Finite Group Databasebeta

← #11780243

Subgroups — #11780243

Order 1152.

460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593865C211yesmaximal, characteristic
2#10592782C211yesmaximal, characteristic
3C3×#5094C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5#10589092C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic
8#71370—31nomaximal
9#71126—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63871—21no—
16#63864—21no—
17#63849—21no—
18#63848—22no—
19Dic3×Dic6—21no—
20#63662—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#810—21no—
23C3×#808—21no—
24C3×#807—22no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5732—31no—
28#5584—31no—
29C3×#500—31no—
30C3×#475—31no—
31#5094D311yescharacteristic, complemented
32#5083—31no—
33#5083—31no—
34#5083—61no—
35#5078D311yescharacteristic, complemented
36#4547—31no—
37#4535—31no—
38#4486—31no—
39#4483—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50#3755—42no—
51#3752—21no—
52C4⋊(C3⋊Dic3)D411yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D412yes—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62#3722—22no—
63#3722—22no—
64Dic32—22no—
65#1650—91noSylow
66C3×C4⋊Q8—21no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×C4×Q8—31no—
71#947—61no—
72#946—61no—
73Q8×Dic3—61no—
74C2×#215—61no—
75C2×#215—61no—
76C2×#215—62no—
77#898—62no—
78#898—62no—
79#897—61no—
80#892—61no—
81#892—61no—
82#875—61no—
83C4×D12—31no—
84C4×D12—31no—
85C4×D12—61no—
86#869C2×D311yescharacteristic
87C4×Dic6—61no—
88C4×Dic6C2×D311yescharacteristic
89C3×#107—62no—
90C3×#106—61no—
91C3×C4⋊C8—31no—
92C3×#103—61no—
93C3×C4×C8—31no—
94#835—61no—
95#835—61no—
96#835—62no—
97#810—21no—
98#808—21no—
99#807—22no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C32×Q8—41no—
107C32×Q8—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)—21no—
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—91no—
128#500—31no—
129#475—31no—
130#461—91no—
131#332—91no—
132Q8⋊C8—91no—
133D4⋊C8—91no—
134C2×C3×Q8—22no—
135C2×C3×Q8—21no—
136C2×C3×Q8—21no—
137C2×C3×Q8—31no—
138C2×C3×Q8—61no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—121no—
145C2×Dic6—21no—
146C2×Dic6#6711yescharacteristic
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—32no—
155C3×C4⋊C4—41no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C42—21no—
160C3×C42—61no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#215—124no—
164#215—122no—
165#215—122no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—61no—
171(C2×D3)⋊C4—61no—
172(C2×D3)⋊C4—121no—
173C4⋊Dic3—21no—
174C4⋊Dic3—31no—
175C4⋊Dic3—31no—
176C4⋊Dic3—61no—
177C4⋊Dic3—62no—
178C4⋊Dic3#6712yes—
179C4⋊Dic3#6711yescharacteristic
180Dic3⋊C4—21no—
181Dic3⋊C4—62no—
182C4×Dic3—21no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—62no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C22×C32#12011yescharacteristic
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C32×C4—21no—
195C32×C4—81no—
196C32×C4#13511yescharacteristic
197C32×C4#13511yescharacteristic
198C32×C4AGL(1,ℤ/8)11yescharacteristic
199C32×C4#13711yescharacteristic
200C3⋊Dic3—41no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C3×Dic3—41no—
204C2×SD16—181no—
205C4⋊Q8—31no—
206C4⋊Q8D3211yescharacteristic
207#126—182no—
208#124—181no—
209C22⋊Q8—181no—
210C4×Q8—31no—
211C4×Q8—181no—
212C4×D4—91no—
213#117—181no—
214#107—62no—
215#106—61no—
216C4⋊C8—31no—
217C4⋊C8—91no—
218#103—61no—
219#103—181no—
220C4×C8—31no—
221C22×D3—61no—
222C22×D3—61no—
223C22×D3—121no—
224C3×Q8—42no—
225C3×Q8—42no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—41no—
230C3×Q8—61no—
231C3×Q8—61no—
232C3×Q8—121no—
233C3×Q8—121no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—62no—
242C2×C3×C4—61no—
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—121no—
255D12—62no—
256D12—61no—
257D12—61no—
258D12—61no—
259D12—61no—
260D12—121no—
261C4×D3—121no—
262C4×D3—121no—
263C4×D3—121no—
264C4×D3—121no—
265C4×D3—241no—
266C4×D3—241no—
267Dic6—21no—
268Dic6—21no—
269Dic6—41no—
270Dic6—41no—
271C3×C8—62no—
272C3×C8—121no—
273C3⋊C8—22no—
274C3⋊C8—41no—
275C3⋊C8—122no—
276C3⋊C8—121no—
277C3⋊C8—121no—
278C2×C32#44911yescharacteristic
279C2×C32#45211yescharacteristic
280C2×C32#45611yescharacteristic
281C3⋊D3—81no—
282C2×Q8—21no—
283C2×Q8—31no—
284C2×Q8—61no—
285C2×D4—91no—
286C22×C4—181no—
287SD16—362no—
288C2×C8—61no—
289C2×C8—61no—
290C2×C8—181no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—31no—
294C4⋊C4—32no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—91no—
298C4⋊C4—182no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C22⋊C4—181no—
302C42—61no—
303C42—182no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3#93711yescharacteristic
307C22×C3#93711yescharacteristic
308C2×D3—122no—
309C2×D3—121no—
310C2×D3—121no—
311C2×D3—121no—
312C2×D3—121no—
313C2×D3—121no—
314C2×D3—121no—
315C2×D3—241no—
316C2×D3—241no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—41no—
324C3×C4—82no—
325C3×C4—81no—
326C3×C4—81no—
327C3×C4—122no—
328C3×C4—121no—
329C3×C4—121no—
330C3×C4#91111yescharacteristic
331C3×C4#91211yescharacteristic
332C3×C4#91411yescharacteristic
333C3×C4#91611yescharacteristic
334C3×C4#91811yescharacteristic
335C3×C4#91911yescharacteristic
336C3×C4#94211yescharacteristic
337C3×C4#95011yescharacteristic
338Dic3—42no—
339Dic3—41no—
340Dic3—41no—
341Dic3—121no—
342Dic3—121no—
343Dic3—241no—
344C32#165011yescharacteristic, complemented, Sylow
345C23—181no—
346Q8—41no—
347Q8—41no—
348Q8—61no—
349Q8—61no—
350Q8—121no—
351Q8—121no—
352D4—181no—
353D4—181no—
354C2×C4—41no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—62no—
358C2×C4—181no—
359C2×C4—361no—
360C2×C4—361no—
361C2×C4D3×#6711yescharacteristic
362C2×C4D3×#6711yescharacteristic
363C2×C4#381111yescharacteristic
364C8—62no—
365C8—121no—
366C8—361no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3#504711yescharacteristic
371C2×C3#509511yescharacteristic
372C2×C3#515811yescharacteristic
373C2×C3#517211yescharacteristic
374C2×C3#518711yescharacteristic
375C2×C3#520511yescharacteristic
376D3—242no—
377D3—241no—
378D3—241no—
379C22—361no—
380C22—361no—
381C22—361no—
382C22#6398311yescharacteristic
383C4—21no—
384C4—81no—
385C4—122no—
386C4—121no—
387C4—121no—
388C4—361no—
389C4#6393611yescharacteristic
390C4#6393711yescharacteristic
391C4#6394811yescharacteristic
392C4#6394911yescharacteristic
393C3—21no—
394C3#7112611yescharacteristic, complemented
395C3#7137011yescharacteristic, complemented
396C2—721no—
397C2#1059152011yescharacteristic
398C2#1059165711yescharacteristic
399C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊Q8D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5094C2semidirect
4. C3×#5078C2semidirect
5. #10589092C2semidirect
6. #10589084C2semidirect
31. #5094D3semidirect
35. #5078D3semidirect
344. C32#1650semidirect
394. C3#71126semidirect
395. C3#71370semidirect

Maximal subgroups

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

subgroupindex
#105938652
#105927822
C3×#50942
C3×#50782
#105890922
#105890842
#105890822
#713703
#711263