Finite Group Databasebeta

← #11780440

Subgroups — #11780440

Order 1152.

626 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 90 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#10596022C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3#10590313C211yesmaximal, characteristic, complemented
4#10590303C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71051—31nomaximal
9#68211—31nomaximal
10C2×#3828—21no—
11C32×C4×D4C2211yescharacteristic
12#64147—21no—
13#64133—21no—
14C4⋊C4×C3⋊D3—21no—
15#64092—22no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#810—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63573—22no—
26#63564—21no—
27#5551—31no—
28#5551—31no—
29#5551—61no—
30C3×#461—31no—
31#5087—31no—
32#5080—31no—
33#5019D311yescharacteristic, complemented
34#4846—31no—
35#4680—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4486—31no—
39#4483—31no—
40#4482—31no—
41#4459—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#638—22no—
45#3828—42no—
46#3828—42no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55#3757—22no—
56#3752—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D412yes—
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—22no—
61C3×#214—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1654—91noSylow
68C2×#235—61no—
69C2×#235—61no—
70C2×#235—62no—
71C2×C3×SD16—61no—
72C3×C4⋊Q8—31no—
73C3×C4×D4—21no—
74C3×C4×D4C2×D311yescharacteristic
75C3×C4×D4C2×D311yescharacteristic
76#938—62no—
77#938—61no—
78#938—61no—
79C2×#214—21no—
80#924—61no—
81#924—61no—
82#924—62no—
83D3×C4⋊C4—62no—
84D3×C4⋊C4—61no—
85D3×C4⋊C4—61no—
86#883—62no—
87#883—62no—
88#883—64no—
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—61no—
92#869—31no—
93#869—31no—
94#869—61no—
95#869C2×D311yescharacteristic
96C3×C4⋊C8—31no—
97C3×C4⋊C8—31no—
98C3×#103—61no—
99C3×C4×C8—31no—
100#821—61no—
101#818—61no—
102#817—62no—
103#810—21no—
104#809—61no—
105#808—62no—
106#807—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C23×C32—21no—
111C22×C3⋊D3—21no—
112C32×D4—21no—
113C32×D4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—44no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—22no—
123C4⋊(C3⋊D3)—21no—
124C4⋊(C3⋊D3)SD1612yescomplemented
125C4×C3⋊D3—44no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128#634—41no—
129#634—41no—
130C2×C3×Dic3—41no—
131C3×Dic6—41no—
132C3×Dic6—41no—
133C3×C3⋊C8—22no—
134C3×C3⋊C8—41no—
135C3×C3⋊C8—41no—
136#547—91no—
137#498—91no—
138#474—91no—
139#461—31no—
140#332—91no—
141D4⋊C8—31no—
142D4⋊C8—91no—
143C2×C3×Q8—61no—
144C2×C3×D4—21no—
145C2×C3×D4D1211yescharacteristic
146C2×C3×D4#6711yescharacteristic
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C2×#67—64no—
151C2×#67—62no—
152C2×#67—62no—
153#235—122no—
154#235—122no—
155#235—124no—
156#235—124no—
157#235—122no—
158#235—122no—
159C2×D12—31no—
160C2×D12—31no—
161C2×D12—61no—
162C2×C4×D3—62no—
163C2×C4×D3—64no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×Dic6—21no—
169C2×Dic6—62no—
170C2×Dic6—61no—
171C2×Dic6—61no—
172C3×SD16—122no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4D1211yescharacteristic
180C3×C4⋊C4#6711yescharacteristic
181C3×C22⋊C4—22no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C42—21no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—64no—
188#217—62no—
189#217—62no—
190#214—42no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—31no—
197C4⋊Dic3—32no—
198C4⋊Dic3—32no—
199C4⋊Dic3—31no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—62no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205Dic3⋊C4—64no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—21no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32#12011yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4C2×SD1611yescharacteristic
221C32×C4#13511yescharacteristic
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C32×C4AGL(1,ℤ/8)11yescharacteristic
224C3⋊Dic3—41no—
225C3⋊Dic3—42no—
226C3×Dic3—81no—
227C2×#41—181no—
228C2×SD16—61no—
229C4⋊Q8—31no—
230C4⋊Q8—91no—
231#123—182no—
232C22⋊Q8—181no—
233#121—181no—
234C4×D4—91no—
235C4×D4D3211yescharacteristic
236C2×C4⋊C4—181no—
237#107—181no—
238#106—182no—
239C4⋊C8—31no—
240C4⋊C8—31no—
241#103—61no—
242#102—181no—
243C4×C8—31no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—21no—
247C22×D3—62no—
248C22×D3—61no—
249C22×D3—61no—
250C3×Q8—121no—
251C3×Q8—121no—
252C3×D4—21no—
253C3×D4—21no—
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—41no—
257C3×D4—41no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—121no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—128no—
278#67—124no—
279#67—124no—
280C2×Dic3—41no—
281C2×Dic3—62no—
282C2×Dic3—64no—
283C2×Dic3—61no—
284C2×Dic3—62no—
285C2×Dic3—61no—
286C2×Dic3—62no—
287D12—32no—
288D12—32no—
289D12—62no—
290D12—62no—
291D12—61no—
292D12—61no—
293C4×D3—122no—
294C4×D3—122no—
295C4×D3—128no—
296C4×D3—124no—
297C4×D3—124no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—121no—
301C4×D3—121no—
302Dic6—41no—
303Dic6—41no—
304Dic6—122no—
305Dic6—122no—
306Dic6—121no—
307Dic6—121no—
308Dic6—121no—
309Dic6—121no—
310C3×C8—62no—
311C3×C8—121no—
312C3×C8—121no—
313C3⋊C8—22no—
314C3⋊C8—41no—
315C3⋊C8—41no—
316C2×C32—81no—
317C2×C32#44911yescharacteristic
318C2×C32#45011yescharacteristic
319C2×C32#45611yescharacteristic
320C3⋊D3—42no—
321#41—362no—
322#41—362no—
323C2×Q8—61no—
324C2×Q8—181no—
325C2×D4—91no—
326C2×D4—182no—
327C2×D4#62611yescharacteristic
328C22×C4—21no—
329C22×C4—182no—
330C22×C4—181no—
331SD16—122no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—92no—
338C4⋊C4—91no—
339C4⋊C4—182no—
340C4⋊C4—181no—
341C4⋊C4#62611yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—182no—
344C22⋊C4—181no—
345C42C2×D3211yescharacteristic
346C22×C3—21no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3#88211yescharacteristic
357C22×C3#93711yescharacteristic
358C2×D3—64no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—121no—
366C2×D3—121no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—42no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—241no—
378C3×C4#90411yescharacteristic
379C3×C4#90811yescharacteristic
380C3×C4#91111yescharacteristic
381C3×C4D3×SD1611yescharacteristic
382C3×C4D3×SD1611yescharacteristic
383C3×C4#91411yescharacteristic
384C3×C4#93211yescharacteristic
385C3×C4#95011yescharacteristic
386Dic3—81no—
387Dic3—124no—
388Dic3—122no—
389Dic3—122no—
390Dic3—121no—
391Dic3—122no—
392Dic3—121no—
393C32#165411yescharacteristic, complemented, Sylow
394C23—21no—
395C23—181no—
396Q8—121no—
397Q8—121no—
398Q8—361no—
399Q8—361no—
400D4—21no—
401D4—21no—
402D4—92no—
403D4—181no—
404D4—364no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—121no—
409C2×C4—181no—
410C2×C4—182no—
411C2×C4—364no—
412C2×C4—361no—
413C2×C4—361no—
414C2×C4C2×#62611yescharacteristic
415C2×C4#381111yescharacteristic
416C2×C4#381111yescharacteristic
417C8—62no—
418C8—121no—
419C8—121no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—82no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3#473411yescharacteristic
427C2×C3#477611yescharacteristic
428C2×C3#482611yescharacteristic
429C2×C3#503711yescharacteristic
430C2×C3#516911yescharacteristic
431C2×C3#520511yescharacteristic
432D3—124no—
433D3—122no—
434D3—122no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—182no—
439C22—361no—
440C22—361no—
441C22#6398111yescharacteristic
442C4—21no—
443C4—41no—
444C4—241no—
445C4—361no—
446C4—362no—
447C4#6382911yescharacteristic
448C4#6383011yescharacteristic
449C4#6393011yescharacteristic
450C4#6393711yescharacteristic
451C3—21no—
452C3#6821111yescharacteristic, complemented
453C3#7105111yescharacteristic, complemented
454C2—81no—
455C2—362no—
456C2#1059118211yescharacteristic
457C2#1059146711yescharacteristic
458C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radical#10596022C2
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. C3×#5019C2semidirect
3. #10590313C2semidirect
4. #10590303C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589094C2semidirect
7. #10589082C2semidirect
33. #5019D3semidirect
37. D4⋊(C3⋊C8)D3semidirect
124. C4⋊(C3⋊D3)SD16semidirect
393. C32#1654semidirect
452. C3#68211semidirect
453. C3#71051semidirect

Maximal subgroups

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

subgroupindex
#105960222
C3×#50192
#105903132
#105903032
C3×D4⋊(C3⋊C8)2
#105890942
#105890822
#710513
#682113