Finite Group Databasebeta

← #11792187

Subgroups — #11792187

Order 1152.

1086 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1086 conjugacy classes of subgroups — too many to draw. Only its 191 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×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
2#10596287C211yesmaximal, characteristic
3C2×#64151C211yesmaximal, characteristic
4C2×#63663C211yesmaximal, characteristic, complemented
5#10592924C211yesmaximal, characteristic, complemented
6C2×#63632C211yesmaximal, characteristic
7#10589389C211yesmaximal, characteristic, complemented
8#71795—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C32×C4⋊Q8—22no—
13C32×C4⋊Q8—22no—
14C2×C32×C4⋊C4—22no—
15C2×C32×C42C2211yescharacteristic
16#64156—21no—
17#64155—22no—
18#64153—21no—
19C2×#3756—21no—
20#64151—22no—
21#64151—22no—
22C2×#3755—21no—
23#64138—22no—
24#64135C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C2×#3748C2211yescharacteristic
27#63663—22no—
28#63662—22no—
29#63632—22no—
30C2×C3×C4⋊Q8D314yescomplemented
31#5816—34no—
32C2×#942—34no—
33C2×#836—34no—
34#5225—34no—
35C2×#805—34no—
36#4523—34no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4D412yes—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61C32×C4⋊C4—28no—
62C32×C42—21no—
63C32×C42D412yes—
64#3757—21no—
65#3756—24no—
66#3755—24no—
67#3752—24no—
68C4⋊(C3⋊Dic3)D412yes—
69#3750—24no—
70C4×C3⋊Dic3—21no—
71#3748—21no—
72#3748—21no—
73#3748—21no—
74#3748D412yes—
75C2×C3⋊(C3⋊C8)—21no—
76C2×C3⋊(C3⋊C8)—21no—
77#2005—91noSylow
78C22×C3×Q8C2×D314yes—
79C22×C3×Q8C2×D314yes—
80C2×#235—34no—
81C3×C4⋊Q8—28no—
82C3×C4⋊Q8—28no—
83C2×C3×C4⋊C4—28no—
84C2×C3×C42C2×D314yes—
85#947—64no—
86#946—68no—
87#944—64no—
88C2×#216—64no—
89#942—68no—
90#942—68no—
91C2×#215—64no—
92#929—68no—
93#926—34no—
94C2×#208—34no—
95C2×#208—34no—
96#836—68no—
97#835—68no—
98#805—68no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—21no—
101C32×Q8—22no—
102C32×Q8—22no—
103C32×Q8—41no—
104C32×Q8—41no—
105C32×Q8—41no—
106C32×Q8—41no—
107C32×Q8—41no—
108C32×Q8—41no—
109C2×C32×C4—24no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123#638—41no—
124#638—41no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C4⋊(C3⋊D3)—21no—
128C4⋊(C3⋊D3)—21no—
129C4×C3⋊D3—41no—
130C4×C3⋊D3—41no—
131#634—21no—
132#634—21no—
133C3⋊(C3⋊C8)—22no—
134C3⋊(C3⋊C8)—41no—
135C2×#137—91no—
136#536—91no—
137C2×C4⋊Q8C3⋊D311yescharacteristic, complemented
138C2×#104—91no—
139#419—91no—
140C2×#101—91no—
141#339—91no—
142C2×C3×Q8—24no—
143C2×C3×Q8—24no—
144C2×C3×Q8—24no—
145C2×C3×Q8—24no—
146C2×C3×Q8—24no—
147C2×C3×Q8—24no—
148C2×C3×Q8—24no—
149C2×C3×Q8—24no—
150C2×C3×Q8—24no—
151C2×C3×Q8—24no—
152C2×C3×Q8—24no—
153C2×C3×Q8#6718yes—
154C22×C3×C4—24no—
155C22×C3×C4—24no—
156C22×C3×C4#6718yes—
157C22×C3×C4C22×D314yes—
158C2×#67—64no—
159#235—64no—
160#235—64no—
161#235—64no—
162#235—64no—
163C2×D12—34no—
164C2×C4×D3—64no—
165C2×Dic6—34no—
166C3×C4⋊C4—232no—
167C3×C42—24no—
168C3×C42#6718yes—
169#217—64no—
170#216—616no—
171#215—616no—
172(C2×D3)⋊C4—616no—
173C4⋊Dic3—38no—
174Dic3⋊C4—616no—
175C4×Dic3—64no—
176#208—38no—
177#208—64no—
178#208—64no—
179#208—64no—
180C2×C3⋊C8—64no—
181C2×C3⋊C8—64no—
182C22×C32—22no—
183C22×C32#12011yescharacteristic
184C22×C32#12011yescharacteristic
185C22×C32#12111yescharacteristic
186C2×C3⋊D3—41no—
187C2×C3⋊D3—42no—
188C32×C4—24no—
189C32×C4—42no—
190C32×C4—42no—
191C32×C4#12011yescharacteristic
192C32×C4#12111yescharacteristic
193C32×C4#12111yescharacteristic
194C32×C4#12711yescharacteristic
195C3⋊Dic3—41no—
196C3⋊Dic3—42no—
197C2×#41—91no—
198C22×Q8C2×C3⋊D311yescharacteristic
199C22×Q8C2×C3⋊D311yescharacteristic
200#137—182no—
201#137—182no—
202C2×Q16—181no—
203C2×SD16—181no—
204C2×M16—91no—
205C2×M16—91no—
206C4⋊Q8—22no—
207C4⋊Q8—22no—
208C4⋊Q8—181no—
209#124—181no—
210#123—182no—
211C22⋊Q8—182no—
212#117—91no—
213C2×C4⋊C4—22no—
214C2×C42C2×C3⋊D311yescharacteristic
215#104—182no—
216#103—182no—
217#101—182no—
218C23×C3C2×#6714yes—
219C22×D3—64no—
220C3×Q8—28no—
221C3×Q8—28no—
222C3×Q8—44no—
223C3×Q8—44no—
224C3×Q8—44no—
225C3×Q8—44no—
226C3×Q8—44no—
227C3×Q8—44no—
228C2×C3×C4—216no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4—28no—
232C2×C3×C4—28no—
233C2×C3×C4—28no—
234C2×C3×C4—44no—
235C2×C3×C4—44no—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4#23714yes—
240C2×C3×C4C2×#6714yes—
241C2×C3×C4C2×#6714yes—
242#67—124no—
243#67—124no—
244C2×Dic3—68no—
245C2×Dic3—64no—
246D12—64no—
247D12—64no—
248C4×D3—124no—
249C4×D3—124no—
250Dic6—64no—
251Dic6—64no—
252C3⋊C8—68no—
253C3⋊C8—124no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32#39211yescharacteristic
257C2×C32#45612yes—
258C3⋊D3—81no—
259#41—181no—
260#41—181no—
261#41—181no—
262#41—181no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—91no—
275C2×Q8#63812yes—
276C2×D4—91no—
277C2×D4—181no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—181no—
281C22×C4#63812yes—
282C22×C4C22×C3⋊D311yescharacteristic
283Q16—184no—
284SD16—184no—
285M16—92no—
286M16—181no—
287M16—181no—
288M16—181no—
289C2×C8—181no—
290C2×C8—181no—
291C4⋊C4—28no—
292C4⋊C4—92no—
293C4⋊C4—184no—
294C22⋊C4—184no—
295C22⋊C4—181no—
296C42—21no—
297C42—181no—
298C42#63812yes—
299C22×C3—28no—
300C22×C3#93714yes—
301C22×C3#93914yes—
302C22×C3#95314yes—
303C2×D3—124no—
304C2×D3—128no—
305C3×C4—216no—
306C3×C4—48no—
307C3×C4—48no—
308C3×C4#93714yes—
309C3×C4#93814yes—
310C3×C4#93914yes—
311C3×C4#94014yes—
312Dic3—124no—
313Dic3—128no—
314C32#200511yescharacteristic, complemented, Sylow
315C23—181no—
316C23C2×#63811yescharacteristic
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321Q8—41no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—181no—
326Q8—181no—
327D4—181no—
328D4—181no—
329D4—361no—
330D4—361no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—182no—
340C2×C4—181no—
341C2×C4—361no—
342C2×C4—361no—
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4D4×C3⋊D311yescharacteristic
346C2×C4#383011yescharacteristic
347C2×C4C2×#63811yescharacteristic
348C2×C4C2×#63811yescharacteristic
349C8—182no—
350C8—361no—
351C2×C3—24no—
352C2×C3—24no—
353C2×C3#509518yes—
354C2×C3#522314yes—
355D3—244no—
356C22—22no—
357C22—362no—
358C22—361no—
359C22#6414611yescharacteristic
360C22#6414811yescharacteristic
361C22#6416211yescharacteristic
362C4—24no—
363C4—42no—
364C4—42no—
365C4—362no—
366C4—361no—
367C4#6414611yescharacteristic
368C4#6414711yescharacteristic
369C4#6414811yescharacteristic
370C4#6414911yescharacteristic
371C3#7179514yescomplemented
372C2—21no—
373C2—21no—
374C2—721no—
375C2#1059279412yes—
376C2#1059292211yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32#120
prime radicalC2×#3828C22
hypercenterC2×C4⋊Q8C3⋊D3
hypocenterC32#2005
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4⋊Q8C2semidirect
4. C2×#63663C2semidirect
5. #10592924C2semidirect
7. #10589389C2semidirect
30. C2×C3×C4⋊Q8D3semidirect
137. C2×C4⋊Q8C3⋊D3semidirect
314. C32#2005semidirect
371. C3#71795semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
#105962872
C2×#641512
C2×#636632
#105929242
C2×#636322
#105893892
#717953