Finite Group Databasebeta

← #11898382

Subgroups — #11898382

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592791C211yesmaximal, characteristic, complemented
4C3×#5083C211yesmaximal, characteristic, complemented
5#10591606C212yesmaximal
6#10591604C212yesmaximal, complemented
7#10591577C212yesmaximal, complemented
8#10591537C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10C4×#3713C211yesmaximal, characteristic
11#10590250C211yesmaximal, characteristic, complemented
12#83670—31nomaximal
13#80421—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C2×#3756C2212yes—
16C2×#3756C2212yes—
17#64078C2211yescharacteristic
18C3×#947C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2212yes—
21C3×#898—22no—
22C3×#897—21no—
23C3×#892—21no—
24C3×C4×D12C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63861—22no—
28#63860C2212yes—
29#63856—21no—
30#63844C2212yes—
31#63841—21no—
32C2×#3716C2212yes—
33C2×#3713C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#835C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63576C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63562C2211yescharacteristic
41#63562C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#556—31no—
44#5732D311yescharacteristic, complemented
45#5584—31no—
46#5542—31no—
47C3×#461—31no—
48#5168—32no—
49#5166—32no—
50#5092—31no—
51#5092—31no—
52#5092—61no—
53#5083D311yescharacteristic, complemented
54#5059—32no—
55#5054—32no—
56C4×#216—32no—
57#5028—32no—
58Q8×C3⋊C8—31no—
59#5019—31no—
60C4×#213—31no—
61C4×#213—31no—
62#4841—31no—
63#4830—31no—
64#4798—32no—
65#4790—32no—
66C2×C32×Q8C2312yes—
67C2×#634C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C32×C4⋊C4—21no—
74C32×C4⋊C4—21no—
75C32×C42C2311yescharacteristic
76#3756—24no—
77#3756—42no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#215—42no—
83C3×(C2×D3)⋊C4—21no—
84C3×(C2×D3)⋊C4—21no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99#3716—42no—
100#3713—22no—
101#3393—91noSylow
102C2×C3×SD16—32no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×#126—62no—
107C3×#124—32no—
108C3×C22⋊Q8—61no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×D4—31no—
112C3×C4×D4—31no—
113C3×#117—61no—
114#947C2×D312yes—
115#946—61no—
116Q8×Dic3C2×D312yes—
117C2×#216—32no—
118C2×#216—32no—
119C2×#216—32no—
120C2×#216—32no—
121C2×#216—62no—
122C2×#216—62no—
123C2×#215C2×D312yes—
124#936—32no—
125C2×#214—32no—
126C2×#213—31no—
127C2×#213—31no—
128#926—61no—
129#924—61no—
130C2×#204—32no—
131#898—22no—
132#898—62no—
133#897—21no—
134#892—21no—
135#892—61no—
136#887—32no—
137#879—62no—
138#875—32no—
139C4×D12C2×D311yescharacteristic
140C4×D12C2×D311yescharacteristic
141#869—31no—
142#869—31no—
143#869—61no—
144C4×Dic6—32no—
145C4×Dic6C2×D311yescharacteristic
146C3×C4⋊C8—31no—
147C3×#103—32no—
148#835C2×D312yes—
149#832—31no—
150#832—31no—
151#816—32no—
152Dic3⋊C8—32no—
153C8×Dic3—32no—
154#810—32no—
155#809—31no—
156#809—31no—
157#807—31no—
158#807—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)C2×D311yescharacteristic
161C4×C3⋊C8—31no—
162C4×C3⋊C8—31no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—61no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C32×Q8—22no—
168C32×Q8—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174#634—22no—
175#634—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)#4112yes—
189C3×C3⋊C8—22no—
190#556—31no—
191#556—91no—
192#495—92no—
193#494—91no—
194#464—92no—
195#464—92no—
196#461—31no—
197#461—91no—
198C8×Q8—91no—
199C4×Q16—92no—
200C4×D8—91no—
201C2×C3×Q8—22no—
202C2×C3×Q8—31no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205C2×C3×D4—31no—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C2×D12C22×D311yescharacteristic
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6#6711yescharacteristic
217C3×SD16—122no—
218C2×C3×C8—32no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—31no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—62no—
237C3×C42C22×D311yescharacteristic
238C3×C42C22×D311yescharacteristic
239#217—62no—
240#217—62no—
241#216—64no—
242#216—64no—
243#216—124no—
244#216—122no—
245#216—122no—
246#216—124no—
247#215—42no—
248#214—122no—
249#213—62no—
250#213—62no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—21no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—22no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—121no—
263C4⋊Dic3—121no—
264C4⋊Dic3#6711yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D311yescharacteristic
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4#6712yes—
270C4×Dic3—22no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—61no—
280C2×C3⋊C8C22×D312yes—
281#204—122no—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C2×Q16—92no—
300C2×Q16—92no—
301C2×SD16—32no—
302C2×SD16—92no—
303C2×D8—91no—
304C4⋊Q8—91no—
305C4⋊Q8D3211yescharacteristic
306#126—62no—
307#126—182no—
308#124—32no—
309#124—92no—
310C22⋊Q8—61no—
311C22⋊Q8—181no—
312C4×Q8—31no—
313C4×Q8—32no—
314C4×Q8—92no—
315C4×D4—31no—
316C4×D4—31no—
317#117—61no—
318#117—181no—
319#107—91no—
320C4⋊C8—31no—
321C4⋊C8—92no—
322#103—32no—
323#103—92no—
324#102—91no—
325#102—91no—
326C4×C8—92no—
327C4×C8—91no—
328C23×C3—61no—
329C23×C3—61no—
330C22×D3—21no—
331C22×D3—21no—
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—42no—
337C3×Q8—42no—
338C3×Q8—62no—
339C3×D4—61no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—61no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4—122no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3C2×#6712yes—
367C2×Dic3C2×#6712yes—
368D12—21no—
369D12—21no—
370D12—21no—
371D12—21no—
372C4×D3—42no—
373C4×D3—42no—
374Dic6—22no—
375Dic6—62no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—122no—
380Dic6—122no—
381C3×C8—62no—
382C3⋊C8—22no—
383C3⋊C8—32no—
384C3⋊C8—32no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C2×C32#55011yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57811yescharacteristic
392C3×D3—81no—
393C3×D3—81no—
394C2×Q8—31no—
395C2×Q8—92no—
396C2×Q8C2×D3212yes—
397C2×D4—31no—
398C2×D4—31no—
399C22×C4—61no—
400C22×C4—61no—
401Q16—184no—
402Q16—362no—
403SD16—122no—
404SD16—362no—
405D8—182no—
406C2×C8—32no—
407C2×C8—91no—
408C2×C8—91no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—31no—
412C4⋊C4—32no—
413C4⋊C4—31no—
414C4⋊C4—31no—
415C4⋊C4—62no—
416C4⋊C4—182no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—61no—
422C22⋊C4—61no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—32no—
426C42—62no—
427C42—182no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×#6711yescharacteristic
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—41no—
443C2×D3—41no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—82no—
455C3×C4—121no—
456C3×C4—121no—
457C3×C4#91612yes—
458C3×C4#95012yes—
459C3×C4#100411yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4#100911yescharacteristic
463Dic3—22no—
464Dic3—22no—
465Dic3—41no—
466Dic3—41no—
467Dic3—122no—
468Dic3—122no—
469Dic3—242no—
470C32#339311yescharacteristic, complemented, Sylow
471C23—61no—
472C23—61no—
473Q8—22no—
474Q8—22no—
475Q8—62no—
476Q8—182no—
477Q8—182no—
478D4—61no—
479D4—61no—
480D4—61no—
481D4—61no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—122no—
488C2×C4—122no—
489C2×C4—182no—
490C2×C4D3×#6711yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4C22×D3211yescharacteristic
493C8—62no—
494C8—92no—
495C8—181no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—241no—
500C2×C3—241no—
501C2×C3#559911yescharacteristic
502C2×C3C2×#91611yescharacteristic
503C2×C3#577911yescharacteristic
504C2×C3C2×#95011yescharacteristic
505C2×C3#583411yescharacteristic
506C2×C3#583811yescharacteristic
507D3—81no—
508D3—81no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22C2×D3×#6711yescharacteristic
516C4—21no—
517C4—42no—
518C4—62no—
519C4—62no—
520C4—121no—
521C4—121no—
522C4—362no—
523C4#6394712yes—
524C4#6431211yescharacteristic
525C4#6431411yescharacteristic
526C3—21no—
527C3#8042111yescharacteristic, complemented
528C3#8367011yescharacteristic, complemented
529C2—241no—
530C2—241no—
531C2#1059523611yescharacteristic
532C2#1059532811yescharacteristic
533C2C2×#6394711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊Q8D32
hypocenterC32#3393
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×#5732C2semidirect
2. #10593879C2semidirect
3. #10592791C2semidirect
4. C3×#5083C2semidirect
6. #10591604C2semidirect
7. #10591577C2semidirect
8. #10591537C2semidirect
9. #10590365C2semidirect
11. #10590250C2semidirect
44. #5732D3semidirect
53. #5083D3semidirect
470. C32#3393semidirect
527. C3#80421semidirect
528. C3#83670semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
#105938792
#105927912
C3×#50832
#105916062
#105916042
#105915772
#105915372
#105903652
C4×#37132
#105902502
#836703
#804213