Finite Group Databasebeta

← #11788718

Subgroups — #11788718

Order 1152.

703 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594866C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic
3#10592705C211yesmaximal, characteristic
4C3×#5004C211yesmaximal, characteristic, complemented
5#10591100C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70350—31nomaximal
9#68712—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63966—22no—
18#63871—22no—
19#63866C412yescomplemented
20#63864C412yescomplemented
21#63818—22no—
22#63817—22no—
23#63817—22no—
24#63633—22no—
25C3×#810—22no—
26#63566—22no—
27#5816—31no—
28#5745—31no—
29#5745—31no—
30#5526—31no—
31C3×#419—31no—
32#5225—31no—
33#5120—31no—
34#5006—31no—
35#5006—31no—
36#5006—61no—
37#5004D311yescharacteristic, complemented
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×#638D412yes—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4×C3⋊D3D412yes—
50C2×#634C2×C411yescharacteristic
51C22×C3×Dic3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6C2×C412yes—
58C32×C4⋊C4—21no—
59C32×C22⋊C4—21no—
60C32×C42—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3—21no—
64C3×#217—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3C2×C412yes—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73Dic3⋊Dic3—24no—
74#3722—24no—
75#3712—24no—
76#3710—24no—
77#1909—91noSylow
78C22×C3×Q8—31no—
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C22×Dic6C2×D311yescharacteristic
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#117—21no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89#947—32no—
90#946—62no—
91#944—32no—
92#929—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#907—62no—
100#907—62no—
101D3×M16—62no—
102D3×M16—62no—
103#901—62no—
104#901—62no—
105#897—62no—
106#886—62no—
107#875—32no—
108#869—32no—
109C3×#103—62no—
110#835—62no—
111#816—62no—
112#810—22no—
113#806—62no—
114#806—62no—
115#806—64no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3C22⋊C412yes—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—22no—
126#638—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3C22⋊C412yes—
129C4⋊(C3⋊D3)—21no—
130C4⋊(C3⋊D3)—21no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—22no—
133#634—21no—
134#634—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—22no—
140C3×Dic6—22no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—22no—
145#568—91no—
146#536—91no—
147#419—31no—
148#419—91no—
149#410—91no—
150H(3,ℤ/4)—31no—
151H(3,ℤ/4)—91no—
152C2×C3×Q8—32no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—32no—
163C2×#67—32no—
164C2×#67—62no—
165C22×Dic3—21no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—121no—
175#235—121no—
176#235—121no—
177#235—121no—
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—62no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6—21no—
189C2×Dic6—31no—
190C2×Dic6—31no—
191C2×Dic6—61no—
192C2×Dic6C4×D312yes—
193C3×M16—61no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—32no—
198C2×C3×C8—32no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—22no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—61no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—32no—
210C3×C42—41no—
211#217—21no—
212#217—62no—
213#217—61no—
214#217—61no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217C4⋊Dic3—21no—
218C4⋊Dic3—64no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—121no—
222Dic3⋊C4—64no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—121no—
226C4×Dic3C4×D312yes—
227#208—21no—
228#208—21no—
229#208—21no—
230#208—21no—
231C2×C3⋊C8D1212yes—
232C2×C3⋊C8#6712yes—
233ΓL(1,𝔽25)—64no—
234ΓL(1,𝔽25)—64no—
235D3×C8—64no—
236D3×C8—64no—
237C22×C32—41no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12111yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—42no—
243C32×C4—81no—
244C32×C4C4×D411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12011yescharacteristic
247C32×C4#12311yescharacteristic
248C3⋊Dic3—22no—
249C3⋊Dic3—81no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C2×#41—91no—
253C22×Q8—31no—
254#131—182no—
255#131—182no—
256C2×M16—31no—
257C2×M16—31no—
258C2×M16—182no—
259C4⋊Q8—92no—
260#124—92no—
261#123—182no—
262C22⋊Q8—182no—
263#117—31no—
264#117—91no—
265#117D3211yescharacteristic
266#103—62no—
267#103—182no—
268#99—182no—
269C23×C3—21no—
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3—32no—
273C22×D3—32no—
274C22×D3—62no—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×Q8—121no—
278C3×Q8—121no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×D1211yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23911yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304#67—62no—
305#67—62no—
306#67—62no—
307#67—62no—
308#67—122no—
309#67—122no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320D12—61no—
321D12—61no—
322D12—61no—
323D12—61no—
324D12—121no—
325D12—121no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—122no—
331C4×D3—122no—
332Dic6—22no—
333Dic6—22no—
334Dic6—41no—
335Dic6—41no—
336Dic6—61no—
337Dic6—61no—
338Dic6—61no—
339Dic6—61no—
340Dic6—121no—
341Dic6—121no—
342C3×C8—62no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32#38611yescharacteristic
350C3⋊D3—42no—
351#41—181no—
352#41—181no—
353#41—181no—
354#41—181no—
355C2×Q8—32no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×Q8—91no—
362C2×D4—92no—
363C2×D4—91no—
364C22×C4—61no—
365C22×C4—92no—
366C22×C4C2×D3211yescharacteristic
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371M16—184no—
372C2×C8—32no—
373C2×C8—32no—
374C2×C8—184no—
375C4⋊C4—21no—
376C4⋊C4—61no—
377C4⋊C4—184no—
378C4⋊C4—181no—
379C22⋊C4—21no—
380C22⋊C4—61no—
381C22⋊C4—184no—
382C22⋊C4—181no—
383C42—21no—
384C42—32no—
385C42—181no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—81no—
392C22×C3D3×C22⋊C411yescharacteristic
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3#88411yescharacteristic
395C22×C3#88411yescharacteristic
396C22×C3#89511yescharacteristic
397C22×C3#93811yescharacteristic
398C2×D3—62no—
399C2×D3—62no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—122no—
403C2×D3—242no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—81no—
409C3×C4—81no—
410C3×C4—82no—
411C3×C4—122no—
412C3×C4—122no—
413C3×C4C4×D1211yescharacteristic
414C3×C4#67⋊C411yescharacteristic
415C3×C4#88211yescharacteristic
416C3×C4#88311yescharacteristic
417C3×C4#89311yescharacteristic
418C3×C4#89411yescharacteristic
419C3×C4C4×#6711yescharacteristic
420C3×C4#93711yescharacteristic
421Dic3—42no—
422Dic3—42no—
423Dic3—62no—
424Dic3—62no—
425Dic3—122no—
426Dic3—241no—
427Dic3—241no—
428Dic3—242no—
429C32#190911yescharacteristic, complemented, Sylow
430C23—92no—
431C23#381111yescharacteristic
432Q8—62no—
433Q8—62no—
434Q8—121no—
435Q8—121no—
436Q8—181no—
437Q8—181no—
438D4—182no—
439D4—182no—
440D4—181no—
441D4—181no—
442C2×C4—41no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—92no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—361no—
451C2×C4#379911yescharacteristic
452C2×C4C4×D3211yescharacteristic
453C2×C4D3×D1211yescharacteristic
454C2×C4#380211yescharacteristic
455C2×C4#380411yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C8—62no—
458C8—62no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3#466511yescharacteristic
470C2×C3#495611yescharacteristic
471D3—122no—
472D3—122no—
473D3—242no—
474C22—41no—
475C22—182no—
476C22—362no—
477C22#6391011yescharacteristic
478C22#6392111yescharacteristic
479C22#6395811yescharacteristic
480C4—81no—
481C4—122no—
482C4—122no—
483C4—182no—
484C4—721no—
485C4#6385411yescharacteristic
486C4#6388011yescharacteristic
487C4#6390411yescharacteristic
488C4#6392211yescharacteristic
489C3—21no—
490C3#6871211yescharacteristic, complemented
491C3#7035011yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—21no—
495C2—362no—
496C2#1059127511yescharacteristic
subgroupG/H
centerC2#10591275
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1909
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C3×#5004C2semidirect
5. #10591100C2semidirect
6. C3×#4531C2semidirect
7. #10589158C2semidirect
19. #63866C4semidirect
20. #63864C4semidirect
37. #5004D3semidirect
41. #4531D3semidirect
429. C32#1909semidirect
490. C3#68712semidirect
491. C3#70350semidirect

Maximal subgroups

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

subgroupindex
#105948662
#105947802
#105927052
C3×#50042
#105911002
C3×#45312
#105891582
#703503
#687123