Finite Group Databasebeta

← #11897556

Subgroups — #11897556

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595274C211yesmaximal, characteristic, complemented
2D4×#627C211yesmaximal, characteristic, complemented
3D8×C3⋊Dic3C211yesmaximal, characteristic
4C3×#5152C212yesmaximal
5#10591495C211yesmaximal, characteristic, complemented
6#10591494C211yesmaximal, characteristic, complemented
7#10591411C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9#10590900C211yesmaximal, characteristic, complemented
10#10590892C212yesmaximal, complemented
11#10590787C211yesmaximal, characteristic, complemented
12#79855—32nomaximal
13C22×#627—21no—
14C2×C32×D8C2211yescharacteristic
15D4×C3⋊Dic3C2211yescharacteristic
16D4×C3⋊Dic3C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C3×D4×Dic3C2212yes—
19#63982—21no—
20#63982—21no—
21C2×#3724—21no—
22#63964—22no—
23#63964—22no—
24#63919C2211yescharacteristic
25#63919C2211yescharacteristic
26#63918C2212yes—
27C4×#627C2211yescharacteristic
28#63869C2212yes—
29#63659C2211yescharacteristic
30#63659C2211yescharacteristic
31#63645C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×#817C2212yes—
36C3×#815C2212yes—
37#63575C2212yes—
38#63574C2212yes—
39#63573C2212yes—
40#63572C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2212yes—
42#5539—32no—
43D4×Dic6—32no—
44C3×#442—32no—
45#5152D312yes—
46Dic3×D8—32no—
47Dic3×D8—61no—
48#5009—32no—
49#5008—32no—
50#4856—32no—
51#4855—32no—
52#4766—32no—
53#4761—32no—
54#4761—32no—
55#4759—32no—
56#4702—32no—
57#4701—32no—
58C2×C32×D4C2311yescharacteristic
59C2×C32×D4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3—21no—
62C22×C3×Dic3—22no—
63C22×C3×Dic3—22no—
64C2×#627—21no—
65C2×#627—22no—
66C2×#627—21no—
67C2×#627—44no—
68C2×#627D411yescharacteristic
69C32×D8Q814yescomplemented
70C2×C32×C8C2311yescharacteristic
71#3757—21no—
72#3757—21no—
73C4⋊(C3⋊Dic3)C2311yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77C3×#217—22no—
78C3×#217—22no—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8C2312yes—
83#3724—21no—
84#3724—21no—
85#3724—22no—
86#3724D411yescharacteristic
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3D412yes—
90#3384—91noSylow
91C22×Dic6—62no—
92C2×C3×D8—21no—
93C2×C3×D8C2×D312yes—
94C3×C4×D4—32no—
95C3×C4×D4—32no—
96D4×Dic3—32no—
97D4×Dic3—32no—
98D4×Dic3—61no—
99D4×Dic3—61no—
100D4×Dic3C2×D312yes—
101D4×Dic3C2×D312yes—
102#924—62no—
103#924—62no—
104C2×Dic3⋊C4—62no—
105#890—32no—
106#888—32no—
107#888—32no—
108#888—32no—
109#878—62no—
110#878—62no—
111#878—62no—
112#878—62no—
113#870—32no—
114#869—32no—
115C4×Dic6—32no—
116C3×#106—32no—
117C3×#102—32no—
118C3×#102—32no—
119C3×#97—32no—
120#832—32no—
121#832—32no—
122#832—61no—
123#832—61no—
124#832C2×D312yes—
125#832C2×D312yes—
126#818—32no—
127#818—32no—
128#818—61no—
129#817—32no—
130#817C2×D312yes—
131#815C2×D312yes—
132Dic3⋊C8—32no—
133Dic3⋊C8—32no—
134C8×Dic3—32no—
135C8×Dic3—61no—
136#808—32no—
137#808—32no—
138#808—32no—
139#807—32no—
140C4⋊(C3⋊C8)—32no—
141C23×C32—21no—
142C23×C32—21no—
143C32×D4—21no—
144C32×D4—21no—
145C32×D4C2×Q812yes—
146C32×D4C2×Q812yescomplemented
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—44no—
157C2×C3×Dic3—82no—
158C2×C3×Dic3C2×D412yes—
159C2×C3×Dic3C2×D412yes—
160#627—22no—
161#627—44no—
162#627—42no—
163#627—81no—
164C32×C8C2×Q812yescomplemented
165C3⋊(C3⋊C8)—21no—
166C3×C3⋊C8—22no—
167#554—91no—
168D4×Q8—91no—
169#501—92no—
170#498—91no—
171#478—92no—
172#476—91no—
173#476—92no—
174#474—91no—
175#446—91no—
176#442—32no—
177C4×D8—91no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4C22×D312yes—
181C2×C3×D4C22×D312yes—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—121no—
189C22×Dic3—121no—
190C2×Dic6—32no—
191C2×Dic6—62no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—128no—
196C3×D8—24no—
197C3×D8Dic618yescomplemented
198C2×C3×C8—21no—
199C2×C3×C8—32no—
200C2×C3×C8C22×D312yes—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—32no—
203C3×C22⋊C4—62no—
204C3×C22⋊C4—62no—
205C3×C42—32no—
206#217—22no—
207#217—22no—
208#217—62no—
209#217—62no—
210#217—121no—
211#217—121no—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3C22×D312yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—32no—
222Dic3⋊C4—32no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229C4×Dic3—32no—
230C4×Dic3—61no—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8C22×D312yes—
235C22×C32—22no—
236C22×C32—22no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32—41no—
240C22×C32—41no—
241C22×C32C22×D411yescharacteristic
242C32×C4C22×Q811yescharacteristic
243C32×C42−1+411yescharacteristic
244C3⋊Dic3—21no—
245C3⋊Dic3—41no—
246C3⋊Dic3—41no—
247C3⋊Dic3AGL(1,ℤ/8)12yes—
248C3×Dic3—22no—
249C3×Dic3—22no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C22×Q8—181no—
253C2×D8D3211yescharacteristic
254C4⋊Q8—92no—
255C4⋊Q8—91no—
256C4⋊Q8—91no—
257#125—92no—
258C22⋊Q8—181no—
259C22⋊Q8—181no—
260C22⋊Q8—182no—
261C22⋊Q8—182no—
262C4×Q8—91no—
263C4×D4—32no—
264C4×D4—32no—
265C4×D4—91no—
266C4×D4—91no—
267C2×C4⋊C4—181no—
268#107—92no—
269#107—91no—
270#106—32no—
271#106—92no—
272#106—92no—
273C4⋊C8—92no—
274C4⋊C8—91no—
275#102—32no—
276#102—32no—
277#102—91no—
278#102—91no—
279#97—32no—
280C4×C8—91no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—41no—
284C23×C3—41no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C3×D4C2×Dic614yes—
292C3×D4C2×Dic614yescomplemented
293C2×C3×C4—21no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—124no—
299C2×C3×C4—242no—
300C2×C3×C4C23×D312yes—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—44no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—82no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—124no—
314C2×Dic3—124no—
315C2×Dic3—242no—
316C2×Dic3—242no—
317C2×Dic3D3×D412yes—
318C2×Dic3D3×D412yes—
319Dic6—64no—
320Dic6—124no—
321Dic6—124no—
322Dic6—124no—
323Dic6—242no—
324C3×C8—22no—
325C3×C8—62no—
326C3×C8C2×Dic614yescomplemented
327C3⋊C8—22no—
328C3⋊C8—62no—
329C3⋊C8—121no—
330C2×C32—42no—
331C2×C32—42no—
332C2×C32D4×Q811yescharacteristic
333C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
334C2×C32#57711yescharacteristic
335C2×Q8—91no—
336C2×Q8—182no—
337C2×Q8—181no—
338C2×Q8—181no—
339C2×Q8—364no—
340C2×D4C2×D3211yescharacteristic
341C2×D4C2×D3211yescharacteristic
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—181no—
345C22×C4—181no—
346D8#62714yescomplemented
347C2×C8—32no—
348C2×C8—91no—
349C2×C8C2×D3211yescharacteristic
350C4⋊C4—32no—
351C4⋊C4—32no—
352C4⋊C4—91no—
353C4⋊C4—92no—
354C4⋊C4—91no—
355C4⋊C4—91no—
356C4⋊C4—182no—
357C4⋊C4—182no—
358C4⋊C4—182no—
359C4⋊C4—181no—
360C4⋊C4—181no—
361C22⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C42—32no—
366C42—91no—
367C22×C3—24no—
368C22×C3—24no—
369C22×C3—21no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—81no—
377C22×C3—81no—
378C22×C3—81no—
379C22×C3—81no—
380C22×C3C2×D3×D412yes—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—62no—
384C3×C4—62no—
385C3×C4—122no—
386C3×C4—122no—
387C3×C4C22×Dic612yes—
388C3×C4#101012yes—
389Dic3—22no—
390Dic3—22no—
391Dic3—34no—
392Dic3—42no—
393Dic3—42no—
394Dic3—62no—
395Dic3—62no—
396Dic3—121no—
397Dic3—122no—
398Dic3—122no—
399Dic3—241no—
400Dic3—241no—
401C32#338411yescharacteristic, complemented, Sylow
402C23—21no—
403C23—21no—
404Q8—182no—
405Q8—364no—
406Q8—362no—
407Q8—721no—
408D4—21no—
409D4—21no—
410D4C2×#62712yes—
411D4C2×#62712yescomplemented
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—124no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—242no—
422C2×C4—362no—
423C2×C4—362no—
424C2×C4C22×D3211yescharacteristic
425C8—62no—
426C8—181no—
427C8C2×#62712yescomplemented
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—44no—
432C2×C3—44no—
433C2×C3—82no—
434C2×C3—82no—
435C2×C3D4×Dic612yes—
436C2×C3D3×AGL(1,ℤ/8)12yes—
437C2×C3#577512yes—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22D32×D411yescharacteristic
445C4—62no—
446C4—62no—
447C4—92no—
448C4—122no—
449C4—122no—
450C4—181no—
451C4—361no—
452C4—361no—
453C4#6430911yescharacteristic
454C4C22×#62711yescharacteristic
455C3—21no—
456C3#7985512yescomplemented
457C2—42no—
458C2—42no—
459C2#1059472611yescharacteristic
460C2#1059473311yescharacteristic
461C2D4×#62711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595274C2semidirect
2. D4×#627C2semidirect
5. #10591495C2semidirect
6. #10591494C2semidirect
7. #10591411C2semidirect
8. #10591408C2semidirect
9. #10590900C2semidirect
10. #10590892C2semidirect
11. #10590787C2semidirect
69. C32×D8Q8semidirect
146. C32×D4C2×Q8semidirect
164. C32×C8C2×Q8semidirect
197. C3×D8Dic6semidirect
292. C3×D4C2×Dic6semidirect
326. C3×C8C2×Dic6semidirect
346. D8#627semidirect
401. C32#3384semidirect
411. D4C2×#627semidirect
427. C8C2×#627semidirect
456. C3#79855semidirect

Maximal subgroups

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

subgroupindex
#105952742
D4×#6272
D8×C3⋊Dic32
C3×#51522
#105914952
#105914942
#105914112
#105914082
#105909002
#105908922
#105907872
#798553