Finite Group Databasebeta

← #11778520

Subgroups — #11778520

Order 1152.

507 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 84 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×#5515C211yesmaximal, characteristic
2#10592680C211yesmaximal, characteristic, complemented
3#10591126C211yesmaximal, characteristic, complemented
4#10591094C211yesmaximal, characteristic
5C3×#4528C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#71886—31nomaximal
9#68134—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×#3750—21no—
13C3×#930C2211yescharacteristic
14C3×#929—21no—
15C3×C4×#67—21no—
16C3×#924C2211yescharacteristic
17C3×#898—21no—
18C3×#896—21no—
19C3×#894—21no—
20C3×#889—21no—
21#63658—21no—
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63566—21no—
28#63563—21no—
29C3×#539—31no—
30#5515D311yescharacteristic
31#5043—31no—
32#5033—31no—
33#4981—31no—
34#4981—31no—
35#4981—61no—
36#4736—31no—
37#4721—31no—
38C3×#324—31no—
39#4538—31no—
40#4537—31no—
41#4528D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×C3×#67—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57#3750—42no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#1609—91noSylow
73C3×#126—61no—
74C3×#125—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×#121—31no—
80C3×C4×D4—61no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C2×D311yescharacteristic
84#930C2×D311yescharacteristic
85#929—21no—
86C4×#67—21no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90#924C2×D311yescharacteristic
91C2×Dic3⋊C4—62no—
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94#898—21no—
95#896—21no—
96#894—21no—
97#889—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8—31no—
100#835—61no—
101#832—61no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108#830C2×D311yescharacteristic
109#830C2×D311yescharacteristic
110#821—61no—
111#818—61no—
112#817—61no—
113#816—61no—
114#808—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
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×C4×D3—81no—
139C3×Dic6—41no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142#539—31no—
143#483—91no—
144#480—91no—
145#398—91no—
146#328—91no—
147#327—91no—
148#324—31no—
149C2×C3×Q8—31no—
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4D1211yescharacteristic
157C22×C3×C4D1211yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—62no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—62no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C2×D12#6711yescharacteristic
170C2×C4×D3—21no—
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×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—61no—
192#217—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—121no—
202C4⋊Dic3—121no—
203C4⋊Dic3#6711yescharacteristic
204C4⋊Dic3#6711yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207Dic3⋊C4—21no—
208Dic3⋊C4—21no—
209Dic3⋊C4—124no—
210Dic3⋊C4—122no—
211Dic3⋊C4—122no—
212C4×Dic3—21no—
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—41no—
226C32×C4—41no—
227C3⋊Dic3—42no—
228C3⋊Dic3—81no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232#126—61no—
233#125—61no—
234#123—61no—
235#123—61no—
236C22⋊Q8—31no—
237C22⋊Q8—61no—
238#121—31no—
239C4×D4—61no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242C2×C4⋊C4D3211yescharacteristic
243#107—181no—
244#106—181no—
245#103—181no—
246#102—181no—
247C22⋊C8—31no—
248C22⋊C8—31no—
249#95—91no—
250#95—181no—
251C23×C3—21no—
252C23×C3—61no—
253C23×C3C2×D1211yescharacteristic
254C23×C3C2×#6711yescharacteristic
255C22×D3—21no—
256C3×Q8—121no—
257C3×D4—121no—
258C3×D4—121no—
259C3×D4—121no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—42no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—241no—
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288#67—41no—
289#67—41no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—122no—
297C2×Dic3—122no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311D12—41no—
312C4×D3—81no—
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—61no—
328C22×C4—181no—
329C22×C4—181no—
330C22×C4#62611yescharacteristic
331C22×C4#62611yescharacteristic
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—61no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C4⋊C4—362no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C42—61no—
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#88211yescharacteristic
365C22×C3#90411yescharacteristic
366C22×C3#90811yescharacteristic
367C22×C3#94911yescharacteristic
368C22×C3#95011yescharacteristic
369C22×C3#95311yescharacteristic
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—42no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—81no—
385C3×C4—121no—
386C3×C4—121no—
387C3×C4—121no—
388Dic3—41no—
389Dic3—41no—
390Dic3—41no—
391Dic3—124no—
392Dic3—122no—
393Dic3—122no—
394Dic3—242no—
395Dic3—241no—
396Dic3—241no—
397C32#160911yescharacteristic, complemented, Sylow
398C23—61no—
399C23C2×#62611yescharacteristic
400Q8—121no—
401D4—121no—
402D4—121no—
403D4—121no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—182no—
414C2×C4—241no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—361no—
418C2×C4—361no—
419C2×C4—361no—
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#473411yescharacteristic
435C2×C3#474211yescharacteristic
436C2×C3#475211yescharacteristic
437C2×C3#523811yescharacteristic
438C2×C3#524311yescharacteristic
439C2×C3#524611yescharacteristic
440D3—81no—
441C22—21no—
442C22—21no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22#6382511yescharacteristic
447C22#6382911yescharacteristic
448C22#6397711yescharacteristic
449C4—21no—
450C4—21no—
451C4—41no—
452C4—41no—
453C4—121no—
454C4—121no—
455C4—121no—
456C4—362no—
457C4—721no—
458C3—21no—
459C3#6813411yescharacteristic, complemented
460C3#7188611yescharacteristic, complemented
461C2—21no—
462C2—21no—
463C2—241no—
464C2#1059116311yescharacteristic
465C2#1059153411yescharacteristic
466C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
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. #10592680C2semidirect
3. #10591126C2semidirect
5. C3×#4528C2semidirect
6. #10589152C2semidirect
41. #4528D3semidirect
397. C32#1609semidirect
459. C3#68134semidirect
460. C3#71886semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
#105926802
#105911262
#105910942
C3×#45282
#105891522
#105891502
#718863
#681343