Finite Group Databasebeta

← #11801166

Subgroups — #11801166

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic
3C3×#4651C211yesmaximal, characteristic, complemented
4C3×#4648C211yesmaximal, characteristic, complemented
5#10591371C212yesmaximal
6#10591355C211yesmaximal, characteristic
7#10591247C212yesmaximal, complemented
8#10591243C212yesmaximal, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591233C212yesmaximal
11#10591223C211yesmaximal, characteristic, complemented
12#74258—31nomaximal
13#73413—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3750C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×#3724C2212yes—
23C2×#3722C2212yes—
24C2×Dic32C2212yes—
25C2×Dic32C2211yescharacteristic
26C2×Dic32C2211yescharacteristic
27C4×#624C418yescomplemented
28C32×#95C2211yescharacteristic
29#63658C2211yescharacteristic
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C42×D3—31no—
39C2×C42×D3—31no—
40C3×#383—31no—
41C3×#376—31no—
42C4×(C2×D3)⋊C4—32no—
43#4937—31no—
44#4932—31no—
45C4×Dic3⋊C4—32no—
46#4667—31no—
47#4667—31no—
48#4667—31no—
49#4667—31no—
50#4667—61no—
51#4666—32no—
52#4664—32no—
53#4664—32no—
54#4651—31no—
55#4651D311yescharacteristic, complemented
56#4650—32no—
57#4650—32no—
58#4649—32no—
59#4648—31no—
60#4648D311yescharacteristic, complemented
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—24no—
67C2×C4×C3⋊D3C2×C414yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×#624—22no—
75C2×#624—22no—
76C2×#624—24no—
77C2×#624C2×C414yes—
78C2×#624C2×C414yes—
79#3752—24no—
80#3750—24no—
81C3×C4×Dic3—24no—
82C3×C4×Dic3C2×C414yes—
83C3×C4×Dic3C2×C414yes—
84#3724—24no—
85#3722—24no—
86Dic32—24no—
87Dic32C2×C414yes—
88Dic32C2×C414yes—
89#2283—91noSylow
90C22×C4×D3—31no—
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—31no—
95C22×C4×D3—31no—
96C22×C4×D3—61no—
97C2×C3×C42—31no—
98C2×C3×C42—31no—
99C2×C3×C42—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—62no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4—62no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3C2×D312yes—
117C2×C4×Dic3C2×D311yescharacteristic
118C2×C4×Dic3C2×D311yescharacteristic
119C42×D3—38no—
120C42×D3—38no—
121C3×#95—21no—
122C3×#95—31no—
123C3×#95—32no—
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—31no—
127C3×#95C2×D311yescharacteristic
128C3×#95C2×D311yescharacteristic
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—61no—
138C3⋊#95C2×D312yes—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D311yescharacteristic
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3C22×C412yes—
147C22×C3⋊D3#4112yes—
148C22×C3⋊D3#4112yes—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C412yes—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3C22×C412yes—
158C2×C3⋊Dic3#4114yes—
159C4×C3⋊D3—28no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3#4114yes—
176#624—28no—
177#624—28no—
178C22×C42—91no—
179#383—31no—
180#383—91no—
181#382—92no—
182#381—92no—
183#380—91no—
184#380—91no—
185C4×C4⋊C4—92no—
186C4×C22⋊C4—92no—
187#376—31no—
188#376—91no—
189C23×D3—31no—
190C23×D3—31no—
191C23×D3—61no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D311yescharacteristic
216C2×C4×D3—34no—
217C2×C4×D3—34no—
218C2×C4×D3—34no—
219C2×C4×D3—34no—
220C2×C4×D3—34no—
221C2×C4×D3—34no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—124no—
232C3×C42—34no—
233C3×C42—34no—
234C3×C42—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—124no—
240Dic3⋊C4—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—64no—
244Dic3⋊C4—124no—
245C4×Dic3—24no—
246C4×Dic3—34no—
247C4×Dic3—34no—
248C4×Dic3—34no—
249C4×Dic3—34no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C4×Dic3C4×D314yes—
253C4×Dic3C4×D314yes—
254C22×C32C23×C411yescharacteristic
255C22×C32C2×#4112yes—
256C22×C32C2×#4111yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C22×C32C2×#4112yes—
259C2×C3⋊D3—22no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—24no—
262C2×C3⋊D3—24no—
263C2×C3⋊D3#11714yes—
264C32×C4—22no—
265C32×C4—42no—
266C3⋊Dic3—42no—
267C3⋊Dic3#11714yes—
268C3×Dic3—22no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3#11714yes—
274C23×C4—91no—
275C23×C4—91no—
276C23×C4—91no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C42—31no—
282C2×C42—31no—
283C2×C42—32no—
284C2×C42—98no—
285C2×C42—91no—
286C2×C42—91no—
287C2×C42—92no—
288#95—31no—
289#95—32no—
290#95—31no—
291#95—32no—
292#95—32no—
293#95—92no—
294#95—92no—
295#95—92no—
296#95—91no—
297#95D3211yescharacteristic
298C23×C3—21no—
299C23×C3C23×D311yescharacteristic
300C23×C3C23×D311yescharacteristic
301C22×D3—32no—
302C22×D3—32no—
303C22×D3—32no—
304C22×D3—32no—
305C22×D3—32no—
306C22×D3—32no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—122no—
315C22×D3—122no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—32no—
326C2×C3×C4—34no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4C2×C4×D312yes—
346C2×C3×C4C2×C4×D312yes—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—62no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3C2×C4×D312yes—
374C2×Dic3C2×C4×D312yes—
375C2×Dic3C2×C4×D312yes—
376C2×Dic3C2×C4×D312yes—
377C2×Dic3#23514yes—
378C4×D3—68no—
379C4×D3—68no—
380C4×D3—68no—
381C4×D3—68no—
382C4×D3—68no—
383C4×D3—68no—
384C4×D3—128no—
385C2×C32C2×#11711yescharacteristic
386C2×C32C2×#11711yescharacteristic
387C2×C32C2×#11711yescharacteristic
388C2×C32#52912yes—
389C2×C32#52912yes—
390C3⋊D3—24no—
391C24—91no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—94no—
399C22×C4—94no—
400C22×C4—91no—
401C22×C4—94no—
402C22×C4—92no—
403C22×C4—184no—
404C22×C4—184no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4C2×D3212yes—
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—184no—
410C4⋊C4—184no—
411C22⋊C4—184no—
412C22⋊C4—184no—
413C42—34no—
414C42—34no—
415C42—64no—
416C42—94no—
417C42—94no—
418C42—184no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3C22×C4×D311yescharacteristic
425C22×C3C22×C4×D311yescharacteristic
426C22×C3C2×#23512yes—
427C22×C3D3×#4112yes—
428C22×C3D3×#4112yes—
429C22×C3D3×#4111yescharacteristic
430C22×C3D3×#4112yes—
431C22×C3D3×#4111yescharacteristic
432C22×C3D3×#4111yescharacteristic
433C22×C3D3×#4111yescharacteristic
434C2×D3—34no—
435C2×D3—34no—
436C2×D3—64no—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—122no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—122no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—34no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—82no—
459C3×C4—122no—
460C3×C4—122no—
461Dic3—22no—
462Dic3—22no—
463Dic3—22no—
464Dic3—34no—
465Dic3—34no—
466Dic3—42no—
467Dic3—42no—
468Dic3—64no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3#87214yes—
473C32#228311yescharacteristic, complemented, Sylow
474C23—92no—
475C23—92no—
476C23—92no—
477C23—182no—
478C23—182no—
479C23C22×D3211yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—32no—
485C2×C4—34no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—92no—
501C2×C4—94no—
502C2×C4—188no—
503C2×C4—188no—
504C2×C4—188no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4C4×D3212yes—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3C2×#87211yescharacteristic
515C2×C3D3×#11711yescharacteristic
516C2×C3D3×#11711yescharacteristic
517C2×C3D3×#11711yescharacteristic
518C2×C3D3×#11711yescharacteristic
519C2×C3D3×#11711yescharacteristic
520C2×C3#552812yes—
521C2×C3#552812yes—
522C2×C3#570612yes—
523C2×C3#570612yes—
524D3—64no—
525D3—64no—
526D3—124no—
527C22—94no—
528C22—182no—
529C22—184no—
530C22—184no—
531C22—182no—
532C22C2×C4×D3211yescharacteristic
533C22D3×#23512yes—
534C22#6431212yes—
535C22#6431211yescharacteristic
536C22#6431911yescharacteristic
537C4—22no—
538C4—34no—
539C4—42no—
540C4—62no—
541C4—62no—
542C4—62no—
543C4—94no—
544C4—122no—
545C4—122no—
546C4—362no—
547C3—21no—
548C3#7341311yescharacteristic, complemented
549C3#7425811yescharacteristic, complemented
550C2—184no—
551C2D3×#87211yescharacteristic
552C2#1059405211yescharacteristic
553C2#1059410612yes—
554C2#1059441712yes—
555C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2283
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4651C2semidirect
4. C3×#4648C2semidirect
7. #10591247C2semidirect
8. #10591243C2semidirect
9. #10591239C2semidirect
11. #10591223C2semidirect
27. C4×#624C4semidirect
55. #4651D3semidirect
60. #4648D3semidirect
473. C32#2283semidirect
548. C3#73413semidirect
549. C3#74258semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
#105923662
C3×#46512
C3×#46482
#105913712
#105913552
#105912472
#105912432
#105912392
#105912332
#105912232
#742583
#734133