Finite Group Databasebeta

← #11788679

Subgroups — #11788679

Order 1152.

705 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
1C2×C3×#951C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic
3#10592931C211yesmaximal, characteristic
4C2×#63566C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72103—31nomaximal
9#72019—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—22no—
15C3×#951C414yescomplemented
16C3×#948—22no—
17C3×#948—22no—
18C2×C3×#216—21no—
19C2×C3×#214—21no—
20C2×C3×#208—21no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25#63662—21no—
26#63659—21no—
27#63566—21no—
28#63566—21no—
29#63560—22no—
30C2×C3×#137—31no—
31C2×C3×#131—31no—
32C2×#951D311yescharacteristic
33C2×#948D311yescharacteristic
34#5232—31no—
35#5232—31no—
36#5232—61no—
37C2×#836—31no—
38C2×#835—31no—
39C2×#824—31no—
40C2×#816—31no—
41#4558—31no—
42#4554—31no—
43#4554—31no—
44#4552—31no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64#3748—21no—
65#3748—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#216—24no—
68C3×#214—24no—
69C3×#208—24no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C3×#208D412yes—
74C2×C3×C3⋊C8—24no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D411yescharacteristic
80C2×C3×C3⋊C8D411yescharacteristic
81#1908—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C2×D311yescharacteristic
85C22×C3×Q8—31no—
86C22×Dic6C2×D311yescharacteristic
87C3×#137—34no—
88C3×#137—62no—
89C2×C3×Q16—61no—
90C2×C3×SD16—61no—
91C3×#131—62no—
92C3×#131—62no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C2×C3×M16—61no—
96C22×C3×C8—31no—
97C22×C3×C8—61no—
98#951—22no—
99#951Dic314yescomplemented
100#948—22no—
101#948—22no—
102C2×#216—21no—
103C2×#214—21no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×#208—21no—
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—61no—
111C2×#208C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8—21no—
114C22×C3⋊C8C2×D311yescharacteristic
115#836—62no—
116#835—62no—
117#835—61no—
118#835—61no—
119#835—61no—
120#835—61no—
121#832—62no—
122#832—61no—
123#832—61no—
124#824—62no—
125#816—61no—
126#816—61no—
127C23×C32—21no—
128C23×C32#4111yescharacteristic
129C32×Q8—21no—
130C32×Q8C22⋊C412yes—
131C32×D4—22no—
132C32×D4—22no—
133C32×D4—21no—
134C32×D4C22⋊C412yes—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—81no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3⋊(C3⋊C8)—41no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—21no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—21no—
158C2×#137—31no—
159C2×#131—31no—
160#417—91no—
161C2×#103—91no—
162C2×#101—91no—
163#343—91no—
164#341—91no—
165C3×#41—21no—
166C3×#41—21no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—41no—
172C3×#41—41no—
173C3×#41C4×D312yes—
174C3×#41C2×Dic312yes—
175C3×#41#6712yes—
176C3×#41#6712yes—
177C2×C3×Q8—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—61no—
183C2×C3×Q8—61no—
184C2×C3×Q8D1211yescharacteristic
185C2×C3×Q8#6711yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—41no—
190C2×C3×D4D1211yescharacteristic
191C2×C3×D4#6711yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×Dic3—21no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—121no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6C2×Dic312yes—
209C3×Q16—64no—
210C3×SD16—64no—
211C3×M16—32no—
212C3×M16—32no—
213C3×M16—64no—
214C3×M16—61no—
215C3×M16—61no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8—64no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223#216—24no—
224#214—24no—
225C4⋊Dic3—62no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—121no—
231#208—24no—
232#208—21no—
233#208—21no—
234#208—61no—
235#208—61no—
236#208—61no—
237#208—61no—
238#208—121no—
239#208—121no—
240#208C2×Dic312yes—
241#208#6712yes—
242C2×C3⋊C8—24no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8#6711yescharacteristic
251C2×C3⋊C8#6711yescharacteristic
252C22×C32—21no—
253C22×C32—21no—
254C22×C32—22no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32C4×D411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12311yescharacteristic
260C32×C4—22no—
261C32×C4C2×C22⋊C411yescharacteristic
262C32×C4C4×D411yescharacteristic
263C32×C4#12011yescharacteristic
264C32×C4#12111yescharacteristic
265C3⋊Dic3—81no—
266C3×Dic3—42no—
267C2×#41D3211yescharacteristic
268C22×Q8—31no—
269#137—34no—
270#137—62no—
271C2×Q16—61no—
272C2×SD16—61no—
273#131—62no—
274#131—62no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—61no—
278C2×M16—91no—
279C22×C8—31no—
280C22×C8—61no—
281C2×C4⋊C4—91no—
282#103—181no—
283#103—181no—
284#103—181no—
285#102—181no—
286#101—182no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—41no—
291C23×C3#23511yescharacteristic
292C23×C3#23711yescharacteristic
293C3×Q8—21no—
294C3×Q8—21no—
295C3×Q8—22no—
296C3×Q8—41no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—121no—
300C3×Q8—121no—
301C3×Q8(C2×D3)⋊C412yes—
302C3×Q8#21712yes—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—21no—
308C3×D4—21no—
309C3×D4—22no—
310C3×D4—41no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4(C2×D3)⋊C412yes—
314C3×D4#21712yes—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—62no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4C22×Dic311yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—242no—
352C2×Dic3—241no—
353C2×Dic3—241no—
354Dic6—22no—
355Dic6—22no—
356Dic6—41no—
357Dic6—41no—
358C3×C8—62no—
359C3×C8—61no—
360C3×C8—61no—
361C3×C8—62no—
362C3⋊C8—22no—
363C3⋊C8—21no—
364C3⋊C8—22no—
365C3⋊C8—21no—
366C3⋊C8—122no—
367C3⋊C8—121no—
368C3⋊C8—121no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—42no—
372C2×C32#38611yescharacteristic
373C2×C32#47111yescharacteristic
374C2×C32#47311yescharacteristic
375#41—21no—
376#41—21no—
377#41D3×Dic312yes—
378#41#62512yes—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8#62611yescharacteristic
386C2×D4—21no—
387C2×D4#62611yescharacteristic
388C22×C4—21no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—64no—
393SD16—64no—
394M16—32no—
395M16—32no—
396M16—64no—
397M16—61no—
398M16—61no—
399M16—181no—
400M16—181no—
401C2×C8—31no—
402C2×C8—31no—
403C2×C8—64no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C2×C8—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—42no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3C4×#6711yescharacteristic
430C22×C3#92911yescharacteristic
431C22×C3#93011yescharacteristic
432C22×C3D4×Dic311yescharacteristic
433C22×C3#93511yescharacteristic
434C22×C3#93911yescharacteristic
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—42no—
442C3×C4—122no—
443C3×C4C2×(C2×D3)⋊C411yescharacteristic
444C3×C4C4×#6711yescharacteristic
445C3×C4#93011yescharacteristic
446C3×C4D4×Dic311yescharacteristic
447C3×C4#93711yescharacteristic
448C3×C4#93911yescharacteristic
449C3×C4C2×#21711yescharacteristic
450C3×C4#95311yescharacteristic
451Dic3—42no—
452Dic3—242no—
453Dic3—241no—
454Dic3—241no—
455C32#190811yescharacteristic, complemented, Sylow
456C23—21no—
457C23#380411yescharacteristic
458Q8—21no—
459Q8—62no—
460Q8—62no—
461Q8—121no—
462Q8—121no—
463Q8(C2×D3)⋊Dic312yes—
464D4—22no—
465D4—22no—
466D4—21no—
467D4(C2×D3)⋊Dic312yes—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—62no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—361no—
475C2×C4—721no—
476C2×C4C2×D3×Dic311yescharacteristic
477C2×C4#380411yescharacteristic
478C2×C4C2×#62511yescharacteristic
479C2×C4C2×#62611yescharacteristic
480C2×C4D3×#6711yescharacteristic
481C2×C4D3×#6711yescharacteristic
482C8—62no—
483C8—61no—
484C8—61no—
485C8—62no—
486C8—361no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—42no—
497C2×C3—42no—
498C2×C3—82no—
499C2×C3#514111yescharacteristic
500C2×C3#514311yescharacteristic
501C2×C3#520311yescharacteristic
502C2×C3#520411yescharacteristic
503C2×C3#521311yescharacteristic
504C2×C3#522011yescharacteristic
505C22—21no—
506C22—21no—
507C22—22no—
508C22—41no—
509C22—41no—
510C22#6396111yescharacteristic
511C22Dic3×#6711yescharacteristic
512C22#6397811yescharacteristic
513C4—22no—
514C4—122no—
515C4—721no—
516C4C2×(C2×D3)⋊Dic311yescharacteristic
517C4Dic3×#6711yescharacteristic
518C4#6397611yescharacteristic
519C4#6397811yescharacteristic
520C3—21no—
521C3#7201911yescharacteristic, complemented
522C3#7210311yescharacteristic, complemented
523C2—21no—
524C2—21no—
525C2—42no—
526C2#1059168011yescharacteristic
527C2#1059168211yescharacteristic
528C2#1059171011yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1908
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63566C2semidirect
5. C2×#63560C2semidirect
6. #10589168C2semidirect
7. #10589166C2semidirect
15. C3×#951C4semidirect
99. #951Dic3semidirect
455. C32#1908semidirect
521. C3#72019semidirect
522. C3#72103semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9512
C2×C3×#9482
#105929312
C2×#635662
C2×#635602
#105891682
#105891662
#721033
#720193