Finite Group Databasebeta

← #11804292

Subgroups — #11804292

Order 1152.

1428 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic
2#10592683C211yesmaximal, characteristic, complemented
3#10592683C211yesmaximal, characteristic, complemented
4#10592679C211yesmaximal, characteristic, complemented
5#10592679C211yesmaximal, characteristic, complemented
6#10592679C211yesmaximal, characteristic, complemented
7C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592650C211yesmaximal, characteristic
9#10592650C211yesmaximal, characteristic
10#10592650C211yesmaximal, characteristic
11#10592649C211yesmaximal, characteristic
12#10592649C211yesmaximal, characteristic
13C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
14#10592635C211yesmaximal, characteristic, complemented
15C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
16#83074—34nomaximal
17C23×C3⋊Dic3C2211yescharacteristic
18C32×#126C418yescomplemented
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C2×C3×#126D314yes—
54#4984—34no—
55#4984—34no—
56#4980—34no—
57#4980—34no—
58#4980—34no—
59Dic3×C4⋊C4—34no—
60#4951—34no—
61#4951—34no—
62#4951—34no—
63#4950—34no—
64#4950—34no—
65Dic3×C22⋊C4—34no—
66#4936—34no—
67C4×C4⋊Dic3—34no—
68C24×C32C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—41no—
77C22×C3⋊Dic3—41no—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C32×C4⋊C4C2×C414yescomplemented
87C32×C4⋊C4C2×C414yescomplemented
88C32×C4⋊C4C2×C414yescomplemented
89C32×C22⋊C4C2×C414yes—
90C32×C22⋊C4C2×C414yes—
91C32×C22⋊C4C2×C414yes—
92C32×C42C2×C414yescomplemented
93#3757—22no—
94#3757—41no—
95#3757—41no—
96C4⋊(C3⋊Dic3)—22no—
97C4⋊(C3⋊Dic3)—22no—
98C4⋊(C3⋊Dic3)—22no—
99C4⋊(C3⋊Dic3)—41no—
100C4⋊(C3⋊Dic3)—41no—
101C4⋊(C3⋊Dic3)—41no—
102C4⋊(C3⋊Dic3)—41no—
103C4×C3⋊Dic3—22no—
104C4×C3⋊Dic3—41no—
105C4×C3⋊Dic3—41no—
106C4×C3⋊Dic3—41no—
107C4×C3⋊Dic3—41no—
108#2334—91noSylow
109C23×Dic3—34no—
110C3×#126Dic3132yescomplemented
111C2×C3×C4⋊C4C2×D314yes—
112C2×C3×C4⋊C4C2×D314yes—
113C2×C3×C4⋊C4C2×D314yes—
114C2×C3×C22⋊C4C2×D314yes—
115C2×C3×C22⋊C4C2×D314yes—
116C2×C3×C22⋊C4C2×D314yes—
117C2×C3×C42C2×D314yes—
118C2×#217—34no—
119C2×#217—34no—
120C2×#217—34no—
121C2×C4⋊Dic3—34no—
122C2×C4⋊Dic3—34no—
123C2×C4⋊Dic3—34no—
124C2×C4⋊Dic3—34no—
125C2×C4⋊Dic3—34no—
126C2×C4⋊Dic3—34no—
127C2×C4⋊Dic3—34no—
128C2×C4×Dic3—34no—
129C2×C4×Dic3—34no—
130C2×C4×Dic3—34no—
131C2×C4×Dic3—34no—
132C2×C4×Dic3—34no—
133C3⋊#95—34no—
134C3⋊#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C3⋊#95—34no—
140C3⋊#95—34no—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C23×C32—21no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32C2411yescharacteristic
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C412yes—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C22×C412yes—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—44no—
194C2×C3⋊Dic3#4112yes—
195C2×C3⋊Dic3#4112yes—
196C2×#126C3⋊D311yescharacteristic
197#389—91no—
198#389—91no—
199#388—91no—
200#388—91no—
201#388—91no—
202#387—91no—
203#387—91no—
204#387—91no—
205#385—91no—
206#385—91no—
207#382—91no—
208C4×C4⋊C4—91no—
209C4×C4⋊C4—91no—
210C4×C22⋊C4—91no—
211C24×C3C22×D314yes—
212C22×C3×C4C22×D314yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D314yes—
215C22×C3×C4C22×D314yes—
216C22×C3×C4C22×D314yes—
217C22×C3×C4C22×D314yes—
218C22×Dic3—34no—
219C22×Dic3—34no—
220C22×Dic3—34no—
221C22×Dic3—34no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C22×Dic3—68no—
227C22×Dic3—124no—
228C22×Dic3—124no—
229C3×C4⋊C4C2×Dic3116yescomplemented
230C3×C4⋊C4C2×Dic3116yescomplemented
231C3×C4⋊C4C2×Dic3116yescomplemented
232C3×C22⋊C4C2×Dic3116yes—
233C3×C22⋊C4C2×Dic3116yes—
234C3×C22⋊C4C2×Dic3116yes—
235C3×C42C2×Dic3116yescomplemented
236#217—68no—
237#217—124no—
238#217—124no—
239C4⋊Dic3—68no—
240C4⋊Dic3—68no—
241C4⋊Dic3—68no—
242C4⋊Dic3—124no—
243C4⋊Dic3—124no—
244C4⋊Dic3—124no—
245C4⋊Dic3—124no—
246C4×Dic3—68no—
247C4×Dic3—124no—
248C4×Dic3—124no—
249C4×Dic3—124no—
250C4×Dic3—124no—
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—22no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—41no—
258C22×C32C23×C411yescharacteristic
259C22×C32C2×#4111yescharacteristic
260C22×C32C2×#4111yescharacteristic
261C22×C32H(5,𝔽2)11yescharacteristic
262C22×C32H(5,𝔽2)11yescharacteristic
263C22×C322−1+411yescharacteristic
264C22×C322−1+411yescharacteristic
265C32×C4—22no—
266C32×C4—22no—
267C32×C4—22no—
268C32×C4—22no—
269C32×C4—22no—
270C32×C4—22no—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—41no—
274C3⋊Dic3—41no—
275C3⋊Dic3—41no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3—41no—
279C23×C4—91no—
280#126C3⋊Dic318yescomplemented
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4C2×C3⋊D311yescharacteristic
289C2×C4⋊C4C2×C3⋊D311yescharacteristic
290C2×C4⋊C4C2×C3⋊D311yescharacteristic
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4C2×C3⋊D311yescharacteristic
295C2×C22⋊C4C2×C3⋊D311yescharacteristic
296C2×C22⋊C4C2×C3⋊D311yescharacteristic
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42C2×C3⋊D311yescharacteristic
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95—91no—
312#95—91no—
313#95—91no—
314#95—91no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3C22×Dic318yes—
322C23×C3C23×D314yes—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4C22×Dic318yes—
336C2×C3×C4C22×Dic318yes—
337C2×C3×C4C22×Dic318yes—
338C2×C3×C4C22×Dic318yes—
339C2×C3×C4C22×Dic318yes—
340C2×C3×C4C22×Dic318yes—
341C2×Dic3—38no—
342C2×Dic3—38no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—1216no—
366C2×C32—42no—
367C2×C32C4×#4111yescharacteristic
368C2×C32#52011yescharacteristic
369C2×C32#52011yescharacteristic
370C2×C32#53811yescharacteristic
371C2×C32#53911yescharacteristic
372C2×C32#54111yescharacteristic
373C2×C32#54211yescharacteristic
374C24C22×C3⋊D311yescharacteristic
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—182no—
384C22×C4—361no—
385C22×C4—361no—
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D311yescharacteristic
388C22×C4C22×C3⋊D311yescharacteristic
389C22×C4C22×C3⋊D311yescharacteristic
390C22×C4C22×C3⋊D311yescharacteristic
391C22×C4C22×C3⋊D311yescharacteristic
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C4⋊C4—361no—
398C4⋊C4—361no—
399C4⋊C4C2×C3⋊Dic314yescomplemented
400C4⋊C4C2×C3⋊Dic314yescomplemented
401C4⋊C4C2×C3⋊Dic314yescomplemented
402C22⋊C4—182no—
403C22⋊C4—361no—
404C22⋊C4—361no—
405C22⋊C4C2×C3⋊Dic314yes—
406C22⋊C4C2×C3⋊Dic314yes—
407C22⋊C4C2×C3⋊Dic314yes—
408C42—182no—
409C42—361no—
410C42—361no—
411C42—361no—
412C42—361no—
413C42C2×C3⋊Dic314yescomplemented
414C22×C3—28no—
415C22×C3—28no—
416C22×C3—28no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3D3×#4114yes—
422C22×C3D3×#4114yes—
423C22×C3#100914yes—
424C22×C3#100914yes—
425C22×C3#101014yes—
426C22×C3#101014yes—
427C22×C3C23×Dic314yes—
428C3×C4—28no—
429C3×C4—28no—
430C3×C4—28no—
431C3×C4—28no—
432C3×C4—28no—
433C3×C4—28no—
434Dic3—68no—
435Dic3—68no—
436Dic3—124no—
437Dic3—124no—
438Dic3—124no—
439Dic3—124no—
440Dic3—124no—
441Dic3—124no—
442C32#233411yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23C22×C3⋊Dic312yes—
450C23C23×C3⋊D311yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—364no—
488C2×C4C22×C3⋊Dic312yes—
489C2×C4C22×C3⋊Dic312yes—
490C2×C4C22×C3⋊Dic312yes—
491C2×C4C22×C3⋊Dic312yes—
492C2×C4C22×C3⋊Dic312yes—
493C2×C4C22×C3⋊Dic312yes—
494C2×C3—48no—
495C2×C3#570114yes—
496C2×C3#570414yes—
497C2×C3#570714yes—
498C2×C3#571014yes—
499C2×C3Dic3×#4114yes—
500C2×C3#582714yes—
501C2×C3#582714yes—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22#41×C3⋊D311yescharacteristic
510C22#41×C3⋊D311yescharacteristic
511C22#6436611yescharacteristic
512C22#6436611yescharacteristic
513C22#6436711yescharacteristic
514C22#6436711yescharacteristic
515C22C23×C3⋊Dic311yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—22no—
522C4—182no—
523C4—182no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4—361no—
528C4—361no—
529C4—361no—
530C3#8307414yescomplemented
531C2—42no—
532C2#1059617211yescharacteristic
533C2#1059617511yescharacteristic
534C2#1059617811yescharacteristic
535C2#1059618111yescharacteristic
536C2#41×C3⋊Dic311yescharacteristic
537C2#1059629811yescharacteristic
538C2#1059629811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×#126C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×#126C3⋊D3
hypocenterC32#2334
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #10592683C2semidirect
3. #10592683C2semidirect
4. #10592679C2semidirect
5. #10592679C2semidirect
6. #10592679C2semidirect
7. C4⋊C4×C3⋊Dic3C2semidirect
14. #10592635C2semidirect
15. C4×C4⋊(C3⋊Dic3)C2semidirect
18. C32×#126C4semidirect
86. C32×C4⋊C4C2×C4semidirect
87. C32×C4⋊C4C2×C4semidirect
88. C32×C4⋊C4C2×C4semidirect
92. C32×C42C2×C4semidirect
110. C3×#126Dic3semidirect
229. C3×C4⋊C4C2×Dic3semidirect
230. C3×C4⋊C4C2×Dic3semidirect
231. C3×C4⋊C4C2×Dic3semidirect
235. C3×C42C2×Dic3semidirect
280. #126C3⋊Dic3semidirect
399. C4⋊C4C2×C3⋊Dic3semidirect
400. C4⋊C4C2×C3⋊Dic3semidirect
401. C4⋊C4C2×C3⋊Dic3semidirect
413. C42C2×C3⋊Dic3semidirect
442. C32#2334semidirect
530. C3#83074semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1262
#105926832
#105926792
C4⋊C4×C3⋊Dic32
#105926502
#105926492
C22⋊C4×C3⋊Dic32
#105926352
C4×C4⋊(C3⋊Dic3)2
#830743