Finite Group Databasebeta

← #11897575

Subgroups — #11897575

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
1#10593956C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3#10592530C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic, complemented
6#10590903C212yesmaximal, complemented
7#10590780C212yesmaximal, complemented
8#10590776C212yesmaximal, complemented
9#10590741C212yesmaximal
10C4×#3713C211yesmaximal, characteristic
11#10590309C211yesmaximal, characteristic, complemented
12#81089—31nomaximal
13#80959—31nomaximal
14C2×D3×Dic6—21no—
15C4×#634C2211yescharacteristic
16C3×C4×D12C2211yescharacteristic
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63919C2212yes—
21#63899—22no—
22#63898C2212yes—
23#63898C2212yes—
24D3×C4⋊Dic3—21no—
25#63887—22no—
26#63872C2212yes—
27#63857—21no—
28#63856—21no—
29C2×#3713C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31#63642C2212yes—
32#63641C2212yes—
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#821C2212yes—
35C3×#821C2212yes—
36C3×#818C2212yes—
37C3×#817C2212yes—
38#63576C2211yescharacteristic
39#63574C2212yes—
40#63574C2212yes—
41#63562C2211yescharacteristic
42#63562C2211yescharacteristic
43#5730—31no—
44#5727—31no—
45#5543—31no—
46D4×Dic6—31no—
47C3×#476—31no—
48C3×#474—31no—
49#5080—31no—
50#5080—31no—
51C4×#213—31no—
52C4×#213—31no—
53#4891—32no—
54#4876—32no—
55#4870—32no—
56#4856—32no—
57#4846D311yescharacteristic, complemented
58#4842D311yescharacteristic, complemented
59#4831—31no—
60#4831—31no—
61#4831—61no—
62#4785—32no—
63#4785—32no—
64#4766—32no—
65#4761—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C2×C32×C8C2312yes—
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)D411yescharacteristic
80#3750D412yes—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2312yes—
92#3724—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3713Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—31no—
103C3×C4×D4—31no—
104C3×C4×D4—31no—
105#946—62no—
106#946—61no—
107D4×Dic3—32no—
108D4×Dic3—32no—
109C2×#213—31no—
110C2×#213—31no—
111C2×C4⋊Dic3—61no—
112#924—61no—
113#924—61no—
114#897—61no—
115#896—62no—
116#893—32no—
117#893—32no—
118D3×C4⋊C4—61no—
119#890—32no—
120#890—32no—
121#888—32no—
122#888—32no—
123#878—62no—
124#878—62no—
125C4×D12C2×D311yescharacteristic
126C4×D12C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C3×#107—32no—
133C3×#106—32no—
134C3×C4⋊C8—21no—
135C3×C4⋊C8C2×D311yescharacteristic
136C3×C4⋊C8C2×D311yescharacteristic
137C3×#102—32no—
138C3×#102—32no—
139#832—31no—
140#832—31no—
141#821C2×D312yes—
142#821C2×D312yes—
143#818C2×D312yes—
144#817C2×D312yes—
145#815—32no—
146#815—32no—
147#815—62no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—62no—
151#809—31no—
152#809—31no—
153#808—32no—
154#808—32no—
155#808—32no—
156#808—32no—
157#807—31no—
158#807—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—61no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×D412yes—
169#634—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C3×D12—21no—
175C3×D12—21no—
176C3×D12C2×Q812yes—
177C3×D12C2×Q812yescomplemented
178C3×C4×D3—42no—
179C3×C4×D3—42no—
180C3×Dic6—42no—
181C3×Dic6—81no—
182#627—44no—
183D3×Dic3—44no—
184D3×Dic3—82no—
185C32×C8—22no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)C2×Q812yescomplemented
188#554—91no—
189D4×Q8—91no—
190#501—92no—
191#498—91no—
192#478—92no—
193#476—31no—
194#476—92no—
195#474—31no—
196#446—91no—
197#442—92no—
198C4×D8—91no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×D4—31no—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×Dic3—62no—
206C22×Dic3—62no—
207D3×Q8—124no—
208C2×D12C22×D311yescharacteristic
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—124no—
222C2×C3×C8—22no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C42—21no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#217—62no—
238#213—34no—
239#213—34no—
240(C2×D3)⋊C4—21no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—31no—
247C4⋊Dic3—31no—
248C4⋊Dic3—61no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3C22×D311yescharacteristic
252C4⋊Dic3C22×D311yescharacteristic
253C4⋊Dic3C22×D312yes—
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—62no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
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—21no—
279C32×C4AGL(1,ℤ/8)12yes—
280C32×C4C22×Q811yescharacteristic
281C32×C42−1+411yescharacteristic
282C3⋊Dic3—22no—
283C3⋊Dic3—22no—
284C3×Dic3—42no—
285C3×Dic3—41no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C22×Q8—181no—
289C2×D8—91no—
290C4⋊Q8—31no—
291C4⋊Q8—31no—
292C4⋊Q8—92no—
293#125—92no—
294C22⋊Q8—182no—
295C22⋊Q8—182no—
296C22⋊Q8—181no—
297C22⋊Q8—181no—
298C4×Q8—91no—
299C4×D4—31no—
300C4×D4—31no—
301C4×D4—92no—
302C4×D4—92no—
303C2×C4⋊C4—181no—
304#107—32no—
305#107—91no—
306#106—32no—
307#106—92no—
308#106—92no—
309C4⋊C8—92no—
310C4⋊C8D3211yescharacteristic
311#102—32no—
312#102—32no—
313#102—91no—
314#102—91no—
315#97—92no—
316C4×C8—91no—
317C23×C3—61no—
318C23×C3—61no—
319C22×D3—21no—
320C22×D3—21no—
321C3×Q8—122no—
322C3×Q8—241no—
323C3×D4—32no—
324C3×D4—32no—
325C3×D4—61no—
326C3×D4—61no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—122no—
335C2×C3×C4—122no—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—124no—
353C2×Dic3—242no—
354D12—21no—
355D12—21no—
356D12D3×Q812yes—
357D12D3×Q812yescomplemented
358C4×D3—42no—
359C4×D3—42no—
360C4×D3—124no—
361C4×D3—242no—
362Dic6—42no—
363Dic6—62no—
364Dic6—62no—
365Dic6—81no—
366Dic6—122no—
367Dic6—124no—
368Dic6—124no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—42no—
372C3⋊C8—32no—
373C3⋊C8—32no—
374C3⋊C8—62no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—121no—
378C2×C32D4×Q811yescharacteristic
379C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
380C2×C32#57711yescharacteristic
381C3×D3—42no—
382C3×D3—42no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—91no—
386C2×Q8—182no—
387C2×Q8—364no—
388C2×D4—31no—
389C2×D4—31no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—182no—
393C22×C4—182no—
394D8—94no—
395C2×C8—91no—
396C2×C8—91no—
397C2×C8C2×D3212yes—
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—91no—
405C4⋊C4—92no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C22⋊C4—182no—
412C22⋊C4—182no—
413C42—92no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—62no—
417C22×C3—62no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3C2×D3×D411yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—121no—
437C3×C4—122no—
438C3×C4—121no—
439C3×C4—122no—
440C3×C4#91112yes—
441C3×C4#91412yes—
442C3×C4C2×D3×Q811yescharacteristic
443C3×C4C2×D3×Q811yescharacteristic
444C3×C4#101011yescharacteristic
445C3×C4#101011yescharacteristic
446Dic3—42no—
447Dic3—41no—
448Dic3—41no—
449Dic3—42no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—122no—
455Dic3—122no—
456C32#338411yescharacteristic, complemented, Sylow
457C23—61no—
458C23—61no—
459Q8—122no—
460Q8—182no—
461Q8—241no—
462Q8—364no—
463D4—32no—
464D4—32no—
465D4—61no—
466D4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—122no—
474C2×C4—122no—
475C2×C4—364no—
476C2×C4—722no—
477C2×C4#380211yescharacteristic
478C2×C4#380211yescharacteristic
479C2×C4C22×D3211yescharacteristic
480C8—22no—
481C8—92no—
482C8—181no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—122no—
487C2×C3—122no—
488C2×C3#563211yescharacteristic
489C2×C3#563211yescharacteristic
490C2×C3C2×#91111yescharacteristic
491C2×C3C2×#91411yescharacteristic
492C2×C3#577511yescharacteristic
493C2×C3#577811yescharacteristic
494D3—42no—
495D3—42no—
496C22—62no—
497C22—62no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—121no—
502C22C2×#380211yescharacteristic
503C4—21no—
504C4—121no—
505C4—121no—
506C4—122no—
507C4—122no—
508C4—182no—
509C4—182no—
510C4#6379812yes—
511C4#6430911yescharacteristic
512C4D32×Q811yescharacteristic
513C3—21no—
514C3#8095911yescharacteristic, complemented
515C3#8108911yescharacteristic, complemented
516C2—122no—
517C2—122no—
518C2#1059452611yescharacteristic
519C2C2×#6379811yescharacteristic
520C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊C8D32
hypocenterC32#3384
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
1. #10593956C2semidirect
2. #10593904C2semidirect
3. #10592530C2semidirect
4. C3×#4846C2semidirect
5. C3×#4842C2semidirect
6. #10590903C2semidirect
7. #10590780C2semidirect
8. #10590776C2semidirect
11. #10590309C2semidirect
57. #4846D3semidirect
58. #4842D3semidirect
97. #3713Q8semidirect
177. C3×D12C2×Q8semidirect
187. C3⋊(C3⋊C8)C2×Q8semidirect
357. D12D3×Q8semidirect
456. C32#3384semidirect
514. C3#80959semidirect
515. C3#81089semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105939042
#105925302
C3×#48462
C3×#48422
#105909032
#105907802
#105907762
#105907412
C4×#37132
#105903092
#810893
#809593