Finite Group Databasebeta

← #11793137

Subgroups — #11793137

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595521C211yesmaximal, characteristic, complemented
2C2×#63661C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C2×C3×#834C211yesmaximal, characteristic
5#10589187C211yesmaximal, characteristic, complemented
6#10589186C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#70025—31nomaximal
9#70025—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3757C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17#63982—22no—
18#63964—22no—
19#63964—22no—
20#63661—22no—
21C3×#834—22no—
22C3×#834—22no—
23#5483—31no—
24#5483—31no—
25C2×C3×#99—31no—
26C2×C3×#99—31no—
27C2×#834—31no—
28C2×#834—31no—
29C2×#834—61no—
30C2×#834D311yescharacteristic
31C2×#834D311yescharacteristic
32#4527—31no—
33#4527—31no—
34#4527—31no—
35#4527—31no—
36#4526—31no—
37#4526—31no—
38C24×C32Q811yescharacteristic, complemented
39C24×C32C2311yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C22×C32×C4Q811yescharacteristic, complemented
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×#627—22no—
54#3757—21no—
55#3757—21no—
56#3757—21no—
57#3757D412yes—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217D412yes—
65C3×#217D412yes—
66#3724—22no—
67Dic3⋊Dic3—22no—
68Dic3⋊Dic3—22no—
69#2032—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C2×D311yescharacteristic
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—31no—
77C2×#217—31no—
78C2×#217—31no—
79C2×#217—31no—
80C2×#217—31no—
81C2×#217—61no—
82C2×#217—61no—
83C2×#217C2×D311yescharacteristic
84C2×#217C2×D311yescharacteristic
85C2×#217C2×D311yescharacteristic
86C2×#217C2×D311yescharacteristic
87#924—62no—
88#924—62no—
89#878—62no—
90#878—62no—
91#878—62no—
92#878—62no—
93C3×#99—62no—
94C3×#99—62no—
95#834—22no—
96#834—22no—
97#834—62no—
98#834—62no—
99#834—64no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32—21no—
103C23×C32—81no—
104C23×C32—81no—
105C23×C32C2×D411yescharacteristic
106C23×C32C2×D411yescharacteristic
107C23×C32C2×D411yescharacteristic
108C23×C32C2×Q811yescharacteristic
109C23×C32#4111yescharacteristic
110C23×C32#4111yescharacteristic
111C23×C32#4111yescharacteristic
112C32×D4—41no—
113C32×D4—41no—
114C32×D4—41no—
115C32×D4—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—81no—
122C2×C3⋊Dic3—81no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C2×C3×Dic3—81no—
130C2×C3×Dic3—81no—
131#627—82no—
132#543—91no—
133C2×#99—31no—
134C2×#99—31no—
135C2×#99—91no—
136#342—91no—
137#342—91no—
138#342—91no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3Dic611yescharacteristic, complemented
142C24×C3Dic611yescharacteristic, complemented
143C24×C3C22×D311yescharacteristic
144C24×C3C22×D311yescharacteristic
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4—41no—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4Dic611yescharacteristic, complemented
169C22×C3×C4Dic611yescharacteristic, complemented
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3—121no—
180C2×Dic6—62no—
181C2×Dic6—62no—
182C3×C22⋊C4—32no—
183C3×C22⋊C4—32no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190#217—21no—
191#217—21no—
192#217—21no—
193#217—21no—
194#217—21no—
195#217—21no—
196#217—32no—
197#217—32no—
198#217—62no—
199#217—61no—
200#217—61no—
201#217—62no—
202#217—61no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—121no—
207#217—121no—
208#217#6712yes—
209#217#6712yes—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32—41no—
224C22×C32—81no—
225C22×C32—81no—
226C22×C32—81no—
227C22×C32#12011yescharacteristic
228C22×C32C22⋊Q811yescharacteristic
229C22×C32C22⋊Q811yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C22×C32#12411yescharacteristic
232C22×C32#12411yescharacteristic
233C22×C32#12411yescharacteristic
234C32×C4—41no—
235C3⋊Dic3—42no—
236C3⋊Dic3—81no—
237C3×Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4D3211yescharacteristic
242C22⋊Q8—182no—
243C22⋊Q8—182no—
244C22⋊Q8—182no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4—31no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—31no—
249C2×C22⋊C4—91no—
250C2×C22⋊C4—91no—
251#99—62no—
252#99—62no—
253#99—182no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—81no—
271C23×C3—81no—
272C23×C3—82no—
273C23×C3—81no—
274C23×C3—81no—
275C23×C3—82no—
276C23×C3C2×Dic611yescharacteristic
277C23×C3C2×Dic611yescharacteristic
278C23×C3#23511yescharacteristic
279C23×C3#23511yescharacteristic
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D411yescharacteristic
282C23×C3D3×D411yescharacteristic
283C23×C3D3×D411yescharacteristic
284C23×C3#23711yescharacteristic
285C23×C3#23711yescharacteristic
286C23×C3#23711yescharacteristic
287C23×C3#23711yescharacteristic
288C23×C3C2×#6711yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C3×D4—42no—
291C3×D4—42no—
292C3×D4—42no—
293C3×D4—42no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—241no—
316C2×C3×C4—241no—
317C2×C3×C4—241no—
318C2×C3×C4—241no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—81no—
326C2×Dic3—81no—
327C2×Dic3—81no—
328C2×Dic3—81no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—241no—
334C2×Dic3—241no—
335C2×Dic3—242no—
336C2×Dic3—242no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339Dic6—242no—
340Dic6—242no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—81no—
349C2×C32#39311yescharacteristic
350C24#62711yescharacteristic, complemented
351C24C2×D3211yescharacteristic
352C2×Q8—182no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4—61no—
363C22×C4—181no—
364C22×C4—181no—
365C22×C4#62711yescharacteristic, complemented
366C4⋊C4—182no—
367C4⋊C4—182no—
368C4⋊C4—182no—
369C22⋊C4—32no—
370C22⋊C4—32no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—92no—
378C22⋊C4—181no—
379C22⋊C4—181no—
380C22⋊C4—181no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—81no—
418C22×C3—82no—
419C22×C3—82no—
420C22×C3—82no—
421C22×C3#87811yescharacteristic
422C22×C3#87811yescharacteristic
423C22×C3#87811yescharacteristic
424C22×C3#87811yescharacteristic
425C22×C3#88511yescharacteristic
426C22×C3#88511yescharacteristic
427C22×C3#88511yescharacteristic
428C22×C3#88511yescharacteristic
429C22×C3#92411yescharacteristic
430C22×C3#92411yescharacteristic
431C22×C3#93611yescharacteristic
432C22×C3#93611yescharacteristic
433C22×C3#93711yescharacteristic
434C22×C3#93711yescharacteristic
435C3×C4—42no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—122no—
439C3×C4—122no—
440C3×C4—241no—
441C3×C4—241no—
442Dic3—42no—
443Dic3—42no—
444Dic3—81no—
445Dic3—81no—
446Dic3—122no—
447Dic3—122no—
448Dic3—242no—
449Dic3—241no—
450Dic3—241no—
451Dic3—242no—
452C32#203211yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—81no—
457C23—81no—
458C23#380411yescharacteristic
459C23#380411yescharacteristic
460C23#380511yescharacteristic
461C23C2×#62711yescharacteristic
462C23D3×#6711yescharacteristic
463C23D3×#6711yescharacteristic
464C23#381111yescharacteristic
465Q8—722no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—41no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—182no—
478C2×C4—241no—
479C2×C4—241no—
480C2×C4—241no—
481C2×C4—241no—
482C2×C4—361no—
483C2×C4—721no—
484C2×C4—721no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—41no—
505C2×C3—41no—
506C2×C3—41no—
507C2×C3—82no—
508C2×C3—81no—
509C2×C3—81no—
510C2×C3#494711yescharacteristic
511C2×C3#494711yescharacteristic
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22#6395311yescharacteristic
524C22#6395911yescharacteristic
525C22#6395911yescharacteristic
526C22#6396411yescharacteristic
527C22#6396411yescharacteristic
528C22#6398211yescharacteristic
529C22#6398311yescharacteristic
530C4—41no—
531C4—122no—
532C4—122no—
533C4—241no—
534C4—241no—
535C4—362no—
536C4—721no—
537C3—21no—
538C3#7002511yescharacteristic, complemented
539C3#7002511yescharacteristic, complemented
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—81no—
548C2#1059169211yescharacteristic
subgroupG/H
centerC2#10591692
commutator, cosocleC24×C32C23
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC2×C32#393
hypercenterC22×D4D32
hypocenterC32#2032
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10595521C2semidirect
5. #10589187C2semidirect
6. #10589186C2semidirect
7. #10589186C2semidirect
38. C24×C32Q8semidirect
46. C22×C32×C4Q8semidirect
141. C24×C3Dic6semidirect
142. C24×C3Dic6semidirect
168. C22×C3×C4Dic6semidirect
169. C22×C3×C4Dic6semidirect
350. C24#627semidirect
365. C22×C4#627semidirect
452. C32#2032semidirect
538. C3#70025semidirect
539. C3#70025semidirect

Maximal subgroups

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

subgroupindex
#105955212
C2×#636612
C2×C3×#8342
#105891872
#105891862
#700253