Finite Group Databasebeta

← #11774659

Subgroups — #11774659

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C3×#4924C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4#10589085C212yesmaximal, complemented
5#10589082C212yesmaximal, complemented
6#70497—31nomaximal
7#69854—31nomaximal
8C2×#3828C411yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C4×#638—21no—
11C4×#638—21no—
12#64135C411yescharacteristic
13C4×C4⋊(C3⋊D3)C411yescharacteristic
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64081—21no—
16C42×C3⋊D3—21no—
17C4×#634C411yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×#208—21no—
20C2×C3×#208—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×#803—21no—
24C3×C4×C3⋊C8C2212yes—
25C4×#235—31no—
26C4×#235—31no—
27C4×#235—61no—
28C3×#423—31no—
29C3×C4×M16—31no—
30#4924D311yescharacteristic, complemented
31C4×#208D311yescharacteristic, complemented
32#4484—32no—
33#4483—32no—
34#4459—32no—
35#4456—32no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×#638—21no—
40#3828—22no—
41#3828—22no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×#634C2×C411yescharacteristic
47C32×C42C2×C411yescharacteristic
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50C32×C42C2311yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55C4⋊(C3⋊Dic3)C2×C411yescharacteristic
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C3×#208—24no—
62C3×#208—42no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—22no—
65#1489—91noSylow
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—61no—
70C2×C3×M16—61no—
71C2×C3×C42—21no—
72C2×C3×C42C2×D311yescharacteristic
73C2×C3×C42C2×D311yescharacteristic
74C4×#67—62no—
75C4×#67—62no—
76C4×#67—61no—
77C4×#67—61no—
78C4×#67—61no—
79C4×#67—61no—
80#926—31no—
81#926—31no—
82#926—61no—
83C2×#208—21no—
84C2×#208—21no—
85C4×D12—31no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—31no—
89C4×D12—61no—
90C4×D12—61no—
91#872—62no—
92#872—61no—
93#872—61no—
94C42×D3—62no—
95C42×D3—61no—
96C42×D3—61no—
97C4×Dic6—31no—
98C4×Dic6—31no—
99C4×Dic6—31no—
100C4×Dic6—31no—
101C4×Dic6—61no—
102C4×Dic6—61no—
103C3×C4⋊C8—32no—
104C3×C4⋊C8—61no—
105C3×#97—61no—
106C3×C4×C8—32no—
107C4⋊(C3⋊C8)—21no—
108C4⋊(C3⋊C8)C2×D312yes—
109#803—21no—
110C4×C3⋊C8C2×D312yes—
111C23×C32C22⋊C411yescharacteristic
112C22×C3⋊D3—21no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—22no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124#638—24no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)M1612yescomplemented
130C4×C3⋊D3—24no—
131C4×C3⋊D3—42no—
132C4×C3⋊D3—41no—
133C4×C3⋊D3—41no—
134#634—21no—
135#634M1612yescomplemented
136C3×C3⋊C8—24no—
137C3×C3⋊C8—42no—
138C4×#41—91no—
139#423—31no—
140C4×M16—31no—
141Q8⋊C8—92no—
142D4⋊C8—92no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4C4×D311yescharacteristic
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4#6711yescharacteristic
152C2×#67—62no—
153C2×#67—61no—
154C2×#67—61no—
155#235—62no—
156#235—62no—
157#235—62no—
158#235—62no—
159#235—64no—
160#235—64no—
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×C4×D3—62no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C3×M16—64no—
177C3×M16—122no—
178C2×C3×C8—62no—
179C2×C3×C8—62no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—21no—
184C3×C42C4×D311yescharacteristic
185C3×C42C4×D311yescharacteristic
186C3×C42D1211yescharacteristic
187C3×C42D1211yescharacteristic
188C3×C42#6711yescharacteristic
189C3×C42#6711yescharacteristic
190C3×C42C22×D311yescharacteristic
191C3×C42C22×D311yescharacteristic
192#217—62no—
193#217—61no—
194#217—61no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201C4⋊Dic3—31no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—61no—
213C4×Dic3—62no—
214C4×Dic3—62no—
215C4×Dic3—62no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222#208—24no—
223#208—42no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8—22no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C2×C3⋊D3—22no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C32×C4—21no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4#10412yes—
237C32×C4C2×M1611yescharacteristic
238C32×C4C2×M1611yescharacteristic
239C32×C4AGL(1,ℤ/8)11yescharacteristic
240C32×C4#13711yescharacteristic
241C3⋊Dic3—22no—
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C2×#41—91no—
245C2×M16—61no—
246C2×M16—61no—
247C4×Q8—91no—
248C4×Q8—91no—
249C4×D4—91no—
250C4×D4—91no—
251C4×D4—181no—
252C4×D4—181no—
253#117—91no—
254#117—181no—
255C2×C42—181no—
256C2×C42D3211yescharacteristic
257C4⋊C8—32no—
258C4⋊C8—61no—
259#97—61no—
260C4×C8—32no—
261C23×C3—21no—
262C23×C3(C2×D3)⋊C411yescharacteristic
263C23×C3(C2×D3)⋊C411yescharacteristic
264C22×D3—62no—
265C22×D3—61no—
266C22×D3—61no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4(C2×D3)⋊C411yescharacteristic
289C2×C3×C4(C2×D3)⋊C411yescharacteristic
290C2×C3×C4(C2×D3)⋊C411yescharacteristic
291C2×C3×C4(C2×D3)⋊C411yescharacteristic
292C2×C3×C4(C2×D3)⋊C411yescharacteristic
293C2×C3×C4(C2×D3)⋊C411yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—68no—
301#67—64no—
302#67—64no—
303C2×Dic3—62no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312D12—32no—
313D12—32no—
314D12—62no—
315D12—62no—
316D12—61no—
317D12—61no—
318C4×D3—68no—
319C4×D3—64no—
320C4×D3—64no—
321C4×D3—124no—
322C4×D3—122no—
323C4×D3—122no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—121no—
327C4×D3—121no—
328C4×D3—121no—
329C4×D3—121no—
330Dic6—32no—
331Dic6—32no—
332Dic6—62no—
333Dic6—62no—
334Dic6—61no—
335Dic6—61no—
336C3×C8—64no—
337C3×C8—122no—
338C3⋊C8—24no—
339C3⋊C8—42no—
340C2×C32—41no—
341C2×C32#40711yescharacteristic
342C2×C32#41711yescharacteristic
343C2×C32C2×#10411yescharacteristic
344C3⋊D3—42no—
345#41—182no—
346#41—182no—
347C2×Q8—91no—
348C2×D4—91no—
349C2×D4—181no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4#62411yescharacteristic
354C22×C4#62611yescharacteristic
355C22×C4#62611yescharacteristic
356M16—64no—
357M16—122no—
358C2×C8—62no—
359C2×C8—62no—
360C4⋊C4—91no—
361C4⋊C4—91no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C42—181no—
368C42—181no—
369C42—181no—
370C42#62411yescharacteristic
371C42#62611yescharacteristic
372C42#62611yescharacteristic
373C42C2×D3211yescharacteristic
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3C2×(C2×D3)⋊C411yescharacteristic
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C2×D3—64no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C2×D3—121no—
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—22no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4#80512yes—
410C3×C4#82512yes—
411C3×C4D3×M1611yescharacteristic
412C3×C4D3×M1611yescharacteristic
413C3×C4D3×M1611yescharacteristic
414C3×C4D3×M1611yescharacteristic
415C3×C4#90811yescharacteristic
416C3×C4#90911yescharacteristic
417C3×C4#93211yescharacteristic
418C3×C4#94211yescharacteristic
419Dic3—64no—
420Dic3—62no—
421Dic3—62no—
422Dic3—122no—
423Dic3—122no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427Dic3—121no—
428C32#148911yescharacteristic, complemented, Sylow
429C23—181no—
430C23#372211yescharacteristic
431Q8—92no—
432Q8—181no—
433D4—92no—
434D4—184no—
435D4—181no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—184no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—362no—
446C2×C4—361no—
447C2×C4—361no—
448C2×C4#372211yescharacteristic
449C2×C4#372211yescharacteristic
450C2×C4#372211yescharacteristic
451C2×C4C2×#62411yescharacteristic
452C2×C4C2×#62611yescharacteristic
453C2×C4C2×#62611yescharacteristic
454C8—64no—
455C8—122no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—42no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3C2×#80511yescharacteristic
463C2×C3#496611yescharacteristic
464C2×C3#512611yescharacteristic
465C2×C3#512611yescharacteristic
466C2×C3#513311yescharacteristic
467C2×C3C2×#82511yescharacteristic
468D3—124no—
469D3—122no—
470D3—122no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—182no—
475C22—361no—
476C22—361no—
477C22C2×#372211yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—182no—
482C4—361no—
483C4—361no—
484C4#6357012yes—
485C4#6381811yescharacteristic
486C4#6381811yescharacteristic
487C4#6383011yescharacteristic
488C4#6383311yescharacteristic
489C3—21no—
490C3#6985411yescharacteristic, complemented
491C3#7049711yescharacteristic, complemented
492C2—41no—
493C2—362no—
494C2#1059107411yescharacteristic
495C2#1059110611yescharacteristic
496C2C2×#6357011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4924C2semidirect
3. C3×C4×#208C2semidirect
4. #10589085C2semidirect
5. #10589082C2semidirect
30. #4924D3semidirect
31. C4×#208D3semidirect
129. C4⋊(C3⋊D3)M16semidirect
135. #634M16semidirect
428. C32#1489semidirect
490. C3#69854semidirect
491. C3#70497semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#49242
C3×C4×#2082
#105890852
#105890822
#704973
#698543