Finite Group Databasebeta

← #11804900

Subgroups — #11804900

Order 1152.

1769 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×C4×#627C211yesmaximal, characteristic, complemented
3C2×#63838C211yesmaximal, characteristic, complemented
4#10592365C211yesmaximal, characteristic
5C3×#4646C212yesmaximal, complemented
6#10591396C211yesmaximal, characteristic, complemented
7#10591396C211yesmaximal, characteristic, complemented
8#10591367C212yesmaximal
9#10591355C211yesmaximal, characteristic
10#10591261C212yesmaximal, complemented
11#10591233C212yesmaximal
12#76614—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2212yes—
15C22×#627C2211yescharacteristic
16C22×#627C2211yescharacteristic
17C22×#624C2212yes—
18C2×#3797—24no—
19C2×#3797—24no—
20C2×#3797C418yescomplemented
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2212yes—
31C2×Dic32C2212yes—
32C4×#627—24no—
33#63838—24no—
34C32×#95C2211yescharacteristic
35#63658C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C22×D3×Q8—32no—
42C2×#887—32no—
43C2×C4×Dic6—32no—
44C3×#391—32no—
45#5229—32no—
46#4987—32no—
47C4×(C2×D3)⋊C4—32no—
48#4667—32no—
49#4667—32no—
50#4666—32no—
51#4666—32no—
52#4666—61no—
53#4646—32no—
54#4646—32no—
55#4646—32no—
56#4646D312yescomplemented
57C23×C3⋊D3C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2×C414yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C2×C3×Dic6—24no—
72C2×C3×Dic6—24no—
73C2×C3×Dic6C2×C418yes—
74C2×#627—22no—
75C2×#627—22no—
76C2×#627C2×C414yes—
77C2×#627C2×C414yes—
78C2×#627D414yes—
79C2×#627D414yes—
80C2×#624—24no—
81C2×#624—24no—
82C2×#624C2×C418yes—
83#3797—232no—
84#3752—22no—
85#3752Q814yescomplemented
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3—22no—
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3—24no—
90#3724—22no—
91#3724—22no—
92Dic3⋊Dic3—24no—
93#3722—24no—
94Dic32—24no—
95Q8×C22⋊C4—91noSylow
96C22×C3×Q8—32no—
97C2×D3×Q8—316no—
98C2×D3×Q8—68no—
99C2×D3×Q8—68no—
100C22×C4×D3—32no—
101C22×C4×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—61no—
104C22×Dic6—32no—
105C22×Dic6—32no—
106C22×Dic6C2×D312yes—
107C2×C3×C4⋊C4—32no—
108C2×C3×C42—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4C2×D312yes—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—61no—
125C2×C4×Dic3—61no—
126C2×C4×Dic3C2×D312yes—
127#887—68no—
128C4×Dic6—68no—
129C3×#95—21no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95C2×D312yes—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—61no—
140C3⋊#95C2×D312yes—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D312yes—
143C23×C32C2411yescharacteristic
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3C22×C412yes—
149C22×C3⋊D3C2×Q812yes—
150C22×C3⋊D3#4112yes—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C2×Q812yescomplemented
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3C22×C412yes—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D412yes—
168C2×C3⋊Dic3C2×Q812yescomplemented
169C4×C3⋊D3—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C22×C414yes—
180C2×C3×Dic3C2×D414yes—
181C2×C3×Dic3C2×D414yes—
182C3×Dic6—216no—
183#627—28no—
184#627C22⋊C4116yescomplemented
185#624—216no—
186C23×Q8—91no—
187C2×C4×Q8—91no—
188C2×C4×Q8—91no—
189#391—32no—
190#391—91no—
191#391—91no—
192#391—92no—
193#380—91no—
194#380—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—91no—
197C23×D3—32no—
198C23×D3—61no—
199C2×C3×Q8—38no—
200C2×C3×Q8—64no—
201C2×C3×Q8—64no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222D3×Q8—664no—
223C2×C4×D3—38no—
224C2×C4×D3—38no—
225C2×C4×D3—38no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C2×Dic6—24no—
236C2×Dic6—24no—
237C2×Dic6—38no—
238C2×Dic6—38no—
239C2×Dic6—38no—
240C2×Dic6—38no—
241C2×Dic6—64no—
242C2×Dic6—64no—
243C2×Dic6C4×D318yes—
244C3×C4⋊C4—64no—
245C3×C42—64no—
246(C2×D3)⋊C4—38no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—64no—
253Dic3⋊C4—24no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257C4×Dic3—24no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—122no—
263C4×Dic3—122no—
264C22×C32C23×C411yescharacteristic
265C22×C32C22×D411yescharacteristic
266C22×C32C22×D411yescharacteristic
267C22×C32C22×Q811yescharacteristic
268C22×C32C2×#4111yescharacteristic
269C22×C322−1+411yescharacteristic
270C22×C322−1+411yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3C4×Q814yescomplemented
278C32×C4—22no—
279C32×C4—22no—
280C32×C4—41no—
281C3⋊Dic3—22no—
282C3⋊Dic3—41no—
283C3⋊Dic3C2×C22⋊C414yes—
284C3×Dic3—24no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C3×Dic3C2×C22⋊C418yes—
288C22×Q8—32no—
289C22×Q8—91no—
290C22×Q8—91no—
291C22×Q8—98no—
292C22×Q8—184no—
293C22×Q8—184no—
294C23×C4—92no—
295C23×C4—91no—
296C4×Q8—184no—
297C4×Q8—184no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—92no—
302C2×C22⋊C4—91no—
303C2×C22⋊C4—92no—
304C2×C22⋊C4—91no—
305C2×C42—32no—
306C2×C42—92no—
307C2×C42—91no—
308C2×C42—91no—
309#95—32no—
310#95—32no—
311#95—32no—
312#95—92no—
313#95—92no—
314#95—91no—
315#95D3211yescharacteristic
316C23×C3—21no—
317C23×C3C23×D312yes—
318C22×D3—34no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—121no—
331C22×D3—121no—
332C3×Q8—616no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—34no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—34no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D314yes—
362C2×C3×C4D3×Q814yescomplemented
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3C2×C4×D314yes—
390C2×Dic3C2×C4×D314yes—
391C2×Dic3D3×D414yes—
392C2×Dic3D3×D414yes—
393C4×D3—616no—
394C4×D3—616no—
395C4×D3—616no—
396C4×D3—128no—
397Dic6—216no—
398Dic6—332no—
399Dic6—616no—
400C2×C32C22×C22⋊C411yescharacteristic
401C2×C32C2×C4×Q811yescharacteristic
402C2×C32#51911yescharacteristic
403C2×C32#54811yescharacteristic
404C2×C32#54811yescharacteristic
405C2×C32D4×Q811yescharacteristic
406C2×C32D4×Q811yescharacteristic
407C3⋊D3—24no—
408C24—91no—
409C2×Q8—38no—
410C2×Q8—64no—
411C2×Q8—64no—
412C2×Q8—94no—
413C2×Q8—94no—
414C2×Q8—94no—
415C2×Q8—94no—
416C2×Q8—182no—
417C2×Q8—182no—
418C2×Q8—1832no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—32no—
423C22×C4—98no—
424C22×C4—91no—
425C22×C4—91no—
426C22×C4—94no—
427C22×C4—91no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—184no—
431C22×C4—184no—
432C22×C4C2×D3211yescharacteristic
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—64no—
436C4⋊C4—184no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C22⋊C4—94no—
440C22⋊C4—182no—
441C22⋊C4—184no—
442C42—64no—
443C42—182no—
444C42—182no—
445C42—184no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3C22×C4×D312yes—
454C22×C3C2×D3×D412yes—
455C22×C3C2×D3×D412yes—
456C22×C3C2×D3×Q812yes—
457C22×C3#100712yes—
458C22×C3D3×#4112yes—
459C22×C3#101012yes—
460C2×D3—38no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C3×C4—24no—
475C3×C4—24no—
476C3×C4—38no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—64no—
482C3×C4—122no—
483C3×C4—122no—
484Dic3—24no—
485Dic3—38no—
486Dic3—42no—
487Dic3—42no—
488Dic3—64no—
489Dic3—64no—
490Dic3—122no—
491Dic3—122no—
492Dic3—122no—
493Dic3D3×C22⋊C418yes—
494C32Q8×C22⋊C411yescharacteristic, complemented, Sylow
495C23—92no—
496C23—92no—
497C23—92no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23—181no—
502C23C22×D3211yescharacteristic
503Q8—616no—
504Q8—916no—
505Q8—188no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—92no—
528C2×C4—92no—
529C2×C4—188no—
530C2×C4—1816no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4#379712yescomplemented
537C2×C4C4×D3212yes—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3C2×D3×C22⋊C412yes—
546C2×C3C4×D3×Q812yes—
547C2×C3#557212yes—
548C2×C3#563212yes—
549C2×C3#563312yes—
550C2×C3#567712yes—
551C2×C3#572712yes—
552D3—68no—
553D3—124no—
554C22—94no—
555C22—182no—
556C22—182no—
557C22—182no—
558C22—182no—
559C22—182no—
560C22—182no—
561C22C2×#379711yescharacteristic
562C22C2×C4×D3211yescharacteristic
563C22#6430611yescharacteristic
564C22#6430911yescharacteristic
565C22D32×D411yescharacteristic
566C22D32×D411yescharacteristic
567C22#6431611yescharacteristic
568C4—22no—
569C4—22no—
570C4—38no—
571C4—41no—
572C4—64no—
573C4—94no—
574C4—122no—
575C4—122no—
576C4—182no—
577C4—361no—
578C3—21no—
579C3#7661412yescomplemented
580C2—184no—
581C2C4×#379711yescharacteristic
582C2#1059407211yescharacteristic
583C2#1059419111yescharacteristic
584C2D32×C22⋊C411yescharacteristic
585C2#1059434711yescharacteristic
586C2#1059437911yescharacteristic
587C2#1059452111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32Q8×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#627C2semidirect
3. C2×#63838C2semidirect
5. C3×#4646C2semidirect
6. #10591396C2semidirect
7. #10591396C2semidirect
10. #10591261C2semidirect
20. C2×#3797C4semidirect
56. #4646D3semidirect
85. #3752Q8semidirect
159. C2×C32×C4C2×Q8semidirect
168. C2×C3⋊Dic3C2×Q8semidirect
184. #627C22⋊C4semidirect
277. C2×C3⋊D3C4×Q8semidirect
362. C2×C3×C4D3×Q8semidirect
494. C32Q8×C22⋊C4semidirect
536. C2×C4#3797semidirect
579. C3#76614semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×C4×#6272
C2×#638382
#105923652
C3×#46462
#105913962
#105913672
#105913552
#105912612
#105912332
#766143