Finite Group Databasebeta

← #11860453

Subgroups — #11860453

Order 1152.

788 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 153 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×#64226C211yesmaximal, characteristic
2#10593966C211yesmaximal, characteristic
3C4×#3797C211yesmaximal, characteristic, complemented
4C4×#3788C211yesmaximal, characteristic, complemented
5#10593445C212yesmaximal, complemented
6#10593433C212yesmaximal, complemented
7#10593432C212yesmaximal, complemented
8#10593394C211yesmaximal, characteristic, complemented
9#10593374C211yesmaximal, characteristic, complemented
10#10593369C212yesmaximal, complemented
11#10593360C211yesmaximal, characteristic
12C2×#3798C2211yescharacteristic
13C2×#3797C2211yescharacteristic
14C2×#3788C2211yescharacteristic
15C2×#3788C2211yescharacteristic
16C2×#3776C2212yes—
17C2×#3775C2212yes—
18#64226C418yescomplemented
19C42×C3⋊D3C2211yescharacteristic
20C3×#872—21no—
21C3×C4×Dic6—21no—
22C4×#627C2212yes—
23#63902C2211yescharacteristic
24#63902C2211yescharacteristic
25#63900C2211yescharacteristic
26#63883—21no—
27C4×#624—21no—
28#63881—21no—
29#63881—21no—
30C4×D3×Dic3—21no—
31#63874C2211yescharacteristic
32#63843—21no—
33#63838C2211yescharacteristic
34#63838C2212yes—
35#63838C2211yescharacteristic
36#63777C2212yes—
37C4×#622C2212yes—
38#63743C2212yes—
39#63742C2212yes—
40#63740C2212yes—
41#63740C2212yes—
42#63740C2212yes—
43#63739C2212yes—
44C4×D3×Q8—61no—
45#5522—61no—
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×#627C2312yes—
52C2×#627C2311yescharacteristic
53C2×#626—21no—
54C2×#625C2311yescharacteristic
55C2×#624—21no—
56C2×#624—21no—
57C2×D3×Dic3—21no—
58C2×D3×Dic3—21no—
59#3798—22no—
60#3798C2×C414yes—
61#3797—22no—
62#3797C2×C414yescomplemented
63C2×#622C2312yes—
64C2×#622C2312yes—
65#3788—22no—
66#3788C2×C414yescomplemented
67#3776C2×C418yescomplemented
68#3775C2×C418yescomplemented
69C32×C42D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C4×C3⋊Dic3C2311yescharacteristic
73C3×(C2×D3)⋊C4—21no—
74C3×(C2×D3)⋊C4—21no—
75C3×C4⋊Dic3—21no—
76C3×Dic3⋊C4—21no—
77C3×Dic3⋊C4—21no—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—22no—
81#3724C2311yescharacteristic
82#3724C2311yescharacteristic
83#3724C2312yes—
84Dic3⋊Dic3—22no—
85#3722—21no—
86Dic32—22no—
87Dic32—21no—
88Dic32—21no—
89C4×#137—91nomaximal, Sylow
90C2×D3×Q8—61no—
91C2×#235—61no—
92C3×C4×Q8—61no—
93C3×#117—61no—
94Q8×Dic3—61no—
95C2×C4×Dic3—61no—
96#893—61no—
97#893—61no—
98D3×C4⋊C4—61no—
99D3×C4⋊C4—62no—
100#887—61no—
101#887—61no—
102#887—62no—
103#887—61no—
104#67⋊C4—61no—
105#67⋊C4—61no—
106#67⋊C4—61no—
107#67⋊C4—61no—
108#872—21no—
109#872—61no—
110C42×D3—61no—
111C42×D3—61no—
112C42×D3—62no—
113C42×D3—61no—
114C4×Dic6—21no—
115C4×Dic6—62no—
116C22×C3⋊D3C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C2×C3⋊Dic3C2×D411yescharacteristic
123C2×C3⋊Dic3C2411yescharacteristic
124C4×C3⋊D3—22no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3C22×C412yes—
127C4×C3⋊D3#4112yes—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C3×C4×D3—24no—
134C3×Dic6—24no—
135#627—22no—
136#627—21no—
137#627C22×C414yes—
138#627C22×C412yes—
139#626—24no—
140#625—21no—
141#625C22×C412yes—
142#624—24no—
143#624—42no—
144D3×Dic3—42no—
145D3×Dic3—42no—
146#622—22no—
147#622C22×C414yes—
148C2×#137—91no—
149C4×#41—91no—
150C2×C4×Q8—91no—
151#441—92no—
152#440—92no—
153C4×Q16—92no—
154C4×SD16—92no—
155#428—91no—
156#419—91no—
157#417—91no—
158C4×M16—91no—
159C2×C3×Q8—61no—
160C22×C3×C4—61no—
161C2×#67—61no—
162C2×#67—61no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165D3×Q8—64no—
166D3×Q8—64no—
167#235—64no—
168#235—64no—
169C2×D12—61no—
170C2×C4×D3—21no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—62no—
178C2×C4×D3—62no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×Dic6—21no—
182C2×Dic6—62no—
183C2×Dic6—61no—
184C3×C4⋊C4—62no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C42—21no—
191C3×C42—21no—
192C3×C42—62no—
193C3×C42—61no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198C4⋊Dic3—21no—
199C4⋊Dic3—62no—
200Dic3⋊C4—22no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—62no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—62no—
207C4×Dic3—22no—
208C4×Dic3—21no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C22×C32C22×D411yescharacteristic
222C2×C3⋊D3—21no—
223C2×C3⋊D3—21no—
224C2×C3⋊D3C4×D412yes—
225C2×C3×D3—22no—
226C2×C3×D3—41no—
227C2×C3×D3—41no—
228C32×C4—21no—
229C32×C4—21no—
230C32×C4C4×D412yes—
231C3⋊Dic3—21no—
232C3⋊Dic3#13712yescomplemented
233C3⋊Dic3C23×C411yescharacteristic
234C3⋊Dic3C2×#4111yescharacteristic
235C3×Dic3—24no—
236C3×Dic3—22no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—42no—
240C2×#41—91no—
241C22×Q8—91no—
242#137—98no—
243C2×Q16—92no—
244C2×SD16—92no—
245C2×M16—91no—
246C2×M16—91no—
247C4×Q8—61no—
248C4×Q8—92no—
249C4×Q8—92no—
250C4×Q8—91no—
251C4×Q8—91no—
252C4×Q8—181no—
253C4×D4—91no—
254C4×D4—91no—
255C4×D4—181no—
256C4×D4—181no—
257#117—61no—
258#117—91no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—181no—
261C2×C42—91no—
262C2×C42—181no—
263C2×C42—181no—
264#107—92no—
265#106—92no—
266#103—92no—
267#103—92no—
268#103—92no—
269#102—92no—
270#97—92no—
271C4×C8—92no—
272C23×C3—61no—
273C22×D3—21no—
274C22×D3—61no—
275C22×D3—61no—
276C3×Q8—64no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—64no—
284C2×C3×C4—61no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289#67—62no—
290#67—64no—
291#67—62no—
292C2×Dic3—22no—
293C2×Dic3—21no—
294C2×Dic3—22no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305D12—64no—
306C4×D3—24no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—62no—
311C4×D3—68no—
312C4×D3—64no—
313C4×D3—122no—
314C4×D3—124no—
315C4×D3—122no—
316C4×D3—122no—
317C4×D3—122no—
318C4×D3—122no—
319Dic6—24no—
320Dic6—62no—
321Dic6—64no—
322Dic6—62no—
323Dic6—64no—
324C2×C32C2×C4×D411yescharacteristic
325C2×C32C2×#13711yescharacteristic
326C2×C32#57511yescharacteristic
327C3⋊D3—22no—
328C3×D3—42no—
329#41—94no—
330#41—182no—
331C2×Q8—61no—
332C2×Q8—92no—
333C2×Q8—91no—
334C2×Q8—94no—
335C2×Q8—182no—
336C2×D4—91no—
337C2×D4—181no—
338C22×C4—61no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4—181no—
345C22×C4—181no—
346Q16—98no—
347SD16—98no—
348M16—94no—
349M16—182no—
350C2×C8—92no—
351C2×C8—92no—
352C4⋊C4—61no—
353C4⋊C4—62no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—92no—
357C4⋊C4—91no—
358C4⋊C4—91no—
359C4⋊C4—182no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—181no—
363C42—61no—
364C42—62no—
365C42—91no—
366C42—91no—
367C42—91no—
368C42—181no—
369C42—181no—
370C42—182no—
371C42GO+(4,𝔽2)11yescharacteristic
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—62no—
375C22×C3—121no—
376C22×C3—121no—
377C2×D3—22no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—121no—
385C2×D3—121no—
386C3×C4—22no—
387C3×C4—22no—
388C3×C4—22no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—64no—
393C3×C4—62no—
394C3×C4—122no—
395C3×C4—121no—
396C3×C4—121no—
397Dic3—24no—
398Dic3—22no—
399Dic3—42no—
400Dic3—41no—
401Dic3—41no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—61no—
406Dic3—62no—
407Dic3—62no—
408Dic3—62no—
409Dic3—121no—
410C32C4×#13711yescharacteristic, complemented, Sylow
411C23—61no—
412C23—91no—
413Q8—64no—
414Q8—94no—
415Q8—92no—
416Q8—182no—
417Q8—181no—
418D4—92no—
419D4—184no—
420D4—181no—
421C2×C4—62no—
422C2×C4—61no—
423C2×C4—64no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—62no—
427C2×C4—91no—
428C2×C4—91no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—91no—
432C2×C4—182no—
433C2×C4—184no—
434C2×C4—361no—
435C2×C4—362no—
436C2×C4—362no—
437C2×C4—362no—
438C2×C4C2×GO+(4,𝔽2)11yescharacteristic
439C2×C4C2×GO+(4,𝔽2)11yescharacteristic
440C2×C4C2×GO+(4,𝔽2)11yescharacteristic
441C8—94no—
442C8—182no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—122no—
450D3—42no—
451D3—64no—
452D3—122no—
453C22—62no—
454C22—92no—
455C22—121no—
456C22—121no—
457C22—181no—
458C22—181no—
459C22C22×GO+(4,𝔽2)11yescharacteristic
460C4—21no—
461C4—21no—
462C4—62no—
463C4—64no—
464C4—92no—
465C4—91no—
466C4—91no—
467C4—121no—
468C4—122no—
469C4—121no—
470C4—181no—
471C4C4×GO+(4,𝔽2)12yes—
472C3—21no—
473C3—21no—
474C2—122no—
475C2—182no—
476C2#1059650211yescharacteristic
477C2#1059650511yescharacteristic
478C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3798C22
cosocleC2×C3⋊Dic3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32C4×#137
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. C4×#3797C2semidirect
4. C4×#3788C2semidirect
5. #10593445C2semidirect
6. #10593433C2semidirect
7. #10593432C2semidirect
8. #10593394C2semidirect
9. #10593374C2semidirect
10. #10593369C2semidirect
18. #64226C4semidirect
62. #3797C2×C4semidirect
66. #3788C2×C4semidirect
67. #3776C2×C4semidirect
68. #3775C2×C4semidirect
232. C3⋊Dic3#137semidirect
410. C32C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×#642262
#105939662
C4×#37972
C4×#37882
#105934452
#105934332
#105934322
#105933942
#105933742
#105933692
#105933602
C4×#1379