Finite Group Databasebeta

← #11861513

Subgroups — #11861513

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×Dic6C211yesmaximal, characteristic
2#10592530C211yesmaximal, characteristic, complemented
3C3×#4837C211yesmaximal, characteristic
4C3×#4830C211yesmaximal, characteristic, complemented
5#10590785C212yesmaximal, complemented
6#10590663C212yesmaximal
7Dic3×ΓL(1,𝔽25)C212yesmaximal
8#10590646C212yesmaximal, complemented
9C4×#3711C211yesmaximal, characteristic
10#10590296C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12Q8×ΓL(1,𝔽25)—31nomaximal
13#79046—31nomaximal
14C2×D3×Dic6C411yescharacteristic
15C4×#634C2211yescharacteristic
16C2×C3×ΓL(1,𝔽25)C2212yes—
17C3×C42×D3C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C4×#627C2212yes—
20D3×C4⋊Dic3C411yescharacteristic
21D3×Dic3⋊C4C412yes—
22C4×D3×Dic3C2212yes—
23#63844C411yescharacteristic
24Dic3×Dic6C411yescharacteristic
25#63837C412yes—
26C2×#3711C2211yescharacteristic
27C2×#3711C2211yescharacteristic
28C32×C4⋊C8C2211yescharacteristic
29#63642C2212yes—
30#63641C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×Dic3⋊C8C2212yes—
33C3×Dic3⋊C8C2212yes—
34C3×C8×Dic3C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63572C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63555C2212yes—
40#63554C2211yescharacteristic
41#63554C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C4×D3×Q8—31no—
44C2×C4×Dic6—31no—
45C3×C8×Q8—31no—
46C3×#423—31no—
47#5118—32no—
48Dic3×M16—32no—
49Q8×C3⋊C8—31no—
50C4×#208—31no—
51#4837—32no—
52#4837D311yescharacteristic
53#4831—31no—
54#4831—31no—
55#4831—32no—
56#4831—31no—
57#4831—61no—
58#4830—31no—
59#4830D311yescharacteristic, complemented
60#4828—32no—
61#4828—32no—
62C4×ΓL(1,𝔽25)—32no—
63C4×ΓL(1,𝔽25)—31no—
64#4679—32no—
65#4679—31no—
66C2×#634C2×C411yescharacteristic
67C2×C3×C4×D3C2×C411yescharacteristic
68C2×C3×C4×D3C2×C411yescharacteristic
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6C2×C411yescharacteristic
71C2×#627C2×C412yes—
72C2×D3×Dic3C2×C412yes—
73C2×D3×Dic3C2×C412yes—
74D3×Dic6—24no—
75C2×C32×C8C2312yes—
76C32×C42C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2×C411yescharacteristic
78#3750C2×C412yes—
79C4×C3⋊Dic3C2312yes—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×C4⋊Dic3C2×C411yescharacteristic
83C3×Dic3⋊C4C2×C412yes—
84C3×C4×Dic3C2×C411yescharacteristic
85C3×C4×Dic3C2×C411yescharacteristic
86C3×C4×Dic3C2312yes—
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×ΓL(1,𝔽25)—24no—
92#3724C2×C412yes—
93Dic3⋊Dic3C2×C412yes—
94Dic3⋊Dic3C2×C412yes—
95Dic32C2×C412yes—
96Dic32C2×C412yes—
97#3711—22no—
98#3711Q814yescomplemented
99Q8×M16—91noSylow
100C2×D3×Q8—31no—
101C22×Dic6—31no—
102C2×C3×M16—32no—
103C3×C4×Q8—31no—
104C2×C3×C42—31no—
105Q8×Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×Dic3⋊C4—32no—
108C2×C4×Dic3—32no—
109C2×#208—31no—
110C2×#208—31no—
111C2×ΓL(1,𝔽25)—31no—
112C2×ΓL(1,𝔽25)—31no—
113C2×ΓL(1,𝔽25)C2×D312yes—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—31no—
116#887—32no—
117#887—31no—
118C42×D3—32no—
119C42×D3C2×D311yescharacteristic
120C4×Dic6—31no—
121C4×Dic6—31no—
122C4×Dic6—31no—
123C4×Dic6—31no—
124C4×Dic6—32no—
125C4×Dic6—32no—
126C4×Dic6—32no—
127C4×Dic6—61no—
128C4×Dic6C2×D311yescharacteristic
129C3×C4⋊C8—21no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132C3×C4⋊C8—31no—
133C3×C4⋊C8C2×D311yescharacteristic
134C3×C4⋊C8C2×D311yescharacteristic
135C3×C4×C8—32no—
136C3×C4×C8—31no—
137#815—32no—
138#815—32no—
139#815—31no—
140#815—31no—
141#815—32no—
142#815—32no—
143#815—62no—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146Dic3⋊C8—32no—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—62no—
150Dic3⋊C8C2×D312yes—
151Dic3⋊C8C2×D312yes—
152C8×Dic3—32no—
153C8×Dic3C2×D312yes—
154C4⋊(C3⋊C8)—32no—
155C4⋊(C3⋊C8)C2×D311yescharacteristic
156#803—31no—
157#803—31no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—32no—
161C4×C3⋊C8—61no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3×D3C22×C411yescharacteristic
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C22×C411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C22×C412yes—
168C2×C3⋊Dic3C22×C412yes—
169#634—22no—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C411yescharacteristic
172C2×C3×Dic3C22×C411yescharacteristic
173C2×C3×Dic3C22×C411yescharacteristic
174C2×C3×Dic3C22×C412yes—
175C3×C4×D3—22no—
176C3×C4×D3—41no—
177C3×C4×D3C2×Q812yes—
178C3×C4×D3#4112yes—
179C3×Dic6M1614yescomplemented
180#627—24no—
181D3×Dic3—24no—
182D3×Dic3—42no—
183C32×C8—22no—
184C3⋊(C3⋊C8)—21no—
185C3⋊(C3⋊C8)C2×Q812yescomplemented
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8C2×Q812yescomplemented
189C2×C4×Q8—91no—
190#446—92no—
191#446—91no—
192#446—92no—
193#446—91no—
194C8×Q8—31no—
195C8×Q8—91no—
196#423—31no—
197#423—92no—
198C4×M16—91no—
199C4×M16—92no—
200C2×C3×Q8—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206D3×Q8—64no—
207C2×C4×D3—32no—
208C2×C4×D3—32no—
209C2×C4×D3C4×D311yescharacteristic
210C2×C4×D3C4×D311yescharacteristic
211C2×C4×D3C22×D311yescharacteristic
212C2×Dic6—31no—
213C2×Dic6—31no—
214C2×Dic6—32no—
215C2×Dic6—32no—
216C2×Dic6—61no—
217C2×Dic6—64no—
218C2×Dic6C4×D311yescharacteristic
219C3×M16—64no—
220C2×C3×C8—22no—
221C2×C3×C8—31no—
222C2×C3×C8—32no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D312yes—
225C2×C3×C8C22×D312yes—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C42—21no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—32no—
232C3×C42—31no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—61no—
240C4⋊Dic3C4×D311yescharacteristic
241Dic3⋊C4—32no—
242Dic3⋊C4—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4—32no—
245Dic3⋊C4—32no—
246Dic3⋊C4—32no—
247Dic3⋊C4—62no—
248Dic3⋊C4C4×D312yes—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256C4×Dic3C4×D311yescharacteristic
257C4×Dic3C4×D311yescharacteristic
258C4×Dic3C22×D312yes—
259C4×Dic3C22×D311yescharacteristic
260#208—34no—
261#208—62no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8C22×D312yes—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271ΓL(1,𝔽25)—24no—
272ΓL(1,𝔽25)—34no—
273ΓL(1,𝔽25)—62no—
274C22×C32C23×C411yescharacteristic
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3C4×Q812yes—
278C32×C4—21no—
279C32×C4C2×M1612yes—
280C32×C4C22×Q811yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—22no—
283C3⋊Dic3—22no—
284C3×Dic3—21no—
285C3×Dic3—22no—
286C3×Dic3—21no—
287C3×Dic3C4×Q812yes—
288C3×Dic3C2×M1614yes—
289C22×Q8—91no—
290C2×M16—32no—
291C2×M16—91no—
292C2×M16—91no—
293C4×Q8—31no—
294C4×Q8—92no—
295C4×Q8—92no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C2×C4⋊C4—92no—
300C2×C4⋊C4—91no—
301C2×C42—31no—
302C2×C42—92no—
303C4⋊C8—32no—
304C4⋊C8—32no—
305C4⋊C8—31no—
306C4⋊C8—92no—
307C4⋊C8—92no—
308C4⋊C8—92no—
309C4⋊C8D3211yescharacteristic
310#97—91no—
311#97—91no—
312#97—92no—
313#97—92no—
314C4×C8—32no—
315C4×C8—31no—
316C4×C8—92no—
317C4×C8—91no—
318C23×C3—31no—
319C22×D3C2×C4×D311yescharacteristic
320C3×Q8—34no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—31no—
330C2×C3×C4—31no—
331C2×C3×C4—62no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—64no—
346C2×Dic3—122no—
347C2×Dic3C2×C4×D312yes—
348C2×Dic3C2×C4×D311yescharacteristic
349C2×Dic3C2×C4×D311yescharacteristic
350C2×Dic3C2×C4×D311yescharacteristic
351C2×Dic3C2×C4×D312yes—
352C4×D3—22no—
353C4×D3—41no—
354C4×D3—64no—
355C4×D3—122no—
356C4×D3#23712yes—
357C4×D3D3×Q812yes—
358Dic6—64no—
359Dic6—62no—
360Dic6—62no—
361Dic6—64no—
362Dic6—122no—
363Dic6ΓL(1,𝔽25)14yescomplemented
364C3×C8—22no—
365C3×C8—22no—
366C3×C8—32no—
367C3×C8—42no—
368C3×C8—61no—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—21no—
372C3⋊C8—32no—
373C3⋊C8—32no—
374C3⋊C8—62no—
375C3⋊C8—61no—
376C3⋊C8—61no—
377C3⋊C8—121no—
378C3⋊C8D3×Q812yescomplemented
379C2×C32C2×C4×Q811yescharacteristic
380C2×C32C22×M1611yescharacteristic
381C2×C32#56811yescharacteristic
382C3×D3—22no—
383C2×Q8—31no—
384C2×Q8—92no—
385C2×Q8—91no—
386C2×Q8—184no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—92no—
391C22×C4—92no—
392M16—64no—
393M16—94no—
394M16—182no—
395C2×C8—31no—
396C2×C8—31no—
397C2×C8—32no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8C2×D3212yes—
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—92no—
404C4⋊C4—92no—
405C4⋊C4—92no—
406C4⋊C4—92no—
407C4⋊C4—91no—
408C42—32no—
409C42—31no—
410C42—31no—
411C42—31no—
412C42—92no—
413C42—92no—
414C42—92no—
415C42C2×D3211yescharacteristic
416C22×C3—21no—
417C22×C3—32no—
418C22×C3—61no—
419C22×C3—61no—
420C22×C3C22×C4×D311yescharacteristic
421C22×C3C22×C4×D311yescharacteristic
422C2×D3—21no—
423C2×D3—21no—
424C2×D3#88712yes—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—34no—
431C3×C4—32no—
432C3×C4—41no—
433C3×C4—61no—
434C3×C4—62no—
435C3×C4—61no—
436C3×C4C2×ΓL(1,𝔽25)12yes—
437C3×C4D3×M1612yes—
438C3×C4C2×#23711yescharacteristic
439C3×C4C2×D3×Q811yescharacteristic
440C3×C4C2×D3×Q811yescharacteristic
441C3×C4D3×#4111yescharacteristic
442Dic3—21no—
443Dic3—21no—
444Dic3—22no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—62no—
449Dic3—122no—
450Dic3—122no—
451Dic3#88712yes—
452Dic3C2×ΓL(1,𝔽25)14yes—
453C32Q8×M1611yescharacteristic, complemented, Sylow
454C23—31no—
455Q8—34no—
456Q8—184no—
457Q8—182no—
458C2×C4—31no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—32no—
465C2×C4—62no—
466C2×C4—92no—
467C2×C4—92no—
468C2×C4—121no—
469C2×C4—184no—
470C2×C4—362no—
471C2×C4C4×D3211yescharacteristic
472C2×C4C4×D3211yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—22no—
475C8—32no—
476C8—62no—
477C8—61no—
478C8—92no—
479C8—181no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—62no—
484C2×C3C2×#88711yescharacteristic
485C2×C3C4×D3×Q811yescharacteristic
486C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
487C2×C3C2×D3×M1611yescharacteristic
488C2×C3#574511yescharacteristic
489C2×C3#575011yescharacteristic
490D3—22no—
491C22—32no—
492C22—61no—
493C22—61no—
494C22C2×C4×D3211yescharacteristic
495C4—21no—
496C4—32no—
497C4—34no—
498C4—61no—
499C4—61no—
500C4—62no—
501C4—182no—
502C4—182no—
503C4D3×ΓL(1,𝔽25)12yes—
504C4D3×#23711yescharacteristic
505C4D32×Q811yescharacteristic
506C3—21no—
507C3#7904611yescharacteristic, complemented
508C3Q8×ΓL(1,𝔽25)11yescharacteristic, complemented
509C2—62no—
510C2D3×#88711yescharacteristic
511C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
512C2#1059470611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×C3×D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32Q8×M16
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592530C2semidirect
4. C3×#4830C2semidirect
5. #10590785C2semidirect
8. #10590646C2semidirect
10. #10590296C2semidirect
11. #10590250C2semidirect
59. #4830D3semidirect
98. #3711Q8semidirect
179. C3×Dic6M16semidirect
185. C3⋊(C3⋊C8)C2×Q8semidirect
188. C3×C3⋊C8C2×Q8semidirect
363. Dic6ΓL(1,𝔽25)semidirect
378. C3⋊C8D3×Q8semidirect
453. C32Q8×M16semidirect
507. C3#79046semidirect
508. C3Q8×ΓL(1,𝔽25)semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Dic62
#105925302
C3×#48372
C3×#48302
#105907852
#105906632
Dic3×ΓL(1,𝔽25)2
#105906462
C4×#37112
#105902962
#105902502
Q8×ΓL(1,𝔽25)3
#790463