Finite Group Databasebeta

← #11824473

Subgroups — #11824473

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#64155C211yesmaximal, characteristic, complemented
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×C4×#638C211yesmaximal, characteristic
5C2×#64133C211yesmaximal, characteristic, complemented
6C2×#64106C211yesmaximal, characteristic, complemented
7#10592692C212yesmaximal, complemented
8#10592674C212yesmaximal, complemented
9C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592656C212yesmaximal
11#10592648C212yesmaximal, complemented
12#82780—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic
18C32×C22⋊Q8—24no—
19C2×C32×C4⋊C4C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2212yes—
22C2×#3757C2211yescharacteristic
23C2×#3757C2212yes—
24#64155—24no—
25#64153—24no—
26C4×#638—24no—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×#3752C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2212yes—
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32#64133—24no—
33C2×#3750C2212yes—
34C2×#3750C2212yes—
35C2×#3750C2212yes—
36C2×#3750C2212yes—
37C2×#3750C2211yescharacteristic
38C2×C4×C3⋊Dic3C2212yes—
39C2×C4×C3⋊Dic3C2211yescharacteristic
40#64106—24no—
41#63658C2212yes—
42C2×C3×C22⋊Q8D314yescomplemented
43C2×#946—34no—
44C2×#944—34no—
45C2×C4×#67—34no—
46C2×#924—34no—
47C2×#897—34no—
48#4993—38no—
49#4975—38no—
50Dic3×C4⋊C4—34no—
51#4957—38no—
52#4949—38no—
53C24×C32C2311yescharacteristic
54C23×C3⋊D3C2311yescharacteristic
55C2×C32×Q8—22no—
56C2×C32×Q8—22no—
57C2×C32×Q8—22no—
58C22×C32×C4—22no—
59C22×C32×C4—22no—
60C22×C32×C4—22no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×#638—22no—
66C2×#638—22no—
67C2×#638Q814yescomplemented
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×#634—22no—
77C2×#634—22no—
78C2×#634—22no—
79C32×C4⋊C4—24no—
80C32×C4⋊C4D414yescomplemented
81C32×C22⋊C4—24no—
82#3757—24no—
83#3757—22no—
84#3752—24no—
85#3752—22no—
86#3752—24no—
87C4⋊(C3⋊Dic3)—24no—
88C4⋊(C3⋊Dic3)D414yescomplemented
89#3750—24no—
90#3750—22no—
91#3750—24no—
92#3750—24no—
93#3750—24no—
94C4×C3⋊Dic3—24no—
95C4×C3⋊Dic3D414yes—
96#2542—91noSylow
97C22×C3×Q8C2×D314yes—
98C23×C3×C4C2×D314yes—
99C22×#67—34no—
100C22×C4×D3—34no—
101C22×Dic6—34no—
102C3×C22⋊Q8—216no—
103C2×C3×C4⋊C4C2×D318yes—
104C2×C3×C4⋊C4C2×D314yes—
105C2×C3×C22⋊C4C2×D318yes—
106C2×#217—34no—
107C2×#217—38no—
108#946—616no—
109#944—616no—
110C4×#67—616no—
111C2×(C2×D3)⋊C4—38no—
112C2×(C2×D3)⋊C4—38no—
113C2×(C2×D3)⋊C4—34no—
114C2×C4⋊Dic3—34no—
115C2×C4⋊Dic3—38no—
116#924—616no—
117C2×Dic3⋊C4—38no—
118C2×Dic3⋊C4—38no—
119C2×Dic3⋊C4—38no—
120C2×Dic3⋊C4—34no—
121C2×Dic3⋊C4—38no—
122C2×C4×Dic3—34no—
123C2×C4×Dic3—38no—
124#897—616no—
125C3⋊#95—38no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32—21no—
132C23×C32C2×Q812yes—
133C23×C32C2411yescharacteristic
134C22×C3⋊D3—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3C2×Q812yes—
141C32×Q8—44no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—21no—
145C2×C32×C4—22no—
146C2×C32×C4—21no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—21no—
150C2×C32×C4—44no—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D414yes—
154C2×C32×C4C2×D412yes—
155#638—28no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D414yes—
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×Q812yes—
170C2×C3⋊Dic3#4112yes—
171C4×C3⋊D3—44no—
172#634—44no—
173C2×C4⋊Q8—91no—
174C2×C22⋊Q8—91no—
175C2×C22⋊Q8—91no—
176C2×C22⋊Q8—91no—
177C2×C22⋊Q8C3⋊D311yescharacteristic, complemented
178C2×C4×D4—91no—
179#399—92no—
180#399—92no—
181#390—92no—
182#384—92no—
183C4×C4⋊C4—91no—
184C24×C3C22×D314yes—
185C23×D3—34no—
186C2×C3×Q8—28no—
187C2×C3×Q8—28no—
188C2×C3×Q8—28no—
189C22×C3×C4—28no—
190C22×C3×C4—28no—
191C22×C3×C4—28no—
192C22×C3×C4C22×D318yes—
193C22×C3×C4C22×D314yes—
194C22×C3×C4C22×D318yes—
195C22×C3×C4C22×D314yes—
196C2×#67—316no—
197C2×#67—68no—
198C2×#67—68no—
199C22×Dic3—34no—
200C22×Dic3—34no—
201C22×Dic3—38no—
202C22×Dic3—34no—
203C22×Dic3—38no—
204C2×C4×D3—68no—
205C2×C4×D3—68no—
206C2×C4×D3—68no—
207C2×Dic6—68no—
208C2×Dic6—68no—
209C2×Dic6—68no—
210C3×C4⋊C4—216no—
211C3×C4⋊C4#67116yescomplemented
212C3×C22⋊C4—216no—
213#217—616no—
214#217—68no—
215(C2×D3)⋊C4—68no—
216(C2×D3)⋊C4—616no—
217(C2×D3)⋊C4—616no—
218C4⋊Dic3—316no—
219C4⋊Dic3—616no—
220Dic3⋊C4—616no—
221Dic3⋊C4—68no—
222Dic3⋊C4—616no—
223Dic3⋊C4—616no—
224Dic3⋊C4—616no—
225C4×Dic3—316no—
226C4×Dic3—616no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32C22×D411yescharacteristic
235C22×C32C22×D411yescharacteristic
236C22×C32C22×D411yescharacteristic
237C22×C32C22×Q811yescharacteristic
238C22×C32C2×#4111yescharacteristic
239C22×C322−1+411yescharacteristic
240C22×C322−1+411yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C32×C4—24no—
249C32×C4—41no—
250C32×C4—42no—
251C32×C4#12714yes—
252C3⋊Dic3—22no—
253C3⋊Dic3—24no—
254C3⋊Dic3—42no—
255C3⋊Dic3—41no—
256C3⋊Dic3C22⋊Q814yescomplemented
257C22×Q8—91no—
258C22×Q8C2×C3⋊D311yescharacteristic
259C22×D4—91no—
260C23×C4—91no—
261C23×C4C2×C3⋊D311yescharacteristic
262C4⋊Q8—184no—
263C22⋊Q8—24no—
264C22⋊Q8—184no—
265C22⋊Q8—184no—
266C22⋊Q8—184no—
267C4×D4—184no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—92no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4—92no—
275C2×C4⋊C4C2×C3⋊D312yes—
276C2×C4⋊C4C2×C3⋊D311yescharacteristic
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4C2×C3⋊D312yes—
283C2×C42—91no—
284C2×C42—92no—
285#95—92no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—24no—
289C23×C3—24no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3D3×Q818yes—
293C23×C3C23×D314yes—
294C22×D3—38no—
295C22×D3—64no—
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3—64no—
301C3×Q8—416no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4—24no—
305C2×C3×C4—28no—
306C2×C3×C4—24no—
307C2×C3×C4—28no—
308C2×C3×C4—28no—
309C2×C3×C4—24no—
310C2×C3×C4—416no—
311C2×C3×C4D3×D418yes—
312C2×C3×C4D3×D418yes—
313C2×C3×C4C2×#67116yes—
314C2×C3×C4C2×#6718yes—
315#67—632no—
316C2×Dic3—38no—
317C2×Dic3—38no—
318C2×Dic3—38no—
319C2×Dic3—38no—
320C2×Dic3—316no—
321C2×Dic3—64no—
322C2×Dic3—68no—
323C2×Dic3—68no—
324C2×Dic3—64no—
325C2×Dic3—68no—
326C2×Dic3—64no—
327C2×Dic3—68no—
328C2×Dic3—64no—
329C2×Dic3—64no—
330C2×Dic3—68no—
331C4×D3—1216no—
332Dic6—1216no—
333C2×C32—42no—
334C2×C32C2×C22⋊Q811yescharacteristic
335C2×C32C2×#12711yescharacteristic
336C2×C32#53611yescharacteristic
337C2×C32#54711yescharacteristic
338C2×C32#54711yescharacteristic
339C2×C32D4×Q811yescharacteristic
340C2×C32D4×Q811yescharacteristic
341C3⋊D3—42no—
342C24—91no—
343C24C22×C3⋊D311yescharacteristic
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—182no—
348C2×Q8—182no—
349C2×Q8—182no—
350C2×D4—94no—
351C2×D4—182no—
352C2×D4—182no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—91no—
361C22×C4—182no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4C22×C3⋊D312yes—
365C22×C4C22×C3⋊D311yescharacteristic
366C22×C4C22×C3⋊D312yes—
367C22×C4C22×C3⋊D311yescharacteristic
368C4⋊C4—24no—
369C4⋊C4—94no—
370C4⋊C4—182no—
371C4⋊C4—184no—
372C4⋊C4—184no—
373C4⋊C4—184no—
374C4⋊C4—184no—
375C4⋊C4—184no—
376C4⋊C4#63814yescomplemented
377C22⋊C4—24no—
378C22⋊C4—182no—
379C22⋊C4—184no—
380C22⋊C4—182no—
381C22⋊C4—184no—
382C22⋊C4—184no—
383C42—94no—
384C42—184no—
385C22×C3—28no—
386C22×C3—28no—
387C22×C3—28no—
388C22×C3—44no—
389C22×C3—44no—
390C22×C3—44no—
391C22×C3—44no—
392C22×C3C2×D3×D414yes—
393C22×C3C2×D3×D414yes—
394C22×C3C2×D3×Q814yes—
395C22×C3#100714yes—
396C22×C3D3×#4114yes—
397C22×C3#101014yes—
398C22×C3C22×#6714yes—
399C2×D3—68no—
400C2×D3—68no—
401C2×D3—68no—
402C2×D3—124no—
403C2×D3—124no—
404C2×D3—124no—
405C2×D3—124no—
406C3×C4—216no—
407C3×C4—44no—
408C3×C4—48no—
409C3×C4#940116yes—
410Dic3—316no—
411Dic3—68no—
412Dic3—616no—
413Dic3—128no—
414Dic3—124no—
415C32#254211yescharacteristic, complemented, Sylow
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—92no—
423C23—181no—
424C23—181no—
425C23—181no—
426C23—181no—
427C23—181no—
428C23—181no—
429C23Q8×C3⋊D312yes—
430C23C23×C3⋊D311yescharacteristic
431Q8—44no—
432Q8—364no—
433D4—188no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—44no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—92no—
447C2×C4—94no—
448C2×C4—181no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—182no—
454C2×C4—181no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—181no—
458C2×C4—364no—
459C2×C4D4×C3⋊D312yes—
460C2×C4D4×C3⋊D312yes—
461C2×C4C2×#63814yes—
462C2×C4C2×#63812yes—
463C2×C3—48no—
464C2×C3D3×C22⋊Q814yes—
465C2×C3#562814yes—
466C2×C3#563114yes—
467C2×C3#563214yes—
468C2×C3C2×#94014yes—
469C2×C3Q8×#6714yes—
470C2×C3#582414yes—
471D3—128no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—182no—
480C22—182no—
481C22—182no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22—361no—
486C22C2×D4×C3⋊D311yescharacteristic
487C22C2×D4×C3⋊D311yescharacteristic
488C22C2×Q8×C3⋊D311yescharacteristic
489C22#6436411yescharacteristic
490C22#41×C3⋊D311yescharacteristic
491C22#6436711yescharacteristic
492C22C22×#63811yescharacteristic
493C4—24no—
494C4—41no—
495C4—42no—
496C4—94no—
497C4—182no—
498C4—184no—
499C4—361no—
500C4—362no—
501C4#6414914yes—
502C3#8278014yescomplemented
503C2—42no—
504C2—362no—
505C2C3⋊D3×C22⋊Q811yescharacteristic
506C2#1059609911yescharacteristic
507C2#1059610211yescharacteristic
508C2#1059610311yescharacteristic
509C2C2×#6414911yescharacteristic
510C2Q8×#63811yescharacteristic
511C2#1059629511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊Q8C2
prime radicalC22×#638C22
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C22⋊Q8C2semidirect
2. C2×#64155C2semidirect
3. C2×#64153C2semidirect
5. C2×#64133C2semidirect
6. C2×#64106C2semidirect
7. #10592692C2semidirect
8. #10592674C2semidirect
9. C4⋊C4×C3⋊Dic3C2semidirect
11. #10592648C2semidirect
42. C2×C3×C22⋊Q8D3semidirect
67. C2×#638Q8semidirect
80. C32×C4⋊C4D4semidirect
88. C4⋊(C3⋊Dic3)D4semidirect
177. C2×C22⋊Q8C3⋊D3semidirect
211. C3×C4⋊C4#67semidirect
256. C3⋊Dic3C22⋊Q8semidirect
376. C4⋊C4#638semidirect
415. C32#2542semidirect
502. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C2×#641552
C2×#641532
C2×C4×#6382
C2×#641332
C2×#641062
#105926922
#105926742
C4⋊C4×C3⋊Dic32
#105926562
#105926482
#827803