Finite Group Databasebeta

← #11779505

Subgroups — #11779505

Order 1152.

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

normal subgroups only

This group has 490 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#10593987C211yesmaximal, characteristic
2#10592541C211yesmaximal, characteristic, complemented
3#10590386C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68493—31nomaximal
9#68203—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63916—21no—
15#63909—21no—
16#63907—22no—
17#63849—21no—
18#63841—21no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21#63648—21no—
22#63644—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—21no—
26#63563—21no—
27#5734—31no—
28#5563—31no—
29#5092—31no—
30#5008—31no—
31#4842—31no—
32#4842—31no—
33#4842—31no—
34#4842—61no—
35#4699—31no—
36C3×#333—31no—
37C3×D4⋊C8—31no—
38#4483—31no—
39#4483D311yescharacteristic, complemented
40#4481D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C2×C3×D12D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6D412yes—
48C2×#626—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51#3752—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C3×(C2×D3)⋊C4—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61#3722—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3719—44no—
65#1634—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×D4—31no—
68#947—62no—
69C2×#216—62no—
70#938—61no—
71#930—61no—
72#926—61no—
73C2×Dic12—62no—
74#895—61no—
75#895—61no—
76#892—61no—
77#892—61no—
78#892—61no—
79#885—62no—
80C4×D12—31no—
81C4×D12—31no—
82C4×D12—61no—
83C4×D12C2×D311yescharacteristic
84#869—31no—
85#869—31no—
86#869—61no—
87#869C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4×C8—31no—
93#832—61no—
94#821—61no—
95#821—61no—
96#821—62no—
97#821—61no—
98#817—61no—
99#817—61no—
100#817—62no—
101#817—61no—
102#808—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊D3—21no—
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—41no—
112C4⋊(C3⋊D3)—21no—
113C4⋊(C3⋊D3)—21no—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—41no—
116#634—42no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—42no—
124#626—82no—
125C32×C8—41no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#555—91no—
129#494—91no—
130#476—91no—
131#476—91no—
132#333—31no—
133D4⋊C8—31no—
134D4⋊C8—91no—
135C2×C3×Q8—32no—
136C2×C3×D4—31no—
137C22×C3×C4—61no—
138C2×#67—62no—
139C2×D12—31no—
140C2×D12—31no—
141C2×D12—61no—
142C2×D12—62no—
143C2×D12D1211yescharacteristic
144C2×C4×D3—21no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—121no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—121no—
151C2×Dic6D1212yes—
152C2×C3×C8—22no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C42—21no—
162C3×C42C22×D311yescharacteristic
163C3×C42C22×D311yescharacteristic
164#217—62no—
165#216—124no—
166(C2×D3)⋊C4—21no—
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—21no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3—62no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—121no—
184C4⋊Dic3D1211yescharacteristic
185C4×Dic3—62no—
186C4×Dic3—62no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189Dic12—124no—
190C22×C32#12011yescharacteristic
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—41no—
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4#13511yescharacteristic
199C32×C4#13511yescharacteristic
200C32×C4#13711yescharacteristic
201C32×C4#13711yescharacteristic
202C3⋊Dic3—41no—
203C3⋊Dic3—81no—
204C3×Dic3—41no—
205C3×Dic3—42no—
206C2×Q16—182no—
207C4⋊Q8—31no—
208C4⋊Q8—91no—
209#124—182no—
210#121—181no—
211#121—181no—
212C4×D4—31no—
213C4×D4—91no—
214#117—181no—
215#117—181no—
216#106—181no—
217#106—181no—
218C4⋊C8—31no—
219C4⋊C8D3211yescharacteristic
220#102—181no—
221#102—181no—
222C4×C8—31no—
223C23×C3—61no—
224C22×D3—21no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—121no—
228C3×Q8—122no—
229C3×D4—61no—
230C3×D4—61no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244#67—242no—
245C2×Dic3—21no—
246C2×Dic3—22no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—121no—
250C2×Dic3—122no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253D12—21no—
254D12—21no—
255D12—62no—
256D12—61no—
257D12—61no—
258D12—61no—
259D12—61no—
260D12—121no—
261D12—242no—
262C4×D3—41no—
263C4×D3—41no—
264C4×D3—121no—
265C4×D3—121no—
266C4×D3—121no—
267C4×D3—121no—
268C4×D3—241no—
269C4×D3—241no—
270Dic6—42no—
271Dic6—122no—
272Dic6—122no—
273Dic6—242no—
274C3×C8—42no—
275C3×C8—41no—
276C3×C8—41no—
277C3×C8—62no—
278C3×C8—121no—
279C3⋊C8—22no—
280C3⋊C8—41no—
281C2×C32#45211yescharacteristic
282C2×C32#45211yescharacteristic
283C2×C32#45311yescharacteristic
284C3⋊D3—81no—
285C3×D3—81no—
286C2×Q8—32no—
287C2×Q8—181no—
288C2×D4—31no—
289C2×D4—91no—
290C2×D4—182no—
291C22×C4—61no—
292C22×C4—181no—
293Q16—364no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—61no—
297C4⋊C4—31no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—91no—
301C4⋊C4—181no—
302C4⋊C4—181no—
303C22⋊C4—61no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C22⋊C4—181no—
307C42—182no—
308C42C2×D3211yescharacteristic
309C22×C3—21no—
310C22×C3—121no—
311C22×C3—121no—
312C22×C3—121no—
313C22×C3#88211yescharacteristic
314C22×C3#88211yescharacteristic
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—122no—
319C2×D3—121no—
320C2×D3—121no—
321C2×D3—121no—
322C2×D3—121no—
323C2×D3—121no—
324C2×D3—121no—
325C2×D3—241no—
326C2×D3—241no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—41no—
334C3×C4—121no—
335C3×C4—122no—
336C3×C4#90411yescharacteristic
337C3×C4#90911yescharacteristic
338C3×C4#91211yescharacteristic
339C3×C4#91511yescharacteristic
340C3×C4#91611yescharacteristic
341C3×C4#91611yescharacteristic
342C3×C4#91811yescharacteristic
343C3×C4#91811yescharacteristic
344Dic3—42no—
345Dic3—41no—
346Dic3—121no—
347Dic3—121no—
348Dic3—241no—
349Dic3—242no—
350Dic3—241no—
351Dic3—241no—
352C32#163411yescharacteristic, complemented, Sylow
353C23—61no—
354C23—181no—
355Q8—122no—
356Q8—362no—
357D4—61no—
358D4—61no—
359D4—181no—
360D4—181no—
361D4—722no—
362C2×C4—61no—
363C2×C4—62no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—181no—
367C2×C4—361no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4D3×D1211yescharacteristic
371C2×C4D3×D1211yescharacteristic
372C2×C4#381111yescharacteristic
373C8—41no—
374C8—62no—
375C8—121no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—241no—
380C2×C3#473311yescharacteristic
381C2×C3#474711yescharacteristic
382C2×C3#478311yescharacteristic
383C2×C3#480811yescharacteristic
384C2×C3#480811yescharacteristic
385C2×C3#482211yescharacteristic
386D3—81no—
387D3—242no—
388D3—241no—
389D3—241no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—361no—
394C22—361no—
395C22—361no—
396C22#6392311yescharacteristic
397C4—21no—
398C4—122no—
399C4—121no—
400C4—361no—
401C4—721no—
402C4#6380111yescharacteristic
403C4#6380611yescharacteristic
404C4#6393611yescharacteristic
405C4#6395111yescharacteristic
406C3—21no—
407C3#6820311yescharacteristic, complemented
408C3#6849311yescharacteristic, complemented
409C2—241no—
410C2—721no—
411C2#1059061811yescharacteristic
412C2#1059097011yescharacteristic
413C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593987C2
hypercenterC4⋊C8D32
hypocenterC32#1634
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. #10592541C2semidirect
3. #10590386C2semidirect
4. #10590268C2semidirect
5. C3×#4483C2semidirect
6. C3×#4481C2semidirect
7. #10589082C2semidirect
39. #4483D3semidirect
40. #4481D3semidirect
352. C32#1634semidirect
407. C3#68203semidirect
408. C3#68493semidirect

Maximal subgroups

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

subgroupindex
#105939872
#105925412
#105903862
#105902682
C3×#44832
C3×#44812
#105890822
#684933
#682033