Finite Group Databasebeta

← #11793172

Subgroups — #11793172

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70634—31nomaximal
9#70206—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20#63916—22no—
21#63916—22no—
22#63658—21no—
23C3×#809—22no—
24C3×#807—22no—
25#63563—22no—
26#63557—22no—
27C2×#938—31no—
28C2×#895—31no—
29C2×C3×#107—31no—
30C2×C3×#102—31no—
31C2×#832—31no—
32C2×#821—31no—
33C2×(C2×D3)⋊C8—31no—
34C2×(C2×D3)⋊C8—31no—
35#4987—31no—
36#4987—31no—
37#4987—61no—
38C2×#809D311yescharacteristic, complemented
39C2×#807D311yescharacteristic, complemented
40#4551—31no—
41#4529—31no—
42C23×C3⋊D3D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C2×#626—24no—
62C2×#626—42no—
63C2×#626—42no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66#3752—42no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77(C2×D3)⋊Dic3—24no—
78#2033—91noSylow
79C22×C3×D4—31no—
80C22×#67—61no—
81C22×D12—61no—
82C22×D12C2×D311yescharacteristic
83C22×C4×D3—31no—
84C22×C4×D3—31no—
85C22×C4×D3—61no—
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×#217—61no—
93#938—62no—
94#938—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—62no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#895—62no—
106#895—62no—
107C3×#107—62no—
108C3×#102—62no—
109#832—62no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95—62no—
113#821—62no—
114(C2×D3)⋊C8—62no—
115(C2×D3)⋊C8—62no—
116#809—22no—
117#807—22no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3D812yes—
126C22×C3×D3—22no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—41no—
148C4×C3⋊D3—41no—
149C4×C3⋊D3—41no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3—41no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159#626—48no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×#121—91no—
163C2×#107—31no—
164C2×#102—31no—
165C2×#102—91no—
166C2×C22⋊C8—91no—
167#380—91no—
168#340—91no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3—31no—
172C23×D3—31no—
173C23×D3—61no—
174C2×C3×D4—32no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—64no—
188C2×#67—122no—
189C2×#67—122no—
190C22×Dic3—21no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—62no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—64no—
203C2×D12—122no—
204C2×D12—122no—
205C2×D12#6712yes—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
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—121no—
221C2×C4×D3—121no—
222C2×C4×D3—121no—
223C2×C4×D3—121no—
224C2×C3×C8—32no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—61no—
238#217—64no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—122no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4—124no—
243C4⋊Dic3—21no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—121no—
249C4⋊Dic3—121no—
250C4⋊Dic3#6712yes—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8D1212yescomplemented
257C22×C32#12011yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12311yescharacteristic
260C22×C32C2×D811yescharacteristic
261C22×C32#13511yescharacteristic
262C22×C32AGL(1,ℤ/8)11yescharacteristic
263C22×C32#13711yescharacteristic
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3⋊D3—41no—
270C2×C3⋊D3—41no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C32×C4—81no—
279C32×C4#12111yescharacteristic
280C32×C4#12111yescharacteristic
281C32×C4#12311yescharacteristic
282C32×C4#12411yescharacteristic
283C3⋊Dic3—41no—
284C3⋊Dic3—81no—
285C3×Dic3—42no—
286C22×D4—31no—
287C22×D4—181no—
288C23×C4—91no—
289C22×C8—31no—
290C22×C8—31no—
291#121—182no—
292#121—182no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—181no—
297C2×C22⋊C4—181no—
298#107—62no—
299#102—62no—
300#102—182no—
301C22⋊C8—182no—
302#95—181no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3—121no—
311C23×C3D3×D411yescharacteristic
312C23×C3D3×D411yescharacteristic
313C22×D3—22no—
314C22×D3—32no—
315C22×D3—32no—
316C22×D3—41no—
317C22×D3—41no—
318C22×D3—41no—
319C22×D3—41no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—121no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—62no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4#23511yescharacteristic
365C2×C3×C4#23511yescharacteristic
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23911yescharacteristic
372C2×C3×C4#23911yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375#67—128no—
376C2×Dic3—22no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—122no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397D12—22no—
398D12—22no—
399D12—41no—
400D12—41no—
401D12—128no—
402C4×D3—122no—
403C4×D3—122no—
404C4×D3—122no—
405C4×D3—122no—
406C4×D3—121no—
407C4×D3—121no—
408C4×D3—121no—
409C4×D3—121no—
410C4×D3—121no—
411C4×D3—121no—
412C4×D3—121no—
413C4×D3—121no—
414C3×C8—62no—
415C3×C8—121no—
416C3⋊C8—22no—
417C3⋊C8—41no—
418C2×C32#39411yescharacteristic
419C2×C32#44711yescharacteristic
420C2×C32#45211yescharacteristic
421C2×C32#46611yescharacteristic
422C2×C32#46811yescharacteristic
423C2×C32#48011yescharacteristic
424C2×C32#48211yescharacteristic
425C3⋊D3—42no—
426C3×D3—82no—
427C24—61no—
428C24—91no—
429C2×D4—32no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—184no—
436C2×D4—362no—
437C2×D4—362no—
438C22×C4—21no—
439C22×C4—61no—
440C22×C4—91no—
441C22×C4—181no—
442C22×C4—181no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4—181no—
448C22×C4C2×D3211yescharacteristic
449C2×C8—32no—
450C2×C8—61no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8—61no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—32no—
458C4⋊C4—61no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—184no—
462C22⋊C4—362no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3—241no—
476C22×C3—241no—
477C22×C3#88311yescharacteristic
478C22×C3#88411yescharacteristic
479C22×C3#89411yescharacteristic
480C22×C3#89511yescharacteristic
481C22×C3D3×D811yescharacteristic
482C22×C3D3×D811yescharacteristic
483C22×C3#91111yescharacteristic
484C22×C3#91111yescharacteristic
485C22×C3#91511yescharacteristic
486C22×C3#91611yescharacteristic
487C22×C3#91811yescharacteristic
488C22×C3#91911yescharacteristic
489C22×C3#93711yescharacteristic
490C22×C3#93711yescharacteristic
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—64no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—81no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—81no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—82no—
524C3×C4—81no—
525C3×C4—81no—
526C3×C4—122no—
527C3×C4#88411yescharacteristic
528C3×C4#88511yescharacteristic
529C3×C4#89411yescharacteristic
530C3×C4#89511yescharacteristic
531C3×C4#92911yescharacteristic
532C3×C4#93011yescharacteristic
533C3×C4#93911yescharacteristic
534C3×C4#94711yescharacteristic
535Dic3—42no—
536Dic3—122no—
537Dic3—121no—
538Dic3—121no—
539Dic3—242no—
540Dic3—241no—
541Dic3—241no—
542C32#203311yescharacteristic, complemented, Sylow
543C23—62no—
544C23—92no—
545C23—121no—
546C23—121no—
547C23—121no—
548C23—121no—
549C23—121no—
550C23—121no—
551C23—181no—
552C23—181no—
553C23—181no—
554C23—181no—
555C23—181no—
556C23—181no—
557C23#381111yescharacteristic
558D4—62no—
559D4—62no—
560D4—121no—
561D4—121no—
562D4—368no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—62no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—361no—
573C2×C4—361no—
574C2×C4—361no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4—361no—
578C2×C4—361no—
579C2×C4#379611yescharacteristic
580C2×C4#379811yescharacteristic
581C2×C4#379911yescharacteristic
582C2×C4D3×D1211yescharacteristic
583C2×C4D3×#6711yescharacteristic
584C2×C4D3×#6711yescharacteristic
585C8—62no—
586C8—121no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—242no—
595C2×C3#477411yescharacteristic
596C2×C3#477511yescharacteristic
597C2×C3#477911yescharacteristic
598C2×C3#478011yescharacteristic
599C2×C3#488211yescharacteristic
600C2×C3#488311yescharacteristic
601C2×C3#488511yescharacteristic
602C2×C3#488611yescharacteristic
603C2×C3#495911yescharacteristic
604C2×C3#499111yescharacteristic
605C2×C3#515611yescharacteristic
606C2×C3#515611yescharacteristic
607C2×C3#517311yescharacteristic
608C2×C3#518711yescharacteristic
609D3—82no—
610D3—124no—
611D3—122no—
612D3—122no—
613C22—122no—
614C22—122no—
615C22—122no—
616C22—182no—
617C22—182no—
618C22—182no—
619C22—241no—
620C22—241no—
621C22—241no—
622C22—241no—
623C22—361no—
624C22—361no—
625C22—361no—
626C22—361no—
627C22#6385311yescharacteristic
628C22#6391011yescharacteristic
629C22#6392611yescharacteristic
630C22#6392711yescharacteristic
631C22#6395011yescharacteristic
632C22#6395111yescharacteristic
633C22#6398311yescharacteristic
634C4—81no—
635C4—122no—
636C4—361no—
637C4—721no—
638C4#6385011yescharacteristic
639C4#6388611yescharacteristic
640C4#6390611yescharacteristic
641C4#6390711yescharacteristic
642C3—21no—
643C3#7020611yescharacteristic, complemented
644C3#7063411yescharacteristic, complemented
645C2—242no—
646C2—362no—
647C2#1059050611yescharacteristic
648C2#1059050911yescharacteristic
649C2#1059051011yescharacteristic
650C2#1059051211yescharacteristic
651C2#1059129111yescharacteristic
652C2#1059151611yescharacteristic
653C2#1059165611yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2033
LCSG ▷ C22×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. #10592686C2semidirect
3. C2×C3×#809C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63563C2semidirect
6. C2×#63557C2semidirect
7. #10589164C2semidirect
38. C2×#809D3semidirect
39. C2×#807D3semidirect
76. C2×C3×C3⋊C8D4semidirect
256. C2×C3⋊C8D12semidirect
542. C32#2033semidirect
643. C3#70206semidirect
644. C3#70634semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
#105926862
C2×C3×#8092
C2×C3×#8072
C2×#635632
C2×#635572
#105891642
#706343
#702063