Finite Group Databasebeta

← #11778643

Subgroups — #11778643

Order 1152.

589 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 589 conjugacy classes of subgroups — too many to draw. Only its 80 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#10596115C211yesmaximal, characteristic
2C3×#5043C211yesmaximal, characteristic, complemented
3#10591326C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#71173—31nomaximal
9#68321—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11#64156—21no—
12#64139C2211yescharacteristic
13C2×#3752C2211yescharacteristic
14#64107—21no—
15#64104—21no—
16#64103—21no—
17#64091—21no—
18#64090—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×#3722—21no—
21C3×#835—21no—
22C3×C3⋊#95C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5644—31no—
30#5644—31no—
31#5644—61no—
32C3×#483—31no—
33#5043D311yescharacteristic, complemented
34#4992—31no—
35#4967—31no—
36#4736—31no—
37#4674—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4470—31no—
41#4468—31no—
42#4468—31no—
43#4451—31no—
44C23×C3⋊D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3752—21no—
59#3752—21no—
60#3752—21no—
61#3752—21no—
62#3752—21no—
63#3752—21no—
64C4⋊(C3⋊Dic3)D411yescharacteristic
65#3750—21no—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3722—42no—
72#1612—91noSylow
73C3×C22⋊Q8—21no—
74C3×C22⋊Q8C2×D311yescharacteristic
75C3×C22⋊Q8C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77#947—62no—
78#947—61no—
79#947—61no—
80#930—31no—
81#930—31no—
82#930—61no—
83C2×(C2×D3)⋊C4—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—61no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89#898—61no—
90#898—61no—
91#898—62no—
92#895—61no—
93#895—61no—
94#895—62no—
95#894—62no—
96#894—61no—
97#894—61no—
98#882—61no—
99#882—61no—
100#882—62no—
101#67⋊C4—61no—
102#67⋊C4—61no—
103#67⋊C4—62no—
104C3×#106—61no—
105C3×#103—61no—
106C3×C22⋊C8—31no—
107C3×C22⋊C8—31no—
108C3×#95—31no—
109#835—21no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#821—61no—
116#818—61no—
117#809—61no—
118#808—21no—
119#807—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C32×Q8—41no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—41no—
138C4⋊(C3⋊D3)—41no—
139C4⋊(C3⋊D3)—81no—
140C4⋊(C3⋊D3)—81no—
141C4×C3⋊D3—81no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150#538—91no—
151#483—31no—
152#480—91no—
153#397—91no—
154#328—31no—
155#327—91no—
156#323—91no—
157C23×D3—31no—
158C23×D3—31no—
159C23×D3—61no—
160C2×C3×Q8—21no—
161C2×C3×Q8D1211yescharacteristic
162C2×C3×Q8#6711yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—62no—
169C2×#67—61no—
170C2×#67—61no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C2×D12—31no—
177C2×D12—31no—
178C2×D12—61no—
179C2×D12—62no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×C4×D3—62no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4D1211yescharacteristic
197C3×C4⋊C4#6711yescharacteristic
198C3×C22⋊C4—22no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—122no—
220(C2×D3)⋊C4—122no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—31no—
224C4⋊Dic3—31no—
225C4⋊Dic3—61no—
226Dic3⋊C4—62no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229C4×Dic3—62no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32#12011yescharacteristic
237C22×C32#13511yescharacteristic
238C22×C32AGL(1,ℤ/8)11yescharacteristic
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—41no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—81no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—41no—
250C32×C4—41no—
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
253C3×Dic3—81no—
254C3×Dic3—81no—
255#126—181no—
256#124—181no—
257#123—181no—
258C22⋊Q8D3211yescharacteristic
259#121—91no—
260#121—181no—
261#120—181no—
262C4×D4—181no—
263C2×C4⋊C4—31no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—181no—
266#107—181no—
267#106—61no—
268#103—61no—
269#102—181no—
270C22⋊C8—31no—
271C22⋊C8—31no—
272#95—31no—
273#95—181no—
274C23×C3—21no—
275C23×C3D3×D411yescharacteristic
276C23×C3D3×D411yescharacteristic
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—241no—
294C22×D3—241no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—81no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—81no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319#67—122no—
320#67—122no—
321#67—121no—
322#67—121no—
323#67—121no—
324#67—121no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—241no—
340D12—121no—
341D12—121no—
342D12—241no—
343D12—242no—
344D12—242no—
345D12—241no—
346D12—241no—
347D12—241no—
348D12—241no—
349C4×D3—242no—
350C4×D3—241no—
351C4×D3—241no—
352C3×C8—121no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—41no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#44911yescharacteristic
359C2×C32#45511yescharacteristic
360C2×C32#45811yescharacteristic
361C3⋊D3—81no—
362C3⋊D3—81no—
363C24—91no—
364C2×Q8#62611yescharacteristic
365C2×D4—91no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—91no—
372C22×C4—181no—
373C22×C4C2×D3211yescharacteristic
374C2×C8—61no—
375C2×C8—61no—
376C4⋊C4—21no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—91no—
380C4⋊C4—181no—
381C4⋊C4#62611yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—362no—
390C42—181no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3#88211yescharacteristic
401C22×C3#91411yescharacteristic
402C22×C3#91411yescharacteristic
403C22×C3#91611yescharacteristic
404C22×C3#91911yescharacteristic
405C22×C3#93711yescharacteristic
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—121no—
415C2×D3—121no—
416C2×D3—121no—
417C2×D3—121no—
418C2×D3—121no—
419C2×D3—121no—
420C2×D3—121no—
421C2×D3—121no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—242no—
427C2×D3—242no—
428C2×D3—241no—
429C2×D3—241no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—241no—
443C3×C4—241no—
444Dic3—81no—
445Dic3—81no—
446Dic3—122no—
447Dic3—122no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452C32#161211yescharacteristic, complemented, Sylow
453C23—181no—
454C23—181no—
455C23—181no—
456C23—181no—
457C23—361no—
458C23—361no—
459C23#381111yescharacteristic
460Q8—41no—
461D4—361no—
462D4—361no—
463D4—361no—
464D4—721no—
465D4—721no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—361no—
478C2×C4—721no—
479C2×C4C2×#62611yescharacteristic
480C2×C4#381111yescharacteristic
481C8—121no—
482C8—121no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—41no—
491C2×C3—41no—
492C2×C3#474211yescharacteristic
493C2×C3#481011yescharacteristic
494C2×C3#482511yescharacteristic
495C2×C3#505311yescharacteristic
496C2×C3#517211yescharacteristic
497C2×C3#520211yescharacteristic
498D3—242no—
499D3—242no—
500D3—241no—
501D3—241no—
502D3—241no—
503D3—241no—
504C22—21no—
505C22—21no—
506C22—362no—
507C22—361no—
508C22—361no—
509C22—361no—
510C22—361no—
511C22—361no—
512C22—361no—
513C22—721no—
514C22#6394111yescharacteristic
515C22#6395011yescharacteristic
516C22#6398111yescharacteristic
517C4—21no—
518C4—21no—
519C4—41no—
520C4—41no—
521C4—241no—
522C4—241no—
523C4—361no—
524C4—361no—
525C3—21no—
526C3#6832111yescharacteristic, complemented
527C3#7117311yescharacteristic, complemented
528C2—21no—
529C2—21no—
530C2—721no—
531C2—721no—
532C2#1059153511yescharacteristic
533C2#1059159311yescharacteristic
534C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radical#10596115C2
hypercenterC22⋊Q8D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5043C2semidirect
3. #10591326C2semidirect
4. #10591133C2semidirect
5. C3×#4538C2semidirect
6. #10589151C2semidirect
7. #10589146C2semidirect
33. #5043D3semidirect
39. #4538D3semidirect
452. C32#1612semidirect
526. C3#68321semidirect
527. C3#71173semidirect

Maximal subgroups

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

subgroupindex
#105961152
C3×#50432
#105913262
#105911332
C3×#45382
#105891512
#105891462
#711733
#683213