Finite Group Databasebeta

← #11787084

Subgroups — #11787084

Order 1152.

891 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 891 conjugacy classes of subgroups — too many to draw. Only its 130 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#10595510C211yesmaximal, characteristic
2#10592657C211yesmaximal, characteristic
3#10591719C212yesmaximal, complemented
4C2×#63581C211yesmaximal, characteristic
5C3×#4527C212yesmaximal, complemented
6#68961—32nomaximal
7C22×#638C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×C3×#217C2212yes—
12C2×C3×#217C2212yes—
13#63974—21no—
14C2×Dic3⋊Dic3—22no—
15#63957—21no—
16#63952—22no—
17#63952—22no—
18#63658—21no—
19#63581C414yescomplemented
20#63579—22no—
21#5486—32no—
22#4958—32no—
23#4958—61no—
24C2×#806—32no—
25#4950—32no—
26#4946—32no—
27C3×#342—32no—
28#4527D312yescomplemented
29C24×C32C2311yescharacteristic
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C2×#638—22no—
33C2×#638—22no—
34C2×#638C2×C412yes—
35C2×#638Q812yes—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—22no—
38C22×C3⋊Dic3—42no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3×Dic3—22no—
41C22×C3×Dic3D412yes—
42C22×C3×Dic3D412yes—
43C2×#624—21no—
44C2×#624—21no—
45C32×C22⋊C4—22no—
46#3752—42no—
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—22no—
50C3×#217C2×C414yescomplemented
51#3724—21no—
52#3724—21no—
53Dic3⋊Dic3—44no—
54#3722—22no—
55Dic32—22no—
56#1867—91noSylow
57C22×#67—32no—
58C22×#67—61no—
59C23×Dic3—32no—
60C23×Dic3—61no—
61C2×C3×C22⋊C4—21no—
62C2×C3×C22⋊C4—32no—
63C2×C3×C22⋊C4—32no—
64C2×C3×C22⋊C4C2×D312yes—
65C2×#217C2×D312yes—
66C2×#217C2×D312yes—
67C4×#67—62no—
68C4×#67—62no—
69C2×(C2×D3)⋊C4—62no—
70C2×(C2×D3)⋊C4—62no—
71C2×C4⋊Dic3—62no—
72C2×Dic3⋊C4—62no—
73#67⋊C4—62no—
74#67⋊C4—62no—
75D3×C22⋊C4—62no—
76#877—62no—
77C3⋊#95—62no—
78C3⋊#95—62no—
79C3⋊#95—62no—
80C3⋊#95—62no—
81#806—38no—
82C23×C32—41no—
83C23×C32—41no—
84C23×C32C22×C411yescharacteristic
85C23×C32C2×D412yes—
86C23×C32C2×D411yescharacteristic
87C23×C32C2×Q811yescharacteristic
88C23×C32#4112yes—
89C22×C3⋊D3—21no—
90C22×C3⋊D3—21no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3C4⋊C412yescomplemented
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97#638—24no—
98#638—24no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—24no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—42no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3C4⋊C412yescomplemented
107C2×C3×Dic3—24no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114#624—81no—
115#624—81no—
116#518—91no—
117C2×#99—91no—
118#386—91no—
119#385—92no—
120#342—32no—
121C24×C3—21no—
122C24×C3C22×D312yes—
123C23×D3—32no—
124C23×D3—61no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4—62no—
130C2×#67—34no—
131C2×#67—34no—
132C2×#67—62no—
133C2×#67—62no—
134C2×#67—62no—
135C2×#67—62no—
136C2×#67—62no—
137C2×#67—62no—
138C2×#67—122no—
139C2×#67—122no—
140C22×Dic3—22no—
141C22×Dic3—32no—
142C22×Dic3—61no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147C22×Dic3—122no—
148C22×Dic3—124no—
149C22×Dic3—124no—
150C22×Dic3D1212yes—
151C22×Dic3D1212yes—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C3×C22⋊C4—22no—
155C3×C22⋊C4—22no—
156C3×C22⋊C4—34no—
157C3×C22⋊C4—42no—
158C3×C22⋊C4—62no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—62no—
161#217—22no—
162#217—22no—
163#217—22no—
164#217C4×D314yescomplemented
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—124no—
168(C2×D3)⋊C4—124no—
169C4⋊Dic3—124no—
170Dic3⋊C4—62no—
171Dic3⋊C4—62no—
172Dic3⋊C4—124no—
173C4×Dic3—62no—
174C4×Dic3—62no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—22no—
178C22×C32—22no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32—42no—
182C22×C32C2×C4⋊C411yescharacteristic
183C22×C32C4×D412yes—
184C22×C32#12011yescharacteristic
185C22×C32C22⋊Q812yes—
186C22×C32#12311yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—81no—
192C32×C4—81no—
193C3⋊Dic3—22no—
194C3⋊Dic3—42no—
195C3×Dic3—44no—
196C3×Dic3—42no—
197C3×Dic3—42no—
198C22×D4—91no—
199C23×C4—91no—
200C4×D4—182no—
201C4×D4—182no—
202#117—181no—
203C2×C4⋊C4—182no—
204C2×C22⋊C4—32no—
205C2×C22⋊C4—32no—
206C2×C22⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C22⋊C4D3211yescharacteristic
209#99—94no—
210#95—181no—
211#95—182no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—22no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—42no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3C2×C4×D312yes—
222C23×C3C2×D1212yes—
223C23×C3#23512yes—
224C23×C3D3×D412yes—
225C23×C3D3×D412yes—
226C23×C3#23712yes—
227C23×C3D3×Q812yes—
228C22×D3—34no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—121no—
233C22×D3—121no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—122no—
237C22×D3—122no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—64no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4—122no—
251#67—64no—
252#67—64no—
253#67—64no—
254#67—64no—
255#67—124no—
256#67—124no—
257C2×Dic3—24no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—34no—
261C2×Dic3—42no—
262C2×Dic3—42no—
263C2×Dic3—42no—
264C2×Dic3—42no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3—121no—
273C2×Dic3—121no—
274C2×Dic3—124no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—124no—
281C2×Dic3—122no—
282C4×D3—242no—
283C4×D3—242no—
284C2×C32—21no—
285C2×C32—21no—
286C2×C32—22no—
287C2×C32—22no—
288C2×C32#38511yescharacteristic
289C2×C32B(4,𝔽2)11yescharacteristic
290C2×C32#45811yescharacteristic
291C3⋊D3—42no—
292C24—91no—
293C24C2×D3211yescharacteristic
294C2×D4—92no—
295C2×D4—92no—
296C2×D4—182no—
297C2×D4—182no—
298C22×C4—21no—
299C22×C4—32no—
300C22×C4—32no—
301C22×C4—62no—
302C22×C4—91no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—182no—
306C22×C4—181no—
307C22×C4—362no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C4⋊C4—364no—
311C22⋊C4—22no—
312C22⋊C4—34no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—182no—
317C22⋊C4—362no—
318C42—182no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—44no—
341C22×C3C4×D1212yes—
342C22×C3#67⋊C412yes—
343C22×C3#88212yes—
344C22×C3#88312yes—
345C22×C3D3×C4⋊C412yes—
346C22×C3#89612yes—
347C22×C3#89712yes—
348C2×D3—64no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—122no—
352C2×D3—124no—
353C2×D3—124no—
354C2×D3—241no—
355C2×D3—241no—
356C2×D3—242no—
357C2×D3—242no—
358C3×C4—82no—
359C3×C4—82no—
360C3×C4—124no—
361C3×C4—122no—
362C3×C4—122no—
363Dic3—44no—
364Dic3—42no—
365Dic3—42no—
366Dic3—64no—
367Dic3—122no—
368Dic3—124no—
369Dic3—124no—
370C32#186711yescharacteristic, complemented, Sylow
371C23—41no—
372C23—41no—
373C23—92no—
374C23—181no—
375C23—181no—
376C23—361no—
377C23—361no—
378C23#379711yescharacteristic
379C23C4×D3211yescharacteristic
380C23D3×D1212yes—
381C23#380412yes—
382C23#381111yescharacteristic
383D4—184no—
384D4—184no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—64no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—92no—
392C2×C4—122no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—181no—
397C2×C4—181no—
398C2×C4—182no—
399C2×C4—184no—
400C2×C4—361no—
401C2×C4—362no—
402C2×C4—361no—
403C2×C4—721no—
404C2×C4—721no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—22no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3—42no—
418C2×C3#466812yes—
419C2×C3#474112yes—
420C2×C3#474212yes—
421D3—124no—
422D3—242no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—42no—
430C22—182no—
431C22—362no—
432C22—361no—
433C22—361no—
434C22—721no—
435C22#6388012yes—
436C22#6388311yescharacteristic
437C22#6389512yes—
438C22#6392311yescharacteristic
439C22#6397511yescharacteristic
440C4—81no—
441C4—124no—
442C4—122no—
443C4—122no—
444C4—182no—
445C4—362no—
446C3—21no—
447C3#6896112yescomplemented
448C2—21no—
449C2—22no—
450C2—21no—
451C2—22no—
452C2—362no—
453C2#1059040911yescharacteristic
454C2#1059041011yescharacteristic
455C2#1059137511yescharacteristic
subgroupG/H
centerC22#63923
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC22×#638C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10591719C2semidirect
5. C3×#4527C2semidirect
19. #63581C4semidirect
28. #4527D3semidirect
50. C3×#217C2×C4semidirect
93. C22×C3⋊D3C4⋊C4semidirect
106. C2×C3⋊Dic3C4⋊C4semidirect
164. #217C4×D3semidirect
370. C32#1867semidirect
447. C3#68961semidirect

Maximal subgroups

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

subgroupindex
#105955102
#105926572
#105917192
C2×#635812
C3×#45272
#689613