Finite Group Databasebeta

← #11798770

Subgroups — #11798770

Order 1152.

503 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 503 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5735C211yesmaximal, characteristic, complemented
2#10592794C211yesmaximal, characteristic, complemented
3#10591650C211yesmaximal, characteristic, complemented
4#10591647C211yesmaximal, characteristic
5C3×#4548C211yesmaximal, characteristic, complemented
6#10589184C211yesmaximal, characteristic, complemented
7#10589182C211yesmaximal, characteristic, complemented
8#71959—31nomaximal
9#69167—31nomaximal
10#64364C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12#64151—21no—
13C3×#947C2211yescharacteristic
14C3×#946—21no—
15C3×#944C2211yescharacteristic
16C3×#898—21no—
17C3×#896—21no—
18C3×#894—21no—
19C3×#889—21no—
20C3×#876—21no—
21#63833—21no—
22#63830—21no—
23#63663C2211yescharacteristic
24#63632—21no—
25C3×#836C2211yescharacteristic
26C3×#836C2211yescharacteristic
27#63570—21no—
28#63570—21no—
29C3×#563—31no—
30#5735D311yescharacteristic, complemented
31#5095—31no—
32#5095—31no—
33#5095—31no—
34#5095—61no—
35#5062—31no—
36#4753—31no—
37#4752—31no—
38C3×#356—31no—
39#4548—31no—
40#4548D311yescharacteristic, complemented
41#4542—31no—
42#4478—31no—
43#4477—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×Q8C2311yescharacteristic
46#3832—41no—
47Q8×C3⋊D3—41no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C42D411yescharacteristic
57#3756—41no—
58#3755—41no—
59#3748—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3D411yescharacteristic
72C3×C4×Dic3D411yescharacteristic
73C3×#208—21no—
74C3×#208—21no—
75#3719—41no—
76#3717—41no—
77#3716—41no—
78#3714—41no—
79#2203—91noSylow
80#1007—31no—
81#1007—31no—
82#1007—61no—
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8—31no—
85C3×C4⋊Q8C2×D311yescharacteristic
86C3×C4⋊Q8C2×D311yescharacteristic
87C3×#126—61no—
88C3×#126—61no—
89C3×#125—61no—
90C3×#124—31no—
91C3×#123—61no—
92C3×C22⋊Q8—61no—
93C3×C22⋊Q8—61no—
94#947C2×D311yescharacteristic
95#946—21no—
96#944C2×D311yescharacteristic
97#942—61no—
98#942—62no—
99#942—61no—
100#942—61no—
101#932—61no—
102#909—61no—
103#908—61no—
104#898—21no—
105#896—21no—
106#894—21no—
107#889—21no—
108#876—21no—
109C3×#101—31no—
110C3×#101—31no—
111#836—31no—
112#836—31no—
113#836—61no—
114#836C2×D311yescharacteristic
115#836C2×D311yescharacteristic
116#825—61no—
117#825—61no—
118#805—61no—
119#805—61no—
120#805—62no—
121#805—61no—
122#805—61no—
123C22×C3×D3—21no—
124C32×Q8—41no—
125C32×Q8—41no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131#638—41no—
132C4⋊(C3⋊D3)—21no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—21no—
135C4×C3⋊D3—41no—
136C4×C3⋊D3—41no—
137C4×C3⋊D3—41no—
138#634—21no—
139#634—21no—
140#634—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C3×D12—41no—
145C3×C4×D3—81no—
146C3×Dic6—41no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150#563—31no—
151#456—91no—
152#456—91no—
153#454—91no—
154#356—31no—
155#356—91no—
156#355—91no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—31no—
160C2×C3×Q8D1211yescharacteristic
161C2×C3×Q8#6711yescharacteristic
162C2×C3×Q8C22×D311yescharacteristic
163C2×C3×Q8C22×D311yescharacteristic
164C2×C3×D4—31no—
165C22×C3×C4—61no—
166#239—121no—
167#239—121no—
168#239—122no—
169D3×Q8—121no—
170D3×Q8—121no—
171D3×Q8—122no—
172#235—62no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—121no—
180#235—121no—
181C2×D12#6711yescharacteristic
182C2×C4×D3—21no—
183C2×Dic6#6711yescharacteristic
184C3×M16—61no—
185C3×M16—61no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—41no—
191C3×C4⋊C4—41no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—61no—
203C3×C42—21no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42D1211yescharacteristic
207C3×C42#6711yescharacteristic
208#216—121no—
209#216—121no—
210#216—121no—
211#216—122no—
212#215—121no—
213#215—121no—
214#215—121no—
215#215—122no—
216#214—121no—
217#213—121no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—21no—
223C4⋊Dic3—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—21no—
226Dic3⋊C4—21no—
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229C4×Dic3#6711yescharacteristic
230C4×Dic3#6711yescharacteristic
231#208—21no—
232#208—21no—
233#208—62no—
234#208—61no—
235#208—61no—
236Dic12—121no—
237D24—121no—
238#204—121no—
239#204—121no—
240C22×C32#12011yescharacteristic
241C2×C3⋊D3—41no—
242C2×C3×D3—42no—
243C2×C3×D3—41no—
244C32×C4—21no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—41no—
248C32×C4—41no—
249C3⋊Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
2532−1+4—91no—
254#137—181no—
255#137—181no—
256AGL(1,ℤ/8)—181no—
257C4⋊Q8—31no—
258C4⋊Q8D3211yescharacteristic
259#126—61no—
260#126—61no—
261#125—61no—
262#124—31no—
263#123—61no—
264C22⋊Q8—61no—
265C22⋊Q8—61no—
266#104—181no—
267#104—181no—
268#104—181no—
269#101—31no—
270#101—31no—
271#101—91no—
272C23×C3—61no—
273C22×D3—21no—
274C3×Q8—41no—
275C3×Q8—41no—
276C3×Q8—41no—
277C3×Q8—41no—
278C3×Q8—42no—
279C3×Q8—42no—
280C3×Q8—121no—
281C3×D4—121no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—241no—
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—122no—
302#67—121no—
303#67—121no—
304C2×Dic3—21no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307D12—41no—
308D12—61no—
309D12—61no—
310D12—61no—
311D12—62no—
312D12—61no—
313D12—61no—
314D12—61no—
315D12—121no—
316D12—121no—
317C4×D3—81no—
318C4×D3—122no—
319C4×D3—121no—
320C4×D3—121no—
321C4×D3—121no—
322C4×D3—121no—
323C4×D3—121no—
324C4×D3—121no—
325C4×D3—122no—
326C4×D3—122no—
327Dic6—41no—
328Dic6—61no—
329Dic6—61no—
330Dic6—61no—
331Dic6—62no—
332Dic6—61no—
333Dic6—61no—
334Dic6—61no—
335Dic6—121no—
336Dic6—121no—
337C3×C8—121no—
338C3×C8—121no—
339C3⋊C8—41no—
340C3⋊C8—41no—
341C3⋊C8—122no—
342C3⋊C8—121no—
343C3⋊C8—121no—
344C2×C32—21no—
345C2×C32B(4,𝔽2)11yescharacteristic
346C3⋊D3—81no—
347C3×D3—81no—
348#41—181no—
349#41—181no—
350#41—181no—
351#41—361no—
352C2×Q8—31no—
353C2×Q8—361no—
354C2×Q8#62611yescharacteristic
355C2×Q8C2×D3211yescharacteristic
356C2×D4—31no—
357C22×C4—61no—
358Q16—361no—
359Q16—361no—
360SD16—361no—
361SD16—361no—
362SD16—361no—
363D8—361no—
364M16—61no—
365M16—61no—
366M16—181no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C42—31no—
381C42—31no—
382C42#62611yescharacteristic
383C22×C3—21no—
384C22×C3—122no—
385C22×C3—121no—
386C22×C3#88211yescharacteristic
387C22×C3#95311yescharacteristic
388C2×D3—42no—
389C2×D3—41no—
390C2×D3—122no—
391C2×D3—121no—
392C2×D3—121no—
393C3×C4—22no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—42no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—81no—
408C3×C4—121no—
409C3×C4—121no—
410C3×C4—121no—
411Dic3—41no—
412Dic3—41no—
413Dic3—41no—
414Dic3—122no—
415Dic3—121no—
416Dic3—121no—
417C32#220311yescharacteristic, complemented, Sylow
418C23—61no—
419Q8—41no—
420Q8—41no—
421Q8—121no—
422Q8—181no—
423Q8—181no—
424Q8—181no—
425D4—121no—
426D4—181no—
427D4—181no—
428D4—181no—
429D4—361no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—241no—
436C2×C4—361no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4C2×#62611yescharacteristic
440C2×C4D3×#6711yescharacteristic
441C2×C4D3×#6711yescharacteristic
442C8—121no—
443C8—121no—
444C8—361no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—241no—
450C2×C3#474111yescharacteristic
451C2×C3#524411yescharacteristic
452D3—81no—
453D3—242no—
454D3—241no—
455D3—241no—
456C22—122no—
457C22—121no—
458C22—361no—
459C22#6397711yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—41no—
464C4—41no—
465C4—121no—
466C4—121no—
467C4—121no—
468C4—361no—
469C3—21no—
470C3#6916711yescharacteristic, complemented
471C3#7195911yescharacteristic, complemented
472C2—21no—
473C2—241no—
474C2—721no—
475C2#1059153111yescharacteristic
subgroupG/H
centerC2#10591531
commutator, cosocleC2×C32×Q8C23
FrattiniC2×Q8C2×D32
FittingC32×C4⋊Q8C22
socleC2×C32B(4,𝔽2)
prime radical#10591647C2
hypercenterC4⋊Q8D32
hypocenterC32#2203
LCSG ▷ C2×C32×Q8 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5735C2semidirect
2. #10592794C2semidirect
3. #10591650C2semidirect
5. C3×#4548C2semidirect
6. #10589184C2semidirect
7. #10589182C2semidirect
30. #5735D3semidirect
40. #4548D3semidirect
417. C32#2203semidirect
470. C3#69167semidirect
471. C3#71959semidirect

Maximal subgroups

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

subgroupindex
C3×#57352
#105927942
#105916502
#105916472
C3×#45482
#105891842
#105891822
#719593
#691673