Finite Group Databasebeta

← #11859119

Subgroups — #11859119

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C3×#5110C211yesmaximal, characteristic
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591120C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7#10591057C211yesmaximal, characteristic, complemented
8#10590697C212yesmaximal, complemented
9#10590696C212yesmaximal, complemented
10#10590660C212yesmaximal, complemented
11#10590655C212yesmaximal, complemented
12#78650—31nomaximal
13#78552—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#67⋊Dic3C412yes—
22#67⋊Dic3C412yes—
23#63898C411yescharacteristic
24#63898C411yescharacteristic
25C4×D3×Dic3C2212yes—
26#63855C2212yes—
27#63843C411yescharacteristic
28#63843C411yescharacteristic
29#63641C2211yescharacteristic
30#63641C2211yescharacteristic
31#63641C2211yescharacteristic
32#63641C2211yescharacteristic
33C3×(C2×D3)⋊C8C2212yes—
34C3×(C2×D3)⋊C8C2212yes—
35C3×#815C2212yes—
36C3×C8×Dic3C2212yes—
37#63572C2212yes—
38#63572C2212yes—
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#5129—31no—
49#5122—31no—
50#5118—31no—
51#5118—31no—
52#5110D311yescharacteristic
53#5101D311yescharacteristic, complemented
54C2×Dic3⋊C8—31no—
55C2×Dic3⋊C8—31no—
56C2×Dic3⋊C8—61no—
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—
77C2×C32×C8—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C4×C3⋊Dic3C2×C411yescharacteristic
81C4×C3⋊Dic3C2×C411yescharacteristic
82C4×C3⋊Dic3C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#217C2×C412yes—
88C3×C4⋊Dic3C2×C411yescharacteristic
89C3×C4⋊Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2312yes—
91C3×#208—22no—
92C3×#208—22no—
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2312yes—
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—31no—
105C2×C3×M16—31no—
106C22×C3×C8—21no—
107C22×C3×C8C2×D311yescharacteristic
108C22×C3×C8C2×D311yescharacteristic
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×#208C2×D311yescharacteristic
123C2×#208C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
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—31no—
148Dic3⋊C8—31no—
149Dic3⋊C8—31no—
150Dic3⋊C8—31no—
151Dic3⋊C8—31no—
152Dic3⋊C8—31no—
153Dic3⋊C8—31no—
154Dic3⋊C8—31no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—61no—
160Dic3⋊C8—61no—
161Dic3⋊C8—61no—
162Dic3⋊C8—61no—
163C8×Dic3—32no—
164C8×Dic3C2×D312yes—
165#803—32no—
166C4×C3⋊C8—32no—
167C23×C32C22×C411yescharacteristic
168C22×C3×D3C22×C412yes—
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4#4112yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—41no—
175C2×C3⋊Dic3C22×C411yescharacteristic
176C2×C3⋊Dic3C22×C411yescharacteristic
177C2×C3⋊Dic3C22×C411yescharacteristic
178C2×C3⋊Dic3C22×C411yescharacteristic
179C3×#67—24no—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C3×D12—22no—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×Dic6—22no—
187D3×Dic3—24no—
188D3×Dic3—42no—
189C32×C8—21no—
190C32×C8—21no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C4×#41—91no—
196#433—92no—
197#433—92no—
198#432—92no—
199#431—92no—
200#423—91no—
201C2×C4⋊C8—91no—
202#408—31no—
203#408—91no—
204#405—31no—
205#405—91no—
206C3×#41—62no—
207C3×#41—62no—
208C2×C3×Q8—31no—
209C2×C3×D4—32no—
210C2×C3×D4—31no—
211C22×C3×C4—21no—
212C22×C3×C4—32no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67C4×D312yes—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224#235—22no—
225#235—22no—
226C2×D12C4×D311yescharacteristic
227C2×C4×D3—32no—
228C2×C4×D3—32no—
229C2×C4×D3C22×D312yes—
230C2×Dic6C4×D311yescharacteristic
231C3×M16—62no—
232C3×M16—62no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8—32no—
239C2×C3×C8—42no—
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C3×C4⋊C4—31no—
245C3×C4⋊C4—31no—
246C3×C22⋊C4—32no—
247C3×C42—32no—
248#217—32no—
249#217—32no—
250#217C4×D312yes—
251(C2×D3)⋊C4—32no—
252(C2×D3)⋊C4—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3C4×D311yescharacteristic
256C4⋊Dic3C4×D311yescharacteristic
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—31no—
265C4×Dic3—31no—
266C4×Dic3—31no—
267C4×Dic3—32no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—32no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3C22×D312yes—
276#208—22no—
277#208—22no—
278C2×C3⋊C8—31no—
279C2×C3⋊C8—31no—
280C2×C3⋊C8—31no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—61no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8—122no—
287C2×C3⋊C8C22×D312yes—
288C2×C3⋊C8C22×D312yes—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32#11712yes—
292C22×C32C23×C411yescharacteristic
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C32×C4#11712yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3#13112yes—
303C3×Dic3—22no—
304C3×Dic3—22no—
305C3×Dic3—22no—
306C2×#41—31no—
307C2×M16—31no—
308C2×M16—31no—
309C22×C8—91no—
310C22×C8D3211yescharacteristic
311C4×Q8—91no—
312C4×Q8—91no—
313C4×D4—92no—
314C4×D4—92no—
315C4×D4—91no—
316C4×D4—91no—
317#117—31no—
318#117—92no—
319C2×C42—92no—
320C2×C42—91no—
321C4⋊C8—92no—
322C4⋊C8—92no—
323C4⋊C8—91no—
324C4⋊C8—91no—
325C4⋊C8—91no—
326C4⋊C8—91no—
327C22⋊C8—32no—
328C22⋊C8—32no—
329C22⋊C8—92no—
330C22⋊C8—92no—
331#97—32no—
332#97—92no—
333C4×C8—32no—
334C4×C8—92no—
335C23×C3—21no—
336C23×C3—32no—
337C23×C3C2×C4×D311yescharacteristic
338C23×C3C2×C4×D311yescharacteristic
339C22×D3C2×C4×D312yes—
340C3×Q8—62no—
341C3×D4—64no—
342C3×D4—62no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4C2×C4×D311yescharacteristic
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4#23512yes—
355C2×C3×C4#23512yes—
356C2×C3×C4#23712yes—
357C2×C3×C4#23712yes—
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—24no—
361C2×Dic3—31no—
362C2×Dic3—31no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—31no—
367C2×Dic3—31no—
368C2×Dic3—31no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—64no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—122no—
381C2×Dic3C2×C4×D312yes—
382C2×Dic3C2×C4×D312yes—
383C2×Dic3C2×C4×D312yes—
384D12—22no—
385C4×D3—22no—
386C4×D3—22no—
387C4×D3—64no—
388C4×D3—122no—
389Dic6—22no—
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—41no—
395C3×C8—41no—
396C3×C8—62no—
397C3×C8—62no—
398C3⋊C8—22no—
399C3⋊C8—22no—
400C3⋊C8—61no—
401C3⋊C8—61no—
402C3⋊C8—61no—
403C3⋊C8—61no—
404C3⋊C8—121no—
405C3⋊C8—121no—
406C2×C32—22no—
407C2×C32C2×#11711yescharacteristic
408C2×C32C2×#13111yescharacteristic
409C2×C32#56811yescharacteristic
410C3×D3—42no—
411#41—62no—
412#41—62no—
413C2×Q8—31no—
414C2×D4—32no—
415C2×D4—31no—
416C22×C4—32no—
417C22×C4—92no—
418C22×C4—92no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4C2×D3211yescharacteristic
422M16—62no—
423M16—62no—
424C2×C8—22no—
425C2×C8—32no—
426C2×C8—32no—
427C2×C8—91no—
428C2×C8—91no—
429C2×C8—182no—
430C2×C8C2×D3211yescharacteristic
431C2×C8C2×D3211yescharacteristic
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—92no—
435C4⋊C4—92no—
436C22⋊C4—32no—
437C22⋊C4—92no—
438C22⋊C4—92no—
439C42—32no—
440C42—92no—
441C42—92no—
442C42—91no—
443C42—91no—
444C42—91no—
445C42—91no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—62no—
455C22×C3—62no—
456C22×C3—62no—
457C22×C3#87212yes—
458C22×C3#87712yes—
459C22×C3C22×C4×D311yescharacteristic
460C22×C3C22×C4×D311yescharacteristic
461C2×D3—22no—
462C2×D3—22no—
463C2×D3—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—62no—
468C3×C4—62no—
469C3×C4—62no—
470C3×C4#87212yes—
471C3×C4#87712yes—
472C3×C4C2×#23511yescharacteristic
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×#23711yescharacteristic
475C3×C4C2×#23711yescharacteristic
476Dic3—22no—
477Dic3—22no—
478Dic3—22no—
479Dic3—32no—
480Dic3—32no—
481Dic3—62no—
482Dic3—62no—
483Dic3—61no—
484Dic3—61no—
485Dic3—61no—
486Dic3—61no—
487Dic3—61no—
488Dic3—61no—
489Dic3—121no—
490Dic3—121no—
491C32#292511yescharacteristic, complemented, Sylow
492C23—32no—
493C23C4×D3211yescharacteristic
494Q8—62no—
495D4—64no—
496D4—62no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—91no—
503C2×C4—91no—
504C2×C4—91no—
505C2×C4—91no—
506C2×C4—184no—
507C2×C4—182no—
508C2×C4—362no—
509C2×C4—361no—
510C2×C4#379512yes—
511C2×C4C4×D3211yescharacteristic
512C2×C4#380412yes—
513C2×C4C22×D3211yescharacteristic
514C8—21no—
515C8—21no—
516C8—62no—
517C8—62no—
518C8—181no—
519C8—181no—
520C2×C3—24no—
521C2×C3—22no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—122no—
527C2×C3C2×#87211yescharacteristic
528C2×C3C2×#87711yescharacteristic
529C2×C3D3×#13111yescharacteristic
530C2×C3D3×#13111yescharacteristic
531C2×C3#575011yescharacteristic
532C2×C3#575011yescharacteristic
533D3—42no—
534C22—21no—
535C22—21no—
536C22—62no—
537C22—62no—
538C22—62no—
539C22#6387712yes—
540C22C2×C4×D3211yescharacteristic
541C4—62no—
542C4—62no—
543C4—62no—
544C4—92no—
545C4—181no—
546C4—181no—
547C4—181no—
548C4#6387712yes—
549C4C2×#379511yescharacteristic
550C4C2×#380411yescharacteristic
551C3—21no—
552C3#7855211yescharacteristic, complemented
553C3#7865011yescharacteristic, complemented
554C2—22no—
555C2—122no—
556C2#1059466911yescharacteristic
557C2#1059467011yescharacteristic
558C2C2×#6387711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
4. C3×#5101C2semidirect
5. #10591120C2semidirect
7. #10591057C2semidirect
8. #10590697C2semidirect
9. #10590696C2semidirect
10. #10590660C2semidirect
11. #10590655C2semidirect
53. #5101D3semidirect
491. C32#2925semidirect
552. C3#78552semidirect
553. C3#78650semidirect

Maximal subgroups

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

subgroupindex
#105949582
C2×#636412
C3×#51102
C3×#51012
#105911202
#105910712
#105910572
#105906972
#105906962
#105906602
#105906552
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