Finite Group Databasebeta

← #11877003

Subgroups — #11877003

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596187C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic, complemented
3C3×#5073C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591454C214yesmaximal, complemented
6#10591436C214yesmaximal, complemented
7C4×#3712C211yesmaximal, characteristic, complemented
8#10590303C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#81777—31nomaximal
11#81560—31nomaximal
12C2×#3830—21no—
13C2×#3796—21no—
14C32×#127C2211yescharacteristic
15#64147—21no—
16#64147C2212yes—
17#64145—21no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2212yes—
20C42×C3⋊D3C2211yescharacteristic
21#64078C2211yescharacteristic
22C2×C3×#213C2214yes—
23C3×#874C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63916—21no—
26#63916C2212yes—
27#63898—21no—
28#63898C2212yes—
29#63863—21no—
30C2×#3712C2212yes—
31C3×#832C2214yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63573C2214yes—
35#63563C2214yes—
36#63555C2212yes—
37#5725—31no—
38#5716—31no—
39#5716—31no—
40#5716—31no—
41#5716—61no—
42C3×#493—31no—
43C3×#486—31no—
44#5159—34no—
45#5152—34no—
46#5080—31no—
47#5073D311yescharacteristic, complemented
48#5070—31no—
49#5070D311yescharacteristic, complemented
50#4785—34no—
51#4782—34no—
52#4694—31no—
53C4×ΓL(1,𝔽25)—31no—
54C4×ΓL(1,𝔽25)—31no—
55#4680—31no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×#638—22no—
60C22×C3⋊Dic3—22no—
61#3830—44no—
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×#634—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×D3×Dic3—22no—
72#3796—44no—
73C32×C42C2311yescharacteristic
74#3757—22no—
75#3757—22no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80C4×C3⋊Dic3C2311yescharacteristic
81C3×#213—28no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3712—24no—
89#3184—91noSylow
90C2×#239—61no—
91C2×#237—61no—
92C2×#237—61no—
93C2×#237—61no—
94C2×#237—62no—
95C2×C3×D8—34no—
96C3×C4⋊Q8—31no—
97C3×#127—21no—
98C3×#127—31no—
99C3×#127C2×D311yescharacteristic
100C3×#127C2×D311yescharacteristic
101#947—61no—
102#938—32no—
103#938—32no—
104#938—32no—
105#938—62no—
106#938—61no—
107#938—61no—
108#938—61no—
109#938—62no—
110#936—61no—
111#936—61no—
112#936—61no—
113#936—62no—
114D4×Dic3—32no—
115D4×Dic3—32no—
116D4×Dic3—32no—
117D4×Dic3—62no—
118D4×Dic3—61no—
119D4×Dic3—61no—
120D4×Dic3—61no—
121D4×Dic3—62no—
122C2×#213C2×D314yes—
123C2×ΓL(1,𝔽25)—32no—
124C2×ΓL(1,𝔽25)—32no—
125#895—32no—
126#895—61no—
127#893—32no—
128#893—61no—
129#874C2×D311yescharacteristic
130C42×D3—31no—
131C42×D3—31no—
132C42×D3—61no—
133#869—31no—
134#869—31no—
135#869—61no—
136#869C2×D311yescharacteristic
137C3×#102—34no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#832—34no—
141#832C2×D314yes—
142#821—34no—
143#817—34no—
144#815—32no—
145#815—32no—
146#808—34no—
147C4×C3⋊C8C2×D311yescharacteristic
148C4×C3⋊C8C2×D311yescharacteristic
149C23×C32—22no—
150C22×C3⋊D3C2×D411yescharacteristic
151C22×C3×D3—22no—
152C32×D4—24no—
153C32×D4—42no—
154C32×D4—42no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2411yescharacteristic
158#638—44no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—44no—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4×C3⋊D3—22no—
165C4×C3⋊D3—22no—
166C4×C3⋊D3—22no—
167#634—42no—
168C2×C3×Dic3—22no—
169C3×D12—24no—
170C3×D12—42no—
171C3×D12—42no—
172C3×Dic6—42no—
173#626—44no—
174D3×Dic3—44no—
175C3×C3⋊C8—22no—
176C3×C3⋊C8#4114yescomplemented
177#532—91no—
178#532—91no—
179#498—91no—
180#493—31no—
181#486—31no—
182#486—91no—
183#469—94no—
184#442—94no—
185C4×M16—91no—
186C2×C3×Q8—61no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C2×#67—62no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—64no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206C22×Dic3—64no—
207#239—124no—
208#237—124no—
209#237—128no—
210#237—124no—
211#237—124no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—62no—
215C2×D12C22×D312yes—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—31no—
220C2×C4×D3—31no—
221C2×C4×D3—31no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—62no—
226C2×Dic6—21no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C3×D8—68no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C42—21no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#217—62no—
241#217—62no—
242#217—62no—
243#217—62no—
244#217—64no—
245#217—64no—
246#213—28no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3C22×D312yes—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—31no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C2×C3⋊C8C22×D312yes—
267C2×C3⋊C8C22×D312yes—
268ΓL(1,𝔽25)—64no—
269ΓL(1,𝔽25)—64no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32—42no—
273C22×C32C22×D411yescharacteristic
274C2×C3⋊D3—21no—
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C32×C4AGL(1,ℤ/8)12yes—
281C32×C4AGL(1,ℤ/8)12yes—
282C32×C4C2×#4112yes—
283C3⋊Dic3—21no—
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3—42no—
287C3×Dic3—42no—
288C2×#41—181no—
289C2×#41—181no—
290C2×D8—34no—
291C2×M16—92no—
292C4⋊Q8—31no—
293C4⋊Q8—91no—
294#127—31no—
295#127D3211yescharacteristic
296#124—181no—
297#124—181no—
298#121—92no—
299#121—92no—
300#121—181no—
301#121—181no—
302C4×D4—92no—
303C4×D4—92no—
304C4×D4—181no—
305C4×D4—181no—
306C2×C42—91no—
307#106—94no—
308#102—34no—
309#102—94no—
310#97—92no—
311C4×C8—31no—
312C4×C8—31no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—62no—
317C22×D3—22no—
318C22×D3—31no—
319C22×D3—31no—
320C22×D3—61no—
321C3×Q8—122no—
322C3×D4—24no—
323C3×D4—24no—
324C3×D4—44no—
325C3×D4—44no—
326C3×D4—44no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—64no—
332C3×D4—122no—
333C3×D4—122no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—62no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344#67—124no—
345#67—128no—
346#67—124no—
347#67—124no—
348C2×Dic3—22no—
349C2×Dic3—31no—
350C2×Dic3—31no—
351C2×Dic3—31no—
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—31no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—124no—
362C2×Dic3—128no—
363C2×Dic3—124no—
364C2×Dic3—124no—
365D12—24no—
366D12—42no—
367D12—42no—
368D12—124no—
369C4×D3—64no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—124no—
379Dic6—42no—
380Dic6—124no—
381Dic6—122no—
382Dic6—122no—
383C3×C8—34no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8#23714yescomplemented
387C2×C32—82no—
388C2×C32#53211yescharacteristic
389C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
390C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
391C3⋊D3—41no—
392C3×D3—82no—
393#41—364no—
394#41—364no—
395C2×Q8—61no—
396C2×Q8—181no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—32no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—182no—
403C2×D4—182no—
404C2×D4C2×D3212yes—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—182no—
409C22×C4—182no—
410D8—68no—
411M16—184no—
412C2×C8—32no—
413C2×C8—32no—
414C4⋊C4—32no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—181no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C42—91no—
423C42—91no—
424C42—91no—
425C42C2×D3211yescharacteristic
426C22×C3—21no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—42no—
444C2×D3—62no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—61no—
448C2×D3—61no—
449C2×D3—61no—
450C2×D3—61no—
451C2×D3—121no—
452C2×D3—121no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—122no—
457C3×C4#91112yes—
458C3×C4#91112yes—
459C3×C4#91112yes—
460C3×C4#91412yes—
461C3×C4C2×#23712yes—
462C3×C4D3×#4112yes—
463Dic3—42no—
464Dic3—62no—
465Dic3—61no—
466Dic3—61no—
467Dic3—61no—
468Dic3—61no—
469Dic3—61no—
470Dic3—61no—
471Dic3—121no—
472Dic3—121no—
473Dic3—124no—
474Dic3—122no—
475Dic3—122no—
476C32#318411yescharacteristic, complemented, Sylow
477C23—22no—
478C23—62no—
479C23—91no—
480Q8—122no—
481Q8—362no—
482D4—24no—
483D4—42no—
484D4—42no—
485D4—64no—
486D4—122no—
487D4—122no—
488D4—364no—
489D4—364no—
490C2×C4—62no—
491C2×C4—91no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—364no—
499C2×C4—364no—
500C2×C4#381111yescharacteristic
501C2×C4#381111yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—34no—
504C8—62no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—84no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3—242no—
512C2×C3#566811yescharacteristic
513C2×C3#571611yescharacteristic
514C2×C3C2×#91111yescharacteristic
515C2×C3C2×#91111yescharacteristic
516C2×C3C2×#91111yescharacteristic
517C2×C3C2×#91411yescharacteristic
518D3—82no—
519D3—122no—
520D3—121no—
521D3—121no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—122no—
526C22—122no—
527C22—122no—
528C22—181no—
529C22—181no—
530C22—181no—
531C22C2×#381111yescharacteristic
532C4—122no—
533C4—181no—
534C4—181no—
535C4—181no—
536C4—362no—
537C4#6392712yes—
538C4#6393712yes—
539C4D3×#23712yes—
540C3—21no—
541C3#8156011yescharacteristic, complemented
542C3#8177711yescharacteristic, complemented
543C2—82no—
544C2—242no—
545C2—361no—
546C2C2×#6392711yescharacteristic
547C2C2×#6393711yescharacteristic
548C2#1059516711yescharacteristic
subgroupG/H
centerC22C2×#3811
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. #10596187C2semidirect
2. #10593907C2semidirect
3. C3×#5073C2semidirect
4. C3×#5070C2semidirect
5. #10591454C2semidirect
6. #10591436C2semidirect
7. C4×#3712C2semidirect
8. #10590303C2semidirect
9. #10590273C2semidirect
47. #5073D3semidirect
49. #5070D3semidirect
176. C3×C3⋊C8#41semidirect
386. C3⋊C8#237semidirect
476. C32#3184semidirect
541. C3#81560semidirect
542. C3#81777semidirect

Maximal subgroups

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

subgroupindex
#105961872
#105939072
C3×#50732
C3×#50702
#105914542
#105914362
C4×#37122
#105903032
#105902732
#817773
#815603