Finite Group Databasebeta

← #11778756

Subgroups — #11778756

Order 1152.

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

normal subgroups only

This group has 525 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#10596116C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic, complemented
3#10591227C211yesmaximal, characteristic, complemented
4#10591125C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic, complemented
8#71178—31nomaximal
9#68330—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11#64155—21no—
12#64139C2211yescharacteristic
13C2×#3750C2211yescharacteristic
14#64107—21no—
15#64103—21no—
16#64099—21no—
17#64095—21no—
18#64090—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#835—21no—
21C3×C3⋊#95C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#807—21no—
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63564—21no—
29#5645—31no—
30#5645—31no—
31#5645—61no—
32C3×#484—31no—
33#5044D311yescharacteristic, complemented
34#4985—31no—
35#4968—31no—
36#4735—31no—
37#4659—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4470—31no—
41#4469—31no—
42#4469—31no—
43#4451—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56#3752—21no—
57#3752—21no—
58#3752—21no—
59#3752—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)D411yescharacteristic
63#3750—21no—
64#3750—21no—
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#1615—91noSylow
72C3×C22⋊Q8—21no—
73C3×C22⋊Q8C2×D311yescharacteristic
74C3×C22⋊Q8C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
76#946—62no—
77#946—61no—
78#946—61no—
79#930—31no—
80#930—31no—
81#930—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83C2×Dic3⋊C4—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—61no—
86#898—62no—
87#898—61no—
88#898—61no—
89#894—61no—
90#894—61no—
91#894—62no—
92#890—61no—
93#890—61no—
94#890—62no—
95#886—61no—
96#886—61no—
97#886—62no—
98#67⋊C4—61no—
99#67⋊C4—61no—
100#67⋊C4—62no—
101C3×#107—61no—
102C3×#103—61no—
103C3×C22⋊C8—31no—
104C3×C22⋊C8—31no—
105C3×#95—31no—
106#835—21no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830C2×D311yescharacteristic
113#830C2×D311yescharacteristic
114#821—61no—
115#817—61no—
116#809—61no—
117#808—61no—
118#807—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C32×Q8—41no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127#638—41no—
128#638—41no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C4⋊(C3⋊D3)—41no—
136C4×C3⋊D3—81no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144#539—91no—
145#484—31no—
146#481—91no—
147#400—91no—
148#328—31no—
149#327—91no—
150#324—91no—
151C2×C3×Q8—21no—
152C2×C3×Q8D1211yescharacteristic
153C2×C3×Q8#6711yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—62no—
160C2×#67—61no—
161C2×#67—61no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C2×D12—31no—
171C2×D12—31no—
172C2×D12—61no—
173C2×C4×D3—62no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4D1211yescharacteristic
185C3×C4⋊C4#6711yescharacteristic
186C3×C22⋊C4—22no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—62no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—62no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—61no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—61no—
206C4⋊Dic3—62no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212Dic3⋊C4—62no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—62no—
216Dic3⋊C4—62no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221C4×Dic3—62no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32#12011yescharacteristic
229C22×C32#13511yescharacteristic
230C22×C32#13711yescharacteristic
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—41no—
237C32×C4—41no—
238C3⋊Dic3—41no—
239C3⋊Dic3—41no—
240C3⋊Dic3—41no—
241C3×Dic3—81no—
242C3×Dic3—81no—
243#126—181no—
244#125—181no—
245#123—181no—
246#123—181no—
247C22⋊Q8—181no—
248C22⋊Q8D3211yescharacteristic
249#121—91no—
250C4×D4—181no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—91no—
253#107—61no—
254#106—181no—
255#103—61no—
256#102—181no—
257C22⋊C8—31no—
258C22⋊C8—31no—
259#95—31no—
260#95—181no—
261#95—181no—
262C23×C3—21no—
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—62no—
266C22×D3—61no—
267C22×D3—61no—
268C3×Q8—41no—
269C3×Q8—41no—
270C3×Q8—81no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—122no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291#67—122no—
292#67—122no—
293#67—121no—
294#67—121no—
295#67—121no—
296#67—121no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—42no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—241no—
320D12—121no—
321D12—121no—
322D12—241no—
323C4×D3—242no—
324C4×D3—241no—
325C4×D3—241no—
326C3×C8—121no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—41no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32#45211yescharacteristic
333C2×C32#45411yescharacteristic
334C2×C32#45811yescharacteristic
335C3⋊D3—81no—
336C2×Q8#62611yescharacteristic
337C2×D4—91no—
338C2×D4—181no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—61no—
346C2×C8—61no—
347C4⋊C4—21no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—91no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4—181no—
356C4⋊C4#62611yescharacteristic
357C22⋊C4—21no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C22⋊C4—181no—
361C22⋊C4—181no—
362C42—181no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3#88211yescharacteristic
373C22×C3#91611yescharacteristic
374C22×C3#91811yescharacteristic
375C22×C3#91811yescharacteristic
376C22×C3#91911yescharacteristic
377C22×C3#93711yescharacteristic
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—121no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—121no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—241no—
400C3×C4—241no—
401Dic3—81no—
402Dic3—81no—
403Dic3—122no—
404Dic3—122no—
405Dic3—122no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411Dic3—121no—
412C32#161511yescharacteristic, complemented, Sylow
413C23—181no—
414C23#381111yescharacteristic
415Q8—41no—
416D4—361no—
417D4—361no—
418D4—361no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—122no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—361no—
433C2×C4—721no—
434C2×C4C2×#62611yescharacteristic
435C2×C4#381111yescharacteristic
436C8—121no—
437C8—121no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3#474211yescharacteristic
448C2×C3#480811yescharacteristic
449C2×C3#482711yescharacteristic
450C2×C3#505311yescharacteristic
451C2×C3#518711yescharacteristic
452C2×C3#520111yescharacteristic
453D3—242no—
454D3—241no—
455D3—241no—
456C22—21no—
457C22—21no—
458C22—361no—
459C22—361no—
460C22—361no—
461C22#6394511yescharacteristic
462C22#6395011yescharacteristic
463C22#6398111yescharacteristic
464C4—21no—
465C4—21no—
466C4—41no—
467C4—41no—
468C4—241no—
469C4—241no—
470C4—361no—
471C4—361no—
472C4—361no—
473C3—21no—
474C3#6833011yescharacteristic, complemented
475C3#7117811yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—721no—
479C2#1059153511yescharacteristic
480C2#1059160211yescharacteristic
481C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊Q8D32
hypocenterC32#1615
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×#5044C2semidirect
3. #10591227C2semidirect
5. C3×#4538C2semidirect
7. #10589148C2semidirect
33. #5044D3semidirect
39. #4538D3semidirect
412. C32#1615semidirect
474. C3#68330semidirect
475. C3#71178semidirect

Maximal subgroups

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

subgroupindex
#105961162
C3×#50442
#105912272
#105911252
C3×#45382
#105891512
#105891482
#711783
#683303