398Dic6#23912yes—
399C3×C8—61no—
400C3×C8—61no—
401C3×C8—62no—
402C3⋊C8—21no—
403C3⋊C8—21no—
404C3⋊C8—22no—
405C2×C32#54611yescharacteristic
406C2×C32C22×Q1611yescharacteristic
407C2×C32#57711yescharacteristic
408C3⋊D3—24no—
409C2×Q8—21no—
410C2×Q8—31no—
411C2×Q8—32no—
412C2×Q8—91no—
413C2×Q8—182no—
414C2×Q8—184no—
415C2×Q8—362no—
416C2×D4—91no—
417C22×C4—92no—
418C22×C4—182no—
419C22×C4—182no—
420Q16—182no—
421Q16—362no—
422C2×C8—31no—
423C2×C8—31no—
424C2×C8—32no—
425C2×C8—362no—
426C4⋊C4—21no—
427C4⋊C4—31no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4—91no—
432C4⋊C4—91no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C4⋊C4—182no—
436C4⋊C4—181no—
437C4⋊C4C2×D3212yes—
438C22⋊C4—92no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C42—61no—
442C42—181no—
443C42C2×D3211yescharacteristic
444C22×C3—21no—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
447C2×D3—34no—
448C2×D3—34no—
449C2×D3—64no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—122no—
455C2×D3—122no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—44no—
463C3×C4—42no—
464C3×C4—42no—
465C3×C4—62no—
466C3×C4—121no—
467C3×C4—122no—
468C3×C4D3×Q1612yes—
469C3×C4D3×Q1612yes—
470C3×C4C2×#23911yescharacteristic
471C3×C4D3×#4111yescharacteristic
472C3×C4#100911yescharacteristic
473C3×C4#100911yescharacteristic
474Dic3—22no—
475Dic3—42no—
476Dic3—41no—
477Dic3—62no—
478Dic3—62no—
479Dic3—122no—
480Dic3—122no—
481Dic3—122no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486C32#329911yescharacteristic, complemented, Sylow
487C23—92no—
488Q8—32no—
489Q8—61no—
490Q8—62no—
491Q8—62no—
492Q8—81no—
493Q8—181no—
494Q8—181no—
495Q8—364no—
496D4—94no—
497C2×C4—22no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—92no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—364no—
507C2×C4—722no—
508C2×C4#381111yescharacteristic
509C2×C4#381111yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—61no—
512C8—61no—
513C8—62no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3#563011yescharacteristic
518C2×C3#567611yescharacteristic
519C2×C3#576211yescharacteristic
520C2×C3C2×D3×Q1611yescharacteristic
521C2×C3C2×D3×Q1611yescharacteristic
522C2×C3#577511yescharacteristic
523D3—64no—
524D3—64no—
525D3—124no—
526C22—94no—
527C22—182no—
528C22—182no—
529C22C2×#381111yescharacteristic
530C4—21no—
531C4—42no—
532C4—62no—
533C4—121no—
534C4—122no—
535C4—182no—
536C4—361no—
537C4—361no—
538C4#6394412yes—
539C4D3×#23911yescharacteristic
540C4#6432011yescharacteristic
541C3—21no—
542C3#8111911yescharacteristic, complemented
543C3#8161311yescharacteristic, complemented
544C2—184no—
545C2#1059511511yescharacteristic
546C2C2×#6394411yescharacteristic
547C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊Q8D32
hypocenterC32#3299
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
3. C3×#5093C2semidirect
4. C3×#5091C2semidirect
5. #10590605C2semidirect
6. #10590601C2semidirect
7. #10590528C2semidirect
8. #10590525C2semidirect
9. #10590388C2semidirect
10. C4×#3719C2semidirect
50. #5093D3semidirect
51. #5091D3semidirect
177. C4⋊(C3⋊D3)Q16semidirect
486. C32#3299semidirect
542. C3#81119semidirect
543. C3#81613semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105939032
C3×#50932
C3×#50912
#105906052
#105906012
#105905282
#105905252
#105903882
C4×#37192
#105903272
#816133
#811193