Finite Group Databasebeta

← #11786516

Subgroups — #11786516

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63849C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic
3C2×#63575C211yesmaximal, characteristic, complemented
4C2×#63573C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8#68877—31nomaximal
9#68876—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—21no—
19C2×Dic32—21no—
20#63849—22no—
21#63849—22no—
22#63658—21no—
23#63575—22no—
24#63573—22no—
25#63557C414yescomplemented
26C2×#892—31no—
27C2×#892—31no—
28C2×(C2×D3)⋊C8—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×#818—31no—
31C2×#817—31no—
32#4987—31no—
33#4987—31no—
34#4987—61no—
35C2×#808—31no—
36C2×#807—31no—
37C3×#340—31no—
38C3×#340—31no—
39#4529D311yescharacteristic, complemented
40#4529D311yescharacteristic, complemented
41C23×C3⋊D3D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3C2×C412yes—
51C2×C4×C3⋊D3Q812yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56#3752—42no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8C2×C412yes—
69#3722—24no—
70Dic32—24no—
71#1854—91noSylow
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—61no—
75C22×C3×C8—31no—
76C22×C3×C8—31no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×(C2×D3)⋊C4—62no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96#892—62no—
97#892—62no—
98#892—62no—
99#892—62no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—62no—
103(C2×D3)⋊C8—34no—
104(C2×D3)⋊C8—34no—
105#818—62no—
106#817—62no—
107#808—62no—
108#807—62no—
109C23×C32C2×D411yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3C4⋊C412yes—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3C4⋊C412yes—
132C4×C3⋊D3—22no—
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C2×#117—91no—
145C2×#107—91no—
146C2×#106—91no—
147C2×C22⋊C8—91no—
148#380—91no—
149#340—31no—
150#340—31no—
151C23×D3—31no—
152C23×D3—31no—
153C23×D3—61no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C2×C4×D3—32no—
171C2×C4×D3—32no—
172C2×C4×D3—32no—
173C2×C4×D3—32no—
174C2×C4×D3—62no—
175C2×C4×D3—62no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—121no—
185C2×C4×D3—121no—
186C2×C4×D3—121no—
187C2×C4×D3—121no—
188C2×C3×C8—32no—
189C2×C3×C8—32no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204(C2×D3)⋊C4—64no—
205(C2×D3)⋊C4—64no—
206(C2×D3)⋊C4—124no—
207(C2×D3)⋊C4—122no—
208(C2×D3)⋊C4—122no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217C4⋊Dic3D1212yes—
218C4⋊Dic3D1212yes—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C4×D312yes—
226C2×C3⋊C8C4×D312yes—
227C22×C32C2×C4⋊C411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32#12311yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32#13511yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32#13711yescharacteristic
234C2×C3⋊D3—22no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—22no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C32×C4—81no—
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—22no—
247C3⋊Dic3—81no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C23×C4—91no—
251C22×C8—31no—
252C22×C8—31no—
253#117—182no—
254#117—182no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—181no—
260C2×C22⋊C4—181no—
261C2×C42—181no—
262#107—182no—
263#106—182no—
264C22⋊C8—94no—
265#95—181no—
266C23×C3—21no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—32no—
270C22×D3—32no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—62no—
274C22×D3—61no—
275C22×D3—61no—
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—121no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—121no—
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—62no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×C4×D311yescharacteristic
312C2×C3×C4C2×C4×D311yescharacteristic
313C2×C3×C4C2×D1211yescharacteristic
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4D3×Q811yescharacteristic
322C2×C3×C4D3×Q811yescharacteristic
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—62no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—122no—
356C4×D3—122no—
357C4×D3—122no—
358C4×D3—122no—
359C3×C8—62no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—22no—
363C2×C32#38511yescharacteristic
364C2×C32#42711yescharacteristic
365C2×C32#42811yescharacteristic
366C2×C32#44911yescharacteristic
367C2×C32#45211yescharacteristic
368C2×C32#48211yescharacteristic
369C2×C32#48511yescharacteristic
370C3⋊D3—42no—
371C24—91no—
372C22×C4—21no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—91no—
376C22×C4—92no—
377C22×C4—92no—
378C22×C4—181no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384C2×C8—32no—
385C2×C8—32no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—32no—
393C4⋊C4—32no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—184no—
399C22⋊C4—362no—
400C42—184no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3#88211yescharacteristic
409C22×C3#88211yescharacteristic
410C22×C3#88311yescharacteristic
411C22×C3#88311yescharacteristic
412C22×C3D3×C4⋊C411yescharacteristic
413C22×C3D3×C4⋊C411yescharacteristic
414C22×C3#91111yescharacteristic
415C22×C3#91211yescharacteristic
416C22×C3#91411yescharacteristic
417C22×C3#91511yescharacteristic
418C22×C3#91611yescharacteristic
419C22×C3#91611yescharacteristic
420C22×C3#91811yescharacteristic
421C22×C3#91911yescharacteristic
422C2×D3—64no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—121no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—82no—
448C3×C4—81no—
449C3×C4—81no—
450C3×C4—122no—
451C3×C4—122no—
452C3×C4C4×D1211yescharacteristic
453C3×C4C4×D1211yescharacteristic
454C3×C4#67⋊C411yescharacteristic
455C3×C4#67⋊C411yescharacteristic
456C3×C4#89611yescharacteristic
457C3×C4#89611yescharacteristic
458C3×C4#89711yescharacteristic
459C3×C4#89711yescharacteristic
460Dic3—42no—
461Dic3—42no—
462Dic3—62no—
463Dic3—62no—
464Dic3—122no—
465Dic3—242no—
466Dic3—241no—
467Dic3—241no—
468C32#185411yescharacteristic, complemented, Sylow
469C23—92no—
470C23—181no—
471C23—181no—
472C23—181no—
473C23—181no—
474C23—181no—
475C23—181no—
476C23#381111yescharacteristic
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—92no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—182no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—182no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4—361no—
496C2×C4#379711yescharacteristic
497C2×C4C4×D3211yescharacteristic
498C2×C4D3×D1211yescharacteristic
499C2×C4D3×D1211yescharacteristic
500C2×C4#380411yescharacteristic
501C2×C4#380411yescharacteristic
502C8—62no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3#466811yescharacteristic
512C2×C3#466811yescharacteristic
513C2×C3#477911yescharacteristic
514C2×C3#478111yescharacteristic
515C2×C3#478311yescharacteristic
516C2×C3#478411yescharacteristic
517C2×C3#480811yescharacteristic
518C2×C3#481011yescharacteristic
519C2×C3#481411yescharacteristic
520C2×C3#481511yescharacteristic
521C2×C3#486011yescharacteristic
522C2×C3#486111yescharacteristic
523C2×C3#488011yescharacteristic
524C2×C3#488111yescharacteristic
525D3—124no—
526D3—122no—
527D3—122no—
528C22—182no—
529C22—182no—
530C22—182no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22#6388311yescharacteristic
536C22#6392311yescharacteristic
537C22#6393611yescharacteristic
538C22#6393711yescharacteristic
539C22#6395011yescharacteristic
540C22#6395111yescharacteristic
541C22#6397511yescharacteristic
542C4—81no—
543C4—122no—
544C4—122no—
545C4—182no—
546C4—721no—
547C4#6388011yescharacteristic
548C4#6388011yescharacteristic
549C4#6389511yescharacteristic
550C4#6389511yescharacteristic
551C3—21no—
552C3#6887611yescharacteristic, complemented
553C3#6887711yescharacteristic, complemented
554C2—362no—
555C2#1059057411yescharacteristic
556C2#1059058311yescharacteristic
557C2#1059061711yescharacteristic
558C2#1059061811yescharacteristic
559C2#1059137511yescharacteristic
560C2#1059142511yescharacteristic
561C2#1059156111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1854
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
3. C2×#63575C2semidirect
4. C2×#63573C2semidirect
6. C3×#4529C2semidirect
7. C3×#4529C2semidirect
25. #63557C4semidirect
39. #4529D3semidirect
40. #4529D3semidirect
468. C32#1854semidirect
552. C3#68876semidirect
553. C3#68877semidirect

Maximal subgroups

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

subgroupindex
C2×#638492
#105926862
C2×#635752
C2×#635732
C2×#635572
C3×#45292
#688773
#688763