Finite Group Databasebeta

← #11869389

Subgroups — #11869389

Order 1152.

1129 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1129 conjugacy classes of subgroups — too many to draw. Only its 178 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10594925C211yesmaximal, characteristic
3C3×#4971C212yesmaximal, complemented
4#10591152C211yesmaximal, characteristic
5#10591126C212yesmaximal, complemented
6#10590601C212yesmaximal, complemented
7#10590575C212yesmaximal, complemented
8#10590529C214yesmaximal, complemented
9D3×#483—32nomaximal
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3797C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C4⋊C4×C3⋊D3—21no—
17C4⋊C4×C3⋊D3—21no—
18C4⋊C4×C3⋊D3C2212yes—
19C4⋊C4×C3⋊D3C2212yes—
20C3×#924C2212yes—
21#63982—21no—
22#63974—21no—
23#63900C2211yescharacteristic
24#63883—21no—
25#63871C2212yes—
26#63865—21no—
27C2×#3710C2212yes—
28C3×#830C2212yes—
29C3×#810C2214yescomplemented
30C3×#808C2214yescomplemented
31#63573C2214yescomplemented
32#63566C2214yescomplemented
33#63557C2212yes—
34D3×C22⋊Q8—32no—
35C2×D3×C4⋊C4—32no—
36C2×D3×C4⋊C4—61no—
37C3×#483—32no—
38#5043—32no—
39#4971D312yescomplemented
40#4862—34no—
41D3×#106—34no—
42#4805—34no—
43D3×#103—34no—
44D3×C22⋊C8—32no—
45#4721—32no—
46C23×C3⋊D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—44no—
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×Dic6C2312yes—
60C2×#627—21no—
61C2×#624—21no—
62C2×#624—21no—
63#3797—24no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2312yes—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68#3750—22no—
69#3750—22no—
70C3×#217—22no—
71C3×C4⋊Dic3C2312yes—
72C3×Dic3⋊C4—22no—
73C2×C3×C3⋊C8C2314yes—
74#3724—21no—
75Dic3⋊Dic3—22no—
76#3722—22no—
77#3710—24no—
78C2×#483—91noSylow
79C2×D3×Q8—32no—
80C22×C4×D3—32no—
81C22×C4×D3—61no—
82C22×C4×D3—62no—
83C22×C4×D3—62no—
84C3×C22⋊Q8—32no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×D312yes—
87#946—32no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—61no—
90#924C2×D312yes—
91C2×Dic3⋊C4—62no—
92C2×Dic3⋊C4—62no—
93C2×D3×C8—34no—
94#897—32no—
95#896—62no—
96D3×C4⋊C4—34no—
97D3×C4⋊C4—34no—
98D3×C4⋊C4—32no—
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101D3×C4⋊C4—62no—
102D3×C4⋊C4—62no—
103D3×C4⋊C4—62no—
104D3×C4⋊C4—62no—
105D3×C4⋊C4—62no—
106D3×C22⋊C4—62no—
107#878—62no—
108C3×#106—34no—
109C3×#103—34no—
110C3×C22⋊C8—32no—
111#835—34no—
112#830C2×D312yes—
113(C2×D3)⋊C8—34no—
114#817—34no—
115#816—34no—
116#810C2×D314yescomplemented
117#808—34no—
118#808C2×D314yescomplemented
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—22no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3SD1614yes—
123C22×C3⋊D3C2×D411yescharacteristic
124C22×C3⋊D3C2×D411yescharacteristic
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—42no—
133C2×C3⋊Dic3C2×D411yescharacteristic
134C2×C3⋊Dic3C2×D411yescharacteristic
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—44no—
139C4×C3⋊D3—44no—
140C4×C3⋊D3#4114yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C3×Dic6—24no—
144#627—42no—
145#624—42no—
146#624—42no—
147C3×C3⋊C8—24no—
148C2×C22⋊Q8—91no—
149C22×C4⋊C4—91no—
150#483—32no—
151#483—92no—
152#483—94no—
153C2×#106—92no—
154C2×#103—92no—
155C2×C22⋊C8—91no—
156C23×D3—32no—
157C23×D3—61no—
158C2×C3×Q8—32no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4C22×D312yes—
163C22×Dic3—32no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167D3×Q8—68no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—61no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—68no—
177C2×C4×D3—68no—
178C2×C4×D3—62no—
179C2×C4×D3—62no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—128no—
185C2×C4×D3—128no—
186C2×Dic6—62no—
187C2×Dic6C22×D312yes—
188C2×C3×C8—34no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4C22×D314yes—
195C3×C22⋊C4—62no—
196#217—22no—
197(C2×D3)⋊C4—62no—
198(C2×D3)⋊C4—62no—
199C4⋊Dic3—34no—
200C4⋊Dic3—62no—
201C4⋊Dic3—62no—
202C4⋊Dic3—62no—
203C4⋊Dic3—62no—
204C4⋊Dic3C22×D312yes—
205Dic3⋊C4—22no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—64no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212C2×C3⋊C8C22×D314yes—
213D3×C8—68no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32C2×SD1612yes—
217C22×C32C22×D411yescharacteristic
218C2×C3⋊D3—21no—
219C2×C3⋊D3—21no—
220C2×C3⋊D3—28no—
221C2×C3⋊D3#12312yes—
222C2×C3⋊D3C2×SD1612yes—
223C2×C3⋊D3C2×SD1612yes—
224C2×C3⋊D3#13712yes—
225C32×C4—21no—
226C32×C4—42no—
227C32×C4C2×#4112yes—
228C3⋊Dic3—21no—
229C3⋊Dic3—42no—
230C3⋊Dic3#12312yes—
231C3×Dic3—42no—
232C3×Dic3—42no—
233C22×Q8—91no—
234C23×C4—91no—
235C23×C4—181no—
236C22×C8—92no—
237C22⋊Q8—32no—
238C22⋊Q8—92no—
239C22⋊Q8—181no—
240C22⋊Q8—181no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4—181no—
249C2×C4⋊C4D3211yescharacteristic
250C2×C22⋊C4—181no—
251#106—34no—
252#106—94no—
253#103—34no—
254#103—94no—
255C22⋊C8—32no—
256C22⋊C8—92no—
257C23×C3—21no—
258C23×C3D3×D412yes—
259C22×D3—32no—
260C22×D3—38no—
261C22×D3—32no—
262C22×D3—64no—
263C22×D3—61no—
264C22×D3—61no—
265C22×D3—64no—
266C22×D3—64no—
267C22×D3—64no—
268C22×D3—64no—
269C3×Q8—64no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—44no—
277C2×C3×C4—44no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4D3×D412yes—
281C2×C3×C4C23×D312yes—
282C2×Dic3—22no—
283C2×Dic3—22no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—64no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—124no—
293C2×Dic3—124no—
294C4×D3—38no—
295C4×D3—64no—
296C4×D3—64no—
297C4×D3—64no—
298C4×D3—64no—
299C4×D3—64no—
300C4×D3—64no—
301C4×D3—64no—
302C4×D3—124no—
303C4×D3—124no—
304C4×D3—128no—
305C4×D3—128no—
306C4×D3—128no—
307C4×D3—128no—
308Dic6—24no—
309Dic6—124no—
310C3×C8—64no—
311C3⋊C8—24no—
312C2×C32—22no—
313C2×C32C2×#12311yescharacteristic
314C2×C32C22×SD1611yescharacteristic
315C2×C32C2×#13711yescharacteristic
316C3⋊D3—22no—
317C3⋊D3#48314yescomplemented
318C24—91no—
319C2×Q8—32no—
320C2×Q8—181no—
321C2×Q8—184no—
322C22×C4—21no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C22×C4—91no—
328C22×C4—184no—
329C22×C4—182no—
330C22×C4—182no—
331C22×C4—181no—
332C22×C4—181no—
333C22×C4—181no—
334C22×C4—364no—
335C22×C4C2×D3211yescharacteristic
336C2×C8—34no—
337C2×C8—184no—
338C4⋊C4—21no—
339C4⋊C4—32no—
340C4⋊C4—62no—
341C4⋊C4—92no—
342C4⋊C4—182no—
343C4⋊C4—182no—
344C4⋊C4—181no—
345C4⋊C4—182no—
346C4⋊C4—181no—
347C4⋊C4C2×D3212yes—
348C22⋊C4—62no—
349C22⋊C4—182no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3D3×SD1614yes—
357C22×C3C2×D3×D412yes—
358C2×D3—34no—
359C2×D3—34no—
360C2×D3—34no—
361C2×D3—34no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—616no—
367C2×D3—62no—
368C2×D3—616no—
369C2×D3—62no—
370C2×D3—62no—
371C2×D3—62no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—44no—
376C3×C4—44no—
377C3×C4—122no—
378C3×C4—122no—
379C3×C4D3×#4114yes—
380Dic3—34no—
381Dic3—42no—
382Dic3—42no—
383Dic3—62no—
384Dic3—62no—
385Dic3—62no—
386Dic3—124no—
387Dic3—124no—
388C32C2×#48311yescharacteristic, complemented, Sylow
389C23—91no—
390C23—91no—
391C23—94no—
392C23—182no—
393C23—182no—
394C23#381111yescharacteristic
395Q8—64no—
396Q8—362no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—42no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—91no—
403C2×C4—94no—
404C2×C4—91no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—364no—
411C2×C4—364no—
412C2×C4—362no—
413C2×C4—362no—
414C2×C4—362no—
415C2×C4#381111yescharacteristic
416C2×C4C22×D3211yescharacteristic
417C8—64no—
418C2×C3—24no—
419C2×C3—24no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3D3×#12312yes—
424C2×C3C2×D3×SD1612yes—
425C2×C3D3×#13712yes—
426D3—38no—
427D3—64no—
428D3—64no—
429D3—64no—
430C22—21no—
431C22—21no—
432C22—92no—
433C22—92no—
434C22—92no—
435C22—92no—
436C22—188no—
437C22—181no—
438C22—181no—
439C22#6393012yes—
440C22C2×#381111yescharacteristic
441C4—21no—
442C4—42no—
443C4—92no—
444C4—122no—
445C4—122no—
446C4—181no—
447C4—362no—
448C4#6430612yes—
449C3—21no—
450C3D3×#48312yescomplemented
451C2—22no—
452C2—94no—
453C2—182no—
454C2#1059507911yescharacteristic
455C2C2×#6393011yescharacteristic
456C2#1059532211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4971C2semidirect
5. #10591126C2semidirect
6. #10590601C2semidirect
7. #10590575C2semidirect
8. #10590529C2semidirect
29. C3×#810C22semidirect
30. C3×#808C22semidirect
31. #63573C22semidirect
32. #63566C22semidirect
39. #4971D3semidirect
116. #810C2×D3semidirect
118. #808C2×D3semidirect
317. C3⋊D3#483semidirect
388. C32C2×#483semidirect
450. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105949252
C3×#49712
#105911522
#105911262
#105906012
#105905752
#105905292
D3×#4833