Finite Group Databasebeta

← #11861568

Subgroups — #11861568

Order 1152.

963 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3795C211yesmaximal, characteristic
2#10592529C211yesmaximal, characteristic, complemented
3C3×#4834C211yesmaximal, characteristic, complemented
4C3×#4833C211yesmaximal, characteristic, complemented
5#10590718C212yesmaximal, complemented
6#10590717C212yesmaximal, complemented
7#10590655C212yesmaximal, complemented
8D3×C8×Dic3C212yesmaximal, complemented
9#10590329C211yesmaximal, characteristic, complemented
10C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12C8×#237—31nomaximal
13#79276—31nomaximal
14C2×#3795C411yescharacteristic
15C4×#634C2211yescharacteristic
16C2×C3×D3×C8C2212yes—
17C3×C4×D12C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19C4×#625C2212yes—
20Dic3×D12C411yescharacteristic
21#63879C412yes—
22#63877C412yes—
23C4×D3×Dic3C2212yes—
24#63844C411yescharacteristic
25#63841C411yescharacteristic
26C2×D3×C3⋊C8C2211yescharacteristic
27C2×D3×C3⋊C8C2211yescharacteristic
28C2×D3×C3⋊C8C2212yes—
29C32×C4⋊C8C2211yescharacteristic
30#63641C2212yes—
31C8×C3⋊Dic3C2212yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×(C2×D3)⋊C8C2212yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×C8×Dic3C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63553C2212yes—
41Dic3×C3⋊C8C2211yescharacteristic
42Dic3×C3⋊C8C2211yescharacteristic
43C4×#237—31no—
44C4×#235—31no—
45C3×C8×D4—31no—
46C3×#431—31no—
47C8×#67—32no—
48C2×C8×Dic3—32no—
49D4×C3⋊C8—31no—
50C2×C4×C3⋊C8—31no—
51#4834—31no—
52#4834D311yescharacteristic, complemented
53#4833D311yescharacteristic, complemented
54#4830—31no—
55#4830—31no—
56#4830—31no—
57#4830—61no—
58#67⋊C8—32no—
59#67⋊C8—32no—
60#67⋊C8—32no—
61#4718—32no—
62#4685—32no—
63C4×D3×C8—32no—
64C4×D3×C8—31no—
65C8×Dic6—31no—
66C2×#634C2×C411yescharacteristic
67C2×C3×D12C2×C411yescharacteristic
68C2×C3×C4×D3C2×C411yescharacteristic
69C2×C3×C4×D3C2×C411yescharacteristic
70C2×C3×C4×D3C2312yes—
71C2×C3×C4×D3C2311yescharacteristic
72C2×#625C2×C412yes—
73C2×D3×Dic3C2×C412yes—
74C2×D3×Dic3C2×C412yes—
75#3795C818yescomplemented
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2×C411yescharacteristic
79#3750C2×C412yes—
80C4×C3⋊Dic3C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C3×(C2×D3)⋊C4C2×C412yes—
84C3×C4⋊Dic3C2×C411yescharacteristic
85C3×C4×Dic3C2×C411yescharacteristic
86C3×C4×Dic3C2×C411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D3×C8—24no—
92#3724C2×C412yes—
93(C2×D3)⋊Dic3C2×C412yes—
94(C2×D3)⋊Dic3C2×C412yes—
95Dic32C2×C412yes—
96Dic32C2×C412yes—
97D3×C3⋊C8—22no—
98D3×C3⋊C8—24no—
99D3×C3⋊C8—22no—
100C8×#41—91noSylow
101C2×#237—31no—
102C2×#235—31no—
103C22×C3×C8—32no—
104C3×C4×D4—31no—
105C2×C3×C42—31no—
106D4×Dic3—31no—
107C4×#67—32no—
108C4×#67—32no—
109C4×#67—32no—
110#926—31no—
111C2×C4×Dic3—32no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—32no—
115C2×D3×C8—31no—
116C2×D3×C8—32no—
117C2×D3×C8—31no—
118C2×D3×C8C2×D312yes—
119#892—31no—
120#887—31no—
121#67⋊C4—32no—
122#877—32no—
123C4×D12—31no—
124C4×D12C2×D311yescharacteristic
125#872—32no—
126C42×D3—32no—
127C42×D3C2×D311yescharacteristic
128C4×Dic6—31no—
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C3×C4⋊C8—21no—
133C3×C4⋊C8—31no—
134C3×C4⋊C8C2×D311yescharacteristic
135C3×C4⋊C8C2×D311yescharacteristic
136C3×C22⋊C8—32no—
137C3×C22⋊C8—32no—
138C3×C4×C8—32no—
139C3×C4×C8—31no—
140#830—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8C2×D312yes—
143(C2×D3)⋊C8C2×D312yes—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146Dic3⋊C8—32no—
147Dic3⋊C8—32no—
148Dic3⋊C8—62no—
149C8×Dic3—32no—
150C8×Dic3—32no—
151C8×Dic3—31no—
152C8×Dic3—31no—
153C8×Dic3—32no—
154C8×Dic3—32no—
155C8×Dic3—62no—
156C8×Dic3C2×D312yes—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3×D3C22×C411yescharacteristic
165C22×C3×D3C22×C412yes—
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3C22×C412yes—
170C2×C3⋊Dic3C22×C412yes—
171#634C2×C814yescomplemented
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C411yescharacteristic
174C2×C3×Dic3C22×C411yescharacteristic
175C2×C3×Dic3C22×C411yescharacteristic
176C3×D12C2×C814yescomplemented
177C3×C4×D3—21no—
178C3×C4×D3—22no—
179C3×C4×D3—21no—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3C2×C814yescomplemented
183#625C2×C818yescomplemented
184D3×Dic3—24no—
185D3×Dic3C2×C818yescomplemented
186C32×C8—22no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)#4112yescomplemented
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8#4112yescomplemented
192C4×#41—91no—
193C8×Q8—91no—
194C8×Q8—91no—
195C8×D4—31no—
196C8×D4—92no—
197C8×D4—92no—
198C8×D4—91no—
199#431—31no—
200#431—92no—
201C2×C4×C8—91no—
202C2×C4×C8—92no—
203C2×C3×D4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—31no—
208C2×#67—32no—
209C2×#67—32no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212#237—38no—
213#235—38no—
214C2×D12C4×D311yescharacteristic
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3C4×D311yescharacteristic
218C2×C4×D3C4×D311yescharacteristic
219C2×C4×D3C22×D312yes—
220C2×C4×D3C22×D311yescharacteristic
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C2×C3×C8—22no—
225C2×C3×C8—31no—
226C2×C3×C8—31no—
227C2×C3×C8—32no—
228C2×C3×C8—64no—
229C2×C3×C8C22×D312yes—
230C2×C3×C8C22×D312yes—
231C3×C4⋊C4—31no—
232C3×C22⋊C4—32no—
233C3×C42—21no—
234C3×C42—31no—
235C3×C42—31no—
236C3×C42—31no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—32no—
240#217—32no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4C4×D312yes—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3C4×D311yescharacteristic
248Dic3⋊C4—32no—
249Dic3⋊C4—32no—
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252Dic3⋊C4—62no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—32no—
256C4×Dic3—32no—
257C4×Dic3—32no—
258C4×Dic3—32no—
259C4×Dic3—62no—
260C4×Dic3C4×D311yescharacteristic
261C4×Dic3C4×D311yescharacteristic
262C4×Dic3C22×D311yescharacteristic
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8—64no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D312yes—
274C2×C3⋊C8C22×D311yescharacteristic
275D3×C8—24no—
276D3×C8—64no—
277D3×C8—62no—
278D3×C8—62no—
279C22×C32C23×C411yescharacteristic
280C2×C3×D3—21no—
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—21no—
284C2×C3×D3C22×C814yes—
285C2×C3×D3C22×C812yes—
286C32×C4—21no—
287C32×C4C22×C812yes—
288C32×C4C2×#4111yescharacteristic
289C32×C4C2×#4111yescharacteristic
290C3⋊Dic3—22no—
291C3⋊Dic3C22×C814yes—
292C3×Dic3—21no—
293C3×Dic3—22no—
294C3×Dic3C22×C812yes—
295C3×Dic3#13112yes—
296C2×#41—91no—
297C22×C8—32no—
298C22×C8—91no—
299C22×C8—91no—
300C22×C8—92no—
301C4×Q8—91no—
302C4×Q8—91no—
303C4×D4—31no—
304C4×D4—91no—
305C4×D4—92no—
306C4×D4—92no—
307#117—92no—
308#117—91no—
309C2×C42—31no—
310C2×C42—92no—
311C4⋊C8—31no—
312C4⋊C8—92no—
313C4⋊C8—92no—
314C4⋊C8D3211yescharacteristic
315C22⋊C8—32no—
316C22⋊C8—32no—
317C22⋊C8—92no—
318C4×C8—32no—
319C4×C8—31no—
320C4×C8—91no—
321C4×C8—91no—
322C4×C8—92no—
323C4×C8—92no—
324C4×C8—91no—
325C23×C3—31no—
326C23×C3—32no—
327C22×D3C2×C4×D311yescharacteristic
328C22×D3C2×C4×D312yes—
329C3×D4—34no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—31no—
334C2×C3×C4—31no—
335C2×C3×C4—34no—
336C2×C3×C4—32no—
337C2×C3×C4—31no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—38no—
350#67—38no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—38no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—64no—
359C2×Dic3C2×C4×D312yes—
360C2×Dic3C2×C4×D311yescharacteristic
361C2×Dic3C2×C4×D311yescharacteristic
362C2×Dic3C2×C4×D311yescharacteristic
363D12D3×C814yescomplemented
364C4×D3—22no—
365C4×D3—21no—
366C4×D3—21no—
367C4×D3—22no—
368C4×D3—22no—
369C4×D3—38no—
370C4×D3—64no—
371C4×D3D3×C814yescomplemented
372Dic6—34no—
373Dic6—34no—
374Dic6—64no—
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—32no—
378C3×C8—42no—
379C3×C8—61no—
380C3×C8—62no—
381C3⋊C8—22no—
382C3⋊C8—21no—
383C3⋊C8—32no—
384C3⋊C8—32no—
385C3⋊C8—62no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—121no—
389C3⋊C8#23712yescomplemented
390C2×C32C4×#4111yescharacteristic
391C2×C32C23×C811yescharacteristic
392C2×C32C2×#13111yescharacteristic
393C3×D3—24no—
394C3×D3—22no—
395#41—98no—
396C2×Q8—91no—
397C2×D4—31no—
398C2×D4—92no—
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—31no—
403C22×C4—92no—
404C22×C4—92no—
405C2×C8—31no—
406C2×C8—31no—
407C2×C8—32no—
408C2×C8—64no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—182no—
412C2×C8—182no—
413C2×C8—184no—
414C2×C8C2×D3212yes—
415C4⋊C4—31no—
416C4⋊C4—92no—
417C4⋊C4—92no—
418C4⋊C4—91no—
419C22⋊C4—32no—
420C22⋊C4—92no—
421C22⋊C4—92no—
422C42—31no—
423C42—31no—
424C42—31no—
425C42—92no—
426C42—92no—
427C42—92no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—34no—
431C22×C3—32no—
432C22×C3—62no—
433C22×C3—61no—
434C22×C3—62no—
435C22×C3—61no—
436C22×C3C22×C4×D311yescharacteristic
437C22×C3C22×C4×D311yescharacteristic
438C2×D3—21no—
439C2×D3—22no—
440C2×D3—21no—
441C2×D3—22no—
442C2×D3C2×D3×C814yes—
443C2×D3C2×D3×C812yes—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—32no—
450C3×C4—32no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—61no—
454C3×C4C2×D3×C812yes—
455C3×C4C2×D3×C812yes—
456C3×C4C2×#23711yescharacteristic
457C3×C4D3×#4111yescharacteristic
458C3×C4D3×#4111yescharacteristic
459C3×C4D3×#4111yescharacteristic
460Dic3—21no—
461Dic3—22no—
462Dic3—34no—
463Dic3—34no—
464Dic3—64no—
465Dic3—62no—
466Dic3—62no—
467Dic3—122no—
468Dic3C2×D3×C812yes—
469Dic3#90712yes—
470C32C8×#4111yescharacteristic, complemented, Sylow
471C23—32no—
472C23—31no—
473Q8—94no—
474D4—34no—
475D4—98no—
476C2×C4—31no—
477C2×C4—31no—
478C2×C4—34no—
479C2×C4—31no—
480C2×C4—32no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—98no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—184no—
490C2×C4C4×D3211yescharacteristic
491C2×C4C4×D3211yescharacteristic
492C2×C4C22×D3211yescharacteristic
493C8—22no—
494C8—32no—
495C8—61no—
496C8—62no—
497C8—92no—
498C8—181no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—62no—
503C2×C3—64no—
504C2×C3#552211yescharacteristic
505C2×C3C4×#23711yescharacteristic
506C2×C3C22×D3×C811yescharacteristic
507C2×C3C22×D3×C811yescharacteristic
508C2×C3C2×#90711yescharacteristic
509C2×C3D3×#13111yescharacteristic
510D3—24no—
511D3—22no—
512C22—32no—
513C22—34no—
514C22—62no—
515C22—61no—
516C22—61no—
517C22—62no—
518C22C2×C4×D3211yescharacteristic
519C4—21no—
520C4—32no—
521C4—32no—
522C4—61no—
523C4—62no—
524C4—94no—
525C4—182no—
526C4D32×C812yes—
527C4D3×#23711yescharacteristic
528C4#6431911yescharacteristic
529C3—21no—
530C3#7927611yescharacteristic, complemented
531C3C8×#23711yescharacteristic, complemented
532C2—62no—
533C2—64no—
534C2#1059435811yescharacteristic
535C2C2×D32×C811yescharacteristic
536C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C23×C8
FittingC32×C4⋊C8C22
socleC22×C32C23×C4
prime radicalC2×#3795C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592529C2semidirect
3. C3×#4834C2semidirect
4. C3×#4833C2semidirect
5. #10590718C2semidirect
6. #10590717C2semidirect
7. #10590655C2semidirect
8. D3×C8×Dic3C2semidirect
9. #10590329C2semidirect
10. C4×D3×C3⋊C8C2semidirect
11. #10590254C2semidirect
52. #4834D3semidirect
53. #4833D3semidirect
75. #3795C8semidirect
171. #634C2×C8semidirect
176. C3×D12C2×C8semidirect
182. C3×C4×D3C2×C8semidirect
183. #625C2×C8semidirect
185. D3×Dic3C2×C8semidirect
188. C3⋊(C3⋊C8)#41semidirect
191. C3×C3⋊C8#41semidirect
363. D12D3×C8semidirect
371. C4×D3D3×C8semidirect
389. C3⋊C8#237semidirect
470. C32C8×#41semidirect
530. C3#79276semidirect
531. C3C8×#237semidirect

Maximal subgroups

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

subgroupindex
C4×#37952
#105925292
C3×#48342
C3×#48332
#105907182
#105907172
#105906552
D3×C8×Dic32
#105903292
C4×D3×C3⋊C82
#105902542
C8×#2373
#792763