Finite Group Databasebeta

← #11873298

Subgroups — #11873298

Order 1152.

849 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 849 conjugacy classes of subgroups — too many to draw. Only its 164 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
1#10596283C211yesmaximal, characteristic
2#10594826C211yesmaximal, characteristic
3C3×#5228C212yesmaximal
4#10591633C212yesmaximal, complemented
5#10591615C212yesmaximal, complemented
6#10591582C212yesmaximal, complemented
7#10591581C212yesmaximal, complemented
8#10591127C212yesmaximal
9#10591062C211yesmaximal, characteristic
10#80177—32nomaximal
11C22×C32×Q8C2211yescharacteristic
12Q8×C3⋊Dic3—22no—
13Q8×C3⋊Dic3C2212yes—
14Q8×C3⋊Dic3C2212yes—
15#64135—22no—
16#64135C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C3×#216C2212yes—
19C2×C3×#216C2212yes—
20C3×#924C2212yes—
21#63956—22no—
22#63873C2211yescharacteristic
23#63872C2211yescharacteristic
24#63845—22no—
25#63843C2212yes—
26C3×#835C2212yes—
27C3×#835C2212yes—
28C3×#830C2212yes—
29#63575C2212yes—
30#63573C2212yes—
31#63572C2212yes—
32#63566C2212yes—
33#63566C2212yes—
34#63555C2211yescharacteristic
35#63553C2211yescharacteristic
36#5812—32no—
37#5812—61no—
38#5625—32no—
39C3×#451—32no—
40#5228D312yes—
41#5184—32no—
42#5182—32no—
43#5182—32no—
44Dic3×Q16—32no—
45#5045—32no—
46#4799—32no—
47#4796—32no—
48#4790—32no—
49#4789—32no—
50#4723—32no—
51#4720—32no—
52C2×C32×Q8—24no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×Dic6C2312yes—
58#3757—21no—
59#3757D412yes—
60C4⋊(C3⋊Dic3)—22no—
61C4⋊(C3⋊Dic3)—22no—
62C4⋊(C3⋊Dic3)D412yes—
63C4⋊(C3⋊Dic3)C2312yes—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3C2311yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C3×#217—22no—
70C3×#216—24no—
71C3×#216—24no—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76#3724—22no—
77Dic3⋊Dic3—22no—
78Dic3⋊Dic3—22no—
79Dic32—22no—
80#3127—91noSylow
81C22×C3×Q8—21no—
82C22×C3×Q8C2×D312yes—
83C2×C3×Q16—32no—
84C2×C3×Q16—32no—
85C3×C22⋊Q8—32no—
86Q8×Dic3—32no—
87Q8×Dic3—32no—
88Q8×Dic3—32no—
89Q8×Dic3—32no—
90Q8×Dic3—32no—
91Q8×Dic3—62no—
92Q8×Dic3—62no—
93Q8×Dic3—62no—
94Q8×Dic3—62no—
95Q8×Dic3—64no—
96#944—32no—
97C2×#216C2×D312yes—
98C2×#216C2×D312yes—
99#926—32no—
100#926—32no—
101#926—61no—
102#926—61no—
103#926—62no—
104#926—62no—
105#926—64no—
106#924C2×D312yes—
107#890—32no—
108#890—62no—
109#889—62no—
110#887—32no—
111#879—62no—
112#879—62no—
113C3×#103—32no—
114C3×#103—32no—
115C3×C22⋊C8—32no—
116#835—32no—
117#835—32no—
118#835C2×D312yes—
119#835C2×D312yes—
120#830C2×D312yes—
121#818—32no—
122#817—32no—
123#816—32no—
124#816—32no—
125#815—32no—
126Dic3⋊C8—32no—
127Dic3⋊C8—32no—
128C8×Dic3—32no—
129#808—32no—
130#807—32no—
131C23×C32C2×D411yescharacteristic
132C32×Q8—24no—
133C32×Q8—22no—
134C32×Q8#4114yes—
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—22no—
149#541—91no—
150#519—91no—
151#485—92no—
152#479—92no—
153#462—92no—
154#451—32no—
155#441—92no—
156C4×Q16—92no—
157#433—91no—
158C2×C3×Q8—22no—
159C2×C3×Q8—28no—
160C2×C3×Q8—24no—
161C2×C3×Q8—24no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8—32no—
165C2×C3×Q8C22×D312yes—
166C2×C3×Q8C22×D312yes—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—21no—
170C22×C3×C4C22×D312yes—
171C2×Dic6C22×D312yes—
172C3×Q16—64no—
173C3×Q16—64no—
174C2×C3×C8—32no—
175C2×C3×C8—32no—
176C3×C4⋊C4—32no—
177C3×C4⋊C4—62no—
178C3×C22⋊C4—62no—
179#217—22no—
180#217—32no—
181#217—32no—
182#217—62no—
183#217—62no—
184#217—62no—
185#216—24no—
186#216—24no—
187C4⋊Dic3—32no—
188C4⋊Dic3—32no—
189C4⋊Dic3—32no—
190C4⋊Dic3—32no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3—62no—
194C4⋊Dic3—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—62no—
197C4⋊Dic3—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3—64no—
200C4⋊Dic3—64no—
201C4⋊Dic3C22×D312yes—
202Dic3⋊C4—22no—
203Dic3⋊C4—62no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207C4×Dic3—32no—
208C4×Dic3—32no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C4×Dic3—62no—
215C4×Dic3—62no—
216C4×Dic3—62no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C4×Dic3—62no—
220C4×Dic3—62no—
221C2×C3⋊C8C22×D312yes—
222C2×C3⋊C8C22×D312yes—
223C22×C32—21no—
224C22×C32—22no—
225C22×C32C22×D411yescharacteristic
226C32×C4—24no—
227C32×C4—21no—
228C32×C4C2×#4112yes—
229C3⋊Dic3—22no—
230C3⋊Dic3—22no—
231C3⋊Dic3—42no—
232C3×Dic3—42no—
233C3×Dic3—42no—
234C22×Q8D3211yescharacteristic
235C2×Q16—32no—
236C2×Q16—32no—
237C4⋊Q8—91no—
238#126—182no—
239#125—91no—
240#125—182no—
241C22⋊Q8—32no—
242C4×Q8—92no—
243C4×Q8—92no—
244C4×Q8—92no—
245C4×Q8—182no—
246#117—91no—
247#117—91no—
248#117—182no—
249#107—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—32no—
253#103—32no—
254#103—92no—
255#103—92no—
256C22⋊C8—32no—
257#97—91no—
258C4×C8—91no—
259C23×C3—21no—
260C23×C3D3×D412yes—
261C3×Q8—28no—
262C3×Q8—28no—
263C3×Q8—24no—
264C3×Q8—22no—
265C3×Q8—22no—
266C3×Q8—24no—
267C3×Q8—62no—
268C3×Q8—62no—
269C3×Q8#23714yes—
270C3×Q8#23714yes—
271C2×C3×C4—24no—
272C2×C3×C4—28no—
273C2×C3×C4—28no—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4D3×D412yes—
284C2×C3×C4C23×D312yes—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296Dic6—22no—
297Dic6—22no—
298C3×C8—62no—
299C3×C8—62no—
300C3⋊C8—22no—
301C3⋊C8—22no—
302C2×C32—41no—
303C2×C32#52511yescharacteristic
304C2×C32#57812yes—
305C2×Q8—24no—
306C2×Q8—21no—
307C2×Q8—32no—
308C2×Q8C2×D3212yes—
309C22×C4—21no—
310C22×C4C2×D3211yescharacteristic
311Q16—64no—
312Q16—64no—
313C2×C8—32no—
314C2×C8—32no—
315C4⋊C4—32no—
316C4⋊C4—62no—
317C4⋊C4—92no—
318C4⋊C4—92no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—182no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C22⋊C4—62no—
325C22⋊C4—92no—
326C22⋊C4—181no—
327C42—91no—
328C42—91no—
329C42—182no—
330C42—182no—
331C42—182no—
332C42—181no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—42no—
339C22×C3C2×D3×D412yes—
340C3×C4—28no—
341C3×C4—22no—
342C3×C4—24no—
343C3×C4—24no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—122no—
347C3×C4—122no—
348C3×C4C2×#23712yes—
349C3×C4C2×#23712yes—
350Dic3—42no—
351Dic3—42no—
352Dic3—62no—
353Dic3—62no—
354Dic3—62no—
355Dic3—62no—
356Dic3—122no—
357Dic3—122no—
358Dic3—124no—
359Dic3—122no—
360Dic3—122no—
361C32#312711yescharacteristic, complemented, Sylow
362C23#381111yescharacteristic
363Q8—24no—
364Q8—22no—
365Q8—62no—
366Q8—62no—
367Q8#380514yes—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—62no—
372C2×C4—62no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—182no—
376C2×C4#381111yescharacteristic
377C2×C4C22×D3211yescharacteristic
378C8—62no—
379C8—62no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3—42no—
383C2×C3—42no—
384C2×C3#558612yes—
385C2×C3#576612yes—
386C2×C3#577912yes—
387C22—22no—
388C22—21no—
389C22C2×#381111yescharacteristic
390C4—24no—
391C4—21no—
392C4—122no—
393C4—122no—
394C4—182no—
395C4—182no—
396C4—362no—
397C4C2×#380512yes—
398C3—21no—
399C3#8017712yescomplemented
400C2—41no—
401C2#1059533712yes—
402C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. #10591633C2semidirect
5. #10591615C2semidirect
6. #10591582C2semidirect
7. #10591581C2semidirect
361. C32#3127semidirect
399. C3#80177semidirect

Maximal subgroups

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

subgroupindex
#105962832
#105948262
C3×#52282
#105916332
#105916152
#105915822
#105915812
#105911272
#105910622
#801773