Finite Group Databasebeta

← #11793138

Subgroups — #11793138

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595521C211yesmaximal, characteristic, complemented
2C2×C3×#806C211yesmaximal, characteristic
3C2×#63580C211yesmaximal, characteristic
4C2×#63580C211yesmaximal, characteristic
5#10589392C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589187C211yesmaximal, characteristic, complemented
8#70025—31nomaximal
9#68967—31nomaximal
10C22×C3×#67C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17#63982—22no—
18#63964—22no—
19#63964—22no—
20C3×#806—22no—
21#63580—22no—
22#63580—22no—
23#5483—31no—
24#5483—31no—
25C2×C3×#99—31no—
26C2×#834—31no—
27C2×#834—31no—
28C2×#806—31no—
29C2×#806—31no—
30C2×#806D311yescharacteristic
31C3×#342—31no—
32#4527—31no—
33#4527—31no—
34#4527D311yescharacteristic, complemented
35#4526—31no—
36#4526—31no—
37#4526—61no—
38C24×C32C2311yescharacteristic
39C23×C3×D3Q811yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C2×C3×#67—21no—
44C2×C3×#67—21no—
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3Q811yescharacteristic, complemented
53C2×#627—22no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4—21no—
56#3757—21no—
57#3757—21no—
58#3757—21no—
59#3757D412yes—
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—31no—
71C22×#67C2×D311yescharacteristic
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4C2×D311yescharacteristic
77C2×C3×C22⋊C4C2×D311yescharacteristic
78C2×#217—31no—
79C2×#217—31no—
80C2×#217—31no—
81C2×#217—31no—
82C2×#217—61no—
83C2×#217—61no—
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—
94#834—62no—
95#834—62no—
96#806—22no—
97#806—62no—
98#806—62no—
99C23×C32—81no—
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×Q811yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C23×C32#4111yescharacteristic
107C22×C3×D3—21no—
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C22×C3×D3—81no—
111C2×C32×C4—41no—
112C2×C32×C4—81no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—81no—
116C2×C3⋊Dic3—81no—
117C3×#67—41no—
118C3×#67—41no—
119C3×#67—41no—
120C3×#67—41no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C2×C3×Dic3—81no—
130#627—82no—
131#543—91no—
132C2×#99—31no—
133C2×#99—91no—
134C2×#99—91no—
135#342—31no—
136#342—91no—
137#342—91no—
138C24×C3—21no—
139C24×C3—31no—
140C24×C3C22×D311yescharacteristic
141C24×C3C22×D311yescharacteristic
142C23×D3Dic611yescharacteristic, complemented
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C2×#67—21no—
157C2×#67—21no—
158C2×#67—21no—
159C2×#67—21no—
160C2×#67—21no—
161C2×#67—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3—121no—
171C22×Dic3Dic611yescharacteristic, complemented
172C2×Dic6—62no—
173C2×Dic6—62no—
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—32no—
179C3×C22⋊C4—32no—
180C3×C22⋊C4—41no—
181C3×C22⋊C4—41no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186#217—21no—
187#217—21no—
188#217—21no—
189#217—21no—
190#217—32no—
191#217—32no—
192#217—62no—
193#217—61no—
194#217—61no—
195#217—62no—
196#217—61no—
197#217—61no—
198#217—61no—
199#217—61no—
200#217—121no—
201#217—121no—
202#217D1212yes—
203#217#6712yes—
204C4⋊Dic3—62no—
205C4⋊Dic3—62no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—62no—
209Dic3⋊C4—62no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32#12011yescharacteristic
218C22×C32C22⋊Q811yescharacteristic
219C22×C32C22⋊Q811yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C22×C32#12411yescharacteristic
222C22×C32#12411yescharacteristic
223C22×C32#12411yescharacteristic
224C2×C3×D3—41no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C32×C4—81no—
229C3⋊Dic3—42no—
230C3⋊Dic3—81no—
231C3×Dic3—42no—
232C3×Dic3—42no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235C22×D4—31no—
236C22⋊Q8—182no—
237C22⋊Q8—182no—
238C22⋊Q8—182no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C22⋊C4—31no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—91no—
244C2×C22⋊C4D3211yescharacteristic
245#99—62no—
246#99—182no—
247#99—182no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—61no—
258C23×C3—81no—
259C23×C3—81no—
260C23×C3—82no—
261C23×C3—241no—
262C23×C3C2×Dic611yescharacteristic
263C23×C3C2×D1211yescharacteristic
264C23×C3#23511yescharacteristic
265C23×C3#23511yescharacteristic
266C23×C3#23511yescharacteristic
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C23×C3D3×D411yescharacteristic
270C23×C3D3×D411yescharacteristic
271C23×C3#23711yescharacteristic
272C23×C3#23711yescharacteristic
273C23×C3#23711yescharacteristic
274C23×C3D3×Q811yescharacteristic
275C23×C3C2×#6711yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—81no—
280C3×D4—121no—
281C3×D4—121no—
282C3×D4—121no—
283C3×D4—121no—
284C2×C3×C4—42no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—62no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—81no—
293C2×C3×C4—81no—
294C2×C3×C4—82no—
295C2×C3×C4—121no—
296C2×C3×C4—241no—
297C2×C3×C4—241no—
298C2×C3×C4—241no—
299#67—41no—
300#67—41no—
301#67—41no—
302#67—41no—
303C2×Dic3—21no—
304C2×Dic3—21no—
305C2×Dic3—22no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—41no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—81no—
312C2×Dic3—81no—
313C2×Dic3—81no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—241no—
319C2×Dic3—241no—
320C2×Dic3—242no—
321C2×Dic3—242no—
322C2×Dic3—241no—
323C2×Dic3—241no—
324Dic6—242no—
325Dic6—242no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32#39311yescharacteristic
334C3×D3—81no—
335C24—31no—
336C24C2×D3211yescharacteristic
337C2×Q8—182no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—61no—
344C22×C4—21no—
345C22×C4—31no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—181no—
350C22×C4—181no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C4⋊C4—182no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—32no—
357C22⋊C4—32no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—92no—
363C22⋊C4—181no—
364C22⋊C4—181no—
365C22⋊C4—181no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—81no—
391C22×C3—81no—
392C22×C3—81no—
393C22×C3—81no—
394C22×C3—121no—
395C22×C3—241no—
396C22×C3—241no—
397C22×C3—241no—
398C22×C3#87511yescharacteristic
399C22×C3#87811yescharacteristic
400C22×C3#87811yescharacteristic
401C22×C3#88211yescharacteristic
402C22×C3#88511yescharacteristic
403C22×C3#88511yescharacteristic
404C22×C3#88511yescharacteristic
405C22×C3#88511yescharacteristic
406C22×C3#89611yescharacteristic
407C22×C3#89611yescharacteristic
408C22×C3#89711yescharacteristic
409C22×C3#92411yescharacteristic
410C22×C3#93611yescharacteristic
411C22×C3#93711yescharacteristic
412C2×D3—41no—
413C2×D3—81no—
414C2×D3—81no—
415C2×D3—81no—
416C3×C4—82no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4—121no—
422C3×C4—241no—
423Dic3—42no—
424Dic3—42no—
425Dic3—41no—
426Dic3—81no—
427Dic3—122no—
428Dic3—122no—
429Dic3—242no—
430Dic3—241no—
431Dic3—241no—
432Dic3—242no—
433C32#203211yescharacteristic, complemented, Sylow
434C23—61no—
435C23—61no—
436C23—61no—
437C23—81no—
438C23—241no—
439C23D3×Dic611yescharacteristic
440C23#379811yescharacteristic
441C23D3×D1211yescharacteristic
442C23#380211yescharacteristic
443C23#380411yescharacteristic
444C23#380511yescharacteristic
445C23D3×#6711yescharacteristic
446Q8—722no—
447D4—121no—
448D4—121no—
449D4—121no—
450D4—121no—
451C2×C4—41no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—81no—
458C2×C4—121no—
459C2×C4—182no—
460C2×C4—241no—
461C2×C4—241no—
462C2×C4—241no—
463C2×C4—361no—
464C2×C4—721no—
465C2×C4—721no—
466C2×C3—22no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3—241no—
489C2×C3#467311yescharacteristic
490C2×C3#494711yescharacteristic
491D3—81no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—121no—
500C22—241no—
501C22—241no—
502C22—241no—
503C22#6385111yescharacteristic
504C22#6385211yescharacteristic
505C22#6389311yescharacteristic
506C22#6389911yescharacteristic
507C22#6391511yescharacteristic
508C22#6392211yescharacteristic
509C22#6395911yescharacteristic
510C4—81no—
511C4—122no—
512C4—122no—
513C4—121no—
514C4—241no—
515C4—362no—
516C4—721no—
517C3—21no—
518C3#6896711yescharacteristic, complemented
519C3#7002511yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—21no—
527C2—241no—
528C2#1059129311yescharacteristic
subgroupG/H
centerC2#10591293
commutator, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#393
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2032
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595521C2semidirect
5. #10589392C2semidirect
6. C3×#4527C2semidirect
7. #10589187C2semidirect
34. #4527D3semidirect
39. C23×C3×D3Q8semidirect
52. C22×C3×Dic3Q8semidirect
142. C23×D3Dic6semidirect
171. C22×Dic3Dic6semidirect
433. C32#2032semidirect
518. C3#68967semidirect
519. C3#70025semidirect

Maximal subgroups

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

subgroupindex
#105955212
C2×C3×#8062
C2×#635802
#105893922
C3×#45272
#105891872
#700253
#689673