Finite Group Databasebeta

← #11877002

Subgroups — #11877002

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10592772C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591453C214yesmaximal, complemented
6#10591404C214yesmaximal, complemented
7C4×#3711C211yesmaximal, characteristic, complemented
8#10590309C211yesmaximal, characteristic, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#83295—31nomaximal
11#81560—31nomaximal
12C2×C3×#237—21no—
13C2×#3799—21no—
14C32×#127C2211yescharacteristic
15C2×#3753C2214yes—
16#64083C2211yescharacteristic
17C3×#938—21no—
18C3×#938C2212yes—
19C3×#936—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×C42×D3C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63909—21no—
26#63909C2212yes—
27#63894—21no—
28#63894C2212yes—
29#63864—21no—
30C2×#3711C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#832C2214yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34#63574C2214yes—
35#63564C2214yes—
36#63554C2212yes—
37C3×#532—31no—
38#5725—31no—
39#5716D311yescharacteristic, complemented
40#5477—31no—
41C3×#486—31no—
42#5088—31no—
43#5080—31no—
44#5080—31no—
45#5073—31no—
46#5073—31no—
47#5073—61no—
48#5070D311yescharacteristic, complemented
49#5039—34no—
50#5014—34no—
51C4×#208—31no—
52#4785—34no—
53#4782—34no—
54#4694—31no—
55C4×ΓL(1,𝔽25)—31no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C3×#67—22no—
63C22×C3×Dic3—22no—
64C3×#237—44no—
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×#624—22no—
72#3799—44no—
73C32×C42C2311yescharacteristic
74#3753—28no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—22no—
77C3×#217—22no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2312yes—
86#3722—22no—
87#3722—22no—
88#3711—24no—
89#3184—91noSylow
90C2×C3×#41—61no—
91C2×#239—61no—
92C2×#237—21no—
93C2×#235—61no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8—31no—
96C3×#127—21no—
97C3×#127C2×D311yescharacteristic
98C3×#127C2×D311yescharacteristic
99C3×#124—61no—
100C3×#121—32no—
101C3×#121—61no—
102C3×C4×D4—32no—
103C3×C4×D4—61no—
104C2×C3×C42—31no—
105#947—61no—
106#938—21no—
107#938C2×D312yes—
108#936—21no—
109D4×Dic3—21no—
110D4×Dic3C2×D312yes—
111C2×#213—34no—
112C2×#213—34no—
113C2×#213—64no—
114#930—32no—
115#930—61no—
116C2×#208—32no—
117C2×ΓL(1,𝔽25)—32no—
118#895—32no—
119#895—61no—
120#893—32no—
121#893—61no—
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×#102—34no—
132C3×C4×C8—31no—
133#832C2×D314yes—
134#821—34no—
135#815—32no—
136#809—34no—
137#808—34no—
138#808—34no—
139#803—32no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—61no—
143C4×C3⋊C8C2×D311yescharacteristic
144C23×C32—22no—
145C22×C3⋊D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C32×D4—24no—
148C32×D4—42no—
149C32×D4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2411yescharacteristic
153C4⋊(C3⋊D3)—24no—
154C4⋊(C3⋊D3)—42no—
155C4⋊(C3⋊D3)—42no—
156C3×#67—44no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—44no—
160C2×C3×Dic3C2×D411yescharacteristic
161C2×C3×Dic3C2×D411yescharacteristic
162C2×C3×Dic3C2×D411yescharacteristic
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×Dic6—42no—
167C3×Dic6—42no—
168#626—44no—
169#624—44no—
170C3⋊(C3⋊C8)#4114yescomplemented
171C3×C3⋊C8—22no—
172#532—31no—
173#532—91no—
174#498—91no—
175#493—91no—
176#486—31no—
177#486—91no—
178#469—94no—
179#442—94no—
180C4×M16—91no—
181C3×#41—124no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4—62no—
192C2×C3×D4C22×D312yes—
193C2×C3×D4C22×D312yes—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—62no—
198C2×#67—22no—
199C2×#67—62no—
200C22×Dic3—22no—
201#239—124no—
202#237—44no—
203#235—124no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—121no—
213C2×D12—121no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3#6711yescharacteristic
217C2×C4×D3#6711yescharacteristic
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×C3×C8—32no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—62no—
227C3×C22⋊C4—62no—
228C3×C42—21no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—22no—
235#217—22no—
236#213—68no—
237#213—68no—
238#213—128no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3C22×D312yes—
246C4⋊Dic3C22×D312yes—
247C4×Dic3#6711yescharacteristic
248C4×Dic3#6711yescharacteristic
249C4×Dic3C22×D311yescharacteristic
250#208—64no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8C22×D312yes—
255ΓL(1,𝔽25)—64no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3×D3—21no—
264C2×C3×D3—21no—
265C2×C3×D3—21no—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4AGL(1,ℤ/8)12yes—
268C32×C4C2×#4112yes—
269C3×Dic3—21no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C2×#41—61no—
275C2×#41—181no—
276C2×D8—94no—
277C2×M16—92no—
278C4⋊Q8—31no—
279C4⋊Q8—31no—
280#127—91no—
281#127D3211yescharacteristic
282#124—61no—
283#124—181no—
284#121—32no—
285#121—61no—
286#121—92no—
287#121—181no—
288C4×D4—32no—
289C4×D4—61no—
290C4×D4—92no—
291C4×D4—181no—
292C2×C42—31no—
293#106—94no—
294#102—34no—
295#102—94no—
296#97—92no—
297C4×C8—31no—
298C4×C8—91no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—31no—
302C23×C3—42no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3C2×#6711yescharacteristic
307C3×Q8—122no—
308C3×Q8—122no—
309C3×D4—24no—
310C3×D4—24no—
311C3×D4—44no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—42no—
316C3×D4—82no—
317C3×D4—82no—
318C3×D4—124no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—31no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—124no—
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—44no—
338#67—124no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—44no—
342C2×Dic3C2×#6711yescharacteristic
343C2×Dic3C2×#6711yescharacteristic
344C2×Dic3C2×#6711yescharacteristic
345D12—64no—
346D12—64no—
347D12—124no—
348D12—124no—
349D12—122no—
350D12—122no—
351D12—122no—
352D12—122no—
353D12—242no—
354D12—242no—
355C4×D3—22no—
356C4×D3—22no—
357C4×D3—22no—
358C4×D3—124no—
359C4×D3—124no—
360Dic6—42no—
361Dic6—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C3⋊C8—34no—
365C3⋊C8—34no—
366C3⋊C8—64no—
367C2×C32—82no—
368C2×C32#53211yescharacteristic
369C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
370C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
371C3⋊D3—82no—
372C3×D3—41no—
373#41—124no—
374#41—364no—
375C2×Q8—61no—
376C2×Q8—61no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—62no—
380C2×D4—92no—
381C2×D4—182no—
382C2×D4—181no—
383C2×D4—181no—
384C2×D4C2×D3212yes—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—62no—
389C22×C4—182no—
390D8—188no—
391M16—184no—
392C2×C8—32no—
393C2×C8—92no—
394C4⋊C4—32no—
395C4⋊C4—32no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C22⋊C4—62no—
399C22⋊C4—62no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C42—31no—
403C42—31no—
404C42—31no—
405C42C2×D3211yescharacteristic
406C22×C3—21no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—61no—
414C22×C3—61no—
415C22×C3—61no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—82no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—242no—
431C2×D3—242no—
432C2×D3—242no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—61no—
437C3×C4—61no—
438C3×C4—61no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4#91112yes—
442C3×C4#91412yes—
443C3×C4#93212yes—
444C3×C4#94912yes—
445C3×C4D3×#4112yes—
446C3×C4D3×#4112yes—
447Dic3—21no—
448Dic3—21no—
449Dic3—21no—
450Dic3—42no—
451Dic3—42no—
452C32#318411yescharacteristic, complemented, Sylow
453C23—22no—
454C23—31no—
455C23—182no—
456Q8—122no—
457Q8—122no—
458D4—24no—
459D4—42no—
460D4—42no—
461D4—124no—
462D4—184no—
463D4—364no—
464D4—362no—
465D4—362no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—124no—
475C2×C4—364no—
476C2×C4D3×#6711yescharacteristic
477C2×C4D3×#6711yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—62no—
480C8—94no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—82no—
485C2×C3—82no—
486C2×C3—121no—
487C2×C3—162no—
488C2×C3#566811yescharacteristic
489C2×C3C2×#91111yescharacteristic
490C2×C3C2×#91411yescharacteristic
491C2×C3C2×#93211yescharacteristic
492C2×C3C2×#94911yescharacteristic
493C2×C3#583211yescharacteristic
494D3—41no—
495D3—242no—
496D3—242no—
497D3—482no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—362no—
505C22—362no—
506C22—362no—
507C22C2×D3×#6711yescharacteristic
508C4—61no—
509C4—61no—
510C4—61no—
511C4—122no—
512C4—122no—
513C4#6392512yes—
514C4#6393412yes—
515C4#6431212yes—
516C3—21no—
517C3#8156011yescharacteristic, complemented
518C3#8329511yescharacteristic, complemented
519C2—82no—
520C2—121no—
521C2—722no—
522C2C2×#6392511yescharacteristic
523C2C2×#6393411yescharacteristic
524C2#1059515311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. #10593970C2semidirect
3. #10592772C2semidirect
4. C3×#5070C2semidirect
5. #10591453C2semidirect
6. #10591404C2semidirect
7. C4×#3711C2semidirect
8. #10590309C2semidirect
9. #10590281C2semidirect
39. #5716D3semidirect
48. #5070D3semidirect
170. C3⋊(C3⋊C8)#41semidirect
452. C32#3184semidirect
517. C3#81560semidirect
518. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
#105939702
#105927722
C3×#50702
#105914532
#105914042
C4×#37112
#105903092
#105902812
#832953
#815603