Finite Group Databasebeta

← #11889324

Subgroups — #11889324

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic
2#10596110C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4#10592924C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592885C211yesmaximal, characteristic, complemented
7#10592883C211yesmaximal, characteristic, complemented
8#10592881C211yesmaximal, characteristic, complemented
9#10592751C211yesmaximal, characteristic, complemented
10#10592504C211yesmaximal, characteristic, complemented
11C3⋊D3×#103C211yesmaximal, characteristic, complemented
12#10592496C211yesmaximal, characteristic, complemented
13#10592495C211yesmaximal, characteristic, complemented
14#10592427C211yesmaximal, characteristic
15#10592422C211yesmaximal, characteristic, complemented
16#80196—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64155—21no—
23#64155C2211yescharacteristic
24#64155C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic
27#64153—21no—
28#64153C2211yescharacteristic
29C2×#3756C2211yescharacteristic
30C4×#638—21no—
31C4×#638C2211yescharacteristic
32#64135C2211yescharacteristic
33#64133—21no—
34#64133C2211yescharacteristic
35C2×#3748C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37#64101—21no—
38C4⋊C4×C3⋊D3C2211yescharacteristic
39#64099C2211yescharacteristic
40#64098—21no—
41#64092—21no—
42#64088—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63662C2211yescharacteristic
50#63662C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic
53#63644C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63642C2211yescharacteristic
57#63641C2211yescharacteristic
58#63637C2211yescharacteristic
59#63635C2211yescharacteristic
60Q8×#67—34no—
61#5639—34no—
62C3×#451D314yescomplemented
63#5225—34no—
64#5188—34no—
65#5186—34no—
66#5184—34no—
67#5182—34no—
68#5052—34no—
69#4805—34no—
70D3×#103—34no—
71#4797—34no—
72#4796—34no—
73#4728—34no—
74#4723—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8—22no—
77C2×C32×Q8—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638D411yescharacteristic
84Q8×C3⋊D3—22no—
85Q8×C3⋊D3—41no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C32×Q16—22no—
92C32×Q16—41no—
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4C2311yescharacteristic
97C32×C22⋊C4—21no—
98#3757—21no—
99#3757—21no—
100#3757D411yescharacteristic
101#3756—41no—
102#3752—21no—
103#3752—21no—
104#3752D411yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123#3748—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3312—91noSylow
128C22×C3×Q8C2×D314yes—
129C2×D3×Q8—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×Q16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#946—34no—
134#946—34no—
135#946—64no—
136Q8×Dic3—34no—
137Q8×Dic3—34no—
138#944—34no—
139#944—64no—
140C2×#216—34no—
141C4×#67—34no—
142C4×#67—64no—
143#926—34no—
144#924—34no—
145#924—64no—
146C2×#208—34no—
147C2×D3×C8—34no—
148#892—64no—
149D3×C4⋊C4—34no—
150#890—34no—
151#889—64no—
152#883—64no—
153#879—64no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#835—34no—
159#835—34no—
160#835—34no—
161#835—34no—
162(C2×D3)⋊C8—34no—
163#818—34no—
164#817—34no—
165#816—34no—
166#816—34no—
167#815—34no—
168Dic3⋊C8—34no—
169#810—34no—
170#808—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8—42no—
179C32×Q8#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201#634—21no—
202#634—21no—
203#634—42no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#552—91no—
209D4×Q8—91no—
210#491—91no—
211#485—91no—
212#483—91no—
213#479—91no—
214#470—91no—
215#467—91no—
216#462—91no—
217#451—91no—
218#451C3⋊D311yescharacteristic, complemented
219#441—91no—
220#435—91no—
221#419—91no—
222C2×#103—91no—
223C2×C3×Q8—24no—
224C2×C3×Q8—28no—
225C2×C3×Q8—44no—
226C2×C3×Q8C22×D314yes—
227C2×C3×Q8C22×D314yes—
228C2×C3×Q8C22×D314yes—
229C22×C3×C4—24no—
230C22×C3×C4C22×D314yes—
231C2×#67—34no—
232D3×Q8—68no—
233D3×Q8—124no—
234C2×C4×D3—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×Dic6—34no—
238C2×Dic6—64no—
239C3×Q16—28no—
240C3×Q16—44no—
241C2×C3×C8C22×D314yes—
242C2×C3×C8C22×D314yes—
243C3×C4⋊C4—24no—
244C3×C4⋊C4C22×D314yes—
245C3×C22⋊C4—24no—
246#217—34no—
247#217—64no—
248#217—64no—
249#216—124no—
250(C2×D3)⋊C4—34no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255C4⋊Dic3—34no—
256C4⋊Dic3—64no—
257C4⋊Dic3—64no—
258C4⋊Dic3—64no—
259Dic3⋊C4—34no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271#208—124no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274D3×C8—124no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3#13712yes—
282C32×C4—22no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4—41no—
287C32×C4C2×#4111yescharacteristic
288C32×C4H(5,𝔽2)11yescharacteristic
289C3⋊Dic3—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—21no—
292C3⋊Dic3—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C22×Q8—91no—
297C22×Q8C2×C3⋊D311yescharacteristic
298C2×Q16—91no—
299C2×Q16C2×C3⋊D311yescharacteristic
300C2×Q16C2×C3⋊D311yescharacteristic
301C2×M16—91no—
302C22×C8—91no—
303C4⋊Q8—91no—
304C4⋊Q8—181no—
305#126—181no—
306#125—91no—
307#125—181no—
308#123—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—181no—
313C22⋊Q8—181no—
314C22⋊Q8C2×C3⋊D311yescharacteristic
315C4×Q8—91no—
316C4×Q8—91no—
317C4×D4—91no—
318C4×D4—181no—
319#117—91no—
320#117—181no—
321C2×C4⋊C4—91no—
322#107—91no—
323#106—91no—
324#106—91no—
325C4⋊C8—91no—
326#103—91no—
327#103—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336C22⋊C8—91no—
337C22⋊C8C2×C3⋊D311yescharacteristic
338#97—91no—
339C23×C3D3×D414yes—
340C22×D3—34no—
341C3×Q8—24no—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×Q8—24no—
345C3×Q8—24no—
346C3×Q8—48no—
347C3×Q8#23718yes—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—48no—
355C2×C3×C4D3×D414yes—
356C2×C3×C4C23×D314yes—
357#67—68no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—128no—
368C4×D3—128no—
369Dic6—64no—
370Dic6—64no—
371Dic6—128no—
372C3×C8—24no—
373C3×C8—24no—
374C3⋊C8—64no—
375C3⋊C8—64no—
376C2×C32—41no—
377C2×C32#54611yescharacteristic
378C2×C32C2×#13711yescharacteristic
379C2×C32#57811yescharacteristic
380C3⋊D3—22no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—41no—
384C2×Q8—91no—
385C2×Q8—181no—
386C2×Q8—182no—
387C2×Q8—361no—
388C2×Q8C22×C3⋊D311yescharacteristic
389C2×Q8C22×C3⋊D311yescharacteristic
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×D4—91no—
392C22×C4—21no—
393C22×C4—91no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4C22×C3⋊D311yescharacteristic
397Q16—22no—
398Q16—41no—
399Q16—361no—
400M16—361no—
401C2×C8—91no—
402C2×C8—91no—
403C2×C8—361no—
404C2×C8C22×C3⋊D311yescharacteristic
405C2×C8C22×C3⋊D311yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4—181no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C42—91no—
430C42—181no—
431C42—181no—
432C42—181no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3C2×D3×D414yes—
437C2×D3—38no—
438C2×D3—64no—
439C2×D3—64no—
440C3×C4—28no—
441C3×C4—24no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4—44no—
445C3×C4C2×#23714yes—
446C3×C4#100414yes—
447Dic3—64no—
448Dic3—64no—
449Dic3—64no—
450Dic3—124no—
451Dic3—124no—
452Dic3—124no—
453Dic3—124no—
454C32#331211yescharacteristic, complemented, Sylow
455C23—91no—
456C23D4×C3⋊D311yescharacteristic
457Q8—21no—
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8—21no—
462Q8—42no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8#383012yes—
467D4—182no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—362no—
485C2×C4—362no—
486C2×C4D4×C3⋊D311yescharacteristic
487C2×C4C23×C3⋊D311yescharacteristic
488C8—21no—
489C8—21no—
490C8—181no—
491C8—181no—
492C2×C3—44no—
493C2×C3#559114yes—
494C2×C3#576614yes—
495C2×C3D3×#13714yes—
496D3—68no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—92no—
501C22—181no—
502C22—181no—
503C22C2×D4×C3⋊D311yescharacteristic
504C4—21no—
505C4—22no—
506C4—41no—
507C4—41no—
508C4—41no—
509C4—181no—
510C4—181no—
511C4—181no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4—361no—
516C4C2×#383011yescharacteristic
517C4#6436111yescharacteristic
518C3#8019614yescomplemented
519C2—41no—
520C2—182no—
521C2#1059606211yescharacteristic
522C2#1059623711yescharacteristic
523C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenter#451C3⋊D3
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. C32×#451C2semidirect
4. #10592924C2semidirect
5. #10592887C2semidirect
6. #10592885C2semidirect
7. #10592883C2semidirect
8. #10592881C2semidirect
9. #10592751C2semidirect
10. #10592504C2semidirect
11. C3⋊D3×#103C2semidirect
12. #10592496C2semidirect
13. #10592495C2semidirect
15. #10592422C2semidirect
62. C3×#451D3semidirect
218. #451C3⋊D3semidirect
454. C32#3312semidirect
518. C3#80196semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105961102
C32×#4512
#105929242
#105928872
#105928852
#105928832
#105928812
#105927512
#105925042
C3⋊D3×#1032
#105924962
#105924952
#105924272
#105924222
#801963