Finite Group Databasebeta

← #11779739

Subgroups — #11779739

Order 1152.

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

normal subgroups only

This group has 658 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
2C3×#4846C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71108—31nomaximal
9#68196—31nomaximal
10C2×D3×D12—21no—
11C2×D3×D12—21no—
12#64083C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C3×#869C2211yescharacteristic, complemented
16#63923—22no—
17#63909—21no—
18#63909—21no—
19C2×#3715—21no—
20C32×C4⋊C8C2211yescharacteristic, complemented
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C3×#821—21no—
23C3×#818—21no—
24C3×C4×C3⋊C8C2211yescharacteristic, complemented
25#63565—21no—
26#63564—22no—
27D4×D12—31no—
28D4×D12—31no—
29C3×#474—31no—
30#5088—31no—
31#5083—31no—
32#5019—31no—
33#4846D311yescharacteristic, complemented
34#4694—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4485—31no—
38#4485—31no—
39#4485—61no—
40#4483D311yescharacteristic, complemented
41#4459—31no—
42C22×D32—22no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D412yes—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—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
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67#3722—22no—
68#3715—42no—
69#1639—91noSylow
70C2×D3×D4—61no—
71C2×D3×D4—61no—
72C22×D12—61no—
73C22×D12—61no—
74C3×C4⋊Q8—31no—
75C3×C4×D4—31no—
76C3×C4×D4—31no—
77C2×#215—61no—
78C2×#214—61no—
79#930—61no—
80#930—61no—
81#895—61no—
82#895—61no—
83#882—62no—
84#882—62no—
85#874—31no—
86#874—31no—
87#874—61no—
88C4×D12C2×D311yescharacteristic
89C4×D12C2×D311yescharacteristic
90#869C2×D311yescharacteristic, complemented
91C3×#107—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8C2×D311yescharacteristic, complemented
94C3×C4⋊C8C2×D311yescharacteristic, complemented
95C3×#102—61no—
96C3×C4×C8—31no—
97#835—61no—
98#821—21no—
99#821—62no—
100#818—21no—
101#810—61no—
102#809—62no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—31no—
105C4⋊(C3⋊C8)—61no—
106C4×C3⋊C8C2×D311yescharacteristic, complemented
107C22×C3⋊D3—22no—
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C2×D32—44no—
111C2×D32—44no—
112C2×D32—82no—
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—
123C2×C3×Dic3—41no—
124C3×D12—21no—
125C3×D12—21no—
126C3×D12D812yes—
127C3×D12SD1612yescomplemented
128C3×C4×D3—41no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×Dic6—41no—
133C3×Dic6—41no—
134#626—44no—
135#626—44no—
136C32×C8—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—41no—
139D42—91no—
140#486—91no—
141#474—31no—
142#461—91no—
143#331—91no—
144D4⋊C8—31no—
145D4⋊C8—91no—
146C23×D3—62no—
147C23×D3—62no—
148C2×C3×Q8—61no—
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×D12#6711yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—21no—
178C2×Dic6—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—41no—
182C2×C3×C8—61no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42C22×D311yescharacteristic
191C3×C42C22×D311yescharacteristic
192#215—122no—
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—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3D1211yescharacteristic
201C4⋊Dic3#6711yescharacteristic
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C22×C32#12011yescharacteristic
207C2×C3⋊D3—42no—
208C2×C3⋊D3—42no—
209C2×C3⋊D3—42no—
210C2×C3×D3—22no—
211C2×C3×D3—22no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216D32—88no—
217C32×C4—21no—
218C32×C4C2×D811yescharacteristic
219C32×C4C2×SD1611yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C22×D4—181no—
226C22×D4—181no—
227C2×SD16—181no—
228C4⋊Q8—31no—
229#127—91no—
230#121—181no—
231#121—181no—
232#120—182no—
233C4×D4—31no—
234C4×D4—31no—
235#107—61no—
236C4⋊C8—91no—
237C4⋊C8D3211yescharacteristic, complemented
238#103—181no—
239#102—61no—
240#102—182no—
241C4×C8—31no—
242C23×C3—61no—
243C23×C3—61no—
244C22×D3—21no—
245C22×D3—21no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—124no—
252C22×D3—124no—
253C22×D3—242no—
254C22×D3—242no—
255C3×Q8—121no—
256C3×Q8—121no—
257C3×D4—32no—
258C3×D4—32no—
259C3×D4—61no—
260C3×D4—61no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—124no—
278#67—124no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—41no—
282D12—21no—
283D12—21no—
284D12—122no—
285D12—122no—
286D12—124no—
287D12—124no—
288D12—121no—
289D12—121no—
290D12—121no—
291D12—121no—
292D12—121no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—241no—
297D12—241no—
298D12—241no—
299D12—241no—
300D12—242no—
301D12D2412yes—
302D12#21512yescomplemented
303C4×D3—41no—
304C4×D3—41no—
305C4×D3—41no—
306C4×D3—41no—
307Dic6—41no—
308Dic6—41no—
309C3×C8—41no—
310C3×C8—41no—
311C3×C8—81no—
312C3×C8—121no—
313C3⋊C8—41no—
314C3⋊C8—121no—
315C3⋊C8—121no—
316C3⋊C8—241no—
317C2×C32#44711yescharacteristic
318C2×C32#45011yescharacteristic
319C2×C32#45511yescharacteristic
320C3⋊D3—82no—
321C3×D3—42no—
322C3×D3—42no—
323C24—182no—
324C2×Q8—61no—
325C2×D4—31no—
326C2×D4—31no—
327C2×D4—92no—
328C2×D4—182no—
329C2×D4—182no—
330C2×D4—181no—
331C2×D4—181no—
332C2×D4—362no—
333C2×D4—362no—
334C2×D4—362no—
335C2×D4—362no—
336C22×C4—61no—
337C22×C4—61no—
338SD16—362no—
339C2×C8—21no—
340C2×C8—61no—
341C2×C8—181no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—182no—
349C42C2×D3211yescharacteristic
350C22×C3—21no—
351C22×C3—62no—
352C22×C3—62no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3—121no—
356C22×C3—121no—
357C22×C3#88211yescharacteristic
358C22×C3#93711yescharacteristic
359C2×D3—22no—
360C2×D3—22no—
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—242no—
372C2×D3—242no—
373C2×D3—242no—
374C2×D3—248no—
375C2×D3—248no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—41no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—241no—
386C3×C4C2×D2411yescharacteristic
387C3×C4#90811yescharacteristic
388C3×C4D3×D811yescharacteristic
389C3×C4#91111yescharacteristic
390C3×C4#91111yescharacteristic
391C3×C4D3×SD1611yescharacteristic
392C3×C4C2×#21511yescharacteristic
393C3×C4#94911yescharacteristic
394Dic3—41no—
395Dic3—41no—
396Dic3—81no—
397C32#163911yescharacteristic, complemented, Sylow
398C23—61no—
399C23—61no—
400C23—182no—
401C23—364no—
402C23—364no—
403C23—722no—
404Q8—121no—
405Q8—121no—
406D4—32no—
407D4—32no—
408D4—61no—
409D4—61no—
410D4—362no—
411D4—364no—
412D4—364no—
413D4—361no—
414D4—361no—
415D4—361no—
416D4—361no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4D3×D1211yescharacteristic
425C2×C4#380211yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C8—41no—
428C8—121no—
429C8—361no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—122no—
434C2×C3—122no—
435C2×C3#473211yescharacteristic
436C2×C3#477611yescharacteristic
437C2×C3#482511yescharacteristic
438C2×C3#504611yescharacteristic
439C2×C3#515611yescharacteristic
440C2×C3#520211yescharacteristic
441D3—42no—
442D3—42no—
443D3—242no—
444D3—242no—
445D3—482no—
446C22—62no—
447C22—62no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—121no—
452C22—362no—
453C22—362no—
454C22—362no—
455C22—728no—
456C22#6392211yescharacteristic
457C4—21no—
458C4—121no—
459C4—121no—
460C4—241no—
461C4D3×D2411yescharacteristic
462C4#6379511yescharacteristic
463C4#6392511yescharacteristic
464C4D3×#21511yescharacteristic
465C3—21no—
466C3#6819611yescharacteristic, complemented
467C3#7110811yescharacteristic, complemented
468C2—122no—
469C2—122no—
470C2—722no—
471C2#1059059611yescharacteristic
472C2#1059094411yescharacteristic
473C2#1059101111yescharacteristic
subgroupG/H
centerC22#63922
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. C3×#4846C2semidirect
3. #10590363C2semidirect
4. #10590281C2semidirect
5. #10589351C2semidirect
6. C3×#4483C2semidirect
7. #10589081C2semidirect
15. C3×#869C22semidirect
20. C32×C4⋊C8C22semidirect
21. C4⋊(C3⋊(C3⋊C8))C22semidirect
24. C3×C4×C3⋊C8C22semidirect
33. #4846D3semidirect
40. #4483D3semidirect
90. #869C2×D3semidirect
93. C3×C4⋊C8C2×D3semidirect
94. C3×C4⋊C8C2×D3semidirect
106. C4×C3⋊C8C2×D3semidirect
127. C3×D12SD16semidirect
237. C4⋊C8D32semidirect
302. D12#215semidirect
397. C32#1639semidirect
466. C3#68196semidirect
467. C3#71108semidirect

Maximal subgroups

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

subgroupindex
D1222
C3×#48462
#105903632
#105902812
#105893512
C3×#44832
#105890812
#711083
#681963