Finite Group Databasebeta

← #11805652

Subgroups — #11805652

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64286C211yesmaximal, characteristic, complemented
2C22×C4⋊#157C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic
4#10593826C212yesmaximal
5#10593812C211yesmaximal, characteristic, complemented
6#10593812C211yesmaximal, characteristic, complemented
7#10593758C212yesmaximal, complemented
8#10593747C212yesmaximal, complemented
9C22⋊C4×#157C212yesmaximal, complemented
10#10593736C211yesmaximal, characteristic, complemented
11C4×C4⋊#157C211yesmaximal, characteristic, complemented
12C23×#157C2212yes—
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C22⋊#157C2212yes—
17C2×C22⋊#157C2212yes—
18C2×C22⋊#157C2212yes—
19#64286—24no—
20C2×C4⋊#157—24no—
21C2×C4⋊#157C2211yescharacteristic
22C2×C4⋊#157C2211yescharacteristic
23C2×C4⋊#157C2211yescharacteristic
24C2×C4⋊#157C2212yes—
25C2×C4⋊#157C2211yescharacteristic
26C2×C4×#157C2212yes—
27C2×C4×#157C2212yes—
28C32×C4×D4C411yescharacteristic, complemented
29D4×C3⋊Dic3C411yescharacteristic, complemented
30C4×#638C411yescharacteristic, complemented
31C4×#638C411yescharacteristic, complemented
32#64102C411yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64090C411yescharacteristic, complemented
35#64090C411yescharacteristic, complemented
36C22⋊C4×C3⋊D3C2211yescharacteristic
37C22⋊C4×C3⋊D3C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
39C42×C3⋊D3C2211yescharacteristic
40#63781C2212yes—
41#63781C2212yes—
42#63781C2212yes—
43#63781C2212yes—
44#63781C2212yes—
45C4×D3×D4—62no—
46C23×C3⋊D3C2311yescharacteristic
47C23×C3⋊D3C2311yescharacteristic
48C22×#157—24no—
49C22×#157—24no—
50C22×#157—42no—
51C22×#157C2312yes—
52C22×#157C2312yes—
53C22×#157C2312yes—
54C22×#157C2312yes—
55C2×C32×D4C2×C411yescharacteristic
56C22×C32×C4C2×C411yescharacteristic
57C22×C32×C4C2×C411yescharacteristic, complemented
58C2×#638C2×C411yescharacteristic
59C2×#638C2×C411yescharacteristic
60C22×C3⋊Dic3C2×C411yescharacteristic
61C22×C3⋊Dic3C2×C411yescharacteristic, complemented
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C411yescharacteristic
70C2×C4×C3⋊D3C2×C411yescharacteristic
71C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
72C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×C4×C3⋊D3C2311yescharacteristic
77C2×C4×C3⋊D3C2311yescharacteristic
78C22⋊#157—24no—
79C22⋊#157—24no—
80C22⋊#157—42no—
81C4⋊#157—24no—
82C4⋊#157—22no—
83C4⋊#157—22no—
84C4⋊#157—22no—
85C4⋊#157D414yescomplemented
86C4×#157—24no—
87C4×#157—42no—
88C32×C4⋊C4C2×C411yescharacteristic, complemented
89C32×C22⋊C4C2×C411yescharacteristic
90C32×C22⋊C4C2×C411yescharacteristic, complemented
91C32×C42C2×C411yescharacteristic, complemented
92#3757C2×C411yescharacteristic
93#3757C2×C411yescharacteristic, complemented
94#3752C2×C411yescharacteristic
95#3752C2×C411yescharacteristic
96#3752C2×C411yescharacteristic, complemented
97#3752C2×C411yescharacteristic, complemented
98C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
99#3750C2×C411yescharacteristic, complemented
100#3750C2×C411yescharacteristic, complemented
101C4×C3⋊Dic3C2×C411yescharacteristic, complemented
102C4×C3⋊Dic3C2×C411yescharacteristic, complemented
103C4×C3⋊Dic3C2×C411yescharacteristic, complemented
104#2352—91nomaximal, Sylow
105C2×D3×D4—62no—
106C22×C4×D3—62no—
107C22×C4×D3—62no—
108C3×C4×D4—22no—
109D4×Dic3—62no—
110C4×#67—62no—
111C4×#67—62no—
112#893—62no—
113D3×C4⋊C4—62no—
114#67⋊C4—62no—
115#67⋊C4—62no—
116D3×C22⋊C4—62no—
117D3×C22⋊C4—62no—
118C4×D12—62no—
119C42×D3—62no—
120C23×C32C22×C411yescharacteristic
121C23×C32C22×C411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3C22×C411yescharacteristic
133C22×C3⋊D3C22×C411yescharacteristic
134C22×C3⋊D3#4112yes—
135C22×C3⋊D3#4112yes—
136C22×C3⋊D3C2411yescharacteristic
137C2×#157—22no—
138C2×#157—22no—
139C2×#157—22no—
140C2×#157—22no—
141C2×#157—22no—
142C2×#157—22no—
143C2×#157—22no—
144C2×#157—22no—
145C2×#157—22no—
146C2×#157—22no—
147C2×#157—22no—
148C2×#157—48no—
149C2×#157C2×D414yes—
150C32×D4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C22×C411yescharacteristic
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C22×C411yescharacteristic
157C2×C32×C4C22×C411yescharacteristic
158#638—22no—
159#638—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C411yescharacteristic
163C2×C3⋊Dic3C22×C411yescharacteristic
164C2×C3⋊Dic3C22×C411yescharacteristic
165C2×C3⋊Dic3C22×C411yescharacteristic
166C2×C3⋊Dic3C22×C411yescharacteristic
167C4⋊(C3⋊D3)—22no—
168C4×C3⋊D3—21no—
169C4×C3⋊D3—21no—
170C4×C3⋊D3—21no—
171C4×C3⋊D3—21no—
172C4×C3⋊D3—21no—
173C4×C3⋊D3—21no—
174C4×C3⋊D3—21no—
175C4×C3⋊D3—21no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—22no—
178C4×C3⋊D3—22no—
179C4×C3⋊D3—22no—
180C4×C3⋊D3C2×D412yes—
181C4×C3⋊D3#4112yes—
182C2×C4×D4—91no—
183C2×#117—91no—
184C22×C4⋊C4—91no—
185#388—92no—
186#387—92no—
187#386—92no—
188#382—91no—
189#380—91no—
190#380—91no—
191C4×C4⋊C4—91no—
192C4×C22⋊C4—92no—
193C23×D3—62no—
194C23×D3—62no—
195C2×C3×D4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C2×#67—62no—
199C2×#67—62no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202D3×D4—68no—
203D3×D4—68no—
204C2×D12—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—124no—
215C2×C4×D3—124no—
216C2×C4×D3—124no—
217C2×C4×D3—124no—
218C3×C4⋊C4—22no—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C42—22no—
222#217—62no—
223#217—62no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231C4×Dic3—62no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32—21no—
239C22×C32#11712yescomplemented
240C22×C32C23×C411yescharacteristic
241C2×C3⋊D3—21no—
242C2×C3⋊D3—21no—
243C2×C3⋊D3—21no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3—22no—
246C2×C3⋊D3—22no—
247C2×C3⋊D3—22no—
248C2×C3⋊D3—21no—
249C2×C3⋊D3—21no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3#11712yescomplemented
255C2×C3⋊D3C22×D411yescharacteristic
256C2×C3⋊D3C2×#4111yescharacteristic
257C2×C3⋊D3C2×#4111yescharacteristic
258C2×C3⋊D3C2×#4111yescharacteristic
259C2×C3⋊D3H(5,𝔽2)11yescharacteristic
260C2×C3⋊D32−1+411yescharacteristic
261#157—24no—
262#157—42no—
263#157—42no—
264#157—42no—
265C32×C4—21no—
266C32×C4—21no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4C4×D412yes—
270C3⋊Dic3—21no—
271C3⋊Dic3—21no—
272C3⋊Dic3—21no—
273C3⋊Dic3—21no—
274C3⋊Dic3C4×D412yes—
275C22×D4—91no—
276C23×C4—91no—
277C23×C4—91no—
278C23×C4—92no—
279C4×D4—91no—
280C4×D4—91no—
281C4×D4—91no—
282C4×D4—91no—
283C4×D4—91no—
284C4×D4—91no—
285C4×D4—91no—
286C4×D4#15711yescharacteristic, complemented
287#117—184no—
288C2×C4⋊C4—91no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—91no—
294C2×C4⋊C4—184no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—92no—
298C2×C22⋊C4—92no—
299C2×C22⋊C4—92no—
300C2×C42—91no—
301C2×C42—92no—
302C2×C42—92no—
303#95—92no—
304#95—92no—
305#95—92no—
306#95—92no—
307#95—92no—
308C23×C3—22no—
309C23×C3—22no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—122no—
325C3×D4—28no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—44no—
332C2×C3×C4—44no—
333#67—68no—
334#67—68no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—124no—
341C2×Dic3—124no—
342D12—68no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—64no—
346C4×D3—64no—
347C4×D3—124no—
348C4×D3—124no—
349C4×D3—124no—
350C4×D3—124no—
351C4×D3—122no—
352C4×D3—122no—
353C4×D3—122no—
354C4×D3—122no—
355C4×D3—122no—
356C4×D3—122no—
357C2×C32—22no—
358C2×C32—41no—
359C2×C32C2×#11711yescharacteristic
360C2×C32C2×C4×D411yescharacteristic
361C2×C32#52011yescharacteristic
362C3⋊D3—22no—
363C3⋊D3—41no—
364C3⋊D3#54611yescharacteristic
365C3⋊D3#54811yescharacteristic
366C3⋊D3#55211yescharacteristic
367C3⋊D3#55311yescharacteristic
368C24—91no—
369C24—91no—
370C2×D4—91no—
371C2×D4—91no—
372C2×D4—91no—
373C2×D4—182no—
374C2×D4—182no—
375C2×D4C2×#15711yescharacteristic
376C22×C4—91no—
377C22×C4—92no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—91no—
388C22×C4—92no—
389C22×C4—92no—
390C22×C4—92no—
391C22×C4—182no—
392C22×C4—182no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—184no—
396C22×C4—184no—
397C22×C4—362no—
398C22×C4C2×#15711yescharacteristic
399C22×C4C2×#15711yescharacteristic, complemented
400C4⋊C4—94no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—182no—
405C4⋊C4—184no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4C2×#15711yescharacteristic, complemented
409C22⋊C4—91no—
410C22⋊C4—91no—
411C22⋊C4—91no—
412C22⋊C4—91no—
413C22⋊C4—91no—
414C22⋊C4—91no—
415C22⋊C4—184no—
416C22⋊C4—184no—
417C22⋊C4—362no—
418C22⋊C4C2×#15711yescharacteristic
419C22⋊C4C2×#15711yescharacteristic, complemented
420C42—91no—
421C42—91no—
422C42—91no—
423C42—184no—
424C42—362no—
425C42C2×#15711yescharacteristic, complemented
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—22no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—124no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C3×C4—24no—
454C3×C4—24no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—42no—
458Dic3—64no—
459Dic3—64no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463C32#235211yescharacteristic, complemented, Sylow
464C23—91no—
465C23—92no—
466C23—92no—
467C23—91no—
468C23—91no—
469C23—181no—
470C23—181no—
471C23—181no—
472C23—181no—
473C23—181no—
474C23—181no—
475C23—181no—
476C23—181no—
477C23—181no—
478C23—181no—
479C23C22×#15711yescharacteristic
480C23C22×#15711yescharacteristic
481D4—22no—
482D4—182no—
483D4—182no—
484D4—182no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—91no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—94no—
491C2×C4—91no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4—368no—
521C2×C4C22×#15711yescharacteristic
522C2×C4C22×#15711yescharacteristic
523C2×C4C22×#15711yescharacteristic
524C2×C4C22×#15711yescharacteristic
525C2×C4C22×#15711yescharacteristic
526C2×C3—22no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—44no—
530C2×C3—44no—
531D3—62no—
532D3—62no—
533D3—62no—
534D3—62no—
535D3—124no—
536D3—124no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—91no—
543C22—91no—
544C22—91no—
545C22—91no—
546C22—91no—
547C22—91no—
548C22—92no—
549C22—182no—
550C22—182no—
551C22—182no—
552C22—182no—
553C22—181no—
554C22—181no—
555C22—181no—
556C22—181no—
557C22—181no—
558C22—361no—
559C22—361no—
560C22—361no—
561C22—361no—
562C22#6428612yescomplemented
563C22C23×#15711yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—92no—
569C4—184no—
570C4—181no—
571C4—181no—
572C4—181no—
573C4—181no—
574C4—362no—
575C4—362no—
576C4—362no—
577C4D4×#15712yes—
578C3—22no—
579C2—22no—
580C2—41no—
581C2—91no—
582C2—91no—
583C2—91no—
584C2—91no—
585C2—182no—
586C2—361no—
587C2C2×#6428611yescharacteristic
588C2C2×D4×#15711yescharacteristic
589C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC4×D4#157
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64286C2semidirect
2. C22×C4⋊#157C2semidirect
5. #10593812C2semidirect
6. #10593812C2semidirect
7. #10593758C2semidirect
8. #10593747C2semidirect
9. C22⋊C4×#157C2semidirect
10. #10593736C2semidirect
11. C4×C4⋊#157C2semidirect
28. C32×C4×D4C4semidirect
29. D4×C3⋊Dic3C4semidirect
30. C4×#638C4semidirect
31. C4×#638C4semidirect
32. #64102C4semidirect
34. #64090C4semidirect
35. #64090C4semidirect
38. C4×C4⋊(C3⋊D3)C4semidirect
57. C22×C32×C4C2×C4semidirect
61. C22×C3⋊Dic3C2×C4semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
72. C2×C4×C3⋊D3C2×C4semidirect
85. C4⋊#157D4semidirect
88. C32×C4⋊C4C2×C4semidirect
90. C32×C22⋊C4C2×C4semidirect
91. C32×C42C2×C4semidirect
93. #3757C2×C4semidirect
96. #3752C2×C4semidirect
97. #3752C2×C4semidirect
98. C4⋊(C3⋊Dic3)C2×C4semidirect
99. #3750C2×C4semidirect
100. #3750C2×C4semidirect
101. C4×C3⋊Dic3C2×C4semidirect
102. C4×C3⋊Dic3C2×C4semidirect
103. C4×C3⋊Dic3C2×C4semidirect
239. C22×C32#117semidirect
254. C2×C3⋊D3#117semidirect
286. C4×D4#157semidirect
399. C22×C4C2×#157semidirect
408. C4⋊C4C2×#157semidirect
419. C22⋊C4C2×#157semidirect
425. C42C2×#157semidirect
463. C32#2352semidirect
562. C22#64286semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C22×C4⋊#1572
C4×D4×C3⋊D32
#105938262
#105938122
#105937582
#105937472
C22⋊C4×#1572
#105937362
C4×C4⋊#1572
#23529