Finite Group Databasebeta

← #11895662

Subgroups — #11895662

Order 1152.

744 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×#5585C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592719C211yesmaximal, characteristic, complemented
4C3×C4×#216C211yesmaximal, characteristic, complemented
5#10591614C212yesmaximal, complemented
6#10591578C212yesmaximal, complemented
7#10590542C212yesmaximal, complemented
8#10590475C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic
10#10590273C211yesmaximal, characteristic
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83717—31nomaximal
13#79701—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#947C2212yes—
17C2×C3×#216C2211yescharacteristic
18C3×#894—22no—
19C3×#893C2212yes—
20C3×#875—21no—
21C3×#874C2211yescharacteristic
22C3×C4×D12—21no—
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63869C2212yes—
26#63866—21no—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3715C2212yes—
31#63662C2212yes—
32#63635C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#835C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#807C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#559—31no—
44#5585D311yescharacteristic
45#5570—31no—
46#5567—31no—
47C3×C4×Q16—31no—
48#5185—32no—
49#5075—31no—
50#5070—31no—
51#5056—32no—
52#5054—32no—
53C4×#216D311yescharacteristic, complemented
54#5027—31no—
55Q8×C3⋊C8—31no—
56#5020—31no—
57#5020—31no—
58#5020—61no—
59C4×#214—32no—
60#5009—32no—
61#4891—32no—
62#4800—32no—
63#4788—32no—
64#4694—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×#634—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2311yescharacteristic
76C32×C42—21no—
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×#216—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic32—22no—
97#3715—24no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C3×#127—31no—
101C3×#124—32no—
102C3×#124—61no—
103C3×#123—62no—
104C3×C4×Q8—21no—
105C3×C4×Q8—31no—
106C3×C4×Q8—31no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—32no—
110C3×C4×D4—61no—
111#947C2×D312yes—
112Q8×Dic3—32no—
113#944—61no—
114C2×#216C2×D311yescharacteristic
115C2×#215—32no—
116C2×#214—32no—
117#894—22no—
118#893C2×D312yes—
119#890—32no—
120#890—62no—
121#889—62no—
122#887—61no—
123#875—21no—
124#874C2×D311yescharacteristic
125C4×D12—21no—
126#870—32no—
127#869—31no—
128#869—31no—
129#869—61no—
130#869—61no—
131C4×Dic6—32no—
132C4×Dic6—61no—
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D311yescharacteristic
135C3×#107—31no—
136C3×#103—31no—
137C3×#103—31no—
138C3×C4×C8—31no—
139#835—32no—
140#835—32no—
141#835—62no—
142#835C2×D311yescharacteristic
143#832—32no—
144#832—32no—
145#832—32no—
146#821—32no—
147#821—32no—
148Dic3⋊C8—32no—
149C8×Dic3—32no—
150#810C2×D311yescharacteristic
151#809—32no—
152#808—32no—
153#808—32no—
154#808—62no—
155#807C2×D311yescharacteristic
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)—61no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3—22no—
163C32×Q8—21no—
164C32×Q8—21no—
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—42no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3C2×D412yes—
175C2×C3×Dic3C2×D412yes—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179C3×D12—81no—
180C3×C4×D3—82no—
181C3×Dic6—22no—
182C3×Dic6—21no—
183C3×Dic6#4112yes—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8—21no—
187#559—31no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—31no—
197C4×SD16—92no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8C22×D311yescharacteristic
202C2×C3×Q8C22×D311yescharacteristic
203C2×C3×D4—32no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C22×C3×C4—62no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12C22×D312yes—
210C2×C4×D3—22no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—121no—
214C2×Dic6#6711yescharacteristic
215C2×Dic6C22×D311yescharacteristic
216C3×Q16—62no—
217C2×C3×C8—31no—
218C2×C3×C8—31no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—41no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4C22×D311yescharacteristic
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—62no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42—41no—
237C3×C42—61no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#216—22no—
241#215—64no—
242#214—64no—
243(C2×D3)⋊C4—22no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—22no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—121no—
254C4⋊Dic3#6711yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256Dic3⋊C4—21no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4#6712yes—
262C4×Dic3—21no—
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—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C32×C4—21no—
276C32×C4—41no—
277C32×C4—41no—
278C32×C4#13512yes—
279C32×C4C2×#4111yescharacteristic
280C32×C42−1+411yescharacteristic
281C3⋊Dic3—42no—
282C3×Dic3—22no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—41no—
286C2×Q16—31no—
287C2×SD16—92no—
288C4⋊Q8—91no—
289C4⋊Q8—181no—
290#127—31no—
291#125—92no—
292#125—182no—
293#124—32no—
294#124—61no—
295#123—62no—
296C4×Q8—31no—
297C4×Q8—31no—
298C4×Q8—92no—
299C4×Q8—181no—
300C4×Q8D3211yescharacteristic
301C4×D4—32no—
302C4×D4—61no—
303#107—31no—
304#106—92no—
305C4⋊C8—92no—
306C4⋊C8—91no—
307#103—31no—
308#103—31no—
309#103—92no—
310#102—92no—
311#102—92no—
312#102—92no—
313C4×C8—31no—
314C4×C8—92no—
315C23×C3—62no—
316C22×D3—22no—
317C3×Q8—22no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—32no—
323C3×Q8—41no—
324C3×Q8—62no—
325C3×Q8—61no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—122no—
329C3×D4—241no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—242no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3C2×#6712yes—
356C2×Dic3C2×#6712yes—
357D12—22no—
358D12—22no—
359D12—42no—
360D12—81no—
361C4×D3—82no—
362Dic6—22no—
363Dic6—21no—
364Dic6—122no—
365Dic6—122no—
366Dic6—242no—
367Dic6#23512yes—
368C3×C8—61no—
369C3×C8—61no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32#54811yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C2×C32#57711yescharacteristic
378C3×D3—82no—
379C2×Q8—31no—
380C2×Q8—31no—
381C2×Q8—181no—
382C2×Q8C2×D3211yescharacteristic
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C22×C4—62no—
387Q16—62no—
388SD16—184no—
389C2×C8—31no—
390C2×C8—31no—
391C2×C8—92no—
392C4⋊C4—21no—
393C4⋊C4—31no—
394C4⋊C4—32no—
395C4⋊C4—31no—
396C4⋊C4—61no—
397C4⋊C4—92no—
398C4⋊C4—182no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C4⋊C4—181no—
402C4⋊C4C2×D3211yescharacteristic
403C22⋊C4—62no—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C42—21no—
407C42—32no—
408C42—61no—
409C42—182no—
410C42C2×D3211yescharacteristic
411C22×C3—21no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—41no—
426C3×C4—42no—
427C3×C4—41no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—62no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—81no—
435C3×C4—121no—
436C3×C4#91912yes—
437C3×C4#95012yes—
438C3×C4C2×#23511yescharacteristic
439C3×C4D3×#4111yescharacteristic
440C3×C4#101011yescharacteristic
441C3×C4#101011yescharacteristic
442Dic3—22no—
443Dic3—22no—
444Dic3—22no—
445Dic3—41no—
446Dic3—122no—
447Dic3—122no—
448Dic3—242no—
449C32#336511yescharacteristic, complemented, Sylow
450C23—62no—
451Q8—21no—
452Q8—21no—
453Q8—32no—
454Q8—61no—
455Q8—62no—
456Q8—362no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—241no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—182no—
468C2×C4—242no—
469C2×C4D3×#6711yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—61no—
473C8—61no—
474C8—182no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—242no—
479C2×C3#555211yescharacteristic
480C2×C3C2×#91911yescharacteristic
481C2×C3#577011yescharacteristic
482C2×C3C2×#95011yescharacteristic
483C2×C3#583111yescharacteristic
484C2×C3#583611yescharacteristic
485D3—82no—
486C22—122no—
487C22—122no—
488C22—122no—
489C22C2×D3×#6711yescharacteristic
490C4—21no—
491C4—41no—
492C4—41no—
493C4—62no—
494C4—62no—
495C4—62no—
496C4—121no—
497C4—362no—
498C4#6394912yes—
499C4#6429811yescharacteristic
500C4D3×#23511yescharacteristic
501C3—21no—
502C3#7970111yescharacteristic, complemented
503C3#8371711yescharacteristic, complemented
504C2—242no—
505C2#1059489911yescharacteristic
506C2C2×#6394911yescharacteristic
507C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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
2. #10593860C2semidirect
3. #10592719C2semidirect
4. C3×C4×#216C2semidirect
5. #10591614C2semidirect
6. #10591578C2semidirect
7. #10590542C2semidirect
8. #10590475C2semidirect
11. C3⋊C8×Dic6C2semidirect
53. C4×#216D3semidirect
449. C32#3365semidirect
502. C3#79701semidirect
503. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
#105938602
#105927192
C3×C4×#2162
#105916142
#105915782
#105905422
#105904752
#105903642
#105902732
C3⋊C8×Dic62
#837173
#797013