Finite Group Databasebeta

← #11889333

Subgroups — #11889333

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#10595984C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4#10592927C211yesmaximal, characteristic, complemented
5#10592815C211yesmaximal, characteristic, complemented
6#10592810C211yesmaximal, characteristic
7#10592670C211yesmaximal, characteristic, complemented
8#10592515C211yesmaximal, characteristic, complemented
9#10592513C211yesmaximal, characteristic, complemented
10#10592508C211yesmaximal, characteristic, complemented
11#10592501C211yesmaximal, characteristic, complemented
12#10592496C211yesmaximal, characteristic, complemented
13#10592495C211yesmaximal, characteristic, complemented
14#10592494C211yesmaximal, characteristic, complemented
15#10592488C211yesmaximal, characteristic, complemented
16#78810—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64155—21no—
22#64155C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24#64153—21no—
25#64153C2211yescharacteristic
26C2×#3756C2211yescharacteristic
27C2×#3756C2211yescharacteristic
28#64138—21no—
29C4×#638—21no—
30C4×#638C2211yescharacteristic
31#64135—21no—
32#64133—21no—
33#64133C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×#3746C2211yescharacteristic
36C2×#3743C2211yescharacteristic
37#64107—21no—
38#64106C2211yescharacteristic
39#64101C2211yescharacteristic
40#64099C2211yescharacteristic
41#64098—21no—
42#64096C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63657C2211yescharacteristic
50#63647C2211yescharacteristic
51#63645C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55#63641C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63635C2211yescharacteristic
59#63635C2211yescharacteristic
60Q8×#67—34no—
61#5513—34no—
62C2×C3×#103D314yescomplemented
63#5228—34no—
64#5116—34no—
65#5111—34no—
66#4971—34no—
67#4816—34no—
68#4814—34no—
69#4809—34no—
70#4802—34no—
71#4797—34no—
72#4796—34no—
73#4795—34no—
74#4789—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8—22no—
77C2×C32×Q8—41no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C22×C32×C4—21no—
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⋊D3C2311yescharacteristic
88C2×#634—21no—
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×C32×C8—41no—
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97#3757—21no—
98#3757—21no—
99#3757D411yescharacteristic
100#3756—22no—
101#3756—41no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752D411yescharacteristic
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
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
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3746—41no—
126#3743—41no—
127#3312—91noSylow
128C22×C3×Q8C2×D314yes—
129C2×D3×Q8—34no—
130C22×C3×C8C2×D314yes—
131C2×C3×C4⋊C4C2×D314yes—
132#946—34no—
133#946—64no—
134Q8×Dic3—34no—
135#944—34no—
136#944—64no—
137C2×#216—34no—
138C2×#216—34no—
139#929—64no—
140C4×#67—34no—
141C4×#67—64no—
142#926—64no—
143#924—34no—
144#924—34no—
145#924—64no—
146C2×Dic12—34no—
147C2×ΓL(1,𝔽25)—34no—
148#898—64no—
149#897—34no—
150#892—34no—
151#890—34no—
152#889—64no—
153#887—34no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×#103C2×D314yes—
157C3×#103C2×D314yes—
158#835—34no—
159#835—34no—
160#830—34no—
161(C2×D3)⋊C8—34no—
162#818—34no—
163#816—34no—
164#816—34no—
165#815—34no—
166Dic3⋊C8—34no—
167#810—34no—
168#810—34no—
169#808—34no—
170#808—34no—
171C23×C32C2×D411yescharacteristic
172C22×C3⋊D3C2×D411yescharacteristic
173C32×Q8—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—42no—
177C32×Q8#4112yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188#638—22no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—42no—
199#634—21no—
200#634—21no—
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#451—91no—
219#441—91no—
220#435—91no—
221#419—91no—
222C2×#103C3⋊D311yescharacteristic, complemented
223C2×C3×Q8—24no—
224C2×C3×Q8—28no—
225C2×C3×Q8—44no—
226C2×C3×Q8C22×D314yes—
227C2×C3×Q8C22×D314yes—
228C22×C3×C4—24no—
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×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—64no—
239C2×C3×C8—44no—
240C2×C3×C8C22×D314yes—
241C2×C3×C8C22×D314yes—
242C3×C4⋊C4—24no—
243C3×C4⋊C4C22×D314yes—
244C3×C4⋊C4C22×D314yes—
245#217—34no—
246#217—64no—
247#217—64no—
248#216—68no—
249#216—124no—
250(C2×D3)⋊C4—34no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
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—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273Dic12—124no—
274ΓL(1,𝔽25)—124no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32#13712yes—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
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×Q16—91no—
300C2×Q16—91no—
301C2×M16—91no—
302C22×C8C2×C3⋊D311yescharacteristic
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—91no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×D4—91no—
318C4×D4—181no—
319#117—91no—
320#117—181no—
321C2×C4⋊C4C2×C3⋊D311yescharacteristic
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#103C2×C3⋊D311yescharacteristic
333#103C2×C3⋊D311yescharacteristic
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336C22⋊C8—91no—
337C22⋊C8—91no—
338#97—91no—
339C23×C3D3×D414yes—
340C22×D3—34no—
341C3×Q8—24no—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×Q8—48no—
345C3×Q8#23518yes—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—48no—
353C2×C3×C4—48no—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356#67—68no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C4×D3—64no—
365C4×D3—64no—
366C4×D3—128no—
367Dic6—64no—
368Dic6—64no—
369Dic6—64no—
370Dic6—64no—
371Dic6—128no—
372C3×C8—24no—
373C3×C8—24no—
374C3⋊C8—64no—
375C3⋊C8—64no—
376C2×C32—22no—
377C2×C32#54611yescharacteristic
378C2×C32C2×#13711yescharacteristic
379C2×C32#57811yescharacteristic
380C3⋊D3—41no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—41no—
384C2×Q8—91no—
385C2×Q8—91no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—361no—
389C2×Q8C22×C3⋊D311yescharacteristic
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×D4—91no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—91no—
395C22×C4—181no—
396C22×C4C22×C3⋊D311yescharacteristic
397Q16—182no—
398Q16—361no—
399Q16—361no—
400M16—361no—
401C2×C8—41no—
402C2×C8—91no—
403C2×C8—91no—
404C2×C8C22×C3⋊D311yescharacteristic
405C2×C8C22×C3⋊D311yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—91no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—181no—
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⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C22⋊C4—91no—
423C22⋊C4—91no—
424C22⋊C4—181no—
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#91518yes—
436C22×C3C2×D3×D414yes—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—64no—
440C3×C4—28no—
441C3×C4—24no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4—44no—
445C3×C4C2×#23514yes—
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—42no—
461Q8—181no—
462Q8—181no—
463Q8—181no—
464Q8—181no—
465Q8—362no—
466Q8#382812yes—
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—42no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—91no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—362no—
486C2×C4D4×C3⋊D311yescharacteristic
487C2×C4C23×C3⋊D311yescharacteristic
488C8—21no—
489C8—21no—
490C8—181no—
491C8—181no—
492C2×C3—28no—
493C2×C3#549014yes—
494C2×C3C2×#91514yes—
495C2×C3#576614yes—
496D3—124no—
497C22—21no—
498C22—21no—
499C22—181no—
500C22—181no—
501C22—181no—
502C22#6412412yes—
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×#382811yescharacteristic
517C4#6436111yescharacteristic
518C3#7881014yescomplemented
519C2—22no—
520C2—361no—
521C2#1059596111yescharacteristic
522C2C2×#6412411yescharacteristic
523C2#1059623711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#103C2
socleC22×C32C22×D4
prime radicalC2×#638D4
hypercenterC2×#103C3⋊D3
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×C32×#103C2semidirect
4. #10592927C2semidirect
5. #10592815C2semidirect
7. #10592670C2semidirect
8. #10592515C2semidirect
9. #10592513C2semidirect
10. #10592508C2semidirect
11. #10592501C2semidirect
12. #10592496C2semidirect
13. #10592495C2semidirect
14. #10592494C2semidirect
15. #10592488C2semidirect
62. C2×C3×#103D3semidirect
222. C2×#103C3⋊D3semidirect
454. C32#3312semidirect
518. C3#78810semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105959842
C2×C32×#1032
#105929272
#105928152
#105928102
#105926702
#105925152
#105925132
#105925082
#105925012
#105924962
#105924952
#105924942
#105924882
#788103