Finite Group Databasebeta

← #11807128

Subgroups — #11807128

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C3×#4928C211yesmaximal, characteristic
5#10591357C211yesmaximal, characteristic
6#10591274C211yesmaximal, characteristic
7#10591274C211yesmaximal, characteristic
8#10591256C212yesmaximal
9#10591243C212yesmaximal
10#10591235C212yesmaximal
11#10591191C212yesmaximal
12#75987—31nomaximal
13#73657—31nomaximal
14C22×#627C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63919C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#888—31no—
39C2×#888—31no—
40C3×#389—31no—
41C3×C4×C4⋊C4—31no—
42#4984—31no—
43#4976—32no—
44Dic3×C4⋊C4—31no—
45Dic3×C4⋊C4—31no—
46Dic3×C4⋊C4—31no—
47Dic3×C4⋊C4—31no—
48#4973—32no—
49#4972—31no—
50C4×C4⋊Dic3D311yescharacteristic
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—31no—
53C4×Dic3⋊C4—32no—
54C4×Dic3⋊C4—61no—
55#4929—32no—
56#4928D311yescharacteristic
57#4649—32no—
58#4647—32no—
59#4646—32no—
60#4646—32no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×#627—42no—
73C2×#627—42no—
74C2×#627C2×C418yes—
75C32×C42—22no—
76#3750—22no—
77#3750Q814yescomplemented
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2×C414yes—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2×C414yes—
82C3×C4⋊Dic3C2×C414yes—
83C3×C4⋊Dic3Q814yescomplemented
84C3×Dic3⋊C4—42no—
85C3×C4×Dic3—42no—
86#3724C2×C418yes—
87Dic3⋊Dic3—42no—
88Dic32—24no—
89Dic32—42no—
90#2369—91noSylow
91C22×Dic6—32no—
92C22×Dic6—32no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C42—21no—
99C2×C3×C42—32no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—61no—
115C2×Dic3⋊C4—61no—
116C2×Dic3⋊C4C2×D312yes—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—61no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3C2×D312yes—
128#888—38no—
129#888—38no—
130C3×#95—32no—
131C3×#95—32no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—61no—
143C3⋊#95—61no—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C23×C32C2411yescharacteristic
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×Q812yes—
154C2×C32×C4C2×Q812yes—
155C2×C32×C4#4112yes—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C22×C412yes—
165C2×C3⋊Dic3C2×Q812yes—
166C2×C3⋊Dic3C2×Q812yes—
167C2×C3⋊Dic3#4112yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C414yes—
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C2×Q814yes—
180#627—48no—
181C2×C4⋊Q8—91no—
182#391—92no—
183#391—92no—
184#389—31no—
185#389—92no—
186#389—91no—
187C4×C4⋊C4—31no—
188C4×C4⋊C4—92no—
189C4×C4⋊C4—91no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—91no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C2×Dic6—38no—
222C2×Dic6—38no—
223C2×Dic6—122no—
224C2×Dic6—122no—
225C2×Dic6—122no—
226C2×Dic6—122no—
227C3×C4⋊C4—34no—
228C3×C4⋊C4—34no—
229C3×C4⋊C4—34no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—122no—
232C3×C42—22no—
233C3×C42—22no—
234C3×C42—42no—
235C3×C42—122no—
236C4⋊Dic3—22no—
237C4⋊Dic3—122no—
238C4⋊Dic3Dic614yescomplemented
239C4⋊Dic3C4×D314yes—
240C4⋊Dic3C4×D314yes—
241Dic3⋊C4—34no—
242Dic3⋊C4—34no—
243Dic3⋊C4—38no—
244Dic3⋊C4—38no—
245Dic3⋊C4—42no—
246Dic3⋊C4—64no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—64no—
250Dic3⋊C4—122no—
251C4×Dic3—34no—
252C4×Dic3—34no—
253C4×Dic3—42no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—122no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C22×C32C23×C411yescharacteristic
263C22×C32C22×Q811yescharacteristic
264C22×C32C22×Q811yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)11yescharacteristic
268C22×C32H(5,𝔽2)11yescharacteristic
269C32×C4—22no—
270C32×C4—41no—
271C32×C4C4×Q814yes—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—41no—
275C3⋊Dic3C4×Q814yes—
276C3×Dic3—24no—
277C3×Dic3—24no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C22×Q8—92no—
281C4⋊Q8—98no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—32no—
287C2×C4⋊C4—92no—
288C2×C4⋊C4—91no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—92no—
291C2×C42—32no—
292C2×C42—91no—
293C2×C42—92no—
294C2×C42—91no—
295C2×C42—92no—
296C2×C42D3211yescharacteristic
297#95—32no—
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—91no—
303#95—91no—
304C23×C3—21no—
305C23×C3C23×D311yescharacteristic
306C23×C3C23×D311yescharacteristic
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—34no—
323C2×C3×C4—34no—
324C2×C3×C4—34no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4C2×Dic612yes—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4#23512yes—
342C2×C3×C4#23712yes—
343C2×C3×C4D3×Q812yes—
344C2×C3×C4D3×Q812yes—
345C2×C3×C4D3×Q812yes—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3C2×Dic614yes—
392C2×Dic3C2×C4×D314yes—
393C2×Dic3C2×C4×D314yes—
394Dic6—128no—
395Dic6—128no—
396C2×C32C2×C4×Q811yescharacteristic
397C2×C32C2×C4×Q811yescharacteristic
398C2×C32#51811yescharacteristic
399C2×C32#55411yescharacteristic
400C2×C32#55411yescharacteristic
401C2×C32#55511yescharacteristic
402C2×C32Q8211yescharacteristic
403C2×Q8—98no—
404C2×Q8—362no—
405C2×Q8—362no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—91no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4C2×D3211yescharacteristic
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—34no—
418C4⋊C4—34no—
419C4⋊C4—34no—
420C4⋊C4—62no—
421C4⋊C4—98no—
422C4⋊C4—94no—
423C4⋊C4—122no—
424C4⋊C4—182no—
425C4⋊C4—362no—
426C42—22no—
427C42—94no—
428C42—122no—
429C42—184no—
430C42—182no—
431C42—362no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3C22×Dic611yescharacteristic
440C22×C3C22×C4×D311yescharacteristic
441C22×C3C22×C4×D311yescharacteristic
442C22×C3C2×#23511yescharacteristic
443C22×C3C2×#23711yescharacteristic
444C22×C3#100411yescharacteristic
445C22×C3#100411yescharacteristic
446C22×C3C2×D3×Q811yescharacteristic
447C22×C3C2×D3×Q811yescharacteristic
448C22×C3C2×D3×Q811yescharacteristic
449C22×C3D3×#4111yescharacteristic
450C22×C3D3×#4111yescharacteristic
451C22×C3#100911yescharacteristic
452C22×C3#100911yescharacteristic
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—24no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—64no—
461C3×C4—64no—
462C3×C4—64no—
463C3×C4—122no—
464C3×C4C4×Dic614yes—
465C3×C4#88714yes—
466Dic3—24no—
467Dic3—24no—
468Dic3—24no—
469Dic3—34no—
470Dic3—34no—
471Dic3—42no—
472Dic3—64no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482C32#236911yescharacteristic, complemented, Sylow
483C23C22×D3211yescharacteristic
484Q8—368no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—34no—
491C2×C4—34no—
492C2×C4—34no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—92no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4—181no—
512C2×C4—181no—
513C2×C4—181no—
514C2×C4D3×Dic612yes—
515C2×C4#379712yes—
516C2×C4C4×D3212yes—
517C2×C4#380412yes—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3C2×C4×Dic611yescharacteristic
526C2×C3C2×#88711yescharacteristic
527C2×C3#551111yescharacteristic
528C2×C3#553211yescharacteristic
529C2×C3#553911yescharacteristic
530C2×C3#554511yescharacteristic
531C2×C3#554511yescharacteristic
532C2×C3Q8×Dic611yescharacteristic
533C2×C3C4×D3×Q811yescharacteristic
534C2×C3C4×D3×Q811yescharacteristic
535C2×C3#561611yescharacteristic
536C2×C3#563511yescharacteristic
537C2×C3#569011yescharacteristic
538C2×C3#572211yescharacteristic
539C22C2×D3×Dic611yescharacteristic
540C22C2×#379711yescharacteristic
541C22C2×C4×D3211yescharacteristic
542C22#6430611yescharacteristic
543C22#6430711yescharacteristic
544C22#6430711yescharacteristic
545C22C2×#380411yescharacteristic
546C4—22no—
547C4—41no—
548C4—64no—
549C4—64no—
550C4—64no—
551C4—94no—
552C4—122no—
553C4—182no—
554C4—182no—
555C4—361no—
556C4#6383714yes—
557C3—21no—
558C3#7365711yescharacteristic, complemented
559C3#7598711yescharacteristic, complemented
560C2#1059385611yescharacteristic
561C2C4×#379711yescharacteristic
562C2#1059394111yescharacteristic
563C2#1059399611yescharacteristic
564C2C2×#6383711yescharacteristic
565C2#1059496111yescharacteristic
566C2#1059499111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
30. #63919C4semidirect
77. #3750Q8semidirect
83. C3×C4⋊Dic3Q8semidirect
238. C4⋊Dic3Dic6semidirect
482. C32#2369semidirect
558. C3#73657semidirect
559. C3#75987semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C4×#37502
C3×C4×C4⋊Dic32
C3×#49282
#105913572
#105912742
#105912562
#105912432
#105912352
#105911912
#759873
#736573