Finite Group Databasebeta

← #11779730

Subgroups — #11779730

Order 1152.

675 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 675 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D122C211yesmaximal, characteristic
2#10592393C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic, complemented
4#10590272C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#68196—31nomaximal
9#68182—31nomaximal
10C2×D3×D12—21no—
11C2×D3×D12—21no—
12#64083C2211yescharacteristic
13#64078C2211yescharacteristic, complemented
14C3×C4×D12C2211yescharacteristic
15C3×C4×D12C2211yescharacteristic
16#63923—22no—
17#63909—21no—
18#63909—21no—
19C2×#3716—21no—
20C32×C4×C8C2211yescharacteristic, complemented
21#63648—22no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
24#63575—21no—
25#63567—21no—
26#63563—21no—
27D4×D12—31no—
28D4×D12—31no—
29#5019—31no—
30#5007—31no—
31#4846—31no—
32#4841—31no—
33#4694—31no—
34#4694—31no—
35#4694—61no—
36C3×D4⋊C8—31no—
37C3×D4⋊C8—31no—
38#4485—31no—
39#4485—31no—
40#4459D311yescharacteristic, complemented
41#4459D311yescharacteristic, complemented
42C22×D32—22no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D412yes—
46C2×#634—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×#626—22no—
52C2×#626—22no—
53D3×D12—42no—
54D3×D12—42no—
55D3×D12—42no—
56D3×D12—42no—
57C2×C32×C8—21no—
58C32×C42C2311yescharacteristic
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3D411yescharacteristic
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3722—22no—
68#3716—42no—
69#1639—91noSylow
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C22×D12—61no—
73C22×D12—61no—
74C3×C4×D4—31no—
75C3×C4×D4—31no—
76C2×#214—61no—
77#930—61no—
78#930—61no—
79C2×#204—61no—
80#895—61no—
81#895—61no—
82#882—62no—
83#882—62no—
84#874—31no—
85#874—31no—
86#874—61no—
87C4×D12C2×D311yescharacteristic
88C4×D12C2×D311yescharacteristic
89#869—31no—
90#869—31no—
91#869—61no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8—31no—
94C3×C4×C8—21no—
95C3×C4×C8C2×D311yescharacteristic, complemented
96C3×C4×C8C2×D311yescharacteristic, complemented
97#832—61no—
98#821—62no—
99#821—62no—
100#821—64no—
101#821—61no—
102#818—61no—
103#816—61no—
104#810—61no—
105#807—61no—
106C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
107C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
108C22×C3⋊D3—22no—
109C22×C3×D3—21no—
110C22×C3×D3—21no—
111C2×D32—44no—
112C2×D32—44no—
113C2×D32—82no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—41no—
118C4⋊(C3⋊D3)—42no—
119C4⋊(C3⋊D3)—41no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—41no—
123#634—41no—
124#634—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C3×D12—21no—
128C3×D12—21no—
129C3×D12D812yes—
130C3×D12SD1612yescomplemented
131C3×C4×D3—41no—
132C3×C4×D3—41no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135#626—44no—
136#626—44no—
137C32×C8—41no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140D42—91no—
141#486—91no—
142#474—91no—
143#461—91no—
144#331—91no—
145D4⋊C8—31no—
146D4⋊C8—31no—
147C23×D3—62no—
148C23×D3—62no—
149C2×C3×D4—31no—
150C2×C3×D4—31no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C2×#67—62no—
154C2×#67—62no—
155D3×D4—122no—
156D3×D4—122no—
157D3×D4—122no—
158D3×D4—122no—
159C2×D12—32no—
160C2×D12—32no—
161C2×D12—62no—
162C2×D12—62no—
163C2×D12—62no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—61no—
168C2×D12—121no—
169C2×D12—121no—
170C2×D12—122no—
171C2×D12—122no—
172C2×D12—122no—
173C2×D12—122no—
174C2×D12D1211yescharacteristic
175C2×D12D1211yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—21no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—121no—
181C2×C3×C8—22no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—31no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—21no—
191C3×C42C22×D311yescharacteristic
192C3×C42C22×D311yescharacteristic
193#214—122no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—62no—
198C4⋊Dic3—62no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—121no—
204C4⋊Dic3D1211yescharacteristic
205C4⋊Dic3D1211yescharacteristic
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208#204—122no—
209C22×C32#12011yescharacteristic
210C2×C3⋊D3—42no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—42no—
213C2×C3×D3—22no—
214C2×C3×D3—22no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219D32—88no—
220C32×C4—21no—
221C32×C4C2×D811yescharacteristic
222C32×C4C2×SD1611yescharacteristic
223C32×C4AGL(1,ℤ/8)11yescharacteristic
224C32×C4AGL(1,ℤ/8)11yescharacteristic
225C3⋊Dic3—81no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C22×D4—181no—
229C22×D4—181no—
230C2×SD16—181no—
231C4⋊Q8—91no—
232#127—91no—
233#121—181no—
234#121—181no—
235#120—182no—
236C4×D4—31no—
237C4×D4—31no—
238#107—181no—
239C4⋊C8—31no—
240C4⋊C8—31no—
241#103—181no—
242#102—182no—
243#102—181no—
244C4×C8D3211yescharacteristic, complemented
245C23×C3—61no—
246C23×C3—61no—
247C22×D3—21no—
248C22×D3—21no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—122no—
252C22×D3—124no—
253C22×D3—124no—
254C22×D3—124no—
255C22×D3—124no—
256C22×D3—242no—
257C22×D3—242no—
258C3×D4—32no—
259C3×D4—32no—
260C3×D4—61no—
261C3×D4—61no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277#67—124no—
278#67—124no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—122no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284D12—21no—
285D12—21no—
286D12—122no—
287D12—122no—
288D12—124no—
289D12—124no—
290D12—124no—
291D12—121no—
292D12—121no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—241no—
300D12—241no—
301D12—241no—
302D12—241no—
303D12#20412yescomplemented
304D12D2412yes—
305C4×D3—41no—
306C4×D3—41no—
307C4×D3—41no—
308C4×D3—41no—
309Dic6—121no—
310Dic6—121no—
311Dic6—121no—
312Dic6—121no—
313Dic6—241no—
314Dic6—241no—
315C3×C8—42no—
316C3×C8—41no—
317C3×C8—41no—
318C3×C8—121no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—41no—
322C2×C32#44711yescharacteristic
323C2×C32#45011yescharacteristic
324C2×C32#45511yescharacteristic
325C3⋊D3—82no—
326C3×D3—42no—
327C3×D3—42no—
328C24—182no—
329C2×Q8—181no—
330C2×D4—31no—
331C2×D4—31no—
332C2×D4—92no—
333C2×D4—182no—
334C2×D4—182no—
335C2×D4—181no—
336C2×D4—181no—
337C2×D4—362no—
338C2×D4—362no—
339C2×D4—362no—
340C2×D4—362no—
341C22×C4—61no—
342C22×C4—61no—
343SD16—362no—
344C2×C8—21no—
345C2×C8—61no—
346C2×C8—61no—
347C4⋊C4—31no—
348C4⋊C4—31no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C22⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—182no—
354C42C2×D3211yescharacteristic
355C22×C3—21no—
356C22×C3—62no—
357C22×C3—62no—
358C22×C3—121no—
359C22×C3—121no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3#88211yescharacteristic
363C22×C3#88211yescharacteristic
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—41no—
367C2×D3—41no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—122no—
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—122no—
375C2×D3—122no—
376C2×D3—242no—
377C2×D3—242no—
378C2×D3—242no—
379C2×D3—248no—
380C2×D3—248no—
381C3×C4—22no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—121no—
389C3×C4—121no—
390C3×C4C2×#20411yescharacteristic
391C3×C4C2×D2411yescharacteristic
392C3×C4#90811yescharacteristic
393C3×C4#90811yescharacteristic
394C3×C4D3×D811yescharacteristic
395C3×C4#91111yescharacteristic
396C3×C4D3×SD1611yescharacteristic
397C3×C4#91411yescharacteristic
398Dic3—41no—
399Dic3—41no—
400Dic3—242no—
401Dic3—241no—
402Dic3—241no—
403C32#163911yescharacteristic, complemented, Sylow
404C23—61no—
405C23—61no—
406C23—182no—
407C23—364no—
408C23—364no—
409C23—722no—
410Q8—361no—
411Q8—361no—
412D4—32no—
413D4—32no—
414D4—61no—
415D4—61no—
416D4—362no—
417D4—364no—
418D4—364no—
419D4—361no—
420D4—361no—
421D4—361no—
422D4—361no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—361no—
430C2×C4D3×D1211yescharacteristic
431C2×C4D3×D1211yescharacteristic
432C2×C4#381111yescharacteristic
433C8—41no—
434C8—121no—
435C8—121no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—122no—
440C2×C3—122no—
441C2×C3#473111yescharacteristic
442C2×C3#473211yescharacteristic
443C2×C3#477311yescharacteristic
444C2×C3#477611yescharacteristic
445C2×C3#482511yescharacteristic
446C2×C3#482511yescharacteristic
447D3—42no—
448D3—42no—
449D3—242no—
450D3—242no—
451D3—482no—
452C22—62no—
453C22—62no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—362no—
459C22—362no—
460C22—362no—
461C22—728no—
462C22#6392311yescharacteristic
463C4—21no—
464C4—121no—
465C4—121no—
466C4—721no—
467C4D3×#20411yescharacteristic
468C4D3×D2411yescharacteristic
469C4#6379411yescharacteristic
470C4#6379511yescharacteristic
471C3—21no—
472C3#6818211yescharacteristic, complemented
473C3#6819611yescharacteristic, complemented
474C2—122no—
475C2—122no—
476C2—722no—
477C2#1059039811yescharacteristic
478C2#1059094611yescharacteristic
479C2#1059094711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalD122C2
hypercenterC4×C8D32
hypocenterC32#1639
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592393C2semidirect
3. #10590365C2semidirect
4. #10590272C2semidirect
5. C3×#4459C2semidirect
6. C3×#4459C2semidirect
7. #10589091C2semidirect
13. #64078C22semidirect
20. C32×C4×C8C22semidirect
22. C3×C4⋊(C3⋊C8)C22semidirect
23. C3×C4⋊(C3⋊C8)C22semidirect
40. #4459D3semidirect
41. #4459D3semidirect
95. C3×C4×C8C2×D3semidirect
96. C3×C4×C8C2×D3semidirect
106. C4⋊(C3⋊C8)C2×D3semidirect
107. C4⋊(C3⋊C8)C2×D3semidirect
130. C3×D12SD16semidirect
244. C4×C8D32semidirect
303. D12#204semidirect
403. C32#1639semidirect
472. C3#68182semidirect
473. C3#68196semidirect

Maximal subgroups

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

subgroupindex
D1222
#105923932
#105903652
#105902722
C3×#44592
#105890912
#681963
#681823