Finite Group Databasebeta

← #11861344

Subgroups — #11861344

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593873C211yesmaximal, characteristic
2#10592530C211yesmaximal, characteristic, complemented
3C3×#4837C211yesmaximal, characteristic
4C3×#4830C211yesmaximal, characteristic, complemented
5#10590908C212yesmaximal
6#10590695C212yesmaximal
7#10590646C212yesmaximal, complemented
8#10590644C212yesmaximal, complemented
9C4×D3×C3⋊C8C211yesmaximal, characteristic
10#10590259C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#79917—31nomaximal
13#79044—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×ΓL(1,𝔽25)C2212yes—
16C3×C42×D3C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18#63918C411yescharacteristic
19C4×#627C2212yes—
20#63867C412yes—
21#63866C411yescharacteristic
22#63857C411yescharacteristic
23#63856C411yescharacteristic
24#63855C2212yes—
25#63851C412yes—
26C2×D3×C3⋊C8C2211yescharacteristic
27C2×D3×C3⋊C8C2211yescharacteristic
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#63554C2212yes—
40#63553C2212yes—
41Dic3×C3⋊C8C2211yescharacteristic
42Dic3×C3⋊C8C2211yescharacteristic
43#5578—31no—
44#5470—31no—
45C3×C8×Q8—31no—
46C3×#423—31no—
47#5122—32no—
48#5119—32no—
49#5024—31no—
50C2×C4×C3⋊C8—31no—
51#4839—32no—
52#4837D311yescharacteristic
53#4831—31no—
54#4831—31no—
55#4831—31no—
56#4831—32no—
57#4831—61no—
58#4830—32no—
59#4830—31no—
60#4830D311yescharacteristic, complemented
61#4828—32no—
62#4689—32no—
63C4×D3×C8—31no—
64C8×Dic6—32no—
65C8×Dic6—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×C32×C8C2312yes—
73C32×C42C2311yescharacteristic
74C4⋊(C3⋊Dic3)C2×C411yescharacteristic
75#3750C2×C412yes—
76C4×C3⋊Dic3C2312yes—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×C4⋊Dic3C2×C411yescharacteristic
80C3×Dic3⋊C4C2×C412yes—
81C3×C4×Dic3C2×C411yescharacteristic
82C3×C4×Dic3C2×C411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C3×C4×Dic3C2312yes—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×ΓL(1,𝔽25)—24no—
89#3724C2×C412yes—
90Dic3⋊Dic3C2×C412yes—
91Dic3⋊Dic3C2×C412yes—
92Dic3⋊Dic3C2×C412yes—
93Dic3⋊Dic3C2×C412yes—
94(C2×D3)⋊Dic3C2×C412yes—
95(C2×D3)⋊Dic3C2×C412yes—
96D3×C3⋊C8—22no—
97D3×C3⋊C8Q814yescomplemented
98#2960—91noSylow
99C2×C3×M16—32no—
100C3×C4×Q8—31no—
101C2×C3×C42—31no—
102#946—31no—
103#944—31no—
104#926—32no—
105#924—31no—
106#924—31no—
107#924—32no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C2×ΓL(1,𝔽25)C2×D312yes—
111C2×D3×C8—31no—
112C2×D3×C8—31no—
113#897—31no—
114#896—32no—
115#889—32no—
116#888—31no—
117#872—32no—
118C42×D3C2×D311yescharacteristic
119#870—32no—
120#869—31no—
121#869—31no—
122C4×Dic6—31no—
123C4×Dic6—31no—
124C4×Dic6—32no—
125C4×Dic6—32no—
126C4×Dic6—61no—
127C4×Dic6C2×D311yescharacteristic
128C3×C4⋊C8—21no—
129C3×C4⋊C8—32no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—31no—
132C3×C4⋊C8C2×D311yescharacteristic
133C3×C4⋊C8C2×D311yescharacteristic
134C3×C4×C8—32no—
135C3×C4×C8—31no—
136#815—32no—
137#815—32no—
138#815—32no—
139#815—62no—
140Dic3⋊C8—32no—
141Dic3⋊C8—32no—
142Dic3⋊C8—32no—
143Dic3⋊C8—32no—
144Dic3⋊C8—32no—
145Dic3⋊C8—62no—
146Dic3⋊C8C2×D312yes—
147Dic3⋊C8C2×D312yes—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—32no—
151C8×Dic3—32no—
152C8×Dic3C2×D312yes—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)C2×D311yescharacteristic
155#803—32no—
156C4×C3⋊C8—31no—
157C4×C3⋊C8—31no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—61no—
161C4×C3⋊C8C2×D311yescharacteristic
162C22×C3×D3C22×C411yescharacteristic
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C22×C411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C22×C412yes—
168#634—22no—
169C2×C3×Dic3C22×C412yes—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C411yescharacteristic
172C2×C3×Dic3C22×C411yescharacteristic
173C2×C3×Dic3C22×C411yescharacteristic
174C3×C4×D3—22no—
175C3×C4×D3—22no—
176C3×C4×D3C2×Q812yes—
177C3×C4×D3#4112yes—
178C3×Dic6—22no—
179#627—24no—
180C32×C8—22no—
181C3⋊(C3⋊C8)—21no—
182C3⋊(C3⋊C8)C2×Q812yes—
183C3×C3⋊C8—21no—
184C3×C3⋊C8—22no—
185C3×C3⋊C8C2×Q812yes—
186#533—91no—
187#446—92no—
188#446—91no—
189#446—91no—
190C8×Q8—31no—
191C8×Q8—92no—
192C8×Q8—91no—
193#424—92no—
194#423—31no—
195#405—92no—
196C2×C4×C8—91no—
197C2×C3×Q8—31no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C2×C4×D3C4×D311yescharacteristic
202C2×C4×D3C4×D311yescharacteristic
203C2×C4×D3C22×D311yescharacteristic
204C2×Dic6—31no—
205C2×Dic6—31no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—61no—
209C2×Dic6C4×D311yescharacteristic
210C3×M16—64no—
211C2×C3×C8—22no—
212C2×C3×C8—31no—
213C2×C3×C8—32no—
214C2×C3×C8—31no—
215C2×C3×C8C22×D312yes—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—32no—
219C3×C42—21no—
220C3×C42—31no—
221C3×C42—31no—
222C3×C42—31no—
223C3×C42—32no—
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226#217—32no—
227#217—32no—
228(C2×D3)⋊C4—32no—
229(C2×D3)⋊C4—32no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—61no—
237C4⋊Dic3C4×D311yescharacteristic
238Dic3⋊C4—32no—
239Dic3⋊C4—32no—
240Dic3⋊C4—32no—
241Dic3⋊C4—32no—
242Dic3⋊C4—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4—32no—
245Dic3⋊C4—32no—
246Dic3⋊C4—62no—
247Dic3⋊C4C4×D312yes—
248C4×Dic3—32no—
249C4×Dic3—32no—
250C4×Dic3—62no—
251C4×Dic3C4×D311yescharacteristic
252C4×Dic3C4×D311yescharacteristic
253C4×Dic3C22×D311yescharacteristic
254C4×Dic3C22×D312yes—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—34no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—62no—
263C2×C3⋊C8C22×D311yescharacteristic
264C2×C3⋊C8C22×D312yes—
265C2×C3⋊C8C22×D311yescharacteristic
266ΓL(1,𝔽25)—24no—
267D3×C8—34no—
268D3×C8—62no—
269C22×C32C23×C411yescharacteristic
270C2×C3×D3—21no—
271C2×C3×D3—21no—
272C2×C3×D3C4×Q812yes—
273C32×C4—21no—
274C32×C4#13112yes—
275C32×C4C22×Q811yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—22no—
281C3×Dic3—21no—
282C3×Dic3C4×Q812yes—
283C3×Dic3#13112yes—
284C2×M16—32no—
285C22×C8—91no—
286C22×C8—91no—
287C4⋊Q8—91no—
288C4⋊Q8—91no—
289#125—92no—
290C22⋊Q8—92no—
291C22⋊Q8—91no—
292C22⋊Q8—91no—
293C4×Q8—31no—
294C4×Q8—92no—
295C4×Q8—91no—
296#117—92no—
297C2×C42—31no—
298C4⋊C8—32no—
299C4⋊C8—32no—
300C4⋊C8—31no—
301C4⋊C8—92no—
302C4⋊C8—92no—
303C4⋊C8—92no—
304C4⋊C8D3211yescharacteristic
305#97—92no—
306#97—92no—
307C4×C8—32no—
308C4×C8—31no—
309C4×C8—91no—
310C4×C8—91no—
311C4×C8—92no—
312C4×C8—91no—
313C23×C3—31no—
314C22×D3C2×C4×D311yescharacteristic
315C3×Q8—62no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—31no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×Dic3—32no—
335C2×Dic3—32no—
336C2×Dic3—32no—
337C2×Dic3—32no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3C2×C4×D311yescharacteristic
341C2×Dic3C2×C4×D312yes—
342C2×Dic3C2×C4×D312yes—
343C2×Dic3C2×C4×D311yescharacteristic
344C2×Dic3C2×C4×D311yescharacteristic
345C4×D3—22no—
346C4×D3—22no—
347C4×D3#23712yes—
348C4×D3D3×Q812yes—
349Dic6—22no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—64no—
354Dic6—122no—
355C3×C8—22no—
356C3×C8—22no—
357C3×C8—32no—
358C3×C8—42no—
359C3×C8—61no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—21no—
363C3⋊C8—32no—
364C3⋊C8—32no—
365C3⋊C8—62no—
366C3⋊C8—61no—
367C3⋊C8—61no—
368C3⋊C8—121no—
369C3⋊C8D3×Q812yes—
370C2×C32C2×C4×Q811yescharacteristic
371C2×C32C2×#13111yescharacteristic
372C2×C32C2×#13111yescharacteristic
373C3×D3—22no—
374C2×Q8—31no—
375C2×Q8—92no—
376C2×Q8—91no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—31no—
380M16—64no—
381C2×C8—31no—
382C2×C8—31no—
383C2×C8—32no—
384C2×C8—94no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8—182no—
388C2×C8C2×D3212yes—
389C4⋊C4—32no—
390C4⋊C4—31no—
391C4⋊C4—92no—
392C4⋊C4—92no—
393C4⋊C4—92no—
394C4⋊C4—92no—
395C4⋊C4—92no—
396C4⋊C4—92no—
397C4⋊C4—91no—
398C22⋊C4—92no—
399C22⋊C4—92no—
400C42—32no—
401C42—31no—
402C42—31no—
403C42—31no—
404C42—92no—
405C42C2×D3211yescharacteristic
406C22×C3—21no—
407C22×C3—32no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3C22×C4×D311yescharacteristic
411C22×C3C22×C4×D311yescharacteristic
412C2×D3—21no—
413C2×D3—21no—
414C2×D3#88712yes—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—21no—
420C3×C4—32no—
421C3×C4—32no—
422C3×C4—41no—
423C3×C4—61no—
424C3×C4—62no—
425C3×C4—62no—
426C3×C4#90112yes—
427C3×C4#90712yes—
428C3×C4C2×#23711yescharacteristic
429C3×C4C2×D3×Q811yescharacteristic
430C3×C4C2×D3×Q811yescharacteristic
431C3×C4D3×#4111yescharacteristic
432Dic3—22no—
433Dic3—21no—
434Dic3—22no—
435Dic3—62no—
436Dic3—62no—
437Dic3—62no—
438Dic3—62no—
439Dic3—122no—
440Dic3—122no—
441Dic3#88712yes—
442Dic3#90712yes—
443C32#296011yescharacteristic, complemented, Sylow
444C23—31no—
445Q8—62no—
446Q8—184no—
447Q8—182no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—32no—
451C2×C4—32no—
452C2×C4—31no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—92no—
458C2×C4—92no—
459C2×C4C4×D3211yescharacteristic
460C2×C4C4×D3211yescharacteristic
461C2×C4C22×D3211yescharacteristic
462C8—22no—
463C8—32no—
464C8—61no—
465C8—62no—
466C8—92no—
467C8—181no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—62no—
472C2×C3C2×#88711yescharacteristic
473C2×C3C4×D3×Q811yescharacteristic
474C2×C3C2×#90111yescharacteristic
475C2×C3C2×#90711yescharacteristic
476C2×C3C2×#90711yescharacteristic
477C2×C3D3×#13111yescharacteristic
478D3—22no—
479C22—32no—
480C22—61no—
481C22—61no—
482C22C2×C4×D3211yescharacteristic
483C4—21no—
484C4—32no—
485C4—32no—
486C4—61no—
487C4—62no—
488C4—62no—
489C4—182no—
490C4—182no—
491C4#6380412yes—
492C4D3×#23711yescharacteristic
493C4D32×Q811yescharacteristic
494C3—21no—
495C3#7904411yescharacteristic, complemented
496C3#7991711yescharacteristic, complemented
497C2—62no—
498C2D3×#88711yescharacteristic
499C2C2×#6380411yescharacteristic
500C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×C3×D3C22×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2960
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
7. #10590646C2semidirect
8. #10590644C2semidirect
10. #10590259C2semidirect
11. #10590254C2semidirect
60. #4830D3semidirect
97. D3×C3⋊C8Q8semidirect
443. C32#2960semidirect
495. C3#79044semidirect
496. C3#79917semidirect

Maximal subgroups

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

subgroupindex
#105938732
#105925302
C3×#48372
C3×#48302
#105909082
#105906952
#105906462
#105906442
C4×D3×C3⋊C82
#105902592
#105902542
#799173
#790443