Finite Group Databasebeta

← #11920385

Subgroups — #11920385

Order 1152.

900 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 76 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×C4×C22⋊C9C211yesmaximal, characteristic, complemented
2C2×#63694C212yesmaximal, complemented
3C2×C4⋊((C22⋊C9)⋊C2)C211yesmaximal, characteristic, complemented
4(C2×(C22⋊C9)⋊C2)⋊C4C212yesmaximal, complemented
5C4⋊((C22⋊C9)⋊C4)C211yesmaximal, characteristic, complemented
6#84032—31nomaximal
7C23×C22⋊C9C2211yescharacteristic
8C22×(C22⋊C9)⋊C2C2212yes—
9C2×C4×C22⋊C9—22no—
10C2×C4×C22⋊C9C2211yescharacteristic
11C2×C4×C22⋊C9C2211yescharacteristic
12#63694—24no—
13C2×(C22⋊C9)⋊C4C2212yes—
14C4⋊((C22⋊C9)⋊C2)—22no—
15#63492—41nomaximal
16C24×C3×C4D311yescharacteristic
17C2×#953—32no—
18C2×#930—31no—
19C2×#930—31no—
20C2×#930—31no—
21#5213—32no—
22#5213—32no—
23#5213—32no—
24#5212—31no—
25#5212—31no—
26#5212—31no—
27C22×C22⋊C9—21no—
28C22×C22⋊C9—21no—
29C22×C22⋊C9D412yescomplemented
30C22×C22⋊C9C2311yescharacteristic
31C2×(C22⋊C9)⋊C2—22no—
32C2×(C22⋊C9)⋊C2—22no—
33C2×(C22⋊C9)⋊C2—22no—
34C22×C4×C9—41no—
35C2×#611—42no—
36C2×D36—41no—
37C4×C22⋊C9—21no—
38C4×C22⋊C9D412yescomplemented
39(C22⋊C9)⋊C4—22no—
40(C2×D9)⋊C4—42no—
41C4⋊Dic9—41no—
42#2847—91noSylow
43C25×C3C2×D311yescharacteristic
44C23×C3×C4—22no—
45C23×C3×C4—31no—
46C23×C3×C4—31no—
47C23×C3×C4—31no—
48C23×C3×C4—31no—
49C23×C3×C4—62no—
50C23×C3×C4C2×D311yescharacteristic
51C23×C3×C4C2×D311yescharacteristic
52C22×#67—32no—
53C22×#67—32no—
54C22×#67—32no—
55C22×D12—31no—
56#953—64no—
57#953—64no—
58C2×#217—32no—
59C2×#217—32no—
60C2×#217—32no—
61#930—62no—
62#930—64no—
63#930—61no—
64#930—61no—
65#930—61no—
66#930—62no—
67#930—61no—
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—32no—
70C2×(C2×D3)⋊C4—32no—
71C2×C4⋊Dic3—31no—
72C2×C4⋊Dic3—31no—
73C2×C4⋊Dic3—31no—
74C3⋊#95—32no—
75C3⋊#95—32no—
76C3⋊#95—32no—
77C23×C9—41no—
78C22×D9—42no—
79C2×C22⋊C9—22no—
80C2×C22⋊C9C2×D411yescharacteristic
81C2×C22⋊C9C2×D411yescharacteristic
82C2×C22⋊C9#4111yescharacteristic
83(C22⋊C9)⋊C2—42no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9—82no—
87#611—84no—
88C2×Dic9—42no—
89D36—82no—
90C24×C4D911yescharacteristic, complemented
91C2×#121—91no—
92C2×#121—91no—
93C2×#121—91no—
94C2×#120—92no—
95#386—92no—
96#386—92no—
97#386—92no—
98#380—91no—
99#380—91no—
100#380—91no—
101C24×C3—21no—
102C24×C3—21no—
103C24×C3—31no—
104C24×C3—31no—
105C24×C3—32no—
106C24×C3—61no—
107C24×C3—61no—
108C24×C3D1212yes—
109C24×C3C22×D311yescharacteristic
110C23×D3—32no—
111C22×C3×C4—21no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4—32no—
116C22×C3×C4—34no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—62no—
122C22×C3×C4—62no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4—62no—
126C22×C3×C4—62no—
127C22×C3×C4—62no—
128C22×C3×C4—62no—
129C22×C3×C4—62no—
130C22×C3×C4#6712yes—
131C22×C3×C4S411yescharacteristic
132C2×#67—62no—
133C2×#67—64no—
134C2×#67—62no—
135C2×#67—64no—
136C2×#67—62no—
137C2×#67—64no—
138C2×#67—62no—
139C2×#67—64no—
140C2×#67—64no—
141C2×#67—62no—
142C2×#67—62no—
143C2×#67—62no—
144C2×#67—62no—
145C22×Dic3—32no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C2×D12—61no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—61no—
152#217—64no—
153#217—62no—
154#217—64no—
155#217—62no—
156(C2×D3)⋊C4—64no—
157(C2×D3)⋊C4—64no—
158(C2×D3)⋊C4—62no—
159(C2×D3)⋊C4—62no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C22×C9—42no—
165C22×C9—41no—
166C22×C9—81no—
167C22×C9—81no—
168C2×D9—82no—
169C2×D9—82no—
170C2×D9—82no—
171C22⋊C9#12111yescharacteristic, complemented
172C4×C9—42no—
173C4×C9—81no—
174Dic9—82no—
175C25C2×D911yescharacteristic
176C22×D4—91no—
177C22×D4—92no—
178C22×D4—92no—
179C22×D4—92no—
180C23×C4—22no—
181C23×C4—31no—
182C23×C4—31no—
183C23×C4—31no—
184C23×C4—31no—
185C23×C4—62no—
186C23×C4C2×D911yescharacteristic
187C23×C4C2×D911yescharacteristic
188#121—182no—
189#121—184no—
190#121—181no—
191#121—181no—
192#121—181no—
193#121—182no—
194#121—181no—
195#120—184no—
196#120—184no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—91no—
199C2×C4⋊C4—91no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—92no—
202C2×C22⋊C4—92no—
203C2×C22⋊C4—92no—
204C2×C22⋊C4—92no—
205C2×C22⋊C4—92no—
206#95—92no—
207#95—92no—
208#95—92no—
209C23×C3—22no—
210C23×C3—31no—
211C23×C3—32no—
212C23×C3—31no—
213C23×C3—31no—
214C23×C3—31no—
215C23×C3—32no—
216C23×C3—32no—
217C23×C3—32no—
218C23×C3—32no—
219C23×C3—31no—
220C23×C3—61no—
221C23×C3—61no—
222C23×C3—61no—
223C23×C3—61no—
224C23×C3—62no—
225C23×C3—61no—
226C23×C3—61no—
227C23×C3—62no—
228C23×C3—62no—
229C23×C3—61no—
230C23×C3—64no—
231C23×C3C2×D1211yescharacteristic
232C23×C3#23511yescharacteristic
233C23×C3C2×#6711yescharacteristic
234C23×C3C2×S411yescharacteristic
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—62no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—62no—
242C2×C3×C4—22no—
243C2×C3×C4—31no—
244C2×C3×C4—32no—
245C2×C3×C4—32no—
246C2×C3×C4—32no—
247C2×C3×C4—32no—
248C2×C3×C4—31no—
249C2×C3×C4—62no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—61no—
253C2×C3×C4—62no—
254C2×C3×C4—64no—
255C2×C3×C4—62no—
256C2×C3×C4—61no—
257C2×C3×C4C2×S411yescharacteristic
258C2×C3×C4C2×S411yescharacteristic
259#67—122no—
260#67—122no—
261#67—122no—
262#67—128no—
263#67—124no—
264#67—122no—
265#67—124no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275D12—122no—
276D12—122no—
277C2×C9—41no—
278C2×C9—41no—
279C2×C9—41no—
280C2×C9—82no—
281D9—162no—
282C24—21no—
283C24—21no—
284C24—31no—
285C24—31no—
286C24—32no—
287C24—61no—
288C24—61no—
289C24—92no—
290C24D3612yescomplemented
291C24C22×D911yescharacteristic
292C2×D4—181no—
293C2×D4—182no—
294C2×D4—182no—
295C2×D4—184no—
296C2×D4—182no—
297C2×D4—184no—
298C2×D4—182no—
299C2×D4—184no—
300C2×D4—182no—
301C2×D4—182no—
302C2×D4—184no—
303C2×D4—184no—
304C2×D4—182no—
305C2×D4—182no—
306C2×D4—182no—
307C2×D4—182no—
308C2×D4—181no—
309C22×C4—21no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—32no—
314C22×C4—34no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—62no—
320C22×C4—62no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—62no—
324C22×C4—62no—
325C22×C4—62no—
326C22×C4—62no—
327C22×C4—62no—
328C22×C4—92no—
329C22×C4—92no—
330C22×C4—92no—
331C22×C4#61112yescomplemented
332C22×C4(C22⋊C9)⋊C211yescharacteristic, complemented
333C4⋊C4—181no—
334C4⋊C4—182no—
335C4⋊C4—182no—
336C4⋊C4—181no—
337C22⋊C4—184no—
338C22⋊C4—184no—
339C22⋊C4—182no—
340C22⋊C4—184no—
341C22⋊C4—182no—
342C22⋊C4—184no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—31no—
348C22×C3—31no—
349C22×C3—31no—
350C22×C3—31no—
351C22×C3—31no—
352C22×C3—31no—
353C22×C3—31no—
354C22×C3—31no—
355C22×C3—31no—
356C22×C3—34no—
357C22×C3—32no—
358C22×C3—62no—
359C22×C3—62no—
360C22×C3—62no—
361C22×C3—62no—
362C22×C3—61no—
363C22×C3—62no—
364C22×C3—62no—
365C22×C3—62no—
366C22×C3—61no—
367C22×C3—61no—
368C22×C3#93011yescharacteristic
369C22×C3C4⋊S412yes—
370C22×C3C22×S411yescharacteristic
371C2×D3—122no—
372C2×D3—122no—
373C2×D3—122no—
374C2×D3—122no—
375C2×D3—122no—
376C2×D3—122no—
377C2×D3—122no—
378C3×C4—21no—
379C3×C4—32no—
380C3×C4—61no—
381C3×C4GL(2,ℤ/4)12yes—
382Dic3—122no—
383Dic3—122no—
384Dic3—122no—
385C9—41noSylow
386C23—22no—
387C23—31no—
388C23—32no—
389C23—31no—
390C23—31no—
391C23—31no—
392C23—32no—
393C23—32no—
394C23—31no—
395C23—32no—
396C23—32no—
397C23—61no—
398C23—61no—
399C23—61no—
400C23—61no—
401C23—62no—
402C23—61no—
403C23—61no—
404C23—62no—
405C23—62no—
406C23—61no—
407C23—64no—
408C23—182no—
409C23—182no—
410C23—182no—
411C23—182no—
412C23—182no—
413C23—182no—
414C23—182no—
415C23C2×D3611yescharacteristic
416C23#369711yescharacteristic
417C23C2×#61111yescharacteristic
418C23C2×(C22⋊C9)⋊C211yescharacteristic
419D4—362no—
420D4—362no—
421D4—362no—
422D4—362no—
423D4—368no—
424D4—364no—
425D4—362no—
426D4—364no—
427D4—362no—
428C2×C4—22no—
429C2×C4—31no—
430C2×C4—32no—
431C2×C4—32no—
432C2×C4—32no—
433C2×C4—32no—
434C2×C4—31no—
435C2×C4—62no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—62no—
440C2×C4—64no—
441C2×C4—62no—
442C2×C4—61no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
453C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
454C2×C3—22no—
455C2×C3—31no—
456C2×C3—31no—
457C2×C3—31no—
458C2×C3—31no—
459C2×C3—62no—
460C2×C3C2×C4⋊S411yescharacteristic
461C2×C3#591211yescharacteristic
462C2×C3C2×GL(2,ℤ/4)11yescharacteristic
463D3—242no—
464C22—21no—
465C22—21no—
466C22—31no—
467C22—31no—
468C22—31no—
469C22—31no—
470C22—31no—
471C22—31no—
472C22—31no—
473C22—31no—
474C22—31no—
475C22—34no—
476C22—32no—
477C22—62no—
478C22—62no—
479C22—62no—
480C22—62no—
481C22—61no—
482C22—62no—
483C22—62no—
484C22—62no—
485C22—61no—
486C22—61no—
487C22—362no—
488C22—362no—
489C22—362no—
490C22—362no—
491C22—362no—
492C22—362no—
493C22—362no—
494C22#6349211yescharacteristic, complemented
495C22C4⋊((C22⋊C9)⋊C2)12yescomplemented
496C22C22×(C22⋊C9)⋊C211yescharacteristic
497C4—21no—
498C4—32no—
499C4—61no—
500C4—362no—
501C4—362no—
502C4—362no—
503C4#6369412yescomplemented
504C3#8548611yescharacteristic
505C2—22no—
506C2—31no—
507C2—31no—
508C2—31no—
509C2—31no—
510C2—62no—
511C2—722no—
512C2C2×C4⋊((C22⋊C9)⋊C2)11yescharacteristic
513C2#1059308711yescharacteristic
514C2C2×#6369411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC22×C22⋊C9C23
FrattiniC22×C3C22×S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterC22⋊C9#121
LCSG ▷ C22×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊C9C2semidirect
2. C2×#63694C2semidirect
3. C2×C4⋊((C22⋊C9)⋊C2)C2semidirect
4. (C2×(C22⋊C9)⋊C2)⋊C4C2semidirect
5. C4⋊((C22⋊C9)⋊C4)C2semidirect
29. C22×C22⋊C9D4semidirect
38. C4×C22⋊C9D4semidirect
90. C24×C4D9semidirect
171. C22⋊C9#121semidirect
290. C24D36semidirect
331. C22×C4#611semidirect
332. C22×C4(C22⋊C9)⋊C2semidirect
494. C22#63492semidirect
495. C22C4⋊((C22⋊C9)⋊C2)semidirect
503. C4#63694semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊C92
C2×#636942
C2×C4⋊((C22⋊C9)⋊C2)2
(C2×(C22⋊C9)⋊C2)⋊C42
C4⋊((C22⋊C9)⋊C4)2
#840323
#634924