Finite Group Databasebeta

← #11786438

Subgroups — #11786438

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C2×C3×#818C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic
5C2×#63576C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70632—31nomaximal
9#68874—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#624—21no—
12C22×C32×C8C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×#3724—21no—
19C2×#3722—21no—
20#63900—22no—
21#63900—22no—
22#63647C414yescomplemented
23C3×#818—22no—
24#63579—21no—
25#63576—22no—
26C2×D3×C4⋊C4—31no—
27C2×D3×C4⋊C4—31no—
28C2×C3×#107—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8—61no—
32C2×#818D311yescharacteristic, complemented
33#4987—31no—
34#4987—31no—
35C2×#807—31no—
36C2×#807—31no—
37C3×#340—31no—
38#4551D311yescharacteristic, complemented
39#4529—31no—
40#4529—31no—
41C23×C3⋊D3D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3C2×C412yes—
49C2×C4×C3⋊D3Q812yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C2×#624—24no—
55C2×#624—42no—
56C2×#624—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8C2×C412yescomplemented
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)C2×C412yescomplemented
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3D412yes—
70C3×C4⋊Dic3D412yes—
71#3724—24no—
72#3722—42no—
73#1852—91noSylow
74C22×C4×D3—31no—
75C22×C4×D3—31no—
76C22×C4×D3—61no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C22×C3×C8—21no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×(C2×D3)⋊C4—61no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97D3×C4⋊C4—62no—
98D3×C4⋊C4—62no—
99D3×C4⋊C4—62no—
100D3×C4⋊C4—62no—
101C3×#107—62no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104(C2×D3)⋊C8—34no—
105(C2×D3)⋊C8—34no—
106(C2×D3)⋊C8—64no—
107#818—22no—
108#807—62no—
109#807—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3⋊D3—21no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3C4⋊C412yes—
116C22×C3⋊D3D812yes—
117C22×C3⋊D3Q1612yes—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3C4⋊C412yes—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—22no—
130C4×C3⋊D3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143#624—48no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146C22×C4⋊C4—91no—
147C2×#107—31no—
148C2×#107—91no—
149C2×C22⋊C8—91no—
150#380—91no—
151#340—31no—
152#340—91no—
153C23×D3—31no—
154C23×D3—31no—
155C23×D3—61no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—31no—
168C22×Dic3—31no—
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—64no—
185C2×C4×D3—64no—
186C2×C4×D3—121no—
187C2×C4×D3—121no—
188C2×C4×D3—121no—
189C2×C4×D3—121no—
190C2×C4×D3—122no—
191C2×C4×D3—122no—
192C2×C4×D3—122no—
193C2×C4×D3—122no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—22no—
199C2×C3×C8—41no—
200C2×C3×C8—41no—
201C2×C3×C8C4×D312yescomplemented
202C2×C3×C8C4×D312yescomplemented
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211(C2×D3)⋊C4—122no—
212(C2×D3)⋊C4—122no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3D1212yes—
220C4⋊Dic3#6712yes—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32C2×D811yescharacteristic
236C22×C32C2×Q1611yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C22×C32#13711yescharacteristic
239C2×C3⋊D3—22no—
240C2×C3⋊D3—22no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3#10714yescomplemented
246C32×C4C4×D411yescharacteristic
247C32×C4C4×D411yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4C22⋊Q811yescharacteristic
250C3⋊Dic3—22no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3—81no—
254C3×Dic3—81no—
255C23×C4—91no—
256C23×C4—181no—
257C22×C8—91no—
258C22×C8D3211yescharacteristic
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—182no—
264C2×C4⋊C4—182no—
265C2×C4⋊C4—181no—
266C2×C22⋊C4—181no—
267#107—62no—
268#107—182no—
269C22⋊C8—94no—
270#95—181no—
271C23×C3—21no—
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C22×D3—32no—
275C22×D3—32no—
276C22×D3—32no—
277C22×D3—32no—
278C22×D3—32no—
279C22×D3—32no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4D3×Q811yescharacteristic
322C2×C3×C4D3×Q811yescharacteristic
323C2×C3×C4#23911yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—62no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C4×D3—62no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—122no—
355C4×D3—122no—
356C4×D3—122no—
357C4×D3—122no—
358C4×D3—128no—
359C4×D3—128no—
360C3×C8—22no—
361C3×C8—22no—
362C3×C8—42no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C3⋊C8—122no—
366C2×C32#38511yescharacteristic
367C2×C32C2×#10711yescharacteristic
368C2×C32#42811yescharacteristic
369C2×C32#44711yescharacteristic
370C2×C32#45111yescharacteristic
371C2×C32#48011yescharacteristic
372C2×C32#48411yescharacteristic
373C3⋊D3—24no—
374C24—91no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—91no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—184no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—181no—
387C22×C4—362no—
388C22×C4—362no—
389C22×C4C2×D3211yescharacteristic
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—92no—
393C2×C8—181no—
394C2×C8—181no—
395C2×C8#62412yescomplemented
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—184no—
405C22⋊C4—362no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3#88211yescharacteristic
414C22×C3#88311yescharacteristic
415C22×C3D3×C4⋊C411yescharacteristic
416C22×C3D3×C4⋊C411yescharacteristic
417C22×C3#89411yescharacteristic
418C22×C3D3×D811yescharacteristic
419C22×C3D3×D811yescharacteristic
420C22×C3#91111yescharacteristic
421C22×C3#91411yescharacteristic
422C22×C3#91511yescharacteristic
423C22×C3D3×Q1611yescharacteristic
424C22×C3D3×Q1611yescharacteristic
425C22×C3#91811yescharacteristic
426C22×C3#93711yescharacteristic
427C2×D3—34no—
428C2×D3—34no—
429C2×D3—64no—
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—122no—
453C3×C4—122no—
454C3×C4—241no—
455C3×C4—241no—
456C3×C4C4×D1211yescharacteristic
457C3×C4#67⋊C411yescharacteristic
458C3×C4#89311yescharacteristic
459C3×C4#89611yescharacteristic
460C3×C4#89611yescharacteristic
461C3×C4#89711yescharacteristic
462C3×C4C4×#6711yescharacteristic
463C3×C4#94611yescharacteristic
464Dic3—42no—
465Dic3—42no—
466Dic3—62no—
467Dic3—62no—
468Dic3—81no—
469Dic3—81no—
470Dic3—122no—
471C32#185211yescharacteristic, complemented, Sylow
472C23—92no—
473C23—92no—
474C23—92no—
475C23—181no—
476C23—181no—
477C23—181no—
478C23—181no—
479C23#380211yescharacteristic
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—92no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—368no—
500C2×C4#379711yescharacteristic
501C2×C4#379911yescharacteristic
502C2×C4D3×D1211yescharacteristic
503C2×C4#380411yescharacteristic
504C2×C4C2×#62411yescharacteristic
505C2×C4D3×#6711yescharacteristic
506C8—22no—
507C8—182no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3#466811yescharacteristic
516C2×C3#477311yescharacteristic
517C2×C3#477411yescharacteristic
518C2×C3#480911yescharacteristic
519C2×C3#481111yescharacteristic
520C2×C3#486111yescharacteristic
521C2×C3D3×#10711yescharacteristic
522C2×C3D3×#10711yescharacteristic
523C2×C3#488111yescharacteristic
524C2×C3#488211yescharacteristic
525C2×C3#488411yescharacteristic
526C2×C3#498911yescharacteristic
527C2×C3#515611yescharacteristic
528C2×C3#518611yescharacteristic
529D3—64no—
530D3—64no—
531D3—124no—
532C22—94no—
533C22—182no—
534C22—182no—
535C22—182no—
536C22—182no—
537C22—182no—
538C22—182no—
539C22#6379711yescharacteristic
540C22#6379811yescharacteristic
541C22#6380211yescharacteristic
542C22#6381111yescharacteristic
543C22#6385411yescharacteristic
544C22#6390011yescharacteristic
545C22#6392211yescharacteristic
546C4—122no—
547C4—122no—
548C4—182no—
549C4—241no—
550C4—241no—
551C4#6388811yescharacteristic
552C4#6389411yescharacteristic
553C4#6389511yescharacteristic
554C4#6395211yescharacteristic
555C3—21no—
556C3#6887411yescharacteristic, complemented
557C3#7063211yescharacteristic, complemented
558C2—184no—
559C2#1059065011yescharacteristic
560C2#1059068711yescharacteristic
561C2#1059068811yescharacteristic
562C2#1059068911yescharacteristic
563C2#1059094511yescharacteristic
564C2#1059095011yescharacteristic
565C2#1059137811yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1852
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#818C2semidirect
5. C2×#63576C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
22. #63647C4semidirect
32. C2×#818D3semidirect
38. #4551D3semidirect
59. C2×C32×C8C2×C4semidirect
62. C2×C3⋊(C3⋊C8)C2×C4semidirect
201. C2×C3×C8C4×D3semidirect
202. C2×C3×C8C4×D3semidirect
245. C2×C3⋊D3#107semidirect
395. C2×C8#624semidirect
471. C32#1852semidirect
556. C3#68874semidirect
557. C3#70632semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#636472
C2×C3×#8182
#105913252
C2×#635762
C3×#45512
#105891632
#706323
#688743