Finite Group Databasebeta

← #11861692

Subgroups — #11861692

Order 1152.

841 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595033C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×C8×#67C212yesmaximal, complemented
4#10591158C212yesmaximal, complemented
5#10591066C211yesmaximal, characteristic, complemented
6#10590788C211yesmaximal, characteristic, complemented
7C8×#627C211yesmaximal, characteristic, complemented
8#10590734C211yesmaximal, characteristic, complemented
9C8×#625C211yesmaximal, characteristic, complemented
10#10590698C212yesmaximal, complemented
11#10590692C212yesmaximal, complemented
12#79400—32nomaximal
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4×#67C2212yes—
17C2×C3×D3×C8C2212yes—
18#63982C411yescharacteristic
19#63980C411yescharacteristic
20#63962C412yes—
21C4×#627C2211yescharacteristic
22#63915C411yescharacteristic
23C4×#625C2211yescharacteristic
24#63870C411yescharacteristic
25#63862C412yes—
26#63855C2212yes—
27C2×#3711C2212yes—
28C8×C3⋊Dic3C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C3×#830C2212yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C8×Dic3C2212yes—
36#63572C2211yescharacteristic
37#63572C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63555C2212yes—
41#63554C2212yes—
42#5538—32no—
43C3×C8×D4—32no—
44C8×#67—32no—
45C8×#67D312yescomplemented
46#5101—32no—
47C2×C8×Dic3—32no—
48C2×C8×Dic3—61no—
49#5011—32no—
50#4840—32no—
51#4828—32no—
52#4730—32no—
53#4729—32no—
54#4720—32no—
55#4719—32no—
56#4689—32no—
57C8×Dic6—32no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2×C411yescharacteristic
60C22×C3⋊Dic3C2×C411yescharacteristic
61C2×C3×#67C2×C412yes—
62C2×C3×C4×D3C2312yes—
63C2×#627C2×C411yescharacteristic
64C2×#625C2×C411yescharacteristic
65C2×C32×C8—22no—
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C3×#217C2×C412yes—
76C3×(C2×D3)⋊C4C2×C412yes—
77C3×Dic3⋊C4C2×C412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81C3×D3×C8—24no—
82#3724C2×C411yescharacteristic
83#3724C2×C411yescharacteristic
84Dic3⋊Dic3C2×C412yes—
85Dic3⋊Dic3C2×C412yes—
86Dic3⋊Dic3C2×C412yes—
87(C2×D3)⋊Dic3C2×C412yes—
88(C2×D3)⋊Dic3C2×C412yes—
89(C2×D3)⋊Dic3C2×C412yes—
90#3711—24no—
91#2966—91noSylow
92C22×C3×C8—21no—
93C22×C3×C8—32no—
94C22×C3×C8C2×D312yes—
95C3×C4×D4—32no—
96#939—32no—
97#935—32no—
98C4×#67—32no—
99C4×#67C2×D312yes—
100#926—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—61no—
103C2×#208—32no—
104C22×C3⋊C8—32no—
105C22×C3⋊C8—61no—
106C2×ΓL(1,𝔽25)—32no—
107C2×D3×C8C2×D312yes—
108#898—32no—
109#889—32no—
110#886—32no—
111#885—32no—
112#879—32no—
113#878—32no—
114#872—32no—
115C4×Dic6—32no—
116C3×C4⋊C8—32no—
117C3×C22⋊C8—32no—
118C3×C22⋊C8—32no—
119C3×C4×C8—32no—
120#830—32no—
121#830C2×D312yes—
122(C2×D3)⋊C8—32no—
123(C2×D3)⋊C8C2×D312yes—
124#815—32no—
125#815—32no—
126#815—32no—
127Dic3⋊C8—32no—
128Dic3⋊C8—32no—
129Dic3⋊C8—32no—
130Dic3⋊C8C2×D312yes—
131C8×Dic3—32no—
132C8×Dic3—32no—
133C8×Dic3—32no—
134C8×Dic3—32no—
135C8×Dic3—61no—
136C8×Dic3—61no—
137C8×Dic3—61no—
138C8×Dic3—61no—
139C8×Dic3C2×D312yes—
140C4⋊(C3⋊C8)—32no—
141#803—32no—
142C23×C32C22×C411yescharacteristic
143C22×C3×D3C22×C412yes—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4C22×C411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3C22×C411yescharacteristic
151C2×C3⋊Dic3C22×C411yescharacteristic
152C2×C3⋊Dic3C22×C411yescharacteristic
153C2×C3⋊Dic3C22×C411yescharacteristic
154C3×#67—24no—
155C2×C3×Dic3C22×C412yes—
156C2×C3×Dic3C22×C412yes—
157C2×C3×Dic3C22×C412yes—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160#627—22no—
161#625—22no—
162C32×C8—21no—
163C32×C8#4112yes—
164C3⋊(C3⋊C8)—21no—
165C3⋊(C3⋊C8)#4112yes—
166C3×C3⋊C8—22no—
167C3×C3⋊C8—22no—
168#529—91no—
169#446—91no—
170C8×Q8—91no—
171#436—91no—
172#435—92no—
173C8×D4—32no—
174C8×D4—91no—
175#433—92no—
176#432—91no—
177#405—92no—
178C2×C4×C8—91no—
179C2×C3×D4—32no—
180C22×C3×C4—21no—
181C22×C3×C4—32no—
182C22×C3×C4C22×D312yes—
183C2×#67—32no—
184C2×#67C4×D312yes—
185C22×Dic3—32no—
186C22×Dic3—32no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C2×C4×D3C22×D312yes—
190C2×Dic6—32no—
191C2×C3×C8—24no—
192C2×C3×C8—24no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C2×C3×C8—64no—
198C2×C3×C8C22×D312yes—
199C2×C3×C8C22×D312yes—
200C3×C4⋊C4—32no—
201C3×C22⋊C4—32no—
202C3×C22⋊C4—32no—
203C3×C42—32no—
204#217—32no—
205#217—32no—
206#217—32no—
207#217C4×D312yes—
208(C2×D3)⋊C4—32no—
209(C2×D3)⋊C4—32no—
210(C2×D3)⋊C4—32no—
211(C2×D3)⋊C4C4×D312yes—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215Dic3⋊C4—32no—
216Dic3⋊C4—32no—
217Dic3⋊C4—32no—
218Dic3⋊C4—32no—
219Dic3⋊C4—32no—
220Dic3⋊C4C4×D312yes—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3C22×D312yes—
230#208—64no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—64no—
236C2×C3⋊C8—64no—
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239ΓL(1,𝔽25)—64no—
240D3×C8—24no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#13112yes—
244C22×C32C23×C411yescharacteristic
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3—22no—
248C32×C4—21no—
249C32×C4C2×#4111yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—21no—
252C3⋊Dic3—21no—
253C3⋊Dic3—21no—
254C3⋊Dic3#13112yes—
255C3×Dic3—22no—
256C3×Dic3—22no—
257C3×Dic3—22no—
258C2×M16—92no—
259C22×C8—32no—
260C22×C8—91no—
261C22×C8D3211yescharacteristic
262#126—92no—
263#125—91no—
264#124—91no—
265#123—92no—
266C22⋊Q8—91no—
267#121—91no—
268C4×Q8—91no—
269C4×D4—32no—
270C4×D4—91no—
271#117—92no—
272C2×C42—91no—
273C4⋊C8—32no—
274C4⋊C8—92no—
275C4⋊C8—91no—
276C4⋊C8—91no—
277C22⋊C8—32no—
278C22⋊C8—32no—
279C22⋊C8—92no—
280#97—92no—
281#97—92no—
282C4×C8—32no—
283C4×C8—91no—
284C4×C8—91no—
285C4×C8—91no—
286C4×C8—91no—
287C23×C3—21no—
288C23×C3—32no—
289C23×C3C2×C4×D312yes—
290C22×D3C2×C4×D312yes—
291C3×D4—64no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—32no—
299C2×C3×C4—32no—
300C2×C3×C4—32no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4C2×C4×D312yes—
304C2×C3×C4C23×D312yes—
305#67—24no—
306#67—64no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—32no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3C2×C4×D312yes—
320C2×Dic3C2×C4×D312yes—
321C2×Dic3C2×C4×D312yes—
322C4×D3—22no—
323C4×D3—22no—
324Dic6—64no—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—22no—
328C3×C8—62no—
329C3×C8—62no—
330C3×C8#23714yes—
331C3⋊C8—22no—
332C3⋊C8—22no—
333C3⋊C8—34no—
334C3⋊C8—62no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32—22no—
338C2×C32C4×#4111yescharacteristic
339C2×C32C2×#13111yescharacteristic
340C2×C32C2×#13111yescharacteristic
341C3×D3—42no—
342C2×Q8—91no—
343C2×D4—32no—
344C2×D4—91no—
345C22×C4—32no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4C2×D3211yescharacteristic
349M16—184no—
350C2×C8—22no—
351C2×C8—32no—
352C2×C8—32no—
353C2×C8—64no—
354C2×C8—91no—
355C2×C8—91no—
356C2×C8—182no—
357C2×C8C2×D3211yescharacteristic
358C2×C8C2×D3211yescharacteristic
359C4⋊C4—32no—
360C4⋊C4—92no—
361C4⋊C4—92no—
362C4⋊C4—91no—
363C4⋊C4—91no—
364C4⋊C4—92no—
365C22⋊C4—32no—
366C22⋊C4—32no—
367C22⋊C4—92no—
368C22⋊C4—92no—
369C22⋊C4—92no—
370C42—32no—
371C42—91no—
372C42—91no—
373C42—91no—
374C42—91no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—22no—
381C22×C3—62no—
382C22×C3—62no—
383C22×C3—62no—
384C22×C3#90114yes—
385C22×C3C22×C4×D312yes—
386C2×D3—22no—
387C2×D3—22no—
388C2×D3—22no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—62no—
394C3×C4—62no—
395C3×C4—62no—
396C3×C4C2×#23712yes—
397C3×C4D3×#4112yes—
398Dic3—22no—
399Dic3—22no—
400Dic3—22no—
401Dic3—34no—
402Dic3—62no—
403Dic3—62no—
404Dic3—62no—
405Dic3—62no—
406Dic3—62no—
407Dic3—62no—
408Dic3—62no—
409C32#296611yescharacteristic, complemented, Sylow
410C23—32no—
411C23C4×D3211yescharacteristic
412Q8—182no—
413D4—64no—
414D4—182no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—32no—
418C2×C4—32no—
419C2×C4—32no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—91no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4C4×D3211yescharacteristic
429C2×C4C22×D3211yescharacteristic
430C8—21no—
431C8—62no—
432C8—62no—
433C8—92no—
434C8—181no—
435C8#380512yes—
436C2×C3—24no—
437C2×C3—24no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—122no—
442C2×C3C4×#23712yes—
443C2×C3C2×#90112yes—
444C2×C3D3×#13112yes—
445D3—42no—
446C22—21no—
447C22—21no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22#6380312yes—
452C22C2×C4×D3211yescharacteristic
453C4—21no—
454C4—62no—
455C4—62no—
456C4—62no—
457C4—92no—
458C4—181no—
459C4—181no—
460C4—181no—
461C4#6430611yescharacteristic
462C4C2×#380511yescharacteristic
463C3—21no—
464C3#7940012yescomplemented
465C2—22no—
466C2—122no—
467C2#1059466911yescharacteristic
468C2C2×#6380311yescharacteristic
469C2C4×#380511yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#63980C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C8×C3⋊Dic3C2semidirect
3. C3×C8×#67C2semidirect
4. #10591158C2semidirect
5. #10591066C2semidirect
6. #10590788C2semidirect
7. C8×#627C2semidirect
8. #10590734C2semidirect
9. C8×#625C2semidirect
10. #10590698C2semidirect
11. #10590692C2semidirect
45. C8×#67D3semidirect
409. C32#2966semidirect
464. C3#79400semidirect

Maximal subgroups

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

subgroupindex
#105950332
C2×C8×C3⋊Dic32
C3×C8×#672
#105911582
#105910662
#105907882
C8×#6272
#105907342
C8×#6252
#105906982
#105906922
#794003