Finite Group Databasebeta

← #11786835

Subgroups — #11786835

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2#10592671C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70638—31nomaximal
9#70167—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20#63898—22no—
21#63898—22no—
22#63658—21no—
23C3×#809—22no—
24C3×#807—22no—
25#63563C414yescomplemented
26C2×D4×Dic3—31no—
27C2×#893—31no—
28C2×C3×#107—31no—
29C2×C3×#102—31no—
30C2×#832—31no—
31C2×#821—31no—
32#4972—31no—
33#4972—31no—
34#4972—61no—
35C2×#809D311yescharacteristic
36C2×#807D311yescharacteristic, complemented
37#4551—31no—
38#4550—31no—
39#4550—31no—
40#4529—31no—
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2×C412yescomplemented
61#3750—42no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72(C2×D3)⋊Dic3—24no—
73#1862—91noSylow
74C22×C3×D4—31no—
75C23×Dic3—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—61no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×#217—61no—
85D4×Dic3—62no—
86D4×Dic3—62no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—62no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100#893—62no—
101#893—62no—
102C3×#107—62no—
103C3×#102—62no—
104#832—34no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95—62no—
108#821—34no—
109#809—22no—
110#807—22no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3D812yes—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12C4⋊C414yescomplemented
144D3×Dic3—48no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147C2×C4×D4—91no—
148C2×#107—31no—
149C2×#102—31no—
150C2×#102—91no—
151#389—91no—
152#340—91no—
153#336—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—64no—
177C22×Dic3—62no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—122no—
181C22×Dic3—122no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12Dic612yes—
186C2×D12C4×D312yes—
187C2×D12#6712yes—
188C2×C4×D3—64no—
189C2×C4×D3—122no—
190C2×C4×D3—122no—
191C2×C3×C8—32no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—61no—
205#217—64no—
206(C2×D3)⋊C4—64no—
207C4⋊Dic3—21no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3#6712yes—
215Dic3⋊C4—122no—
216Dic3⋊C4—122no—
217Dic3⋊C4—124no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—121no—
223C4×Dic3—121no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C4×D312yescomplemented
230C22×C32C4×D411yescharacteristic
231C22×C32#12011yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C22×C32C2×D811yescharacteristic
234C22×C32#13511yescharacteristic
235C22×C32AGL(1,ℤ/8)11yescharacteristic
236C22×C32#13711yescharacteristic
237C2×C3×D3—24no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C32×C4—81no—
245C32×C4C2×C4⋊C411yescharacteristic
246C32×C4C4×D411yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C32×C4#12311yescharacteristic
249C3⋊Dic3—22no—
250C3⋊Dic3—42no—
251C3⋊Dic3—41no—
252C3×Dic3—42no—
253C22×D4—31no—
254C23×C4—181no—
255C22×C8—31no—
256C22×C8—31no—
257C4×D4—182no—
258C4×D4—182no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4—181no—
262C2×C4⋊C4D3211yescharacteristic
263C2×C22⋊C4—181no—
264C2×C42—91no—
265#107—62no—
266#102—62no—
267#102—94no—
268#95—181no—
269C23×C3—21no—
270C23×C3—62no—
271C23×C3—62no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3D3×D411yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C3×D4—34no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—62no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—62no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4C2×Dic611yescharacteristic
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4D3×Q811yescharacteristic
317C2×C3×C4#23911yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—64no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—128no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351D12—22no—
352D12—22no—
353D12—22no—
354D12Dic3⋊C414yescomplemented
355C4×D3—128no—
356C3×C8—62no—
357C3×C8—121no—
358C3⋊C8—22no—
359C3⋊C8—41no—
360C2×C32#38511yescharacteristic
361C2×C32C4×D811yescharacteristic
362C2×C32#44011yescharacteristic
363C2×C32#44711yescharacteristic
364C2×C32#45211yescharacteristic
365C2×C32#47411yescharacteristic
366C2×C32#47811yescharacteristic
367C3×D3—44no—
368C24—61no—
369C2×D4—32no—
370C2×D4—32no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C22×C4—21no—
376C22×C4—61no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—184no—
380C22×C4—181no—
381C22×C4—362no—
382C22×C4—362no—
383C22×C4C2×D3211yescharacteristic
384C2×C8—32no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—32no—
393C4⋊C4—61no—
394C4⋊C4—92no—
395C4⋊C4—181no—
396C4⋊C4—362no—
397C22⋊C4—184no—
398C42—181no—
399C42—181no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—64no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3#87811yescharacteristic
415C22×C3#67⋊C411yescharacteristic
416C22×C3#89311yescharacteristic
417C22×C3#89611yescharacteristic
418C22×C3D3×D811yescharacteristic
419C22×C3D3×D811yescharacteristic
420C22×C3#91111yescharacteristic
421C22×C3#91111yescharacteristic
422C22×C3#91511yescharacteristic
423C22×C3#91611yescharacteristic
424C22×C3#91811yescharacteristic
425C22×C3#91911yescharacteristic
426C22×C3#93711yescharacteristic
427C22×C3#93711yescharacteristic
428C2×D3—24no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—82no—
440C3×C4—81no—
441C3×C4—81no—
442C3×C4—122no—
443C3×C4#87811yescharacteristic
444C3×C4#67⋊C411yescharacteristic
445C3×C4D3×C4⋊C411yescharacteristic
446C3×C4#89411yescharacteristic
447C3×C4C2×Dic3⋊C411yescharacteristic
448C3×C4C4×#6711yescharacteristic
449C3×C4#93511yescharacteristic
450C3×C4#94611yescharacteristic
451Dic3—42no—
452Dic3—62no—
453Dic3—62no—
454Dic3—122no—
455Dic3—122no—
456Dic3—124no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460Dic3—122no—
461C32#186211yescharacteristic, complemented, Sylow
462C23—62no—
463C23—62no—
464C23—62no—
465C23—121no—
466C23—121no—
467C23—121no—
468C23—121no—
469C23#381111yescharacteristic
470D4—34no—
471D4—62no—
472D4—62no—
473D4—62no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—62no—
478C2×C4—92no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—182no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—368no—
488C2×C4—361no—
489C2×C4—361no—
490C2×C4D3×Dic611yescharacteristic
491C2×C4#379511yescharacteristic
492C2×C4#379611yescharacteristic
493C2×C4C4×D3211yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C2×C4D3×#6711yescharacteristic
496C8—62no—
497C8—121no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—124no—
506C2×C3#475611yescharacteristic
507C2×C3#475711yescharacteristic
508C2×C3#475911yescharacteristic
509C2×C3#476311yescharacteristic
510C2×C3#487211yescharacteristic
511C2×C3#488911yescharacteristic
512C2×C3#489011yescharacteristic
513C2×C3#489111yescharacteristic
514C2×C3#494611yescharacteristic
515C2×C3#498911yescharacteristic
516C2×C3#515611yescharacteristic
517C2×C3#515611yescharacteristic
518C2×C3#517311yescharacteristic
519C2×C3#518711yescharacteristic
520D3—44no—
521C22—64no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—122no—
526C22—122no—
527C22—122no—
528C22#6388111yescharacteristic
529C22#6389611yescharacteristic
530C22#6392611yescharacteristic
531C22#6392711yescharacteristic
532C22#6395011yescharacteristic
533C22#6395111yescharacteristic
534C22#6398311yescharacteristic
535C4—81no—
536C4—122no—
537C4—182no—
538C4—361no—
539C4—362no—
540C4D3×Dic3⋊C411yescharacteristic
541C4#6387911yescharacteristic
542C4#6388411yescharacteristic
543C4#6388711yescharacteristic
544C3—21no—
545C3#7016711yescharacteristic, complemented
546C3#7063811yescharacteristic, complemented
547C2—124no—
548C2#1059045911yescharacteristic
549C2#1059046111yescharacteristic
550C2#1059047111yescharacteristic
551C2#1059047311yescharacteristic
552C2#1059137211yescharacteristic
553C2#1059151611yescharacteristic
554C2#1059165611yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1862
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592671C2semidirect
4. C2×C3×#807C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
25. #63563C4semidirect
36. C2×#807D3semidirect
60. C4⋊(C3⋊Dic3)C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
143. C3×D12C4⋊C4semidirect
229. C2×C3⋊C8C4×D3semidirect
354. D12Dic3⋊C4semidirect
461. C32#1862semidirect
545. C3#70167semidirect
546. C3#70638semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
#105926712
C2×C3×#8092
C2×C3×#8072
C2×#635632
#105891642
#105891562
#706383
#701673