Finite Group Databasebeta

← #11778634

Subgroups — #11778634

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#10595965C211yesmaximal, characteristic
2C3×#4953C211yesmaximal, characteristic, complemented
3#10591133C211yesmaximal, characteristic, complemented
4#10591124C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#69709—31nomaximal
9#68111—31nomaximal
10C2×C32×C22⋊C4C2211yescharacteristic
11#64162—21no—
12#64139C2211yescharacteristic
13C4×#638—21no—
14#64133C2211yescharacteristic
15#64094—21no—
16#64093—21no—
17#64092—21no—
18#64088—21no—
19C2×C3×#217—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×C3⋊#95—21no—
22C3×C3⋊#95C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63575—21no—
26#63573—21no—
27#63567—21no—
28#63564—21no—
29#5494—31no—
30#5494—31no—
31#5494—61no—
32C3×#397—31no—
33#4971—31no—
34#4967—31no—
35#4953D311yescharacteristic, complemented
36#4736—31no—
37#4721—31no—
38C3×#323—31no—
39#4525D311yescharacteristic, complemented
40#4470—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C24×C32D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57#3757—21no—
58#3757—21no—
59#3757—21no—
60#3752—21no—
61#3752—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63C4⋊(C3⋊Dic3)D411yescharacteristic
64#3750—21no—
65#3750—21no—
66C4×C3⋊Dic3—21no—
67C3×#217—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#1612—91noSylow
73C2×C3×C4⋊C4—31no—
74C2×C3×C22⋊C4—21no—
75C2×C3×C22⋊C4—61no—
76C2×C3×C22⋊C4C2×D311yescharacteristic
77C2×C3×C22⋊C4C2×D311yescharacteristic
78#953—62no—
79#953—61no—
80#953—61no—
81C2×#217—21no—
82#930—31no—
83#930—31no—
84#930—61no—
85C4×#67—62no—
86C4×#67—61no—
87C4×#67—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89#924—31no—
90#924—31no—
91#924—61no—
92#885—61no—
93#885—61no—
94#885—62no—
95#884—61no—
96#884—61no—
97#884—62no—
98#883—61no—
99#883—61no—
100#883—62no—
101#879—61no—
102#879—61no—
103#879—62no—
104C3×C22⋊C8—31no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3×#95—61no—
108C3⋊#95—21no—
109C3⋊#95C2×D311yescharacteristic
110#830C2×D311yescharacteristic
111#830C2×D311yescharacteristic
112#821—61no—
113#818—61no—
114#817—61no—
115#816—61no—
116#810—61no—
117#809—61no—
118#808—61no—
119#807—61no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—21no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132#638—41no—
133#638—41no—
134#638—81no—
135#638—81no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C4⋊(C3⋊D3)—41no—
140C4×C3⋊D3—81no—
141#634—41no—
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—91no—
152#480—91no—
153#397—31no—
154#328—91no—
155#327—91no—
156#323—31no—
157C24×C3—21no—
158C24×C3D1211yescharacteristic
159C24×C3#6711yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—62no—
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—62no—
172C2×#67—61no—
173C2×#67—61no—
174C2×#67—62no—
175C2×#67—61no—
176C2×#67—61no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—61no—
182C2×C4×D3—62no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×Dic6—31no—
186C2×Dic6—31no—
187C2×Dic6—61no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—22no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—122no—
199#217—42no—
200#217—62no—
201#217—61no—
202#217—61no—
203#217—62no—
204#217—61no—
205#217—61no—
206#217—62no—
207#217—61no—
208#217—61no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—31no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223Dic3⋊C4—62no—
224Dic3⋊C4—61no—
225Dic3⋊C4—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—41no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32—42no—
240C22×C32—81no—
241C22×C32#12011yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C32×C4—21no—
248C32×C4—21no—
249C32×C4—41no—
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C3⋊Dic3—41no—
253C3×Dic3—81no—
254C3×Dic3—81no—
255#126—181no—
256#124—181no—
257#123—181no—
258C22⋊Q8—91no—
259#121—91no—
260#121—181no—
261#120—181no—
262C4×D4—181no—
263C2×C4⋊C4—31no—
264C2×C22⋊C4—61no—
265C2×C22⋊C4D3211yescharacteristic
266#107—181no—
267#106—181no—
268#103—181no—
269#102—181no—
270C22⋊C8—31no—
271C22⋊C8—31no—
272#95—31no—
273#95—61no—
274C23×C3—22no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—81no—
289C23×C3—81no—
290C23×C3C2×D1211yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—62no—
293C22×D3—61no—
294C22×D3—61no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—81no—
305C2×C3×C4—81no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316#67—122no—
317#67—122no—
318#67—121no—
319#67—121no—
320#67—121no—
321#67—121no—
322#67—242no—
323#67—242no—
324#67—241no—
325#67—241no—
326#67—241no—
327#67—241no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343D12—121no—
344D12—121no—
345D12—241no—
346C4×D3—242no—
347C4×D3—241no—
348C4×D3—241no—
349Dic6—121no—
350Dic6—121no—
351Dic6—241no—
352C3×C8—121no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—41no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—81no—
359C2×C32#44911yescharacteristic
360C2×C32#45511yescharacteristic
361C2×C32#45811yescharacteristic
362C3⋊D3—81no—
363C24#62611yescharacteristic
364C2×Q8—91no—
365C2×D4—91no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4—181no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—181no—
372C22×C4#62611yescharacteristic
373C22×C4C2×D3211yescharacteristic
374C2×C8—61no—
375C2×C8—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—91no—
379C4⋊C4—91no—
380C4⋊C4—181no—
381C4⋊C4—181no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—122no—
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—181no—
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—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—82no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—82no—
415C22×C3#88211yescharacteristic
416C22×C3#90411yescharacteristic
417C22×C3#90811yescharacteristic
418C22×C3#93211yescharacteristic
419C22×C3#93711yescharacteristic
420C22×C3#95011yescharacteristic
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—42no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—241no—
440C3×C4—241no—
441Dic3—81no—
442Dic3—81no—
443Dic3—122no—
444Dic3—122no—
445Dic3—122no—
446Dic3—121no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452C32#161211yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—41no—
457C23—41no—
458C23—181no—
459C23C2×#62611yescharacteristic
460Q8—361no—
461D4—361no—
462D4—361no—
463D4—361no—
464D4—721no—
465D4—721no—
466C2×C4—21no—
467C2×C4—41no—
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—181no—
478C2×C4—721no—
479C2×C4#381111yescharacteristic
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—82no—
493C2×C3—81no—
494C2×C3—81no—
495C2×C3#473411yescharacteristic
496C2×C3#474211yescharacteristic
497C2×C3#474611yescharacteristic
498C2×C3#503711yescharacteristic
499C2×C3#505311yescharacteristic
500C2×C3#506111yescharacteristic
501D3—242no—
502D3—241no—
503D3—241no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—81no—
511C22—361no—
512C22—361no—
513C22—361no—
514C22#6382911yescharacteristic
515C22#6383011yescharacteristic
516C22#6398111yescharacteristic
517C4—21no—
518C4—21no—
519C4—41no—
520C4—241no—
521C4—241no—
522C4—361no—
523C4—361no—
524C4—361no—
525C3—21no—
526C3#6811111yescharacteristic, complemented
527C3#6970911yescharacteristic, complemented
528C2—21no—
529C2—21no—
530C2—81no—
531C2—721no—
532C2#1059118211yescharacteristic
533C2#1059151411yescharacteristic
534C2#1059153511yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radical#10595965C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4953C2semidirect
3. #10591133C2semidirect
4. #10591124C2semidirect
5. C3×#4525C2semidirect
6. #10589154C2semidirect
7. #10589151C2semidirect
35. #4953D3semidirect
39. #4525D3semidirect
452. C32#1612semidirect
526. C3#68111semidirect
527. C3#69709semidirect

Maximal subgroups

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

subgroupindex
#105959652
C3×#49532
#105911332
#105911242
C3×#45252
#105891542
#105891512
#697093
#681113