Finite Group Databasebeta

← #11801898

Subgroups — #11801898

Order 1152.

2317 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
1C22×#3828C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C3×C4×#217C212yesmaximal, complemented
5#10591722C212yesmaximal, complemented
6#10591704C212yesmaximal, complemented
7#10591380C212yesmaximal, complemented
8C4×#3722C212yesmaximal, complemented
9#10591273C212yesmaximal, complemented
10#73563—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C2×#3828—24no—
15C2×#3828—24no—
16C2×#3828C418yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×#624C2212yes—
22C2×C3×#217C2214yes—
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2214yes—
28C2×Dic32C2212yes—
29C4×#624—24no—
30#63874—24no—
31C3×C3⋊#95C2214yes—
32#63579C2214yes—
33C22×#235—32no—
34C22×#235—61no—
35C2×#872—32no—
36C2×C42×D3—32no—
37C3×C4×C22⋊C4—32no—
38C4×#217D312yescomplemented
39#4957—34no—
40#4956—34no—
41C4×(C2×D3)⋊C4—32no—
42C4×(C2×D3)⋊C4—32no—
43#4665—34no—
44#4646—34no—
45C24×C32C2311yescharacteristic
46C23×C3⋊D3C2311yescharacteristic
47C23×C3⋊D3C2311yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2×C414yescomplemented
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C2×#638—22no—
54C2×#638—22no—
55C2×#638—22no—
56C2×#638—22no—
57C2×#638C2×C414yes—
58C2×#638C2×C414yescomplemented
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61#3828—232no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)C2×C414yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3C2×C414yes—
68C2×C4×C3⋊D3C2×C414yescomplemented
69C2×C4×C3⋊D3D414yes—
70C2×C4×C3⋊D3D414yes—
71C2×#634—22no—
72C2×#634—22no—
73C2×#634C2×C414yescomplemented
74C22×C3×Dic3C2314yes—
75C22×C3×Dic3C2314yes—
76C2×#624—24no—
77C2×#624—28no—
78C3×#217—28no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3—24no—
81#3724—24no—
82#3722—24no—
83#3722—28no—
84Dic32—24no—
85#2297—91noSylow
86C23×C3×C4—21no—
87C23×C3×C4C2×D312yes—
88C22×#67—32no—
89C22×#67—32no—
90C22×#67—61no—
91C22×#67—61no—
92C2×#235—316no—
93C2×#235—68no—
94C2×#235—68no—
95C2×#235—68no—
96C2×#235—68no—
97C2×#235—68no—
98C22×D12—32no—
99C22×D12—61no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—34no—
103C22×C4×D3—61no—
104C22×C4×D3—61no—
105C22×Dic6—32no—
106C22×Dic6—61no—
107C2×C3×C22⋊C4—34no—
108C2×C3×C42—32no—
109C2×C3×C42—32no—
110C2×#217C2×D314yes—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×(C2×D3)⋊C4—34no—
114C2×Dic3⋊C4—34no—
115C2×C4×Dic3—34no—
116C2×C4×Dic3C2×D312yes—
117C2×C4×Dic3C2×D312yes—
118#872—68no—
119C42×D3—68no—
120C3×#95—34no—
121C3⋊#95—34no—
122C3⋊#95—34no—
123C3⋊#95C2×D314yes—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32—24no—
127C23×C32C22×C412yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—24no—
132C22×C3⋊D3—24no—
133C22×C3⋊D3C22×C412yes—
134C22×C3⋊D3C22×C412yes—
135C22×C3⋊D3C2×D412yes—
136C22×C3⋊D3C2×D412yes—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—28no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144#638—28no—
145#638—28no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3C22×C412yes—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3⋊Dic3C2×D412yes—
152C4⋊(C3⋊D3)—28no—
153C4×C3⋊D3—28no—
154C4×C3⋊D3C22⋊C4116yescomplemented
155#634—28no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—24no—
161C2×C3×Dic3#4118yescomplemented
162#624—216no—
163C22×#41—91no—
164C2×#117—91no—
165C22×C42—91no—
166#391—92no—
167#390—92no—
168#386—92no—
169#386—92no—
170C4×C22⋊C4—32no—
171C4×C22⋊C4—92no—
172C24×C3—21no—
173C24×C3C22×D312yes—
174C23×D3—32no—
175C23×D3—32no—
176C23×D3—61no—
177C23×D3—61no—
178C22×C3×C4—24no—
179C22×C3×C4—24no—
180C22×C3×C4—24no—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—34no—
186C22×C3×C4—34no—
187C22×C3×C4C4×D318yescomplemented
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C2×#67—38no—
191C2×#67—38no—
192C2×#67—64no—
193C2×#67—64no—
194C2×#67—64no—
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—64no—
198C2×#67—64no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—64no—
202C22×Dic3—32no—
203C22×Dic3—32no—
204C22×Dic3—61no—
205C22×Dic3—61no—
206C22×Dic3C22×D314yes—
207C22×Dic3C22×D314yes—
208#235—664no—
209#235—664no—
210C2×D12—38no—
211C2×D12—64no—
212C2×D12—64no—
213C2×D12—64no—
214C2×D12—64no—
215C2×D12—64no—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—38no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—68no—
225C2×C4×D3—68no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—68no—
231C2×Dic6—38no—
232C2×Dic6—64no—
233C2×Dic6—64no—
234C2×Dic6—64no—
235C2×Dic6—64no—
236C2×Dic6—64no—
237C3×C22⋊C4—68no—
238C3×C42—64no—
239C3×C42—64no—
240#217—28no—
241(C2×D3)⋊C4—68no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—68no—
244Dic3⋊C4—68no—
245C4×Dic3—24no—
246C4×Dic3—24no—
247C4×Dic3—68no—
248C22×C32—22no—
249C22×C32—24no—
250C22×C32—42no—
251C22×C32—42no—
252C22×C32C23×C411yescharacteristic
253C22×C32C22×D411yescharacteristic
254C22×C32C22×D411yescharacteristic
255C22×C32C2×#4114yes—
256C2×C3⋊D3—22no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3—24no—
259C2×C3⋊D3—24no—
260C2×C3⋊D3—24no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3C2×C22⋊C414yes—
264C32×C4—22no—
265C32×C4C2×C22⋊C414yes—
266C3⋊Dic3—22no—
267C3⋊Dic3C2×C22⋊C414yes—
268C3×Dic3—28no—
269C3×Dic3—44no—
270C2×#41—98no—
271C2×#41—184no—
272C2×#41—184no—
273C22×Q8—91no—
274C22×D4—91no—
275C22×D4—91no—
276C22×D4—91no—
277C23×C4—92no—
278C23×C4—91no—
279C23×C4—91no—
280C23×C4D3211yescharacteristic
281#117—184no—
282C2×C4⋊C4—92no—
283C2×C22⋊C4—34no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—94no—
286C2×C42—32no—
287C2×C42—32no—
288C2×C42—92no—
289C2×C42—184no—
290#95—34no—
291#95—94no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—24no—
298C23×C3—21no—
299C23×C3—22no—
300C23×C3—44no—
301C23×C3C2×C4×D314yes—
302C23×C3C23×D312yes—
303C22×D3—34no—
304C22×D3—34no—
305C22×D3—34no—
306C22×D3—34no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—64no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—64no—
319C22×D3—124no—
320C22×D3—124no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—216no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—216no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—38no—
332C2×C3×C4—64no—
333C2×C3×C4—64no—
334C2×C3×C4—64no—
335C2×C3×C4—64no—
336C2×C3×C4—64no—
337C2×C3×C4C2×C4×D314yes—
338C2×C3×C4C2×C4×D314yes—
339C2×C3×C4D3×D414yes—
340C2×C3×C4D3×D414yes—
341#67—616no—
342#67—616no—
343#67—616no—
344#67—616no—
345C2×Dic3—24no—
346C2×Dic3—24no—
347C2×Dic3—24no—
348C2×Dic3—24no—
349C2×Dic3—24no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3#23518yescomplemented
363D12—616no—
364D12—616no—
365C4×D3—332no—
366C4×D3—616no—
367C4×D3—632no—
368C4×D3—616no—
369C4×D3—616no—
370Dic6—616no—
371Dic6—616no—
372C2×C32—42no—
373C2×C32C22×C22⋊C411yescharacteristic
374C2×C32C4×#4112yes—
375C2×C32#52512yes—
376C2×C32#53212yes—
377C3⋊D3—24no—
378C3⋊D3—42no—
379C24—91no—
380C24—91no—
381C24C2×D3211yescharacteristic
382#41—1832no—
383C2×Q8—94no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×D4—94no—
387C2×D4—94no—
388C2×D4—94no—
389C2×D4—182no—
390C2×D4—182no—
391C2×D4—182no—
392C2×D4—182no—
393C2×D4—182no—
394C2×D4—182no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—34no—
398C22×C4—34no—
399C22×C4—91no—
400C22×C4—94no—
401C22×C4—94no—
402C22×C4—94no—
403C22×C4—91no—
404C22×C4—94no—
405C22×C4—188no—
406C22×C4—184no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4#62414yescomplemented
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C4⋊C4—184no—
413C22⋊C4—68no—
414C22⋊C4—188no—
415C22⋊C4—184no—
416C42—64no—
417C42—64no—
418C42—184no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—24no—
422C22×C3—24no—
423C22×C3—24no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3C22×C4×D312yes—
433C22×C3C2×#23514yes—
434C22×C3C2×D3×D412yes—
435C22×C3C2×D3×D412yes—
436C22×C3D3×#4114yes—
437C2×D3—38no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—68no—
442C2×D3—68no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—124no—
454C2×D3—124no—
455C3×C4—24no—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—68no—
459C3×C4—124no—
460C3×C4D3×C22⋊C418yes—
461Dic3—28no—
462Dic3—38no—
463Dic3—44no—
464Dic3—64no—
465Dic3—64no—
466Dic3—64no—
467C32#229711yescharacteristic, complemented, Sylow
468C23—24no—
469C23—21no—
470C23—21no—
471C23—92no—
472C23—92no—
473C23—92no—
474C23—92no—
475C23—184no—
476C23—184no—
477C23—181no—
478C23—181no—
479C23C2×#62412yes—
480C23C22×D3211yescharacteristic
481Q8—188no—
482D4—188no—
483D4—188no—
484D4—188no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—28no—
488C2×C4—38no—
489C2×C4—64no—
490C2×C4—64no—
491C2×C4—64no—
492C2×C4—64no—
493C2×C4—64no—
494C2×C4—92no—
495C2×C4—92no—
496C2×C4—92no—
497C2×C4—916no—
498C2×C4—92no—
499C2×C4—1816no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—188no—
503C2×C4C2×#62412yes—
504C2×C4C2×#62412yes—
505C2×C4#381112yes—
506C2×C4#381112yes—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—44no—
512C2×C3—44no—
513C2×C3C4×#23512yes—
514C2×C3C2×D3×C22⋊C412yes—
515C2×C3#552212yes—
516C2×C3#554714yes—
517C2×C3#554814yes—
518D3—68no—
519D3—124no—
520D3—124no—
521D3—124no—
522C22—24no—
523C22—22no—
524C22—42no—
525C22—42no—
526C22—94no—
527C22—184no—
528C22—184no—
529C22—184no—
530C22—184no—
531C22—182no—
532C22—362no—
533C22—362no—
534C22D3×#23514yes—
535C22C22×#62411yescharacteristic
536C22C2×#381111yescharacteristic
537C22C2×#381111yescharacteristic
538C4—22no—
539C4—68no—
540C4—94no—
541C4—124no—
542C4—182no—
543C4#6397414yes—
544C3—21no—
545C3#7356312yescomplemented
546C2—42no—
547C2—184no—
548C2—362no—
549C2#1059495412yes—
550C2#1059501712yes—
551C2#1059507612yes—
552C2C2×#6397411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32#2297
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
3. C2×#63874C2semidirect
4. C3×C4×#217C2semidirect
5. #10591722C2semidirect
6. #10591704C2semidirect
7. #10591380C2semidirect
8. C4×#3722C2semidirect
9. #10591273C2semidirect
16. C2×#3828C4semidirect
38. C4×#217D3semidirect
50. C22×C32×C4C2×C4semidirect
58. C2×#638C2×C4semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
73. C2×#634C2×C4semidirect
154. C4×C3⋊D3C22⋊C4semidirect
161. C2×C3×Dic3#41semidirect
187. C22×C3×C4C4×D3semidirect
362. C2×Dic3#235semidirect
409. C22×C4#624semidirect
467. C32#2297semidirect
545. C3#73563semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C4×#6242
C2×#638742
C3×C4×#2172
#105917222
#105917042
#105913802
C4×#37222
#105912732
#735633