Finite Group Databasebeta

← #11780212

Subgroups — #11780212

Order 1152.

509 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 509 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×D4×Dic6C211yesmaximal, characteristic
2C3×#5007C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic, complemented
4#10590312C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
6#10589092C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71916—31nomaximal
9#71114—31nomaximal
10C22×C3×Dic6—21no—
11C32×C4×D4C2211yescharacteristic
12C3×D4×Dic3—21no—
13C3×#924—21no—
14C3×#888—21no—
15C3×#878—22no—
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3718—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#832—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—22no—
26#63565—21no—
27C3×D4×Q8—31no—
28D4×Dic6D311yescharacteristic
29C3×#474—31no—
30#5090—31no—
31#5078—31no—
32#5078—31no—
33#5031—31no—
34#5007D311yescharacteristic
35#4547—31no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4486—31no—
41#4484—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3×Dic3—22no—
45C2×C3×Dic6—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—42no—
49C2×C3×Dic6—42no—
50C2×C3×Dic6D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—22no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66#3718—42no—
67#1649—91noSylow
68C22×C3×Q8—61no—
69C22×Dic6—21no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—61no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—61no—
75C3×C4×Q8—31no—
76C3×C4×D4—21no—
77C3×C4×D4—61no—
78C3×C4×D4C2×D311yescharacteristic
79C3×C4×D4C2×D311yescharacteristic
80C2×#216—61no—
81C2×#216—61no—
82D4×Dic3—21no—
83#924—21no—
84#888—21no—
85#878—22no—
86#869C2×D311yescharacteristic
87#869C2×D311yescharacteristic
88C4×Dic6C2×D311yescharacteristic
89C3×#107—61no—
90C3×C4⋊C8—31no—
91C3×#102—61no—
92#835—61no—
93#832—21no—
94#810—61no—
95#807—21no—
96#807—62no—
97#807—62no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C23×C32—21no—
106C32×D4—21no—
107C32×D4Q1612yescomplemented
108C2×C32×C4—21no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—44no—
118C2×C3×Dic3—41no—
119C3×Dic6—21no—
120C3×Dic6—44no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6D812yes—
126C3⋊(C3⋊C8)—22no—
127C3⋊(C3⋊C8)—41no—
128C3×C3⋊C8—41no—
129D4×Q8—31no—
130#500—91no—
131#474—31no—
132#462—91no—
133#332—91no—
134Q8⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—62no—
138C2×C3×Q8—61no—
139C2×C3×Q8—61no—
140C2×C3×Q8—122no—
141C2×C3×Q8—122no—
142C2×C3×D4—21no—
143C2×C3×D4#6711yescharacteristic
144C2×C3×D4#6711yescharacteristic
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—41no—
148C22×C3×C4—62no—
149C22×Dic3—22no—
150C2×Dic6—22no—
151C2×Dic6—21no—
152C2×Dic6—21no—
153C2×Dic6—42no—
154C2×Dic6—42no—
155C2×Dic6#6711yescharacteristic
156C2×C3×C8—61no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—32no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—62no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4#6711yescharacteristic
166C3×C4⋊C4#6711yescharacteristic
167C3×C22⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C22⋊C4—41no—
170C3×C22⋊C4—62no—
171C3×C42—21no—
172C3×C42—61no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#217—22no—
176#216—122no—
177#216—122no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3#6712yes—
182C4⋊Dic3#6711yescharacteristic
183Dic3⋊C4—22no—
184Dic3⋊C4—21no—
185C4×Dic3—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—121no—
192C2×C3⋊C8—121no—
193C22×C32—22no—
194C22×C32—41no—
195C22×C32—41no—
196C22×C32#12011yescharacteristic
197C32×C4—21no—
198C32×C4—41no—
199C32×C4C2×D811yescharacteristic
200C32×C4C2×Q1611yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4#13711yescharacteristic
203C3×Dic3—22no—
204C3×Dic3—42no—
205C3×Dic3—41no—
206C3×Dic3—81no—
207C22×Q8—61no—
208C2×Q16—181no—
209C4⋊Q8—31no—
210C4⋊Q8—31no—
211C4⋊Q8—61no—
212C22⋊Q8—62no—
213C22⋊Q8—61no—
214C4×Q8—31no—
215C4×D4—61no—
216C4×D4D3211yescharacteristic
217#107—61no—
218#107—182no—
219C4⋊C8—31no—
220C4⋊C8—91no—
221#103—181no—
222#102—61no—
223C4×C8—91no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—41no—
227C3×Q8—32no—
228C3×Q8—61no—
229C3×Q8—124no—
230C3×Q8—121no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×Q8—121no—
234C3×D4—21no—
235C3×D4—21no—
236C3×D4—22no—
237C3×D4—41no—
238C3×D4#21612yescomplemented
239C3×D4#21612yescomplemented
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—62no—
253C2×C3×C4—81no—
254C2×C3×C4—81no—
255C2×C3×C4—124no—
256C2×C3×C4—121no—
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—22no—
266C2×Dic3—44no—
267C2×Dic3—41no—
268Dic6—21no—
269Dic6—44no—
270Dic6—41no—
271Dic6—41no—
272Dic6—41no—
273Dic6—41no—
274Dic6#21312yes—
275C3×C8—121no—
276C3⋊C8—41no—
277C3⋊C8—62no—
278C3⋊C8—62no—
279C3⋊C8—122no—
280C3⋊C8—121no—
281C3⋊C8—121no—
282C3⋊C8—241no—
283C2×C32—42no—
284C2×C32#44711yescharacteristic
285C2×C32#45111yescharacteristic
286C2×C32#45611yescharacteristic
287C2×Q8—31no—
288C2×Q8—62no—
289C2×Q8—61no—
290C2×Q8—61no—
291C2×Q8—122no—
292C2×Q8—122no—
293C2×D4#62511yescharacteristic
294C22×C4—21no—
295C22×C4—62no—
296Q16—362no—
297C2×C8—61no—
298C2×C8—181no—
299C2×C8—181no—
300C4⋊C4—31no—
301C4⋊C4—32no—
302C4⋊C4—62no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4#62511yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—62no—
310C42—61no—
311C42C2×D3211yescharacteristic
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—42no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3#93711yescharacteristic
323C22×C3#95311yescharacteristic
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—41no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—62no—
334C3×C4—81no—
335C3×C4—122no—
336C3×C4—121no—
337C3×C4—241no—
338C3×C4D3×D811yescharacteristic
339C3×C4#91111yescharacteristic
340C3×C4C2×#21311yescharacteristic
341C3×C4#93211yescharacteristic
342C3×C4#94211yescharacteristic
343C3×C4C2×#21611yescharacteristic
344C3×C4C2×#21611yescharacteristic
345C3×C4#95111yescharacteristic
346Dic3—22no—
347Dic3—42no—
348Dic3—41no—
349Dic3—81no—
350C32#164911yescharacteristic, complemented, Sylow
351C23—21no—
352Q8—32no—
353Q8—61no—
354Q8—124no—
355Q8—121no—
356Q8—121no—
357Q8—121no—
358Q8—121no—
359D4—21no—
360D4#371812yescomplemented
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—62no—
367C2×C4—124no—
368C2×C4—121no—
369C2×C4C2×#62511yescharacteristic
370C2×C4D3×#6711yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C8—121no—
373C8—182no—
374C8—361no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—42no—
379C2×C3—42no—
380C2×C3—82no—
381C2×C3#505011yescharacteristic
382C2×C3#515611yescharacteristic
383C2×C3#520511yescharacteristic
384C2×C3#521711yescharacteristic
385C2×C3#522811yescharacteristic
386C2×C3#524611yescharacteristic
387C22—22no—
388C22—41no—
389C22—41no—
390C22#6397611yescharacteristic
391C4—21no—
392C4—41no—
393C4—62no—
394C4—121no—
395C4—122no—
396C4—241no—
397C4#6382711yescharacteristic
398C4C2×#371811yescharacteristic
399C4D3×#21311yescharacteristic
400C4#6393211yescharacteristic
401C3—21no—
402C3#7111411yescharacteristic, complemented
403C3#7191611yescharacteristic, complemented
404C2—42no—
405C2#1059118511yescharacteristic
406C2#1059144711yescharacteristic
407C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590384C2semidirect
4. #10590312C2semidirect
6. #10589092C2semidirect
7. #10589083C2semidirect
107. C32×D4Q16semidirect
238. C3×D4#216semidirect
239. C3×D4#216semidirect
350. C32#1649semidirect
360. D4#3718semidirect
402. C3#71114semidirect
403. C3#71916semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
C3×#50072
#105903842
#105903122
D4⋊(C3⋊(C3⋊C8))2
#105890922
#105890832
#719163
#711143