Finite Group Databasebeta

← #11870452

Subgroups — #11870452

Order 1152.

1139 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1139 conjugacy classes of subgroups — too many to draw. Only its 172 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
1#10596187C211yesmaximal, characteristic, complemented
2C4×#3802C211yesmaximal, characteristic, complemented
3C3×#5072C212yesmaximal, complemented
4#10591516C212yesmaximal, complemented
5#10591435C214yesmaximal, complemented
6#10591417C212yesmaximal, complemented
7#10590272C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic, complemented
9#80312—32nomaximal
10C2×#3830—21no—
11C2×#3802C2211yescharacteristic
12C2×C4×D32—21no—
13C32×#127C2211yescharacteristic, complemented
14#64147—21no—
15#64147C2212yes—
16#64145—21no—
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3C2212yescomplemented
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C2×C3×#213C2214yes—
22C3×C4×D12C2212yes—
23#63921—21no—
24#63902—21no—
25C4×#625—21no—
26#63900C2211yescharacteristic
27#63898C2212yes—
28C3×#832C2214yescomplemented
29C3×C4⋊(C3⋊C8)C2212yescomplemented
30#63575C2214yescomplemented
31#63563C2214yes—
32#63557C2212yes—
33#63553C2212yescomplemented
34#5716—32no—
35#5716—61no—
36C4×D3×D4—32no—
37C3×#459—32no—
38#5156—34no—
39Dic3×D8—34no—
40#5072D312yescomplemented
41#5007—32no—
42#4846—32no—
43#4833—32no—
44#4774—34no—
45#4756—34no—
46C22×D32—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2312yes—
50C2×#638—22no—
51C22×C3⋊Dic3—22no—
52#3830—44no—
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×#634—21no—
57C2×C3×D12C2312yes—
58C2×C3×C4×D3—22no—
59C2×#625—21no—
60C2×#624—21no—
61C2×D3×Dic3—22no—
62#3802—24no—
63C4×D32—44no—
64C32×C42C2311yescharacteristic
65#3757—22no—
66#3757—22no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
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
79C2×#237—62no—
80C2×#237—62no—
81C2×D3×D4—32no—
82C22×C4×D3—62no—
83C2×C3×D8—34no—
84C3×#127—21no—
85C3×#127C2×D312yescomplemented
86C3×C4×D4—32no—
87#938—34no—
88#938—62no—
89#938—62no—
90#938—62no—
91#936—62no—
92#936—62no—
93D4×Dic3—34no—
94D4×Dic3—32no—
95D4×Dic3—62no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98C2×#213C2×D314yes—
99C4×#67—62no—
100#893—32no—
101D3×C4⋊C4—32no—
102#67⋊C4—62no—
103D3×C22⋊C4—62no—
104C4×D12C2×D312yes—
105C42×D3—32no—
106C42×D3—61no—
107#869—32no—
108#869—61no—
109C3×C4⋊C8—32no—
110C3×#102—34no—
111#832—34no—
112#832C2×D314yescomplemented
113#821—34no—
114(C2×D3)⋊C8—34no—
115#818—34no—
116C8×Dic3—34no—
117#807—34no—
118C4⋊(C3⋊C8)C2×D312yescomplemented
119C23×C32—22no—
120C22×C3⋊D3C2×D411yescharacteristic
121C22×C3×D3—22no—
122C2×D32—24no—
123C2×D32—42no—
124C2×D32—42no—
125C32×D4—24no—
126C32×D4—42no—
127C32×D4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131#638—44no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—44no—
134C2×C3⋊Dic3C2×D411yescharacteristic
135C2×C3⋊Dic3C2×D411yescharacteristic
136C2×C3⋊Dic3C2×D411yescharacteristic
137C4×C3⋊D3—22no—
138C4×C3⋊D3—41no—
139C4×C3⋊D3D814yescomplemented
140#634—42no—
141C2×C3×Dic3—22no—
142C3×D12—22no—
143C3×D12#4114yescomplemented
144C3×C4×D3—44no—
145#625—24no—
146#624—42no—
147D3×Dic3—44no—
148C3×C3⋊C8—24no—
149#532—91no—
150C2×C4×D4—91no—
151#480—92no—
152#474—92no—
153#459—32no—
154#447—92no—
155C4×D8—94no—
156#431—91no—
157C23×D3—62no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—32no—
164C2×C3×D4C22×D314yes—
165C22×C3×C4—62no—
166C2×#67—62no—
167C2×#67—64no—
168C2×#67—64no—
169C22×Dic3—62no—
170C22×Dic3—64no—
171C22×Dic3—64no—
172#237—128no—
173#237—128no—
174D3×D4—64no—
175D3×D4—64no—
176C2×D12C22×D312yes—
177C2×C4×D3—22no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—128no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C3×D8—68no—
190C2×C3×C8—34no—
191C3×C4⋊C4—32no—
192C3×C22⋊C4—62no—
193C3×C42—21no—
194C3×C42C22×D312yes—
195#217—62no—
196#217—64no—
197#217—64no—
198#217—64no—
199#217—64no—
200#213—28no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4—62no—
203C4⋊Dic3—34no—
204C4⋊Dic3—62no—
205C4⋊Dic3—62no—
206C4⋊Dic3—62no—
207C4⋊Dic3C22×D312yes—
208Dic3⋊C4—62no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—32no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C2×C3⋊C8C22×D314yes—
216C22×C32—42no—
217C22×C32—42no—
218C22×C32—42no—
219C22×C32C22×D411yescharacteristic
220C2×C3⋊D3—21no—
221C2×C3⋊D3—21no—
222C2×C3⋊D3C2×D812yes—
223C2×C3×D3—24no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226D32—48no—
227C32×C4—21no—
228C32×C4C2×D812yes—
229C32×C4C2×#4112yes—
230C3⋊Dic3—21no—
231C3⋊Dic3—21no—
232C3⋊Dic3—42no—
233C3⋊Dic3C2×D812yes—
234C3×Dic3—42no—
235C2×#41—181no—
236C22×D4—91no—
237C23×C4—181no—
238C2×D8—34no—
239C4⋊Q8—91no—
240#127D3211yescharacteristic, complemented
241#124—181no—
242#121—92no—
243#121—181no—
244C4×D4—32no—
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—32no—
255#102—34no—
256#102—94no—
257C22⋊C8—92no—
258C4×C8—92no—
259C23×C3—24no—
260C23×C3—24no—
261C23×C3—62no—
262C22×D3—22no—
263C22×D3—32no—
264C22×D3—61no—
265C22×D3—68no—
266C22×D3—124no—
267C22×D3—124no—
268C3×D4—24no—
269C3×D4—24no—
270C3×D4—34no—
271C3×D4—44no—
272C3×D4—44no—
273C3×D4—44no—
274C3×D4—44no—
275C3×D4—44no—
276C3×D4—62no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—62no—
281C2×C3×C4—124no—
282C2×C3×C4D3×D412yes—
283C2×C3×C4D3×D412yes—
284C2×C3×C4C23×D312yes—
285#67—68no—
286#67—128no—
287#67—128no—
288C2×Dic3—22no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—32no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—64no—
296C2×Dic3—64no—
297C2×Dic3—124no—
298C2×Dic3—128no—
299C2×Dic3—128no—
300D12—22no—
301D12#23714yescomplemented
302C4×D3—38no—
303C4×D3—44no—
304C4×D3—64no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—122no—
308C4×D3—124no—
309C4×D3—124no—
310C4×D3—122no—
311C4×D3—122no—
312Dic6—124no—
313Dic6—124no—
314C3×C8—64no—
315C3⋊C8—24no—
316C2×C32—82no—
317C2×C32#52511yescharacteristic
318C2×C32C22×D811yescharacteristic
319C2×C32#57511yescharacteristic
320C3⋊D3—22no—
321C3×D3—44no—
322C24—181no—
323#41—364no—
324C2×Q8—181no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—32no—
328C2×D4—181no—
329C2×D4—184no—
330C2×D4—182no—
331C2×D4C2×D3212yes—
332C22×C4—62no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—181no—
337C22×C4—182no—
338C22×C4—182no—
339C22×C4—364no—
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—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—44no—
356C22×C3—44no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3—44no—
360C22×C3—44no—
361C22×C3—64no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3C2×D3×D412yes—
365C2×D3—24no—
366C2×D3—34no—
367C2×D3—42no—
368C2×D3—42no—
369C2×D3—62no—
370C2×D3—62no—
371C2×D3—62no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3—1216no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—122no—
380C3×C4D3×D814yes—
381C3×C4C2×#23712yes—
382C3×C4D3×#4112yes—
383Dic3—34no—
384Dic3—42no—
385Dic3—62no—
386Dic3—62no—
387Dic3—62no—
388Dic3—121no—
389Dic3—121no—
390Dic3—124no—
391Dic3—124no—
392C32#310011yescharacteristic, complemented, Sylow
393C23—22no—
394C23—62no—
395C23—91no—
396C23—184no—
397C23—362no—
398C23—362no—
399Q8—362no—
400D4—24no—
401D4—34no—
402D4—42no—
403D4—42no—
404D4—62no—
405D4—184no—
406D4—364no—
407C2×C4—62no—
408C2×C4—91no—
409C2×C4—94no—
410C2×C4—91no—
411C2×C4—91no—
412C2×C4—124no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4—361no—
416C2×C4—364no—
417C2×C4—364no—
418C2×C4—362no—
419C2×C4#381111yescharacteristic
420C2×C4#381111yescharacteristic
421C2×C4C22×D3211yescharacteristic
422C8—64no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—84no—
427C2×C3—84no—
428C2×C3—124no—
429C2×C3#560612yes—
430C2×C3C2×D3×D812yes—
431C2×C3#577312yes—
432D3—44no—
433D3—64no—
434D3—122no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—64no—
439C22—92no—
440C22—122no—
441C22—122no—
442C22—181no—
443C22—181no—
444C22—368no—
445C22C2×#381111yescharacteristic
446C4—21no—
447C4—92no—
448C4—122no—
449C4—181no—
450C4—181no—
451C4—362no—
452C4#6392612yes—
453C4D3×#23712yes—
454C3—21no—
455C3#8031212yescomplemented
456C2—82no—
457C2—124no—
458C2—182no—
459C2C2×#6392611yescharacteristic
460C2#1059510111yescharacteristic
461C2#1059530611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
hypercenter#127D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596187C2semidirect
2. C4×#3802C2semidirect
3. C3×#5072C2semidirect
4. #10591516C2semidirect
5. #10591435C2semidirect
6. #10591417C2semidirect
7. #10590272C2semidirect
8. #10590256C2semidirect
13. C32×#127C22semidirect
18. D4×C3⋊Dic3C22semidirect
20. #64078C22semidirect
28. C3×#832C22semidirect
29. C3×C4⋊(C3⋊C8)C22semidirect
30. #63575C22semidirect
33. #63553C22semidirect
40. #5072D3semidirect
85. C3×#127C2×D3semidirect
112. #832C2×D3semidirect
118. C4⋊(C3⋊C8)C2×D3semidirect
139. C4×C3⋊D3D8semidirect
143. C3×D12#41semidirect
240. #127D32semidirect
301. D12#237semidirect
392. C32#3100semidirect
455. C3#80312semidirect

Maximal subgroups

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

subgroupindex
#105961872
C4×#38022
C3×#50722
#105915162
#105914352
#105914172
#105902722
#105902562
#803123