Finite Group Databasebeta

← #11779232

Subgroups — #11779232

Order 1152.

640 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 98 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
1D4×#634C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3#10590377C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71014—31nomaximal
9#68187—31nomaximal
10C22×#634—21no—
11C32×C4×D4C2211yescharacteristic
12D4×C3⋊Dic3—21no—
13#64133—21no—
14#64097—21no—
15#64087—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#213—21no—
19C3×#874C2211yescharacteristic
20C2×#3716—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63563—21no—
27D4×Dic6—31no—
28D4×Dic6—31no—
29D4×Dic6—61no—
30C3×#459—31no—
31#5075—31no—
32#5070—31no—
33#5015D311yescharacteristic
34#4848—31no—
35#4694—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic, complemented
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3⋊Dic3—22no—
45C2×#634—22no—
46C2×#634—21no—
47C2×#634—42no—
48C2×#634—42no—
49C2×#634D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56#3757—22no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59C4⋊(C3⋊Dic3)D412yes—
60#3750—22no—
61#3750—21no—
62C4×C3⋊Dic3—21no—
63C3×#213—42no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#3716—42no—
68#1627—91noSylow
69C22×Dic6—61no—
70C22×Dic6—61no—
71C22×Dic6—62no—
72C2×C3×D8—61no—
73C3×#127—31no—
74C3×C4×D4—21no—
75C3×C4×D4C2×D311yescharacteristic
76C3×C4×D4C2×D311yescharacteristic
77D4×Dic3—62no—
78D4×Dic3—61no—
79D4×Dic3—61no—
80C2×#214—61no—
81C2×#213—21no—
82#924—61no—
83#924—61no—
84#924—62no—
85C2×#204—61no—
86#888—62no—
87#888—61no—
88#888—61no—
89#878—62no—
90#878—62no—
91#878—64no—
92#874C2×D311yescharacteristic
93#869—31no—
94#869—31no—
95#869—61no—
96C4×Dic6—31no—
97C4×Dic6—31no—
98C4×Dic6—61no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—31no—
101C3×#102—61no—
102C3×C4×C8—31no—
103#832—62no—
104#832—61no—
105#821—62no—
106#821—61no—
107#809—21no—
108C4⋊(C3⋊C8)C2×D311yescharacteristic
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8C2×D311yescharacteristic
111C23×C32—21no—
112C22×C3×D3—41no—
113C32×D4—21no—
114C32×D4SD1612yescomplemented
115C2×C32×C4—21no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—44no—
125#634—21no—
126#634—44no—
127#634—41no—
128#634—41no—
129#634D812yescomplemented
130C3×D12—42no—
131C3×D12—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8—41no—
138D4×Q8—91no—
139#486—91no—
140#460—91no—
141#459—31no—
142#332—91no—
143Q8⋊C8—91no—
144D4⋊C8—31no—
145C2×C3×D4—21no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4D1211yescharacteristic
150C2×C3×D4#6711yescharacteristic
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×Dic3—64no—
155C22×Dic3—62no—
156C22×Dic3—62no—
157C2×D12—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×Dic6—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C2×Dic6—62no—
164C2×Dic6—64no—
165C2×Dic6—62no—
166C2×Dic6—62no—
167C2×Dic6—61no—
168C2×Dic6—61no—
169C2×Dic6—122no—
170C2×Dic6—122no—
171C2×Dic6—124no—
172C2×Dic6—124no—
173C2×Dic6—122no—
174C2×Dic6—122no—
175C3×D8—122no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—22no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C42—21no—
186C3×C42C22×D311yescharacteristic
187C3×C42C22×D311yescharacteristic
188#217—64no—
189#217—62no—
190#217—62no—
191#214—122no—
192#213—42no—
193C4⋊Dic3—31no—
194C4⋊Dic3—32no—
195C4⋊Dic3—31no—
196C4⋊Dic3—32no—
197C4⋊Dic3—61no—
198C4⋊Dic3—62no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202Dic3⋊C4—62no—
203Dic3⋊C4—64no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208C4×Dic3—62no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214#204—122no—
215C22×C32—22no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32#12011yescharacteristic
219C2×C3×D3—81no—
220C2×C3×D3—81no—
221C2×C3×D3—81no—
222C32×C4—21no—
223C32×C4—41no—
224C32×C4C2×D811yescharacteristic
225C32×C4C2×SD1611yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4#13711yescharacteristic
228C3⋊Dic3—22no—
229C3⋊Dic3—42no—
230C3⋊Dic3—41no—
231C22×Q8—181no—
232C2×SD16—181no—
233C2×D8—61no—
234C4⋊Q8—91no—
235C4⋊Q8—181no—
236#127—31no—
237C22⋊Q8—182no—
238C22⋊Q8—181no—
239C4×Q8—91no—
240C4×D4—181no—
241C4×D4D3211yescharacteristic
242C4⋊C8—31no—
243C4⋊C8—31no—
244#102—61no—
245#102—181no—
246#102—182no—
247C4×C8—31no—
248C23×C3—22no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—121no—
252C22×D3—41no—
253C3×D4—22no—
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—22no—
257C3×D4—122no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C3×D4—121no—
262C3×D4#20412yescomplemented
263C3×D4#21412yescomplemented
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4C2×D1211yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×Dic3—62no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—62no—
286C2×Dic3—64no—
287C2×Dic3—61no—
288C2×Dic3—62no—
289C2×Dic3—61no—
290C2×Dic3—62no—
291C2×Dic3—128no—
292C2×Dic3—124no—
293C2×Dic3—124no—
294D12—42no—
295D12—41no—
296D12—41no—
297D12—41no—
298D12—41no—
299Dic6—32no—
300Dic6—32no—
301Dic6—62no—
302Dic6—62no—
303Dic6—61no—
304Dic6—61no—
305Dic6—128no—
306Dic6—124no—
307Dic6—124no—
308Dic6—122no—
309Dic6—122no—
310Dic6—121no—
311Dic6—121no—
312Dic6—121no—
313Dic6—121no—
314C3×C8—121no—
315C3×C8—121no—
316C3×C8—121no—
317C3⋊C8—41no—
318C3⋊C8—41no—
319C3⋊C8—41no—
320C2×C32—42no—
321C2×C32#44711yescharacteristic
322C2×C32#44811yescharacteristic
323C2×C32#45411yescharacteristic
324C3×D3—161no—
325C2×Q8—91no—
326C2×Q8—182no—
327C2×Q8—181no—
328C2×Q8—362no—
329C2×Q8—362no—
330C2×D4—61no—
331C2×D4—61no—
332C2×D4—61no—
333C2×D4#62611yescharacteristic
334C22×C4—21no—
335C22×C4—182no—
336SD16—362no—
337D8—122no—
338C2×C8—61no—
339C2×C8—61no—
340C2×C8—61no—
341C4⋊C4—91no—
342C4⋊C4—92no—
343C4⋊C4—182no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C4⋊C4#62611yescharacteristic
347C22⋊C4—21no—
348C22⋊C4—182no—
349C42—181no—
350C42C2×D3211yescharacteristic
351C22×C3—24no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—241no—
362C22×C3—241no—
363C22×C3—241no—
364C22×C3#88211yescharacteristic
365C22×C3#93711yescharacteristic
366C2×D3—81no—
367C2×D3—81no—
368C2×D3—81no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—42no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4C2×#20411yescharacteristic
380C3×C4#90911yescharacteristic
381C3×C4D3×D811yescharacteristic
382C3×C4D3×D811yescharacteristic
383C3×C4#91111yescharacteristic
384C3×C4#91411yescharacteristic
385C3×C4C2×#21411yescharacteristic
386C3×C4#95111yescharacteristic
387Dic3—64no—
388Dic3—62no—
389Dic3—62no—
390Dic3—124no—
391Dic3—122no—
392Dic3—122no—
393Dic3—121no—
394Dic3—122no—
395Dic3—121no—
396C32#162711yescharacteristic, complemented, Sylow
397C23—21no—
398C23—121no—
399Q8—92no—
400Q8—181no—
401Q8—364no—
402Q8—361no—
403Q8—361no—
404D4—21no—
405D4—122no—
406D4—121no—
407D4—121no—
408D4—121no—
409D4—121no—
410D4#371612yescomplemented
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—182no—
417C2×C4—364no—
418C2×C4C2×#62611yescharacteristic
419C2×C4#381111yescharacteristic
420C2×C4#381111yescharacteristic
421C8—121no—
422C8—121no—
423C8—121no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—44no—
428C2×C3—42no—
429C2×C3—42no—
430C2×C3—481no—
431C2×C3#473811yescharacteristic
432C2×C3#477311yescharacteristic
433C2×C3#482711yescharacteristic
434C2×C3#504011yescharacteristic
435C2×C3#515611yescharacteristic
436C2×C3#520111yescharacteristic
437D3—161no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—241no—
442C22—241no—
443C22—241no—
444C22#6398111yescharacteristic
445C4—21no—
446C4—41no—
447C4—182no—
448C4—361no—
449C4—362no—
450C4C2×#371611yescharacteristic
451C4#6383111yescharacteristic
452C4#6392611yescharacteristic
453C4#6393711yescharacteristic
454C3—21no—
455C3#6818711yescharacteristic, complemented
456C3#7101411yescharacteristic, complemented
457C2—42no—
458C2—481no—
459C2#1059118111yescharacteristic
460C2#1059145611yescharacteristic
461C2#1059168611yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1627
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
3. #10590377C2semidirect
4. #10590273C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589094C2semidirect
7. #10589085C2semidirect
37. D4⋊(C3⋊C8)D3semidirect
114. C32×D4SD16semidirect
129. #634D8semidirect
262. C3×D4#204semidirect
263. C3×D4#214semidirect
396. C32#1627semidirect
410. D4#3716semidirect
455. C3#68187semidirect
456. C3#71014semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#50152
#105903772
#105902732
C3×D4⋊(C3⋊C8)2
#105890942
#105890852
#710143
#681873