Finite Group Databasebeta

← #11895672

Subgroups — #11895672

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
1#10593951C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C8×#634C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×#4694C211yesmaximal, characteristic
6#10590868C212yesmaximal, complemented
7#10590797C212yesmaximal, complemented
8#10590780C212yesmaximal, complemented
9#10590742C212yesmaximal, complemented
10#10590364C211yesmaximal, characteristic
11#10590285C211yesmaximal, characteristic, complemented
12#81589—31nomaximal
13#79701—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×Dic12C2211yescharacteristic
16C3×#874C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63898C2212yes—
21Dic3×D12—21no—
22#63884—22no—
23#63872C2212yes—
24#63866—21no—
25#63863C2212yes—
26#63860—21no—
27#63846—22no—
28#63843C2212yes—
29Dic3×Dic6—21no—
30C2×#3715C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×#818C2211yescharacteristic
38C3×#816C2211yescharacteristic
39C3×#816C2211yescharacteristic
40#63574C2212yes—
41#63565C2212yes—
42#63562C2212yes—
43#5721—31no—
44#5713—31no—
45#5585—31no—
46#5570—31no—
47C3×#486—31no—
48C3×C4×Q16—31no—
49#5185—32no—
50#5094—31no—
51#5075—31no—
52#5027—31no—
53#5020—31no—
54#4891—32no—
55#4800—32no—
56#4788—32no—
57#4768—32no—
58#4767—32no—
59#4766—32no—
60#4758—32no—
61C4×Dic12D311yescharacteristic, complemented
62#4694D311yescharacteristic
63C8×Dic6—31no—
64C8×Dic6—31no—
65C8×Dic6—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×C3×Dic6C2311yescharacteristic
73C2×D3×Dic3—22no—
74C2×C32×C8C2311yescharacteristic
75C2×C32×C8C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)D411yescharacteristic
78#3750D412yes—
79C4×C3⋊Dic3C2312yes—
80C2×C3⋊(C3⋊C8)C2312yes—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2311yescharacteristic
83C3×C4⋊Dic3C2312yes—
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4—21no—
86C3×Dic3⋊C4—21no—
87C3×C4×Dic3—21no—
88C3×C4×Dic3—21no—
89C3×Dic12—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97#3715—24no—
98#3365—91noSylow
99C2×C3×Q16—31no—
100C3×C4⋊Q8—31no—
101C3×#127—31no—
102C3×C4×Q8—31no—
103C3×C4×Q8—31no—
104#947—32no—
105Q8×Dic3—32no—
106Q8×Dic3—61no—
107#944—61no—
108C2×#215—32no—
109#936—32no—
110#936—61no—
111#935—62no—
112D4×Dic3—32no—
113D4×Dic3—61no—
114C2×#214—32no—
115C2×Dic12C2×D311yescharacteristic
116#894—62no—
117#893—32no—
118#890—32no—
119#890—32no—
120#890—62no—
121#889—62no—
122#887—32no—
123#875—61no—
124#874C2×D311yescharacteristic
125C4×D12—61no—
126#869—61no—
127#869C2×D311yescharacteristic
128C4×Dic6—31no—
129C4×Dic6—31no—
130C4×Dic6—61no—
131C4×Dic6—61no—
132C4×Dic6C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C3×#107—31no—
135C3×#103—31no—
136C3×#103—31no—
137C3×#102—32no—
138C3×#102—32no—
139C3×C4×C8—21no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821C2×D312yes—
145#821C2×D312yes—
146#818C2×D311yescharacteristic
147#816C2×D311yescharacteristic
148#816C2×D311yescharacteristic
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—62no—
152C8×Dic3—32no—
153C8×Dic3—32no—
154C8×Dic3—62no—
155#810—32no—
156#809—32no—
157#808—32no—
158#808—32no—
159C4⋊(C3⋊C8)—31no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—61no—
162C22×C3×D3—22no—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168#634—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×D12—81no—
178C3×Dic6—21no—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—42no—
182C3×Dic6#4112yes—
183D3×Dic3—82no—
184C32×C8—21no—
185C32×C8—21no—
186C3⋊(C3⋊C8)—22no—
187#559—91no—
188#557—91no—
189#488—92no—
190#486—31no—
191#478—92no—
192#475—91no—
193#464—92no—
194#460—91no—
195C8×Q8—91no—
196C4×Q16—31no—
197C4×SD16—92no—
198C2×C3×Q8—31no—
199C2×C3×Q8—31no—
200C2×C3×Q8—61no—
201C2×C3×D4—32no—
202C2×C3×D4—61no—
203C2×C3×D4—61no—
204C22×Dic3—62no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12C22×D312yes—
208C2×C4×D3—62no—
209C2×Dic6—21no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—61no—
213C2×Dic6C22×D311yescharacteristic
214C2×Dic6C22×D311yescharacteristic
215C3×Q16—62no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C42—21no—
229C3×C42—61no—
230C3×C42—61no—
231C3×C42C22×D311yescharacteristic
232C3×C42C22×D311yescharacteristic
233#217—62no—
234#217—62no—
235#217—62no—
236#215—64no—
237#214—64no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—61no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3C22×D311yescharacteristic
249C4⋊Dic3C22×D312yes—
250C4⋊Dic3C22×D311yescharacteristic
251Dic3⋊C4—21no—
252Dic3⋊C4—21no—
253Dic3⋊C4—32no—
254Dic3⋊C4—32no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—32no—
268C2×C3⋊C8—62no—
269Dic12—22no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C32×C4—21no—
275C32×C4#13512yes—
276C32×C4C2×#4111yescharacteristic
277C32×C42−1+411yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—22no—
280C3×Dic3—22no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C3×Dic3—41no—
285C2×Q16—31no—
286C2×SD16—92no—
287C4⋊Q8—31no—
288C4⋊Q8—181no—
289#127—31no—
290#125—92no—
291#125—182no—
292#124—92no—
293#124—181no—
294#123—182no—
295C4×Q8—31no—
296C4×Q8—31no—
297C4×Q8—91no—
298C4×Q8—92no—
299C4×Q8—181no—
300C4×D4—92no—
301C4×D4—181no—
302#107—31no—
303#106—92no—
304C4⋊C8—92no—
305C4⋊C8—91no—
306#103—31no—
307#103—31no—
308#103—92no—
309#102—32no—
310#102—32no—
311#102—92no—
312C4×C8—92no—
313C4×C8D3211yescharacteristic
314C23×C3—62no—
315C22×D3—22no—
316C3×Q8—32no—
317C3×Q8—61no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×Q8—122no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—122no—
324C3×D4—241no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—242no—
351D12—22no—
352D12—22no—
353D12—42no—
354D12—81no—
355C4×D3—242no—
356Dic6—21no—
357Dic6—21no—
358Dic6—21no—
359Dic6—42no—
360Dic6—64no—
361Dic6—62no—
362Dic6—62no—
363Dic6#23512yes—
364C3×C8—22no—
365C3×C8—21no—
366C3×C8—21no—
367C3×C8—21no—
368C3×C8—21no—
369C3×C8—41no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32#54811yescharacteristic
374C2×C32C2×#13511yescharacteristic
375C2×C32#57711yescharacteristic
376C3×D3—82no—
377C2×Q8—31no—
378C2×Q8—31no—
379C2×Q8—61no—
380C2×Q8—91no—
381C2×D4—32no—
382C2×D4—61no—
383C2×D4—61no—
384C22×C4—182no—
385Q16—62no—
386SD16—184no—
387C2×C8—92no—
388C2×C8C2×D3211yescharacteristic
389C2×C8C2×D3211yescharacteristic
390C4⋊C4—32no—
391C4⋊C4—31no—
392C4⋊C4—31no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—91no—
397C4⋊C4—92no—
398C4⋊C4—182no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C22⋊C4—182no—
404C42—61no—
405C42—61no—
406C42—92no—
407C42—182no—
408C42C2×D3211yescharacteristic
409C22×C3—21no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—41no—
424C3×C4—62no—
425C3×C4—121no—
426C3×C4—121no—
427C3×C4—121no—
428C3×C4—122no—
429C3×C4#91212yes—
430C3×C4#91912yes—
431C3×C4C2×#23511yescharacteristic
432C3×C4D3×#4111yescharacteristic
433C3×C4#101011yescharacteristic
434C3×C4#101011yescharacteristic
435Dic3—22no—
436Dic3—42no—
437Dic3—41no—
438Dic3—41no—
439Dic3—41no—
440Dic3—64no—
441Dic3—62no—
442Dic3—62no—
443Dic3—62no—
444Dic3—62no—
445Dic3—122no—
446C32#336511yescharacteristic, complemented, Sylow
447C23—62no—
448Q8—32no—
449Q8—61no—
450Q8—61no—
451Q8—61no—
452Q8—122no—
453Q8—182no—
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—92no—
464C2×C4—92no—
465C2×C4—722no—
466C2×C4#380211yescharacteristic
467C2×C4#380211yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—21no—
470C8—21no—
471C8—182no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—242no—
476C2×C3#555211yescharacteristic
477C2×C3#567711yescharacteristic
478C2×C3C2×#91211yescharacteristic
479C2×C3#576211yescharacteristic
480C2×C3C2×#91911yescharacteristic
481C2×C3#577011yescharacteristic
482D3—82no—
483C22—122no—
484C22—122no—
485C22—122no—
486C22C2×#380211yescharacteristic
487C4—21no—
488C4—62no—
489C4—121no—
490C4—121no—
491C4—121no—
492C4—122no—
493C4—182no—
494C4—182no—
495C4#6381012yes—
496C4#6429811yescharacteristic
497C4D3×#23511yescharacteristic
498C3—21no—
499C3#7970111yescharacteristic, complemented
500C3#8158911yescharacteristic, complemented
501C2—242no—
502C2#1059390511yescharacteristic
503C2#1059468611yescharacteristic
504C2C2×#6381011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC4×C8D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. C8×#634C2semidirect
4. C3×C4×Dic12C2semidirect
6. #10590868C2semidirect
7. #10590797C2semidirect
8. #10590780C2semidirect
9. #10590742C2semidirect
11. #10590285C2semidirect
61. C4×Dic12D3semidirect
446. C32#3365semidirect
499. C3#79701semidirect
500. C3#81589semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105938612
C8×#6342
C3×C4×Dic122
C3×#46942
#105908682
#105907972
#105907802
#105907422
#105903642
#105902852
#815893
#797013