Finite Group Databasebeta

← #11775368

Subgroups — #11775368

Order 1152.

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

normal subgroups only

This group has 499 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#10594965C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic, complemented
3#10591360C211yesmaximal, characteristic, complemented
4C3×#4470C211yesmaximal, characteristic
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic
8#68312—31nomaximal
9#68280—31nomaximal
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C3×#924C2211yescharacteristic
13#67⋊Dic3—21no—
14C2×#3724—21no—
15#63962—21no—
16#63898C411yescharacteristic, complemented
17#63878—21no—
18#63872C411yescharacteristic, complemented
19#63863C411yescharacteristic, complemented
20#63862—21no—
21#63843C411yescharacteristic, complemented
22C32×C22⋊C8C2211yescharacteristic
23#63657C2211yescharacteristic
24#63642—21no—
25#63641—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×C3⋊#95C2211yescharacteristic
28#63579—21no—
29#5624—31no—
30#5600—31no—
31#4719—31no—
32#4719—31no—
33#4719—61no—
34#4650—31no—
35#4650—31no—
36C3×#328—31no—
37C3×#327—31no—
38#4538—31no—
39#4537—31no—
40#4470D311yescharacteristic
41#4467D311yescharacteristic, complemented
42#4452—31no—
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12C2×C411yescharacteristic
51C2×C3×Dic6C2×C411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×C4⋊Dic3C2×C411yescharacteristic
63C3×Dic3⋊C4—21no—
64#3724—42no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1512—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75#947—31no—
76Q8×Dic3—31no—
77#936—31no—
78#935—61no—
79D4×Dic3—31no—
80D4×Dic3—61no—
81#930C2×D311yescharacteristic
82#924C2×D311yescharacteristic
83C2×Dic3⋊C4—61no—
84C2×Dic3⋊C4—61no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—31no—
87C2×C4×Dic3—61no—
88#898—61no—
89#893—31no—
90#892—61no—
91#890—31no—
92#890—31no—
93#887—31no—
94#886—61no—
95#67⋊C4—61no—
96#879—61no—
97#877—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102C3×#95—31no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#815—61no—
111#815—61no—
112#815—62no—
113Dic3⋊C8—61no—
114Dic3⋊C8—61no—
115Dic3⋊C8—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C2×C3⋊Dic3C22⋊C411yescharacteristic
127C2×C3⋊Dic3C22⋊C411yescharacteristic
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×D12—41no—
140C3×Dic6—41no—
141D3×Dic3—42no—
142C32×C8—41no—
143C3⋊(C3⋊C8)—41no—
144#529—91no—
145#432—91no—
146#382—91no—
147#328—31no—
148#328—91no—
149#327—31no—
150#327—91no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—21no—
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C2×D12C4×D311yescharacteristic
170C2×C4×D3—61no—
171C2×Dic6C4×D311yescharacteristic
172C2×C3×C8—22no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180#217—21no—
181#217—61no—
182#217—61no—
183#217—61no—
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3C4×D311yescharacteristic
192C4⋊Dic3C4×D311yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—122no—
198Dic3⋊C4—122no—
199C4×Dic3—31no—
200C4×Dic3—31no—
201C4×Dic3—31no—
202C4×Dic3—31no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C2×C3⋊C8—62no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32C2×C22⋊C411yescharacteristic
219C22×C32AGL(1,ℤ/8)11yescharacteristic
220C22×C32#13711yescharacteristic
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C32×C4—21no—
225C32×C4—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C3⋊Dic3—21no—
229C3⋊Dic3—21no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—81no—
234C3×Dic3—81no—
235#126—181no—
236#125—91no—
237#124—91no—
238#123—181no—
239C22⋊Q8—31no—
240#121—31no—
241C4×Q8—91no—
242C4×D4—91no—
243C4×D4—181no—
244#117—181no—
245C2×C4⋊C4—181no—
246C2×C42—91no—
247C4⋊C8—181no—
248C22⋊C8—91no—
249C22⋊C8D3211yescharacteristic
250#97—181no—
251#95—31no—
252#95—31no—
253#95—181no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3D3×D411yescharacteristic
257C23×C3D3×D411yescharacteristic
258C22×D3—21no—
259C3×Q8—121no—
260C3×D4—121no—
261C3×D4—121no—
262C3×D4—121no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—42no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4—121no—
275C2×C3×C4—121no—
276C2×C3×C4—121no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281#67—41no—
282#67—41no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—31no—
287C2×Dic3—31no—
288C2×Dic3—31no—
289C2×Dic3—31no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—122no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—122no—
314D12—41no—
315C4×D3—122no—
316Dic6—41no—
317C3×C8—42no—
318C3×C8—41no—
319C3×C8—41no—
320C3⋊C8—122no—
321C3⋊C8—121no—
322C3⋊C8—121no—
323C2×C32—21no—
324C2×C32—21no—
325C2×C32#41011yescharacteristic
326C2×C32#41711yescharacteristic
327C2×C32#42111yescharacteristic
328C3×D3—81no—
329C2×Q8—31no—
330C2×D4—31no—
331C2×D4—61no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—181no—
337C22×C4C2×D3211yescharacteristic
338C2×C8—21no—
339C2×C8—181no—
340C4⋊C4—31no—
341C4⋊C4—31no—
342C4⋊C4—61no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4—362no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—181no—
350C22⋊C4—181no—
351C22⋊C4—181no—
352C42—91no—
353C42—91no—
354C42—91no—
355C42—91no—
356C42—181no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—121no—
367C22×C3—121no—
368C22×C3—121no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3D3×C22⋊C411yescharacteristic
371C22×C3#91111yescharacteristic
372C22×C3#91411yescharacteristic
373C22×C3#91511yescharacteristic
374C22×C3#91811yescharacteristic
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—41no—
384C3×C4—121no—
385C3×C4—121no—
386C3×C4—121no—
387C3×C4—241no—
388C3×C4—241no—
389Dic3—41no—
390Dic3—41no—
391Dic3—41no—
392Dic3—62no—
393Dic3—61no—
394Dic3—61no—
395Dic3—61no—
396Dic3—61no—
397Dic3—61no—
398Dic3—61no—
399Dic3—61no—
400Dic3—61no—
401Dic3—81no—
402Dic3—81no—
403Dic3—121no—
404Dic3—121no—
405Dic3—121no—
406C32#151211yescharacteristic, complemented, Sylow
407C23—61no—
408C23#380211yescharacteristic
409Q8—121no—
410D4—121no—
411D4—121no—
412D4—121no—
413C2×C4—41no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—91no—
420C2×C4—91no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—362no—
430C2×C4—361no—
431C2×C4C4×D3211yescharacteristic
432C2×C4#381111yescharacteristic
433C8—41no—
434C8—361no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—241no—
445C2×C3#474011yescharacteristic
446C2×C3#474011yescharacteristic
447C2×C3#477111yescharacteristic
448C2×C3#480311yescharacteristic
449C2×C3#482111yescharacteristic
450C2×C3#482111yescharacteristic
451D3—81no—
452C22—21no—
453C22—21no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22#6379811yescharacteristic
458C22#6381111yescharacteristic
459C22#6392111yescharacteristic
460C4—21no—
461C4—21no—
462C4—121no—
463C4—121no—
464C4—121no—
465C4—181no—
466C4—181no—
467C4—181no—
468C4—181no—
469C4—241no—
470C4—241no—
471C3—21no—
472C3#6828011yescharacteristic, complemented
473C3#6831211yescharacteristic, complemented
474C2—21no—
475C2—21no—
476C2—241no—
477C2#1059040611yescharacteristic
478C2#1059095711yescharacteristic
479C2#1059100911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. #10591360C2semidirect
5. C3×#4467C2semidirect
6. #10589153C2semidirect
16. #63898C4semidirect
18. #63872C4semidirect
19. #63863C4semidirect
21. #63843C4semidirect
41. #4467D3semidirect
406. C32#1512semidirect
472. C3#68280semidirect
473. C3#68312semidirect

Maximal subgroups

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

subgroupindex
#105949652
#105924182
#105913602
C3×#44702
C3×#44672
#105891532
#105891492
#683123
#682803