Finite Group Databasebeta

← #11791193

Subgroups — #11791193

Order 1152.

679 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#950C211yesmaximal, characteristic
2#10592933C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#72084—31nomaximal
9#70373—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#950—22no—
15C3×#950—22no—
16C2×C3×#216C411yescharacteristic, complemented
17C2×C3×#215C411yescharacteristic, complemented
18C2×C3×#214C411yescharacteristic, complemented
19C2×C3×#213C411yescharacteristic, complemented
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23#63657—22no—
24C3×#837—22no—
25#63577—22no—
26#63569—22no—
27(C2×D3)⋊(C3⋊C8)—22no—
28Dic3×C3⋊C8—22no—
29C2×C3×#135—31no—
30C2×#950D311yescharacteristic
31C2×C3×#104—31no—
32C2×#837—31no—
33C2×#837D311yescharacteristic, complemented
34#5234—31no—
35#5234—31no—
36#5234—31no—
37#5234—61no—
38#5129—31no—
39C2×#822—31no—
40C2×#819—31no—
41C2×C8×Dic3—31no—
42C2×#805—31no—
43C2×C4×C3⋊C8—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6C2×C411yescharacteristic
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×#216—22no—
69C3×#215—22no—
70C3×#214—22no—
71C3×#213—22no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3D412yes—
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8C2×C411yescharacteristic
78C2×C3×C3⋊C8C2×C411yescharacteristic
79C2×C3×C3⋊C8D412yes—
80C2×C3×C3⋊C8D412yes—
81#1974—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41—31no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C2×D311yescharacteristic
86C2×#235C2×D311yescharacteristic
87C3×#135—62no—
88C3×#135—62no—
89C2×C3×Q16—31no—
90C2×C3×SD16—31no—
91C2×C3×SD16—31no—
92C2×C3×D8—31no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C2×C3×C42—31no—
96#950—22no—
97#950—22no—
98C2×#216Dic311yescharacteristic, complemented
99C2×#215Dic311yescharacteristic, complemented
100C2×#214Dic311yescharacteristic, complemented
101C2×#213Dic311yescharacteristic, complemented
102C2×C4×Dic3C2×D311yescharacteristic
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—61no—
106C2×#208C2×D311yescharacteristic
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C3×#104—62no—
112#837—22no—
113#837—62no—
114#830—62no—
115#830—62no—
116#830—62no—
117#830—64no—
118#822—62no—
119(C2×D3)⋊C8—62no—
120#819—62no—
121C8×Dic3—62no—
122#805—62no—
123C4×C3⋊C8—62no—
124C23×C32—21no—
125C23×C32#4111yescharacteristic
126C22×C3×D3—21no—
127C32×Q8—21no—
128C32×Q8—21no—
129C32×D4—21no—
130C32×D4—21no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—21no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C3×#67—41no—
143C3×#67—41no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—21no—
147C3×D12—21no—
148C3×D12—21no—
149C3×C4×D3—41no—
150C3×C4×D3—41no—
151C3×Dic6—21no—
152C3×Dic6—21no—
153C3⋊(C3⋊C8)—22no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—41no—
156C3×C3⋊C8C22⋊C412yes—
157C3×C3⋊C8C22⋊C412yes—
158C2×#135—31no—
159C2×#108—91no—
160C2×#104—31no—
161C2×#104—91no—
162#408—91no—
163#408—91no—
164C2×C4×C8—91no—
165C3×#41—21no—
166C3×#41—21no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—41no—
174C3×#41—41no—
175C3×#41—41no—
176C3×#41—41no—
177C3×#41—61no—
178C3×#41—61no—
179C3×#41—61no—
180C3×#41—61no—
181C2×C3×Q8—21no—
182C2×C3×Q8—31no—
183C2×C3×Q8C4×D311yescharacteristic
184C2×C3×Q8C2×Dic311yescharacteristic
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C2×C3×D4C4×D311yescharacteristic
192C2×C3×D4C2×Dic311yescharacteristic
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—21no—
202C22×Dic3—21no—
203#235—21no—
204#235—21no—
205#235—21no—
206#235—21no—
207C2×D12C2×Dic311yescharacteristic
208C2×C4×D3—21no—
209C2×Dic6C2×Dic311yescharacteristic
210C3×Q16—62no—
211C3×SD16—62no—
212C3×SD16—62no—
213C3×D8—62no—
214C3×M16—61no—
215C3×M16—61no—
216C2×C3×C8—31no—
217C2×C3×C8—31no—
218C2×C3×C8—32no—
219C2×C3×C8—32no—
220C2×C3×C8—61no—
221C3×C42—32no—
222C3×C42—61no—
223#216—22no—
224#215—22no—
225#214—22no—
226#213—22no—
227C4×Dic3—21no—
228C4×Dic3#6712yes—
229#208—21no—
230#208—21no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—61no—
235#208—121no—
236#208—121no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—121no—
249C2×C3⋊C8—121no—
250C2×C3⋊C8C2×Dic311yescharacteristic
251C2×C3⋊C8C2×Dic311yescharacteristic
252C2×C3⋊C8#6712yes—
253C2×C3⋊C8#6712yes—
254C22×C32—22no—
255C22×C32—41no—
256C22×C32—42no—
257C22×C32C4×D411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12411yescharacteristic
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C32×C4—41no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12711yescharacteristic
267C3×Dic3—24no—
268C3×Dic3—41no—
269C2×#41—31no—
270C2×#41D3211yescharacteristic
271#135—62no—
272#135—62no—
273C2×Q16—31no—
274C2×SD16—31no—
275C2×SD16—31no—
276C2×D8—31no—
277C2×M16—31no—
278C2×M16—91no—
279C22×C8—31no—
280C22×C8—91no—
281C2×C42—31no—
282#108—182no—
283#104—62no—
284#104—182no—
285C22⋊C8—182no—
286C22⋊C8—182no—
287C4×C8—182no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—61no—
293C23×C3#23711yescharacteristic
294C23×C3#23711yescharacteristic
295C22×D3—21no—
296C3×Q8—21no—
297C3×Q8—21no—
298C3×Q8—21no—
299C3×Q8—21no—
300C3×Q8—41no—
301C3×Q8—41no—
302C3×Q8—61no—
303C3×Q8—61no—
304C3×D4—21no—
305C3×D4—21no—
306C3×D4—21no—
307C3×D4—21no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—42no—
311C3×D4—42no—
312C3×D4—41no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—61no—
317C3×D4—61no—
318C3×D4—121no—
319C3×D4—121no—
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—21no—
328C2×C3×C4—21no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—64no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4C22×Dic311yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352#67—41no—
353#67—41no—
354C2×Dic3—24no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357D12—21no—
358D12—21no—
359C4×D3—41no—
360C4×D3—41no—
361Dic6—21no—
362Dic6—21no—
363C3×C8—32no—
364C3×C8—32no—
365C3×C8—121no—
366C3⋊C8—41no—
367C3⋊C8—62no—
368C3⋊C8—62no—
369C3⋊C8—122no—
370C3⋊C8—122no—
371C3⋊C8—121no—
372C3⋊C8—121no—
373C3⋊C8#21712yes—
374C3⋊C8#21712yes—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—81no—
378C2×C32#39011yescharacteristic
379C2×C32#44312yes—
380C3×D3—81no—
381#41—21no—
382#41—21no—
383#41—21no—
384#41—21no—
385#41—61no—
386#41—61no—
387#41—61no—
388#41—61no—
389C2×Q8—31no—
390C2×Q8D3×Dic311yescharacteristic
391C2×D4—21no—
392C2×D4—31no—
393C2×D4—61no—
394C2×D4D3×Dic311yescharacteristic
395C22×C4—21no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4C2×D3211yescharacteristic
399Q16—62no—
400SD16—62no—
401SD16—62no—
402D8—62no—
403M16—61no—
404M16—61no—
405M16—181no—
406M16—181no—
407C2×C8—31no—
408C2×C8—31no—
409C2×C8—32no—
410C2×C8—32no—
411C2×C8—61no—
412C2×C8—92no—
413C2×C8—181no—
414C2×C8—181no—
415C2×C8—181no—
416C42—32no—
417C42—61no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—121no—
431C22×C3—122no—
432C22×C3#67⋊C411yescharacteristic
433C22×C3#88511yescharacteristic
434C22×C3D4×Dic311yescharacteristic
435C22×C3#93611yescharacteristic
436C22×C3#93811yescharacteristic
437C22×C3#93911yescharacteristic
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—64no—
448C3×C4—121no—
449C3×C4D3×C22⋊C411yescharacteristic
450C3×C4#88411yescharacteristic
451C3×C4C4×#6711yescharacteristic
452C3×C4D4×Dic311yescharacteristic
453C3×C4#93811yescharacteristic
454C3×C4#94011yescharacteristic
455C3×C4#94011yescharacteristic
456C3×C4C2×#21711yescharacteristic
457Dic3—24no—
458Dic3—41no—
459C32#197411yescharacteristic, complemented, Sylow
460C23—21no—
461C23—61no—
462C23#380511yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—61no—
466Q8—61no—
467D4—21no—
468D4—21no—
469D4—41no—
470D4—41no—
471D4—61no—
472D4—61no—
473D4—121no—
474D4—121no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—64no—
479C2×C4—62no—
480C2×C4—61no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4C2×D3×Dic311yescharacteristic
484C2×C4#380411yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4#381111yescharacteristic
489C8—32no—
490C8—32no—
491C8—121no—
492C8—182no—
493C8—361no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—82no—
503C2×C3—81no—
504C2×C3—81no—
505C2×C3—241no—
506C2×C3#482412yes—
507C2×C3#495711yescharacteristic
508C2×C3#519612yes—
509C2×C3#522111yescharacteristic
510D3—81no—
511C22—22no—
512C22—42no—
513C22—41no—
514C22—122no—
515C22—121no—
516C22#6395911yescharacteristic
517C22#6397011yescharacteristic
518C22#67⋊Dic311yescharacteristic
519C4—41no—
520C4—64no—
521C4—121no—
522C4#6395811yescharacteristic
523C4D3×#21711yescharacteristic
524C4Dic3×#6711yescharacteristic
525C4#6397911yescharacteristic
526C3—21no—
527C3#7037311yescharacteristic, complemented
528C3#7208411yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—81no—
532C2—241no—
533C2#1059167512yes—
534C2#1059170711yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1974
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592933C2semidirect
3. C2×C3×#837C2semidirect
4. C2×#63577C2semidirect
5. C2×#63569C2semidirect
6. #10591071C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
16. C2×C3×#216C4semidirect
17. C2×C3×#215C4semidirect
18. C2×C3×#214C4semidirect
19. C2×C3×#213C4semidirect
33. C2×#837D3semidirect
98. C2×#216Dic3semidirect
99. C2×#215Dic3semidirect
100. C2×#214Dic3semidirect
101. C2×#213Dic3semidirect
459. C32#1974semidirect
527. C3#70373semidirect
528. C3#72084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9502
#105929332
C2×C3×#8372
C2×#635772
C2×#635692
#105910712
C2×Dic3×C3⋊C82
#720843
#703733