Finite Group Databasebeta

← #11887642

Subgroups — #11887642

Order 1152.

916 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
1Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2#10593958C211yesmaximal, characteristic
3C3×C4×#216C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591603C212yesmaximal, complemented
6#10591552C212yesmaximal, complemented
7#10590525C212yesmaximal, complemented
8#10590444C212yesmaximal, complemented
9#10590385C211yesmaximal, characteristic, complemented
10#10590327C211yesmaximal, characteristic
11#10590288C211yesmaximal, characteristic, complemented
12#81119—31nomaximal
13#79735—31nomaximal
14C2×Q8×C3⋊D3C2212yes—
15C32×C4×Q8C2211yescharacteristic
16#64106—22no—
17#64106C2212yes—
18C4×C4⋊(C3⋊D3)—21no—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64078—21no—
21#64078C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900C2212yes—
26#63894—21no—
27#63888—22no—
28#63871C2212yes—
29#63869—21no—
30C2×#3719C2212yes—
31C2×#3710C2212yes—
32C3×#835C2211yescharacteristic
33C3×#835C2212yes—
34C3×#810C2211yescharacteristic
35C3×#807C2212yes—
36C3×#807C2211yescharacteristic
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63557C2212yes—
43#5730—31no—
44#5579—31no—
45Q8×D12—31no—
46Q8×D12—31no—
47Q8×D12—61no—
48C3×#477—31no—
49C3×C4×Q16—31no—
50#5186—32no—
51#5093—31no—
52#5031—31no—
53C4×#216D311yescharacteristic, complemented
54#5021D311yescharacteristic, complemented
55#4887—32no—
56#4884—32no—
57#4884—32no—
58#4849—31no—
59#4834—31no—
60#4813—32no—
61#4809—32no—
62D3×#103—32no—
63D3×#103—32no—
64C8×D12—31no—
65#4681—31no—
66C2×C32×Q8C2311yescharacteristic
67Q8×C3⋊D3—24no—
68Q8×C3⋊D3—42no—
69C2×C4⋊(C3⋊D3)D411yescharacteristic
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2312yes—
72C2×#634—22no—
73C2×#634C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×#624—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3752—22no—
82#3752D412yes—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C3×#216—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99#3719—42no—
100#3710—42no—
101#3299—91noSylow
102C2×D3×Q8—32no—
103C2×D3×Q8—32no—
104C2×D3×Q8—62no—
105C2×C3×Q16—31no—
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—62no—
113C2×#216—32no—
114C2×#216C2×D311yescharacteristic
115C2×Dic12—32no—
116C2×D3×C8—32no—
117C2×D3×C8—32no—
118#897—32no—
119#897—32no—
120#897—32no—
121#897—62no—
122#897—62no—
123#897—62no—
124#897—64no—
125#896—62no—
126#893—61no—
127D3×C4⋊C4—32no—
128D3×C4⋊C4—32no—
129#890—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#869—31no—
139#869—31no—
140#869—61no—
141#869—61no—
142#869—61no—
143#869—62no—
144#869C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C3×#107—31no—
147C3×#107—32no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#103—32no—
151C3×#103—31no—
152C3×C4×C8—31no—
153#835C2×D312yes—
154#835C2×D311yescharacteristic
155(C2×D3)⋊C8—32no—
156(C2×D3)⋊C8—32no—
157#816—32no—
158#816—32no—
159#816—32no—
160#810—32no—
161#810—32no—
162#810—32no—
163#810C2×D311yescharacteristic
164#807C2×D311yescharacteristic
165#807C2×D312yes—
166C4⋊(C3⋊C8)C2×D311yescharacteristic
167C4×C3⋊C8C2×D311yescharacteristic
168C22×C3⋊D3C2×D412yes—
169C32×Q8—21no—
170C32×Q8#4112yes—
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—44no—
182#634—22no—
183#634—22no—
184#634—44no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C3×Dic6—21no—
189C3×Dic6—21no—
190C3×Dic6—81no—
191#624—82no—
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—31no—
200#467—92no—
201#462—91no—
202#451—92no—
203C4×Q16—31no—
204C8×D4—91no—
205C2×#103—92no—
206C2×C3×Q8—21no—
207C2×C3×Q8—31no—
208C2×C3×Q8—61no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C22×D311yescharacteristic
211D3×Q8—64no—
212D3×Q8—64no—
213D3×Q8—124no—
214D3×Q8—122no—
215D3×Q8—122no—
216D3×Q8—124no—
217C2×D12—31no—
218C2×D12—31no—
219C2×D12—61no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—64no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×Dic6—21no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—62no—
232C2×Dic6—62no—
233C2×Dic6—62no—
234C2×Dic6—64no—
235C2×Dic6C22×D311yescharacteristic
236C3×Q16—62no—
237C2×C3×C8—31no—
238C2×C3×C8—31no—
239C2×C3×C8—32no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C42—22no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—61no—
255C3×C42C22×D311yescharacteristic
256C3×C42C22×D311yescharacteristic
257#216—22no—
258#216—122no—
259(C2×D3)⋊C4—32no—
260(C2×D3)⋊C4—32no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—64no—
267C4⋊Dic3—21no—
268C4⋊Dic3—31no—
269C4⋊Dic3—31no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274C4⋊Dic3—62no—
275C4⋊Dic3—64no—
276C4⋊Dic3—62no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—21no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287C4×Dic3—21no—
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D311yescharacteristic
290C2×C3⋊C8C22×D312yes—
291Dic12—122no—
292D3×C8—122no—
293D3×C8—122no—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—22no—
296C2×C3⋊D3—22no—
297C2×C3⋊D3C2×Q1614yes—
298C32×C4—22no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4C2×Q1612yes—
302C32×C4C2×#4111yescharacteristic
303C32×C4H(5,𝔽2)11yescharacteristic
304C3⋊Dic3—22no—
305C3⋊Dic3—42no—
306C3×Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C22×Q8—92no—
310C2×Q16—31no—
311C2×Q16—92no—
312C22×C8—92no—
313C4⋊Q8—31no—
314C4⋊Q8—91no—
315C4⋊Q8—181no—
316#125—181no—
317C22⋊Q8—92no—
318C22⋊Q8—92no—
319C22⋊Q8—182no—
320C22⋊Q8—182no—
321C4×Q8—31no—
322C4×Q8D3211yescharacteristic
323C4×D4—91no—
324C4×D4—181no—
325C4×D4—181no—
326C2×C4⋊C4—92no—
327#107—31no—
328#107—32no—
329C4⋊C8—31no—
330#103—31no—
331#103—32no—
332#103—31no—
333#103—92no—
334#103—92no—
335#103—92no—
336C22⋊C8—92no—
337C4×C8—31no—
338C22×D3—32no—
339C22×D3—32no—
340C22×D3—62no—
341C3×Q8—22no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—22no—
345C3×Q8—61no—
346C3×Q8—61no—
347C3×Q8—241no—
348C3×Q8#23512yes—
349C3×Q8#23912yes—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—62no—
374C2×Dic3—64no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377D12—34no—
378D12—34no—
379D12—64no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3—124no—
387C4×D3—124no—
388C4×D3—128no—
389C4×D3—242no—
390C4×D3—242no—
391Dic6—21no—
392Dic6—21no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—62no—
397Dic6—81no—
398Dic6—122no—
399Dic6—122no—
400Dic6—124no—
401Dic6—124no—
402Dic6—128no—
403C3×C8—61no—
404C3×C8—61no—
405C3×C8—62no—
406C3⋊C8—21no—
407C3⋊C8—21no—
408C3⋊C8—22no—
409C2×C32#54611yescharacteristic
410C2×C32C22×Q1611yescharacteristic
411C2×C32#57711yescharacteristic
412C3⋊D3—24no—
413C2×Q8—31no—
414C2×Q8—61no—
415C2×Q8—92no—
416C2×Q8—182no—
417C2×Q8—184no—
418C2×Q8—362no—
419C2×Q8C2×D3211yescharacteristic
420C2×D4—91no—
421C22×C4—92no—
422C22×C4—182no—
423C22×C4—182no—
424Q16—62no—
425Q16—362no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8—32no—
429C2×C8—362no—
430C4⋊C4—21no—
431C4⋊C4—31no—
432C4⋊C4—32no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—91no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4C2×D3211yescharacteristic
442C22⋊C4—92no—
443C22⋊C4—182no—
444C22⋊C4—182no—
445C42—21no—
446C42—61no—
447C42C2×D3211yescharacteristic
448C22×C3—21no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—34no—
452C2×D3—34no—
453C2×D3—64no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—122no—
459C2×D3—122no—
460C3×C4—24no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—22no—
468C3×C4—41no—
469C3×C4—42no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—122no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4D3×Q1612yes—
476C3×C4D3×Q1612yes—
477C3×C4C2×#23511yescharacteristic
478C3×C4C2×#23911yescharacteristic
479C3×C4#100911yescharacteristic
480C3×C4#100911yescharacteristic
481Dic3—41no—
482Dic3—42no—
483Dic3—41no—
484Dic3—62no—
485Dic3—62no—
486Dic3—122no—
487Dic3—124no—
488Dic3—122no—
489Dic3—122no—
490C32#329911yescharacteristic, complemented, Sylow
491C23—92no—
492Q8—21no—
493Q8—61no—
494Q8—61no—
495Q8—182no—
496Q8—182no—
497Q8—241no—
498Q8—364no—
499Q8#379912yes—
500D4—94no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—62no—
506C2×C4—92no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—364no—
511C2×C4—722no—
512C2×C4#381111yescharacteristic
513C2×C4#381111yescharacteristic
514C2×C4C22×D3211yescharacteristic
515C8—61no—
516C8—61no—
517C8—62no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3#555011yescharacteristic
522C2×C3#563011yescharacteristic
523C2×C3C2×D3×Q1611yescharacteristic
524C2×C3C2×D3×Q1611yescharacteristic
525C2×C3#577011yescharacteristic
526C2×C3#577511yescharacteristic
527D3—64no—
528D3—64no—
529D3—124no—
530C22—94no—
531C22—182no—
532C22—182no—
533C22C2×#381111yescharacteristic
534C4—21no—
535C4—22no—
536C4—41no—
537C4—121no—
538C4—122no—
539C4—121no—
540C4—182no—
541C4—362no—
542C4#6394412yes—
543C4C2×#379911yescharacteristic
544C4#6430811yescharacteristic
545C3—21no—
546C3#7973511yescharacteristic, complemented
547C3#8111911yescharacteristic, complemented
548C2—184no—
549C2#1059501811yescharacteristic
550C2C2×#6394411yescharacteristic
551C2#1059546211yescharacteristic
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×C4×#216C2semidirect
4. C3×#5021C2semidirect
5. #10591603C2semidirect
6. #10591552C2semidirect
7. #10590525C2semidirect
8. #10590444C2semidirect
9. #10590385C2semidirect
11. #10590288C2semidirect
53. C4×#216D3semidirect
54. #5021D3semidirect
178. C4⋊(C3⋊D3)Q16semidirect
490. C32#3299semidirect
546. C3#79735semidirect
547. C3#81119semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊(C3⋊D3)2
#105939582
C3×C4×#2162
C3×#50212
#105916032
#105915522
#105905252
#105904442
#105903852
#105903272
#105902882
#811193
#797353