Finite Group Databasebeta

← #11779124

Subgroups — #11779124

Order 1152.

571 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 571 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5726C211yesmaximal, characteristic, complemented
2#10592787C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589080C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71910—31nomaximal
9#68432—31nomaximal
10C2×C3×#239—21no—
11C32×C4⋊Q8C2211yescharacteristic
12#64083C2211yescharacteristic
13C3×#946—21no—
14C3×#895—21no—
15C3×#894—22no—
16C3×D3×C4⋊C4—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C2×#3714—21no—
20C2×#3714—21no—
21#63636—22no—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63564—21no—
26#63564—21no—
27C3×#547—31no—
28#5726D311yescharacteristic, complemented
29#5088—31no—
30#5088—31no—
31#5088—61no—
32#5015—31no—
33#5015—31no—
34#4843—31no—
35#4843—31no—
36C3×#332—31no—
37#4547D311yescharacteristic, complemented
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—31no—
40#4483—31no—
41#4483—31no—
42C2×C32×Q8—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C3×#239—42no—
47C3×#239—42no—
48C2×C3×D12—22no—
49C2×C3×D12D411yescharacteristic
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—22no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56C32×C42C2311yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—22no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3714—42no—
67#3714—42no—
68#1625—91noSylow
69C2×C3×#41—61no—
70C2×#239—21no—
71C3×C4⋊Q8—21no—
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×#123—62no—
75C3×C22⋊Q8—61no—
76C3×#121—61no—
77C3×C4×D4—31no—
78C3×C4×D4—31no—
79C2×C3×C4⋊C4—61no—
80#946—21no—
81C2×#213—61no—
82C2×#213—61no—
83C2×D24—61no—
84C2×D24—61no—
85#895—21no—
86#894—22no—
87D3×C4⋊C4—21no—
88#874—31no—
89#874—31no—
90#874—61no—
91C4×D12C2×D311yescharacteristic
92C4×D12C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×C4⋊C8—31no—
95#821—61no—
96#821—61no—
97#809—61no—
98#809—61no—
99#809—64no—
100#809—62no—
101#809—62no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8—31no—
105C4×C3⋊C8—31no—
106C4×C3⋊C8—61no—
107C22×C3⋊D3—41no—
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C32×Q8—41no—
111C32×Q8—41no—
112C2×C32×C4—22no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12—21no—
125C3×D12—21no—
126C3×D12—44no—
127C3×D12D812yescomplemented
128C3×C4×D3—44no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×C4×D3—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135C3×C3⋊C8—41no—
136#547—31no—
137#486—91no—
138#459—91no—
139#459—91no—
140#332—31no—
141D4⋊C8—91no—
142D4⋊C8—91no—
143C3×#41—122no—
144C3×#41—122no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—41no—
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C2×C3×D4—62no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154#239—42no—
155#239—42no—
156C2×D12—22no—
157C2×D12—62no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—61no—
162C2×D12—61no—
163C2×D12—61no—
164C2×D12—121no—
165C2×D12—121no—
166C2×D12#6711yescharacteristic
167C2×D12#6711yescharacteristic
168C2×C4×D3—22no—
169C2×C4×D3—21no—
170C2×C4×D3—21no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—62no—
180C3×C4⋊C4D1212yes—
181C3×C4⋊C4#6712yes—
182C3×C22⋊C4—62no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C42—21no—
186C3×C42C22×D311yescharacteristic
187C3×C42C22×D311yescharacteristic
188#213—122no—
189#213—122no—
190(C2×D3)⋊C4—22no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3#6711yescharacteristic
194C4⋊Dic3#6711yescharacteristic
195Dic3⋊C4—22no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201D24—122no—
202D24—122no—
203C22×C32#12011yescharacteristic
204C2×C3⋊D3—81no—
205C2×C3⋊D3—81no—
206C2×C3⋊D3—81no—
207C2×C3×D3—22no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C32×C4—21no—
214C32×C4—42no—
215C32×C4C2×D811yescharacteristic
216C32×C4#13511yescharacteristic
217C32×C4AGL(1,ℤ/8)11yescharacteristic
218C32×C4AGL(1,ℤ/8)11yescharacteristic
219C3×Dic3—41no—
220C3×Dic3—41no—
221C2×#41—61no—
222C2×D8—181no—
223C2×D8—181no—
224C4⋊Q8D3211yescharacteristic
225#127—91no—
226#123—62no—
227C22⋊Q8—61no—
228#121—61no—
229C4×D4—31no—
230C4×D4—31no—
231C2×C4⋊C4—61no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#102—181no—
235#102—181no—
236#102—182no—
237C4×C8—91no—
238C23×C3—61no—
239C23×C3—61no—
240C22×D3—21no—
241C22×D3—21no—
242C22×D3—122no—
243C22×D3—121no—
244C22×D3—121no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×Q8—81no—
250C3×Q8—81no—
251C3×D4—32no—
252C3×D4—61no—
253C3×D4—61no—
254C3×D4—61no—
255C3×D4—124no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—42no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—124no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—21no—
277D12—21no—
278D12—21no—
279D12—21no—
280D12—44no—
281D12—124no—
282D12—122no—
283D12—122no—
284D12—121no—
285D12—121no—
286D12—121no—
287D12—121no—
288D12—121no—
289D12—121no—
290D12—121no—
291D12—121no—
292D12—241no—
293D12—241no—
294D12—241no—
295D12—241no—
296D12#21312yescomplemented
297C4×D3—44no—
298C4×D3—41no—
299C4×D3—41no—
300C4×D3—41no—
301C4×D3—41no—
302C3×C8—121no—
303C3×C8—121no—
304C3⋊C8—41no—
305C3⋊C8—41no—
306C3⋊C8—122no—
307C3⋊C8—121no—
308C3⋊C8—121no—
309C2×C32#44711yescharacteristic
310C2×C32#44911yescharacteristic
311C2×C32#45411yescharacteristic
312C3⋊D3—161no—
313C3×D3—42no—
314C3×D3—81no—
315#41—122no—
316#41—122no—
317C2×Q8—21no—
318C2×D4—31no—
319C2×D4—31no—
320C2×D4—62no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C22×C4—62no—
325C22×C4—61no—
326C22×C4—61no—
327D8—362no—
328D8—362no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—181no—
332C4⋊C4—21no—
333C4⋊C4—31no—
334C4⋊C4—31no—
335C4⋊C4—62no—
336C4⋊C4#62612yes—
337C22⋊C4—62no—
338C22⋊C4—61no—
339C22⋊C4—61no—
340C42C2×D3211yescharacteristic
341C22×C3—21no—
342C22×C3—62no—
343C22×C3—121no—
344C22×C3—121no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3#88211yescharacteristic
349C22×C3#95311yescharacteristic
350C2×D3—22no—
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—41no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—242no—
357C2×D3—242no—
358C2×D3—242no—
359C2×D3—241no—
360C2×D3—241no—
361C2×D3—241no—
362C2×D3—241no—
363C2×D3—241no—
364C2×D3—241no—
365C3×C4—22no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—82no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4D3×D811yescharacteristic
378C3×C4#91411yescharacteristic
379C3×C4#91411yescharacteristic
380C3×C4#91911yescharacteristic
381C3×C4C2×#21311yescharacteristic
382C3×C4#93211yescharacteristic
383C3×C4#94911yescharacteristic
384C3×C4#95011yescharacteristic
385Dic3—41no—
386Dic3—41no—
387C32#162511yescharacteristic, complemented, Sylow
388C23—61no—
389C23—61no—
390C23—361no—
391Q8—41no—
392Q8—41no—
393D4—32no—
394D4—61no—
395D4—61no—
396D4—61no—
397D4—124no—
398D4—362no—
399D4—361no—
400D4—361no—
401D4—361no—
402D4—361no—
403C2×C4—22no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—124no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4C2×#62611yescharacteristic
412C2×C4D3×#6711yescharacteristic
413C2×C4D3×#6711yescharacteristic
414C8—121no—
415C8—121no—
416C8—361no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—122no—
421C2×C3—241no—
422C2×C3#475311yescharacteristic
423C2×C3#477311yescharacteristic
424C2×C3#481011yescharacteristic
425C2×C3#521711yescharacteristic
426C2×C3#523811yescharacteristic
427C2×C3#524511yescharacteristic
428D3—42no—
429D3—81no—
430D3—482no—
431D3—481no—
432D3—481no—
433C22—62no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—721no—
440C22—721no—
441C22—721no—
442C22#6397711yescharacteristic
443C4—21no—
444C4—42no—
445C4—121no—
446C4—121no—
447C4D3×#21311yescharacteristic
448C4#6393411yescharacteristic
449C4#6393911yescharacteristic
450C4#6394911yescharacteristic
451C3—21no—
452C3#6843211yescharacteristic, complemented
453C3#7191011yescharacteristic, complemented
454C2—122no—
455C2—241no—
456C2—1441no—
457C2#1059144811yescharacteristic
458C2#1059158811yescharacteristic
459C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1625
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. #10592787C2semidirect
3. #10590349C2semidirect
4. #10590349C2semidirect
5. C3×#4547C2semidirect
6. #10589080C2semidirect
7. #10589080C2semidirect
28. #5726D3semidirect
37. #4547D3semidirect
127. C3×D12D8semidirect
296. D12#213semidirect
387. C32#1625semidirect
452. C3#68432semidirect
453. C3#71910semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
#105927872
#105903492
C3×#45472
#105890802
#719103
#684323