Finite Group Databasebeta

← #11779233

Subgroups — #11779233

Order 1152.

541 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 104 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×D4×Dic6C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3#10590364C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71914—31nomaximal
9#71014—31nomaximal
10C22×C3×Dic6—21no—
11C32×C4×D4C2211yescharacteristic
12C3×D4×Dic3—21no—
13C2×C3×#213—21no—
14C3×#924—21no—
15C3×#888—21no—
16C3×#878—22no—
17C3×#874C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C2×#3715—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#809—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63562—22no—
26#63562—21no—
27C3×D4×Q8—31no—
28D4×Dic6D311yescharacteristic, complemented
29C3×#459—31no—
30#5088—31no—
31#5075—31no—
32#5070—31no—
33#5027—31no—
34#5015D311yescharacteristic
35#4547—31no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4486—31no—
41#4484—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3×Dic3—22no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6—21no—
50C2×C3×Dic6—42no—
51C2×C3×Dic6—42no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—22no—
59C3×#213—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—22no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67#3715—42no—
68#1627—91noSylow
69C22×C3×Q8—61no—
70C22×Dic6—21no—
71C2×C3×D8—61no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8—61no—
74C3×#127—31no—
75C3×C22⋊Q8—62no—
76C3×C22⋊Q8—61no—
77C3×C4×Q8—31no—
78C3×C4×D4—21no—
79C3×C4×D4—61no—
80C3×C4×D4C2×D311yescharacteristic
81C3×C4×D4C2×D311yescharacteristic
82C2×#215—61no—
83D4×Dic3—21no—
84C2×#214—61no—
85C2×#213—21no—
86#924—21no—
87#888—21no—
88#878—22no—
89#874C2×D311yescharacteristic
90#869C2×D311yescharacteristic
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×#102—61no—
94#832—62no—
95#832—61no—
96#809—21no—
97#809—61no—
98#809—62no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—31no—
104C4×C3⋊C8—31no—
105C4×C3⋊C8—61no—
106C23×C32—21no—
107C22×C3×D3—41no—
108C32×D4—21no—
109C32×D4SD1612yescomplemented
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—44no—
120C3×D12—42no—
121C3×D12—41no—
122C3×D12—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×Dic6—21no—
126C3×Dic6—44no—
127C3×Dic6—41no—
128C3×Dic6—41no—
129C3×Dic6D812yescomplemented
130C3⋊(C3⋊C8)—41no—
131C3⋊(C3⋊C8)—41no—
132C3×C3⋊C8—41no—
133D4×Q8—31no—
134#486—91no—
135#460—91no—
136#459—31no—
137#332—91no—
138Q8⋊C8—91no—
139D4⋊C8—91no—
140C2×C3×Q8—31no—
141C2×C3×Q8—62no—
142C2×C3×Q8—61no—
143C2×C3×Q8—122no—
144C2×C3×Q8—122no—
145C2×C3×D4—21no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4#6711yescharacteristic
150C2×C3×D4#6711yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—41no—
154C22×C3×C4—62no—
155C22×Dic3—22no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12—21no—
159C2×Dic6—22no—
160C2×Dic6—21no—
161C2×Dic6—42no—
162C2×Dic6—42no—
163C2×Dic6#6711yescharacteristic
164C3×D8—122no—
165C2×C3×C8—61no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4#6711yescharacteristic
173C3×C4⋊C4#6711yescharacteristic
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—41no—
177C3×C22⋊C4—62no—
178C3×C42—21no—
179C3×C42—61no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#217—22no—
183#215—122no—
184#214—122no—
185#213—42no—
186C4⋊Dic3—21no—
187C4⋊Dic3#6711yescharacteristic
188C4⋊Dic3#6712yes—
189Dic3⋊C4—22no—
190Dic3⋊C4—21no—
191C4×Dic3—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—121no—
198C2×C3⋊C8—121no—
199C22×C32—22no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32#12011yescharacteristic
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—81no—
206C32×C4—21no—
207C32×C4—41no—
208C32×C4C2×D811yescharacteristic
209C32×C4C2×SD1611yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C32×C4#13711yescharacteristic
212C3×Dic3—22no—
213C3×Dic3—42no—
214C3×Dic3—41no—
215C22×Q8—61no—
216C2×SD16—181no—
217C2×D8—61no—
218C4⋊Q8—31no—
219C4⋊Q8—61no—
220#127—31no—
221C22⋊Q8—62no—
222C22⋊Q8—61no—
223C4×Q8—31no—
224C4×D4—61no—
225C4×D4D3211yescharacteristic
226C4⋊C8—31no—
227C4⋊C8—91no—
228#102—61no—
229#102—181no—
230#102—182no—
231C4×C8—91no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—41no—
235C23×C3—121no—
236C22×D3—41no—
237C3×Q8—32no—
238C3×Q8—61no—
239C3×Q8—124no—
240C3×Q8—121no—
241C3×Q8—121no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—22no—
245C3×D4—41no—
246C3×D4—122no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C3×D4—121no—
251C3×D4#21412yescomplemented
252C3×D4#21512yescomplemented
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—62no—
266C2×C3×C4—81no—
267C2×C3×C4—81no—
268C2×C3×C4—124no—
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—22no—
278C2×Dic3—44no—
279D12—42no—
280D12—41no—
281D12—41no—
282D12—41no—
283D12—41no—
284Dic6—21no—
285Dic6—44no—
286Dic6—41no—
287Dic6—41no—
288Dic6#21312yescomplemented
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—121no—
292C3⋊C8—121no—
293C3⋊C8—122no—
294C3⋊C8—121no—
295C3⋊C8—121no—
296C3⋊C8—241no—
297C2×C32—42no—
298C2×C32#44711yescharacteristic
299C2×C32#44811yescharacteristic
300C2×C32#45411yescharacteristic
301C3×D3—161no—
302C2×Q8—31no—
303C2×Q8—62no—
304C2×Q8—61no—
305C2×Q8—122no—
306C2×Q8—122no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—61no—
310C2×D4#62511yescharacteristic
311C22×C4—21no—
312C22×C4—62no—
313SD16—362no—
314D8—122no—
315C2×C8—61no—
316C2×C8—181no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—32no—
320C4⋊C4—62no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4#62511yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—62no—
326C42—61no—
327C42C2×D3211yescharacteristic
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—42no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—81no—
337C22×C3—81no—
338C22×C3—241no—
339C22×C3—241no—
340C22×C3—241no—
341C22×C3#93711yescharacteristic
342C22×C3#95311yescharacteristic
343C2×D3—81no—
344C2×D3—81no—
345C2×D3—81no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—62no—
356C3×C4—81no—
357C3×C4—122no—
358C3×C4—121no—
359C3×C4D3×D811yescharacteristic
360C3×C4#91111yescharacteristic
361C3×C4C2×#21311yescharacteristic
362C3×C4#93211yescharacteristic
363C3×C4C2×#21411yescharacteristic
364C3×C4C2×#21511yescharacteristic
365C3×C4#94211yescharacteristic
366C3×C4#95111yescharacteristic
367Dic3—22no—
368Dic3—42no—
369Dic3—41no—
370C32#162711yescharacteristic, complemented, Sylow
371C23—21no—
372C23—121no—
373Q8—32no—
374Q8—61no—
375Q8—124no—
376Q8—121no—
377Q8—121no—
378D4—21no—
379D4—122no—
380D4—121no—
381D4—121no—
382D4—121no—
383D4—121no—
384D4#371512yescomplemented
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—62no—
391C2×C4—124no—
392C2×C4C2×#62511yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—121no—
396C8—361no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—42no—
402C2×C3—42no—
403C2×C3—82no—
404C2×C3—481no—
405C2×C3#504011yescharacteristic
406C2×C3#515611yescharacteristic
407C2×C3#520111yescharacteristic
408C2×C3#521711yescharacteristic
409C2×C3#522711yescharacteristic
410C2×C3#524511yescharacteristic
411D3—161no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—241no—
416C22—241no—
417C22—241no—
418C22#6397611yescharacteristic
419C4—21no—
420C4—41no—
421C4—62no—
422C4—121no—
423C4—122no—
424C4C2×#371511yescharacteristic
425C4#6382711yescharacteristic
426C4D3×#21311yescharacteristic
427C4#6393211yescharacteristic
428C3—21no—
429C3#7101411yescharacteristic, complemented
430C3#7191411yescharacteristic, complemented
431C2—42no—
432C2—481no—
433C2#1059117111yescharacteristic
434C2#1059144711yescharacteristic
435C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×D4×Dic6C2semidirect
3. #10590364C2semidirect
4. #10590277C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589092C2semidirect
7. #10589083C2semidirect
28. D4×Dic6D3semidirect
109. C32×D4SD16semidirect
129. C3×Dic6D8semidirect
251. C3×D4#214semidirect
252. C3×D4#215semidirect
288. Dic6#213semidirect
370. C32#1627semidirect
384. D4#3715semidirect
429. C3#71014semidirect
430. C3#71914semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
C3×#50152
#105903642
#105902772
D4⋊(C3⋊(C3⋊C8))2
#105890922
#105890832
#719143
#710143