Finite Group Databasebeta

← #11787559

Subgroups — #11787559

Order 1152.

780 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C22×#3774C211yesmaximal, characteristic
2C2×C4×#625C211yesmaximal, characteristic, complemented
3C2×#63739C211yesmaximal, characteristic, complemented
4C2×#63739C211yesmaximal, characteristic, complemented
5#10591385C211yesmaximal, characteristic, complemented
6#10590207C211yesmaximal, characteristic, complemented
7#10590075C211yesmaximal, characteristic, complemented
8C22×C3×C4×D3—21no—
9C22×#625C2211yescharacteristic
10C22×#625C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3774—22no—
14C2×#3774—22no—
15C2×#3774C414yescomplemented
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C4×#625—22no—
23C4×#625—22no—
24#63739—22no—
25#63739—22no—
26C2×C4×#67—61no—
27#4957—61no—
28C23×C3×D3—21no—
29C23×C3×D3—21no—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C2×C3×C4×D3—24no—
36C2×C3×C4×D3—42no—
37C2×C3×C4×D3—42no—
38C2×#625—21no—
39C2×#625—21no—
40C2×#625—21no—
41C2×#625—21no—
42C2×#625—21no—
43C2×#625—21no—
44C2×#625—21no—
45C2×#625—21no—
46C2×#625C2×C412yes—
47C2×#625C2×C412yescomplemented
48C2×#625D412yes—
49C2×#625D412yes—
50C2×#622—21no—
51C2×#622—21no—
52C2×#622—21no—
53C2×#622—21no—
54C2×#622—21no—
55C2×#622C2×C412yescomplemented
56#3774—28no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C3×(C2×D3)⋊C4—42no—
60#3724—21no—
61#3724—21no—
62#3724—21no—
63#3724D412yes—
64(C2×D3)⋊Dic3—24no—
65(C2×D3)⋊Dic3—42no—
66#1879—91nomaximal, Sylow
67C23×C3×C4—61no—
68C22×#67—61no—
69C22×#67—61no—
70C22×C4×D3—21no—
71C2×C3×C22⋊C4—61no—
72C2×#217—61no—
73C2×#217—61no—
74C4×#67—64no—
75C4×#67—64no—
76C2×(C2×D3)⋊C4—21no—
77C2×(C2×D3)⋊C4—61no—
78C2×(C2×D3)⋊C4—61no—
79C2×Dic3⋊C4—61no—
80C2×Dic3⋊C4—61no—
81C2×C4×Dic3—61no—
82C2×C4×Dic3—61no—
83C23×C32C2×D411yescharacteristic
84C22×C3×D3—22no—
85C22×C3×D3—22no—
86C22×C3×D3—22no—
87C22×C3×D3—22no—
88C22×C3×D3—41no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C22×C3×D3—41no—
92C22×C3×D3—41no—
93C22×C3×D3—41no—
94C22×C3×D3—41no—
95C22×C3×D3—41no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4D812yescomplemented
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3C22×C411yescharacteristic
105C2×C3⋊Dic3C2×D411yescharacteristic
106C2×C3⋊Dic3C2×D411yescharacteristic
107C2×C3⋊Dic3C2×D411yescharacteristic
108C2×C3⋊Dic3#4111yescharacteristic
109C2×C3⋊Dic3#4111yescharacteristic
110C2×C3×Dic3—22no—
111C2×C3×Dic3—41no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C3×C4×D3—48no—
117#625—22no—
118#625—22no—
119#625—22no—
120#625—22no—
121#625—22no—
122#625—41no—
123#625—41no—
124#625C22⋊C414yescomplemented
125#622—22no—
126#622—41no—
127C22×D8—91no—
128C2×C4×D4—91no—
129C2×#102—91no—
130C2×#102—91no—
131#390—91no—
132#340—91no—
133#336—91no—
134C24×C3—61no—
135C24×C3—61no—
136C23×D3—21no—
137C23×D3—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—64no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C22×C3×C4—122no—
144C22×C3×C4—122no—
145C2×#67—62no—
146C2×#67—62no—
147C2×#67—62no—
148C2×#67—62no—
149C2×#67—62no—
150C2×#67—62no—
151C2×#67—62no—
152C2×#67—62no—
153C2×#67—121no—
154C2×#67—121no—
155C2×#67—121no—
156C2×#67—121no—
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C2×C4×D3—24no—
164C2×C4×D3—42no—
165C2×C4×D3—42no—
166C3×C22⋊C4—122no—
167#217—64no—
168#217—122no—
169(C2×D3)⋊C4—42no—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—122no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—121no—
175Dic3⋊C4—121no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—121no—
179C4×Dic3—121no—
180C22×C32C4×D411yescharacteristic
181C22×C32#12011yescharacteristic
182C22×C32#12111yescharacteristic
183C22×C32C2×D811yescharacteristic
184C22×C32#13511yescharacteristic
185C22×C32AGL(1,ℤ/8)11yescharacteristic
186C22×C32AGL(1,ℤ/8)11yescharacteristic
187C2×C3×D3—24no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C2×C3×D3—42no—
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—81no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—22no—
202C3⋊Dic3—41no—
203C3⋊Dic3C2×C22⋊C411yescharacteristic
204C3⋊Dic3C4×D411yescharacteristic
205C3⋊Dic3#12111yescharacteristic
206C3⋊Dic3#12311yescharacteristic
207C3×Dic3—42no—
208C3×Dic3—81no—
209C22×D4—91no—
210C22×D4—91no—
211C23×C4—61no—
212C2×D8—94no—
213C2×D8—182no—
214C2×D8—182no—
215C22×C8—91no—
216C22×C8—91no—
217C4×D4—182no—
218C4×D4—182no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—91no—
221C2×C22⋊C4—61no—
222C2×C22⋊C4—181no—
223C2×C22⋊C4—181no—
224C2×C42—91no—
225#102—182no—
226#102—182no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—62no—
231C23×C3—62no—
232C23×C3—62no—
233C23×C3—121no—
234C23×C3—121no—
235C23×C3—121no—
236C23×C3—121no—
237C23×C3—121no—
238C23×C3—121no—
239C23×C3—121no—
240C23×C3—121no—
241C23×C3—121no—
242C23×C3—121no—
243C22×D3—22no—
244C22×D3—22no—
245C22×D3—22no—
246C22×D3—22no—
247C22×D3—41no—
248C22×D3—41no—
249C22×D3—41no—
250C22×D3—41no—
251C22×D3—41no—
252C22×D3—41no—
253C22×D3—41no—
254C22×D3—41no—
255C22×D3—41no—
256C22×D3—41no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—62no—
264C2×C3×C4—128no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270#67—64no—
271#67—64no—
272#67—64no—
273#67—64no—
274#67—122no—
275#67—122no—
276#67—122no—
277#67—122no—
278C2×Dic3—22no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C4×D3—48no—
303C2×C32#38611yescharacteristic
304C2×C32C4×D811yescharacteristic
305C2×C32#44211yescharacteristic
306C2×C32#44711yescharacteristic
307C2×C32#44911yescharacteristic
308C2×C32#45911yescharacteristic
309C2×C32#46311yescharacteristic
310C3×D3—44no—
311C3×D3—82no—
312C24—61no—
313C24—61no—
314C2×D4—92no—
315C2×D4—92no—
316C2×D4—92no—
317C2×D4—92no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C2×D4—181no—
326C22×C4—64no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—122no—
332C22×C4—122no—
333C22×C4GO+(4,𝔽2)11yescharacteristic
334D8—188no—
335C2×C8—92no—
336C2×C8—181no—
337C2×C8—181no—
338C2×C8—181no—
339C2×C8—181no—
340C2×C8—181no—
341C4⋊C4—92no—
342C4⋊C4—181no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C22⋊C4—122no—
346C22⋊C4—184no—
347C22⋊C4—362no—
348C42—181no—
349C42—181no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—64no—
365C22×C3—122no—
366C22×C3—122no—
367C22×C3—122no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3—122no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—241no—
375C22×C3—241no—
376C22×C3—241no—
377C22×C3—241no—
378C2×D3—24no—
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—42no—
386C2×D3—42no—
387C2×D3—42no—
388C2×D3—81no—
389C2×D3—81no—
390C2×D3—81no—
391C2×D3—81no—
392C3×C4—24no—
393C3×C4—42no—
394C3×C4—122no—
395C3×C4—241no—
396Dic3—42no—
397Dic3—61no—
398Dic3—61no—
399Dic3—61no—
400Dic3—61no—
401Dic3—61no—
402Dic3—61no—
403Dic3—61no—
404Dic3—61no—
405Dic3—81no—
406Dic3—122no—
407Dic3—122no—
408C32#187911yescharacteristic, complemented, Sylow
409C23—62no—
410C23—62no—
411C23—62no—
412C23—62no—
413C23—121no—
414C23—121no—
415C23—121no—
416C23—121no—
417C23—121no—
418C23—121no—
419C23—121no—
420C23—121no—
421C23—121no—
422C23—121no—
423C23C2×GO+(4,𝔽2)11yescharacteristic
424D4—94no—
425D4—182no—
426D4—182no—
427D4—182no—
428D4—182no—
429D4—182no—
430D4—361no—
431D4—361no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—62no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—128no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4#377412yescomplemented
451C8—182no—
452C8—361no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—124no—
468C2×C3—242no—
469D3—44no—
470D3—82no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22—122no—
475C22—122no—
476C22—122no—
477C22—122no—
478C22—122no—
479C22—122no—
480C22—122no—
481C22—241no—
482C22—241no—
483C22—241no—
484C22—241no—
485C22#6422311yescharacteristic
486C22#6422411yescharacteristic
487C22C4×GO+(4,𝔽2)11yescharacteristic
488C22#6423011yescharacteristic
489C22C2×#377411yescharacteristic
490C22#6423611yescharacteristic
491C22#6424111yescharacteristic
492C4—22no—
493C4—91no—
494C4—91no—
495C4—91no—
496C4—91no—
497C4—122no—
498C4—241no—
499C4—361no—
500C3—21no—
501C3—21no—
502C2—124no—
503C2—242no—
504C2C4×#377411yescharacteristic
505C2#1059341711yescharacteristic
506C2#1059341911yescharacteristic
507C2#1059342111yescharacteristic
508C2#1059342211yescharacteristic
509C2#1059345311yescharacteristic
510C2#1059351911yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#3774C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1879
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#625C2semidirect
3. C2×#63739C2semidirect
4. C2×#63739C2semidirect
5. #10591385C2semidirect
6. #10590207C2semidirect
7. #10590075C2semidirect
15. C2×#3774C4semidirect
47. C2×#625C2×C4semidirect
55. C2×#622C2×C4semidirect
100. C2×C32×C4D8semidirect
124. #625C22⋊C4semidirect
408. C32#1879semidirect
450. C2×C4#3774semidirect

Maximal subgroups

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

subgroupindex
C22×#37742
C2×C4×#6252
C2×#637392
#105913852
#105902072
#105900752
#18799