Finite Group Databasebeta

← #11780437

Subgroups — #11780437

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#10596197C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic, complemented
3#10590379C211yesmaximal, characteristic, complemented
4#10590313C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589082C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#71343—31nomaximal
9#68439—31nomaximal
10C2×#3832—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64155—21no—
13#64104—21no—
14#64103—22no—
15C4⋊C4×C3⋊D3—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3717—21no—
20C3×#808—22no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—21no—
25#63566—21no—
26#63564—21no—
27#5726—31no—
28#5726—31no—
29#5726—61no—
30C3×#498—31no—
31#5087—31no—
32#5083—31no—
33#5080D311yescharacteristic, complemented
34#4846—31no—
35#4841—31no—
36C3×#332—31no—
37#4547D311yescharacteristic, complemented
38#4483—31no—
39#4483—31no—
40#4459—31no—
41#4459—31no—
42C2×C32×Q8—21no—
43#3832—42no—
44#3832—42no—
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)D411yescharacteristic
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4×C3⋊D3—22no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C3×Dic6—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4D412yes—
54C32×C42C2311yescharacteristic
55#3752—22no—
56#3752—21no—
57#3752—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C4⋊(C3⋊Dic3)D411yescharacteristic
60#3750—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3717—42no—
67#1654—91noSylow
68C2×#239—61no—
69C2×#239—61no—
70C2×#239—62no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75#946—61no—
76#946—61no—
77#946—62no—
78C2×#215—61no—
79C2×#204—61no—
80#895—61no—
81#895—61no—
82#895—62no—
83#894—64no—
84#894—62no—
85#894—62no—
86D3×C4⋊C4—61no—
87D3×C4⋊C4—61no—
88D3×C4⋊C4—62no—
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—31no—
92C4×D12—31no—
93C4×D12—61no—
94C4×D12—61no—
95#869C2×D311yescharacteristic
96C3×#106—62no—
97C3×C4⋊C8—31no—
98C3×C4⋊C8—31no—
99C3×C4×C8—31no—
100#835—61no—
101#821—61no—
102#818—61no—
103#816—61no—
104#809—61no—
105#808—22no—
106#807—61no—
107C4⋊(C3⋊C8)C2×D311yescharacteristic
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4×C3⋊C8C2×D311yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C32×Q8—41no—
113C32×Q8—41no—
114C2×C32×C4—22no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)—44no—
124C4⋊(C3⋊D3)SD1612yescomplemented
125C4×C3⋊D3—44no—
126C4×C3⋊D3—41no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—41no—
129C4×C3⋊D3—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—31no—
138#474—91no—
139#461—91no—
140#332—31no—
141D4⋊C8—91no—
142D4⋊C8—91no—
143C2×C3×Q8—22no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—61no—
147#239—122no—
148#239—122no—
149#239—124no—
150#239—124no—
151#239—122no—
152#239—122no—
153C2×D12—31no—
154C2×D12—31no—
155C2×D12—31no—
156C2×D12—31no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—64no—
160C2×D12—62no—
161C2×D12—62no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—64no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×Dic6—21no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4D1212yes—
182C3×C4⋊C4#6712yes—
183C3×C42—21no—
184C3×C42C22×D311yescharacteristic
185C3×C42C22×D311yescharacteristic
186#215—122no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—62no—
189(C2×D3)⋊C4—64no—
190(C2×D3)⋊C4—62no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3—31no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204Dic3⋊C4—64no—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210#204—122no—
211C22×C32#12011yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—41no—
214C2×C3⋊D3—41no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—42no—
220C32×C4C2×SD1611yescharacteristic
221C32×C4#13511yescharacteristic
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C32×C4AGL(1,ℤ/8)11yescharacteristic
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3×Dic3—81no—
227C2×#41—181no—
228C2×SD16—181no—
229C4⋊Q8—31no—
230C4⋊Q8D3211yescharacteristic
231#123—182no—
232C22⋊Q8—181no—
233#121—181no—
234C4×D4—91no—
235C4×D4—91no—
236C2×C4⋊C4—181no—
237#107—181no—
238#106—62no—
239C4⋊C8—31no—
240C4⋊C8—31no—
241#103—181no—
242#102—181no—
243C4×C8—31no—
244C22×D3—62no—
245C22×D3—61no—
246C22×D3—61no—
247C22×D3—62no—
248C22×D3—61no—
249C22×D3—61no—
250C3×Q8—42no—
251C3×Q8—42no—
252C3×Q8—41no—
253C3×Q8—41no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—121no—
257C3×Q8—121no—
258C2×C3×C4—24no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—41no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278D12—32no—
279D12—32no—
280D12—62no—
281D12—62no—
282D12—61no—
283D12—61no—
284D12—61no—
285D12—61no—
286D12—61no—
287D12—61no—
288D12—121no—
289D12—121no—
290D12—128no—
291D12—124no—
292D12—124no—
293C4×D3—122no—
294C4×D3—122no—
295C4×D3—122no—
296C4×D3—122no—
297C4×D3—128no—
298C4×D3—124no—
299C4×D3—124no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—121no—
303C4×D3—121no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308Dic6—41no—
309Dic6—41no—
310C3×C8—62no—
311C3×C8—121no—
312C3×C8—121no—
313C3⋊C8—22no—
314C3⋊C8—41no—
315C3⋊C8—41no—
316C2×C32#44911yescharacteristic
317C2×C32#45011yescharacteristic
318C2×C32#45611yescharacteristic
319C3⋊D3—42no—
320C3⋊D3—81no—
321#41—362no—
322#41—362no—
323C2×Q8—21no—
324C2×Q8—61no—
325C2×D4—91no—
326C2×D4—91no—
327C2×D4—182no—
328C22×C4—182no—
329C22×C4—181no—
330C22×C4—181no—
331SD16—362no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—21no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—91no—
339C4⋊C4—91no—
340C4⋊C4—182no—
341C4⋊C4#62612yes—
342C22⋊C4—182no—
343C22⋊C4—181no—
344C22⋊C4—181no—
345C42C2×D3211yescharacteristic
346C22×C3—21no—
347C22×C3#88211yescharacteristic
348C22×C3#93711yescharacteristic
349C2×D3—64no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—122no—
359C2×D3—122no—
360C2×D3—122no—
361C2×D3—121no—
362C2×D3—121no—
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—44no—
375C3×C4—42no—
376C3×C4—42no—
377C3×C4—241no—
378C3×C4#91111yescharacteristic
379C3×C4D3×SD1611yescharacteristic
380C3×C4D3×SD1611yescharacteristic
381C3×C4#91411yescharacteristic
382C3×C4#91411yescharacteristic
383C3×C4#91411yescharacteristic
384C3×C4#91611yescharacteristic
385C3×C4#91911yescharacteristic
386Dic3—81no—
387Dic3—122no—
388Dic3—122no—
389Dic3—121no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393C32#165411yescharacteristic, complemented, Sylow
394C23—181no—
395C23—181no—
396Q8—41no—
397Q8—41no—
398Q8—121no—
399Q8—121no—
400D4—92no—
401D4—181no—
402D4—181no—
403D4—181no—
404D4—364no—
405C2×C4—22no—
406C2×C4—121no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—364no—
410C2×C4—361no—
411C2×C4—361no—
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#475211yescharacteristic
424C2×C3#477611yescharacteristic
425C2×C3#481011yescharacteristic
426C2×C3#509511yescharacteristic
427C2×C3#516911yescharacteristic
428C2×C3#517211yescharacteristic
429D3—124no—
430D3—122no—
431D3—122no—
432D3—242no—
433D3—241no—
434D3—241no—
435C22—182no—
436C22—361no—
437C22—361no—
438C22—361no—
439C22—361no—
440C22—361no—
441C22#6398111yescharacteristic
442C4—21no—
443C4—42no—
444C4—241no—
445C4—361no—
446C4—361no—
447C4#6393011yescharacteristic
448C4#6393711yescharacteristic
449C4#6394111yescharacteristic
450C4#6395011yescharacteristic
451C3—21no—
452C3#6843911yescharacteristic, complemented
453C3#7134311yescharacteristic, complemented
454C2—362no—
455C2—721no—
456C2#1059146711yescharacteristic
457C2#1059159311yescharacteristic
458C2#1059165011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radical#10596197C2
hypercenterC4⋊Q8D32
hypocenterC32#1654
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
2. C3×#5080C2semidirect
3. #10590379C2semidirect
4. #10590313C2semidirect
5. C3×#4547C2semidirect
6. #10589082C2semidirect
7. #10589082C2semidirect
33. #5080D3semidirect
37. #4547D3semidirect
124. C4⋊(C3⋊D3)SD16semidirect
393. C32#1654semidirect
452. C3#68439semidirect
453. C3#71343semidirect

Maximal subgroups

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

subgroupindex
#105961972
C3×#50802
#105903792
#105903132
C3×#45472
#105890822
#713433
#684393