Finite Group Databasebeta

← #11780439

Subgroups — #11780439

Order 1152.

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

normal subgroups only

This group has 540 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×#5551C211yesmaximal, characteristic
2#10592718C211yesmaximal, characteristic, complemented
3#10590303C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71913—31nomaximal
9#68211—31nomaximal
10C2×C3×#235—21no—
11C32×C4×D4C2211yescharacteristic
12C2×#3754—21no—
13#64078C2211yescharacteristic
14C3×#938—21no—
15C3×#924—21no—
16C3×D3×C4⋊C4—21no—
17C3×#883—22no—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63637—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63573—22no—
26#63563—21no—
27C3×#547—31no—
28#5551D311yescharacteristic
29#5080—31no—
30#5019—31no—
31#5019—31no—
32#5019—61no—
33#5007—31no—
34#4846—31no—
35#4680—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4482—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C2×C3×#67—22no—
46C3×#235—42no—
47C3×#235—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55#3754—42no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—22no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1654—91noSylow
68C2×C3×#41—61no—
69C2×#235—21no—
70C3×C4⋊Q8—31no—
71C3×#123—62no—
72C3×C22⋊Q8—61no—
73C3×#121—61no—
74C3×C4×D4—21no—
75C3×C4×D4—31no—
76C3×C4×D4C2×D311yescharacteristic
77C3×C4×D4C2×D311yescharacteristic
78C2×C3×C4⋊C4—61no—
79#938—21no—
80C2×#214—62no—
81C2×#214—61no—
82C2×#214—61no—
83#924—21no—
84D3×C4⋊C4—21no—
85#883—22no—
86C4×D12C2×D311yescharacteristic
87#869—31no—
88#869—31no—
89#869—61no—
90#869C2×D311yescharacteristic
91C3×C4⋊C8—31no—
92C3×C4×C8—31no—
93#832—61no—
94#821—61no—
95#818—61no—
96#817—62no—
97#810—62no—
98#810—61no—
99#810—61no—
100#808—62no—
101#807—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C23×C32—21no—
108C22×C3×D3—21no—
109C32×D4—21no—
110C32×D4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—41no—
118#634—41no—
119#634—41no—
120C3×#67—44no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—22no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—44no—
126C3×C4×D3—41no—
127C3×C4×D3—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133#547—31no—
134#498—91no—
135#474—91no—
136#461—91no—
137#332—91no—
138D4⋊C8—31no—
139D4⋊C8—91no—
140C3×#41—122no—
141C3×#41—122no—
142C2×C3×Q8—61no—
143C2×C3×D4—21no—
144C2×C3×D4—31no—
145C2×C3×D4—62no—
146C2×C3×D4D1211yescharacteristic
147C2×C3×D4#6711yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—41no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153C2×#67—22no—
154#235—42no—
155#235—42no—
156C2×D12#6711yescharacteristic
157C2×C4×D3—22no—
158C2×C4×D3—21no—
159C2×Dic6—21no—
160C2×Dic6—62no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—32no—
168C3×C4⋊C4—62no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4D1211yescharacteristic
171C3×C4⋊C4#6711yescharacteristic
172C3×C22⋊C4—21no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—41no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—22no—
181#214—124no—
182#214—122no—
183#214—122no—
184(C2×D3)⋊C4—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3—121no—
192C4⋊Dic3#6712yes—
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—22no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32—41no—
203C22×C32#12011yescharacteristic
204C2×C3×D3—22no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C32×C4—21no—
208C32×C4—41no—
209C32×C4C2×SD1611yescharacteristic
210C32×C4#13511yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C32×C4AGL(1,ℤ/8)11yescharacteristic
213C3⋊Dic3—81no—
214C3×Dic3—41no—
215C3×Dic3—42no—
216C2×#41—61no—
217C2×SD16—181no—
218C4⋊Q8—31no—
219C4⋊Q8—91no—
220#123—62no—
221C22⋊Q8—61no—
222#121—61no—
223C4×D4—31no—
224C4×D4D3211yescharacteristic
225C2×C4⋊C4—61no—
226#107—181no—
227#106—182no—
228C4⋊C8—31no—
229C4⋊C8—91no—
230#103—181no—
231#102—181no—
232C4×C8—31no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—41no—
236C23×C3—61no—
237C22×D3—21no—
238C3×Q8—121no—
239C3×Q8—121no—
240C3×D4—22no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4—21no—
245C3×D4—32no—
246C3×D4—41no—
247C3×D4—61no—
248C3×D4—124no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—61no—
260C2×C3×C4—62no—
261C2×C3×C4—81no—
262C2×C3×C4—81no—
263C2×C3×C4—124no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4C2×D1211yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272#67—44no—
273C2×Dic3—21no—
274C2×Dic3—22no—
275C2×Dic3—122no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278D12—21no—
279D12#21412yescomplemented
280C4×D3—44no—
281C4×D3—41no—
282C4×D3—41no—
283Dic6—41no—
284Dic6—41no—
285Dic6—122no—
286Dic6—122no—
287Dic6—121no—
288Dic6—121no—
289Dic6—121no—
290Dic6—121no—
291C3×C8—62no—
292C3×C8—121no—
293C3⋊C8—22no—
294C3⋊C8—41no—
295C3⋊C8—122no—
296C3⋊C8—121no—
297C3⋊C8—121no—
298C2×C32—81no—
299C2×C32#44911yescharacteristic
300C2×C32#45011yescharacteristic
301C2×C32#45611yescharacteristic
302C3×D3—42no—
303#41—122no—
304#41—122no—
305C2×Q8—61no—
306C2×Q8—181no—
307C2×D4—31no—
308C2×D4—62no—
309C2×D4#62611yescharacteristic
310C22×C4—21no—
311C22×C4—62no—
312C22×C4—61no—
313SD16—362no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—181no—
317C4⋊C4—32no—
318C4⋊C4—31no—
319C4⋊C4—62no—
320C4⋊C4—61no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4#62611yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—62no—
326C22⋊C4—61no—
327C42C2×D3211yescharacteristic
328C22×C3—21no—
329C22×C3—42no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—62no—
337C22×C3—81no—
338C22×C3—81no—
339C22×C3—121no—
340C22×C3—121no—
341C22×C3#88211yescharacteristic
342C22×C3#95311yescharacteristic
343C2×D3—22no—
344C2×D3—41no—
345C2×D3—41no—
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—81no—
356C3×C4—121no—
357C3×C4—122no—
358C3×C4#90411yescharacteristic
359C3×C4#90811yescharacteristic
360C3×C4#91111yescharacteristic
361C3×C4D3×SD1611yescharacteristic
362C3×C4#93211yescharacteristic
363C3×C4C2×#21411yescharacteristic
364C3×C4#94911yescharacteristic
365C3×C4#95011yescharacteristic
366Dic3—42no—
367Dic3—41no—
368Dic3—242no—
369Dic3—241no—
370Dic3—241no—
371C32#165411yescharacteristic, complemented, Sylow
372C23—21no—
373C23—61no—
374Q8—121no—
375Q8—121no—
376Q8—361no—
377Q8—361no—
378D4—21no—
379D4—21no—
380D4—32no—
381D4—61no—
382D4—124no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—61no—
387C2×C4—62no—
388C2×C4—124no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—361no—
392C2×C4C2×#62611yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—62no—
396C8—121no—
397C8—361no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—82no—
402C2×C3—81no—
403C2×C3—81no—
404C2×C3—122no—
405C2×C3#473411yescharacteristic
406C2×C3#477611yescharacteristic
407C2×C3#482611yescharacteristic
408C2×C3#521811yescharacteristic
409C2×C3#523811yescharacteristic
410C2×C3#524611yescharacteristic
411D3—42no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—62no—
416C22—121no—
417C22—121no—
418C22#6397711yescharacteristic
419C4—21no—
420C4—41no—
421C4—121no—
422C4—122no—
423C4—721no—
424C4#6382511yescharacteristic
425C4#6382911yescharacteristic
426C4D3×#21411yescharacteristic
427C4#6393211yescharacteristic
428C3—21no—
429C3#6821111yescharacteristic, complemented
430C3#7191311yescharacteristic, complemented
431C2—81no—
432C2—122no—
433C2#1059116311yescharacteristic
434C2#1059145911yescharacteristic
435C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5551C2
hypercenterC4×D4D32
hypocenterC32#1654
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
2. #10592718C2semidirect
3. #10590303C2semidirect
4. #10590272C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589093C2semidirect
7. #10589081C2semidirect
39. D4⋊(C3⋊C8)D3semidirect
124. C3×D12SD16semidirect
279. D12#214semidirect
371. C32#1654semidirect
429. C3#68211semidirect
430. C3#71913semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
#105927182
#105903032
#105902722
C3×D4⋊(C3⋊C8)2
#105890932
#105890812
#719133
#682113