Finite Group Databasebeta

← #11788726

Subgroups — #11788726

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic
3#10592924C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic
6#10589158C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#71865—31nomaximal
9#70350—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947C412yescomplemented
15C3×#946—22no—
16C3×#944C412yescomplemented
17C3×#929—22no—
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24#63662—22no—
25C3×#835—22no—
26#63580—22no—
27C3×#536—31no—
28#5819—31no—
29#5816D311yescharacteristic
30#5745—31no—
31C3×#419—31no—
32#5240—31no—
33#5225—31no—
34#5225—31no—
35#5225—61no—
36#5225D311yescharacteristic, complemented
37#5006—31no—
38#4557—31no—
39#4531—31no—
40#4531—31no—
41#4531—31no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67D412yes—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3D412yes—
57C2×C3×Dic6C2×C411yescharacteristic
58#3757—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4×C3⋊Dic3—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64C3×#217—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×Dic3⋊C4—24no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yes—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8D412yes—
75#3711—24no—
76D3×C3⋊C8—24no—
77#1909—91noSylow
78C2×C3×#41—31no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C2×D311yescharacteristic
82C2×#235C2×D311yescharacteristic
83C2×C3×M16—31no—
84C3×C4⋊Q8—32no—
85C3×#124—32no—
86C3×#123—62no—
87C3×C22⋊Q8—62no—
88C3×#117—31no—
89C3×#117—31no—
90#948—62no—
91#948—62no—
92#947Dic312yescomplemented
93#946—22no—
94#944Dic312yescomplemented
95#929—22no—
96#926—31no—
97#926—31no—
98#926—61no—
99#926C2×D311yescharacteristic
100#926C2×D311yescharacteristic
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—61no—
104C2×#208—62no—
105C2×#208C2×D311yescharacteristic
106#907—62no—
107D3×M16—62no—
108#901—62no—
109C3×#103—62no—
110#835—22no—
111#835—62no—
112#835—62no—
113#835—64no—
114#834—62no—
115#806—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3C22⋊C412yes—
118C32×Q8—22no—
119C32×Q8—22no—
120C32×Q8—41no—
121C32×Q8—41no—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—41no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C22⋊C412yes—
137C3×D12—21no—
138C3×D12—21no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×Dic6—21no—
142C3×Dic6—21no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145#568—91no—
146#536—31no—
147#419—31no—
148#419—91no—
149#410—91no—
150H(3,ℤ/4)—91no—
151H(3,ℤ/4)—91no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—22no—
159C2×C3×Q8—22no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—31no—
170C2×C3×Q8—41no—
171C2×C3×Q8—41no—
172C2×C3×Q8—41no—
173C2×C3×Q8C4×D312yes—
174C2×C3×Q8C2×Dic312yes—
175C2×C3×D4—32no—
176C2×C3×D4—31no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—41no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67#6712yes—
185#235—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189C2×D12C2×Dic311yescharacteristic
190C2×C4×D3#6712yes—
191C2×Dic6C2×Dic311yescharacteristic
192C3×M16—61no—
193C3×M16—61no—
194C2×C3×C8—32no—
195C3×C4⋊C4—64no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—64no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C42—32no—
202C3×C42—61no—
203#217—21no—
204#217—21no—
205#217—61no—
206#217—61no—
207#217—121no—
208(C2×D3)⋊C4—24no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214Dic3⋊C4—24no—
215C4×Dic3—21no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—121no—
219C4×Dic3C2×Dic312yes—
220#208—21no—
221#208—21no—
222#208—64no—
223#208—61no—
224#208—61no—
225#208—61no—
226#208—61no—
227#208—121no—
228#208—121no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—64no—
233C2×C3⋊C8#6712yes—
234ΓL(1,𝔽25)—64no—
235D3×C8—64no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C32×C4—42no—
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4#12011yescharacteristic
246C32×C4#12311yescharacteristic
247C3⋊Dic3—81no—
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—81no—
251C2×#41—31no—
252C22×Q8D3211yescharacteristic
253#131—182no—
254#131—182no—
255C2×M16—31no—
256C2×M16—91no—
257C2×M16—182no—
258C4⋊Q8—32no—
259#124—32no—
260#123—62no—
261C22⋊Q8—62no—
262#117—31no—
263#117—31no—
264#117—91no—
265#103—62no—
266#103—182no—
267#99—182no—
268C23×C3—21no—
269C23×C3—32no—
270C23×C3D3×D411yescharacteristic
271C23×C3C2×#6711yescharacteristic
272C22×D3#21712yes—
273C3×Q8—24no—
274C3×Q8—22no—
275C3×Q8—22no—
276C3×Q8—22no—
277C3×Q8—22no—
278C3×Q8—42no—
279C3×Q8—42no—
280C3×Q8—42no—
281C3×Q8—41no—
282C3×Q8—41no—
283C3×Q8—41no—
284C3×Q8—41no—
285C3×Q8—61no—
286C3×Q8—61no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—61no—
290C3×D4—61no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—32no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—121no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4C22×Dic311yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323#67—22no—
324#67—22no—
325C2×Dic3—22no—
326C2×Dic3—41no—
327C2×Dic3—122no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3#21712yes—
331D12—21no—
332D12—21no—
333C4×D3—22no—
334C4×D3—22no—
335Dic6—21no—
336Dic6—21no—
337C3×C8—62no—
338C3⋊C8—22no—
339C3⋊C8—62no—
340C3⋊C8—62no—
341C3⋊C8—122no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#38611yescharacteristic
346C3×D3—42no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—31no—
357C2×Q8D3×Dic312yes—
358C2×D4—32no—
359C2×D4—31no—
360C22×C4—21no—
361C22×C4—32no—
362C22×C4C2×D3211yescharacteristic
363M16—61no—
364M16—61no—
365M16—184no—
366M16—181no—
367M16—181no—
368C2×C8—32no—
369C2×C8—92no—
370C2×C8—184no—
371C4⋊C4—64no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—181no—
375C22⋊C4—64no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—181no—
379C42—32no—
380C42—61no—
381C42—181no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—62no—
389C22×C3—122no—
390C22×C3D3×C22⋊C411yescharacteristic
391C22×C3#88411yescharacteristic
392C22×C3#93811yescharacteristic
393C22×C3#93911yescharacteristic
394C22×C3#93911yescharacteristic
395C22×C3C2×#21711yescharacteristic
396C2×D3—22no—
397C2×D3—42no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—44no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—62no—
406C3×C4—122no—
407C3×C4—241no—
408C3×C4#67⋊C411yescharacteristic
409C3×C4#88311yescharacteristic
410C3×C4C4×#6711yescharacteristic
411C3×C4D4×Dic311yescharacteristic
412C3×C4D4×Dic311yescharacteristic
413C3×C4#93511yescharacteristic
414C3×C4#93711yescharacteristic
415C3×C4#93711yescharacteristic
416Dic3—22no—
417Dic3—42no—
418Dic3—81no—
419Dic3—242no—
420Dic3—241no—
421Dic3—241no—
422C32#190911yescharacteristic, complemented, Sylow
423C23—32no—
424C23D3×#6711yescharacteristic
425Q8—22no—
426Q8—22no—
427Q8—41no—
428Q8—41no—
429Q8—61no—
430Q8—61no—
431D4—62no—
432D4—62no—
433D4—61no—
434D4—61no—
435C2×C4—22no—
436C2×C4—32no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—121no—
443C2×C4—361no—
444C2×C4C2×D3×Dic311yescharacteristic
445C2×C4#380411yescharacteristic
446C2×C4#380511yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C2×C4D3×#6711yescharacteristic
449C2×C4#381111yescharacteristic
450C8—62no—
451C8—182no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—122no—
463C2×C3#495611yescharacteristic
464C2×C3#522011yescharacteristic
465D3—42no—
466C22—41no—
467C22—62no—
468C22—122no—
469C22D3×#21711yescharacteristic
470C22#6397011yescharacteristic
471C22#6397111yescharacteristic
472C4—42no—
473C4—62no—
474C4—122no—
475C4—241no—
476C4—721no—
477C4#6396911yescharacteristic
478C4Dic3×#6711yescharacteristic
479C4#67⋊Dic311yescharacteristic
480C4#6398311yescharacteristic
481C3—21no—
482C3#7035011yescharacteristic, complemented
483C3#7186511yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—21no—
487C2—122no—
488C2#1059172111yescharacteristic
subgroupG/H
centerC2#10591721
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1909
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10592924C2semidirect
4. C3×#5225C2semidirect
6. #10589158C2semidirect
7. #10589157C2semidirect
14. C3×#947C4semidirect
16. C3×#944C4semidirect
36. #5225D3semidirect
92. #947Dic3semidirect
94. #944Dic3semidirect
422. C32#1909semidirect
482. C3#70350semidirect
483. C3#71865semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
#105947762
#105929242
C3×#52252
#105912312
#105891582
#105891572
#718653
#703503