Finite Group Databasebeta

← #11802693

Subgroups — #11802693

Order 1152.

1374 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1374 conjugacy classes of subgroups — too many to draw. Only its 199 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
1C22×#3797C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic
3#10594969C211yesmaximal, characteristic
4#10593488C214yesmaximal
5#10593342C214yesmaximal, complemented
6#10593341C214yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6—21no—
9C22×#627—21no—
10C22×#624C2212yes—
11C2×#3797—21no—
12C2×#3797—21no—
13C2×#3797—24no—
14C2×#3797C418yescomplemented
15C2×#3797C2212yes—
16C2×#3797C2212yes—
17C2×C22⋊#157C2212yes—
18#64286—24no—
19C2×C4⋊#157C2212yes—
20C2×C4×#157C2212yes—
21C3×#926—21no—
22#63974C2212yes—
23#63957—21no—
24#63900C2212yes—
25C4×#624C2212yes—
26#63874—21no—
27#63849—21no—
28#63737C22116yes—
29C22×D3×Q8—61no—
30D3×#117—61no—
31C23×C3⋊D3C2311yescharacteristic
32C22×#157C2314yes—
33C22×C32×C4D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C2×C4×C3⋊D3C2×C414yes—
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D414yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C4×C3⋊D3C2311yescharacteristic
41C22×C3×Dic3—22no—
42C2×C3×Dic6—28no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45C2×#627—28no—
46C2×#627—22no—
47C2×#627—22no—
48C2×#624—22no—
49C2×#624—24no—
50C2×#624C2×C418yes—
51C2×#624C2314yes—
52C2×#624C2314yes—
53#3797—28no—
54#3797—28no—
55#3797—24no—
56#3797—24no—
57#3797C2×C418yes—
58#3797C2×C418yes—
59C22⋊#157—24no—
60C4⋊#157—24no—
61C4×#157—24no—
62C3×#217—22no—
63C3×C4⋊Dic3—22no—
64C3×C4×Dic3—22no—
65#3724—22no—
66#3722—22no—
67Dic32—22no—
68#2310—91nomaximal, Sylow
69C22×C3×Q8—61no—
70C2×D3×Q8—68no—
71C2×D3×Q8—62no—
72C2×D3×Q8—62no—
73C2×D3×Q8—62no—
74C2×D3×Q8—62no—
75C2×D3×Q8—68no—
76C22×C4×D3—62no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C22×Dic6—21no—
80C22×Dic6—62no—
81C3×#117—61no—
82#926—21no—
83#892—62no—
84D3×C4⋊C4—62no—
85D3×C22⋊C4—62no—
86#877—62no—
87#872—62no—
88C42×D3—62no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—24no—
91C22×C3⋊D3C22×C412yes—
92C22×C3⋊D3C2×D411yescharacteristic
93C22×C3⋊D3C2×D412yes—
94C22×C3⋊D3C2411yescharacteristic
95C2×#157—24no—
96C2×#157—28no—
97C2×C32×C4C22⋊C414yes—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3⋊Dic3C22⋊C414yes—
101C2×C3⋊Dic3C2×D411yescharacteristic
102C2×C3⋊Dic3C2×D411yescharacteristic
103C4×C3⋊D3C22⋊C414yes—
104C4×C3⋊D3C22⋊C414yes—
105C4×C3⋊D3C22×C412yes—
106C4×C3⋊D3C22×C412yes—
107C4×C3⋊D3C2×D412yes—
108C4×C3⋊D3C2×D412yes—
109C2×C3×Dic3—28no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C3×Dic6—28no—
113C3×Dic6—28no—
114#627—28no—
115#627—28no—
116#624—28no—
117#624—24no—
118#624—28no—
119#624C22×C418yes—
120C23×Q8—91no—
121C2×#117—91no—
122C2×#117—91no—
123#391—94no—
124#391—94no—
125#381—94no—
126C23×D3—61no—
127C23×D3—61no—
128C2×C3×Q8—62no—
129C2×C3×Q8—62no—
130C2×C3×Q8—68no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×Dic3—22no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137D3×Q8—68no—
138D3×Q8—68no—
139D3×Q8—616no—
140D3×Q8—616no—
141D3×Q8—68no—
142D3×Q8—68no—
143C2×C4×D3—68no—
144C2×C4×D3—64no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—64no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—64no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—68no—
160C2×Dic6—22no—
161C2×Dic6—22no—
162C2×Dic6—28no—
163C2×Dic6—616no—
164C2×Dic6—64no—
165C2×Dic6—64no—
166C3×C4⋊C4—62no—
167C3×C22⋊C4—62no—
168C3×C42—62no—
169#217—22no—
170(C2×D3)⋊C4—64no—
171C4⋊Dic3—22no—
172Dic3⋊C4—64no—
173C4×Dic3—22no—
174C4×Dic3—64no—
175C22×C32—22no—
176C22×C32C2×C22⋊C412yes—
177C22×C32C22×D411yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—24no—
180C2×C3⋊D3—24no—
181C2×C3⋊D3C2×C22⋊C412yes—
182C2×C3⋊D3C23×C411yescharacteristic
183C2×C3⋊D3C22×D411yescharacteristic
184C2×C3⋊D32−1+414yes—
185#157—44no—
186C32×C4C2×C22⋊C412yes—
187C32×C4C2×C22⋊C412yes—
188C3⋊Dic3C2×C22⋊C412yes—
189C3⋊Dic3C2×C22⋊C412yes—
190C3×Dic3—28no—
191C3×Dic3—44no—
192C22×Q8—61no—
193C22×Q8—92no—
194C22×Q8—92no—
195C22×Q8—98no—
196C22×Q8—181no—
197C22×Q8—181no—
198C22×Q8—181no—
199C22×Q8—184no—
200C23×C4—92no—
201C23×C4—91no—
202#117—61no—
203#117—181no—
204#117—181no—
205#117—181no—
206#117—184no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—92no—
209C2×C22⋊C4—92no—
210C2×C22⋊C4—92no—
211C2×C42—92no—
212C2×C42—92no—
213#95—916no—
214C23×C3—21no—
215C23×C3—21no—
216C22×D3—62no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—61no—
220C22×D3—61no—
221C22×D3—62no—
222C22×D3—61no—
223C22×D3—62no—
224C22×D3—68no—
225C22×D3—124no—
226C3×Q8—68no—
227C3×Q8—68no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—64no—
235C2×C3×C4—68no—
236C2×C3×C4—64no—
237C2×Dic3—24no—
238C2×Dic3—28no—
239C2×Dic3—24no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C4×D3—68no—
247C4×D3—64no—
248C4×D3—64no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—62no—
256C4×D3—62no—
257C4×D3—62no—
258C4×D3—62no—
259C4×D3—616no—
260C4×D3—68no—
261C4×D3—128no—
262Dic6—28no—
263Dic6—28no—
264Dic6—616no—
265Dic6—616no—
266C2×C32—22no—
267C2×C32C22×C22⋊C411yescharacteristic
268C2×C32#53612yes—
269C3⋊D3—22no—
270C3⋊D3#51912yes—
271C3⋊D3#53612yes—
272C24—91no—
273C2×Q8—62no—
274C2×Q8—62no—
275C2×Q8—68no—
276C2×Q8—98no—
277C2×Q8—98no—
278C2×Q8—182no—
279C2×Q8—182no—
280C2×Q8—188no—
281C2×Q8—184no—
282C2×Q8—184no—
283C2×Q8—188no—
284C2×Q8—188no—
285C22×C4—62no—
286C22×C4—94no—
287C22×C4—98no—
288C22×C4—94no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—94no—
295C22×C4—94no—
296C22×C4—94no—
297C22×C4—182no—
298C22×C4—184no—
299C22×C4GO+(4,𝔽2)11yescharacteristic
300C4⋊C4—62no—
301C4⋊C4—182no—
302C4⋊C4—184no—
303C22⋊C4—62no—
304C22⋊C4—182no—
305C22⋊C4—184no—
306C42—62no—
307C42—182no—
308C42—184no—
309C22×C3—24no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—42no—
315C2×D3—62no—
316C2×D3—61no—
317C2×D3—61no—
318C2×D3—61no—
319C2×D3—61no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—62no—
323C2×D3—68no—
324C2×D3—68no—
325C2×D3—64no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—122no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—22no—
333C3×C4—68no—
334C3×C4—124no—
335Dic3—28no—
336Dic3—44no—
337Dic3—62no—
338Dic3—62no—
339Dic3—62no—
340Dic3—62no—
341C32#231011yescharacteristic, complemented, Sylow
342C23—91no—
343C23—91no—
344C23—92no—
345C23—92no—
346C23—184no—
347C23C2×GO+(4,𝔽2)11yescharacteristic
348Q8—68no—
349Q8—68no—
350Q8—188no—
351Q8—188no—
352C2×C4—64no—
353C2×C4—68no—
354C2×C4—64no—
355C2×C4—98no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—94no—
359C2×C4—92no—
360C2×C4—92no—
361C2×C4—92no—
362C2×C4—92no—
363C2×C4—94no—
364C2×C4—94no—
365C2×C4—184no—
366C2×C4—188no—
367C2×C4—188no—
368C2×C4—184no—
369C2×C4—188no—
370C2×C4D32⋊C414yes—
371C2×C4C2×GO+(4,𝔽2)11yescharacteristic
372C2×C4C2×GO+(4,𝔽2)11yescharacteristic
373C2×C3—24no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—42no—
379D3—62no—
380D3—62no—
381D3—62no—
382D3—62no—
383D3—64no—
384D3—122no—
385C22—22no—
386C22—94no—
387C22—91no—
388C22—91no—
389C22—92no—
390C22—184no—
391C22—184no—
392C22—182no—
393C22C2×D32⋊C412yes—
394C22C22×GO+(4,𝔽2)11yescharacteristic
395C4—68no—
396C4—92no—
397C4—92no—
398C4—124no—
399C4—364no—
400C4C2×D32⋊C412yes—
401C4C2×D32⋊C412yes—
402C3—21no—
403C3—21no—
404C2—22no—
405C2—92no—
406C2—92no—
407C2—182no—
408C2#1059649412yes—
409C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2310
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. #10593342C2semidirect
6. #10593341C2semidirect
14. C2×#3797C4semidirect
341. C32#2310semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#642862
#105949692
#105934882
#105933422
#105933412
#23109