Finite Group Databasebeta

← #11859126

Subgroups — #11859126

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic
4C3×#5122C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic
7#10591055C211yesmaximal, characteristic, complemented
8#10590697C212yesmaximal, complemented
9#10590696C212yesmaximal, complemented
10#10590660C212yesmaximal, complemented
11#10590655C212yesmaximal, complemented
12#78650—31nomaximal
13#78552—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#67⋊Dic3C412yes—
22#67⋊Dic3C412yes—
23#63898C411yescharacteristic
24#63898C411yescharacteristic
25C4×D3×Dic3C2212yes—
26#63855C2212yes—
27#63843C411yescharacteristic
28#63843C411yescharacteristic
29#63641C2212yes—
30#63641C2212yes—
31C3×(C2×D3)⋊C8C2212yes—
32C3×(C2×D3)⋊C8C2212yes—
33C3×#815C2212yes—
34C3×C8×Dic3C2212yes—
35#63572C2211yescharacteristic
36#63572C2211yescharacteristic
37#63572C2211yescharacteristic
38#63572C2211yescharacteristic
39(C2×D3)⋊(C3⋊C8)C2212yes—
40(C2×D3)⋊(C3⋊C8)C2212yes—
41#63554C2212yes—
42Dic3×C3⋊C8C2212yes—
43Dic3×#41—31no—
44#5522—31no—
45C3×#408—31no—
46C3×#405—31no—
47#5234—31no—
48#5129D311yescharacteristic
49#5122D311yescharacteristic, complemented
50#5118—31no—
51#5118—31no—
52#5118—61no—
53#5110—31no—
54#5101—31no—
55C2×Dic3⋊C8—31no—
56C2×Dic3⋊C8—31no—
57#4997—31no—
58#4720—32no—
59#4720—32no—
60#4719—32no—
61#4718—32no—
62#4709—32no—
63#4705—32no—
64#4690—32no—
65#4685—32no—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2×C411yescharacteristic
68C22×C3⋊Dic3C2×C411yescharacteristic
69C2×C3×#67C2×C412yes—
70C3×#235—22no—
71C3×#235—22no—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6C2×C411yescharacteristic
75C2×D3×Dic3C2×C412yes—
76C2×D3×Dic3C2×C412yes—
77C32×M16—22no—
78C2×C32×C8C2312yes—
79C4×C3⋊Dic3C2×C411yescharacteristic
80C4×C3⋊Dic3C2×C411yescharacteristic
81C4×C3⋊Dic3C2311yescharacteristic
82C4×C3⋊Dic3C2311yescharacteristic
83#3748—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217C2×C412yes—
86C3×C4⋊Dic3C2×C411yescharacteristic
87C3×C4⋊Dic3C2×C411yescharacteristic
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3C2×C412yes—
96Dic3⋊Dic3C2×C412yes—
97(C2×D3)⋊Dic3C2×C412yes—
98(C2×D3)⋊Dic3C2×C412yes—
99Dic32C2×C412yes—
100Dic32C2×C412yes—
101#2925—91noSylow
102C2×C3×#41—31no—
103C2×#235C2×D311yescharacteristic
104C2×C3×M16—21no—
105C2×C3×M16C2×D311yescharacteristic
106C2×C3×M16C2×D311yescharacteristic
107C22×C3×C8—31no—
108C22×C3×C8—31no—
109C3×#117—31no—
110Q8×Dic3—31no—
111Q8×Dic3—31no—
112D4×Dic3—32no—
113D4×Dic3—32no—
114D4×Dic3—31no—
115D4×Dic3—31no—
116#926—32no—
117#926C2×D311yescharacteristic
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—61no—
122C2×#208—31no—
123C2×#208—31no—
124C2×#208—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126C22×C3⋊C8C2×D311yescharacteristic
127#893—31no—
128#893—31no—
129#887—31no—
130#887—31no—
131#67⋊C4—32no—
132#67⋊C4—32no—
133#872—32no—
134C42×D3—32no—
135C3×C22⋊C8—32no—
136C3×C22⋊C8—32no—
137C3×#97—32no—
138C3×C4×C8—32no—
139#830—32no—
140#830—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8C2×D312yes—
144(C2×D3)⋊C8C2×D312yes—
145#815—32no—
146#815C2×D312yes—
147Dic3⋊C8—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—32no—
151Dic3⋊C8—31no—
152Dic3⋊C8—31no—
153Dic3⋊C8—31no—
154Dic3⋊C8—31no—
155Dic3⋊C8—31no—
156Dic3⋊C8—31no—
157Dic3⋊C8—31no—
158Dic3⋊C8—31no—
159Dic3⋊C8—62no—
160Dic3⋊C8—62no—
161C8×Dic3—32no—
162C8×Dic3C2×D312yes—
163#803—32no—
164C4×C3⋊C8—32no—
165C23×C32C22×C411yescharacteristic
166C22×C3×D3C22×C412yes—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4#4112yes—
169C2×C32×C4#4112yes—
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—41no—
173C2×C3⋊Dic3C22×C411yescharacteristic
174C2×C3⋊Dic3C22×C411yescharacteristic
175C2×C3⋊Dic3C22×C411yescharacteristic
176C2×C3⋊Dic3C22×C411yescharacteristic
177C3×#67—24no—
178C2×C3×Dic3C22×C412yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C3×D12—22no—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6—22no—
185D3×Dic3—24no—
186D3×Dic3—42no—
187C32×C8—22no—
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193C4×#41—91no—
194#433—92no—
195#433—92no—
196#432—92no—
197#431—92no—
198#423—91no—
199C2×C4⋊C8—91no—
200#408—31no—
201#408—91no—
202#405—31no—
203#405—91no—
204C3×#41—62no—
205C3×#41—62no—
206C2×C3×Q8—31no—
207C2×C3×D4—32no—
208C2×C3×D4—31no—
209C22×C3×C4—21no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67C4×D312yes—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222#235—22no—
223#235—22no—
224C2×D12C4×D311yescharacteristic
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3C22×D312yes—
228C2×Dic6C4×D311yescharacteristic
229C3×M16—22no—
230C3×M16—22no—
231C3×M16—42no—
232C2×C3×C8—22no—
233C2×C3×C8—31no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C2×C3×C8—62no—
238C2×C3×C8—62no—
239C2×C3×C8C22×D312yes—
240C2×C3×C8C22×D312yes—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C22⋊C4—32no—
244C3×C42—32no—
245#217—32no—
246#217—32no—
247#217C4×D312yes—
248(C2×D3)⋊C4—32no—
249(C2×D3)⋊C4—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3C4×D311yescharacteristic
253C4⋊Dic3C4×D311yescharacteristic
254Dic3⋊C4—32no—
255Dic3⋊C4—32no—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—32no—
265C4×Dic3—32no—
266C4×Dic3—32no—
267C4×Dic3—32no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3C22×D312yes—
273#208—62no—
274#208—62no—
275#208—122no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285C22×C32—21no—
286C22×C32—21no—
287C22×C32#11712yes—
288C22×C32C23×C411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C32×C4#11712yes—
293C32×C4C2×#4111yescharacteristic
294C32×C4C2×#4111yescharacteristic
295C3⋊Dic3—21no—
296C3⋊Dic3—21no—
297C3⋊Dic3—21no—
298C3⋊Dic3#13112yes—
299C3×Dic3—22no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C2×#41—31no—
303C2×M16—91no—
304C2×M16D3211yescharacteristic
305C22×C8—31no—
306C22×C8—31no—
307C4×Q8—91no—
308C4×Q8—91no—
309C4×D4—92no—
310C4×D4—92no—
311C4×D4—91no—
312C4×D4—91no—
313#117—31no—
314#117—92no—
315C2×C42—92no—
316C2×C42—91no—
317C4⋊C8—91no—
318C4⋊C8—91no—
319C4⋊C8—91no—
320C4⋊C8—91no—
321C4⋊C8—92no—
322C4⋊C8—92no—
323C22⋊C8—32no—
324C22⋊C8—32no—
325C22⋊C8—92no—
326C22⋊C8—92no—
327#97—32no—
328#97—92no—
329C4×C8—32no—
330C4×C8—92no—
331C23×C3—21no—
332C23×C3—32no—
333C23×C3C2×C4×D311yescharacteristic
334C23×C3C2×C4×D311yescharacteristic
335C22×D3C2×C4×D312yes—
336C3×Q8—62no—
337C3×D4—64no—
338C3×D4—62no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4#23512yes—
351C2×C3×C4#23512yes—
352C2×C3×C4#23712yes—
353C2×C3×C4#23712yes—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—24no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—64no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—122no—
377C2×Dic3C2×C4×D312yes—
378C2×Dic3C2×C4×D312yes—
379C2×Dic3C2×C4×D312yes—
380D12—22no—
381C4×D3—22no—
382C4×D3—22no—
383C4×D3—64no—
384C4×D3—122no—
385Dic6—22no—
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3×C8—61no—
392C3×C8—61no—
393C3⋊C8—21no—
394C3⋊C8—21no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C3⋊C8—62no—
398C3⋊C8—62no—
399C3⋊C8—122no—
400C2×C32—22no—
401C2×C32C2×#11711yescharacteristic
402C2×C32C2×#13111yescharacteristic
403C2×C32#56811yescharacteristic
404C3×D3—42no—
405#41—62no—
406#41—62no—
407C2×Q8—31no—
408C2×D4—32no—
409C2×D4—31no—
410C22×C4—32no—
411C22×C4—92no—
412C22×C4—92no—
413C22×C4—91no—
414C22×C4—91no—
415C22×C4C2×D3211yescharacteristic
416M16—22no—
417M16—182no—
418C2×C8—31no—
419C2×C8—31no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—62no—
423C2×C8—62no—
424C2×C8—92no—
425C2×C8C2×D3212yes—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—92no—
429C4⋊C4—92no—
430C22⋊C4—32no—
431C22⋊C4—92no—
432C22⋊C4—92no—
433C42—32no—
434C42—92no—
435C42—92no—
436C42—91no—
437C42—91no—
438C42—91no—
439C42—91no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3#87212yes—
452C22×C3#87712yes—
453C22×C3C22×C4×D311yescharacteristic
454C22×C3C22×C4×D311yescharacteristic
455C2×D3—22no—
456C2×D3—22no—
457C2×D3—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—62no—
464C3×C4#87212yes—
465C3×C4#87712yes—
466C3×C4C2×#23511yescharacteristic
467C3×C4C2×#23511yescharacteristic
468C3×C4C2×#23711yescharacteristic
469C3×C4C2×#23711yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—22no—
473Dic3—32no—
474Dic3—32no—
475Dic3—62no—
476Dic3—62no—
477Dic3—61no—
478Dic3—61no—
479Dic3—61no—
480Dic3—61no—
481Dic3—61no—
482Dic3—61no—
483Dic3—121no—
484Dic3—121no—
485C32#292511yescharacteristic, complemented, Sylow
486C23—32no—
487C23C4×D3211yescharacteristic
488Q8—62no—
489D4—64no—
490D4—62no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—91no—
497C2×C4—91no—
498C2×C4—91no—
499C2×C4—91no—
500C2×C4—184no—
501C2×C4—182no—
502C2×C4—362no—
503C2×C4—361no—
504C2×C4#379512yes—
505C2×C4C4×D3211yescharacteristic
506C2×C4#380412yes—
507C2×C4C22×D3211yescharacteristic
508C8—22no—
509C8—61no—
510C8—61no—
511C8—61no—
512C8—61no—
513C8—182no—
514C2×C3—22no—
515C2×C3—22no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—42no—
520C2×C3—122no—
521C2×C3C2×#87211yescharacteristic
522C2×C3C2×#87711yescharacteristic
523C2×C3D3×#13111yescharacteristic
524C2×C3D3×#13111yescharacteristic
525C2×C3#575011yescharacteristic
526C2×C3#575011yescharacteristic
527D3—42no—
528C22—21no—
529C22—21no—
530C22—62no—
531C22—62no—
532C22—62no—
533C22#6387712yes—
534C22C2×C4×D3211yescharacteristic
535C4—62no—
536C4—62no—
537C4—62no—
538C4—92no—
539C4—181no—
540C4—181no—
541C4—181no—
542C4#6387712yes—
543C4C2×#379511yescharacteristic
544C4C2×#380411yescharacteristic
545C3—21no—
546C3#7855211yescharacteristic, complemented
547C3#7865011yescharacteristic, complemented
548C2—22no—
549C2—122no—
550C2#1059470711yescharacteristic
551C2#1059470811yescharacteristic
552C2C2×#6387711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592817C2semidirect
4. C3×#5122C2semidirect
5. C2×#63572C2semidirect
7. #10591055C2semidirect
8. #10590697C2semidirect
9. #10590696C2semidirect
10. #10590660C2semidirect
11. #10590655C2semidirect
49. #5122D3semidirect
485. C32#2925semidirect
546. C3#78552semidirect
547. C3#78650semidirect

Maximal subgroups

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

subgroupindex
#105949582
#105928172
C3×#51292
C3×#51222
C2×#635722
#105910702
#105910552
#105906972
#105906962
#105906602
#105906552
#786503
#785523