Finite Group Databasebeta

← #11878716

Subgroups — #11878716

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic
3C3×#5085C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591592C214yesmaximal, complemented
6#10591569C214yesmaximal, complemented
7#10590369C211yesmaximal, characteristic, complemented
8#10590297C211yesmaximal, characteristic, complemented
9#10590288C211yesmaximal, characteristic, complemented
10#81764—31nomaximal
11#81602—31nomaximal
12C2×Q8×C3⋊D3C2212yes—
13C2×#3796—21no—
14C32×C4⋊Q8C2211yescharacteristic
15#64153C2212yes—
16C4⋊C4×C3⋊D3—21no—
17C4⋊C4×C3⋊D3—21no—
18#64097—21no—
19#64097—21no—
20C42×C3⋊D3C2211yescharacteristic
21#64078C2211yescharacteristic
22C2×C3×#215C2214yes—
23C3×#874C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63916—21no—
26#63916C2212yes—
27#63898—21no—
28#63898C2212yes—
29#63863—21no—
30C2×#3716C2214yes—
31C3×#835C2214yes—
32C3×C4×C3⋊C8C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34#63572C2212yes—
35#63567C2214yes—
36#63557C2212yes—
37#5725—31no—
38D3×C4⋊Q8—31no—
39D3×C4⋊Q8—31no—
40D3×C4⋊Q8—61no—
41#5716—31no—
42C3×#492—31no—
43C3×#487—31no—
44#5170—34no—
45#5162—34no—
46#5093—31no—
47#5085D311yescharacteristic, complemented
48#5079D311yescharacteristic, complemented
49#5076—31no—
50#4818—34no—
51#4806—34no—
52#4693—31no—
53#4685—31no—
54#4685—31no—
55#4681—31no—
56C2×C32×Q8C2312yes—
57Q8×C3⋊D3—44no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3D411yescharacteristic
60C2×C4×C3⋊D3D411yescharacteristic
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×#634—22no—
63C2×#634C2312yes—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—21no—
68C2×#626—22no—
69C2×D3×Dic3—22no—
70#3796—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C42C2311yescharacteristic
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)—21no—
76#3750—22no—
77#3750—22no—
78C4×C3⋊Dic3D411yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80C4×C3⋊Dic3C2311yescharacteristic
81C3×#215—44no—
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#3716—44no—
89#3206—91noSylow
90C2×#239—61no—
91C2×D3×Q8—32no—
92C2×D3×Q8—32no—
93C2×D3×Q8—62no—
94C2×#237—61no—
95C2×C3×SD16—34no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—31no—
98C3×C4⋊Q8C2×D311yescharacteristic
99C3×C4⋊Q8C2×D311yescharacteristic
100C3×#127—31no—
101#947—61no—
102#944—32no—
103#944—32no—
104#944—62no—
105C2×#215C2×D314yes—
106#938—32no—
107#938—61no—
108#936—61no—
109D4×Dic3—32no—
110D4×Dic3—61no—
111C2×#214—34no—
112C2×#204—34no—
113#895—32no—
114#895—61no—
115#893—32no—
116#893—61no—
117D3×C4⋊C4—61no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—62no—
122D3×C4⋊C4—62no—
123#888—61no—
124#888—61no—
125#888—61no—
126#888—61no—
127#888—62no—
128#888—62no—
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×#103—34no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140#835C2×D314yes—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143#816—34no—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146#810—34no—
147C4×C3⋊C8C2×D311yescharacteristic
148C4×C3⋊C8C2×D311yescharacteristic
149C22×C3⋊D3C2×D411yescharacteristic
150C22×C3×D3—22no—
151C32×Q8—24no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4×C3⋊D3—22no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—44no—
163C4×C3⋊D3SD1614yescomplemented
164#634—24no—
165#634—44no—
166C2×C3×Dic3—22no—
167C3×D12—24no—
168C3×D12—42no—
169C3×D12—42no—
170C3×Dic6—42no—
171#626—44no—
172D3×Dic3—44no—
173C3×C3⋊C8—22no—
174C3×C3⋊C8—22no—
175#532—91no—
176C2×C4⋊Q8—91no—
177#492—31no—
178#492—91no—
179#487—31no—
180#487—91no—
181#461—94no—
182#448—94no—
183#431—91no—
184C2×C3×Q8—22no—
185C2×C3×Q8—61no—
186C2×C3×Q8C22×D312yes—
187C2×C3×Q8C22×D312yes—
188C2×C3×D4—32no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×#67—62no—
192C22×Dic3—62no—
193#239—124no—
194D3×Q8—124no—
195D3×Q8—124no—
196D3×Q8—128no—
197#237—124no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—62no—
201C2×D12C22×D312yes—
202C2×C4×D3—31no—
203C2×C4×D3—31no—
204C2×C4×D3—31no—
205C2×C4×D3—31no—
206C2×C4×D3—31no—
207C2×C4×D3—31no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—64no—
215C2×Dic6—21no—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—64no—
222C3×SD16—124no—
223C2×C3×C8—32no—
224C2×C3×C8—32no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C42—21no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#217—62no—
237#217—62no—
238#215—44no—
239#214—124no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242C4⋊Dic3—21no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—61no—
249C4⋊Dic3C22×D312yes—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8C22×D312yes—
266C2×C3⋊C8C22×D312yes—
267#204—124no—
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—21no—
270C2×C3⋊D3—21no—
271C2×C3⋊D3C2×SD1612yes—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C32×C4—42no—
276C32×C4C2×SD1612yes—
277C32×C4#13712yes—
278C32×C4H(5,𝔽2)12yes—
279C3⋊Dic3—21no—
280C3⋊Dic3—21no—
281C3⋊Dic3—42no—
282C3⋊Dic3C2×SD1612yes—
283C3×Dic3—42no—
284C2×#41—181no—
285C22×Q8—92no—
286C2×SD16—34no—
287C2×SD16—94no—
288C4⋊Q8—31no—
289C4⋊Q8—92no—
290C4⋊Q8—91no—
291C4⋊Q8—181no—
292C4⋊Q8—181no—
293C4⋊Q8D3211yescharacteristic
294#127—31no—
295#124—181no—
296#121—92no—
297#121—181no—
298C4×D4—92no—
299C4×D4—181no—
300C2×C4⋊C4—181no—
301C2×C4⋊C4—181no—
302C2×C42—91no—
303C4⋊C8—92no—
304#103—34no—
305#103—94no—
306C22⋊C8—92no—
307C4×C8—31no—
308C4×C8—31no—
309C23×C3—62no—
310C22×D3—22no—
311C22×D3—31no—
312C22×D3—31no—
313C22×D3—61no—
314C3×Q8—24no—
315C3×Q8—24no—
316C3×Q8—44no—
317C3×Q8—122no—
318C3×D4—64no—
319C3×D4—122no—
320C3×D4—122no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—62no—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334#67—124no—
335C2×Dic3—22no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—31no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—124no—
349D12—24no—
350D12—42no—
351D12—42no—
352D12—124no—
353C4×D3—34no—
354C4×D3—34no—
355C4×D3—64no—
356C4×D3—64no—
357C4×D3—64no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—62no—
362C4×D3—124no—
363C4×D3—128no—
364C4×D3—124no—
365C4×D3—124no—
366Dic6—42no—
367Dic6—64no—
368Dic6—64no—
369Dic6—124no—
370Dic6—128no—
371Dic6—124no—
372Dic6—124no—
373C3×C8—62no—
374C3×C8—62no—
375C3⋊C8—22no—
376C3⋊C8—22no—
377C2×C32#53511yescharacteristic
378C2×C32C22×SD1611yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C3⋊D3—22no—
381C3×D3—82no—
382#41—364no—
383C2×Q8—61no—
384C2×Q8—92no—
385C2×Q8—182no—
386C2×Q8—364no—
387C2×Q8C2×D3212yes—
388C2×D4—32no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—182no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—182no—
396C22×C4—182no—
397SD16—124no—
398SD16—364no—
399C2×C8—32no—
400C2×C8—32no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—32no—
404C4⋊C4—61no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—91no—
412C42—91no—
413C42—91no—
414C42C2×D3211yescharacteristic
415C22×C3—21no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—32no—
422C2×D3—32no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—61no—
430C2×D3—61no—
431C2×D3—61no—
432C2×D3—61no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—44no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—122no—
440C3×C4D3×SD1612yes—
441C3×C4D3×SD1612yes—
442C3×C4#91512yes—
443C3×C4#91812yes—
444C3×C4#100412yes—
445C3×C4#100912yes—
446Dic3—32no—
447Dic3—32no—
448Dic3—42no—
449Dic3—62no—
450Dic3—62no—
451Dic3—62no—
452Dic3—61no—
453Dic3—61no—
454Dic3—61no—
455Dic3—61no—
456Dic3—124no—
457Dic3—122no—
458Dic3—122no—
459C32#320611yescharacteristic, complemented, Sylow
460C23—62no—
461C23—91no—
462Q8—24no—
463Q8—122no—
464Q8—184no—
465Q8—364no—
466D4—64no—
467D4—122no—
468D4—122no—
469D4—364no—
470C2×C4—22no—
471C2×C4—62no—
472C2×C4—91no—
473C2×C4—94no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4—364no—
481C2×C4#381111yescharacteristic
482C2×C4#381111yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—62no—
485C8—62no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—242no—
490C2×C3#567411yescharacteristic
491C2×C3#571511yescharacteristic
492C2×C3C2×D3×SD1611yescharacteristic
493C2×C3C2×D3×SD1611yescharacteristic
494C2×C3C2×#91511yescharacteristic
495C2×C3C2×#91811yescharacteristic
496D3—64no—
497D3—62no—
498D3—62no—
499D3—82no—
500C22—92no—
501C22—122no—
502C22—122no—
503C22—122no—
504C22—181no—
505C22—181no—
506C22C2×#381111yescharacteristic
507C4—42no—
508C4—92no—
509C4—122no—
510C4—181no—
511C4—181no—
512C4—362no—
513C4#6394012yes—
514C4#6395112yes—
515C4#6431412yes—
516C3—21no—
517C3#8160211yescharacteristic, complemented
518C3#8176411yescharacteristic, complemented
519C2—182no—
520C2—242no—
521C2#1059516811yescharacteristic
522C2C2×#6394011yescharacteristic
523C2C2×#6395111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593907C2
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. C3×#5085C2semidirect
4. C3×#5079C2semidirect
5. #10591592C2semidirect
6. #10591569C2semidirect
7. #10590369C2semidirect
8. #10590297C2semidirect
9. #10590288C2semidirect
47. #5085D3semidirect
48. #5079D3semidirect
163. C4×C3⋊D3SD16semidirect
459. C32#3206semidirect
517. C3#81602semidirect
518. C3#81764semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105939072
C3×#50852
C3×#50792
#105915922
#105915692
#105903692
#105902972
#105902882
#817643
#816023