Finite Group Databasebeta

← #11780448

Subgroups — #11780448

Order 1152.

534 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5555C211yesmaximal, characteristic
2#10592706C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590303C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71913—31nomaximal
9#68185—31nomaximal
10C2×C3×#237—21no—
11C32×C4×D4C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×#930—21no—
14C2×C3×C4⋊Dic3—21no—
15C3×#897—21no—
16C3×#886—22no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3716—21no—
20#63659—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63573—22no—
26#63567—21no—
27C3×#547—31no—
28#5555D311yescharacteristic
29#5080—31no—
30#5019—31no—
31#5007—31no—
32#5007—31no—
33#5007—61no—
34#4841—31no—
35#4680—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)D311yescharacteristic, complemented
40#4486—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#237—42no—
48C3×#237—42no—
49C2×C3×D12D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D412yes—
63C3×C4⋊Dic3D411yescharacteristic
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3716—42no—
67#1654—91noSylow
68C2×C3×#41—61no—
69C2×#237—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—
79C2×#214—61no—
80#930—21no—
81C2×C4⋊Dic3—21no—
82C2×#204—61no—
83#897—21no—
84#886—22no—
85C4×D12C2×D311yescharacteristic
86#869—31no—
87#869—31no—
88#869—61no—
89#869C2×D311yescharacteristic
90C3×C4⋊C8—31no—
91C3×C4×C8—31no—
92#832—62no—
93#832—61no—
94#832—61no—
95#817—62no—
96#816—61no—
97#810—61no—
98#808—62no—
99#807—62no—
100#807—61no—
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×D4SD1612yescomplemented
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—22no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—44no—
124C3×D12—21no—
125C3×D12—21no—
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—
154C22×Dic3—22no—
155#237—42no—
156#237—42no—
157C2×D12#6711yescharacteristic
158C2×C4×D3—21no—
159C2×Dic6—21no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—121no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—32no—
167C3×C4⋊C4—31no—
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#214—122no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—22no—
184C4⋊Dic3—21no—
185C4⋊Dic3—62no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—121no—
191C4⋊Dic3#6711yescharacteristic
192C4⋊Dic3#6712yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198#204—122no—
199C22×C32—22no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32#12011yescharacteristic
203C2×C3×D3—41no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C32×C4—21no—
207C32×C4—41no—
208C32×C4C2×SD1611yescharacteristic
209C32×C4#13511yescharacteristic
210C32×C4AGL(1,ℤ/8)11yescharacteristic
211C32×C4AGL(1,ℤ/8)11yescharacteristic
212C3⋊Dic3—81no—
213C3×Dic3—42no—
214C3×Dic3—41no—
215C2×#41—61no—
216C2×SD16—181no—
217C4⋊Q8—31no—
218C4⋊Q8—91no—
219#123—62no—
220C22⋊Q8—61no—
221#121—61no—
222C4×D4—31no—
223C4×D4D3211yescharacteristic
224C2×C4⋊C4—61no—
225#107—181no—
226#106—182no—
227C4⋊C8—31no—
228C4⋊C8—91no—
229#103—181no—
230#102—181no—
231C4×C8—31no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—41no—
235C23×C3—61no—
236C22×D3—21no—
237C3×Q8—121no—
238C3×Q8—121no—
239C3×D4—21no—
240C3×D4—21no—
241C3×D4—22no—
242C3×D4—41no—
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—124no—
246C3×D4#20412yescomplemented
247C3×D4#21412yescomplemented
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—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—61no—
259C2×C3×C4—62no—
260C2×C3×C4—81no—
261C2×C3×C4—81no—
262C2×C3×C4—124no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—44no—
272C2×Dic3—22no—
273C2×Dic3—21no—
274C2×Dic3—44no—
275C2×Dic3—122no—
276C2×Dic3—121no—
277C2×Dic3—121no—
278D12—21no—
279D12—21no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—41no—
283Dic6—41no—
284Dic6—121no—
285Dic6—121no—
286Dic6—121no—
287Dic6—121no—
288Dic6—241no—
289Dic6—241no—
290C3×C8—62no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—41no—
294C3⋊C8—122no—
295C3⋊C8—121no—
296C3⋊C8—121no—
297C2×C32—42no—
298C2×C32#44911yescharacteristic
299C2×C32#45011yescharacteristic
300C2×C32#45611yescharacteristic
301C3×D3—81no—
302#41—122no—
303#41—122no—
304C2×Q8—61no—
305C2×Q8—181no—
306C2×D4—31no—
307C2×D4—62no—
308C2×D4#62611yescharacteristic
309C22×C4—21no—
310C22×C4—62no—
311C22×C4—61no—
312SD16—362no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—31no—
317C4⋊C4—32no—
318C4⋊C4—62no—
319C4⋊C4—61no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4#62611yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—62no—
325C22⋊C4—61no—
326C42C2×D3211yescharacteristic
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—21no—
330C22×C3—42no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3#88211yescharacteristic
341C22×C3#95311yescharacteristic
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—81no—
355C3×C4—121no—
356C3×C4—122no—
357C3×C4C2×#20411yescharacteristic
358C3×C4#90811yescharacteristic
359C3×C4#91111yescharacteristic
360C3×C4#91611yescharacteristic
361C3×C4#93211yescharacteristic
362C3×C4C2×#21411yescharacteristic
363C3×C4#94911yescharacteristic
364C3×C4#95011yescharacteristic
365Dic3—42no—
366Dic3—41no—
367Dic3—242no—
368Dic3—241no—
369Dic3—241no—
370C32#165411yescharacteristic, complemented, Sylow
371C23—21no—
372C23—61no—
373Q8—121no—
374Q8—121no—
375Q8—361no—
376Q8—361no—
377D4—21no—
378D4—61no—
379D4—61no—
380D4—124no—
381D4#371612yescomplemented
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—61no—
386C2×C4—62no—
387C2×C4—124no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—361no—
391C2×C4C2×#62611yescharacteristic
392C2×C4D3×#6711yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C8—62no—
395C8—121no—
396C8—361no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—42no—
401C2×C3—42no—
402C2×C3—82no—
403C2×C3—241no—
404C2×C3#473111yescharacteristic
405C2×C3#478111yescharacteristic
406C2×C3#482611yescharacteristic
407C2×C3#521811yescharacteristic
408C2×C3#523811yescharacteristic
409C2×C3#524611yescharacteristic
410D3—81no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—121no—
415C22—121no—
416C22—121no—
417C22#6397711yescharacteristic
418C4—21no—
419C4—41no—
420C4—121no—
421C4—122no—
422C4—721no—
423C4C2×#371611yescharacteristic
424C4#6383011yescharacteristic
425C4#6392511yescharacteristic
426C4#6393511yescharacteristic
427C3—21no—
428C3#6818511yescharacteristic, complemented
429C3#7191311yescharacteristic, complemented
430C2—42no—
431C2—241no—
432C2#1059117211yescharacteristic
433C2#1059145211yescharacteristic
434C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5555C2
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. #10592706C2semidirect
3. #10590365C2semidirect
4. #10590303C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589092C2semidirect
7. #10589081C2semidirect
39. D4⋊(C3⋊C8)D3semidirect
110. C32×D4SD16semidirect
246. C3×D4#204semidirect
247. C3×D4#214semidirect
370. C32#1654semidirect
381. D4#3716semidirect
428. C3#68185semidirect
429. C3#71913semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
#105927062
#105903652
#105903032
C3×D4⋊(C3⋊C8)2
#105890922
#105890812
#719133
#681853