Finite Group Databasebeta

← #11861461

Subgroups — #11861461

Order 1152.

783 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593882C211yesmaximal, characteristic
2C4×#3743C211yesmaximal, characteristic
3C3×#4679C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590910C212yesmaximal
6#10590784C212yesmaximal, complemented
7#10590702C212yesmaximal
8#10590646C212yesmaximal, complemented
9#10590331C211yesmaximal, characteristic
10#10590259C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#79960—31nomaximal
13#79918—31nomaximal
14C2×#3743C2211yescharacteristic
15C2×#3743C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19#63919C411yescharacteristic
20C4×#627C2212yes—
21#63874C2212yes—
22#63873C411yescharacteristic
23#63871C411yescharacteristic
24#63871C411yescharacteristic
25#63870C412yes—
26#63865C412yes—
27C2×#3710C2212yes—
28C32×C4×C8C2211yescharacteristic
29#63642C2211yescharacteristic
30#63642C2211yescharacteristic
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#815C2212yes—
33C3×Dic3⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×C8×Dic3C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4⋊(C3⋊C8)C2211yescharacteristic
38#63572C2212yes—
39Dic3⋊(C3⋊C8)C2212yes—
40Dic3⋊(C3⋊C8)C2212yes—
41#63554C2212yes—
42Dic3×C3⋊C8C2212yes—
43#5578—31no—
44#5578—31no—
45C3×#446—31no—
46C3×C8×Q8—31no—
47#5024—31no—
48Q8×C3⋊C8—31no—
49#4839—32no—
50#4839—32no—
51D3×C4⋊C8—31no—
52D3×C4⋊C8—31no—
53#4831—31no—
54#4831—32no—
55#4830—31no—
56#4828—32no—
57#4708—32no—
58#4701—32no—
59#4689—32no—
60C4×ΓL(1,𝔽25)—31no—
61C4×ΓL(1,𝔽25)—31no—
62C4×ΓL(1,𝔽25)—61no—
63#4679—32no—
64#4679D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×Dic6C2×C411yescharacteristic
70C2×C3×Dic6C2×C411yescharacteristic
71C2×#627C2×C412yes—
72C2×C32×C8C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C32×C42C2311yescharacteristic
75C4×C3⋊Dic3C2×C411yescharacteristic
76C4×C3⋊Dic3C2×C411yescharacteristic
77C4×C3⋊Dic3C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80#3743—22no—
81#3743Q814yescomplemented
82C3×C4⋊Dic3C2×C411yescharacteristic
83C3×C4⋊Dic3C2×C411yescharacteristic
84C3×Dic3⋊C4C2×C412yes—
85C3×Dic3⋊C4C2×C412yes—
86C3×C4×Dic3C2312yes—
87C3×C4×Dic3C2312yes—
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3724C2×C412yes—
91#3724C2×C412yes—
92#3724C2×C412yes—
93Dic3⋊Dic3C2×C412yes—
94Dic3⋊Dic3C2×C412yes—
95#3722C2×C412yes—
96#3722C2×C412yes—
97#3710—24no—
98#2962—91noSylow
99C3×C4×Q8—31no—
100C3×C4×Q8—31no—
101#946—31no—
102#946—31no—
103#944—31no—
104#944—31no—
105C2×ΓL(1,𝔽25)—31no—
106C2×ΓL(1,𝔽25)—31no—
107C2×ΓL(1,𝔽25)—31no—
108C2×ΓL(1,𝔽25)—31no—
109C2×ΓL(1,𝔽25)—61no—
110C2×ΓL(1,𝔽25)—61no—
111C2×D3×C8—32no—
112C2×D3×C8—32no—
113#897—31no—
114#897—31no—
115#896—32no—
116#896—32no—
117#889—32no—
118#889—32no—
119#888—31no—
120#888—31no—
121#872—32no—
122#872—32no—
123C42×D3—31no—
124C42×D3—31no—
125C42×D3—61no—
126C4×Dic6—32no—
127C4×Dic6—32no—
128C4×Dic6C2×D311yescharacteristic
129C4×Dic6C2×D311yescharacteristic
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132C3×C4⋊C8—31no—
133C3×C4⋊C8—31no—
134C3×#97—32no—
135C3×C4×C8—21no—
136C3×C4×C8—32no—
137C3×C4×C8C2×D311yescharacteristic
138C3×C4×C8C2×D311yescharacteristic
139#815—31no—
140#815—31no—
141#815—31no—
142#815—31no—
143#815—32no—
144#815—61no—
145#815—61no—
146#815C2×D312yes—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8C2×D312yes—
152Dic3⋊C8C2×D312yes—
153C8×Dic3—32no—
154C8×Dic3C2×D312yes—
155C4⋊(C3⋊C8)—32no—
156C4⋊(C3⋊C8)—32no—
157C4⋊(C3⋊C8)C2×D311yescharacteristic
158C4⋊(C3⋊C8)C2×D311yescharacteristic
159#803—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—61no—
164C22×C3⋊D3C22×C411yescharacteristic
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C22×C411yescharacteristic
169C2×C3⋊Dic3C22×C411yescharacteristic
170C2×C3⋊Dic3C22×C411yescharacteristic
171C4×C3⋊D3—22no—
172C4×C3⋊D3—41no—
173C4×C3⋊D3C2×Q812yes—
174C4×C3⋊D3#4112yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C412yes—
179C3×Dic6—22no—
180C3×Dic6—22no—
181#627—42no—
182C32×C8—21no—
183C32×C8C2×Q812yes—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)C2×Q812yes—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—22no—
188#533—91no—
189#446—31no—
190#446—92no—
191#446—92no—
192#446—91no—
193C8×Q8—31no—
194C8×Q8—91no—
195#424—92no—
196C2×C4⋊C8—91no—
197#405—92no—
198C4×M16—91no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C4×D3—31no—
202C2×C4×D3—31no—
203C2×C4×D3—31no—
204C2×C4×D3—31no—
205C2×C4×D3—31no—
206C2×C4×D3—31no—
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×Dic6—32no—
211C2×Dic6—32no—
212C2×Dic6C4×D311yescharacteristic
213C2×Dic6C4×D311yescharacteristic
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8—32no—
218C2×C3×C8C22×D311yescharacteristic
219C2×C3×C8C22×D311yescharacteristic
220C2×C3×C8C22×D311yescharacteristic
221C2×C3×C8C22×D311yescharacteristic
222C3×C4⋊C4—31no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C42—21no—
227C3×C42—32no—
228C3×C42—32no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231(C2×D3)⋊C4—32no—
232(C2×D3)⋊C4—32no—
233(C2×D3)⋊C4—32no—
234(C2×D3)⋊C4—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3C4×D311yescharacteristic
238C4⋊Dic3C4×D311yescharacteristic
239Dic3⋊C4—32no—
240Dic3⋊C4—32no—
241Dic3⋊C4—32no—
242Dic3⋊C4—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4—32no—
245Dic3⋊C4—32no—
246Dic3⋊C4—32no—
247Dic3⋊C4C4×D312yes—
248Dic3⋊C4C4×D312yes—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—31no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3C22×D312yes—
259C4×Dic3C22×D312yes—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8C22×D312yes—
267C2×C3⋊C8C22×D312yes—
268ΓL(1,𝔽25)—34no—
269ΓL(1,𝔽25)—34no—
270ΓL(1,𝔽25)—64no—
271ΓL(1,𝔽25)—62no—
272ΓL(1,𝔽25)—62no—
273ΓL(1,𝔽25)—64no—
274D3×C8—64no—
275D3×C8—64no—
276C22×C32C23×C411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3C4×Q812yes—
280C32×C4—21no—
281C32×C4#13112yes—
282C32×C4C22×Q811yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3⋊Dic3C4×Q812yes—
287C3×Dic3—22no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C2×M16—91no—
292C2×M16—91no—
293C22×C8—92no—
294C4⋊Q8—91no—
295C4⋊Q8—91no—
296#125—92no—
297C22⋊Q8—92no—
298C22⋊Q8—91no—
299C22⋊Q8—91no—
300C4×Q8—31no—
301C4×Q8—31no—
302C4×Q8—92no—
303#117—92no—
304C2×C42—91no—
305C4⋊C8—32no—
306C4⋊C8—32no—
307C4⋊C8—31no—
308C4⋊C8—31no—
309C4⋊C8—92no—
310C4⋊C8—92no—
311C4⋊C8—92no—
312#97—32no—
313#97—92no—
314#97—91no—
315#97—91no—
316C4×C8—32no—
317C4×C8—92no—
318C4×C8—91no—
319C4×C8D3211yescharacteristic
320C22×D3—31no—
321C22×D3—31no—
322C22×D3—61no—
323C3×Q8—62no—
324C3×Q8—62no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×Dic3—31no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—31no—
343C2×Dic3—31no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3C2×C4×D312yes—
348C2×Dic3C2×C4×D312yes—
349C2×Dic3C2×C4×D312yes—
350C2×Dic3C2×C4×D312yes—
351C4×D3—32no—
352C4×D3—32no—
353C4×D3—32no—
354C4×D3—32no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—122no—
360C4×D3—121no—
361C4×D3—121no—
362C4×D3—122no—
363Dic6—22no—
364Dic6—22no—
365Dic6—122no—
366Dic6—122no—
367C3×C8—22no—
368C3×C8—21no—
369C3×C8—21no—
370C3×C8—22no—
371C3×C8—62no—
372C3×C8—62no—
373C3×C8D3×Q812yes—
374C3×C8D3×Q812yes—
375C3⋊C8—22no—
376C3⋊C8—22no—
377C3⋊C8—32no—
378C3⋊C8—32no—
379C3⋊C8—62no—
380C3⋊C8—62no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C2×C32C2×C4×Q811yescharacteristic
384C2×C32C2×#13111yescharacteristic
385C2×C32#56811yescharacteristic
386C3⋊D3—22no—
387C2×Q8—31no—
388C2×Q8—31no—
389C2×Q8—92no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—91no—
393M16—94no—
394M16—182no—
395C2×C8—32no—
396C2×C8—32no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8—184no—
400C2×C8C2×D3211yescharacteristic
401C2×C8C2×D3211yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—32no—
404C4⋊C4—31no—
405C4⋊C4—31no—
406C4⋊C4—92no—
407C4⋊C4—92no—
408C4⋊C4—92no—
409C4⋊C4—92no—
410C4⋊C4—92no—
411C22⋊C4—92no—
412C22⋊C4—92no—
413C42—32no—
414C42—32no—
415C42—91no—
416C42—91no—
417C42—91no—
418C42C2×D3211yescharacteristic
419C22×C3—21no—
420C22×C3C22×C4×D311yescharacteristic
421C22×C3C22×C4×D311yescharacteristic
422C2×D3—32no—
423C2×D3—32no—
424C2×D3—62no—
425C2×D3—61no—
426C2×D3—61no—
427C2×D3—61no—
428C2×D3—61no—
429C2×D3—121no—
430C2×D3—121no—
431C3×C4—22no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—62no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—62no—
441C3×C4#90112yes—
442C3×C4#90712yes—
443C3×C4C2×D3×Q811yescharacteristic
444C3×C4C2×D3×Q811yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4D3×#4111yescharacteristic
447Dic3—22no—
448Dic3—22no—
449Dic3—22no—
450Dic3—22no—
451Dic3—32no—
452Dic3—32no—
453Dic3—62no—
454Dic3—61no—
455Dic3—61no—
456Dic3—61no—
457Dic3—61no—
458Dic3—121no—
459Dic3—121no—
460C32#296211yescharacteristic, complemented, Sylow
461C23—91no—
462Q8—62no—
463Q8—62no—
464Q8—362no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—91no—
470C2×C4—92no—
471C2×C4—92no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—182no—
475C2×C4—361no—
476C2×C4C4×D3211yescharacteristic
477C2×C4C4×D3211yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—21no—
480C8—62no—
481C8—62no—
482C8—92no—
483C8—181no—
484C8#379712yes—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3C4×D3×Q811yescharacteristic
489C2×C3C4×D3×Q811yescharacteristic
490C2×C3C2×#90111yescharacteristic
491C2×C3C2×#90711yescharacteristic
492C2×C3#575011yescharacteristic
493C2×C3#575011yescharacteristic
494D3—62no—
495D3—62no—
496D3—122no—
497C22—92no—
498C22—181no—
499C22—181no—
500C22C2×C4×D3211yescharacteristic
501C4—21no—
502C4—62no—
503C4—62no—
504C4—62no—
505C4—62no—
506C4—92no—
507C4—181no—
508C4—181no—
509C4#6380412yes—
510C4C2×#379711yescharacteristic
511C4#6430611yescharacteristic
512C3—21no—
513C3#7991811yescharacteristic, complemented
514C3#7996011yescharacteristic, complemented
515C2—182no—
516C2C4×#379711yescharacteristic
517C2#1059467011yescharacteristic
518C2C2×#6380411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×C8C22
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2962
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C3×#4679C2semidirect
4. C3×C8×Dic6C2semidirect
6. #10590784C2semidirect
8. #10590646C2semidirect
10. #10590259C2semidirect
11. #10590250C2semidirect
64. #4679D3semidirect
65. C8×Dic6D3semidirect
81. #3743Q8semidirect
460. C32#2962semidirect
513. C3#79918semidirect
514. C3#79960semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×#37432
C3×#46792
C3×C8×Dic62
#105909102
#105907842
#105907022
#105906462
#105903312
#105902592
#105902502
#799603
#799183