Finite Group Databasebeta

← #11793134

Subgroups — #11793134

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595954C211yesmaximal, characteristic, complemented
2C2×C3×#806C211yesmaximal, characteristic
3C2×#63580C211yesmaximal, characteristic
4C2×#63580C211yesmaximal, characteristic
5C3×#4527C211yesmaximal, characteristic, complemented
6#10589186C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#70025—31nomaximal
9#68967—31nomaximal
10C22×C3×#67C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14#64133—22no—
15#64087—22no—
16#64087—22no—
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C3×#806—22no—
21#63580—22no—
22#63580—22no—
23#5483—31no—
24#5483—31no—
25#5483—61no—
26C2×C3×#99—31no—
27C2×#834—31no—
28C2×#834—31no—
29C2×#806—31no—
30C2×#806—31no—
31C2×#806D311yescharacteristic
32C3×#342—31no—
33#4527—31no—
34#4527—31no—
35#4527D311yescharacteristic, complemented
36#4526—31no—
37#4526—31no—
38C24×C32C2311yescharacteristic
39C23×C3×D3Q811yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C2×#634—22no—
44C2×C3×#67—21no—
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3Q811yescharacteristic, complemented
54C32×C22⋊C4—21no—
55C32×C22⋊C4D412yes—
56#3757—21no—
57#3757—21no—
58#3757D412yes—
59#3757D412yes—
60C4⋊(C3⋊Dic3)—22no—
61#3750—24no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×#217—21no—
68#2032—91noSylow
69C22×C3×D4—31no—
70C22×#67C2×D311yescharacteristic
71C2×C3×C22⋊C4—21no—
72C2×C3×C22⋊C4—31no—
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4C2×D311yescharacteristic
76C2×C3×C22⋊C4C2×D311yescharacteristic
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
86#924—62no—
87#924—62no—
88#924—64no—
89#878—62no—
90#878—62no—
91#878—64no—
92#878—64no—
93#878—62no—
94#878—62no—
95C3×#99—62no—
96#834—62no—
97#834—62no—
98#806—22no—
99#806—62no—
100#806—62no—
101C23×C32—81no—
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D411yescharacteristic
105C23×C32C2×Q811yescharacteristic
106C23×C32#4111yescharacteristic
107C23×C32#4111yescharacteristic
108C23×C32#4111yescharacteristic
109C22×C3×D3—21no—
110C22×C3×D3—21no—
111C22×C3×D3—21no—
112C22×C3×D3—81no—
113C2×C32×C4—22no—
114C2×C32×C4—81no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—81no—
118C2×C3⋊Dic3—81no—
119#634—82no—
120C3×#67—41no—
121C3×#67—41no—
122C3×#67—41no—
123C3×#67—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—81no—
131C2×C3×Dic3—81no—
132C2×C3×Dic3—81no—
133#543—91no—
134C2×#99—31no—
135C2×#99—91no—
136C2×#99—91no—
137#342—31no—
138#342—91no—
139#342—91no—
140C24×C3—21no—
141C24×C3—31no—
142C24×C3C22×D311yescharacteristic
143C24×C3C22×D311yescharacteristic
144C23×D3Dic611yescharacteristic, complemented
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C2×#67—21no—
159C2×#67—21no—
160C2×#67—21no—
161C2×#67—21no—
162C2×#67—21no—
163C2×#67—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—62no—
168C22×Dic3—62no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3Dic611yescharacteristic, complemented
174C2×Dic6—64no—
175C2×Dic6—62no—
176C2×Dic6—62no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4D1212yes—
188C3×C22⋊C4#6712yes—
189#217—21no—
190#217—21no—
191#217—21no—
192#217—21no—
193#217—21no—
194#217—21no—
195#217—32no—
196#217—32no—
197#217—32no—
198#217—32no—
199#217—62no—
200#217—62no—
201#217—62no—
202#217—62no—
203#217—61no—
204#217—61no—
205#217—61no—
206#217—61no—
207C4⋊Dic3—64no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210Dic3⋊C4—68no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32#12011yescharacteristic
221C22×C32C22⋊Q811yescharacteristic
222C22×C32C22⋊Q811yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32#12411yescharacteristic
225C22×C32#12411yescharacteristic
226C22×C32#12411yescharacteristic
227C2×C3×D3—41no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C32×C4—42no—
232C3⋊Dic3—42no—
233C3⋊Dic3—42no—
234C3×Dic3—41no—
235C3×Dic3—81no—
236C3×Dic3—81no—
237C3×Dic3—81no—
238C22×D4—31no—
239C22⋊Q8—182no—
240C22⋊Q8—182no—
241C22⋊Q8—182no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—91no—
246C2×C22⋊C4—91no—
247C2×C22⋊C4D3211yescharacteristic
248#99—62no—
249#99—182no—
250#99—182no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—61no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—81no—
262C23×C3—81no—
263C23×C3—82no—
264C23×C3—241no—
265C23×C3C2×Dic611yescharacteristic
266C23×C3C2×D1211yescharacteristic
267C23×C3#23511yescharacteristic
268C23×C3#23511yescharacteristic
269C23×C3#23511yescharacteristic
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C23×C3#23711yescharacteristic
275C23×C3#23711yescharacteristic
276C23×C3#23711yescharacteristic
277C23×C3D3×Q811yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—21no—
282C22×D3—81no—
283C3×D4—121no—
284C3×D4—121no—
285C3×D4—121no—
286C3×D4—121no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—81no—
294C2×C3×C4—81no—
295C2×C3×C4—82no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—241no—
300C2×C3×C4—241no—
301C2×C3×C4—241no—
302#67—41no—
303#67—41no—
304#67—41no—
305#67—41no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—64no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—81no—
319C2×Dic3—81no—
320C2×Dic3—81no—
321C2×Dic3—241no—
322C2×Dic3—241no—
323C2×Dic3—241no—
324C2×Dic3—241no—
325C2×Dic3—242no—
326C2×Dic3—242no—
327Dic6—244no—
328Dic6—242no—
329Dic6—242no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32#39311yescharacteristic
338C3×D3—81no—
339C24—31no—
340C24C2×D3211yescharacteristic
341C2×Q8—182no—
342C2×D4—61no—
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C22×C4—21no—
349C22×C4—31no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4—181no—
355C4⋊C4—184no—
356C4⋊C4—182no—
357C22⋊C4—21no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—61no—
363C22⋊C4—61no—
364C22⋊C4—92no—
365C22⋊C4—92no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4#62612yes—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
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—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—81no—
397C22×C3—121no—
398C22×C3—241no—
399C22×C3—241no—
400C22×C3—241no—
401C22×C3#87511yescharacteristic
402C22×C3#87811yescharacteristic
403C22×C3#87811yescharacteristic
404C22×C3#88211yescharacteristic
405C22×C3#88511yescharacteristic
406C22×C3#88511yescharacteristic
407C22×C3#88511yescharacteristic
408C22×C3#88511yescharacteristic
409C22×C3#89611yescharacteristic
410C22×C3#89611yescharacteristic
411C22×C3#89711yescharacteristic
412C22×C3#92411yescharacteristic
413C22×C3#93611yescharacteristic
414C22×C3#93711yescharacteristic
415C2×D3—41no—
416C2×D3—81no—
417C2×D3—81no—
418C2×D3—81no—
419C3×C4—44no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—121no—
423C3×C4—241no—
424C3×C4—241no—
425C3×C4—241no—
426Dic3—41no—
427Dic3—81no—
428Dic3—81no—
429Dic3—81no—
430Dic3—124no—
431Dic3—124no—
432Dic3—122no—
433Dic3—122no—
434Dic3—122no—
435Dic3—122no—
436C32#203211yescharacteristic, complemented, Sylow
437C23—61no—
438C23—61no—
439C23—61no—
440C23—81no—
441C23—241no—
442C23D3×Dic611yescharacteristic
443C23#379511yescharacteristic
444C23#379511yescharacteristic
445C23#379511yescharacteristic
446C23C2×#62611yescharacteristic
447C23#381111yescharacteristic
448C23#381111yescharacteristic
449Q8—722no—
450D4—121no—
451D4—121no—
452D4—121no—
453D4—121no—
454C2×C4—22no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—81no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—241no—
465C2×C4—241no—
466C2×C4—241no—
467C2×C4—721no—
468C2×C4—721no—
469C2×C3—22no—
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—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—41no—
491C2×C3—241no—
492C2×C3#467311yescharacteristic
493C2×C3#494711yescharacteristic
494D3—81no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—121no—
503C22—241no—
504C22—241no—
505C22—241no—
506C22#6385711yescharacteristic
507C22#6386011yescharacteristic
508C22#6389611yescharacteristic
509C22#6389611yescharacteristic
510C22#6391311yescharacteristic
511C22#6391311yescharacteristic
512C22#6398111yescharacteristic
513C4—42no—
514C4—121no—
515C4—241no—
516C4—241no—
517C4—241no—
518C4—362no—
519C4—362no—
520C3—21no—
521C3#6896711yescharacteristic, complemented
522C3#7002511yescharacteristic, complemented
523C2—21no—
524C2—21no—
525C2—21no—
526C2—21no—
527C2—21no—
528C2—21no—
529C2—21no—
530C2—241no—
531C2#1059132211yescharacteristic
subgroupG/H
centerC2#10591322
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. #10595954C2semidirect
5. C3×#4527C2semidirect
6. #10589186C2semidirect
7. #10589186C2semidirect
35. #4527D3semidirect
39. C23×C3×D3Q8semidirect
53. C22×C3×Dic3Q8semidirect
144. C23×D3Dic6semidirect
173. C22×Dic3Dic6semidirect
436. C32#2032semidirect
521. C3#68967semidirect
522. C3#70025semidirect

Maximal subgroups

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

subgroupindex
#105959542
C2×C3×#8062
C2×#635802
C3×#45272
#105891862
#700253
#689673