Finite Group Databasebeta

← #11778530

Subgroups — #11778530

Order 1152.

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

normal subgroups only

This group has 541 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×#5043C211yesmaximal, characteristic, complemented
3#10591358C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic
7#10589148C211yesmaximal, characteristic, complemented
8#71174—31nomaximal
9#68328—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
20C2×Dic3⋊Dic3—21no—
21C3×#835—21no—
22C3×C3⋊#95C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#808—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5645—31no—
30#5645—31no—
31#5645—61no—
32C3×#483—31no—
33#5043D311yescharacteristic, complemented
34#4983—31no—
35#4967—31no—
36#4736—31no—
37#4661—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—
71Dic3⋊Dic3—42no—
72#1609—91noSylow
73C3×C22⋊Q8—21no—
74C3×C22⋊Q8C2×D311yescharacteristic
75C3×C22⋊Q8C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77#946—62no—
78#946—61no—
79#946—61no—
80#930—31no—
81#930—31no—
82#930—61no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89#898—62no—
90#898—61no—
91#898—61no—
92#894—61no—
93#894—61no—
94#894—62no—
95#890—61no—
96#890—61no—
97#890—62no—
98#886—61no—
99#886—61no—
100#886—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—
122C32×Q8—41no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128#638—41no—
129#638—41no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—41no—
136C4⋊(C3⋊D3)—41no—
137C4×C3⋊D3—81no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146#539—91no—
147#483—31no—
148#480—91no—
149#398—91no—
150#328—31no—
151#327—91no—
152#324—91no—
153C2×C3×Q8—21no—
154C2×C3×Q8D1211yescharacteristic
155C2×C3×Q8#6711yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—62no—
162C2×#67—61no—
163C2×#67—61no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C2×D12—31no—
173C2×D12—31no—
174C2×D12—61no—
175C2×C4×D3—62no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4D1211yescharacteristic
187C3×C4⋊C4#6711yescharacteristic
188C3×C22⋊C4—22no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—62no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—61no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—31no—
206C4⋊Dic3—31no—
207C4⋊Dic3—61no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—122no—
215Dic3⋊C4—62no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—62no—
219Dic3⋊C4—62no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—122no—
225C4×Dic3—62no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32#12011yescharacteristic
233C22×C32#13511yescharacteristic
234C22×C32AGL(1,ℤ/8)11yescharacteristic
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—41no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4—41no—
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C3⋊Dic3—41no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247#126—181no—
248#125—181no—
249#123—181no—
250#123—181no—
251C22⋊Q8—181no—
252C22⋊Q8D3211yescharacteristic
253#121—91no—
254C4×D4—181no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258#107—181no—
259#106—61no—
260#103—61no—
261#102—181no—
262C22⋊C8—31no—
263C22⋊C8—31no—
264#95—31no—
265#95—181no—
266C23×C3—21no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—62no—
270C22×D3—61no—
271C22×D3—61no—
272C3×Q8—41no—
273C3×Q8—41no—
274C3×Q8—81no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—62no—
286C2×C3×C4—81no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296#67—122no—
297#67—122no—
298#67—121no—
299#67—121no—
300#67—121no—
301#67—121no—
302C2×Dic3—22no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—241no—
326D12—121no—
327D12—121no—
328D12—241no—
329C4×D3—242no—
330C4×D3—241no—
331C4×D3—241no—
332C3×C8—121no—
333C3×C8—121no—
334C3⋊C8—41no—
335C3⋊C8—41no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#44911yescharacteristic
339C2×C32#45611yescharacteristic
340C2×C32#45811yescharacteristic
341C3⋊D3—81no—
342C2×Q8#62611yescharacteristic
343C2×D4—91no—
344C2×D4—181no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—181no—
350C22×C4C2×D3211yescharacteristic
351C2×C8—61no—
352C2×C8—61no—
353C4⋊C4—21no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—91no—
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—362no—
363C4⋊C4#62611yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C42—181no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3#88211yescharacteristic
380C22×C3#91411yescharacteristic
381C22×C3#91411yescharacteristic
382C22×C3#91611yescharacteristic
383C22×C3#91911yescharacteristic
384C22×C3#93711yescharacteristic
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—121no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—121no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—42no—
401C3×C4—42no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—41no—
406C3×C4—122no—
407C3×C4—241no—
408Dic3—42no—
409Dic3—81no—
410Dic3—122no—
411Dic3—122no—
412Dic3—122no—
413Dic3—121no—
414Dic3—121no—
415Dic3—121no—
416Dic3—121no—
417Dic3—121no—
418Dic3—121no—
419C32#160911yescharacteristic, complemented, Sylow
420C23—181no—
421C23#381111yescharacteristic
422Q8—41no—
423D4—361no—
424D4—361no—
425D4—361no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—62no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4—181no—
440C2×C4—361no—
441C2×C4—721no—
442C2×C4C2×#62611yescharacteristic
443C2×C4#381111yescharacteristic
444C8—121no—
445C8—121no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—41no—
454C2×C3—41no—
455C2×C3#474211yescharacteristic
456C2×C3#481011yescharacteristic
457C2×C3#482611yescharacteristic
458C2×C3#505311yescharacteristic
459C2×C3#517211yescharacteristic
460C2×C3#520511yescharacteristic
461D3—242no—
462D3—241no—
463D3—241no—
464C22—21no—
465C22—21no—
466C22—361no—
467C22—361no—
468C22—361no—
469C22#6394111yescharacteristic
470C22#6395011yescharacteristic
471C22#6398111yescharacteristic
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—122no—
477C4—241no—
478C4—361no—
479C4—361no—
480C4—361no—
481C3—21no—
482C3#6832811yescharacteristic, complemented
483C3#7117411yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—721no—
487C2#1059153511yescharacteristic
488C2#1059159311yescharacteristic
489C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊Q8D32
hypocenterC32#1609
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. #10591358C2semidirect
5. C3×#4538C2semidirect
7. #10589148C2semidirect
33. #5043D3semidirect
39. #4538D3semidirect
419. C32#1609semidirect
482. C3#68328semidirect
483. C3#71174semidirect

Maximal subgroups

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

subgroupindex
#105961162
C3×#50432
#105913582
#105911332
C3×#45382
#105891512
#105891482
#711743
#683283