Finite Group Databasebeta

← #11779540

Subgroups — #11779540

Order 1152.

517 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 517 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593895C211yesmaximal, characteristic
2#10592380C211yesmaximal, characteristic, complemented
3#10590268C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68204—31nomaximal
9#68181—31nomaximal
10C2×#3795—21no—
11#64078C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15#63908—21no—
16#63891—22no—
17D3×C4⋊Dic3—21no—
18#63857—21no—
19C32×C4×C8C2211yescharacteristic
20#63643—22no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63573—21no—
24#63573—21no—
25#63563—21no—
26#63563—21no—
27#5555—31no—
28#5551—31no—
29#5008—31no—
30#5008—31no—
31#4842—31no—
32#4842—31no—
33#4681—31no—
34#4681—31no—
35#4681—61no—
36C3×D4⋊C8—31no—
37C3×D4⋊C8—31no—
38#4486—31no—
39#4482—31no—
40#4459D311yescharacteristic, complemented
41#4459D311yescharacteristic, complemented
42C2×#634—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×#625—22no—
49C2×D3×Dic3—22no—
50#3795—42no—
51#3795—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D412yes—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#1635—91noSylow
67C2×#237—61no—
68C2×#235—61no—
69C3×C4×D4—31no—
70C3×C4×D4—31no—
71#938—61no—
72#930—61no—
73C2×C4⋊Dic3—61no—
74#924—61no—
75#897—61no—
76D3×C4⋊C4—61no—
77#886—62no—
78#883—62no—
79C4×D12C2×D311yescharacteristic
80C4×D12C2×D311yescharacteristic
81#869—31no—
82#869—31no—
83#869—31no—
84#869—31no—
85#869—61no—
86#869—61no—
87C3×C4⋊C8—31no—
88C3×C4⋊C8—31no—
89C3×C4×C8—21no—
90C3×C4×C8C2×D311yescharacteristic
91C3×C4×C8C2×D311yescharacteristic
92#832—61no—
93#832—61no—
94#821—61no—
95#821—61no—
96#817—61no—
97#817—61no—
98#816—62no—
99#816—62no—
100#816—64no—
101#808—61no—
102#808—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—41no—
112#634—42no—
113#634—41no—
114#634—41no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×D12—21no—
120C3×D12SD1612yes—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125#625—44no—
126D3×Dic3—44no—
127C32×C8—41no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#547—91no—
131#487—91no—
132#476—91no—
133#476—91no—
134#332—91no—
135D4⋊C8—31no—
136D4⋊C8—31no—
137C2×C3×D4—31no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C2×#67—62no—
142C2×#67—62no—
143C22×Dic3—62no—
144#237—122no—
145#237—122no—
146#235—122no—
147#235—122no—
148C2×D12D1211yescharacteristic
149C2×D12D1211yescharacteristic
150C2×C4×D3—21no—
151C2×C4×D3—21no—
152C2×C4×D3—62no—
153C2×Dic6—61no—
154C2×Dic6—61no—
155C2×Dic6—62no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—121no—
159C2×C3×C8—22no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C22⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—62no—
175C4⋊Dic3—32no—
176C4⋊Dic3—32no—
177C4⋊Dic3—62no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3—121no—
187C4⋊Dic3—121no—
188C4⋊Dic3D1211yescharacteristic
189C4⋊Dic3D1211yescharacteristic
190Dic3⋊C4—62no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C32×C4—21no—
201C32×C4C2×SD1611yescharacteristic
202C32×C4#13511yescharacteristic
203C32×C4AGL(1,ℤ/8)11yescharacteristic
204C32×C4#13711yescharacteristic
205C3⋊Dic3—42no—
206C3⋊Dic3—81no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C2×#41—181no—
210C4⋊Q8—91no—
211C4⋊Q8—91no—
212#123—182no—
213C22⋊Q8—181no—
214#121—181no—
215C4×D4—31no—
216C4×D4—31no—
217C2×C4⋊C4—181no—
218#106—181no—
219#106—181no—
220C4⋊C8—31no—
221C4⋊C8—31no—
222#103—182no—
223#102—181no—
224#102—181no—
225C4×C8D3211yescharacteristic
226C23×C3—61no—
227C23×C3—61no—
228C22×D3—21no—
229C22×D3—21no—
230C3×D4—32no—
231C3×D4—61no—
232C3×D4—61no—
233C3×D4—61no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—61no—
238C2×C3×C4—61no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4C2×D1211yescharacteristic
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249#67—124no—
250#67—124no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—124no—
257C2×Dic3—122no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260D12—21no—
261D12—21no—
262D12—21no—
263D12#20412yes—
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—41no—
267C4×D3—41no—
268C4×D3—124no—
269Dic6—121no—
270Dic6—121no—
271Dic6—121no—
272Dic6—121no—
273Dic6—124no—
274Dic6—122no—
275Dic6—122no—
276Dic6—241no—
277Dic6—241no—
278C3×C8—42no—
279C3×C8—41no—
280C3×C8—41no—
281C3×C8—121no—
282C3×C8—121no—
283C3⋊C8—41no—
284C3⋊C8—41no—
285C2×C32#45011yescharacteristic
286C2×C32#45211yescharacteristic
287C2×C32#45411yescharacteristic
288C3×D3—42no—
289C3×D3—81no—
290#41—362no—
291#41—362no—
292C2×Q8—181no—
293C2×Q8—181no—
294C2×D4—31no—
295C2×D4—31no—
296C2×D4—182no—
297C22×C4—61no—
298C22×C4—61no—
299C22×C4—182no—
300C2×C8—21no—
301C2×C8—61no—
302C2×C8—61no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—92no—
306C4⋊C4—182no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—182no—
313C42C2×D3211yescharacteristic
314C22×C3—21no—
315C22×C3—62no—
316C22×C3—121no—
317C22×C3—121no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—121no—
321C22×C3#88211yescharacteristic
322C22×C3#88211yescharacteristic
323C2×D3—22no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C3×C4—22no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—121no—
337C3×C4—121no—
338C3×C4C2×#20411yescharacteristic
339C3×C4#90411yescharacteristic
340C3×C4#90811yescharacteristic
341C3×C4#90911yescharacteristic
342C3×C4#91111yescharacteristic
343C3×C4#91211yescharacteristic
344C3×C4D3×SD1611yescharacteristic
345C3×C4#91511yescharacteristic
346Dic3—41no—
347Dic3—41no—
348Dic3—122no—
349Dic3—122no—
350Dic3—242no—
351Dic3—242no—
352Dic3—241no—
353Dic3—241no—
354C32#163511yescharacteristic, complemented, Sylow
355C23—61no—
356C23—61no—
357Q8—362no—
358Q8—361no—
359Q8—361no—
360D4—32no—
361D4—61no—
362D4—61no—
363D4—61no—
364D4—364no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—182no—
372C2×C4—364no—
373C2×C4—361no—
374C2×C4D3×D1211yescharacteristic
375C2×C4D3×D1211yescharacteristic
376C2×C4#381111yescharacteristic
377C8—41no—
378C8—121no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—122no—
384C2×C3—241no—
385C2×C3#473111yescharacteristic
386C2×C3#473311yescharacteristic
387C2×C3#477611yescharacteristic
388C2×C3#478311yescharacteristic
389C2×C3#482711yescharacteristic
390C2×C3#482711yescharacteristic
391D3—42no—
392D3—81no—
393C22—62no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—121no—
399C22#6392311yescharacteristic
400C4—21no—
401C4—121no—
402C4—121no—
403C4—362no—
404C4—721no—
405C4D3×#20411yescharacteristic
406C4#6379511yescharacteristic
407C4#6380011yescharacteristic
408C4#6380711yescharacteristic
409C3—21no—
410C3#6818111yescharacteristic, complemented
411C3#6820411yescharacteristic, complemented
412C2—122no—
413C2—241no—
414C2#1059040211yescharacteristic
415C2#1059094611yescharacteristic
416C2#1059096911yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radical#10593895C2
hypercenterC4×C8D32
hypocenterC32#1635
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592380C2semidirect
3. #10590268C2semidirect
4. #10590268C2semidirect
5. C3×#4459C2semidirect
6. C3×#4459C2semidirect
7. #10589094C2semidirect
40. #4459D3semidirect
41. #4459D3semidirect
354. C32#1635semidirect
410. C3#68181semidirect
411. C3#68204semidirect

Maximal subgroups

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

subgroupindex
#105938952
#105923802
#105902682
C3×#44592
#105890942
#682043
#681813