Finite Group Databasebeta

← #11863664

Subgroups — #11863664

Order 1152.

1581 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 1581 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C22×#3797C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic
3C2×#63802C212yesmaximal, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic
5C3×#4739C212yesmaximal, complemented
6#10591185C212yesmaximal, complemented
7#10590950C214yesmaximal, complemented
8#10590672C212yesmaximal, complemented
9D3×#451—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×Dic6C2212yes—
12C22×#627—21no—
13C22×#624—21no—
14C2×#3797—21no—
15C2×#3797—21no—
16C2×#3797—28no—
17C2×#3797C2212yes—
18C2×#3797C2211yescharacteristic
19C2×#3797C2212yes—
20C2×C8×C3⋊D3C2212yes—
21C3×#924C2212yes—
22C2×C3×Dic12C2214yescomplemented
23#63982—21no—
24#63974—21no—
25#63900C2211yescharacteristic
26#63883—21no—
27#63871C2212yes—
28#63865—21no—
29C2×#3718C2214yescomplemented
30#63802—28no—
31C32×C22⋊C8C2211yescharacteristic
32#63657C2211yescharacteristic
33#63647C2212yes—
34C3×#816C2214yescomplemented
35#63565C2214yescomplemented
36C22×D3×Q8—32no—
37C2×D3×Q16—34no—
38D3×C22⋊Q8—32no—
39C3×#451—32no—
40#5228—32no—
41#5186—34no—
42#5050—32no—
43#4809—34no—
44D3×#103—34no—
45#4739D312yescomplemented
46D3×C22⋊C8—32no—
47D3×C22⋊C8—61no—
48C23×C3⋊D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C22×C3×Dic3—22no—
57C2×C3×Dic6—22no—
58C2×C3×Dic6—28no—
59C2×C3×Dic6C2312yes—
60C2×C3×Dic6C2314yes—
61C2×#627—28no—
62C2×#627—22no—
63C2×#627—22no—
64C2×#627—21no—
65C2×#624—28no—
66C2×#624—22no—
67C2×#624—22no—
68C2×#624—21no—
69C2×#624—21no—
70#3797—28no—
71#3797—28no—
72#3797—24no—
73#3797—28no—
74#3797—24no—
75#3797D418yes—
76C2×C32×C8C2312yes—
77C2×C3⋊(C3⋊C8)C2312yes—
78C8×C3⋊D3—24no—
79C3×#217—22no—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic12—28no—
83#3724—21no—
84Dic3⋊Dic3—22no—
85#3722—22no—
86#3718—28no—
87C2×#451—91noSylow
88C22×C3×Q8—32no—
89C2×D3×Q8—34no—
90C2×D3×Q8—34no—
91C2×D3×Q8—32no—
92C2×D3×Q8—62no—
93C2×D3×Q8—62no—
94C2×D3×Q8—616no—
95C22×C4×D3—32no—
96C22×C4×D3—61no—
97C22×C4×D3—62no—
98C22×Dic6—62no—
99C22×Dic6C2×D312yes—
100C2×C3×Q16—34no—
101C3×C22⋊Q8—32no—
102#946—32no—
103C2×#216—34no—
104C2×#216—34no—
105#924C2×D312yes—
106D3×Q16—616no—
107C2×Dic12C2×D314yescomplemented
108C2×D3×C8—34no—
109C2×D3×C8—62no—
110#897—32no—
111#896—62no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—62no—
114D3×C22⋊C4—62no—
115#878—62no—
116C3×#103—34no—
117C3×C22⋊C8—21no—
118C3×C22⋊C8C2×D312yes—
119#835—34no—
120#830—32no—
121#830—61no—
122(C2×D3)⋊C8—34no—
123(C2×D3)⋊C8—62no—
124#816C2×D314yescomplemented
125#810—34no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3Q1614yescomplemented
130C22×C3⋊D3C2×D411yescharacteristic
131C22×C3⋊D3C2×D411yescharacteristic
132C2×C32×C4—22no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3C2×D411yescharacteristic
137C2×C3⋊Dic3C2×D411yescharacteristic
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140C4×C3⋊D3—22no—
141C4×C3⋊D3C2×D414yes—
142C2×C3×Dic3—28no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C3×Dic6—28no—
147C3×Dic6—24no—
148C3×Dic6—24no—
149C3×Dic6C2×D418yes—
150#627—28no—
151#627—28no—
152#627—42no—
153#624—28no—
154#624—28no—
155#624—42no—
156#624—42no—
157C32×C8—22no—
158C3⋊(C3⋊C8)—22no—
159C23×Q8—91no—
160C22×Q16—92no—
161C2×C22⋊Q8—91no—
162#451—32no—
163#451—94no—
164#451—92no—
165C2×#103—92no—
166C2×C22⋊C8—91no—
167C23×D3—32no—
168C23×D3—61no—
169C2×C3×Q8—34no—
170C2×C3×Q8—32no—
171C2×C3×Q8—68no—
172C2×C3×Q8—62no—
173C22×C3×C4—21no—
174C22×C3×C4—62no—
175C22×C3×C4C22×D312yes—
176C22×Dic3—22no—
177C22×Dic3—32no—
178C22×Dic3—61no—
179D3×Q8—316no—
180D3×Q8—68no—
181D3×Q8—68no—
182D3×Q8—616no—
183D3×Q8—616no—
184D3×Q8—68no—
185D3×Q8—68no—
186C2×C4×D3—32no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—68no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×C4×D3—616no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—124no—
201C2×Dic6—22no—
202C2×Dic6—28no—
203C2×Dic6—64no—
204C2×Dic6—64no—
205C2×Dic6—616no—
206C2×Dic6—62no—
207C2×Dic6C22×D312yes—
208C2×Dic6C22×D314yes—
209C3×Q16—68no—
210C2×C3×C8—22no—
211C2×C3×C8C22×D314yes—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C22⋊C4—62no—
215#217—22no—
216#216—68no—
217#216—68no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3C22×D312yes—
222Dic3⋊C4—22no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225C2×C3⋊C8—34no—
226C2×C3⋊C8—62no—
227Dic12—28no—
228D3×C8—68no—
229D3×C8—124no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C2×Q1612yescomplemented
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—21no—
235C2×C3⋊D3—21no—
236C2×C3⋊D3—28no—
237C2×C3⋊D3#12012yes—
238C2×C3⋊D3C2×Q1612yes—
239C2×C3⋊D3C2×Q1612yescomplemented
240C2×C3⋊D3#13712yes—
241C32×C4—21no—
242C32×C4C22×D412yes—
243C3⋊Dic3—21no—
244C3⋊Dic3#12012yes—
245C3×Dic3—28no—
246C3×Dic3—42no—
247C3×Dic3—42no—
248C22×Q8—32no—
249C22×Q8—92no—
250C22×Q8—91no—
251C22×Q8—92no—
252C22×Q8—181no—
253C22×Q8—181no—
254C22×Q8—181no—
255C22×Q8—188no—
256C23×C4—91no—
257C23×C4—181no—
258C2×Q16—34no—
259C2×Q16—94no—
260C2×Q16—188no—
261C22×C8—92no—
262C22⋊Q8—32no—
263C22⋊Q8—92no—
264C22⋊Q8—181no—
265C22⋊Q8—181no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—181no—
268C2×C22⋊C4—181no—
269#103—34no—
270#103—94no—
271C22⋊C8—91no—
272C22⋊C8—92no—
273C22⋊C8D3211yescharacteristic
274C23×C3—21no—
275C23×C3D3×D412yes—
276C22×D3—32no—
277C22×D3—38no—
278C22×D3—32no—
279C22×D3—61no—
280C22×D3—64no—
281C22×D3—61no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—122no—
285C22×D3—122no—
286C3×Q8—38no—
287C3×Q8—68no—
288C3×Q8—64no—
289C3×Q8—64no—
290C2×C3×C4—24no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—42no—
294C2×C3×C4—68no—
295C2×C3×C4—64no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4D3×D412yes—
299C2×C3×C4C23×D312yes—
300C2×Dic3—28no—
301C2×Dic3—24no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—64no—
309C2×Dic3—122no—
310C4×D3—38no—
311C4×D3—64no—
312C4×D3—616no—
313C4×D3—616no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—64no—
317C4×D3—122no—
318C4×D3—122no—
319C4×D3—122no—
320C4×D3—124no—
321C4×D3—124no—
322Dic6—28no—
323Dic6—24no—
324Dic6—24no—
325Dic6—616no—
326Dic6—616no—
327Dic6—124no—
328Dic6D3×D418yes—
329C3×C8—24no—
330C3×C8—42no—
331C3⋊C8—64no—
332C3⋊C8—122no—
333C2×C32—22no—
334C2×C32C2×#12011yescharacteristic
335C2×C32C22×Q1611yescharacteristic
336C2×C32C2×#13711yescharacteristic
337C3⋊D3—22no—
338C3⋊D3#45114yescomplemented
339C24—91no—
340C2×Q8—34no—
341C2×Q8—32no—
342C2×Q8—68no—
343C2×Q8—62no—
344C2×Q8—98no—
345C2×Q8—182no—
346C2×Q8—182no—
347C2×Q8—181no—
348C2×Q8—188no—
349C2×Q8—184no—
350C2×Q8—184no—
351C2×Q8—188no—
352C2×Q8—188no—
353C2×Q8—188no—
354C22×C4—62no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—91no—
360C22×C4—184no—
361C22×C4—182no—
362C22×C4—182no—
363C22×C4—188no—
364C22×C4—181no—
365C22×C4—181no—
366C22×C4C2×D3211yescharacteristic
367Q16—68no—
368Q16—188no—
369C2×C8—92no—
370C2×C8—184no—
371C2×C8C2×D3212yes—
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—181no—
375C4⋊C4—182no—
376C22⋊C4—62no—
377C22⋊C4—182no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3D3×Q1614yescomplemented
385C22×C3C2×D3×D412yes—
386C2×D3—34no—
387C2×D3—34no—
388C2×D3—34no—
389C2×D3—34no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—616no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—128no—
398C2×D3—121no—
399C2×D3—121no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—41no—
403C3×C4—68no—
404C3×C4—122no—
405C3×C4—122no—
406C3×C4C2×D3×D414yes—
407Dic3—28no—
408Dic3—34no—
409Dic3—42no—
410Dic3—42no—
411Dic3—62no—
412Dic3—62no—
413Dic3—121no—
414C32C2×#45111yescharacteristic, complemented, Sylow
415C23—91no—
416C23—91no—
417C23—94no—
418C23—182no—
419C23—182no—
420C23#380211yescharacteristic
421Q8—38no—
422Q8—68no—
423Q8—64no—
424Q8—64no—
425Q8—188no—
426Q8—188no—
427Q8—362no—
428C2×C4—22no—
429C2×C4—68no—
430C2×C4—64no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—91no—
434C2×C4—94no—
435C2×C4—91no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—188no—
439C2×C4—188no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—362no—
443C2×C4—362no—
444C2×C4#380211yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—22no—
447C8—182no—
448C2×C3—24no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—42no—
453C2×C3D3×#12012yes—
454C2×C3C2×D3×Q1612yes—
455C2×C3D3×#13712yes—
456D3—38no—
457D3—64no—
458D3—64no—
459D3—122no—
460C22—21no—
461C22—21no—
462C22—92no—
463C22—92no—
464C22—92no—
465C22—92no—
466C22—188no—
467C22—181no—
468C22—181no—
469C22#6380212yescomplemented
470C22C2×#380211yescharacteristic
471C4—21no—
472C4—68no—
473C4—92no—
474C4—122no—
475C4—122no—
476C4—181no—
477C4D32×D412yes—
478C3—21no—
479C3D3×#45112yescomplemented
480C2—22no—
481C2—94no—
482C2—182no—
483C2#1059425811yescharacteristic
484C2C2×#6380211yescharacteristic
485C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC22⋊C8D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#63802C2semidirect
5. C3×#4739C2semidirect
6. #10591185C2semidirect
7. #10590950C2semidirect
8. #10590672C2semidirect
22. C2×C3×Dic12C22semidirect
29. C2×#3718C22semidirect
34. C3×#816C22semidirect
35. #63565C22semidirect
45. #4739D3semidirect
107. C2×Dic12C2×D3semidirect
124. #816C2×D3semidirect
129. C22×C3⋊D3Q16semidirect
232. C22×C32C2×Q16semidirect
239. C2×C3⋊D3C2×Q16semidirect
338. C3⋊D3#451semidirect
384. C22×C3D3×Q16semidirect
414. C32C2×#451semidirect
469. C22#63802semidirect
479. C3D3×#451semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
#105949252
C2×#638022
C3⋊D3×C22⋊C82
C3×#47392
#105911852
#105909502
#105906722
D3×#4513