Finite Group Databasebeta

← #11788209

Subgroups — #11788209

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2#10595034C211yesmaximal, characteristic
3C2×C3×#805C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591074C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70383—31nomaximal
9#68757—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—21no—
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64081—22no—
17#64081—22no—
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63981—21no—
22#63962—21no—
23#63916C412yescomplemented
24C4×#626—22no—
25#63871C412yescomplemented
26C3×#805—22no—
27#63568—22no—
28#63557—22no—
29#5828—31no—
30#5524—31no—
31C2×#872—31no—
32C2×#872—31no—
33C2×#872—61no—
34C2×C3×#104—31no—
35C2×#837—31no—
36C2×#825—31no—
37#5126—31no—
38#5126—31no—
39C2×#805D311yescharacteristic, complemented
40C3×#339—31no—
41#4555—31no—
42#4532—31no—
43#4523D311yescharacteristic, complemented
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3C2×C412yes—
54C2×C4×C3⋊D3D412yes—
55C2×C3×#67—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12C2×C411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6C2×C411yescharacteristic
63C2×#626—22no—
64C32×C42—21no—
65C32×C42D412yescomplemented
66#3752—24no—
67#3750—24no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3D412yescomplemented
70C3×#217—21no—
71C3×C4⋊Dic3C2×C412yes—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82#1897—91noSylow
83C2×C3×#41—31no—
84C2×#235C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C3×#117—31no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C2×D311yescharacteristic
94#946—32no—
95#938—32no—
96#937—61no—
97#935—61no—
98C4×#67—62no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—62no—
102#926C2×D311yescharacteristic
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—62no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—61no—
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#897—32no—
112#895—32no—
113#886—61no—
114#882—61no—
115C4×D12—62no—
116#872—62no—
117#872—62no—
118#872—64no—
119#872—64no—
120#872—62no—
121#872—62no—
122C3×#104—62no—
123#837—62no—
124#825—62no—
125(C2×D3)⋊C8—62no—
126(C2×D3)⋊C8—62no—
127#805—22no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3C22⋊C412yes—
133C22×C3×D3—21no—
134C2×C32×C4—22no—
135C2×C32×C4—42no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—42no—
146C2×C3⋊Dic3C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149C4×C3⋊D3—22no—
150C4×C3⋊D3—22no—
151C3×#67—41no—
152C3×#67—41no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161#626—44no—
162C3×C3⋊C8—41no—
163C3×C3⋊C8—41no—
164#525—91no—
165C2×#117—91no—
166C2×#104—31no—
167C2×#104—91no—
168#407—91no—
169#339—31no—
170#339—91no—
171C23×D3—31no—
172C23×D3—31no—
173C23×D3—61no—
174C3×#41—61no—
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C2×C3×Q8—31no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—21no—
189C2×#67—62no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200C2×D12—62no—
201C2×D12C4×D311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—62no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×Dic6C4×D311yescharacteristic
222C3×M16—61no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C3×C4⋊C4—32no—
229C3×C22⋊C4—61no—
230C3×C42—22no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—22no—
234C3×C42—61no—
235C3×C42D1212yescomplemented
236C3×C42#6712yescomplemented
237#217—21no—
238#217—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—62no—
246C4⋊Dic3C4×D312yes—
247Dic3⋊C4—62no—
248Dic3⋊C4—68no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C4×Dic3—21no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258#208—21no—
259#208—21no—
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C22×C32—22no—
265C22×C32C2×C22⋊C411yescharacteristic
266C22×C32#12011yescharacteristic
267C22×C32#12311yescharacteristic
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3×D3—41no—
274C2×C3×D3—42no—
275C32×C4—42no—
276C32×C4C4×D411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12111yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—42no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C2×#41—31no—
285C23×C4—91no—
286C2×M16—31no—
287C2×M16—31no—
288#123—181no—
289C22⋊Q8—92no—
290#121—92no—
291#120—181no—
292C4×D4—182no—
293#117—31no—
294#117—182no—
295#117—182no—
296C2×C4⋊C4—181no—
297C2×C22⋊C4—181no—
298C2×C42—91no—
299C2×C42D3211yescharacteristic
300#104—62no—
301#104—182no—
302C22⋊C8—182no—
303C23×C3—21no—
304C23×C3—61no—
305C23×C3D3×D411yescharacteristic
306C23×C3D3×D411yescharacteristic
307C22×D3—21no—
308C22×D3—32no—
309C22×D3—32no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—61no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—124no—
320C3×Q8—61no—
321C3×Q8—61no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—44no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23911yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354#67—41no—
355#67—41no—
356#67—124no—
357C2×Dic3—22no—
358C2×Dic3—21no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—124no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374D12—21no—
375D12—21no—
376D12—124no—
377C4×D3—41no—
378C4×D3—41no—
379C4×D3—64no—
380C4×D3—64no—
381C4×D3—64no—
382C4×D3—64no—
383C4×D3—62no—
384C4×D3—62no—
385C4×D3—62no—
386C4×D3—62no—
387C4×D3—62no—
388C4×D3—62no—
389C4×D3—62no—
390C4×D3—62no—
391Dic6—21no—
392Dic6—21no—
393C3×C8—121no—
394C3×C8—121no—
395C3⋊C8—41no—
396C3⋊C8—41no—
397C2×C32—21no—
398C2×C32—21no—
399C2×C32#38611yescharacteristic
400C2×C32#42112yes—
401C3⋊D3—42no—
402C3×D3—81no—
403C24—91no—
404#41—61no—
405#41—61no—
406#41—61no—
407#41—61no—
408C2×Q8—31no—
409C2×D4—31no—
410C2×D4—61no—
411C2×D4—182no—
412C22×C4—21no—
413C22×C4—61no—
414C22×C4—91no—
415C22×C4—92no—
416C22×C4—92no—
417C22×C4—181no—
418C22×C4—181no—
419C22×C4—181no—
420C22×C4—181no—
421C22×C4—181no—
422C22×C4C2×D3211yescharacteristic
423M16—61no—
424M16—61no—
425M16—61no—
426M16—61no—
427C2×C8—61no—
428C2×C8—61no—
429C4⋊C4—32no—
430C4⋊C4—184no—
431C4⋊C4—182no—
432C22⋊C4—61no—
433C22⋊C4—184no—
434C22⋊C4—182no—
435C22⋊C4—182no—
436C42—21no—
437C42—61no—
438C42—92no—
439C42—181no—
440C42#62612yescomplemented
441C22×C3—24no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—121no—
448C22×C3—122no—
449C22×C3D3×C22⋊C411yescharacteristic
450C22×C3D3×C22⋊C411yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3#88311yescharacteristic
453C22×C3#89411yescharacteristic
454C22×C3#93711yescharacteristic
455C2×D3—41no—
456C2×D3—42no—
457C2×D3—64no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—44no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—121no—
480C3×C4—122no—
481C3×C4C4×D1211yescharacteristic
482C3×C4#67⋊C411yescharacteristic
483C3×C4#88411yescharacteristic
484C3×C4#88411yescharacteristic
485C3×C4#89311yescharacteristic
486C3×C4#89511yescharacteristic
487C3×C4C4×#6711yescharacteristic
488C3×C4#93811yescharacteristic
489Dic3—41no—
490Dic3—42no—
491Dic3—64no—
492Dic3—62no—
493Dic3—62no—
494Dic3—124no—
495Dic3—122no—
496Dic3—122no—
497C32#189711yescharacteristic, complemented, Sylow
498C23—61no—
499C23—92no—
500C23—181no—
501C23—181no—
502C23—362no—
503C23#381111yescharacteristic
504Q8—61no—
505Q8—61no—
506D4—61no—
507D4—61no—
508D4—121no—
509D4—121no—
510D4—364no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—62no—
514C2×C4—61no—
515C2×C4—92no—
516C2×C4—121no—
517C2×C4—121no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—182no—
521C2×C4—182no—
522C2×C4—182no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—362no—
526C2×C4#379611yescharacteristic
527C2×C4#379811yescharacteristic
528C2×C4C4×D3211yescharacteristic
529C2×C4#380211yescharacteristic
530C2×C4C2×#62611yescharacteristic
531C2×C4#381111yescharacteristic
532C8—121no—
533C8—121no—
534C2×C3—22no—
535C2×C3—22no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—22no—
542C2×C3—241no—
543C2×C3#466511yescharacteristic
544C2×C3#482112yes—
545C2×C3#482112yes—
546C2×C3#495611yescharacteristic
547D3—81no—
548D3—124no—
549D3—122no—
550D3—122no—
551C22—22no—
552C22—121no—
553C22—122no—
554C22—182no—
555C22—182no—
556C22—182no—
557C22—362no—
558C22—362no—
559C22#6385311yescharacteristic
560C22#6392111yescharacteristic
561C22#6398111yescharacteristic
562C4—42no—
563C4—121no—
564C4—122no—
565C4—182no—
566C4—362no—
567C4#6388111yescharacteristic
568C4C4×#62611yescharacteristic
569C4#6391211yescharacteristic
570C4#6391611yescharacteristic
571C3—21no—
572C3#6875711yescharacteristic, complemented
573C3#7038311yescharacteristic, complemented
574C2—21no—
575C2—21no—
576C2—241no—
577C2—362no—
578C2#1059039412yes—
579C2#1059138711yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595034C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
3. C2×C3×#805C2semidirect
4. C2×#63568C2semidirect
5. #10591074C2semidirect
6. C3×#4523C2semidirect
7. #10589160C2semidirect
23. #63916C4semidirect
25. #63871C4semidirect
39. C2×#805D3semidirect
43. #4523D3semidirect
65. C32×C42D4semidirect
69. C4×C3⋊Dic3D4semidirect
235. C3×C42D12semidirect
236. C3×C42#67semidirect
440. C42#626semidirect
497. C32#1897semidirect
572. C3#68757semidirect
573. C3#70383semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
#105950342
C2×C3×#8052
C2×#635682
#105910742
C3×#45232
#105891602
#703833
#687573