Finite Group Databasebeta

← #11802999

Subgroups — #11802999

Order 1152.

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

normal subgroups only

This group has 974 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
1C2×#64286C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic
3C2×#63900C211yesmaximal, characteristic
4#10593485C214yesmaximal
5#10593413C212yesmaximal, complemented
6#10593412C214yesmaximal, complemented
7#10593344C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C2212yes—
10C2×C22⋊#157C2212yes—
11#64286C418yescomplemented
12C2×C4⋊#157C2212yes—
13C2×C4×#157C2212yes—
14C2×#3773C2218yes—
15C3×#926—21no—
16C2×C3×C4⋊Dic3—21no—
17#63974C2212yes—
18C2×#3724—21no—
19#63957—21no—
20#63900—21no—
21#63900—21no—
22#63900C2211yescharacteristic
23#63900C2212yes—
24#63900C2212yes—
25#63900C2211yescharacteristic
26C4×#624C2212yes—
27#63874—21no—
28#63849—21no—
29#63737C2218yes—
30D3×#117—61no—
31C2×D3×C4⋊C4—61no—
32C23×C3⋊D3C2311yescharacteristic
33C22×#157C2314yes—
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3C2×C414yes—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3Q814yes—
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×C4×C3⋊D3C2311yescharacteristic
42C22×C3×Dic3—22no—
43C2×#624—22no—
44C2×#624—44no—
45C2×#624C2314yes—
46C2×#624C2312yes—
47C2×#624C2312yes—
48C22⋊#157C2×C418yes—
49C4⋊#157C2×C418yescomplemented
50C4×#157C2×C418yescomplemented
51#3773—48no—
52C3×#217—22no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4×Dic3—22no—
58#3724—21no—
59#3724—21no—
60#3724—22no—
61#3724—22no—
62#3722—22no—
63Dic32—22no—
64#2317—91nomaximal, Sylow
65C22×C4×D3—61no—
66C22×C4×D3—61no—
67C22×C4×D3—62no—
68C3×#117—61no—
69C2×C3×C4⋊C4—61no—
70#926—21no—
71C2×C4⋊Dic3—21no—
72C2×Dic3⋊C4—62no—
73#892—61no—
74#892—61no—
75D3×C4⋊C4—62no—
76D3×C4⋊C4—62no—
77D3×C4⋊C4—61no—
78D3×C4⋊C4—61no—
79D3×C4⋊C4—62no—
80D3×C4⋊C4—62no—
81D3×C22⋊C4—62no—
82#877—62no—
83#872—62no—
84C42×D3—62no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—22no—
88C22×C3⋊D3C22×C412yes—
89C22×C3⋊D3C2×D411yescharacteristic
90C22×C3⋊D3C2×Q812yes—
91C22×C3⋊D3C2411yescharacteristic
92C2×#157—24no—
93C2×#157—24no—
94C2×#157C22×C418yes—
95C2×C32×C4C4⋊C414yescomplemented
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3⋊Dic3C4⋊C414yescomplemented
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2×D411yescharacteristic
101C4×C3⋊D3C4⋊C414yescomplemented
102C4×C3⋊D3C4⋊C414yescomplemented
103C4×C3⋊D3C22×C412yes—
104C4×C3⋊D3C22×C412yes—
105C4×C3⋊D3C2×Q812yes—
106C4×C3⋊D3C2×Q812yes—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—44no—
111#624—24no—
112#624—28no—
113#624—24no—
114#624—44no—
115C2×#117—91no—
116C2×#117—91no—
117C22×C4⋊C4—91no—
118#389—94no—
119#385—94no—
120#384—92no—
121#382—92no—
122C23×D3—61no—
123C23×D3—61no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—62no—
127C22×Dic3—22no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—64no—
142C2×C4×D3—62no—
143C2×C4×D3—62no—
144C2×C4×D3—64no—
145C2×C4×D3—64no—
146C2×C4×D3—128no—
147C3×C4⋊C4—62no—
148C3×C4⋊C4—62no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C22⋊C4—62no—
152C3×C42—62no—
153#217—22no—
154(C2×D3)⋊C4—62no—
155(C2×D3)⋊C4—62no—
156C4⋊Dic3—22no—
157C4⋊Dic3—22no—
158C4⋊Dic3—21no—
159C4⋊Dic3—21no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—64no—
163Dic3⋊C4—64no—
164C4×Dic3—22no—
165C4×Dic3—62no—
166C4×Dic3—62no—
167C22×C32—21no—
168C22×C32—21no—
169C22×C32C2×C4⋊C412yes—
170C22×C32C22×D411yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—24no—
174C2×C3⋊D3—24no—
175C2×C3⋊D3C2×C4⋊C412yes—
176C2×C3⋊D3C23×C411yescharacteristic
177C2×C3⋊D3C22×Q811yescharacteristic
178C2×C3⋊D3H(5,𝔽2)12yes—
179C2×C3⋊D32−1+412yes—
180#157—28no—
181C32×C4C2×C4⋊C412yes—
182C32×C4C2×C4⋊C412yes—
183C3⋊Dic3C2×C4⋊C412yes—
184C3⋊Dic3C2×C4⋊C412yes—
185C3×Dic3—44no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C23×C4—92no—
189C23×C4—91no—
190#117—61no—
191#117—98no—
192#117—181no—
193#117—181no—
194#117—181no—
195C2×C4⋊C4—61no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—91no—
200C2×C4⋊C4—92no—
201C2×C4⋊C4—98no—
202C2×C4⋊C4—181no—
203C2×C4⋊C4—181no—
204C2×C4⋊C4—181no—
205C2×C22⋊C4—92no—
206C2×C22⋊C4—92no—
207C2×C42—92no—
208C2×C42—92no—
209#95—98no—
210C23×C3—21no—
211C23×C3—21no—
212C22×D3—62no—
213C22×D3—61no—
214C22×D3—62no—
215C22×D3—61no—
216C22×D3—61no—
217C22×D3—62no—
218C22×D3—61no—
219C22×D3—62no—
220C22×D3—64no—
221C22×D3—64no—
222C22×D3—122no—
223C22×D3—122no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—24no—
229C2×C3×C4—24no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—64no—
233C2×C3×C4—124no—
234C2×Dic3—22no—
235C2×Dic3—22no—
236C2×Dic3—24no—
237C2×Dic3—44no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C4×D3—64no—
245C4×D3—64no—
246C4×D3—64no—
247C4×D3—64no—
248C4×D3—62no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—62no—
256C4×D3—124no—
257C4×D3—124no—
258C4×D3—128no—
259C4×D3—128no—
260C2×C32—22no—
261C2×C32C22×C4⋊C411yescharacteristic
262C2×C32#53511yescharacteristic
263C2×C32#53611yescharacteristic
264C3⋊D3—22no—
265C3⋊D3#52012yes—
266C3⋊D3#54412yes—
267C24—91no—
268C22×C4—62no—
269C22×C4—92no—
270C22×C4—94no—
271C22×C4—92no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—94no—
278C22×C4—94no—
279C22×C4—94no—
280C22×C4—182no—
281C22×C4—364no—
282C22×C4GO+(4,𝔽2)11yescharacteristic
283C4⋊C4—62no—
284C4⋊C4—62no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—98no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—368no—
293C22⋊C4—62no—
294C22⋊C4—98no—
295C22⋊C4—182no—
296C42—62no—
297C42—98no—
298C42—182no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—41no—
306C22×C3—41no—
307C2×D3—62no—
308C2×D3—61no—
309C2×D3—61no—
310C2×D3—61no—
311C2×D3—61no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—62no—
318C2×D3—68no—
319C2×D3—68no—
320C2×D3—62no—
321C2×D3—124no—
322C2×D3—124no—
323C2×D3—121no—
324C2×D3—121no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—124no—
330C3×C4—122no—
331C3×C4—122no—
332Dic3—44no—
333Dic3—42no—
334Dic3—42no—
335Dic3—62no—
336Dic3—62no—
337Dic3—62no—
338Dic3—62no—
339C32#231711yescharacteristic, complemented, Sylow
340C23—91no—
341C23—91no—
342C23—92no—
343C23—92no—
344C23—182no—
345C23—182no—
346C23C2×GO+(4,𝔽2)11yescharacteristic
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—64no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—94no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—94no—
358C2×C4—94no—
359C2×C4—98no—
360C2×C4—124no—
361C2×C4—184no—
362C2×C4—188no—
363C2×C4—184no—
364C2×C4—184no—
365C2×C4—184no—
366C2×C4—364no—
367C2×C4#377314yescomplemented
368C2×C4C2×GO+(4,𝔽2)11yescharacteristic
369C2×C4C2×GO+(4,𝔽2)11yescharacteristic
370C2×C3—24no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—42no—
378D3—62no—
379D3—62no—
380D3—62no—
381D3—62no—
382D3—64no—
383D3—122no—
384C22—21no—
385C22—21no—
386C22—92no—
387C22—92no—
388C22—91no—
389C22—91no—
390C22—92no—
391C22—184no—
392C22—184no—
393C22—181no—
394C22—181no—
395C22C2×#377312yes—
396C22C22×GO+(4,𝔽2)11yescharacteristic
397C4—92no—
398C4—92no—
399C4—122no—
400C4—124no—
401C4—122no—
402C4—188no—
403C4C2×#377312yes—
404C4C2×#377312yes—
405C3—21no—
406C3—21no—
407C2—22no—
408C2—92no—
409C2—92no—
410C2—182no—
411C2#1059649411yescharacteristic
412C2#1059651211yescharacteristic
413C2C22×#377311yescharacteristic
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#2317
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. #10593413C2semidirect
6. #10593412C2semidirect
7. #10593344C2semidirect
11. #64286C4semidirect
49. C4⋊#157C2×C4semidirect
50. C4×#157C2×C4semidirect
95. C2×C32×C4C4⋊C4semidirect
98. C2×C3⋊Dic3C4⋊C4semidirect
101. C4×C3⋊D3C4⋊C4semidirect
102. C4×C3⋊D3C4⋊C4semidirect
339. C32#2317semidirect
367. C2×C4#3773semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105949692
C2×#639002
#105934852
#105934132
#105934122
#105933442
#23179