Finite Group Databasebeta

← #11882282

Subgroups — #11882282

Order 1152.

658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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#10595050C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic
3C2×C4⋊#622C211yesmaximal, characteristic, complemented
4#10593526C214yesmaximal, complemented
5#10593439C212yesmaximal, complemented
6#10593437C212yesmaximal, complemented
7#10593376C212yesmaximal, complemented
8#10593359C212yesmaximal, complemented
9C2×C3×#235—21no—
10C22×#622C2212yes—
11C2×#3775C2214yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926—21no—
14#63982—21no—
15#63982C2212yes—
16#63980—21no—
17#63980C2212yes—
18#63919C2211yescharacteristic
19#63919C2211yescharacteristic
20C4×#627—21no—
21C4×#627C2212yes—
22#63914C2211yescharacteristic
23C4×#625—21no—
24C4×#625C2212yes—
25#63873C2211yescharacteristic
26#63872—21no—
27#63863—21no—
28C4⋊#622C2212yes—
29C4⋊#622C2212yes—
30#63742C2214yes—
31#63740C2214yes—
32#63739C2214yes—
33#5832—61no—
34#5517—61no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3C2311yescharacteristic
38C2×C3×#67—22no—
39C3×#235—44no—
40C2×C3×D12—21no—
41C2×C3×C4×D3—22no—
42C2×C3×Dic6—21no—
43C2×#627—21no—
44C2×#627C2312yes—
45C2×#625—21no—
46C2×#625C2312yes—
47C2×#622—42no—
48C2×#622C2314yes—
49#3775—44no—
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53C4×C3⋊Dic3C2311yescharacteristic
54C3×#217—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4×Dic3—22no—
58#3724—21no—
59#3724—21no—
60#3724C2312yes—
61#3724C2312yes—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#3246—91nomaximal, Sylow
67C2×C3×#41—61no—
68C2×#235—21no—
69C3×#117—61no—
70#947—61no—
71#944—61no—
72#940—61no—
73#939—62no—
74#939—62no—
75#936—61no—
76C4×#67—62no—
77C4×#67—62no—
78#926—21no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3—61no—
81#890—61no—
82#890—61no—
83#888—61no—
84#888—61no—
85#878—62no—
86#878—62no—
87C4×Dic6—62no—
88C4×Dic6—62no—
89C23×C32C2×D411yescharacteristic
90C22×C3×D3—22no—
91C2×C32×C4SD1614yescomplemented
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2×D411yescharacteristic
100C2×C3⋊Dic3C2411yescharacteristic
101C3×#67—44no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C3×D12—42no—
106C3×C4×D3—44no—
107C3×Dic6—42no—
108#627—22no—
109#627—22no—
110#627—42no—
111#625—22no—
112#625—22no—
113#625—42no—
114#622—24no—
115#533—91no—
116#532—91no—
117#476—92no—
118#475—92no—
119#465—94no—
120#461—92no—
121#460—92no—
122C2×C4⋊C8—91no—
123C3×#41—124no—
124C2×C3×Q8—61no—
125C2×C3×D4—61no—
126C2×C3×D4—62no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—62no—
130C2×#67—22no—
131C2×#67—62no—
132C2×#67—62no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137#235—44no—
138C2×D12—21no—
139C2×C4×D3—22no—
140C2×Dic6—21no—
141C2×Dic6—62no—
142C2×Dic6—62no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C22⋊C4—62no—
146C3×C42—62no—
147#217—22no—
148#217—62no—
149#217—62no—
150(C2×D3)⋊C4—62no—
151(C2×D3)⋊C4—62no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162C4×Dic3—22no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C22×C32—21no—
172C22×C32—21no—
173C22×C32C2×SD1612yes—
174C22×C32C22×D411yescharacteristic
175C2×C3×D3—42no—
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178C32×C4C2×SD1612yes—
179C32×C4C2×SD1612yes—
180C3⋊Dic3—21no—
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3H(5,𝔽2)11yescharacteristic
184C3⋊Dic32−1+411yescharacteristic
185C3×Dic3—42no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C2×#41—61no—
189C2×SD16—94no—
190C22×C8—92no—
191C4⋊Q8—91no—
192C4⋊Q8—91no—
193C4⋊Q8—91no—
194#127—91no—
195#125—181no—
196#124—181no—
197C22⋊Q8—92no—
198C22⋊Q8—181no—
199#121—92no—
200#121—181no—
201C4×Q8—92no—
202C4×Q8—181no—
203C4×D4—92no—
204C4×D4—181no—
205#117—61no—
206C2×C42—91no—
207#106—94no—
208C4⋊C8—92no—
209C4⋊C8—92no—
210#103—94no—
211#102—94no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—62no—
215C22×D3—22no—
216C3×Q8—122no—
217C3×D4—122no—
218C3×D4—124no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4—124no—
229#67—44no—
230#67—122no—
231#67—122no—
232#67—124no—
233C2×Dic3—22no—
234C2×Dic3—22no—
235C2×Dic3—22no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C2×Dic3—122no—
249C2×Dic3—122no—
250D12—42no—
251C4×D3—44no—
252Dic6—42no—
253Dic6—122no—
254Dic6—122no—
255Dic6—124no—
256C2×C32—22no—
257C2×C32#53711yescharacteristic
258C2×C32C22×SD1611yescharacteristic
259C2×C32#57511yescharacteristic
260C3×D3—82no—
261#41—124no—
262C2×Q8—61no—
263C2×Q8—92no—
264C2×Q8—181no—
265C2×D4—62no—
266C2×D4—61no—
267C2×D4—92no—
268C2×D4—181no—
269C22×C4—62no—
270C22×C4—91no—
271C22×C4—91no—
272C22×C4GO+(4,𝔽2)11yescharacteristic
273SD16—364no—
274C2×C8—94no—
275C2×C8—362no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C4⋊C4—181no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C22⋊C4—62no—
285C22⋊C4—182no—
286C22⋊C4—182no—
287C42—62no—
288C42—91no—
289C42—91no—
290C42—91no—
291C42—91no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C2×D3—42no—
304C2×D3—42no—
305C2×D3—42no—
306C3×C4—22no—
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—122no—
311C3×C4—122no—
312C3×C4—122no—
313Dic3—42no—
314Dic3—42no—
315Dic3—42no—
316Dic3—61no—
317Dic3—61no—
318Dic3—61no—
319Dic3—61no—
320Dic3—62no—
321Dic3—62no—
322Dic3—121no—
323Dic3—121no—
324Dic3—121no—
325Dic3—121no—
326C32#324611yescharacteristic, complemented, Sylow
327C23—62no—
328C23C2×GO+(4,𝔽2)11yescharacteristic
329Q8—122no—
330Q8—182no—
331Q8—182no—
332Q8—362no—
333D4—124no—
334D4—122no—
335D4—182no—
336D4—182no—
337D4—362no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—124no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—361no—
349C2×C4#377514yescomplemented
350C2×C4C2×GO+(4,𝔽2)11yescharacteristic
351C2×C4C2×GO+(4,𝔽2)11yescharacteristic
352C8—184no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—42no—
360C2×C3—42no—
361C2×C3—242no—
362D3—82no—
363C22—21no—
364C22—21no—
365C22—122no—
366C22—122no—
367C22—122no—
368C22C2×#377512yes—
369C22C22×GO+(4,𝔽2)11yescharacteristic
370C4—91no—
371C4—91no—
372C4—122no—
373C4—122no—
374C4—122no—
375C4—181no—
376C4—181no—
377C4—181no—
378C4C2×#377512yes—
379C4C2×#377512yes—
380C3—21no—
381C3—21no—
382C2—22no—
383C2—242no—
384C2#1059650211yescharacteristic
385C2#1059651311yescharacteristic
386C2C22×#377511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radical#10595032C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3246
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #10595050C2semidirect
3. C2×C4⋊#622C2semidirect
4. #10593526C2semidirect
5. #10593439C2semidirect
6. #10593437C2semidirect
7. #10593376C2semidirect
8. #10593359C2semidirect
91. C2×C32×C4SD16semidirect
326. C32#3246semidirect
349. C2×C4#3775semidirect

Maximal subgroups

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

subgroupindex
#105950502
#105950322
C2×C4⋊#6222
#105935262
#105934392
#105934372
#105933762
#105933592
#32469