Finite Group Databasebeta

← #11779095

Subgroups — #11779095

Order 1152.

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

normal subgroups only

This group has 550 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, complemented
2#10592542C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68491—31nomaximal
9#68199—31nomaximal
10C2×#3745—21no—
11#64083C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63916—21no—
16#63909—21no—
17#63907—22no—
18#63849—21no—
19#63841—21no—
20C2×#3717—22no—
21C2×#3714—21no—
22C32×C4⋊C8C2211yescharacteristic
23#63648—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27#5734—31no—
28#5563—31no—
29#5085—31no—
30#5015—31no—
31#4843—31no—
32#4843—31no—
33#4843—31no—
34#4843—61no—
35#4693—31no—
36C3×#333—31no—
37C3×D4⋊C8—31no—
38#4483—31no—
39#4483D311yescharacteristic, complemented
40#4481D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6D412yes—
50C2×#626—22no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55#3745—42no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3722—22no—
63(C2×D3)⋊Dic3—22no—
64Dic32—22no—
65#3717—44no—
66#3714—42no—
67#1624—91noSylow
68C3×C4⋊Q8—31no—
69C3×C4×D4—31no—
70#947—62no—
71C2×#215—62no—
72#938—61no—
73C2×#213—61no—
74#930—61no—
75#926—61no—
76C2×D24—61no—
77C2×D24—61no—
78C2×D24—62no—
79C2×D24—61no—
80C2×#204—62no—
81#895—61no—
82#895—61no—
83#892—61no—
84#892—61no—
85#892—61no—
86#885—62no—
87#874—31no—
88#874—31no—
89#874—61no—
90C4×D12—31no—
91C4×D12—31no—
92C4×D12—61no—
93C4×D12C2×D311yescharacteristic
94#869C2×D311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C2×D311yescharacteristic
99C3×C4×C8—31no—
100#821—61no—
101#821—61no—
102#821—62no—
103#821—61no—
104#809—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3⋊D3—41no—
109C22×C3×D3—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—21no—
114C4⋊(C3⋊D3)—21no—
115C4⋊(C3⋊D3)—21no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—42no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C4×C3⋊D3—41no—
122C4×C3⋊D3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—22no—
125C3×D12—21no—
126C3×D12—21no—
127C3×C4×D3—41no—
128C3×C4×D3—41no—
129C3×Dic6—42no—
130#626—82no—
131C32×C8—41no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—41no—
134#555—91no—
135#492—91no—
136#459—91no—
137#459—91no—
138#333—31no—
139D4⋊C8—31no—
140D4⋊C8—91no—
141C2×C3×Q8—32no—
142C2×C3×D4—31no—
143C22×C3×C4—61no—
144C2×#67—62no—
145C2×D12—31no—
146C2×D12—31no—
147C2×D12—61no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—62no—
156C2×D12—121no—
157C2×D12—121no—
158C2×D12D1211yescharacteristic
159C2×C4×D3—21no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—121no—
163C2×Dic6D1212yes—
164C2×C3×C8—22no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C42—21no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—62no—
177#215—124no—
178#213—122no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—121no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3D1211yescharacteristic
192C4×Dic3—62no—
193C4×Dic3—62no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196D24—124no—
197D24—122no—
198D24—122no—
199D24—122no—
200#204—124no—
201C22×C32#12011yescharacteristic
202C2×C3⋊D3—41no—
203C2×C3⋊D3—41no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—81no—
206C2×C3⋊D3—81no—
207C2×C3⋊D3—81no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C32×C4—21no—
212C32×C4#13511yescharacteristic
213C32×C4#13511yescharacteristic
214C32×C4AGL(1,ℤ/8)11yescharacteristic
215C32×C4AGL(1,ℤ/8)11yescharacteristic
216C3⋊Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—42no—
219C2×SD16—182no—
220C2×D8—181no—
221C2×D8—181no—
222C4⋊Q8—31no—
223#127—91no—
224#124—182no—
225#121—181no—
226#121—181no—
227C4×D4—31no—
228C4×D4—91no—
229#117—181no—
230#117—181no—
231C4⋊C8—31no—
232C4⋊C8D3211yescharacteristic
233#102—181no—
234#102—181no—
235C4×C8—31no—
236C23×C3—61no—
237C22×D3—21no—
238C22×D3—61no—
239C22×D3—61no—
240C22×D3—121no—
241C22×D3—122no—
242C22×D3—121no—
243C22×D3—121no—
244C3×Q8—122no—
245C3×D4—61no—
246C3×D4—61no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4C2×D1211yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260#67—242no—
261C2×Dic3—21no—
262C2×Dic3—22no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—121no—
266D12—21no—
267D12—21no—
268D12—62no—
269D12—61no—
270D12—61no—
271D12—61no—
272D12—61no—
273D12—121no—
274D12—122no—
275D12—122no—
276D12—122no—
277D12—122no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—121no—
282D12—121no—
283D12—121no—
284D12—121no—
285D12—121no—
286D12—241no—
287D12—241no—
288D12—242no—
289D12—242no—
290C4×D3—41no—
291C4×D3—41no—
292C4×D3—121no—
293C4×D3—121no—
294C4×D3—121no—
295C4×D3—121no—
296C4×D3—241no—
297C4×D3—241no—
298Dic6—42no—
299C3×C8—42no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—62no—
303C3×C8—121no—
304C3⋊C8—22no—
305C3⋊C8—41no—
306C2×C32#44911yescharacteristic
307C2×C32#44911yescharacteristic
308C2×C32#45311yescharacteristic
309C3⋊D3—81no—
310C3⋊D3—161no—
311C3×D3—81no—
312C2×Q8—32no—
313C2×D4—31no—
314C2×D4—91no—
315C2×D4—182no—
316C2×D4—181no—
317C2×D4—181no—
318C2×D4—181no—
319C22×C4—61no—
320C22×C4—181no—
321SD16—364no—
322D8—362no—
323D8—362no—
324C2×C8—21no—
325C2×C8—61no—
326C2×C8—61no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—91no—
331C22⋊C4—61no—
332C22⋊C4—182no—
333C22⋊C4—182no—
334C22⋊C4—181no—
335C42—182no—
336C42C2×D3211yescharacteristic
337C22×C3—21no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3—121no—
341C22×C3#88211yescharacteristic
342C22×C3#88211yescharacteristic
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—122no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—121no—
352C2×D3—121no—
353C2×D3—241no—
354C2×D3—241no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—242no—
358C2×D3—241no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—241no—
362C2×D3—241no—
363C2×D3—241no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—121no—
372C3×C4—122no—
373C3×C4#90411yescharacteristic
374C3×C4#90811yescharacteristic
375C3×C4#91111yescharacteristic
376C3×C4#91411yescharacteristic
377C3×C4#91411yescharacteristic
378C3×C4#91611yescharacteristic
379C3×C4#91911yescharacteristic
380C3×C4#91911yescharacteristic
381Dic3—42no—
382Dic3—41no—
383Dic3—121no—
384Dic3—121no—
385Dic3—241no—
386C32#162411yescharacteristic, complemented, Sylow
387C23—61no—
388C23—181no—
389C23—361no—
390Q8—122no—
391D4—61no—
392D4—61no—
393D4—181no—
394D4—181no—
395D4—362no—
396D4—361no—
397D4—361no—
398D4—361no—
399D4—361no—
400D4—722no—
401C2×C4—61no—
402C2×C4—62no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—181no—
406C2×C4—361no—
407C2×C4—361no—
408C2×C4D3×D1211yescharacteristic
409C2×C4D3×D1211yescharacteristic
410C2×C4#381111yescharacteristic
411C8—41no—
412C8—62no—
413C8—121no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—241no—
418C2×C3#473411yescharacteristic
419C2×C3#474711yescharacteristic
420C2×C3#478111yescharacteristic
421C2×C3#481011yescharacteristic
422C2×C3#481011yescharacteristic
423C2×C3#482211yescharacteristic
424D3—81no—
425D3—242no—
426D3—241no—
427D3—241no—
428D3—482no—
429D3—481no—
430D3—481no—
431C22—121no—
432C22—121no—
433C22—121no—
434C22—361no—
435C22—361no—
436C22—361no—
437C22—721no—
438C22—721no—
439C22—721no—
440C22#6392311yescharacteristic
441C4—21no—
442C4—122no—
443C4—121no—
444C4—361no—
445C4#6379411yescharacteristic
446C4#6380811yescharacteristic
447C4#6393711yescharacteristic
448C4#6395011yescharacteristic
449C3—21no—
450C3#6819911yescharacteristic, complemented
451C3#6849111yescharacteristic, complemented
452C2—241no—
453C2—721no—
454C2—1441no—
455C2#1059061711yescharacteristic
456C2#1059096711yescharacteristic
457C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1624
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
1. #10593987C2semidirect
2. #10592542C2semidirect
3. #10590373C2semidirect
4. #10590349C2semidirect
5. C3×#4483C2semidirect
6. C3×#4481C2semidirect
7. #10589082C2semidirect
39. #4483D3semidirect
40. #4481D3semidirect
386. C32#1624semidirect
450. C3#68199semidirect
451. C3#68491semidirect

Maximal subgroups

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

subgroupindex
#105939872
#105925422
#105903732
#105903492
C3×#44832
C3×#44812
#105890822
#684913
#681993