Finite Group Databasebeta

← #11897558

Subgroups — #11897558

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×Dic6C211yesmaximal, characteristic, complemented
2#10593958C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591411C212yesmaximal, complemented
6#10591404C212yesmaximal
7#10590466C212yesmaximal, complemented
8#10590421C212yesmaximal, complemented
9#10590313C211yesmaximal, characteristic, complemented
10#10590309C211yesmaximal, characteristic, complemented
11#10590259C211yesmaximal, characteristic, complemented
12#83564—31nomaximal
13#81089—31nomaximal
14C22×C3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3753C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×D4×Dic3C2212yes—
19C3×#924—21no—
20C3×#888C2212yes—
21C3×#878—22no—
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63900—21no—
26#63894C2212yes—
27#63888—22no—
28#63871—21no—
29#63869C2212yes—
30#63659C2211yescharacteristic
31#63636C2211yescharacteristic
32#63634C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#832C2212yes—
35C3×#808C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63575C2212yes—
38#63574C2212yes—
39#63574C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63564C2212yes—
42#63554C2212yes—
43C3×D4×Q8—31no—
44#5730—31no—
45#5579—31no—
46D4×Dic6D311yescharacteristic, complemented
47C3×#476—31no—
48#5087—31no—
49#5084—32no—
50#5081—32no—
51#5080—31no—
52#5080—31no—
53#5024—31no—
54#5014—32no—
55C4×#213—31no—
56C4×#213—31no—
57C4×#213—61no—
58#5009—32no—
59#5008D311yescharacteristic, complemented
60#4870—32no—
61#4856—32no—
62#4846—31no—
63#4831—31no—
64#4785—32no—
65#4766—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—44no—
75C2×C3×Dic6D411yescharacteristic
76C2×#624—22no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80#3753Q814yescomplemented
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3384—91noSylow
99C22×C3×Q8—61no—
100C22×Dic6—21no—
101C3×C4⋊Q8—32no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—31no—
104C3×C22⋊Q8—62no—
105C3×C22⋊Q8—61no—
106C3×C4×Q8—31no—
107C3×C4×D4—21no—
108C3×C4×D4—32no—
109C3×C4×D4C2×D311yescharacteristic
110C3×C4×D4C2×D311yescharacteristic
111#946—61no—
112#946—62no—
113D4×Dic3C2×D312yes—
114C2×#213—31no—
115C2×#213—31no—
116C2×#213—61no—
117#924—21no—
118#897—61no—
119#896—62no—
120#893—32no—
121D3×C4⋊C4—61no—
122D3×C4⋊C4—61no—
123#890—32no—
124#888C2×D312yes—
125#878—22no—
126C4×D12—31no—
127C4×D12—31no—
128C4×D12—32no—
129C4×D12—61no—
130#870—32no—
131#869C2×D311yescharacteristic
132#869C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C3×#106—32no—
135C3×C4⋊C8—31no—
136C3×#102—32no—
137#832—31no—
138#832—31no—
139#832—61no—
140#832C2×D312yes—
141#821—32no—
142#818—32no—
143#815—32no—
144Dic3⋊C8—32no—
145#809—31no—
146#809—31no—
147#809—32no—
148#809—61no—
149#808—32no—
150#808—32no—
151#808—32no—
152#808—32no—
153#808C2×D312yes—
154#807—31no—
155#807—31no—
156#807—32no—
157#807—61no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)C2×D311yescharacteristic
160#803—32no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—61no—
164C23×C32—21no—
165C22×C3⋊D3—21no—
166C32×D4—21no—
167C32×D4C2×Q812yes—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)C2×Q812yescomplemented
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—44no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—44no—
184C3×Dic6—42no—
185C3×Dic6—81no—
186#624—82no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)C2×Q812yescomplemented
189C3×C3⋊C8—22no—
190#554—91no—
191D4×Q8—31no—
192#501—92no—
193#498—91no—
194#478—92no—
195#476—31no—
196#476—92no—
197#474—91no—
198#446—91no—
199#442—92no—
200C4×D8—91no—
201C2×C3×Q8—31no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×Q8—124no—
206C2×C3×D4—21no—
207C2×C3×D4C22×D311yescharacteristic
208C2×C3×D4C22×D311yescharacteristic
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4—62no—
213C22×Dic3—22no—
214C2×D12—31no—
215C2×D12—31no—
216C2×D12—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—121no—
222C2×Dic6—21no—
223C2×Dic6—22no—
224C2×Dic6—21no—
225C2×Dic6—44no—
226C2×Dic6#6711yescharacteristic
227C2×C3×C8—32no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—32no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—41no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—22no—
247#213—34no—
248#213—34no—
249#213—64no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—121no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D312yes—
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—22no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4#6712yes—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D312yes—
277C22×C32—22no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C22×D411yescharacteristic
281C2×C3⋊D3—22no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C32×C4—21no—
285C32×C4—41no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C22×Q811yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—41no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C22×Q8—61no—
295C2×D8—91no—
296C4⋊Q8—32no—
297C4⋊Q8—31no—
298C4⋊Q8—31no—
299#125—92no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—182no—
303C22⋊Q8—181no—
304C4×Q8—31no—
305C4×D4—32no—
306C4×D4—92no—
307C4×D4—91no—
308C4×D4D3211yescharacteristic
309C2×C4⋊C4—181no—
310#107—92no—
311#107—91no—
312#106—32no—
313#106—92no—
314#106—92no—
315C4⋊C8—31no—
316C4⋊C8—92no—
317#102—32no—
318#102—92no—
319#102—91no—
320#102—91no—
321#97—92no—
322C4×C8—91no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—41no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—121no—
329C3×Q8—62no—
330C3×Q8—124no—
331C3×Q8—122no—
332C3×Q8—241no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—22no—
336C3×D4—41no—
337C3×D4D3×Q812yes—
338C3×D4D3×Q812yes—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—82no—
352C2×C3×C4—124no—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—44no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—121no—
365C2×Dic3C2×#6712yes—
366C2×Dic3C2×#6712yes—
367D12—32no—
368D12—32no—
369D12—62no—
370D12—61no—
371D12—61no—
372D12—121no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—242no—
376C4×D3—242no—
377C4×D3—242no—
378Dic6—22no—
379Dic6—44no—
380Dic6—42no—
381Dic6—81no—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—32no—
385C3⋊C8—32no—
386C3⋊C8—62no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
390C2×C32—42no—
391C2×C32D4×Q811yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—42no—
395C2×Q8—31no—
396C2×Q8—62no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—124no—
400C2×D4—91no—
401C2×D4C2×D3211yescharacteristic
402C22×C4—21no—
403C22×C4—62no—
404C22×C4—182no—
405C22×C4—181no—
406D8—94no—
407C2×C8—32no—
408C2×C8—91no—
409C2×C8—91no—
410C4⋊C4—31no—
411C4⋊C4—32no—
412C4⋊C4—32no—
413C4⋊C4—32no—
414C4⋊C4—62no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4C2×D3211yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—62no—
423C22⋊C4—182no—
424C22⋊C4—181no—
425C42—32no—
426C42C2×D3211yescharacteristic
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—42no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—81no—
436C22×C3—81no—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C22×#6711yescharacteristic
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—122no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—241no—
447C2×D3—241no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—81no—
459C3×C4—122no—
460C3×C4—122no—
461C3×C4#91412yes—
462C3×C4#93212yes—
463C3×C4C2×D3×Q811yescharacteristic
464C3×C4C2×D3×Q811yescharacteristic
465C3×C4#100711yescharacteristic
466C3×C4#101011yescharacteristic
467Dic3—22no—
468Dic3—22no—
469Dic3—42no—
470Dic3—42no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474C32#338411yescharacteristic, complemented, Sylow
475C23—21no—
476C23—181no—
477Q8—62no—
478Q8—124no—
479Q8—122no—
480Q8—241no—
481D4—21no—
482D4—92no—
483D4—181no—
484D4#379712yes—
485C2×C4—21no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—42no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—124no—
492C2×C4—181no—
493C2×C4—362no—
494C2×C4—722no—
495C2×C4D3×#6711yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—62no—
499C8—92no—
500C8—181no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3—42no—
506C2×C3—82no—
507C2×C3#563211yescharacteristic
508C2×C3C2×#91411yescharacteristic
509C2×C3#577511yescharacteristic
510C2×C3C2×#93211yescharacteristic
511C2×C3Q8×#6711yescharacteristic
512C2×C3#583711yescharacteristic
513D3—122no—
514D3—122no—
515D3—242no—
516C22—22no—
517C22—41no—
518C22—41no—
519C22—182no—
520C22—361no—
521C22—361no—
522C22C2×D3×#6711yescharacteristic
523C4—21no—
524C4—41no—
525C4—62no—
526C4—62no—
527C4—122no—
528C4—122no—
529C4—361no—
530C4#6393412yes—
531C4#6429711yescharacteristic
532C4C2×#379711yescharacteristic
533C3—21no—
534C3#8108911yescharacteristic, complemented
535C3#8356411yescharacteristic, complemented
536C2—42no—
537C2—362no—
538C2#1059480311yescharacteristic
539C2C2×#6393411yescharacteristic
540C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenterC4×D4D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×Dic6C2semidirect
2. #10593958C2semidirect
4. C3×#5008C2semidirect
5. #10591411C2semidirect
7. #10590466C2semidirect
8. #10590421C2semidirect
9. #10590313C2semidirect
10. #10590309C2semidirect
11. #10590259C2semidirect
46. D4×Dic6D3semidirect
59. #5008D3semidirect
80. #3753Q8semidirect
175. C4⋊(C3⋊D3)C2×Q8semidirect
188. C3⋊(C3⋊C8)C2×Q8semidirect
474. C32#3384semidirect
534. C3#81089semidirect
535. C3#83564semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
#105939582
C4×#37532
C3×#50082
#105914112
#105914042
#105904662
#105904212
#105903132
#105903092
#105902592
#835643
#810893