Finite Group Databasebeta

← #11779551

Subgroups — #11779551

Order 1152.

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

normal subgroups only

This group has 522 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#10593896C211yesmaximal, characteristic
2#10592541C211yesmaximal, characteristic, complemented
3#10590288C211yesmaximal, characteristic, complemented
4#10590268C211yesmaximal, characteristic, complemented
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68434—31nomaximal
9#68204—31nomaximal
10C2×#3796—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63909—21no—
16#63890—22no—
17D3×C4⋊Dic3—21no—
18#63871—21no—
19C32×C4⋊C8C2211yescharacteristic
20#63648—21no—
21#63644—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63573—21no—
25#63567—22no—
26#63563—21no—
27#5726—31no—
28#5555—31no—
29#5093—31no—
30#5008—31no—
31#4842—31no—
32#4842—31no—
33#4842—31no—
34#4842—61no—
35#4681—31no—
36C3×#332—31no—
37C3×D4⋊C8—31no—
38#4486D311yescharacteristic, complemented
39#4483—31no—
40#4483D311yescharacteristic, 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×Dic6—21no—
48C2×#626—22no—
49C2×D3×Dic3—22no—
50#3796—42no—
51#3796—42no—
52C2×C32×C8—21no—
53C32×C42C2311yescharacteristic
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D412yes—
61C3×C4⋊Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65#3722—22no—
66#1635—91noSylow
67C2×#239—61no—
68C2×#237—61no—
69C3×C4⋊Q8—31no—
70C3×C4×D4—31no—
71#946—61no—
72#930—61no—
73C2×C4⋊Dic3—61no—
74#897—61no—
75#895—61no—
76#894—62no—
77D3×C4⋊C4—61no—
78#886—62no—
79C4×D12—31no—
80C4×D12—31no—
81C4×D12—61no—
82C4×D12C2×D311yescharacteristic
83#869—31no—
84#869—31no—
85#869—61no—
86#869C2×D311yescharacteristic
87C3×C4⋊C8—21no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8C2×D311yescharacteristic
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4×C8—31no—
92#832—61no—
93#821—61no—
94#821—61no—
95#821—62no—
96#821—61no—
97#817—61no—
98#817—61no—
99#817—62no—
100#817—61no—
101#816—62no—
102#810—62no—
103#808—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊D3—21no—
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—41no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)—21no—
115C4×C3⋊D3—41no—
116C4×C3⋊D3—41no—
117#634—42no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C3×D12—21no—
121C3×D12SD1612yes—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126#626—44no—
127D3×Dic3—44no—
128C32×C8—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#547—91no—
132#487—91no—
133#476—91no—
134#476—91no—
135#332—31no—
136D4⋊C8—31no—
137D4⋊C8—91no—
138C2×C3×Q8—61no—
139C2×C3×D4—31no—
140C22×C3×C4—61no—
141C2×#67—62no—
142C22×Dic3—62no—
143#239—122no—
144#239—122no—
145#237—122no—
146#237—122no—
147C2×D12—31no—
148C2×D12—31no—
149C2×D12—61no—
150C2×D12—62no—
151C2×D12D1211yescharacteristic
152C2×C4×D3—21no—
153C2×C4×D3—62no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—121no—
157C2×Dic6—21no—
158C2×Dic6—61no—
159C2×Dic6—61no—
160C2×Dic6—121no—
161C2×C3×C8—22no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—32no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—21no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—121no—
179C4⋊Dic3—21no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—121no—
190C4⋊Dic3D1212yes—
191C4⋊Dic3D1211yescharacteristic
192Dic3⋊C4—62no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C22×C32#12011yescharacteristic
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3×D3—22no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4C2×SD1611yescharacteristic
204C32×C4#13511yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4#13711yescharacteristic
207C3⋊Dic3—41no—
208C3⋊Dic3—81no—
209C3×Dic3—42no—
210C3×Dic3—41no—
211C2×#41—181no—
212C4⋊Q8—31no—
213C4⋊Q8—91no—
214#123—182no—
215C22⋊Q8—181no—
216#121—181no—
217C4×D4—31no—
218C4×D4—91no—
219C2×C4⋊C4—181no—
220#106—181no—
221#106—181no—
222C4⋊C8—31no—
223C4⋊C8D3211yescharacteristic
224#103—182no—
225#102—181no—
226#102—181no—
227C4×C8—31no—
228C23×C3—61no—
229C22×D3—21no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—121no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×D4—32no—
236C3×D4—61no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—62no—
241C2×C3×C4—61no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4C2×D1211yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250#67—124no—
251C2×Dic3—21no—
252C2×Dic3—22no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—121no—
256C2×Dic3—124no—
257C2×Dic3—122no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260D12—21no—
261D12—62no—
262D12—61no—
263D12—61no—
264D12—61no—
265D12—61no—
266D12—121no—
267D12—124no—
268D12#20412yes—
269C4×D3—41no—
270C4×D3—41no—
271C4×D3—124no—
272C4×D3—121no—
273C4×D3—121no—
274C4×D3—121no—
275C4×D3—121no—
276C4×D3—241no—
277C4×D3—241no—
278Dic6—41no—
279Dic6—41no—
280Dic6—122no—
281Dic6—122no—
282Dic6—242no—
283C3×C8—42no—
284C3×C8—41no—
285C3×C8—41no—
286C3×C8—121no—
287C3×C8—121no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32#45011yescharacteristic
291C2×C32#45211yescharacteristic
292C2×C32#45411yescharacteristic
293C3⋊D3—81no—
294C3×D3—42no—
295#41—362no—
296#41—362no—
297C2×Q8—61no—
298C2×Q8—181no—
299C2×D4—31no—
300C2×D4—91no—
301C2×D4—182no—
302C22×C4—61no—
303C22×C4—182no—
304C22×C4—181no—
305C2×C8—21no—
306C2×C8—61no—
307C2×C8—61no—
308C4⋊C4—32no—
309C4⋊C4—31no—
310C4⋊C4—61no—
311C4⋊C4—91no—
312C4⋊C4—182no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C22⋊C4—61no—
316C22⋊C4—182no—
317C22⋊C4—181no—
318C42C2×D3211yescharacteristic
319C22×C3—21no—
320C22×C3—62no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3#88211yescharacteristic
324C22×C3#88211yescharacteristic
325C2×D3—22no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—122no—
329C2×D3—121no—
330C2×D3—121no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—241no—
336C2×D3—241no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—41no—
344C3×C4—122no—
345C3×C4—121no—
346C3×C4C2×#20411yescharacteristic
347C3×C4#90811yescharacteristic
348C3×C4#91111yescharacteristic
349C3×C4#91211yescharacteristic
350C3×C4D3×SD1611yescharacteristic
351C3×C4#91511yescharacteristic
352C3×C4#91611yescharacteristic
353C3×C4#91811yescharacteristic
354Dic3—42no—
355Dic3—41no—
356Dic3—121no—
357Dic3—121no—
358Dic3—241no—
359Dic3—242no—
360Dic3—241no—
361Dic3—241no—
362C32#163511yescharacteristic, complemented, Sylow
363C23—61no—
364C23—181no—
365Q8—121no—
366Q8—121no—
367Q8—362no—
368D4—32no—
369D4—61no—
370D4—181no—
371D4—181no—
372D4—364no—
373C2×C4—61no—
374C2×C4—62no—
375C2×C4—121no—
376C2×C4—121no—
377C2×C4—181no—
378C2×C4—364no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4—361no—
382C2×C4D3×D1211yescharacteristic
383C2×C4D3×D1211yescharacteristic
384C2×C4#381111yescharacteristic
385C8—41no—
386C8—121no—
387C8—121no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—122no—
392C2×C3#473111yescharacteristic
393C2×C3#475311yescharacteristic
394C2×C3#477611yescharacteristic
395C2×C3#478311yescharacteristic
396C2×C3#480811yescharacteristic
397C2×C3#482711yescharacteristic
398D3—42no—
399D3—242no—
400D3—241no—
401D3—241no—
402C22—62no—
403C22—121no—
404C22—121no—
405C22—361no—
406C22—361no—
407C22—361no—
408C22#6392311yescharacteristic
409C4—21no—
410C4—121no—
411C4—122no—
412C4—361no—
413C4—721no—
414C4D3×#20411yescharacteristic
415C4#6379511yescharacteristic
416C4#6393611yescharacteristic
417C4#6395111yescharacteristic
418C3—21no—
419C3#6820411yescharacteristic, complemented
420C3#6843411yescharacteristic, complemented
421C2—122no—
422C2—721no—
423C2#1059061811yescharacteristic
424C2#1059094611yescharacteristic
425C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10593896C2
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. #10592541C2semidirect
3. #10590288C2semidirect
4. #10590268C2semidirect
5. C3×#4486C2semidirect
6. C3×#4483C2semidirect
7. #10589082C2semidirect
38. #4486D3semidirect
40. #4483D3semidirect
362. C32#1635semidirect
419. C3#68204semidirect
420. C3#68434semidirect

Maximal subgroups

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

subgroupindex
#105938962
#105925412
#105902882
#105902682
C3×#44862
C3×#44832
#105890822
#684343
#682043