Finite Group Databasebeta

← #11895665

Subgroups — #11895665

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C4×#3718C211yesmaximal, characteristic, complemented
5#10590364C211yesmaximal, characteristic
6C4×#3715C212yesmaximal, complemented
7#10590285C211yesmaximal, characteristic, complemented
8#10590278C212yesmaximal, complemented
9#10590277C211yesmaximal, characteristic
10#10590270C212yesmaximal, complemented
11#10590267C212yesmaximal, complemented
12#83717—31nomaximal
13#83697—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#947—21no—
16C3×#944—21no—
17C3×#894—22no—
18C3×#893—21no—
19C3×#889—22no—
20C3×#887—21no—
21C3×#875C2212yes—
22C3×#874C2211yescharacteristic
23C3×C4×D12C2212yes—
24C3×#870C2212yes—
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2212yes—
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29C2×#3718C2211yescharacteristic
30C2×#3715C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2212yes—
35#63576C2211yescharacteristic
36#63574C2212yes—
37#63565C2212yes—
38#63565C2211yescharacteristic
39#63565C2211yescharacteristic
40#63562C2212yes—
41#63562C2212yes—
42#63562C2212yes—
43C3×#559—31no—
44C3×#557—31no—
45#5585D311yescharacteristic
46#5567D311yescharacteristic, complemented
47#5094—31no—
48#5088—31no—
49#5075—31no—
50#5070—31no—
51#5068—32no—
52#5066—32no—
53#5056—32no—
54#5054—32no—
55C4×#216—31no—
56C4×#216—31no—
57#5028—32no—
58#5027—31no—
59C4×#215—32no—
60Q8×C3⋊C8—31no—
61Q8×C3⋊C8—31no—
62Q8×C3⋊C8—61no—
63#5020—31no—
64C4×#214—32no—
65#5009—32no—
66C2×C32×Q8D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2311yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C32×C4⋊C4D411yescharacteristic
75C32×C4⋊C4D412yes—
76C32×C42C2311yescharacteristic
77C32×C42C2312yes—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3C2312yes—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—21no—
96#3718—22no—
97#3715—24no—
98#3365—91noSylow
99C3×C4⋊Q8—31no—
100C3×C4⋊Q8—61no—
101C3×#127—31no—
102C3×#125—32no—
103C3×#125—62no—
104C3×#124—32no—
105C3×#124—61no—
106C3×#123—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—31no—
111C3×C4×Q8—61no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4—32no—
115C3×C4×D4—61no—
116#947—21no—
117#944—21no—
118C2×#216—31no—
119C2×#216—31no—
120C2×#215—32no—
121C2×#214—32no—
122#894—22no—
123#893—21no—
124#889—22no—
125#887—21no—
126#875C2×D312yes—
127#874C2×D311yescharacteristic
128C4×D12C2×D312yes—
129#870C2×D312yes—
130#869C2×D311yescharacteristic
131C4×Dic6C2×D312yes—
132C4×Dic6C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134#835—32no—
135#835—31no—
136#835—31no—
137#832—32no—
138#832—32no—
139#832—32no—
140#810—31no—
141#810—32no—
142#810—31no—
143#809—32no—
144#809—32no—
145#809—32no—
146#808—32no—
147#808—32no—
148#807—31no—
149#807—31no—
150C4⋊(C3⋊C8)—32no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—31no—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)—61no—
155C4⋊(C3⋊C8)—62no—
156C4×C3⋊C8—32no—
157C4×C3⋊C8—32no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—62no—
161C4×C3⋊C8—61no—
162C22×C3×D3—22no—
163C32×Q8—22no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×D12—81no—
178C3×C4×D3—82no—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—21no—
182C3×Dic6—42no—
183C3×Dic6#4112yes—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)—22no—
186C3⋊(C3⋊C8)—21no—
187#559—31no—
188#557—31no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—91no—
197C4×SD16—92no—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×Q8#6711yescharacteristic
203C2×C3×Q8#6711yescharacteristic
204C2×C3×D4—32no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C22×C3×C4—62no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×Dic6—21no—
213C2×Dic6C22×D311yescharacteristic
214C2×Dic6C22×D311yescharacteristic
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—62no—
223C3×C4⋊C4—62no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4#6711yescharacteristic
227C3×C4⋊C4#6712yes—
228C3×C4⋊C4#6711yescharacteristic
229C3×C4⋊C4#6712yes—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C42—22no—
234C3×C42—21no—
235C3×C42—61no—
236C3×C42—62no—
237C3×C42—61no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D312yes—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D312yes—
242#216—62no—
243#216—62no—
244#215—64no—
245#214—64no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—22no—
248(C2×D3)⋊C4—22no—
249C4⋊Dic3—21no—
250C4⋊Dic3C22×D311yescharacteristic
251C4⋊Dic3C22×D311yescharacteristic
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—21no—
254Dic3⋊C4—22no—
255Dic3⋊C4—21no—
256Dic3⋊C4—22no—
257Dic3⋊C4—22no—
258C4×Dic3—22no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—62no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C32×C4—22no—
275C32×C4—22no—
276C32×C4—21no—
277C32×C4#13512yes—
278C32×C4C2×#4111yescharacteristic
279C32×C42−1+411yescharacteristic
280C3×Dic3—22no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C2×Q16—91no—
286C2×SD16—92no—
287C4⋊Q8—31no—
288C4⋊Q8—61no—
289#127—31no—
290#125—32no—
291#125—62no—
292#124—32no—
293#124—61no—
294#123—62no—
295C4×Q8—32no—
296C4×Q8—31no—
297C4×Q8—31no—
298C4×Q8—61no—
299C4×Q8D3211yescharacteristic
300C4×D4—32no—
301C4×D4—61no—
302#107—91no—
303#106—92no—
304C4⋊C8—91no—
305C4⋊C8—92no—
306#103—91no—
307#103—91no—
308#103—92no—
309#102—92no—
310#102—92no—
311#102—92no—
312C4×C8—92no—
313C4×C8—91no—
314C23×C3—62no—
315C22×D3—22no—
316C3×Q8—24no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—32no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×Q8—61no—
323C3×Q8—122no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—122no—
327C3×D4—241no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—242no—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C2×#6712yes—
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354D12—22no—
355D12—22no—
356D12—42no—
357D12—81no—
358C4×D3—82no—
359Dic6—21no—
360Dic6—21no—
361Dic6—21no—
362Dic6—42no—
363Dic6#23912yes—
364C3⋊C8—62no—
365C3⋊C8—62no—
366C3⋊C8—61no—
367C3⋊C8—61no—
368C3⋊C8—62no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—122no—
372C3⋊C8—121no—
373C2×C32#54811yescharacteristic
374C2×C32C2×#13511yescharacteristic
375C2×C32#57711yescharacteristic
376C3×D3—82no—
377C2×Q8—31no—
378C2×Q8—31no—
379C2×Q8—61no—
380C2×Q8#62511yescharacteristic
381C2×D4—32no—
382C2×D4—61no—
383C2×D4—61no—
384C22×C4—62no—
385Q16—182no—
386SD16—184no—
387C2×C8—91no—
388C2×C8—91no—
389C2×C8—92no—
390C4⋊C4—32no—
391C4⋊C4—31no—
392C4⋊C4—31no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—62no—
396C4⋊C4—62no—
397C4⋊C4—62no—
398C4⋊C4—61no—
399C4⋊C4#62511yescharacteristic
400C4⋊C4#62512yes—
401C22⋊C4—62no—
402C22⋊C4—62no—
403C22⋊C4—62no—
404C42—61no—
405C42—62no—
406C42—61no—
407C42C2×D3212yes—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3C22×#6711yescharacteristic
414C22×C3C22×#6711yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C3×C4—24no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—22no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—62no—
431C3×C4—121no—
432C3×C4—122no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4#95012yes—
436C3×C4#95012yes—
437C3×C4C2×#23911yescharacteristic
438C3×C4#100711yescharacteristic
439C3×C4D3×#4111yescharacteristic
440C3×C4#101011yescharacteristic
441Dic3—22no—
442Dic3—42no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446C32#336511yescharacteristic, complemented, Sylow
447C23—62no—
448Q8—22no—
449Q8—32no—
450Q8—61no—
451Q8—61no—
452Q8—61no—
453Q8—122no—
454D4—62no—
455D4—62no—
456D4—122no—
457D4—241no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—62no—
463C2×C4—242no—
464C2×C4C2×#62512yes—
465C2×C4C2×#62512yes—
466C2×C4C2×#62511yescharacteristic
467C2×C4C2×#62511yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—181no—
470C8—182no—
471C8—181no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—242no—
476C2×C3#581711yescharacteristic
477C2×C3C2×#95011yescharacteristic
478C2×C3C2×#95011yescharacteristic
479C2×C3#583111yescharacteristic
480C2×C3#583611yescharacteristic
481C2×C3#583711yescharacteristic
482D3—82no—
483C22—122no—
484C22—122no—
485C22—122no—
486C22C22×#62511yescharacteristic
487C4—22no—
488C4—21no—
489C4—22no—
490C4—62no—
491C4—121no—
492C4—121no—
493C4—121no—
494C4—122no—
495C4#6382212yes—
496C4#6431511yescharacteristic
497C4D3×#23911yescharacteristic
498C3—21no—
499C3#8369711yescharacteristic, complemented
500C3#8371711yescharacteristic, complemented
501C2—242no—
502C2C2×#6382211yescharacteristic
503C2#1059540911yescharacteristic
504C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
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 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5567C2semidirect
3. Q8×C3⋊(C3⋊C8)C2semidirect
4. C4×#3718C2semidirect
6. C4×#3715C2semidirect
7. #10590285C2semidirect
8. #10590278C2semidirect
10. #10590270C2semidirect
11. #10590267C2semidirect
46. #5567D3semidirect
446. C32#3365semidirect
499. C3#83697semidirect
500. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55672
Q8×C3⋊(C3⋊C8)2
C4×#37182
#105903642
C4×#37152
#105902852
#105902782
#105902772
#105902702
#105902672
#837173
#836973