Finite Group Databasebeta

← #11873262

Subgroups — #11873262

Order 1152.

1074 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596283C211yesmaximal, characteristic
2#10596096C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic
4#10592927C211yesmaximal, characteristic
5#10592883C211yesmaximal, characteristic, complemented
6#10592881C211yesmaximal, characteristic, complemented
7#10592881C211yesmaximal, characteristic, complemented
8Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592744C211yesmaximal, characteristic
10#10592498C211yesmaximal, characteristic, complemented
11#10592495C211yesmaximal, characteristic, complemented
12#10592489C211yesmaximal, characteristic, complemented
13#10592488C211yesmaximal, characteristic, complemented
14#10592422C211yesmaximal, characteristic
15#10592419C211yesmaximal, characteristic
16#80177—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×C32×Q16C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21Q8×C3⋊Dic3—21no—
22Q8×C3⋊Dic3—21no—
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic
27Q8×C3⋊Dic3C2211yescharacteristic
28#64153C2211yescharacteristic
29C2×#3756C2211yescharacteristic
30C2×#3756C2211yescharacteristic
31#64135—21no—
32#64135—21no—
33#64135C2211yescharacteristic
34#64135C2211yescharacteristic
35#64133C2211yescharacteristic
36#64099—21no—
37#64099C2211yescharacteristic
38#64098—21no—
39#64096C2211yescharacteristic
40#64088—21no—
41#64088—21no—
42C32×#103C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63657C2211yescharacteristic
50#63645C2211yescharacteristic
51#63644C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63642C2211yescharacteristic
55#63641C2211yescharacteristic
56#63641C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5812—34no—
61#5625—34no—
62C3×#451D314yes—
63#5228—34no—
64#5184—34no—
65#5182—34no—
66#5182—34no—
67Dic3×Q16—34no—
68#5045—34no—
69#4799—34no—
70#4796—34no—
71#4790—34no—
72#4789—34no—
73#4723—34no—
74#4720—34no—
75C2×C32×Q8—22no—
76C2×C32×Q8—22no—
77C2×C32×Q8—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#634C2311yescharacteristic
84C32×Q16—22no—
85C32×Q16—22no—
86C2×C32×C8C2311yescharacteristic
87C2×C32×C8C2311yescharacteristic
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91#3757—21no—
92#3757—21no—
93#3757D411yescharacteristic
94#3757D411yescharacteristic
95#3756—22no—
96#3756—22no—
97C4⋊(C3⋊Dic3)—21no—
98C4⋊(C3⋊Dic3)—21no—
99C4⋊(C3⋊Dic3)—21no—
100C4⋊(C3⋊Dic3)—21no—
101C4⋊(C3⋊Dic3)—21no—
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)D411yescharacteristic
104C4⋊(C3⋊Dic3)D411yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110#3750—21no—
111#3750—21no—
112#3750—21no—
113C4×C3⋊Dic3—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3127—91noSylow
125C22×C3×Q8C2×D314yes—
126C2×C3×Q16C2×D314yes—
127C2×C3×Q16C2×D314yes—
128C3×C22⋊Q8C2×D314yes—
129Q8×Dic3—34no—
130Q8×Dic3—34no—
131Q8×Dic3—34no—
132Q8×Dic3—34no—
133Q8×Dic3—34no—
134Q8×Dic3—64no—
135Q8×Dic3—64no—
136#944—34no—
137C2×#216—34no—
138C2×#216—34no—
139#926—34no—
140#926—34no—
141#926—64no—
142#926—64no—
143#924—34no—
144#890—34no—
145#890—64no—
146#889—64no—
147#887—34no—
148#879—64no—
149#879—64no—
150C3×#103C2×D314yes—
151C3×#103C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#835—34no—
156#835—34no—
157#830—34no—
158#818—34no—
159#817—34no—
160#816—34no—
161#816—34no—
162#815—34no—
163Dic3⋊C8—34no—
164Dic3⋊C8—34no—
165C8×Dic3—34no—
166#808—34no—
167#807—34no—
168C23×C32C2×D411yescharacteristic
169C32×Q8—24no—
170C32×Q8—21no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×Q8#4112yes—
175C32×Q8#4112yes—
176C2×C32×C4—24no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193#634—21no—
194#634—21no—
195C32×C8—21no—
196C32×C8—21no—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)—21no—
199#541—91no—
200#519—91no—
201#485—91no—
202#485—91no—
203#479—91no—
204#479—91no—
205#462—91no—
206#462—91no—
207#451—91no—
208#451C3⋊D311yescharacteristic
209#441—91no—
210#441—91no—
211C4×Q16—91no—
212C4×Q16—91no—
213#433—91no—
214C2×C3×Q8—28no—
215C2×C3×Q8—28no—
216C2×C3×Q8—24no—
217C2×C3×Q8C22×D314yes—
218C2×C3×Q8C22×D314yes—
219C2×C3×Q8C22×D314yes—
220C22×C3×C4—24no—
221C22×C3×C4C22×D314yes—
222C2×Dic6—34no—
223C3×Q16—28no—
224C3×Q16—28no—
225C2×C3×C8C22×D314yes—
226C2×C3×C8C22×D314yes—
227C3×C4⋊C4—24no—
228C3×C4⋊C4C22×D314yes—
229C3×C22⋊C4—24no—
230#217—34no—
231#217—34no—
232#217—64no—
233#217—64no—
234#216—68no—
235#216—68no—
236C4⋊Dic3—34no—
237C4⋊Dic3—34no—
238C4⋊Dic3—34no—
239C4⋊Dic3—34no—
240C4⋊Dic3—34no—
241C4⋊Dic3—64no—
242C4⋊Dic3—64no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252C4×Dic3—34no—
253C4×Dic3—34no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C2×C3⋊C8—34no—
262C2×C3⋊C8—34no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32C22×D411yescharacteristic
267C32×C4—22no—
268C32×C4—22no—
269C32×C4—21no—
270C32×C4—41no—
271C32×C4—41no—
272C32×C4C2×#4111yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3—21no—
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C3⋊Dic3—41no—
281C3⋊Dic3—41no—
282C22×Q8C2×C3⋊D311yescharacteristic
283C2×Q16—91no—
284C2×Q16—91no—
285C2×Q16C2×C3⋊D311yescharacteristic
286C2×Q16C2×C3⋊D311yescharacteristic
287C4⋊Q8—91no—
288#126—181no—
289#126—181no—
290#125—91no—
291#125—181no—
292#125—181no—
293C22⋊Q8—91no—
294C22⋊Q8C2×C3⋊D311yescharacteristic
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C4×Q8—91no—
300C4×Q8—91no—
301C4×Q8—181no—
302C4×Q8—181no—
303#117—91no—
304#117—91no—
305#117—181no—
306#117—181no—
307#107—91no—
308#107—91no—
309#106—91no—
310#106—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313#103—91no—
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103—91no—
319#103C2×C3⋊D311yescharacteristic
320#103C2×C3⋊D311yescharacteristic
321C22⋊C8—91no—
322C22⋊C8C2×C3⋊D311yescharacteristic
323#97—91no—
324C4×C8—91no—
325C23×C3D3×D414yes—
326C3×Q8—216no—
327C3×Q8—24no—
328C3×Q8—24no—
329C3×Q8—24no—
330C3×Q8—24no—
331C3×Q8#23718yes—
332C3×Q8#23718yes—
333C2×C3×C4—216no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4D3×D414yes—
341C2×C3×C4C23×D314yes—
342C2×Dic3—34no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—34no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350Dic6—64no—
351Dic6—64no—
352C3×C8—24no—
353C3×C8—24no—
354C3⋊C8—64no—
355C3⋊C8—64no—
356C2×C32—41no—
357C2×C32#52511yescharacteristic
358C2×C32#57811yescharacteristic
359C2×C32#57811yescharacteristic
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—91no—
364C2×Q8C22×C3⋊D311yescharacteristic
365C2×Q8C22×C3⋊D311yescharacteristic
366C2×Q8C22×C3⋊D311yescharacteristic
367C22×C4—21no—
368C22×C4C22×C3⋊D311yescharacteristic
369Q16—22no—
370Q16—22no—
371Q16—182no—
372Q16—182no—
373C2×C8—91no—
374C2×C8—91no—
375C2×C8C22×C3⋊D311yescharacteristic
376C2×C8C22×C3⋊D311yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—91no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4C22×C3⋊D311yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—91no—
397C22⋊C4—91no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—91no—
401C42—91no—
402C42—181no—
403C42—181no—
404C42—181no—
405C42—181no—
406C42—181no—
407C42—181no—
408C42—181no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3C2×D3×D414yes—
413C3×C4—28no—
414C3×C4—28no—
415C3×C4—24no—
416C3×C4—44no—
417C3×C4—44no—
418C3×C4C2×#23714yes—
419C3×C4C2×#23714yes—
420Dic3—64no—
421Dic3—64no—
422Dic3—64no—
423Dic3—64no—
424Dic3—124no—
425Dic3—124no—
426Dic3—124no—
427Dic3—124no—
428C32#312711yescharacteristic, complemented, Sylow
429C23D4×C3⋊D311yescharacteristic
430Q8—24no—
431Q8—21no—
432Q8—21no—
433Q8—21no—
434Q8—21no—
435Q8—181no—
436Q8—181no—
437Q8#383012yes—
438Q8#383012yes—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4D4×C3⋊D311yescharacteristic
455C2×C4C23×C3⋊D311yescharacteristic
456C8—21no—
457C8—21no—
458C8—181no—
459C8—181no—
460C2×C3—44no—
461C2×C3#558614yes—
462C2×C3#576614yes—
463C2×C3#577914yes—
464C22—21no—
465C22—21no—
466C22—21no—
467C22C2×D4×C3⋊D311yescharacteristic
468C4—22no—
469C4—22no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—181no—
474C4—181no—
475C4—181no—
476C4—181no—
477C4—361no—
478C4—361no—
479C4—361no—
480C4—361no—
481C4C2×#383011yescharacteristic
482C4C2×#383011yescharacteristic
483C3#8017714yescomplemented
484C2—41no—
485C2#1059605711yescharacteristic
486C2#1059623711yescharacteristic
487C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#451C3⋊D3
hypocenterC32#3127
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
5. #10592883C2semidirect
6. #10592881C2semidirect
7. #10592881C2semidirect
8. Q16×C3⋊Dic3C2semidirect
10. #10592498C2semidirect
11. #10592495C2semidirect
12. #10592489C2semidirect
13. #10592488C2semidirect
428. C32#3127semidirect
483. C3#80177semidirect

Maximal subgroups

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

subgroupindex
#105962832
#105960962
C32×#4512
#105929272
#105928832
#105928812
Q16×C3⋊Dic32
#105927442
#105924982
#105924952
#105924892
#105924882
#105924222
#105924192
#801773