Finite Group Databasebeta

← #11897562

Subgroups — #11897562

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590344C212yesmaximal
5C4×#3713C211yesmaximal, characteristic
6#10590315C212yesmaximal, complemented
7#10590309C211yesmaximal, characteristic, complemented
8#10590270C212yesmaximal, complemented
9#10590269C211yesmaximal, characteristic, complemented
10#10590266C212yesmaximal, complemented
11#10590266C211yesmaximal, characteristic, complemented
12#83630—31nomaximal
13#83564—31nomaximal
14C2×C3×D3×Q8—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#946—21no—
17C3×#897—21no—
18C3×#897—22no—
19C3×#896—22no—
20C3×D3×C4⋊C4—21no—
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2212yes—
25C3×#870C2212yes—
26C3×#869C2212yes—
27C3×#869C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C2×#3713C2211yescharacteristic
30C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
31C4⋊(C3⋊(C3⋊C8))C2212yes—
32#63630C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34#63576C2212yes—
35#63576C2211yescharacteristic
36#63574C2212yes—
37#63574C2212yes—
38#63574C2212yes—
39#63562C2211yescharacteristic
40#63562C2212yes—
41#63562C2212yes—
42#63562C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5579D311yescharacteristic, complemented
46Q8×D12D311yescharacteristic, complemented
47#5087—31no—
48#5084—32no—
49#5084—31no—
50#5081—32no—
51#5080—31no—
52#5080—31no—
53#5066—32no—
54#5064—32no—
55#5024—31no—
56#5024—31no—
57#5024—61no—
58#5014—32no—
59#5014—32no—
60C4×#213—31no—
61C4×#213—31no—
62#5009—32no—
63#5008—31no—
64#5008—32no—
65#5007—31no—
66C2×C32×Q8D411yescharacteristic
67C3×D3×Q8—44no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—22no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—21no—
77C32×C4⋊C4D411yescharacteristic
78C32×C4⋊C4D412yes—
79C32×C42C2311yescharacteristic
80C32×C42C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97#3713Q814yescomplemented
98#3384—91noSylow
99C22×C3×Q8—61no—
100C2×D3×Q8—21no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—32no—
104C3×#125—32no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—61no—
108C3×C22⋊Q8—62no—
109C3×C4×Q8—21no—
110C3×C4×Q8C2×D311yescharacteristic
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×D4—31no—
113C3×C4×D4—31no—
114C3×C4×D4—32no—
115C3×C4×D4—32no—
116C2×C3×C4⋊C4—61no—
117#946—21no—
118C2×#213—31no—
119C2×#213—31no—
120#897—21no—
121#897—22no—
122#896—22no—
123D3×C4⋊C4—21no—
124C4×D12C2×D311yescharacteristic
125C4×D12C2×D311yescharacteristic
126C4×D12C2×D312yes—
127C4×D12C2×D312yes—
128#870C2×D312yes—
129#869C2×D311yescharacteristic
130#869C2×D312yes—
131#869C2×D311yescharacteristic
132#832—32no—
133#832—31no—
134#832—32no—
135#832—31no—
136#809—31no—
137#809—31no—
138#809—32no—
139#809—32no—
140#808—32no—
141#808—32no—
142#808—32no—
143#808—32no—
144#808—32no—
145#808—32no—
146#807—32no—
147#807—32no—
148#807—31no—
149#807—31no—
150C4⋊(C3⋊C8)—31no—
151C4⋊(C3⋊C8)—32no—
152C4⋊(C3⋊C8)—31no—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)—61no—
155C4⋊(C3⋊C8)—62no—
156#803—32no—
157#803—32no—
158#803—62no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C32×Q8—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C3×D12—21no—
175C3×D12—21no—
176C3×D12C2×Q812yes—
177C3×D12C2×Q812yescomplemented
178C3×C4×D3—44no—
179C3×C4×D3—42no—
180C3×C4×D3—42no—
181C3×C4×D3—82no—
182C3×Dic6—44no—
183C3×Dic6—42no—
184C3×Dic6—81no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—22no—
187C3⋊(C3⋊C8)C2×Q812yescomplemented
188#554—31no—
189D4×Q8—31no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—92no—
194#476—91no—
195#474—91no—
196#446—91no—
197#442—92no—
198C4×D8—91no—
199C2×C3×Q8—21no—
200C2×C3×Q8—62no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×Q8—124no—
204C2×C3×Q8#6711yescharacteristic
205C2×C3×Q8#6711yescharacteristic
206C2×C3×D4—31no—
207C2×C3×D4—31no—
208C22×C3×C4—61no—
209C22×C3×C4—62no—
210C22×C3×C4—61no—
211C22×C3×C4—62no—
212D3×Q8—44no—
213C2×D12C22×D311yescharacteristic
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—22no—
217C2×C4×D3—21no—
218C2×C4×D3—22no—
219C2×Dic6—22no—
220C2×Dic6—21no—
221C2×Dic6—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4#6711yescharacteristic
234C3×C4⋊C4#6712yes—
235C3×C4⋊C4#6711yescharacteristic
236C3×C4⋊C4#6712yes—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42—22no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D312yes—
246C3×C42C22×D312yes—
247#213—34no—
248#213—34no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—22no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—22no—
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D312yes—
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—62no—
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—22no—
279C32×C4—21no—
280C32×C4—22no—
281C32×C4AGL(1,ℤ/8)12yes—
282C32×C4C22×Q811yescharacteristic
283C32×C42−1+411yescharacteristic
284C3×Dic3—41no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C22×Q8—61no—
289C2×D8—91no—
290C4⋊Q8—31no—
291C4⋊Q8—32no—
292C4⋊Q8—31no—
293#125—32no—
294C22⋊Q8—61no—
295C22⋊Q8—61no—
296C22⋊Q8—62no—
297C22⋊Q8—62no—
298C4×Q8D3211yescharacteristic
299C4×D4—31no—
300C4×D4—32no—
301C4×D4—31no—
302C4×D4—32no—
303C2×C4⋊C4—61no—
304#107—91no—
305#107—92no—
306#106—92no—
307#106—92no—
308#106—92no—
309C4⋊C8—91no—
310C4⋊C8—92no—
311#102—91no—
312#102—91no—
313#102—92no—
314#102—92no—
315#97—92no—
316C4×C8—91no—
317C23×C3—61no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—21no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—42no—
324C3×Q8—124no—
325C3×Q8—122no—
326C3×Q8—241no—
327C3×D4—32no—
328C3×D4—32no—
329C3×D4—61no—
330C3×D4—61no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—124no—
341C2×C3×C4—122no—
342C2×C3×C4—122no—
343C2×C3×C4—242no—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C2×#6712yes—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358D12—21no—
359D12—21no—
360D12D3×Q812yes—
361D12D3×Q812yescomplemented
362C4×D3—44no—
363C4×D3—42no—
364C4×D3—42no—
365C4×D3—82no—
366Dic6—44no—
367Dic6—42no—
368Dic6—81no—
369C3⋊C8—32no—
370C3⋊C8—32no—
371C3⋊C8—62no—
372C3⋊C8—61no—
373C3⋊C8—61no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C3⋊C8—121no—
377C3⋊C8—122no—
378C2×C32D4×Q811yescharacteristic
379C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
380C2×C32#57711yescharacteristic
381C3×D3—42no—
382C3×D3—42no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—124no—
387C2×Q8#62511yescharacteristic
388C2×D4—31no—
389C2×D4—31no—
390C22×C4—61no—
391C22×C4—62no—
392C22×C4—61no—
393C22×C4—62no—
394D8—94no—
395C2×C8—91no—
396C2×C8—91no—
397C2×C8—92no—
398C4⋊C4—32no—
399C4⋊C4—31no—
400C4⋊C4—32no—
401C4⋊C4—31no—
402C4⋊C4—62no—
403C4⋊C4—61no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—62no—
407C4⋊C4#62511yescharacteristic
408C4⋊C4#62512yes—
409C22⋊C4—61no—
410C22⋊C4—62no—
411C22⋊C4—61no—
412C22⋊C4—62no—
413C42C2×D3211yescharacteristic
414C42C2×D3212yes—
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—62no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3C22×#6711yescharacteristic
423C22×C3C22×#6711yescharacteristic
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—41no—
442C3×C4—121no—
443C3×C4—122no—
444C3×C4—121no—
445C3×C4—122no—
446C3×C4#93212yes—
447C3×C4#94912yes—
448C3×C4C2×D3×Q811yescharacteristic
449C3×C4C2×D3×Q811yescharacteristic
450C3×C4#100711yescharacteristic
451C3×C4#100711yescharacteristic
452Dic3—41no—
453Dic3—42no—
454Dic3—41no—
455Dic3—42no—
456C32#338411yescharacteristic, complemented, Sylow
457C23—61no—
458C23—61no—
459Q8—22no—
460Q8—124no—
461Q8—122no—
462Q8—241no—
463D4—32no—
464D4—32no—
465D4—61no—
466D4—61no—
467C2×C4—61no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—124no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—242no—
475C2×C4C2×#62511yescharacteristic
476C2×C4C2×#62512yes—
477C2×C4C2×#62512yes—
478C2×C4C2×#62511yescharacteristic
479C2×C4C22×D3211yescharacteristic
480C8—92no—
481C8—181no—
482C8—182no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—122no—
487C2×C3—122no—
488C2×C3C2×#93211yescharacteristic
489C2×C3Q8×#6711yescharacteristic
490C2×C3Q8×#6711yescharacteristic
491C2×C3C2×#94911yescharacteristic
492C2×C3#583611yescharacteristic
493C2×C3#583711yescharacteristic
494D3—42no—
495D3—42no—
496C22—62no—
497C22—62no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22C22×#62511yescharacteristic
503C4—22no—
504C4—21no—
505C4—22no—
506C4—122no—
507C4—122no—
508C4—121no—
509C4—121no—
510C4#6382312yes—
511C4#6431611yescharacteristic
512C4D32×Q811yescharacteristic
513C3—21no—
514C3#8356411yescharacteristic, complemented
515C3#8363011yescharacteristic, complemented
516C2—122no—
517C2—122no—
518C2C2×#6382311yescharacteristic
519C2Q8×#62511yescharacteristic
520C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4×Q8D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
2. C3×Q8×D12C2semidirect
3. #10592723C2semidirect
6. #10590315C2semidirect
7. #10590309C2semidirect
8. #10590270C2semidirect
9. #10590269C2semidirect
10. #10590266C2semidirect
11. #10590266C2semidirect
45. #5579D3semidirect
46. Q8×D12D3semidirect
97. #3713Q8semidirect
177. C3×D12C2×Q8semidirect
187. C3⋊(C3⋊C8)C2×Q8semidirect
361. D12D3×Q8semidirect
456. C32#3384semidirect
514. C3#83564semidirect
515. C3#83630semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×Q8×D122
#105927232
#105903442
C4×#37132
#105903152
#105903092
#105902702
#105902692
#105902662
#836303
#835643