Finite Group Databasebeta

← #11895678

Subgroups — #11895678

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
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4848C211yesmaximal, characteristic
6#10590868C212yesmaximal, complemented
7#10590796C212yesmaximal, complemented
8#10590782C212yesmaximal, complemented
9#10590775C212yesmaximal, complemented
10C4×#3718C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic
12#81041—31nomaximal
13#80370—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×#204C2212yes—
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×#3718C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#817C2212yes—
37C3×#816C2212yes—
38#63576C2211yescharacteristic
39#63565C2211yescharacteristic
40#63565C2211yescharacteristic
41#63562C2212yes—
42#63562C2212yes—
43#5721—31no—
44#5713—31no—
45#5585—31no—
46#5570—31no—
47C3×#475—31no—
48C3×#460—31no—
49#5166—32no—
50Dic3×SD16—32no—
51#5088—31no—
52#5070—31no—
53C4×#216—31no—
54C4×#216—31no—
55#4871—32no—
56#4852—32no—
57#4851D311yescharacteristic, complemented
58#4848D311yescharacteristic
59#4830—31no—
60#4830—31no—
61#4830—61no—
62#4800—32no—
63#4798—32no—
64#4768—32no—
65#4763—32no—
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×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)D411yescharacteristic
77#3750D412yes—
78C4×C3⋊Dic3C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C3×C4⋊Dic3C2311yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4—21no—
86C3×Dic3⋊C4—21no—
87C3×C4×Dic3—21no—
88C3×C4×Dic3—21no—
89C3×#204—24no—
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#3718—22no—
98#3365—91noSylow
99C2×C3×SD16—32no—
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×#216—31no—
109C2×#216—31no—
110#936—32no—
111#936—61no—
112#935—62no—
113D4×Dic3—32no—
114D4×Dic3—61no—
115C2×#204C2×D312yes—
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×#106—32no—
135C3×C4⋊C8—21no—
136C3×C4⋊C8C2×D311yescharacteristic
137C3×C4⋊C8C2×D311yescharacteristic
138C3×#103—32no—
139C3×#102—32no—
140#835—31no—
141#835—31no—
142#832—32no—
143#832—32no—
144#821C2×D312yes—
145#817C2×D312yes—
146#816C2×D312yes—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—62no—
150C8×Dic3—32no—
151C8×Dic3—32no—
152C8×Dic3—62no—
153#810—31no—
154#810—31no—
155#809—32no—
156#809—32no—
157#807—31no—
158#807—31no—
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—22no—
185C3⋊(C3⋊C8)—21no—
186C3⋊(C3⋊C8)—21no—
187#559—91no—
188#557—91no—
189#488—92no—
190#486—91no—
191#478—92no—
192#475—31no—
193#464—92no—
194#460—31no—
195C8×Q8—91no—
196C4×Q16—91no—
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×SD16—64no—
216C2×C3×C8—22no—
217C2×C3×C8C22×D312yes—
218C2×C3×C8C22×D312yes—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—31no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C42—21no—
226C3×C42—61no—
227C3×C42—61no—
228C3×C42C22×D311yescharacteristic
229C3×C42C22×D311yescharacteristic
230#217—62no—
231#217—62no—
232#217—62no—
233#216—62no—
234#216—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—21no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—61no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3C22×D311yescharacteristic
246C4⋊Dic3C22×D311yescharacteristic
247C4⋊Dic3C22×D312yes—
248Dic3⋊C4—21no—
249Dic3⋊C4—21no—
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—32no—
259C4×Dic3—32no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269#204—24no—
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—91no—
286C2×SD16—32no—
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—91no—
303#106—32no—
304C4⋊C8—92no—
305C4⋊C8D3211yescharacteristic
306#103—32no—
307#103—91no—
308#103—91no—
309#102—32no—
310#102—92no—
311#102—92no—
312C4×C8—92no—
313C4×C8—91no—
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#23712yes—
364C3×C8—22no—
365C3×C8—22no—
366C3×C8—42no—
367C3⋊C8—62no—
368C3⋊C8—61no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—61no—
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—91no—
381C2×D4—32no—
382C2×D4—61no—
383C2×D4—61no—
384C22×C4—182no—
385Q16—182no—
386SD16—64no—
387C2×C8—91no—
388C2×C8—91no—
389C2×C8C2×D3212yes—
390C4⋊C4—31no—
391C4⋊C4—32no—
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—122no—
426C3×C4—121no—
427C3×C4—121no—
428C3×C4—121no—
429C3×C4#91612yes—
430C3×C4#91612yes—
431C3×C4C2×#23711yescharacteristic
432C3×C4#100711yescharacteristic
433C3×C4D3×#4111yescharacteristic
434C3×C4#101011yescharacteristic
435Dic3—22no—
436Dic3—41no—
437Dic3—42no—
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—22no—
470C8—181no—
471C8—181no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—242no—
476C2×C3#559811yescharacteristic
477C2×C3#563311yescharacteristic
478C2×C3C2×#91611yescharacteristic
479C2×C3C2×#91611yescharacteristic
480C2×C3#577511yescharacteristic
481C2×C3#577811yescharacteristic
482D3—82no—
483C22—122no—
484C22—122no—
485C22—122no—
486C22C2×#380211yescharacteristic
487C4—21no—
488C4—62no—
489C4—122no—
490C4—121no—
491C4—121no—
492C4—121no—
493C4—182no—
494C4—182no—
495C4#6380912yes—
496C4D3×#23711yescharacteristic
497C4#6431511yescharacteristic
498C3—21no—
499C3#8037011yescharacteristic, complemented
500C3#8104111yescharacteristic, complemented
501C2—242no—
502C2#1059452511yescharacteristic
503C2C2×#6380911yescharacteristic
504C2#1059471911yescharacteristic
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. #10592529C2semidirect
4. C3×#4851C2semidirect
6. #10590868C2semidirect
7. #10590796C2semidirect
8. #10590782C2semidirect
9. #10590775C2semidirect
10. C4×#3718C2semidirect
57. #4851D3semidirect
446. C32#3365semidirect
499. C3#80370semidirect
500. C3#81041semidirect

Maximal subgroups

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

subgroupindex
#105939512
#105938612
#105925292
C3×#48512
C3×#48482
#105908682
#105907962
#105907822
#105907752
C4×#37182
#105902772
#810413
#803703