Finite Group Databasebeta

← #11896066

Subgroups — #11896066

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×#5542C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592707C211yesmaximal, characteristic
4C3×C4×#214C211yesmaximal, characteristic
5#10591488C212yesmaximal
6#10591442C212yesmaximal
7#10590556C212yesmaximal, complemented
8#10590477C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10#10590287C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83677—31nomaximal
13#79626—31nomaximal
14C32×C4×D4C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#936C2212yes—
17C2×C3×#214C2211yescharacteristic
18C3×#926—21no—
19C3×#924—21no—
20C3×#887C2212yes—
21C3×#879—22no—
22C3×#869C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918—21no—
26#63918C2212yes—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3718C2212yes—
31#63659C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63565C2212yes—
42#63554C2212yes—
43C3×#556—31no—
44Q8×Dic6—31no—
45Q8×Dic6—31no—
46#5542D311yescharacteristic
47C3×C4×SD16—31no—
48#5166—32no—
49#5090—31no—
50#5079—31no—
51#5055—32no—
52#5054—32no—
53#5031—31no—
54#5030—32no—
55#5024—31no—
56#5020—32no—
57C4×#214D311yescharacteristic
58#5008—31no—
59#5008—31no—
60#5008—61no—
61#4854—32no—
62#4789—32no—
63#4765—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C2×C3×Dic6D411yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C22⋊C4—21no—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#217—22no—
80C3×#217—22no—
81C3×#214—22no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4—22no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3718—24no—
98#3369—91noSylow
99C2×C3×SD16—31no—
100C3×C4⋊Q8—31no—
101C3×#126—62no—
102C3×#124—32no—
103C3×C22⋊Q8—61no—
104C3×C4×Q8—31no—
105C3×C4×Q8—32no—
106C3×C4×Q8—31no—
107C3×C4×D4—21no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110C3×#117—61no—
111Q8×Dic3—32no—
112Q8×Dic3—61no—
113C2×#216—32no—
114C2×#216—32no—
115#936C2×D312yes—
116C2×#214C2×D311yescharacteristic
117#926—21no—
118#924—21no—
119#888—32no—
120#888—61no—
121#888—62no—
122#888—62no—
123#887C2×D312yes—
124#879—22no—
125#869—31no—
126#869—31no—
127#869—32no—
128#869—61no—
129#869—61no—
130#869C2×D311yescharacteristic
131C4×Dic6—32no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#106—31no—
136C3×#103—31no—
137C3×#102—31no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—32no—
142#832—32no—
143#832—32no—
144#832—62no—
145#832C2×D311yescharacteristic
146#816—32no—
147#816—32no—
148#815—32no—
149Dic3⋊C8—32no—
150#810—32no—
151#810C2×D311yescharacteristic
152#808—32no—
153#808—32no—
154#808—62no—
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
162C23×C32—21no—
163C32×D4—21no—
164C32×D4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—42no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—22no—
171#634—81no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C3×Dic6—22no—
178C3×Dic6—21no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6#4112yes—
182#627—82no—
183C3⋊(C3⋊C8)—22no—
184C3×C3⋊C8—21no—
185C3×C3⋊C8—21no—
186Q82—91no—
187#556—31no—
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—31no—
198C2×C3×Q8—31no—
199C2×C3×Q8—32no—
200C2×C3×D4—21no—
201C2×C3×D4C22×D311yescharacteristic
202C2×C3×D4C22×D311yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—41no—
206C2×Dic6—62no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—121no—
211C2×Dic6#6711yescharacteristic
212C2×Dic6C22×D312yes—
213C2×Dic6C22×D311yescharacteristic
214C3×SD16—62no—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—62no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4C22×D311yescharacteristic
226C3×C4⋊C4C22×D311yescharacteristic
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—41no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C42—21no—
233C3×C42—32no—
234C3×C42—62no—
235C3×C42—61no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—22no—
239#217—22no—
240#216—64no—
241#216—64no—
242#214—22no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3—121no—
253C4⋊Dic3#6711yescharacteristic
254C4⋊Dic3C22×D311yescharacteristic
255Dic3⋊C4—21no—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4#6712yes—
260C4×Dic3—21no—
261C4×Dic3—22no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3C22×D312yes—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8C22×D311yescharacteristic
269C2×C3⋊C8C22×D311yescharacteristic
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32C22×D411yescharacteristic
274C32×C4—21no—
275C32×C4—41no—
276C32×C4#13712yes—
277C32×C4C2×#4111yescharacteristic
278C32×C42−1+411yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—22no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C2×Q16—92no—
286C2×SD16—31no—
287C4⋊Q8—31no—
288C4⋊Q8—92no—
289C4⋊Q8—91no—
290C4⋊Q8—181no—
291C4⋊Q8—182no—
292#126—62no—
293#124—32no—
294C22⋊Q8—61no—
295C4×Q8—31no—
296C4×Q8—32no—
297C4×Q8—31no—
298C4×Q8—92no—
299C4×Q8—181no—
300C4×D4D3211yescharacteristic
301#117—61no—
302#106—31no—
303#106—92no—
304C4⋊C8—92no—
305C4⋊C8—91no—
306#103—31no—
307#103—92no—
308#103—92no—
309#103—92no—
310#102—31no—
311#102—92no—
312#97—92no—
313C4×C8—31no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—41no—
317C3×Q8—32no—
318C3×Q8—62no—
319C3×Q8—61no—
320C3×Q8—62no—
321C3×Q8—62no—
322C3×D4—22no—
323C3×D4—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—21no—
327C3×D4—41no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—82no—
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—21no—
350C2×Dic3—22no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—122no—
354C2×Dic3C2×#6712yes—
355C2×Dic3C2×#6712yes—
356Dic6—22no—
357Dic6—21no—
358Dic6—22no—
359Dic6—22no—
360Dic6—242no—
361Dic6—242no—
362Dic6—241no—
363Dic6—241no—
364Dic6—242no—
365Dic6#23512yes—
366C3×C8—61no—
367C3×C8—61no—
368C3⋊C8—21no—
369C3⋊C8—21no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32—81no—
374C2×C32#54811yescharacteristic
375C2×C32C2×#13711yescharacteristic
376C2×C32#57711yescharacteristic
377C2×Q8—31no—
378C2×Q8—31no—
379C2×Q8—32no—
380C2×Q8—182no—
381C2×Q8—181no—
382C2×D4C2×D3211yescharacteristic
383C22×C4—21no—
384Q16—184no—
385SD16—62no—
386C2×C8—31no—
387C2×C8—31no—
388C2×C8—92no—
389C4⋊C4—31no—
390C4⋊C4—32no—
391C4⋊C4—31no—
392C4⋊C4—62no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—92no—
397C4⋊C4—182no—
398C4⋊C4—182no—
399C4⋊C4—181no—
400C4⋊C4C2×D3211yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C42—32no—
405C42—62no—
406C42—61no—
407C42—182no—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3—42no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3—81no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—41no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—62no—
430C3×C4—62no—
431C3×C4—62no—
432C3×C4—81no—
433C3×C4—122no—
434C3×C4—121no—
435C3×C4#91512yes—
436C3×C4#95112yes—
437C3×C4C2×#23511yescharacteristic
438C3×C4D3×#4111yescharacteristic
439C3×C4#101011yescharacteristic
440C3×C4#101011yescharacteristic
441Dic3—22no—
442Dic3—22no—
443Dic3—22no—
444Dic3—41no—
445Dic3—42no—
446Dic3—122no—
447Dic3—122no—
448Dic3—242no—
449C32#336911yescharacteristic, complemented, Sylow
450C23—21no—
451Q8—32no—
452Q8—61no—
453Q8—62no—
454Q8—62no—
455Q8—62no—
456Q8—721no—
457Q8—722no—
458D4—21no—
459D4—21no—
460C2×C4—21no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—42no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—182no—
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—82no—
478C2×C3—81no—
479C2×C3—81no—
480C2×C3#555211yescharacteristic
481C2×C3C2×#91511yescharacteristic
482C2×C3#577011yescharacteristic
483C2×C3C2×#95111yescharacteristic
484C2×C3#583111yescharacteristic
485C2×C3#583711yescharacteristic
486C22—41no—
487C22—41no—
488C22—41no—
489C22C2×D3×#6711yescharacteristic
490C4—21no—
491C4—41no—
492C4—62no—
493C4—62no—
494C4—62no—
495C4—122no—
496C4—121no—
497C4—362no—
498C4#6392912yes—
499C4#6429811yescharacteristic
500C4D3×#23511yescharacteristic
501C3—21no—
502C3#7962611yescharacteristic, complemented
503C3#8367711yescharacteristic, complemented
504C2—81no—
505C2#1059489911yescharacteristic
506C2C2×#6392911yescharacteristic
507C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. Dic62C2semidirect
7. #10590556C2semidirect
8. #10590477C2semidirect
9. #10590384C2semidirect
10. #10590287C2semidirect
11. #10590258C2semidirect
449. C32#3369semidirect
502. C3#79626semidirect
503. C3#83677semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
Dic622
#105927072
C3×C4×#2142
#105914882
#105914422
#105905562
#105904772
#105903842
#105902872
#105902582
#836773
#796263