Finite Group Databasebeta

← #11896072

Subgroups — #11896072

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic6C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic
5#10591604C212yesmaximal
6#10591541C212yesmaximal, complemented
7#10590531C212yesmaximal
8#10590487C212yesmaximal, complemented
9#10590288C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic
11#10590258C211yesmaximal, characteristic, complemented
12#83704—31nomaximal
13#79626—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C2×#3756C2212yes—
16#64078C2211yescharacteristic
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2211yescharacteristic
19C3×#888—22no—
20C3×#888C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×#869—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6—21no—
25C3×C4×Dic6C2211yescharacteristic
26#63861—22no—
27#63860C2212yes—
28#63856—21no—
29#63844C2212yes—
30#63841—21no—
31#63637C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#808C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×Q82—31no—
44#5584—31no—
45Q8×Dic6D311yescharacteristic, complemented
46#5542—31no—
47C3×C4×SD16—31no—
48#5166—32no—
49#5094—32no—
50#5093—31no—
51#5089—32no—
52#5084—31no—
53#5031—31no—
54#5031—31no—
55#5031—61no—
56#5030—32no—
57#5028—32no—
58C4×#215D311yescharacteristic
59#5024—31no—
60#5008—31no—
61#4854—32no—
62#4789—32no—
63#4765—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634C2312yes—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—22no—
72C2×C3×Dic6D411yescharacteristic
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2311yescharacteristic
75C32×C42—21no—
76C32×C42C2311yescharacteristic
77#3756—24no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#215—22no—
82C3×(C2×D3)⋊C4—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3369—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—61no—
103C3×C4⋊Q8—62no—
104C3×C4×Q8—21no—
105C3×C4×Q8—31no—
106C3×C4×Q8—32no—
107C3×C4×Q8—61no—
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×D4—31no—
111#946—61no—
112Q8×Dic3C2×D312yes—
113C2×#216—32no—
114C2×#216—32no—
115C2×#216—62no—
116C2×#215C2×D311yescharacteristic
117#936—32no—
118#926—61no—
119#924—61no—
120#898—62no—
121#892—61no—
122#888—22no—
123#888C2×D312yes—
124#887—32no—
125#879—62no—
126#875—32no—
127C4×D12C2×D311yescharacteristic
128#869—21no—
129#869—31no—
130#869—31no—
131#869—61no—
132#869C2×D311yescharacteristic
133C4×Dic6—21no—
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×#103—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#835C2×D311yescharacteristic
141#832—32no—
142#816—32no—
143#816—32no—
144#815—32no—
145Dic3⋊C8—32no—
146#810—32no—
147#810—32no—
148#810—32no—
149#810—32no—
150#810—62no—
151#809—32no—
152#809C2×D311yescharacteristic
153#808—32no—
154#808—32no—
155#808C2×D311yescharacteristic
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—21no—
164C32×Q8#4112yes—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171#634—22no—
172#634—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×D12—21no—
178C3×D12—21no—
179C3×C4×D3—42no—
180C3×Dic6—22no—
181C3×Dic6—82no—
182C3×Dic6—81no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—31no—
187#556—91no—
188#489—92no—
189#487—91no—
190#476—91no—
191#475—92no—
192#464—92no—
193#462—91no—
194#446—91no—
195#441—92no—
196C4×SD16—31no—
197C2×C3×Q8—21no—
198C2×C3×Q8—31no—
199C2×C3×Q8—62no—
200C2×C3×Q8—61no—
201C2×C3×Q8C22×D311yescharacteristic
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C2×D12C22×D311yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6—32no—
210C2×Dic6—32no—
211C2×Dic6—62no—
212C2×Dic6#6711yescharacteristic
213C3×SD16—62no—
214C2×C3×C8—31no—
215C2×C3×C8—31no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—31no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—32no—
234C3×C42—41no—
235C3×C42—62no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#216—64no—
241#216—64no—
242#216—124no—
243#215—22no—
244(C2×D3)⋊C4—21no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—21no—
248C4⋊Dic3—22no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—121no—
254C4⋊Dic3—121no—
255C4⋊Dic3#6711yescharacteristic
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D312yes—
258Dic3⋊C4—22no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4#6712yes—
262C4×Dic3—22no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3C22×D312yes—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271C22×C32C22×D411yescharacteristic
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—22no—
276C32×C4—21no—
277C32×C4—41no—
278C32×C4#13712yes—
279C32×C4C2×#4111yescharacteristic
280C32×C42−1+411yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—41no—
285C3×Dic3—42no—
286C2×Q16—92no—
287C2×SD16—31no—
288C4⋊Q8—32no—
289C4⋊Q8—31no—
290C4⋊Q8—61no—
291C4⋊Q8—62no—
292C4⋊Q8—91no—
293#126—182no—
294#124—92no—
295C22⋊Q8—181no—
296C4×Q8—31no—
297C4×Q8—32no—
298C4×Q8—61no—
299C4×Q8—92no—
300C4×Q8D3211yescharacteristic
301C4×D4—31no—
302#117—181no—
303#106—31no—
304#106—92no—
305C4⋊C8—92no—
306C4⋊C8—91no—
307#103—31no—
308#103—92no—
309#103—92no—
310#103—92no—
311#102—31no—
312#102—92no—
313#97—92no—
314C4×C8—31no—
315C23×C3—61no—
316C22×D3—21no—
317C3×Q8—21no—
318C3×Q8—21no—
319C3×Q8—22no—
320C3×Q8—41no—
321C3×Q8—62no—
322C3×Q8—241no—
323C3×Q8—242no—
324C3×Q8#23512yes—
325C3×Q8#23912yes—
326C3×D4—61no—
327C3×D4—61no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3C2×#6712yes—
354C2×Dic3C2×#6712yes—
355D12—21no—
356D12—21no—
357C4×D3—42no—
358Dic6—22no—
359Dic6—62no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—82no—
364Dic6—81no—
365Dic6—122no—
366Dic6—122no—
367C3×C8—61no—
368C3×C8—61no—
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C3×D3—81no—
378C2×Q8—31no—
379C2×Q8—62no—
380C2×Q8—61no—
381C2×Q8—92no—
382C2×Q8C2×D3211yescharacteristic
383C2×D4—31no—
384C22×C4—61no—
385Q16—184no—
386SD16—62no—
387C2×C8—31no—
388C2×C8—31no—
389C2×C8—92no—
390C4⋊C4—21no—
391C4⋊C4—31no—
392C4⋊C4—32no—
393C4⋊C4—32no—
394C4⋊C4—31no—
395C4⋊C4—62no—
396C4⋊C4—62no—
397C4⋊C4—61no—
398C4⋊C4—182no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C4⋊C4C2×D3211yescharacteristic
402C22⋊C4—61no—
403C22⋊C4—182no—
404C22⋊C4—182no—
405C42—21no—
406C42—32no—
407C42—62no—
408C42—182no—
409C42C2×D3211yescharacteristic
410C22×C3—21no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3C2×D3×D411yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—41no—
417C2×D3—41no—
418C2×D3—41no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—41no—
427C3×C4—42no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—62no—
431C3×C4—62no—
432C3×C4—81no—
433C3×C4—122no—
434C3×C4—121no—
435C3×C4#91512yes—
436C3×C4#94212yes—
437C3×C4C2×#23511yescharacteristic
438C3×C4C2×#23911yescharacteristic
439C3×C4#100711yescharacteristic
440C3×C4#101011yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—41no—
444Dic3—42no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448C32#336911yescharacteristic, complemented, Sylow
449C23—61no—
450Q8—21no—
451Q8—62no—
452Q8—182no—
453Q8—182no—
454Q8—241no—
455Q8—242no—
456Q8#379912yes—
457D4—61no—
458D4—61no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—62no—
464C2×C4—61no—
465C2×C4—122no—
466C2×C4—182no—
467C2×C4D3×#6711yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—61no—
471C8—61no—
472C8—182no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—241no—
477C2×C3#555211yescharacteristic
478C2×C3C2×#91511yescharacteristic
479C2×C3#577011yescharacteristic
480C2×C3C2×#94211yescharacteristic
481C2×C3#581711yescharacteristic
482C2×C3#583611yescharacteristic
483D3—81no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22C2×D3×#6711yescharacteristic
488C4—22no—
489C4—21no—
490C4—41no—
491C4—62no—
492C4—62no—
493C4—121no—
494C4—122no—
495C4—362no—
496C4#6394612yes—
497C4#6429711yescharacteristic
498C4C2×#379911yescharacteristic
499C3—21no—
500C3#7962611yescharacteristic, complemented
501C3#8370411yescharacteristic, complemented
502C2—241no—
503C2#1059490211yescharacteristic
504C2C2×#6394611yescharacteristic
505C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
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×Q8×Dic6C2semidirect
3. #10592730C2semidirect
6. #10591541C2semidirect
8. #10590487C2semidirect
9. #10590288C2semidirect
11. #10590258C2semidirect
45. Q8×Dic6D3semidirect
448. C32#3369semidirect
500. C3#79626semidirect
501. C3#83704semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic62
#105938792
#105927302
C3×C4×#2152
#105916042
#105915412
#105905312
#105904872
#105902882
#105902662
#105902582
#837043
#796263