Finite Group Databasebeta

← #11896079

Subgroups — #11896079

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5722C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic
3#10592783C211yesmaximal, characteristic
4C3×#5093C211yesmaximal, characteristic, complemented
5#10590536C212yesmaximal
6#10590535C212yesmaximal
7#10590486C212yesmaximal, complemented
8#10590477C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10C4×#3717C211yesmaximal, characteristic
11#10590258C211yesmaximal, characteristic, complemented
12#83704—31nomaximal
13#81626—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C3×#944—22no—
17C3×#888—21no—
18C3×#888C2212yes—
19C3×#887—21no—
20C3×#887C2212yes—
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63871—21no—
25#63864C2212yes—
26#63849—21no—
27#63848—22no—
28Dic3×Dic6C2212yes—
29C2×#3718C2212yes—
30C2×#3717C2211yescharacteristic
31#63636C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#810C2212yes—
35C3×#810C2212yes—
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2211yescharacteristic
40#63565C2212yes—
41#63564C2211yescharacteristic
42#63554C2212yes—
43C3×Q82—31no—
44#5732—31no—
45#5722D311yescharacteristic, complemented
46#5584—31no—
47C3×#487—31no—
48#5094—32no—
49#5093D311yescharacteristic, complemented
50#5090—31no—
51#5089—32no—
52#5084—31no—
53#5084—31no—
54#5084—61no—
55#5031—31no—
56#5030—32no—
57#5028—32no—
58C4×#215—31no—
59#5024—31no—
60#4798—32no—
61#4794—32no—
62#4791—32no—
63#4789—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C42C2311yescharacteristic
76#3752—21no—
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3D411yescharacteristic
82C3×C4⋊Dic3C2311yescharacteristic
83C3×Dic3⋊C4—21no—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4—22no—
86C3×Dic3⋊C4D412yes—
87C3×C4×Dic3—21no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92Dic3⋊Dic3—22no—
93#3722—22no—
94#3722—22no—
95Dic32—22no—
96#3718—24no—
97#3717—22no—
98#3369—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4×Q8—31no—
107C3×C4×Q8—32no—
108C3×C4×Q8—31no—
109C3×C4×Q8—61no—
110#947—32no—
111#946—61no—
112Q8×Dic3—32no—
113#944—22no—
114C2×#216—32no—
115C2×#216—32no—
116C2×#215—31no—
117C2×#204—31no—
118#898—62no—
119#898—62no—
120#897—61no—
121#892—61no—
122#892—61no—
123#888—21no—
124#888C2×D312yes—
125#887—21no—
126#887C2×D312yes—
127#875—32no—
128C4×D12—31no—
129C4×D12—31no—
130C4×D12—61no—
131#869C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#103—32no—
136C3×#103—32no—
137C3×C4×C8—31no—
138#835—32no—
139#835—31no—
140#821—31no—
141#817—31no—
142#816—31no—
143#815—32no—
144Dic3⋊C8—32no—
145#810—32no—
146#810C2×D312yes—
147#810C2×D312yes—
148#809—32no—
149#809—32no—
150#809—31no—
151#809—62no—
152#808—32no—
153#808—32no—
154#808—31no—
155#808—62no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160#803—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3⋊D3—21no—
163C32×Q8—81no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)—21no—
171C4×C3⋊D3—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6—82no—
182C3×Dic6#4112yes—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—31no—
187#556—91no—
188#489—92no—
189#487—31no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—91no—
195#441—92no—
196C4×SD16—91no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×Q8—62no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—121no—
210C2×Dic6—22no—
211C2×Dic6#6711yescharacteristic
212C2×Dic6C22×D312yes—
213C2×Dic6C22×D311yescharacteristic
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4C22×D312yes—
229C3×C4⋊C4C22×D312yes—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42—62no—
233C3×C42—61no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#216—64no—
237#216—64no—
238#215—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—61no—
242(C2×D3)⋊C4—61no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—121no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—31no—
249C4⋊Dic3—31no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3#6711yescharacteristic
253C4⋊Dic3C22×D311yescharacteristic
254Dic3⋊C4—21no—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4#6712yes—
259C4×Dic3—21no—
260C4×Dic3—22no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3C22×D312yes—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—62no—
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269#204—62no—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—41no—
272C2×C3⋊D3—41no—
273C2×C3⋊D3—41no—
274C32×C4—21no—
275C32×C4—42no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C2×Q16—92no—
286C2×SD16—91no—
287C4⋊Q8—32no—
288C4⋊Q8—31no—
289C4⋊Q8—61no—
290C4⋊Q8—62no—
291C4⋊Q8D3211yescharacteristic
292#126—182no—
293#124—92no—
294C22⋊Q8—181no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—31no—
298C4×Q8—61no—
299C4×Q8—92no—
300C4×D4—91no—
301#117—181no—
302#106—91no—
303#106—92no—
304C4⋊C8—92no—
305C4⋊C8—91no—
306#103—32no—
307#103—32no—
308#103—92no—
309#103—91no—
310#102—91no—
311#102—92no—
312#97—92no—
313C4×C8—31no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—121no—
317C3×Q8—32no—
318C3×Q8—62no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×Q8—81no—
323C3×Q8—81no—
324C3×Q8—82no—
325C3×Q8—242no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—42no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—21no—
344C2×Dic3—22no—
345C2×Dic3—21no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—121no—
349C2×Dic3C2×#6712yes—
350C2×Dic3C2×#6712yes—
351D12—62no—
352D12—61no—
353D12—61no—
354D12—61no—
355D12—61no—
356D12—121no—
357C4×D3—122no—
358C4×D3—122no—
359C4×D3—242no—
360Dic6—22no—
361Dic6—21no—
362Dic6—22no—
363Dic6—22no—
364Dic6—82no—
365Dic6#23912yes—
366C3×C8—61no—
367C3×C8—61no—
368C3⋊C8—21no—
369C3⋊C8—21no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32#54811yescharacteristic
374C2×C32C2×#13711yescharacteristic
375C2×C32#57711yescharacteristic
376C3⋊D3—81no—
377C2×Q8—21no—
378C2×Q8—31no—
379C2×Q8—31no—
380C2×Q8—32no—
381C2×Q8—62no—
382C2×D4—91no—
383C22×C4—181no—
384Q16—184no—
385SD16—182no—
386C2×C8—31no—
387C2×C8—31no—
388C2×C8—92no—
389C4⋊C4—21no—
390C4⋊C4—31no—
391C4⋊C4—32no—
392C4⋊C4—31no—
393C4⋊C4—62no—
394C4⋊C4—62no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—91no—
399C4⋊C4—182no—
400C4⋊C4C2×D3212yes—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C22⋊C4—181no—
404C42—32no—
405C42—62no—
406C42—61no—
407C42—182no—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—122no—
413C2×D3—121no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—241no—
420C2×D3—241no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—41no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—62no—
430C3×C4—62no—
431C3×C4—62no—
432C3×C4—82no—
433C3×C4—121no—
434C3×C4—122no—
435C3×C4#91812yes—
436C3×C4#94212yes—
437C3×C4C2×#23911yescharacteristic
438C3×C4#100711yescharacteristic
439C3×C4D3×#4111yescharacteristic
440C3×C4#101011yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—22no—
444Dic3—42no—
445Dic3—41no—
446Dic3—121no—
447Dic3—121no—
448Dic3—241no—
449C32#336911yescharacteristic, complemented, Sylow
450C23—181no—
451Q8—32no—
452Q8—61no—
453Q8—62no—
454Q8—62no—
455Q8—62no—
456Q8—81no—
457Q8—242no—
458D4—181no—
459D4—181no—
460C2×C4—22no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—181no—
467C2×C4—362no—
468C2×C4D3×#6711yescharacteristic
469C2×C4D3×#6711yescharacteristic
470C2×C4C22×D3211yescharacteristic
471C8—61no—
472C8—61no—
473C8—182no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3#567711yescharacteristic
478C2×C3#576211yescharacteristic
479C2×C3C2×#91811yescharacteristic
480C2×C3C2×#94211yescharacteristic
481C2×C3#581711yescharacteristic
482C2×C3#583611yescharacteristic
483D3—242no—
484D3—241no—
485D3—241no—
486C22—361no—
487C22—361no—
488C22—361no—
489C22C2×D3×#6711yescharacteristic
490C4—21no—
491C4—42no—
492C4—62no—
493C4—62no—
494C4—62no—
495C4—121no—
496C4—122no—
497C4—361no—
498C4#6394812yes—
499C4#6431511yescharacteristic
500C4D3×#23911yescharacteristic
501C3—21no—
502C3#8162611yescharacteristic, complemented
503C3#8370411yescharacteristic, complemented
504C2—721no—
505C2#1059510511yescharacteristic
506C2C2×#6394811yescharacteristic
507C2#1059540111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊Q8D32
hypocenterC32#3369
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×#5722C2semidirect
4. C3×#5093C2semidirect
7. #10590486C2semidirect
8. #10590477C2semidirect
9. #10590384C2semidirect
11. #10590258C2semidirect
45. #5722D3semidirect
49. #5093D3semidirect
449. C32#3369semidirect
502. C3#81626semidirect
503. C3#83704semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105938652
#105927832
C3×#50932
#105905362
#105905352
#105904862
#105904772
#105903842
C4×#37172
#105902582
#837043
#816263