Finite Group Databasebeta

← #11773857

Subgroups — #11773857

Order 1152.

975 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 975 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4468C212yesmaximal, complemented
5#10589145C212yesmaximal, complemented
6#68120—32nomaximal
7C23×D32C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C411yescharacteristic
10C2×#3743—21no—
11C2×C3×(C2×D3)⋊C4C2212yes—
12C2×(C2×D3)⋊Dic3C412yes—
13#63921—21no—
14#63921—21no—
15#63921—21no—
16#63921—21no—
17C2×#3712—21no—
18C32×C22⋊C8C2211yescharacteristic, complemented
19#63657C2211yescharacteristic, complemented
20#63647—21no—
21C3×#830C2212yescomplemented
22#63557—21no—
23C2×D3×C22⋊C4—32no—
24#4726—32no—
25#4726—32no—
26#4726—61no—
27C3×#323—32no—
28#4525—32no—
29#4468—32no—
30#4468D312yescomplemented
31C23×C3⋊D3C2×C411yescharacteristic
32C23×C3×D3C2×C412yes—
33C22×D32—21no—
34C22×D32—21no—
35C22×D32—24no—
36C22×D32—42no—
37C22×D32—42no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40C2×C4×C3⋊D3—42no—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C22×C3×Dic3C2×C412yes—
46C2×#624—21no—
47C2×#624—21no—
48C2×#624—42no—
49C2×C32×C8—21no—
50C2×C3⋊(C3⋊C8)—21no—
51#3743—42no—
52C3×(C2×D3)⋊C4—22no—
53C3×(C2×D3)⋊C4—22no—
54C2×C3×C3⋊C8—22no—
55(C2×D3)⋊Dic3—22no—
56(C2×D3)⋊Dic3—22no—
57#3712—42no—
58#1462—91noSylow
59C24×D3—32no—
60C22×C4×D3—32no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C2×C3×C22⋊C4—32no—
64C2×#217—32no—
65C2×(C2×D3)⋊C4—32no—
66C2×(C2×D3)⋊C4C2×D312yes—
67C2×ΓL(1,𝔽25)—62no—
68C2×ΓL(1,𝔽25)—62no—
69C2×ΓL(1,𝔽25)—62no—
70D3×C22⋊C4—62no—
71D3×C22⋊C4—62no—
72D3×C22⋊C4—62no—
73D3×C22⋊C4—62no—
74C3×C22⋊C8—21no—
75C3×C22⋊C8—32no—
76C3×C22⋊C8C2×D312yescomplemented
77#830—32no—
78#830—61no—
79#830C2×D312yescomplemented
80(C2×D3)⋊C8—62no—
81(C2×D3)⋊C8—62no—
82(C2×D3)⋊C8—62no—
83C23×C32C22×C411yescharacteristic
84C22×C3⋊D3—22no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3×D3—22no—
90C22×C3×D3—22no—
91C22×C3×D3—42no—
92C22×C3×D3—42no—
93C22×C3×D3M1614yescomplemented
94C2×D32—24no—
95C2×D32—24no—
96C2×D32—416no—
97C2×D32—42no—
98C2×D32—42no—
99C2×D32—42no—
100C2×D32—42no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—41no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—42no—
113#624—42no—
114#624—42no—
115C32×C8—41no—
116C3⋊(C3⋊C8)—41no—
117C3×C3⋊C8—42no—
118C22×C22⋊C4—91no—
119#407—91no—
120#407—91no—
121#323—32no—
122#323—92no—
123C24×C3—32no—
124C23×D3—32no—
125C23×D3—61no—
126C23×D3—62no—
127C23×D3—62no—
128C23×D3—64no—
129C23×D3—64no—
130C23×D3—124no—
131C23×D3—124no—
132C23×D3C4×D312yes—
133C22×C3×C4—21no—
134C22×C3×C4—32no—
135C22×C3×C4C22×D312yes—
136C22×Dic3—32no—
137C22×Dic3—61no—
138C22×Dic3C4×D312yes—
139C2×C4×D3—32no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—124no—
150C2×C4×D3—124no—
151C2×C4×D3—124no—
152C2×C3×C8—22no—
153C2×C3×C8—22no—
154C2×C3×C8—62no—
155C3×C22⋊C4—62no—
156C3×C22⋊C4—62no—
157#217—62no—
158#217—62no—
159(C2×D3)⋊C4—22no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—62no—
162(C2×D3)⋊C4—62no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—62no—
166ΓL(1,𝔽25)—124no—
167ΓL(1,𝔽25)—124no—
168ΓL(1,𝔽25)—124no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32C2×M1612yes—
173C2×C3⋊D3—28no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3#9912yes—
179C2×C3⋊D3#10012yes—
180C2×C3×D3—24no—
181C2×C3×D3—44no—
182C2×C3×D3—42no—
183C2×C3×D3—42no—
184C2×C3×D3—44no—
185D32—48no—
186D32—48no—
187C32×C4—21no—
188C32×C4—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—21no—
191C3×Dic3—42no—
192C25—91no—
193C23×C4—91no—
194C23×C4—91no—
195C2×M16—181no—
196C2×M16—181no—
197C2×C22⋊C4—32no—
198C2×C22⋊C4—92no—
199C2×C22⋊C4—181no—
200C2×C22⋊C4—181no—
201C2×C22⋊C4—181no—
202C2×C22⋊C4—181no—
203C22⋊C8—32no—
204C22⋊C8—91no—
205C22⋊C8—181no—
206C22⋊C8—181no—
207C22⋊C8D3211yescharacteristic, complemented
208C23×C3—21no—
209C23×C3—34no—
210C23×C3—62no—
211C23×C3—62no—
212C23×C3—122no—
213C23×C3—122no—
214C23×C3C2×C4×D312yes—
215C22×D3—22no—
216C22×D3—22no—
217C22×D3—32no—
218C22×D3—32no—
219C22×D3—42no—
220C22×D3—42no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—68no—
224C22×D3—68no—
225C22×D3—64no—
226C22×D3—64no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—122no—
230C22×D3—122no—
231C22×D3—122no—
232C22×D3—124no—
233C22×D3—124no—
234C22×D3—1216no—
235C22×D3—124no—
236C22×D3—124no—
237C22×D3—1216no—
238C22×D3ΓL(1,𝔽25)14yescomplemented
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—62no—
244C2×C3×C4—122no—
245C2×C3×C4D3×D412yes—
246C2×C3×C4D3×D412yes—
247C2×Dic3—22no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—42no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C4×D3—64no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—122no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—122no—
262C4×D3—122no—
263C4×D3—122no—
264C4×D3—122no—
265C3×C8—42no—
266C3×C8—42no—
267C3×C8—122no—
268C3⋊C8—42no—
269C3⋊C8—122no—
270C3⋊C8—122no—
271C2×C32—22no—
272C2×C32#40711yescharacteristic
273C2×C32C2×#9911yescharacteristic
274C2×C32C2×#10011yescharacteristic
275C3⋊D3—22no—
276C3⋊D3—22no—
277C3×D3—44no—
278C24—32no—
279C24—91no—
280C24—184no—
281C24—181no—
282C24—181no—
283C24—362no—
284C24—362no—
285C22×C4—32no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4—362no—
294C22×C4—362no—
295C22×C4C2×D3211yescharacteristic
296M16—362no—
297M16—362no—
298C2×C8—21no—
299C2×C8—62no—
300C2×C8—181no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—182no—
304C22⋊C4—182no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—64no—
312C22×C3—124no—
313C22×C3—124no—
314C22×C3—122no—
315C22×C3—122no—
316C22×C3D3×C22⋊C412yes—
317C22×C3C2×ΓL(1,𝔽25)12yes—
318C22×C3D3×M1612yes—
319C2×D3—24no—
320C2×D3—34no—
321C2×D3—34no—
322C2×D3—44no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—44no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—68no—
329C2×D3—68no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—128no—
339C2×D3—1216no—
340C2×D3—1216no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—41no—
345C3×C4—122no—
346Dic3—42no—
347Dic3—62no—
348Dic3—62no—
349Dic3—62no—
350Dic3—121no—
351C32#146211yescharacteristic, complemented, Sylow
352C23—34no—
353C23—62no—
354C23—62no—
355C23—91no—
356C23—91no—
357C23—122no—
358C23—122no—
359C23—182no—
360C23—182no—
361C23—184no—
362C23—184no—
363C23—182no—
364C23—362no—
365C23—362no—
366C23—3616no—
367C23—362no—
368C23—362no—
369C23C4×D3211yescharacteristic
370C2×C4—41no—
371C2×C4—62no—
372C2×C4—91no—
373C2×C4—91no—
374C2×C4—122no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—361no—
378C2×C4—361no—
379C2×C4—362no—
380C2×C4—362no—
381C2×C4—361no—
382C2×C4#380211yescharacteristic
383C2×C4#381111yescharacteristic
384C8—41no—
385C8—122no—
386C8—361no—
387C2×C3—22no—
388C2×C3—22no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—42no—
393C2×C3—124no—
394C2×C3#472612yes—
395C2×C3D3×#9912yes—
396C2×C3D3×#10012yes—
397D3—44no—
398D3—64no—
399D3—64no—
400D3—122no—
401D3—122no—
402C22—21no—
403C22—21no—
404C22—64no—
405C22—92no—
406C22—92no—
407C22—124no—
408C22—124no—
409C22—122no—
410C22—122no—
411C22—188no—
412C22—181no—
413C22—181no—
414C22—181no—
415C22—181no—
416C22—368no—
417C22—368no—
418C22D3×ΓL(1,𝔽25)12yes—
419C22#6392111yescharacteristic
420C4—21no—
421C4—21no—
422C4—122no—
423C4—181no—
424C4—181no—
425C3—21no—
426C3#6812012yescomplemented
427C2—22no—
428C2—124no—
429C2—182no—
430C2—182no—
431C2#1059040411yescharacteristic
432C2#1059093711yescharacteristic
433C2#1059100111yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×D32C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1462
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. #10591159C2semidirect
4. C3×#4468C2semidirect
5. #10589145C2semidirect
18. C32×C22⋊C8C22semidirect
19. #63657C22semidirect
21. C3×#830C22semidirect
30. #4468D3semidirect
76. C3×C22⋊C8C2×D3semidirect
79. #830C2×D3semidirect
93. C22×C3×D3M16semidirect
207. C22⋊C8D32semidirect
238. C22×D3ΓL(1,𝔽25)semidirect
351. C32#1462semidirect
426. C3#68120semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
#105924252
#105911592
C3×#44682
#105891452
#681203