Finite Group Databasebeta

← #11861346

Subgroups — #11861346

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590340C211yesmaximal, characteristic
5#10590332C212yesmaximal
6#10590321C212yesmaximal
7C4×#3710C211yesmaximal, characteristic
8#10590296C211yesmaximal, characteristic, complemented
9#10590255C212yesmaximal, complemented
10#10590254C212yesmaximal, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#79958—31nomaximal
13#79917—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64155C411yescharacteristic
16#64153C411yescharacteristic
17#64106C411yescharacteristic
18#64105C412yes—
19#64098C412yes—
20#64097C411yescharacteristic
21#64081C2212yes—
22C42×C3⋊D3C2211yescharacteristic
23C4×#634C2212yes—
24C4×#634C2211yescharacteristic
25C2×#3712C2212yes—
26C2×#3710C2211yescharacteristic
27C2×#3710C2211yescharacteristic
28C3×C4⋊(C3⋊C8)C2212yes—
29C3×C4⋊(C3⋊C8)C2211yescharacteristic
30C3×C4⋊(C3⋊C8)C2212yes—
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#803C2212yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34C3×C4×C3⋊C8C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63572C2212yes—
37#63572C2212yes—
38#63572C2212yes—
39#63555C2212yes—
40#63553C2211yescharacteristic
41#63553C2212yes—
42#63553C2211yescharacteristic
43#5578—31no—
44#5578—31no—
45#5578—61no—
46C3×#446—31no—
47C3×C8×Q8—31no—
48#5024D311yescharacteristic, complemented
49Q8×C3⋊C8D311yescharacteristic, complemented
50#4839—32no—
51#4839—32no—
52#4837—31no—
53#4837—31no—
54#4831—31no—
55#4830—31no—
56#4830—32no—
57#4828—32no—
58#4708—32no—
59#4701—32no—
60#4689—32no—
61C4×D3×C8—31no—
62C4×D3×C8—31no—
63#4679—31no—
64C8×Dic6—31no—
65C8×Dic6—32no—
66C2×C32×Q8C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2×C411yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×#634C2×C412yes—
71C2×#634C2×C411yescharacteristic
72C32×C4⋊C4C2×C411yescharacteristic
73C32×C4⋊C4C2×C412yes—
74C32×C42C2311yescharacteristic
75C32×C42C2312yes—
76#3752C2×C412yes—
77#3752C2×C412yes—
78C4⋊(C3⋊Dic3)C2×C411yescharacteristic
79C4⋊(C3⋊Dic3)C2×C412yes—
80#3750C2×C412yes—
81#3750C2×C412yes—
82#3750C2×C412yes—
83#3750C2×C412yes—
84#3750C2×C412yes—
85C4×C3⋊Dic3C2×C411yescharacteristic
86C4×C3⋊Dic3C2×C411yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C4×C3⋊Dic3C2312yes—
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3712—24no—
96#3710—22no—
97#3710Q814yescomplemented
98#2960—91noSylow
99C3×C4×Q8—21no—
100C3×C4×Q8C2×D311yescharacteristic
101C3×C4×Q8C2×D311yescharacteristic
102#946—31no—
103#946—31no—
104#946—61no—
105#944—31no—
106#944—31no—
107#944—61no—
108C2×ΓL(1,𝔽25)—32no—
109C2×ΓL(1,𝔽25)—32no—
110C2×D3×C8—31no—
111C2×D3×C8—31no—
112C2×D3×C8—31no—
113C2×D3×C8—31no—
114#897—31no—
115#897—31no—
116#897—61no—
117#896—32no—
118#896—32no—
119#896—62no—
120#889—32no—
121#889—32no—
122#889—62no—
123#888—31no—
124#888—31no—
125#888—61no—
126#872—32no—
127#872—32no—
128#872—62no—
129C42×D3—31no—
130C42×D3—31no—
131C42×D3—61no—
132C4×Dic6—32no—
133C4×Dic6—31no—
134C4×Dic6—31no—
135C4×Dic6—32no—
136C4×Dic6—62no—
137C4×Dic6—61no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—31no—
140C3×C4⋊C8—31no—
141C3×C4⋊C8—32no—
142C3×#97—32no—
143C3×C4×C8—31no—
144C3×C4×C8—32no—
145C3×C4×C8—31no—
146#815—32no—
147#815—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—32no—
152Dic3⋊C8—32no—
153Dic3⋊C8—32no—
154C8×Dic3—31no—
155C8×Dic3—32no—
156C8×Dic3—31no—
157C8×Dic3—31no—
158C8×Dic3—31no—
159C8×Dic3—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4⋊(C3⋊C8)C2×D312yes—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D312yes—
164#803C2×D312yes—
165C4×C3⋊C8C2×D311yescharacteristic
166C4×C3⋊C8C2×D311yescharacteristic
167C4×C3⋊C8C2×D312yes—
168C22×C3⋊D3C22×C411yescharacteristic
169C32×Q8—22no—
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C22×C412yes—
172C2×C32×C4C22×C412yes—
173C2×C32×C4C22×C411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3C22×C411yescharacteristic
176C2×C3⋊Dic3C22×C412yes—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3C22×C411yescharacteristic
179C2×C3⋊Dic3C22×C411yescharacteristic
180C4×C3⋊D3—22no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3C2×Q812yes—
183C4×C3⋊D3#4112yes—
184#634—22no—
185#634—24no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8C2×Q812yes—
191C3×C3⋊C8C2×Q812yes—
192#533—91no—
193#446—31no—
194#446—91no—
195#446—92no—
196C8×Q8—31no—
197C8×Q8—91no—
198C8×Q8—92no—
199#424—92no—
200#423—91no—
201#405—92no—
202C2×C4×C8—91no—
203C2×C3×Q8—21no—
204C2×C3×Q8C4×D311yescharacteristic
205C2×C3×Q8C4×D311yescharacteristic
206C2×C4×D3—31no—
207C2×C4×D3—31no—
208C2×C4×D3—31no—
209C2×C4×D3—31no—
210C2×C4×D3—31no—
211C2×C4×D3—31no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×Dic6—32no—
216C2×Dic6—32no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—62no—
220C2×Dic6—61no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4C4×D311yescharacteristic
230C3×C4⋊C4C4×D311yescharacteristic
231C3×C4⋊C4C4×D312yes—
232C3×C4⋊C4C4×D312yes—
233C3×C42—21no—
234C3×C42—22no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D312yes—
238C3×C42C22×D312yes—
239(C2×D3)⋊C4—32no—
240(C2×D3)⋊C4—32no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—61no—
250C4⋊Dic3—62no—
251Dic3⋊C4—32no—
252Dic3⋊C4—32no—
253Dic3⋊C4—32no—
254Dic3⋊C4—32no—
255Dic3⋊C4—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4—32no—
260Dic3⋊C4—32no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—31no—
269C4×Dic3—31no—
270C4×Dic3—31no—
271C4×Dic3—31no—
272C4×Dic3—32no—
273C4×Dic3—32no—
274C4×Dic3—61no—
275C4×Dic3—62no—
276C4×Dic3—61no—
277C4×Dic3—61no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C2×C3⋊C8C22×D312yes—
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D311yescharacteristic
284ΓL(1,𝔽25)—64no—
285ΓL(1,𝔽25)—64no—
286D3×C8—34no—
287D3×C8—34no—
288D3×C8—62no—
289D3×C8—62no—
290C22×C32C23×C411yescharacteristic
291C2×C3⋊D3—21no—
292C2×C3⋊D3—21no—
293C2×C3⋊D3C4×Q812yes—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4—22no—
297C32×C4#13112yes—
298C32×C4C22×Q811yescharacteristic
299C32×C4C2×#4111yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—21no—
303C3⋊Dic3C4×Q812yes—
304C3⋊Dic3#13112yes—
305C2×M16—92no—
306C22×C8—91no—
307C22×C8—91no—
308C4⋊Q8—91no—
309C4⋊Q8—91no—
310#125—92no—
311C22⋊Q8—91no—
312C22⋊Q8—92no—
313C22⋊Q8—91no—
314C4×Q8—92no—
315C4×Q8—91no—
316C4×Q8D3211yescharacteristic
317#117—92no—
318C2×C42—91no—
319C4⋊C8—31no—
320C4⋊C8—31no—
321C4⋊C8—32no—
322C4⋊C8—32no—
323C4⋊C8—92no—
324C4⋊C8—92no—
325C4⋊C8—92no—
326#97—32no—
327#97—92no—
328C4×C8—31no—
329C4×C8—31no—
330C4×C8—32no—
331C4×C8—91no—
332C4×C8—91no—
333C4×C8—92no—
334C22×D3—31no—
335C22×D3—31no—
336C22×D3—61no—
337C3×Q8—22no—
338C3×Q8—22no—
339C3×Q8—42no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4C2×C4×D312yes—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×C4×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C4×D3—32no—
371C4×D3—32no—
372C4×D3—32no—
373C4×D3—32no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—122no—
381C4×D3—122no—
382Dic6—64no—
383Dic6—64no—
384Dic6—62no—
385Dic6—62no—
386Dic6—124no—
387Dic6—122no—
388C3×C8—32no—
389C3×C8—32no—
390C3×C8—61no—
391C3×C8—61no—
392C3×C8—62no—
393C3×C8—62no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—22no—
397C3⋊C8—22no—
398C3⋊C8D3×Q812yes—
399C3⋊C8D3×Q812yes—
400C2×C32C2×C4×Q811yescharacteristic
401C2×C32C2×#13111yescharacteristic
402C2×C32C2×#13111yescharacteristic
403C3⋊D3—22no—
404C2×Q8—92no—
405C2×Q8—91no—
406C2×Q8#62411yescharacteristic
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410M16—184no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—32no—
416C2×C8—32no—
417C2×C8—94no—
418C2×C8—182no—
419C4⋊C4—92no—
420C4⋊C4—92no—
421C4⋊C4—92no—
422C4⋊C4—92no—
423C4⋊C4—92no—
424C4⋊C4—92no—
425C4⋊C4—91no—
426C4⋊C4#62412yes—
427C4⋊C4#62411yescharacteristic
428C22⋊C4—92no—
429C22⋊C4—92no—
430C42—91no—
431C42—92no—
432C42—91no—
433C42—91no—
434C42C2×D3211yescharacteristic
435C42C2×D3212yes—
436C22×C3—21no—
437C22×C3C22×C4×D311yescharacteristic
438C22×C3C22×C4×D311yescharacteristic
439C2×D3—32no—
440C2×D3—32no—
441C2×D3—62no—
442C2×D3—61no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—121no—
447C2×D3—121no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—42no—
460C3×C4#90112yes—
461C3×C4#90712yes—
462C3×C4C2×D3×Q811yescharacteristic
463C3×C4C2×D3×Q811yescharacteristic
464C3×C4D3×#4111yescharacteristic
465C3×C4D3×#4111yescharacteristic
466Dic3—32no—
467Dic3—32no—
468Dic3—32no—
469Dic3—32no—
470Dic3—62no—
471Dic3—62no—
472Dic3—62no—
473Dic3—61no—
474Dic3—62no—
475Dic3—61no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—122no—
480Dic3—121no—
481C32#296011yescharacteristic, complemented, Sylow
482C23—91no—
483Q8—22no—
484Q8—184no—
485Q8—182no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—91no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4C2×#62411yescharacteristic
496C2×C4C2×#62412yes—
497C2×C4C2×#62412yes—
498C2×C4C2×#62411yescharacteristic
499C2×C4C22×D3211yescharacteristic
500C8—32no—
501C8—32no—
502C8—61no—
503C8—61no—
504C8—62no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3C4×D3×Q811yescharacteristic
510C2×C3C4×D3×Q811yescharacteristic
511C2×C3C2×#90111yescharacteristic
512C2×C3C2×#90711yescharacteristic
513C2×C3D3×#13111yescharacteristic
514C2×C3D3×#13111yescharacteristic
515D3—62no—
516D3—62no—
517D3—122no—
518C22—92no—
519C22—181no—
520C22—181no—
521C22C22×#62411yescharacteristic
522C4—21no—
523C4—22no—
524C4—22no—
525C4—92no—
526C4—92no—
527C4—182no—
528C4—181no—
529C4—182no—
530C4#6381712yes—
531C4D32×Q811yescharacteristic
532C4#6431911yescharacteristic
533C3—21no—
534C3#7991711yescharacteristic, complemented
535C3#7995811yescharacteristic, complemented
536C2—182no—
537C2C2×#6381711yescharacteristic
538C2Q8×#62411yescharacteristic
539C2#1059544211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C22
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2960
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5024C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
8. #10590296C2semidirect
9. #10590255C2semidirect
10. #10590254C2semidirect
11. #10590254C2semidirect
48. #5024D3semidirect
49. Q8×C3⋊C8D3semidirect
97. #3710Q8semidirect
481. C32#2960semidirect
534. C3#79917semidirect
535. C3#79958semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×#50242
C3×Q8×C3⋊C82
#105903402
#105903322
#105903212
C4×#37102
#105902962
#105902552
#105902542
#799583
#799173