Finite Group Databasebeta

← #11870435

Subgroups — #11870435

Order 1152.

1197 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1197 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10594929C211yesmaximal, characteristic, complemented
3C3×#5217C212yesmaximal, complemented
4#10591494C212yesmaximal, complemented
5#10591486C212yesmaximal, complemented
6#10591435C214yesmaximal, complemented
7#10591094C212yesmaximal, complemented
8#10591061C211yesmaximal, characteristic, complemented
9#79988—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×#3805—21no—
13C2×#3757—21no—
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3—21no—
16D4×C3⋊Dic3C2212yes—
17D4×C3⋊Dic3C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#213C2214yes—
21C3×#930C2212yes—
22#63980—21no—
23#63919C2211yescharacteristic, complemented
24#63915—21no—
25#63914C2211yescharacteristic, complemented
26#63902—21no—
27#63898C2212yescomplemented
28C3×#832C2214yes—
29C3×#830C2212yes—
30#63575C2214yescomplemented
31#63572C2212yescomplemented
32#63563C2214yescomplemented
33#63553C2212yescomplemented
34C2×D4×Dic3—32no—
35C2×D4×Dic3—61no—
36#5596—32no—
37C3×#447—32no—
38#5217D312yescomplemented
39#5150—34no—
40Dic3×D8—34no—
41#5033—32no—
42#4759—34no—
43#4756—34no—
44#4736—32no—
45#4718—32no—
46C24×C32—21no—
47C2×C32×D4—24no—
48C2×C32×D4—21no—
49C2×C32×D4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3—22no—
53C22×C3⋊Dic3—22no—
54C22×C3⋊Dic3—44no—
55C22×C3⋊Dic3D411yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C2×C3×#67—22no—
58C2×C3×D12C2312yes—
59C2×#627—21no—
60C2×#625—21no—
61C2×#625—21no—
62#3805—44no—
63C2×D3×Dic3—22no—
64#3757—22no—
65#3757—22no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×#213—28no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8C2314yes—
76#3724—21no—
77(C2×D3)⋊Dic3—22no—
78#3100—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4C2×D312yes—
81C23×Dic3—62no—
82C23×Dic3—62no—
83C2×#237—62no—
84C2×C3×D8—34no—
85C3×#121—32no—
86C2×#217—62no—
87C2×#217—62no—
88#940—32no—
89#939—62no—
90D4×Dic3—34no—
91D4×Dic3—34no—
92D4×Dic3—32no—
93D4×Dic3—62no—
94D4×Dic3—62no—
95D4×Dic3—62no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98D4×Dic3—62no—
99C2×#213C2×D314yes—
100#930C2×D312yes—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—61no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—61no—
105#893—32no—
106#888—32no—
107#885—62no—
108#67⋊C4—62no—
109C3×#102—34no—
110C3×C22⋊C8—32no—
111#832—34no—
112#832C2×D314yes—
113#830C2×D312yes—
114#821—34no—
115#818—34no—
116Dic3⋊C8—34no—
117C8×Dic3—34no—
118#807—34no—
119C23×C32—24no—
120C23×C32—22no—
121C23×C32—42no—
122C23×C32—42no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C32×D4—24no—
126C32×D4—22no—
127C32×D4#4114yescomplemented
128C2×C32×C4—22no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—42no—
134C2×C3⋊Dic3—44no—
135C2×C3⋊Dic3—44no—
136C2×C3⋊Dic3D814yescomplemented
137C2×C3⋊Dic3C2×D411yescharacteristic
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C3×#67—44no—
142C2×C3×Dic3—22no—
143C3×D12—24no—
144#627—42no—
145#625—42no—
146#625—42no—
147D3×Dic3—44no—
148C3×C3⋊C8—24no—
149#532—91no—
150C2×C4×D4—91no—
151#480—92no—
152#474—92no—
153#459—92no—
154#447—32no—
155C4×D8—94no—
156#431—91no—
157C24×C3—22no—
158C24×C3—22no—
159C2×C3×D4—22no—
160C2×C3×D4—28no—
161C2×C3×D4—28no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—32no—
165C2×C3×D4—62no—
166C2×C3×D4C22×D314yes—
167C22×C3×C4—21no—
168C22×C3×C4C22×D312yes—
169C2×#67—22no—
170C2×#67—62no—
171C2×#67—62no—
172C22×Dic3—32no—
173C22×Dic3—32no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—62no—
177C22×Dic3—64no—
178C22×Dic3—64no—
179C22×Dic3—62no—
180C22×Dic3—64no—
181C22×Dic3—64no—
182C22×Dic3—62no—
183C22×Dic3—128no—
184C22×Dic3—128no—
185#237—128no—
186C2×D12C22×D312yes—
187C2×C4×D3—62no—
188C2×Dic6—62no—
189C3×D8—68no—
190C2×C3×C8—34no—
191C3×C4⋊C4—32no—
192C3×C22⋊C4—62no—
193#217—62no—
194#217—64no—
195#217—64no—
196#217—64no—
197#217—64no—
198#213—28no—
199(C2×D3)⋊C4—22no—
200(C2×D3)⋊C4—62no—
201C4⋊Dic3—34no—
202C4⋊Dic3—62no—
203C4⋊Dic3—62no—
204C4⋊Dic3—62no—
205C4⋊Dic3C22×D312yes—
206Dic3⋊C4—62no—
207C4×Dic3—32no—
208C4×Dic3—32no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C2×C3⋊C8C22×D314yes—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32—24no—
219C22×C32—48no—
220C22×C32—42no—
221C22×C32—42no—
222C22×C32C2×D812yes—
223C22×C32C22×D411yescharacteristic
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C32×C4—21no—
228C32×C4C2×#4112yes—
229C3⋊Dic3—21no—
230C3⋊Dic3—21no—
231C3⋊Dic3—42no—
232C3⋊Dic3C2×D812yes—
233C3⋊Dic3C2×D812yes—
234C3×Dic3—42no—
235C2×#41—181no—
236C22×D4D3211yescharacteristic
237C23×C4—181no—
238C2×D8—34no—
239C4⋊Q8—91no—
240#127—91no—
241#124—181no—
242#121—32no—
243#121—181no—
244C4×D4—92no—
245C4×D4—92no—
246C4×D4—92no—
247C4×D4—181no—
248C4×D4—181no—
249C4×D4—181no—
250C2×C4⋊C4—91no—
251C2×C22⋊C4—181no—
252C2×C42—91no—
253#107—94no—
254C4⋊C8—92no—
255#102—34no—
256#102—94no—
257C22⋊C8—32no—
258C4×C8—92no—
259C23×C3—24no—
260C23×C3—28no—
261C23×C3—28no—
262C23×C3—24no—
263C23×C3—21no—
264C23×C3—44no—
265C23×C3—44no—
266C23×C3—44no—
267C23×C3—44no—
268C23×C3—62no—
269C23×C3D3×D412yes—
270C22×D3—22no—
271C3×D4—28no—
272C3×D4—28no—
273C3×D4—24no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—64no—
277C3×D4—124no—
278C3×D4#23718yescomplemented
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—62no—
284C2×C3×C4D3×D412yes—
285C2×C3×C4C23×D312yes—
286#67—44no—
287#67—124no—
288#67—124no—
289C2×Dic3—22no—
290C2×Dic3—38no—
291C2×Dic3—32no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—64no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—124no—
303C2×Dic3—128no—
304C2×Dic3—128no—
305C2×Dic3—122no—
306C2×Dic3—128no—
307C2×Dic3—128no—
308C2×Dic3—122no—
309C2×Dic3—124no—
310C2×Dic3—124no—
311D12—24no—
312C4×D3—124no—
313Dic6—124no—
314C3×C8—64no—
315C3⋊C8—24no—
316C2×C32—22no—
317C2×C32—44no—
318C2×C32#52511yescharacteristic
319C2×C32C22×D811yescharacteristic
320C2×C32#57511yescharacteristic
321C3×D3—82no—
322C24—21no—
323#41—364no—
324C2×Q8—181no—
325C2×D4—24no—
326C2×D4—21no—
327C2×D4—32no—
328C2×D4—62no—
329C2×D4—181no—
330C2×D4—181no—
331C2×D4C2×D3212yes—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—182no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4—181no—
338C22×C4—364no—
339C22×C4C2×D3211yescharacteristic
340D8—68no—
341C2×C8—34no—
342C4⋊C4—32no—
343C4⋊C4—92no—
344C4⋊C4—181no—
345C4⋊C4—181no—
346C22⋊C4—62no—
347C22⋊C4—182no—
348C22⋊C4—182no—
349C22⋊C4—182no—
350C42—91no—
351C42—91no—
352C42—91no—
353C42—91no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—28no—
359C22×C3—28no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—44no—
363C22×C3—416no—
364C22×C3—416no—
365C22×C3—44no—
366C22×C3—44no—
367C22×C3—44no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3—122no—
371C22×C3D3×D814yes—
372C22×C3C2×D3×D412yes—
373C2×D3—42no—
374C2×D3—42no—
375C2×D3—42no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—122no—
380C3×C4C2×#23714yes—
381Dic3—34no—
382Dic3—34no—
383Dic3—42no—
384Dic3—62no—
385Dic3—62no—
386Dic3—62no—
387Dic3—62no—
388Dic3—121no—
389Dic3—121no—
390Dic3—124no—
391Dic3—124no—
392C32#310011yescharacteristic, complemented, Sylow
393C23—24no—
394C23—22no—
395C23—42no—
396C23—42no—
397C23—62no—
398C23#381111yescharacteristic
399Q8—362no—
400D4—24no—
401D4—22no—
402D4—64no—
403D4—124no—
404D4—362no—
405D4—362no—
406D4#380514yescomplemented
407C2×C4—22no—
408C2×C4—62no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—94no—
412C2×C4—91no—
413C2×C4—91no—
414C2×C4—182no—
415C2×C4—364no—
416C2×C4—364no—
417C2×C4—364no—
418C2×C4—361no—
419C2×C4—362no—
420C2×C4#381111yescharacteristic
421C2×C4C22×D3211yescharacteristic
422C8—64no—
423C2×C3—24no—
424C2×C3—24no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—48no—
429C2×C3—48no—
430C2×C3—242no—
431C2×C3#558612yes—
432C2×C3C2×D3×D812yes—
433C2×C3#577312yes—
434D3—82no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—48no—
439C22—42no—
440C22—42no—
441C22—122no—
442C22—122no—
443C22—122no—
444C22#6392612yes—
445C22C2×#381111yescharacteristic
446C4—21no—
447C4—92no—
448C4—92no—
449C4—122no—
450C4—181no—
451C4—181no—
452C4—362no—
453C4C2×#380512yes—
454C3—21no—
455C3#7998812yescomplemented
456C2—22no—
457C2—44no—
458C2—242no—
459C2C2×#6392611yescharacteristic
460C2#1059510111yescharacteristic
461C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. #10594929C2semidirect
3. C3×#5217C2semidirect
4. #10591494C2semidirect
5. #10591486C2semidirect
6. #10591435C2semidirect
7. #10591094C2semidirect
8. #10591061C2semidirect
23. #63919C22semidirect
25. #63914C22semidirect
27. #63898C22semidirect
30. #63575C22semidirect
31. #63572C22semidirect
32. #63563C22semidirect
33. #63553C22semidirect
38. #5217D3semidirect
127. C32×D4#41semidirect
136. C2×C3⋊Dic3D8semidirect
278. C3×D4#237semidirect
392. C32#3100semidirect
406. D4#3805semidirect
455. C3#79988semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105949292
C3×#52172
#105914942
#105914862
#105914352
#105910942
#105910612
#799883