Finite Group Databasebeta

← #11878715

Subgroups — #11878715

Order 1152.

927 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic
3#10592784C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591584C214yesmaximal, complemented
6#10591565C214yesmaximal, complemented
7#10590373C211yesmaximal, characteristic, complemented
8#10590290C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83213—31nomaximal
11#81602—31nomaximal
12C2×C3×D3×Q8C2212yes—
13C2×#3799—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C2×#3755C2214yes—
16#64083C2211yescharacteristic
17C3×#944C2212yes—
18C3×D3×C4⋊C4—21no—
19C3×D3×C4⋊C4—21no—
20C3×#888—21no—
21C3×#888—21no—
22C3×C42×D3C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63909—21no—
26#63909C2212yes—
27#63894—21no—
28#63894C2212yes—
29#63864—21no—
30C2×#3717C2214yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#835C2214yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34Dic3⋊(C3⋊C8)C2212yes—
35#63565C2214yes—
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C2×C3×C4⋊Q8—31no—
38#5725—31no—
39D3×C4⋊Q8D311yescharacteristic, complemented
40#5477—31no—
41C3×#487—31no—
42#5227—34no—
43#5093—31no—
44#5085—31no—
45#5085—31no—
46#5085—31no—
47#5085—61no—
48#5083—34no—
49#5079—31no—
50#5079D311yescharacteristic, complemented
51#4925—31no—
52#4818—34no—
53#4806—34no—
54#4693—31no—
55#4685—31no—
56C2×C32×Q8C2312yes—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C3×D3×Q8—44no—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3D411yescharacteristic
63C2×C3×C4×D3D411yescharacteristic
64C2×C3×C4×D3C2311yescharacteristic
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6C2312yes—
68C2×#626—22no—
69C2×#624—22no—
70#3799—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C42C2311yescharacteristic
74#3755—44no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86#3722—22no—
87#3722—22no—
88#3717—44no—
89#3206—91noSylow
90C22×C3×Q8—32no—
91C2×#239—61no—
92C2×D3×Q8C2×D312yes—
93C2×#235—61no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—32no—
96C3×C4⋊Q8—31no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8—61no—
99C3×C4⋊Q8—61no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C2×C3×C4⋊C4—61no—
103C2×C3×C4⋊C4—61no—
104C2×C3×C42—31no—
105#947—61no—
106#944C2×D312yes—
107C2×#215—34no—
108C2×#215—34no—
109C2×#215—34no—
110C2×#215—64no—
111#930—32no—
112#930—61no—
113C2×#204—34no—
114#895—32no—
115#895—61no—
116#893—32no—
117#893—61no—
118D3×C4⋊C4—21no—
119D3×C4⋊C4—21no—
120#888—21no—
121#888—21no—
122#875—61no—
123#874—31no—
124#874—31no—
125#874—61no—
126C4×D12—32no—
127C4×D12—61no—
128C42×D3C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130#869C2×D311yescharacteristic
131C3×#103—34no—
132C3×C4×C8—31no—
133#835—34no—
134#835C2×D314yes—
135#830—32no—
136(C2×D3)⋊C8—32no—
137Dic3⋊C8—32no—
138#810—34no—
139C4⋊(C3⋊C8)—32no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—61no—
143C4×C3⋊C8C2×D311yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3×D3C2×D411yescharacteristic
146C32×Q8—24no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151C4⋊(C3⋊D3)—24no—
152C4⋊(C3⋊D3)—42no—
153C4⋊(C3⋊D3)—42no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3C2×D411yescharacteristic
157C2×C3×Dic3C2×D411yescharacteristic
158C2×C3×Dic3C2×D411yescharacteristic
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—44no—
162C3×C4×D3SD1614yescomplemented
163C3×Dic6—24no—
164C3×Dic6—44no—
165C3×Dic6—42no—
166#626—44no—
167#624—44no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170#532—91no—
171C2×C4⋊Q8—31no—
172#492—91no—
173#492—91no—
174#487—31no—
175#487—91no—
176#461—94no—
177#448—94no—
178#431—91no—
179C2×C3×Q8—22no—
180C2×C3×Q8—32no—
181C2×C3×Q8—62no—
182C2×C3×Q8—61no—
183C2×C3×Q8—124no—
184C2×C3×Q8C22×D312yes—
185C2×C3×Q8C22×D312yes—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—62no—
190C2×#67—62no—
191#239—124no—
192D3×Q8—44no—
193#235—124no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—62no—
197C2×D12—62no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—121no—
203C2×D12—121no—
204C2×C4×D3—22no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3#6711yescharacteristic
208C2×C4×D3#6711yescharacteristic
209C2×C4×D3C22×D311yescharacteristic
210C2×Dic6—21no—
211C2×Dic6—22no—
212C2×Dic6C22×D312yes—
213C2×C3×C8—32no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C42—21no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#215—124no—
233#215—124no—
234#215—124no—
235#215—128no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—22no—
245Dic3⋊C4—22no—
246C4×Dic3#6711yescharacteristic
247C4×Dic3#6711yescharacteristic
248C4×Dic3C22×D311yescharacteristic
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8C22×D312yes—
253#204—124no—
254C22×C32C22×D411yescharacteristic
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3×D3—21no—
259C2×C3×D3—21no—
260C2×C3×D3C2×SD1612yes—
261C32×C4—42no—
262C32×C4C2×SD1612yes—
263C32×C4#13712yes—
264C32×C4H(5,𝔽2)12yes—
265C3×Dic3—21no—
266C3×Dic3—21no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C2×SD1612yes—
270C2×#41—181no—
271C22×Q8—32no—
272C2×SD16—94no—
273C2×SD16—94no—
274C4⋊Q8—32no—
275C4⋊Q8—31no—
276C4⋊Q8—31no—
277C4⋊Q8—61no—
278C4⋊Q8—61no—
279C4⋊Q8D3211yescharacteristic
280#127—91no—
281#124—181no—
282#121—92no—
283#121—181no—
284C4×D4—92no—
285C4×D4—181no—
286C2×C4⋊C4—61no—
287C2×C4⋊C4—61no—
288C2×C42—31no—
289C4⋊C8—92no—
290#103—34no—
291#103—94no—
292C22⋊C8—92no—
293C4×C8—31no—
294C4×C8—91no—
295C23×C3—31no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—122no—
299C22×D3C2×#6711yescharacteristic
300C3×Q8—24no—
301C3×Q8—24no—
302C3×Q8—44no—
303C3×Q8—64no—
304C3×Q8—124no—
305C3×Q8—122no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—34no—
313C2×C3×C4—31no—
314C2×C3×C4—31no—
315C2×C3×C4—42no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—124no—
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327#67—124no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3C2×#6711yescharacteristic
331C2×Dic3C2×#6711yescharacteristic
332C2×Dic3C2×#6711yescharacteristic
333D12—64no—
334D12—64no—
335D12—124no—
336D12—124no—
337D12—122no—
338D12—122no—
339D12—122no—
340D12—122no—
341D12—242no—
342D12—242no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—44no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3#21514yescomplemented
349Dic6—24no—
350Dic6—44no—
351Dic6—42no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—64no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C2×C32#53511yescharacteristic
358C2×C32C22×SD1611yescharacteristic
359C2×C32C2×#13711yescharacteristic
360C3⋊D3—82no—
361C3×D3—22no—
362#41—364no—
363C2×Q8—32no—
364C2×Q8—62no—
365C2×Q8—61no—
366C2×Q8—124no—
367C2×Q8C2×D3212yes—
368C2×D4—92no—
369C2×D4—182no—
370C2×D4—181no—
371C2×D4—181no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—62no—
376C22×C4—182no—
377SD16—364no—
378SD16—364no—
379C2×C8—32no—
380C2×C8—92no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—32no—
384C4⋊C4—62no—
385C4⋊C4—62no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C22⋊C4—182no—
390C22⋊C4—182no—
391C42—31no—
392C42—31no—
393C42—31no—
394C42C2×D3211yescharacteristic
395C22×C3—21no—
396C22×C3—32no—
397C22×C3—61no—
398C22×C3—61no—
399C22×C3C2×D3×D411yescharacteristic
400C22×C3C22×#6711yescharacteristic
401C2×D3—21no—
402C2×D3—21no—
403C2×D3—122no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—242no—
410C2×D3—242no—
411C2×D3—242no—
412C2×D3C2×#21512yes—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—32no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—61no—
420C3×C4—61no—
421C3×C4—82no—
422C3×C4—122no—
423C3×C4—122no—
424C3×C4D3×SD1612yes—
425C3×C4#91812yes—
426C3×C4C2×#21512yes—
427C3×C4#94212yes—
428C3×C4#100412yes—
429C3×C4#100912yes—
430Dic3—21no—
431Dic3—21no—
432Dic3—42no—
433Dic3—42no—
434Dic3C2×#21512yes—
435C32#320611yescharacteristic, complemented, Sylow
436C23—31no—
437C23—182no—
438Q8—24no—
439Q8—64no—
440Q8—124no—
441Q8—122no—
442D4—184no—
443D4—364no—
444D4—362no—
445D4—362no—
446C2×C4—22no—
447C2×C4—31no—
448C2×C4—34no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—124no—
456C2×C4—364no—
457C2×C4D3×#6711yescharacteristic
458C2×C4D3×#6711yescharacteristic
459C2×C4C22×D3211yescharacteristic
460C8—62no—
461C8—182no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—62no—
466C2×C3#567411yescharacteristic
467C2×C3C2×D3×SD1611yescharacteristic
468C2×C3C2×#91811yescharacteristic
469C2×C3#580511yescharacteristic
470C2×C3C22×#21511yescharacteristic
471C2×C3C2×#94211yescharacteristic
472D3—22no—
473D3—242no—
474D3—242no—
475D3—482no—
476C22—32no—
477C22—61no—
478C22—61no—
479C22—362no—
480C22—362no—
481C22—362no—
482C22C2×D3×#6711yescharacteristic
483C4—32no—
484C4—42no—
485C4—61no—
486C4—61no—
487C4—122no—
488C4—122no—
489C4D3×#21512yes—
490C4#6394812yes—
491C4#6431412yes—
492C3—21no—
493C3#8160211yescharacteristic, complemented
494C3#8321311yescharacteristic, complemented
495C2—62no—
496C2—722no—
497C2#1059523511yescharacteristic
498C2C2×D3×#21511yescharacteristic
499C2C2×#6394811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593970C2
hypercenterC4⋊Q8D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. #10592784C2semidirect
4. C3×#5079C2semidirect
5. #10591584C2semidirect
6. #10591565C2semidirect
7. #10590373C2semidirect
8. #10590290C2semidirect
9. #10590261C2semidirect
39. D3×C4⋊Q8D3semidirect
50. #5079D3semidirect
162. C3×C4×D3SD16semidirect
348. C4×D3#215semidirect
435. C32#3206semidirect
493. C3#81602semidirect
494. C3#83213semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
#105939702
#105927842
C3×#50792
#105915842
#105915652
#105903732
#105902902
#105902612
#832133
#816023