Finite Group Databasebeta

← #11802748

Subgroups — #11802748

Order 1152.

1534 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1534 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64306C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C2×#63900C211yesmaximal, characteristic, complemented
4#10593514C214yesmaximal, complemented
5#10593407C212yesmaximal, complemented
6#10593403C214yesmaximal, complemented
7#10593342C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C3×#235—21no—
10C2×#3811C2212yes—
11C22×#624C2212yes—
12C2×#3805—21no—
13#64306—24no—
14#64306C418yescomplemented
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2212yes—
17C2×#3798—21no—
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C2×C22⋊#157C2212yes—
21#64286—24no—
22C2×C4⋊#157C2212yes—
23C2×C4×#157C2212yes—
24C2×D32⋊C4C2218yes—
25C2×C3×C4⋊Dic3—21no—
26C2×#3724—21no—
27#63900—21no—
28#63900—21no—
29#63900C2212yes—
30#63900C2212yes—
31#63737C2218yes—
32C2×D3×#41—61no—
33C2×D3×C4⋊C4—61no—
34C23×C3⋊D3C2311yescharacteristic
35C22×D32C2312yes—
36C22×#157C2314yes—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C2×C4×C3⋊D3C2×C414yes—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D414yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#235—28no—
48C2×C3×D12—21no—
49C2×C3×C4×D3—22no—
50C2×C3×Dic6—21no—
51#3811—24no—
52#3811C2×C418yes—
53C2×#627—21no—
54C2×#626—22no—
55C2×#625—21no—
56C2×#624—22no—
57C2×#624—44no—
58C2×#624C2314yes—
59C2×#624C2312yes—
60#3805—28no—
61C2×D3×Dic3—22no—
62#3802—22no—
63#3802C2×C414yescomplemented
64C4×D32—24no—
65C4×D32C2×C418yescomplemented
66#3798—28no—
67#3797—22no—
68#3797C2×C414yescomplemented
69#3796—28no—
70C22⋊#157—24no—
71C4⋊#157—24no—
72C4×#157—24no—
73D32⋊C4—48no—
74C3×C4⋊Dic3—22no—
75C3×C4⋊Dic3—22no—
76#3724—22no—
77#3724—22no—
78#2311—91nomaximal, Sylow
79C2×C3×#41—61no—
80D3×#41—68no—
81D3×#41—68no—
82C2×#239—61no—
83C2×D3×Q8—61no—
84C2×#237—61no—
85C2×#237—62no—
86C2×D3×D4—61no—
87C2×D3×D4—62no—
88C2×#235—21no—
89C2×#235—62no—
90C22×C4×D3—62no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C22×C4×D3—62no—
94C2×C3×C4⋊C4—61no—
95C2×C4⋊Dic3—21no—
96C2×Dic3⋊C4—62no—
97D3×C4⋊C4—62no—
98D3×C4⋊C4—62no—
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3C22×C412yes—
105C22×C3⋊D3C2×D411yescharacteristic
106C22×C3⋊D3C2×D412yes—
107C22×C3⋊D3C2411yescharacteristic
108C22×C3×D3—22no—
109C2×D32—22no—
110C2×D32—24no—
111C2×D32—24no—
112C2×D32C22×C414yes—
113C2×#157—24no—
114C2×#157—24no—
115C2×#157—24no—
116C2×C32×C4C22⋊C414yescomplemented
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3C22⋊C414yescomplemented
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C4×C3⋊D3C22⋊C414yescomplemented
123C4×C3⋊D3C22⋊C414yescomplemented
124C4×C3⋊D3C22×C412yes—
125C4×C3⋊D3C22×C412yes—
126C4×C3⋊D3C2×D412yes—
127C4×C3⋊D3C2×D412yes—
128C3×#67—28no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—44no—
132C3×D12—24no—
133C3×C4×D3—28no—
134C3×Dic6—24no—
135#627—24no—
136#626—28no—
137#625—24no—
138#624—22no—
139#624—28no—
140#624—44no—
141#624C22×C414yes—
142D3×Dic3—28no—
143C22×#41—91no—
144C2×#117—91no—
145C22×C4⋊C4—91no—
146#391—92no—
147#390—92no—
148#386—94no—
149#380—94no—
150C23×D3—62no—
151C23×D3—61no—
152C23×D3—61no—
153C3×#41—68no—
154C2×C3×Q8—61no—
155C2×C3×D4—61no—
156C2×C3×D4—62no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C2×#67—22no—
162C2×#67—62no—
163C2×#67—62no—
164C22×Dic3—22no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168#239—68no—
169D3×Q8—64no—
170D3×Q8—64no—
171#237—68no—
172#237—616no—
173D3×D4—64no—
174D3×D4—68no—
175D3×D4—64no—
176D3×D4—68no—
177#235—28no—
178#235—616no—
179C2×D12—21no—
180C2×D12—62no—
181C2×C4×D3—22no—
182C2×C4×D3—68no—
183C2×C4×D3—62no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—61no—
191C2×C4×D3—61no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×C4×D3—68no—
198C2×C4×D3—62no—
199C2×C4×D3—64no—
200C2×C4×D3—128no—
201C2×Dic6—21no—
202C2×Dic6—62no—
203C3×C4⋊C4—62no—
204C3×C4⋊C4—62no—
205C4⋊Dic3—22no—
206C4⋊Dic3—22no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C2×C22⋊C412yes—
212C22×C32C22×D411yescharacteristic
213C2×C3⋊D3—21no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—24no—
216C2×C3⋊D3—24no—
217C2×C3⋊D3C2×C22⋊C412yes—
218C2×C3⋊D3C23×C411yescharacteristic
219C2×C3⋊D3C22×D411yescharacteristic
220C2×C3⋊D3H(5,𝔽2)12yes—
221C2×C3⋊D32−1+412yes—
222C2×C3×D3—24no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225D32—28no—
226D32—44no—
227#157—44no—
228C32×C4C2×C22⋊C412yes—
229C32×C4C2×C22⋊C412yes—
230C3⋊Dic3C2×C22⋊C412yes—
231C3⋊Dic3C2×C22⋊C412yes—
232C3×Dic3—24no—
233C3×Dic3—44no—
234C2×#41—61no—
235C2×#41—98no—
236C2×#41—181no—
237C2×#41—181no—
238C2×#41—181no—
239C2×#41—184no—
240C22×Q8—91no—
241C22×D4—92no—
242C22×D4—91no—
243C23×C4—92no—
244C23×C4—92no—
245C23×C4—91no—
246#117—184no—
247C2×C4⋊C4—61no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—181no—
252C2×C4⋊C4—181no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—92no—
255C2×C22⋊C4—98no—
256C2×C42—92no—
257#95—98no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—62no—
261C22×D3—22no—
262C22×D3—64no—
263C22×D3—62no—
264C22×D3—61no—
265C22×D3—62no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—62no—
269C22×D3—61no—
270C22×D3—62no—
271C22×D3—64no—
272C22×D3—64no—
273C22×D3—64no—
274C22×D3—124no—
275C22×D3—124no—
276C22×D3—122no—
277C22×D3—122no—
278C3×Q8—64no—
279C3×D4—64no—
280C3×D4—68no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4—68no—
288C2×C3×C4—62no—
289C2×C3×C4—64no—
290C2×C3×C4—124no—
291#67—28no—
292#67—68no—
293#67—68no—
294C2×Dic3—22no—
295C2×Dic3—24no—
296C2×Dic3—44no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—68no—
304D12—24no—
305D12—68no—
306C4×D3—28no—
307C4×D3—64no—
308C4×D3—64no—
309C4×D3—64no—
310C4×D3—64no—
311C4×D3—64no—
312C4×D3—62no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—64no—
321C4×D3—68no—
322C4×D3—128no—
323C4×D3—128no—
324Dic6—24no—
325Dic6—68no—
326C2×C32—22no—
327C2×C32C22×C22⋊C411yescharacteristic
328C2×C32#53511yescharacteristic
329C2×C32#53611yescharacteristic
330C3⋊D3—22no—
331C3⋊D3#52012yes—
332C3⋊D3#53712yes—
333C3×D3—44no—
334C24—92no—
335C24—91no—
336#41—68no—
337#41—188no—
338#41—188no—
339#41—188no—
340C2×Q8—61no—
341C2×Q8—94no—
342C2×Q8—181no—
343C2×Q8—182no—
344C2×D4—62no—
345C2×D4—61no—
346C2×D4—98no—
347C2×D4—94no—
348C2×D4—182no—
349C2×D4—182no—
350C2×D4—181no—
351C2×D4—184no—
352C22×C4—62no—
353C22×C4—62no—
354C22×C4—92no—
355C22×C4—98no—
356C22×C4—94no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—94no—
363C22×C4—94no—
364C22×C4—94no—
365C22×C4—184no—
366C22×C4—182no—
367C22×C4—182no—
368C22×C4—364no—
369C22×C4GO+(4,𝔽2)11yescharacteristic
370C4⋊C4—62no—
371C4⋊C4—62no—
372C4⋊C4—182no—
373C4⋊C4—182no—
374C4⋊C4—184no—
375C22⋊C4—184no—
376C22⋊C4—368no—
377C42—184no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—64no—
387C22×C3—122no—
388C22×C3—122no—
389C2×D3—24no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—61no—
393C2×D3—61no—
394C2×D3—62no—
395C2×D3—61no—
396C2×D3—61no—
397C2×D3—62no—
398C2×D3—62no—
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—62no—
403C2×D3—68no—
404C2×D3—68no—
405C2×D3—62no—
406C2×D3—128no—
407C2×D3—124no—
408C2×D3—124no—
409C2×D3—121no—
410C2×D3—121no—
411C2×D3—128no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—22no—
416C3×C4—64no—
417C3×C4—124no—
418Dic3—24no—
419Dic3—44no—
420Dic3—62no—
421Dic3—62no—
422Dic3—62no—
423Dic3—62no—
424C32#231111yescharacteristic, complemented, Sylow
425C23—62no—
426C23—94no—
427C23—91no—
428C23—91no—
429C23—92no—
430C23—92no—
431C23—182no—
432C23—182no—
433C23—182no—
434C23—184no—
435C23—184no—
436C23C2×GO+(4,𝔽2)11yescharacteristic
437Q8—64no—
438Q8—184no—
439D4—68no—
440D4—64no—
441D4—188no—
442D4—184no—
443C2×C4—62no—
444C2×C4—68no—
445C2×C4—64no—
446C2×C4—94no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—94no—
450C2×C4—92no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—92no—
454C2×C4—94no—
455C2×C4—94no—
456C2×C4—124no—
457C2×C4—182no—
458C2×C4—188no—
459C2×C4—188no—
460C2×C4—184no—
461C2×C4—184no—
462C2×C4—184no—
463C2×C4—364no—
464C2×C4D32⋊C414yescomplemented
465C2×C4C2×GO+(4,𝔽2)11yescharacteristic
466C2×C4C2×GO+(4,𝔽2)11yescharacteristic
467C2×C3—24no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—42no—
475C2×C3—124no—
476D3—44no—
477D3—62no—
478D3—62no—
479D3—62no—
480D3—62no—
481D3—64no—
482D3—122no—
483C22—21no—
484C22—21no—
485C22—64no—
486C22—92no—
487C22—92no—
488C22—91no—
489C22—91no—
490C22—92no—
491C22—122no—
492C22—122no—
493C22—184no—
494C22—184no—
495C22—188no—
496C22—181no—
497C22—181no—
498C22—364no—
499C22C2×D32⋊C412yes—
500C22C22×GO+(4,𝔽2)11yescharacteristic
501C4—64no—
502C4—92no—
503C4—92no—
504C4—124no—
505C4—364no—
506C4C2×D32⋊C412yes—
507C4C2×D32⋊C412yes—
508C3—21no—
509C3—21no—
510C2—22no—
511C2—92no—
512C2—92no—
513C2—124no—
514C2—182no—
515C2#1059649411yescharacteristic
516C2#1059651211yescharacteristic
517C2C22×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2311
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C2×#63900C2semidirect
4. #10593514C2semidirect
5. #10593407C2semidirect
6. #10593403C2semidirect
7. #10593342C2semidirect
14. #64306C4semidirect
63. #3802C2×C4semidirect
65. C4×D32C2×C4semidirect
68. #3797C2×C4semidirect
116. C2×C32×C4C22⋊C4semidirect
119. C2×C3⋊Dic3C22⋊C4semidirect
122. C4×C3⋊D3C22⋊C4semidirect
123. C4×C3⋊D3C22⋊C4semidirect
424. C32#2311semidirect
464. C2×C4D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642862
C2×#639002
#105935142
#105934072
#105934032
#105933422
#23119