Finite Group Databasebeta

← #11887669

Subgroups — #11887669

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#10596050C211yesmaximal, characteristic
2#10593903C211yesmaximal, characteristic
3C3×#5031C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591654C212yesmaximal, complemented
6#10591601C212yesmaximal, complemented
7#10590601C212yesmaximal, complemented
8#10590528C212yesmaximal, complemented
9#10590327C211yesmaximal, characteristic
10#10590287C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#80491—31nomaximal
13#79735—31nomaximal
14C2×#3797C2212yes—
15C32×C4×Q8C2211yescharacteristic
16#64155C2212yes—
17#64105—22no—
18C4⋊C4×C3⋊D3C2212yes—
19C4×C4⋊(C3⋊D3)—21no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21#64079—21no—
22#64078C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2212yes—
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918—21no—
28#63895—22no—
29#63894—21no—
30#63871C2212yes—
31C2×#3710C2212yes—
32C3×#835C2211yescharacteristic
33C3×#810C2212yes—
34C3×#810C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63566C2212yes—
42#63557C2212yes—
43#5727—31no—
44#5579—31no—
45#5579—31no—
46#5579—61no—
47Q8×D12—31no—
48C3×#462—31no—
49C3×C4×Q16—31no—
50#5188—32no—
51#5186—32no—
52#5186—32no—
53#5079—31no—
54#5031D311yescharacteristic, complemented
55C4×#216D311yescharacteristic, complemented
56#5021—31no—
57#4884—32no—
58#4850—31no—
59#4834—31no—
60#4813—32no—
61#4811—32no—
62D3×#103—32no—
63D3×#103—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2312yes—
70C2×#634—21no—
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75#3797—24no—
76#3797—42no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3752—22no—
82#3752D412yes—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)D411yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87#3750—22no—
88C3×#216—22no—
89C3×#216—42no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98Dic3⋊Dic3—22no—
99#3722—22no—
100#3710—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C2×D3×Q8—32no—
104C2×C3×Q16—31no—
105C2×C3×Q16—32no—
106C3×C4⋊Q8—31no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×Q8C2×D311yescharacteristic
111#946—32no—
112#946—32no—
113#946—32no—
114#946—62no—
115C2×#216C2×D311yescharacteristic
116C2×#216C2×D312yes—
117C2×D3×C8—32no—
118C2×D3×C8—32no—
119#897—32no—
120#897—62no—
121#896—62no—
122#896—62no—
123#896—62no—
124#896—64no—
125#893—61no—
126D3×C4⋊C4—32no—
127D3×C4⋊C4—32no—
128D3×C4⋊C4—62no—
129#888—61no—
130C4×D12—31no—
131C4×D12—31no—
132C4×D12—61no—
133C4×D12—61no—
134C4×D12—61no—
135C4×D12—61no—
136C4×D12—62no—
137#870—61no—
138#870—61no—
139#870—62no—
140#869—31no—
141#869—31no—
142#869—61no—
143#869—61no—
144#869C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C3×#107—31no—
147C3×C4⋊C8—31no—
148C3×#103—31no—
149C3×#103—31no—
150C3×#103—32no—
151C3×C4×C8—31no—
152#835—32no—
153#835—32no—
154#835—32no—
155#835C2×D311yescharacteristic
156(C2×D3)⋊C8—32no—
157(C2×D3)⋊C8—32no—
158#818—32no—
159#816—32no—
160#816—32no—
161#816—32no—
162#810C2×D312yes—
163#810C2×D311yescharacteristic
164#807—32no—
165#807C2×D311yescharacteristic
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C4×C3⋊C8C2×D311yescharacteristic
168C22×C3⋊D3C2×D412yes—
169C32×Q8—21no—
170C32×Q8—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×D412yes—
178C4⋊(C3⋊D3)Q1614yescomplemented
179C4×C3⋊D3—22no—
180C4×C3⋊D3—22no—
181C4×C3⋊D3—82no—
182#634—81no—
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—91no—
198#484—92no—
199#477—91no—
200#467—92no—
201#462—31no—
202#451—92no—
203C4×Q16—31no—
204C8×D4—91no—
205C2×#103—92no—
206C2×C3×Q8—21no—
207C2×C3×Q8—31no—
208C2×C3×Q8—32no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C22×D311yescharacteristic
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—62no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—61no—
230C2×Dic6—61no—
231C2×Dic6C22×D312yes—
232C2×Dic6C22×D311yescharacteristic
233C3×Q16—62no—
234C3×Q16—122no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8—32no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4C22×D311yescharacteristic
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C42—22no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—61no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#216—22no—
256#216—42no—
257(C2×D3)⋊C4—32no—
258(C2×D3)⋊C4—32no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3C22×D311yescharacteristic
278Dic3⋊C4—21no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286C4×Dic3—21no—
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D312yes—
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—41no—
298C32×C4—41no—
299C32×C4C2×Q1612yes—
300C32×C4C2×#4111yescharacteristic
301C32×C4H(5,𝔽2)11yescharacteristic
302C3⋊Dic3—22no—
303C3⋊Dic3—42no—
304C3×Dic3—22no—
305C3×Dic3—42no—
306C3×Dic3—41no—
307C22×Q8—92no—
308C2×Q16—31no—
309C2×Q16—32no—
310C22×C8—92no—
311C4⋊Q8—31no—
312C4⋊Q8—91no—
313C4⋊Q8—181no—
314#125—181no—
315C22⋊Q8—92no—
316C22⋊Q8—92no—
317C22⋊Q8—182no—
318C22⋊Q8—182no—
319C4×Q8—31no—
320C4×Q8D3211yescharacteristic
321C4×D4—91no—
322C4×D4—181no—
323C4×D4—181no—
324C2×C4⋊C4—92no—
325#107—31no—
326#107—92no—
327C4⋊C8—31no—
328#103—31no—
329#103—31no—
330#103—32no—
331#103—92no—
332#103—92no—
333#103—92no—
334C22⋊C8—92no—
335C4×C8—31no—
336C22×D3—32no—
337C22×D3—32no—
338C22×D3—62no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—32no—
344C3×Q8—41no—
345C3×Q8—41no—
346C3×Q8—61no—
347C3×Q8—62no—
348C3×Q8—62no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—22no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—62no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376D12—34no—
377D12—34no—
378D12—64no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—122no—
384C4×D3—122no—
385C4×D3—124no—
386C4×D3—124no—
387C4×D3—242no—
388C4×D3—242no—
389C4×D3—244no—
390Dic6—21no—
391Dic6—22no—
392Dic6—22no—
393Dic6—124no—
394Dic6—124no—
395Dic6—241no—
396Dic6—241no—
397Dic6—242no—
398Dic6#23512yes—
399C3×C8—61no—
400C3×C8—61no—
401C3×C8—62no—
402C3⋊C8—21no—
403C3⋊C8—22no—
404C3⋊C8—21no—
405C2×C32#54611yescharacteristic
406C2×C32C22×Q1611yescharacteristic
407C2×C32#57711yescharacteristic
408C3⋊D3—24no—
409C2×Q8—31no—
410C2×Q8—32no—
411C2×Q8—182no—
412C2×Q8—181no—
413C2×Q8—184no—
414C2×Q8—362no—
415C2×Q8C2×D3211yescharacteristic
416C2×D4—91no—
417C22×C4—92no—
418C22×C4—182no—
419C22×C4—182no—
420Q16—62no—
421Q16—122no—
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—92no—
433C4⋊C4—182no—
434C4⋊C4—182no—
435C4⋊C4—182no—
436C4⋊C4—181no—
437C4⋊C4C2×D3211yescharacteristic
438C22⋊C4—92no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C42—21no—
442C42—61no—
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—42no—
463C3×C4—42no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—62no—
469C3×C4—121no—
470C3×C4—122no—
471C3×C4D3×Q1612yes—
472C3×C4D3×Q1612yes—
473C3×C4C2×#23511yescharacteristic
474C3×C4#100411yescharacteristic
475C3×C4D3×#4111yescharacteristic
476C3×C4#100911yescharacteristic
477Dic3—22no—
478Dic3—41no—
479Dic3—42no—
480Dic3—62no—
481Dic3—62no—
482Dic3—122no—
483Dic3—124no—
484Dic3—122no—
485Dic3—122no—
486C32#329911yescharacteristic, complemented, Sylow
487C23—92no—
488Q8—21no—
489Q8—21no—
490Q8—32no—
491Q8—61no—
492Q8—62no—
493Q8—62no—
494Q8—364no—
495Q8—721no—
496D4—94no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
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#555011yescharacteristic
518C2×C3#561211yescharacteristic
519C2×C3C2×D3×Q1611yescharacteristic
520C2×C3C2×D3×Q1611yescharacteristic
521C2×C3#577011yescharacteristic
522C2×C3#577811yescharacteristic
523D3—64no—
524D3—64no—
525D3—124no—
526C22—94no—
527C22—182no—
528C22—182no—
529C22C2×#381111yescharacteristic
530C4—21no—
531C4—41no—
532C4—41no—
533C4—62no—
534C4—122no—
535C4—121no—
536C4—182no—
537C4—362no—
538C4#6394412yes—
539C4D3×#23511yescharacteristic
540C4#6430711yescharacteristic
541C3—21no—
542C3#7973511yescharacteristic, complemented
543C3#8049111yescharacteristic, complemented
544C2—184no—
545C2#1059507811yescharacteristic
546C2C2×#6394411yescharacteristic
547C2#1059547311yescharacteristic
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×#5031C2semidirect
4. C3×C4×#216C2semidirect
5. #10591654C2semidirect
6. #10591601C2semidirect
7. #10590601C2semidirect
8. #10590528C2semidirect
10. #10590287C2semidirect
11. #10590283C2semidirect
54. #5031D3semidirect
55. C4×#216D3semidirect
178. C4⋊(C3⋊D3)Q16semidirect
486. C32#3299semidirect
542. C3#79735semidirect
543. C3#80491semidirect

Maximal subgroups

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

subgroupindex
#105960502
#105939032
C3×#50312
C3×C4×#2162
#105916542
#105916012
#105906012
#105905282
#105903272
#105902872
#105902832
#804913
#797353