Finite Group Databasebeta

← #11898302

Subgroups — #11898302

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590879C212yesmaximal, complemented
7#10590877C212yesmaximal, complemented
8#10590752C212yesmaximal, complemented
9#10590744C212yesmaximal, complemented
10#10590369C211yesmaximal, characteristic, complemented
11C4×#3717C211yesmaximal, characteristic, complemented
12#80378—31nomaximal
13#79911—31nomaximal
14C2×#3796—21no—
15C2×#3744C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#874C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22#63916—21no—
23#63911C2212yes—
24Dic3×D12C2212yes—
25#63886—22no—
26#63869—21no—
27#63866C2212yes—
28#63845—22no—
29#63844C2212yes—
30Dic3×Dic6—21no—
31C2×#3717C2211yescharacteristic
32C2×#3716C2212yes—
33C2×#3716C2212yes—
34C32×C4⋊C8C2211yescharacteristic
35#63643C2212yes—
36C3×#821C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4×C3⋊C8C2211yescharacteristic
40#63573C2211yescharacteristic
41#63566C2211yescharacteristic
42#63564C2211yescharacteristic
43#5718—31no—
44#5577—31no—
45#5570—31no—
46#5567—31no—
47C3×#460—31no—
48C3×C8×Q8—31no—
49#5175—32no—
50#5162—32no—
51#5076—31no—
52C4×#215—31no—
53#4848—32no—
54#4848D311yescharacteristic, complemented
55#4841—32no—
56#4841—31no—
57#4841—31no—
58#4841—61no—
59#4830D311yescharacteristic, complemented
60#4762—32no—
61#4758—32no—
62#4693—32no—
63#4693—31no—
64C4×#204—31no—
65C4×#204—32no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2312yes—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×D3×Dic3—22no—
77#3796—44no—
78C2×C32×C8C2312yes—
79C32×C42C2311yescharacteristic
80#3752—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3744—42no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×#204—42no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99#3717—22no—
100#3716—24no—
101#3716—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#237—61no—
105C2×C3×SD16—32no—
106C3×#127—31no—
107C3×C4×Q8—31no—
108C3×C4×Q8—31no—
109Q8×Dic3—61no—
110#944—32no—
111C2×#215—31no—
112#940—32no—
113#939—62no—
114#938—61no—
115D4×Dic3—32no—
116C2×#214—32no—
117C2×#214—32no—
118C2×#204—32no—
119C2×#204—31no—
120C2×#204—32no—
121C2×#204—32no—
122C2×#204—32no—
123C2×#204—62no—
124C2×#204C2×D312yes—
125#895—62no—
126#895—61no—
127#890—61no—
128#890—62no—
129#889—62no—
130#887—32no—
131#874—32no—
132#874C2×D311yescharacteristic
133C4×D12—32no—
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137#870—61no—
138#869—32no—
139#869—31no—
140#869—31no—
141#869—61no—
142C4×Dic6—32no—
143C4×Dic6—61no—
144C4×Dic6C2×D311yescharacteristic
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—21no—
147C3×C4⋊C8—32no—
148C3×C4⋊C8C2×D311yescharacteristic
149C3×C4⋊C8C2×D311yescharacteristic
150C3×#102—32no—
151C3×C4×C8—32no—
152C3×C4×C8—31no—
153#835—31no—
154#821—31no—
155#821C2×D312yes—
156#817—31no—
157#816—31no—
158#816—32no—
159#816—32no—
160#816—62no—
161Dic3⋊C8C2×D312yes—
162C8×Dic3C2×D312yes—
163#809—31no—
164#808—31no—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—21no—
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)—21no—
175C4×C3⋊D3—42no—
176#634—22no—
177#634—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191D3×Dic3—44no—
192C32×C8—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—91no—
196#550—91no—
197#492—91no—
198#492—92no—
199#461—92no—
200#461—91no—
201#460—31no—
202#460—92no—
203C8×Q8—31no—
204C4×SD16—92no—
205C4×SD16—91no—
206C2×C3×Q8—31no—
207C2×C3×Q8—31no—
208C2×C3×D4—32no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×#67—62no—
212C2×#67—62no—
213C22×Dic3—62no—
214#239—124no—
215#237—124no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—31no—
219C2×D12—31no—
220C2×D12—61no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12C22×D312yes—
224C2×C4×D3—62no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—121no—
228C2×Dic6—32no—
229C2×Dic6—32no—
230C2×Dic6—62no—
231C2×Dic6D1211yescharacteristic
232C2×Dic6C22×D311yescharacteristic
233C3×SD16—122no—
234C2×C3×C8—22no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8C22×D312yes—
238C2×C3×C8C22×D312yes—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—61no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#215—62no—
250#214—64no—
251#214—122no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—121no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—121no—
266C4⋊Dic3—121no—
267C4⋊Dic3D1211yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4D1212yes—
275C4×Dic3—21no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3C22×D312yes—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281#204—42no—
282#204—62no—
283#204—64no—
284#204—122no—
285#204—122no—
286#204—124no—
287#204—122no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C32×C4—21no—
296C32×C4C2×SD1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3⋊Dic3—42no—
300C3⋊Dic3—41no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—181no—
306C2×SD16—32no—
307C2×SD16—92no—
308C2×SD16—91no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—92no—
312C4⋊Q8—91no—
313#127—31no—
314#127—92no—
315#125—181no—
316#125—182no—
317#121—181no—
318#121—182no—
319C4×Q8—31no—
320C4×Q8—31no—
321C4×Q8—92no—
322C4×Q8—181no—
323C4×D4—92no—
324C4×D4—91no—
325#106—91no—
326C4⋊C8—32no—
327C4⋊C8D3211yescharacteristic
328#103—91no—
329#103—92no—
330#102—32no—
331#102—91no—
332C4×C8—32no—
333C4×C8—31no—
334C23×C3—62no—
335C22×D3—22no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—121no—
339C3×Q8—34no—
340C3×Q8—61no—
341C3×Q8—61no—
342C3×D4—62no—
343C3×D4—62no—
344C3×D4—122no—
345C3×D4—241no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—124no—
360#67—242no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—121no—
368C2×Dic3—122no—
369C2×Dic3—124no—
370C2×Dic3C2×D1212yes—
371C2×Dic3C2×D1212yes—
372D12—22no—
373D12—22no—
374D12—42no—
375D12—62no—
376D12—61no—
377D12—61no—
378D12—61no—
379D12—61no—
380D12—81no—
381D12—121no—
382D12—124no—
383D12—242no—
384C4×D3—124no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—242no—
388Dic6—21no—
389Dic6—21no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—122no—
395Dic6—122no—
396Dic6#20414yescomplemented
397C3×C8—22no—
398C3×C8—22no—
399C3×C8—32no—
400C3×C8—42no—
401C3×C8—61no—
402C3⋊C8—21no—
403C3⋊C8#23912yescomplemented
404C2×C32#55011yescharacteristic
405C2×C32C22×SD1611yescharacteristic
406C2×C32#57711yescharacteristic
407C3⋊D3—81no—
408C3×D3—82no—
409#41—364no—
410C2×Q8—31no—
411C2×Q8—31no—
412C2×Q8—92no—
413C2×D4—32no—
414C2×D4—61no—
415C2×D4—61no—
416C2×D4—91no—
417C2×D4—182no—
418C2×D4—182no—
419C22×C4—182no—
420C22×C4—181no—
421SD16—122no—
422SD16—184no—
423SD16—182no—
424SD16—362no—
425SD16—362no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8C2×D3212yes—
429C4⋊C4—32no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4—91no—
434C4⋊C4—182no—
435C4⋊C4—182no—
436C4⋊C4—182no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C22⋊C4—182no—
440C22⋊C4—181no—
441C42—32no—
442C42—61no—
443C42—182no—
444C42C2×D3211yescharacteristic
445C22×C3—21no—
446C22×C3—122no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3C22×D1211yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—122no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—241no—
462C2×D3—241no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—34no—
469C3×C4—41no—
470C3×C4—62no—
471C3×C4—121no—
472C3×C4—121no—
473C3×C4C2×#20412yes—
474C3×C4D3×SD1612yes—
475C3×C4#100411yescharacteristic
476C3×C4C2×#23911yescharacteristic
477C3×C4D3×#4111yescharacteristic
478C3×C4#100911yescharacteristic
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—121no—
483Dic3—121no—
484Dic3—122no—
485Dic3—122no—
486Dic3—242no—
487Dic3—241no—
488Dic3C2×#20414yes—
489C32#339211yescharacteristic, complemented, Sylow
490C23—62no—
491C23—181no—
492Q8—34no—
493Q8—61no—
494Q8—61no—
495Q8—182no—
496Q8—182no—
497D4—62no—
498D4—62no—
499D4—122no—
500D4—181no—
501D4—181no—
502D4—241no—
503D4—364no—
504D4—722no—
505C2×C4—32no—
506C2×C4—32no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—182no—
510C2×C4—181no—
511C2×C4—364no—
512C2×C4—362no—
513C2×C4D3×D1211yescharacteristic
514C2×C4D3×D1211yescharacteristic
515C2×C4C22×D3211yescharacteristic
516C8—22no—
517C8—32no—
518C8—61no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—242no—
523C2×C3#557711yescharacteristic
524C2×C3#559911yescharacteristic
525C2×C3C22×#20411yescharacteristic
526C2×C3#575111yescharacteristic
527C2×C3C2×D3×SD1611yescharacteristic
528C2×C3#577511yescharacteristic
529D3—82no—
530D3—242no—
531D3—241no—
532D3—241no—
533C22—122no—
534C22—122no—
535C22—122no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22C2×D3×D1211yescharacteristic
540C4—21no—
541C4—34no—
542C4—62no—
543C4—121no—
544C4—121no—
545C4—361no—
546C4—362no—
547C4D3×#20412yes—
548C4#6431411yescharacteristic
549C4D3×#23911yescharacteristic
550C3—21no—
551C3#7991111yescharacteristic, complemented
552C3#8037811yescharacteristic, complemented
553C2—242no—
554C2—721no—
555C2#1059452411yescharacteristic
556C2C2×D3×#20411yescharacteristic
557C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4⋊C8D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
3. #10592540C2semidirect
4. C3×#4848C2semidirect
5. C3×#4830C2semidirect
6. #10590879C2semidirect
7. #10590877C2semidirect
8. #10590752C2semidirect
9. #10590744C2semidirect
10. #10590369C2semidirect
11. C4×#3717C2semidirect
54. #4848D3semidirect
59. #4830D3semidirect
188. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
396. Dic6#204semidirect
403. C3⋊C8#239semidirect
489. C32#3392semidirect
551. C3#79911semidirect
552. C3#80378semidirect

Maximal subgroups

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

subgroupindex
#105939002
#105938602
#105925402
C3×#48482
C3×#48302
#105908792
#105908772
#105907522
#105907442
#105903692
C4×#37172
#803783
#799113