Finite Group Databasebeta

← #11895667

Subgroups — #11895667

Order 1152.

796 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596041C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic
3C3×C4×#216C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic
5#10591612C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10590539C212yesmaximal, complemented
8#10590473C212yesmaximal, complemented
9#10590301C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#80370—31nomaximal
13#79701—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15Q8×C3⋊Dic3C2212yes—
16#64099—22no—
17#64099C2212yes—
18#64078—21no—
19#64078C2211yescharacteristic
20C4×#634—21no—
21C4×#634C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#215C2212yes—
24C3×#874C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63898C2212yes—
27Dic3×D12—21no—
28#63884—22no—
29#63863C2212yes—
30#63860—21no—
31C3×#835C2211yescharacteristic
32C3×#810C2211yescharacteristic
33C3×#809C2212yes—
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63566C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63553C2212yes—
43#5713—31no—
44#5585—31no—
45#5570—31no—
46#5570—31no—
47#5570—61no—
48C3×#460—31no—
49C3×C4×Q16—31no—
50#5185—32no—
51#5166—32no—
52Dic3×SD16—32no—
53#5070—31no—
54C4×#216D311yescharacteristic, complemented
55#5027D311yescharacteristic
56#5020—31no—
57#4891—32no—
58#4851—31no—
59#4830—31no—
60#4800—32no—
61#4788—32no—
62#4768—32no—
63#4763—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×#634D411yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×D3×Dic3—22no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)—22no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82C4⋊(C3⋊Dic3)C2312yes—
83#3750—22no—
84#3750D412yes—
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3C2312yes—
87C3×#216—22no—
88C3×#215—24no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C2×C3×SD16—32no—
101C3×#127—31no—
102C3×C4×Q8—21no—
103C3×C4×Q8—31no—
104C3×C4×Q8C2×D311yescharacteristic
105C3×C4×Q8C2×D311yescharacteristic
106#947—32no—
107Q8×Dic3—32no—
108Q8×Dic3—32no—
109Q8×Dic3—62no—
110C2×#216C2×D311yescharacteristic
111C2×#215C2×D312yes—
112#936—32no—
113#936—61no—
114#935—62no—
115D4×Dic3—32no—
116D4×Dic3—61no—
117#894—62no—
118#893—32no—
119#890—32no—
120#890—32no—
121#890—62no—
122#890—62no—
123#890—62no—
124#890—64no—
125#875—61no—
126#874C2×D311yescharacteristic
127C4×D12—61no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869—61no—
132#869—61no—
133#869—62no—
134C4×Dic6—31no—
135C4×Dic6—31no—
136C4×Dic6—61no—
137C4×Dic6—61no—
138C4×Dic6—61no—
139C4×Dic6—62no—
140C4×Dic6C2×D311yescharacteristic
141C3×#107—31no—
142C3×C4⋊C8—31no—
143C3×#103—31no—
144C3×#103—31no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—32no—
148#835C2×D311yescharacteristic
149#832—32no—
150#832—32no—
151#821—32no—
152#821—32no—
153#817—32no—
154#816—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159#810C2×D311yescharacteristic
160#809C2×D312yes—
161#808—32no—
162#807C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3×D3—22no—
166C32×Q8—21no—
167C32×Q8#4112yes—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176#634—22no—
177#634—42no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186D3×Dic3—82no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#559—91no—
191#557—91no—
192#488—92no—
193#486—91no—
194#478—92no—
195#475—91no—
196#464—92no—
197#460—31no—
198C8×Q8—91no—
199C4×Q16—31no—
200C4×SD16—92no—
201C2×C3×Q8—21no—
202C2×C3×Q8—31no—
203C2×C3×Q8C22×D311yescharacteristic
204C2×C3×Q8C22×D311yescharacteristic
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×Dic3—62no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×C4×D3—62no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6C22×D311yescharacteristic
220C3×Q16—62no—
221C3×SD16—64no—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C2×C3×C8—31no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C42—22no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—61no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#216—22no—
244#215—24no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—64no—
259C4⋊Dic3—62no—
260C4⋊Dic3—64no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—32no—
266Dic3⋊C4—32no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—64no—
271C4×Dic3—21no—
272C4×Dic3—32no—
273C4×Dic3—32no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—64no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—22no—
286C32×C4—21no—
287C32×C4—41no—
288C32×C4#13512yes—
289C32×C4C2×#4111yescharacteristic
290C32×C42−1+411yescharacteristic
291C3⋊Dic3—22no—
292C3⋊Dic3—22no—
293C3⋊Dic3—42no—
294C3×Dic3—41no—
295C3×Dic3—41no—
296C2×Q16—31no—
297C2×SD16—32no—
298C4⋊Q8—91no—
299C4⋊Q8—181no—
300#127—31no—
301#125—92no—
302#125—182no—
303#124—92no—
304#124—181no—
305#123—182no—
306C4×Q8—31no—
307C4×Q8—91no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×Q8D3211yescharacteristic
311C4×D4—92no—
312C4×D4—181no—
313#107—31no—
314#106—92no—
315C4⋊C8—31no—
316C4⋊C8—92no—
317#103—31no—
318#103—31no—
319#103—92no—
320#102—32no—
321#102—92no—
322#102—92no—
323C4×C8—31no—
324C4×C8—92no—
325C23×C3—62no—
326C22×D3—22no—
327C3×Q8—22no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—22no—
331C3×Q8—61no—
332C3×Q8—61no—
333C3×Q8#23512yes—
334C3×Q8#23712yes—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C3×D4—241no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—242no—
368D12—22no—
369D12—22no—
370D12—42no—
371D12—81no—
372C4×D3—242no—
373Dic6—21no—
374Dic6—21no—
375Dic6—62no—
376Dic6—62no—
377Dic6—122no—
378Dic6—124no—
379Dic6—122no—
380Dic6—122no—
381C3×C8—62no—
382C3×C8—61no—
383C3×C8—61no—
384C3⋊C8—21no—
385C3⋊C8—22no—
386C3⋊C8—21no—
387C2×C32#54811yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C2×Q8—31no—
392C2×Q8—91no—
393C2×Q8—181no—
394C2×Q8C2×D3211yescharacteristic
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C22×C4—182no—
399Q16—62no—
400SD16—64no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—32no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—61no—
407C4⋊C4—91no—
408C4⋊C4—92no—
409C4⋊C4—92no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—181no—
414C4⋊C4C2×D3211yescharacteristic
415C22⋊C4—182no—
416C22⋊C4—182no—
417C22⋊C4—182no—
418C42—21no—
419C42—61no—
420C42—92no—
421C42—182no—
422C42C2×D3211yescharacteristic
423C22×C3—21no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C3×C4—24no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—41no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—121no—
445C3×C4—121no—
446C3×C4#91612yes—
447C3×C4#91912yes—
448C3×C4C2×#23511yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4#101011yescharacteristic
451C3×C4#101011yescharacteristic
452Dic3—41no—
453Dic3—41no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—62no—
458Dic3—122no—
459Dic3—122no—
460Dic3—124no—
461Dic3—122no—
462Dic3—122no—
463C32#336511yescharacteristic, complemented, Sylow
464C23—62no—
465Q8—21no—
466Q8—61no—
467Q8—61no—
468Q8—182no—
469Q8—362no—
470Q8#379512yes—
471D4—62no—
472D4—62no—
473D4—122no—
474D4—241no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—92no—
480C2×C4—92no—
481C2×C4—182no—
482C2×C4—722no—
483C2×C4#381111yescharacteristic
484C2×C4#381111yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—62no—
487C8—61no—
488C8—61no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—242no—
493C2×C3#555211yescharacteristic
494C2×C3#559811yescharacteristic
495C2×C3C2×#91611yescharacteristic
496C2×C3C2×#91911yescharacteristic
497C2×C3#577011yescharacteristic
498C2×C3#577511yescharacteristic
499D3—82no—
500C22—122no—
501C22—122no—
502C22—122no—
503C22C2×#381111yescharacteristic
504C4—22no—
505C4—21no—
506C4—41no—
507C4—121no—
508C4—121no—
509C4—182no—
510C4—182no—
511C4—362no—
512C4#6395012yes—
513C4C2×#379511yescharacteristic
514C4#6429811yescharacteristic
515C3—21no—
516C3#7970111yescharacteristic, complemented
517C3#8037011yescharacteristic, complemented
518C2—242no—
519C2#1059491811yescharacteristic
520C2C2×#6395011yescharacteristic
521C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4×Q8D32
hypocenterC32#3365
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. #10596041C2semidirect
3. C3×C4×#216C2semidirect
5. #10591612C2semidirect
6. #10591571C2semidirect
7. #10590539C2semidirect
8. #10590473C2semidirect
9. #10590301C2semidirect
11. #10590254C2semidirect
54. C4×#216D3semidirect
463. C32#3365semidirect
516. C3#79701semidirect
517. C3#80370semidirect

Maximal subgroups

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

subgroupindex
#105960412
#105939512
C3×C4×#2162
C3×#50272
#105916122
#105915712
#105905392
#105904732
#105903012
#105902732
#105902542
#803703
#797013