Finite Group Databasebeta

← #11779315

Subgroups — #11779315

Order 1152.

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

normal subgroups only

This group has 670 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×#4842C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic, complemented
4#10590266C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#71143—31nomaximal
9#68195—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×#3717—22no—
20C32×C4⋊C8C2211yescharacteristic, complemented
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C3×#821—21no—
23C3×#817—21no—
24C3×C4×C3⋊C8C2211yescharacteristic, complemented
25#63574—21no—
26#63562—21no—
27D4×D12—31no—
28D4×D12—31no—
29C3×#476—31no—
30#5085—31no—
31#5084—31no—
32#5008—31no—
33#4842D311yescharacteristic, complemented
34#4693—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#3717—44no—
69#1629—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—62no—
78#930—61no—
79#930—61no—
80C2×#204—62no—
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×#106—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8C2×D311yescharacteristic, complemented
94C3×C4⋊C8C2×D311yescharacteristic, complemented
95C3×#102—61no—
96C3×C4×C8—31no—
97#832—61no—
98#821—21no—
99#817—21no—
100#809—61no—
101#808—61no—
102#808—61no—
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×D12SD1612yescomplemented
127C3×D12SD1612yescomplemented
128C3×C4×D3—41no—
129C3×C4×D3—41no—
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×Dic6—42no—
133#626—44no—
134#626—44no—
135C32×C8—41no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—22no—
138D42—91no—
139#492—91no—
140#476—31no—
141#476—91no—
142#331—91no—
143D4⋊C8—31no—
144D4⋊C8—91no—
145C23×D3—62no—
146C23×D3—62no—
147C2×C3×Q8—61no—
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C2×#67—62no—
153C2×#67—62no—
154D3×D4—122no—
155D3×D4—122no—
156D3×D4—122no—
157D3×D4—122no—
158C2×D12—32no—
159C2×D12—32no—
160C2×D12—62no—
161C2×D12—62no—
162C2×D12—62no—
163C2×D12—61no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—121no—
168C2×D12—121no—
169C2×D12—122no—
170C2×D12—122no—
171C2×D12—122no—
172C2×D12—122no—
173C2×D12D1211yescharacteristic
174C2×D12#6711yescharacteristic
175C2×C4×D3—21no—
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#215—124no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—62no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3D1211yescharacteristic
199C4⋊Dic3#6711yescharacteristic
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204#204—124no—
205C22×C32#12011yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—42no—
209C2×C3×D3—22no—
210C2×C3×D3—22no—
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215D32—88no—
216C32×C4—21no—
217C32×C4C2×SD1611yescharacteristic
218C32×C4C2×SD1611yescharacteristic
219C32×C4AGL(1,ℤ/8)11yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C3×Dic3—41no—
222C3×Dic3—41no—
223C3×Dic3—81no—
224C22×D4—181no—
225C22×D4—181no—
226C2×SD16—182no—
227C4⋊Q8—31no—
228#127—91no—
229#121—181no—
230#121—181no—
231#120—182no—
232C4×D4—31no—
233C4×D4—31no—
234#106—61no—
235#106—181no—
236C4⋊C8—91no—
237C4⋊C8D3211yescharacteristic, complemented
238#102—61no—
239#102—181no—
240C4×C8—31no—
241C23×C3—61no—
242C23×C3—61no—
243C22×D3—21no—
244C22×D3—21no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—122no—
248C22×D3—124no—
249C22×D3—124no—
250C22×D3—124no—
251C22×D3—124no—
252C22×D3—242no—
253C22×D3—242no—
254C3×Q8—122no—
255C3×D4—32no—
256C3×D4—32no—
257C3×D4—61no—
258C3×D4—61no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
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×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275#67—124no—
276#67—124no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280D12—21no—
281D12—21no—
282D12—122no—
283D12—122no—
284D12—124no—
285D12—124no—
286D12—121no—
287D12—121no—
288D12—121no—
289D12—121no—
290D12—121no—
291D12—121no—
292D12—121no—
293D12—121no—
294D12—241no—
295D12—241no—
296D12—241no—
297D12—241no—
298D12—242no—
299D12#20412yescomplemented
300D12#21512yescomplemented
301C4×D3—41no—
302C4×D3—41no—
303C4×D3—41no—
304C4×D3—41no—
305Dic6—42no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—62no—
309C3×C8—81no—
310C3⋊C8—22no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C3⋊C8—241no—
314C2×C32#45011yescharacteristic
315C2×C32#45011yescharacteristic
316C2×C32#45311yescharacteristic
317C3⋊D3—82no—
318C3×D3—42no—
319C3×D3—42no—
320C24—182no—
321C2×Q8—61no—
322C2×D4—31no—
323C2×D4—31no—
324C2×D4—92no—
325C2×D4—182no—
326C2×D4—182no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4—362no—
330C2×D4—362no—
331C2×D4—362no—
332C2×D4—362no—
333C22×C4—61no—
334C22×C4—61no—
335SD16—364no—
336C2×C8—21no—
337C2×C8—61no—
338C2×C8—181no—
339C4⋊C4—31no—
340C4⋊C4—31no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—182no—
346C42C2×D3211yescharacteristic
347C22×C3—21no—
348C22×C3—62no—
349C22×C3—62no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3#88211yescharacteristic
355C22×C3#93711yescharacteristic
356C2×D3—22no—
357C2×D3—22no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—41no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—242no—
369C2×D3—242no—
370C2×D3—242no—
371C2×D3—248no—
372C2×D3—248no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—41no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—241no—
383C3×C4C2×#20411yescharacteristic
384C3×C4#90811yescharacteristic
385C3×C4#91111yescharacteristic
386C3×C4D3×SD1611yescharacteristic
387C3×C4D3×SD1611yescharacteristic
388C3×C4#91411yescharacteristic
389C3×C4C2×#21511yescharacteristic
390C3×C4#94911yescharacteristic
391Dic3—41no—
392Dic3—41no—
393Dic3—81no—
394C32#162911yescharacteristic, complemented, Sylow
395C23—61no—
396C23—61no—
397C23—182no—
398C23—364no—
399C23—364no—
400C23—722no—
401Q8—122no—
402D4—32no—
403D4—32no—
404D4—61no—
405D4—61no—
406D4—362no—
407D4—364no—
408D4—364no—
409D4—361no—
410D4—361no—
411D4—361no—
412D4—361no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4D3×D1211yescharacteristic
421C2×C4#380211yescharacteristic
422C2×C4D3×#6711yescharacteristic
423C8—41no—
424C8—62no—
425C8—361no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—122no—
430C2×C3—122no—
431C2×C3#473111yescharacteristic
432C2×C3#477611yescharacteristic
433C2×C3#482211yescharacteristic
434C2×C3#504611yescharacteristic
435C2×C3#516911yescharacteristic
436C2×C3#519811yescharacteristic
437D3—42no—
438D3—42no—
439D3—242no—
440D3—242no—
441D3—482no—
442C22—62no—
443C22—62no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—362no—
449C22—362no—
450C22—362no—
451C22—728no—
452C22#6392211yescharacteristic
453C4—21no—
454C4—121no—
455C4—121no—
456C4—241no—
457C4D3×#20411yescharacteristic
458C4#6379411yescharacteristic
459C4#6392511yescharacteristic
460C4D3×#21511yescharacteristic
461C3—21no—
462C3#6819511yescharacteristic, complemented
463C3#7114311yescharacteristic, complemented
464C2—122no—
465C2—122no—
466C2—722no—
467C2#1059059611yescharacteristic
468C2#1059094211yescharacteristic
469C2#1059101311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalD122C2
hypercenterC4⋊C8D32
hypocenterC32#1629
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×#4842C2semidirect
3. #10590373C2semidirect
4. #10590266C2semidirect
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. #4842D3semidirect
40. #4483D3semidirect
90. #869C2×D3semidirect
93. C3×C4⋊C8C2×D3semidirect
94. C3×C4⋊C8C2×D3semidirect
106. C4×C3⋊C8C2×D3semidirect
126. C3×D12SD16semidirect
127. C3×D12SD16semidirect
237. C4⋊C8D32semidirect
299. D12#204semidirect
300. D12#215semidirect
394. C32#1629semidirect
462. C3#68195semidirect
463. C3#71143semidirect

Maximal subgroups

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

subgroupindex
D1222
C3×#48422
#105903732
#105902662
#105893512
C3×#44832
#105890812
#711433
#681953