Finite Group Databasebeta

← #11778532

Subgroups — #11778532

Order 1152.

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

normal subgroups only

This group has 477 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#10594980C211yesmaximal, characteristic
2C3×#4721C211yesmaximal, characteristic, complemented
3#10591214C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic
5#10589336C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71174—31nomaximal
9#68134—31nomaximal
10#64139C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×#3724—21no—
15#63966—21no—
16#63952—21no—
17#63897—21no—
18#63888—21no—
19#63848—21no—
20#63845—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#817—21no—
25C3×#816—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5645—31no—
30#5515—31no—
31C3×#483—31no—
32#4983—31no—
33#4981—31no—
34#4967—31no—
35#4736—31no—
36#4721D311yescharacteristic, complemented
37C3×#324—31no—
38#4538—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4469D311yescharacteristic, complemented
43#4467—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C2×C32×C8—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—42no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69#3722—21no—
70#3722—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76#946—61no—
77#930—31no—
78#930—31no—
79#930—61no—
80#929—61no—
81C4×#67—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4—61no—
85C2×Dic3⋊C4—61no—
86C2×Dic3⋊C4C2×D311yescharacteristic
87#898—61no—
88#898—61no—
89#896—61no—
90#894—61no—
91#894—61no—
92#890—61no—
93#889—61no—
94#886—61no—
95#67⋊C4—61no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C2×D311yescharacteristic
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#830C2×D311yescharacteristic
108#821—61no—
109#818—61no—
110#817—21no—
111#816—21no—
112#809—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119#638—41no—
120#638—41no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C4⋊(C3⋊D3)—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×Dic6—41no—
137#624—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—91no—
141#483—31no—
142#480—91no—
143#398—91no—
144#328—91no—
145#327—91no—
146#324—31no—
147C2×C3×Q8—31no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—121no—
157C22×Dic3—21no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—121no—
161C22×Dic3D1211yescharacteristic
162C22×Dic3D1211yescharacteristic
163C2×D12—31no—
164C2×D12—31no—
165C2×D12—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×Dic6#6711yescharacteristic
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—61no—
180#217—21no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—121no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3#6711yescharacteristic
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—122no—
206Dic3⋊C4—122no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32AGL(1,ℤ/8)11yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—42no—
221C3⋊Dic3—41no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—181no—
228#125—181no—
229#123—181no—
230#123—181no—
231C22⋊Q8—31no—
232C22⋊Q8—181no—
233#121—91no—
234C4×D4—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—181no—
238#107—181no—
239#106—61no—
240#103—61no—
241#102—181no—
242C22⋊C8—31no—
243C22⋊C8D3211yescharacteristic
244#95—91no—
245#95—181no—
246C23×C3—21no—
247C23×C3C2×D1211yescharacteristic
248C23×C3D3×D411yescharacteristic
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—121no—
252C3×Q8—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—81no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272#67—121no—
273#67—121no—
274#67—121no—
275#67—121no—
276#67—241no—
277#67—241no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—121no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—241no—
299C2×Dic3—241no—
300D12—121no—
301D12—121no—
302D12—241no—
303C4×D3—241no—
304C4×D3—241no—
305Dic6—41no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—81no—
309C3×C8—121no—
310C3⋊C8—41no—
311C2×C32—21no—
312C2×C32—21no—
313C2×C32#44911yescharacteristic
314C2×C32#45611yescharacteristic
315C2×C32#45811yescharacteristic
316C3⋊D3—81no—
317C2×Q8—31no—
318C2×D4—91no—
319C2×D4—181no—
320C22×C4—31no—
321C22×C4—31no—
322C22×C4—61no—
323C22×C4—181no—
324C22×C4—181no—
325C22×C4C2×D3211yescharacteristic
326C2×C8—21no—
327C2×C8—61no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—91no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C4⋊C4—181no—
338C4⋊C4—362no—
339C22⋊C4—61no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C42—181no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3#88211yescharacteristic
355C22×C3#90411yescharacteristic
356C22×C3#90811yescharacteristic
357C22×C3#91411yescharacteristic
358C22×C3#91611yescharacteristic
359C22×C3#93711yescharacteristic
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—121no—
366C2×D3—241no—
367C2×D3—241no—
368C2×D3—241no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—121no—
379C3×C4—241no—
380Dic3—41no—
381Dic3—41no—
382Dic3—41no—
383Dic3—41no—
384Dic3—81no—
385Dic3—122no—
386Dic3—122no—
387Dic3—121no—
388Dic3—121no—
389Dic3—241no—
390Dic3—242no—
391C32#160911yescharacteristic, complemented, Sylow
392C23—181no—
393C23D3×D1211yescharacteristic
394Q8—121no—
395D4—361no—
396D4—361no—
397D4—361no—
398C2×C4—41no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—182no—
410C2×C4—181no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4—721no—
414C2×C4#380211yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—41no—
417C8—121no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3#473411yescharacteristic
428C2×C3#474211yescharacteristic
429C2×C3#475211yescharacteristic
430C2×C3#505311yescharacteristic
431C2×C3#517211yescharacteristic
432C2×C3#520511yescharacteristic
433D3—241no—
434D3—241no—
435D3—481no—
436C22—21no—
437C22—21no—
438C22—361no—
439C22—361no—
440C22—361no—
441C22#6379411yescharacteristic
442C22#6380611yescharacteristic
443C22#6392211yescharacteristic
444C4—21no—
445C4—21no—
446C4—121no—
447C4—121no—
448C4—121no—
449C4—121no—
450C4—241no—
451C4—362no—
452C4—361no—
453C3—21no—
454C3#6813411yescharacteristic, complemented
455C3#7117411yescharacteristic, complemented
456C2—21no—
457C2—21no—
458C2—721no—
459C2#1059040811yescharacteristic
460C2#1059082311yescharacteristic
461C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊C8D32
hypocenterC32#1609
LCSG ▷ C22×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. C3×#4721C2semidirect
3. #10591214C2semidirect
6. C3×#4469C2semidirect
7. #10589152C2semidirect
36. #4721D3semidirect
42. #4469D3semidirect
391. C32#1609semidirect
454. C3#68134semidirect
455. C3#71174semidirect

Maximal subgroups

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

subgroupindex
#105949802
C3×#47212
#105912142
#105911332
#105893362
C3×#44692
#105891522
#711743
#681343