Finite Group Databasebeta

← #11778515

Subgroups — #11778515

Order 1152.

507 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594974C211yesmaximal, characteristic
2#10592682C211yesmaximal, characteristic, complemented
3C3×#4971C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic
5#10589152C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic, complemented
8#71174—31nomaximal
9#71166—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3750—21no—
12C2×#3750C2211yescharacteristic
13C3×#930C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#67⋊Dic3—21no—
16#63962—21no—
17#63887—21no—
18#63884—21no—
19#63858—21no—
20#63846—21no—
21#63658—21no—
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#810—21no—
26C3×#809—21no—
27C3×#808—21no—
28C3×#807—21no—
29#5645—31no—
30#5602—31no—
31C3×#483—31no—
32C3×#480—31no—
33#4983—31no—
34#4983—31no—
35#4983—61no—
36#4971D311yescharacteristic, complemented
37#4967D311yescharacteristic
38#4538—31no—
39#4537—31no—
40#4470—31no—
41#4469—31no—
42#4469—31no—
43#4467—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C3×#67—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×D3×Dic3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3750—21no—
56#3750—21no—
57#3750—42no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
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#1609—91noSylow
73C3×C22⋊Q8—31no—
74C3×#121—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78#946—61no—
79#935—61no—
80#935—61no—
81D4×Dic3—61no—
82#930C2×D311yescharacteristic
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—62no—
90#898—61no—
91#894—61no—
92#890—61no—
93#889—61no—
94#886—61no—
95#67⋊C4—61no—
96#879—61no—
97#878—61no—
98C3×#107—61no—
99C3×#106—61no—
100C3×#103—61no—
101C3×#102—61no—
102C3×C22⋊C8—31no—
103C3×C22⋊C8—31no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—62no—
110#830C2×D311yescharacteristic
111#830C2×D311yescharacteristic
112#810—21no—
113#809—21no—
114#808—21no—
115#807—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C3×#67—41no—
133C3×#67—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C3×D12—41no—
138C3×Dic6—41no—
139D3×Dic3—81no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142#539—91no—
143#483—31no—
144#480—31no—
145#398—91no—
146#328—91no—
147#327—91no—
148#324—91no—
149C2×C3×Q8—31no—
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—21no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—62no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C2×D12#6711yescharacteristic
170C2×C4×D3—61no—
171C2×Dic6#6711yescharacteristic
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185#217—21no—
186#217—61no—
187#217—61no—
188#217—61no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3#6711yescharacteristic
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—121no—
207Dic3⋊C4—121no—
208Dic3⋊C4—124no—
209Dic3⋊C4—122no—
210Dic3⋊C4—122no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32#12011yescharacteristic
218C22×C32#13511yescharacteristic
219C22×C32AGL(1,ℤ/8)11yescharacteristic
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—81no—
226C3⋊Dic3—42no—
227C3⋊Dic3—41no—
228C3⋊Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232#126—181no—
233#125—181no—
234#123—181no—
235#123—181no—
236C22⋊Q8—31no—
237C22⋊Q8—181no—
238#121—31no—
239C4×D4—181no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242C2×C4⋊C4D3211yescharacteristic
243#107—61no—
244#106—61no—
245#103—61no—
246#102—61no—
247C22⋊C8—31no—
248C22⋊C8—31no—
249#95—91no—
250#95—181no—
251C23×C3—21no—
252C23×C3—61no—
253C23×C3D3×D411yescharacteristic
254C23×C3D3×D411yescharacteristic
255C22×D3—21no—
256C3×Q8—121no—
257C3×D4—121no—
258C3×D4—121no—
259C3×D4—121no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281#67—41no—
282#67—41no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—62no—
287C2×Dic3—64no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—122no—
310C2×Dic3—241no—
311D12—41no—
312C4×D3—241no—
313Dic6—41no—
314C3×C8—121no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—41no—
318C2×C32—21no—
319C2×C32—21no—
320C2×C32#44911yescharacteristic
321C2×C32#45611yescharacteristic
322C2×C32#45811yescharacteristic
323C3×D3—81no—
324C2×Q8—31no—
325C2×D4—31no—
326C2×D4—61no—
327C22×C4—21no—
328C22×C4—91no—
329C22×C4—91no—
330C22×C4—181no—
331C22×C4—181no—
332C22×C4C2×D3211yescharacteristic
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—362no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—181no—
349C22⋊C4—181no—
350C22⋊C4—181no—
351C42—181no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3#91111yescharacteristic
365C22×C3#91211yescharacteristic
366C22×C3#91411yescharacteristic
367C22×C3#91611yescharacteristic
368C22×C3#93711yescharacteristic
369C22×C3#93711yescharacteristic
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—82no—
380C3×C4—81no—
381C3×C4—81no—
382C3×C4—121no—
383C3×C4—121no—
384C3×C4—121no—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3—124no—
389Dic3—122no—
390Dic3—122no—
391Dic3—122no—
392Dic3—121no—
393Dic3—121no—
394Dic3—121no—
395Dic3—121no—
396Dic3—241no—
397C32#160911yescharacteristic, complemented, Sylow
398C23—61no—
399C23#381111yescharacteristic
400Q8—121no—
401D4—121no—
402D4—121no—
403D4—121no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—182no—
412C2×C4—181no—
413C2×C4—181no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4—361no—
419C2×C4—721no—
420C2×C4D3×#6711yescharacteristic
421C2×C4D3×#6711yescharacteristic
422C8—121no—
423C8—121no—
424C2×C3—22no—
425C2×C3—22no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—241no—
434C2×C3#505311yescharacteristic
435C2×C3#505311yescharacteristic
436C2×C3#515811yescharacteristic
437C2×C3#517211yescharacteristic
438C2×C3#520511yescharacteristic
439C2×C3#520511yescharacteristic
440D3—81no—
441C22—21no—
442C22—21no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22#6393611yescharacteristic
447C22#6393711yescharacteristic
448C22#6398311yescharacteristic
449C4—21no—
450C4—21no—
451C4—81no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—362no—
456C4—361no—
457C4—361no—
458C3—21no—
459C3#7116611yescharacteristic, complemented
460C3#7117411yescharacteristic, complemented
461C2—21no—
462C2—21no—
463C2—241no—
464C2#1059139811yescharacteristic
465C2#1059152011yescharacteristic
466C2#1059166011yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1609
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592682C2semidirect
3. C3×#4971C2semidirect
5. #10589152C2semidirect
7. #10589148C2semidirect
36. #4971D3semidirect
397. C32#1609semidirect
459. C3#71166semidirect
460. C3#71174semidirect

Maximal subgroups

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

subgroupindex
#105949742
#105926822
C3×#49712
C3×#49672
#105891522
#105891502
#105891482
#711743
#711663