Finite Group Databasebeta

← #11875002

Subgroups — #11875002

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594445C212yesmaximal
2#10592577C211yesmaximal, characteristic, complemented
3C3×#4880C211yesmaximal, characteristic
4C3×#4874C211yesmaximal, characteristic, complemented
5#10590891C211yesmaximal, characteristic, complemented
6#10590875C211yesmaximal, characteristic, complemented
7#10590707C211yesmaximal, characteristic
8D3×C8×Dic3C211yesmaximal, characteristic
9#10590571C212yesmaximal
10#10590417C212yesmaximal, complemented
11#10590412C212yesmaximal, complemented
12#81938—31nomaximal
13#79170—31nomaximal
14#64099C2212yes—
15C2×C3×D3×C8C2211yescharacteristic
16C3×#892C2212yes—
17C3×#888C2212yes—
18#63918C2212yes—
19#63893—22no—
20#63887—22no—
21C4×D3×Dic3C2211yescharacteristic
22#63872C2212yes—
23Dic3×Dic6—22no—
24#63841C2212yes—
25#63837—22no—
26C2×D3×C3⋊C8C2211yescharacteristic
27C32×#107C2211yescharacteristic
28#63645C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30#63635C2212yes—
31C3×#818C2211yescharacteristic
32C3×#818C2211yescharacteristic
33C3×C8×Dic3C2211yescharacteristic
34C3×#808C2212yes—
35C3×#807C2212yes—
36#63575C2212yes—
37#63574C2212yes—
38#63573C2212yes—
39#63553C2211yescharacteristic
40Dic3×C3⋊C8C2211yescharacteristic
41#5728—32no—
42#5517—32no—
43C3×#500—31no—
44C3×#427—31no—
45#5106—31no—
46C2×C8×Dic3—31no—
47#5080—32no—
48#4998—32no—
49#4880—31no—
50#4880—32no—
51#4880D311yescharacteristic
52#4878—31no—
53#4878—31no—
54#4878—31no—
55#4878—31no—
56#4878—32no—
57#4878—61no—
58#4874—31no—
59#4874D311yescharacteristic, complemented
60#4858—32no—
61#4855—32no—
62C4×D3×C8—31no—
63#4682—31no—
64C2×C3×C4×D3C2311yescharacteristic
65C2×C3×Dic6—22no—
66C2×#627—22no—
67C2×D3×Dic3D411yescharacteristic
68C2×D3×Dic3D411yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C4⋊C4C2312yes—
71C4⋊(C3⋊Dic3)—22no—
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74C4×C3⋊Dic3C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C3×D3×C8Q814yescomplemented
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89Dic32—22no—
90Dic32D411yescharacteristic
91Dic32D411yescharacteristic
92D3×C3⋊C8Q814yescomplemented
93#3160—91noSylow
94C22×C3×C8—31no—
95C3×C4⋊Q8—32no—
96C3×#117—32no—
97#946—62no—
98Q8×Dic3—62no—
99#926—32no—
100C2×C4×Dic3—31no—
101C22×C3⋊C8—31no—
102C2×D3×C8—31no—
103C2×D3×C8C2×D311yescharacteristic
104#897—62no—
105#892—32no—
106#892C2×D312yes—
107#890—32no—
108#890—32no—
109#890—32no—
110#890—32no—
111#890—62no—
112#888—32no—
113#888C2×D312yes—
114#887—62no—
115#878—62no—
116#878—62no—
117C42×D3—31no—
118#869—32no—
119C4×Dic6—62no—
120C4×Dic6—62no—
121C3×#107—21no—
122C3×#107—31no—
123C3×#107—31no—
124C3×#107—32no—
125C3×#107C2×D311yescharacteristic
126C3×#107C2×D311yescharacteristic
127C3×#106—32no—
128C3×C4×C8—31no—
129#818—31no—
130#818—31no—
131#818—32no—
132#818—61no—
133#818C2×D311yescharacteristic
134#818C2×D311yescharacteristic
135#817—32no—
136C8×Dic3—31no—
137C8×Dic3—31no—
138C8×Dic3—31no—
139C8×Dic3—31no—
140C8×Dic3—31no—
141C8×Dic3—61no—
142C8×Dic3C2×D311yescharacteristic
143#808—32no—
144#808—32no—
145#808—32no—
146#808—32no—
147#808—32no—
148#808—62no—
149#808C2×D312yes—
150#807—32no—
151#807C2×D312yes—
152C4×C3⋊C8—31no—
153C22×C3×D3C2×D411yescharacteristic
154C2×C32×C4—22no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×D411yescharacteristic
162C2×C3×Dic3C2×D411yescharacteristic
163C2×C3×Dic3C2×D411yescharacteristic
164C3×C4×D3C2×Q812yes—
165C3×C4×D3C2×Q812yes—
166C3×Dic6—44no—
167#627—44no—
168D3×Dic3—22no—
169D3×Dic3—22no—
170C32×C8C2×Q812yes—
171C3⋊(C3⋊C8)C2×Q812yes—
172C3×C3⋊C8C2×Q812yes—
173C3×C3⋊C8C2×Q812yes—
174#533—92no—
175#500—31no—
176#500—91no—
177#499—92no—
178#499—91no—
179#499—91no—
180#498—92no—
181#427—31no—
182#427—92no—
183#427—91no—
184C2×C4×C8—91no—
185C2×C3×Q8—62no—
186C22×C3×C4—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3C22×D311yescharacteristic
192C2×Dic6—22no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×C3×C8—21no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—34no—
199C2×C3×C8C22×D311yescharacteristic
200C2×C3×C8C22×D311yescharacteristic
201C3×C4⋊C4—22no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—62no—
205C3×C4⋊C4C22×D312yes—
206C3×C4⋊C4C22×D312yes—
207C3×C22⋊C4—62no—
208C3×C42—31no—
209C3×C42—62no—
210#217—62no—
211(C2×D3)⋊C4—22no—
212(C2×D3)⋊C4—62no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—62no—
216C4⋊Dic3—62no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3—122no—
222C4⋊Dic3C22×D312yes—
223C4⋊Dic3C22×D312yes—
224Dic3⋊C4—22no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—122no—
231C4×Dic3—22no—
232C4×Dic3—31no—
233C4×Dic3—31no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3—31no—
238C4×Dic3—61no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3C22×D311yescharacteristic
242C2×C3⋊C8—31no—
243C2×C3⋊C8—31no—
244C2×C3⋊C8—34no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C22×D311yescharacteristic
247C2×C3⋊C8C22×D311yescharacteristic
248D3×C8—34no—
249D3×C8Dic614yescomplemented
250C22×C32C22×D411yescharacteristic
251C2×C3×D3—21no—
252C2×C3×D3—21no—
253C2×C3×D3C4⋊Q812yes—
254C32×C4—42no—
255C32×C4C22×Q811yescharacteristic
256C32×C4C22×Q811yescharacteristic
257C3⋊Dic3—21no—
258C3⋊Dic3—21no—
259C3⋊Dic3—42no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C3×Dic3C4⋊Q812yes—
263C3×Dic3#13512yes—
264C3×Dic3#13512yes—
265C22×C8—31no—
266C22×C8—91no—
267C4⋊Q8—32no—
268C4⋊Q8—92no—
269#125—92no—
270#125—92no—
271C22⋊Q8—182no—
272C22⋊Q8—182no—
273C4×Q8—182no—
274C4×Q8—182no—
275#117—32no—
276#117—92no—
277C2×C42—91no—
278#107—31no—
279#107—31no—
280#107—32no—
281#107—92no—
282#107—91no—
283#107D3211yescharacteristic
284#106—32no—
285#106—92no—
286#106—92no—
287#106—92no—
288C4×C8—31no—
289C4×C8—91no—
290C4×C8—91no—
291C4×C8—91no—
292C23×C3—31no—
293C22×D3D3×D411yescharacteristic
294C3×Q8—124no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—31no—
301C2×C3×C4—32no—
302C2×C3×C4—32no—
303C2×C3×C4—42no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4C23×D311yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—31no—
311C2×Dic3—31no—
312C2×Dic3—31no—
313C2×Dic3—31no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3D3×D411yescharacteristic
322C2×Dic3D3×D411yescharacteristic
323C2×Dic3D3×D411yescharacteristic
324C4×D3—62no—
325C4×D3—62no—
326C4×D3C2×Dic612yes—
327C4×D3D3×Q812yes—
328Dic6—44no—
329Dic6—124no—
330Dic6—124no—
331C3×C8—22no—
332C3×C8—32no—
333C3×C8—32no—
334C3×C8C2×Dic612yes—
335C3×C8D3×Q812yes—
336C3⋊C8—32no—
337C3⋊C8—32no—
338C3⋊C8—62no—
339C3⋊C8C2×Dic612yes—
340C3⋊C8D3×Q812yes—
341C2×C32C2×C4⋊Q811yescharacteristic
342C2×C32C2×#13511yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C3×D3—22no—
345C2×Q8—62no—
346C2×Q8—182no—
347C22×C4—31no—
348C22×C4—91no—
349C22×C4—91no—
350C2×C8—31no—
351C2×C8—31no—
352C2×C8—34no—
353C2×C8—94no—
354C2×C8—91no—
355C2×C8C2×D3211yescharacteristic
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—62no—
359C4⋊C4—92no—
360C4⋊C4—182no—
361C4⋊C4—182no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4C2×D3212yes—
366C22⋊C4—62no—
367C22⋊C4—182no—
368C42—31no—
369C42—62no—
370C42—91no—
371C42—91no—
372C42—91no—
373C42—182no—
374C22×C3—21no—
375C22×C3—32no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3C2×D3×D411yescharacteristic
379C22×C3C2×D3×D411yescharacteristic
380C2×D3—21no—
381C2×D3—21no—
382C2×D3#88812yes—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—32no—
386C3×C4—32no—
387C3×C4—32no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—82no—
391C3×C4—122no—
392C3×C4—122no—
393C3×C4C22×Dic611yescharacteristic
394C3×C4C2×D3×Q811yescharacteristic
395C3×C4C2×D3×Q811yescharacteristic
396C3×C4C2×D3×Q811yescharacteristic
397Dic3—42no—
398Dic3—42no—
399Dic3—61no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—121no—
404Dic3—121no—
405Dic3—122no—
406Dic3—122no—
407Dic3—242no—
408Dic3#88812yes—
409Dic3#91212yes—
410Dic3#91912yes—
411C32#316011yescharacteristic, complemented, Sylow
412C23—31no—
413Q8—124no—
414Q8—364no—
415C2×C4—22no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—32no—
420C2×C4—32no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—91no—
424C2×C4—91no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4C22×D3211yescharacteristic
429C8—32no—
430C8—32no—
431C8—92no—
432C8D3×Dic612yes—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—62no—
437C2×C3C2×#88811yescharacteristic
438C2×C3D3×C4⋊Q811yescharacteristic
439C2×C3C2×#91211yescharacteristic
440C2×C3C2×#91911yescharacteristic
441C2×C3D3×#13511yescharacteristic
442C2×C3D3×#13511yescharacteristic
443D3—22no—
444C22—32no—
445C22—61no—
446C22—61no—
447C22D32×D411yescharacteristic
448C4—32no—
449C4—32no—
450C4—32no—
451C4—42no—
452C4—122no—
453C4—122no—
454C4—181no—
455C4—181no—
456C4—362no—
457C4C2×D3×Dic611yescharacteristic
458C4D32×Q811yescharacteristic
459C3—21no—
460C3#7917011yescharacteristic, complemented
461C3#8193811yescharacteristic, complemented
462C2—62no—
463C2D3×#88811yescharacteristic
464C2D3×#91211yescharacteristic
465C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10592577C2semidirect
4. C3×#4874C2semidirect
5. #10590891C2semidirect
6. #10590875C2semidirect
10. #10590417C2semidirect
11. #10590412C2semidirect
59. #4874D3semidirect
84. C3×D3×C8Q8semidirect
92. D3×C3⋊C8Q8semidirect
249. D3×C8Dic6semidirect
411. C32#3160semidirect
460. C3#79170semidirect
461. C3#81938semidirect

Maximal subgroups

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

subgroupindex
#105944452
#105925772
C3×#48802
C3×#48742
#105908912
#105908752
#105907072
D3×C8×Dic32
#105905712
#105904172
#105904122
#819383
#791703