Finite Group Databasebeta

← #11779025

Subgroups — #11779025

Order 1152.

536 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#5579C211yesmaximal, characteristic, complemented
2#10592726C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71923—31nomaximal
9#68244—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64083C2211yescharacteristic
13C3×#946—21no—
14C3×#896—22no—
15C3×D3×C4⋊C4—21no—
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#870—21no—
19C3×#869C2211yescharacteristic
20C2×#3717—22no—
21C2×#3714—21no—
22#63636—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27C3×#554—31no—
28#5579D311yescharacteristic, complemented
29#5085—31no—
30#5027—31no—
31#5027—31no—
32#5027—61no—
33#5015—31no—
34#4843—31no—
35#4693—31no—
36C3×Q8⋊C8—31no—
37#4546—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4481—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54#3755—42no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—22no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—22no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#3717—44no—
66#3714—42no—
67#1622—91noSylow
68C3×C4⋊Q8—31no—
69C3×#125—61no—
70C3×C22⋊Q8—62no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—21no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C2×C3×C4⋊C4—61no—
78#946—21no—
79C2×#215—62no—
80C2×#215—62no—
81C2×#215—61no—
82C2×#215—61no—
83C2×#213—61no—
84C2×D24—61no—
85C2×#204—62no—
86#896—22no—
87D3×C4⋊C4—21no—
88#874—31no—
89#874—31no—
90#874—61no—
91C4×D12—21no—
92C4×D12C2×D311yescharacteristic
93#870—21no—
94#869C2×D311yescharacteristic
95C3×C4⋊C8—31no—
96C3×C4×C8—31no—
97#821—61no—
98#809—61no—
99#809—62no—
100#809—61no—
101#809—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—41no—
108C22×C3×D3—21no—
109C32×Q8—21no—
110C32×Q8—21no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—42no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—22no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×C4×D3—82no—
128C3×Dic6—42no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#554—31no—
133#492—91no—
134#460—91no—
135#459—91no—
136#333—91no—
137Q8⋊C8—31no—
138D4⋊C8—91no—
139C2×C3×Q8—21no—
140C2×C3×Q8—32no—
141C2×C3×Q8D1211yescharacteristic
142C2×C3×Q8#6711yescharacteristic
143C2×C3×D4—31no—
144C22×C3×C4—62no—
145C22×C3×C4—61no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—121no—
154C2×D12—121no—
155C2×D12#6711yescharacteristic
156C2×C4×D3—21no—
157C2×C4×D3—22no—
158C2×Dic6#6712yes—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—41no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—62no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4D1211yescharacteristic
171C3×C4⋊C4#6711yescharacteristic
172C3×C22⋊C4—62no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—41no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#215—124no—
181#215—124no—
182#215—122no—
183#215—122no—
184#213—122no—
185(C2×D3)⋊C4—22no—
186(C2×D3)⋊C4—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3#6711yescharacteristic
190Dic3⋊C4—22no—
191Dic3⋊C4—22no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197D24—122no—
198#204—124no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—81no—
201C2×C3⋊D3—81no—
202C2×C3⋊D3—81no—
203C2×C3×D3—22no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C32×C4—21no—
207C32×C4—41no—
208C32×C4—41no—
209C32×C4C2×SD1611yescharacteristic
210C32×C4#13511yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4#13711yescharacteristic
213C3×Dic3—41no—
214C3×Dic3—42no—
215C2×SD16—182no—
216C2×SD16—181no—
217C2×D8—181no—
218C4⋊Q8—31no—
219#127—91no—
220#125—61no—
221C22⋊Q8—62no—
222C22⋊Q8—61no—
223C4×Q8D3211yescharacteristic
224C4×D4—31no—
225C4×D4—61no—
226C2×C4⋊C4—61no—
227C4⋊C8—31no—
228C4⋊C8—91no—
229#102—181no—
230#102—181no—
231C4×C8—31no—
232C23×C3—61no—
233C22×D3—21no—
234C22×D3—122no—
235C22×D3—121no—
236C22×D3—121no—
237C3×Q8—22no—
238C3×Q8—21no—
239C3×Q8—21no—
240C3×Q8—21no—
241C3×Q8—21no—
242C3×Q8—41no—
243C3×Q8—122no—
244C3×D4—32no—
245C3×D4—61no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—61no—
256C2×C3×C4—62no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—242no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266C2×Dic3—21no—
267C2×Dic3—22no—
268D12—21no—
269D12—122no—
270D12—122no—
271D12—122no—
272D12—122no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—121no—
278D12—121no—
279D12—121no—
280D12—121no—
281D12—241no—
282D12—241no—
283D12—242no—
284D12#21512yescomplemented
285C4×D3—41no—
286C4×D3—41no—
287C4×D3—82no—
288Dic6—42no—
289C3×C8—62no—
290C3×C8—121no—
291C3⋊C8—22no—
292C3⋊C8—41no—
293C3⋊C8—122no—
294C3⋊C8—121no—
295C3⋊C8—121no—
296C2×C32#44811yescharacteristic
297C2×C32#44911yescharacteristic
298C2×C32#45311yescharacteristic
299C3⋊D3—161no—
300C3×D3—42no—
301C2×Q8—32no—
302C2×Q8#62611yescharacteristic
303C2×D4—31no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—62no—
308C22×C4—61no—
309SD16—364no—
310SD16—362no—
311D8—362no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—181no—
315C4⋊C4—21no—
316C4⋊C4—31no—
317C4⋊C4—62no—
318C4⋊C4—62no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4#62611yescharacteristic
322C22⋊C4—62no—
323C22⋊C4—61no—
324C42—21no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—62no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3#88211yescharacteristic
331C22×C3#95311yescharacteristic
332C2×D3—22no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—242no—
336C2×D3—242no—
337C2×D3—242no—
338C2×D3—241no—
339C2×D3—241no—
340C2×D3—241no—
341C2×D3—241no—
342C2×D3—241no—
343C2×D3—241no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—42no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—81no—
357C3×C4—121no—
358C3×C4—122no—
359C3×C4#90411yescharacteristic
360C3×C4#90811yescharacteristic
361C3×C4D3×SD1611yescharacteristic
362C3×C4#91811yescharacteristic
363C3×C4C2×#21511yescharacteristic
364C3×C4#94211yescharacteristic
365C3×C4#94911yescharacteristic
366C3×C4#95011yescharacteristic
367Dic3—41no—
368Dic3—42no—
369C32#162211yescharacteristic, complemented, Sylow
370C23—61no—
371C23—361no—
372Q8—21no—
373Q8—21no—
374Q8—122no—
375D4—32no—
376D4—61no—
377D4—362no—
378D4—361no—
379D4—361no—
380D4—361no—
381D4—361no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—61no—
385C2×C4—62no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—242no—
389C2×C4C2×#62611yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—62no—
393C8—121no—
394C8—361no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—122no—
399C2×C3#473411yescharacteristic
400C2×C3#480611yescharacteristic
401C2×C3#482211yescharacteristic
402C2×C3#522711yescharacteristic
403C2×C3#523811yescharacteristic
404C2×C3#524111yescharacteristic
405D3—42no—
406D3—482no—
407D3—481no—
408D3—481no—
409C22—62no—
410C22—121no—
411C22—121no—
412C22—721no—
413C22—721no—
414C22—721no—
415C22#6397711yescharacteristic
416C4—21no—
417C4—41no—
418C4—41no—
419C4—122no—
420C4—121no—
421C4#6382511yescharacteristic
422C4#6382911yescharacteristic
423C4D3×#21511yescharacteristic
424C4#6394811yescharacteristic
425C3—21no—
426C3#6824411yescharacteristic, complemented
427C3#7192311yescharacteristic, complemented
428C2—122no—
429C2—1441no—
430C2#1059116311yescharacteristic
431C2#1059158411yescharacteristic
432C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590349C2
hypercenterC4×Q8D32
hypocenterC32#1622
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
1. C3×#5579C2semidirect
2. #10592726C2semidirect
3. #10590373C2semidirect
5. C3×#4535C2semidirect
6. #10589095C2semidirect
7. #10589081C2semidirect
28. #5579D3semidirect
38. #4535D3semidirect
124. C3×D12SD16semidirect
284. D12#215semidirect
369. C32#1622semidirect
426. C3#68244semidirect
427. C3#71923semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
#105927262
#105903732
#105903492
C3×#45352
#105890952
#105890812
#719233
#682443