Finite Group Databasebeta

← #11793165

Subgroups — #11793165

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70206—31nomaximal
9#70175—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#638—21no—
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×#3757—21no—
14#64147—22no—
15#64147—22no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C3×#832—22no—
23C3×#832—22no—
24#63579—21no—
25#63575—22no—
26#63557—22no—
27C2×#938—31no—
28C2×#938—31no—
29C2×#938—61no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C2×#832D311yescharacteristic, complemented
33C2×#832D311yescharacteristic, complemented
34C2×(C2×D3)⋊C8—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×#818—31no—
37#4987—31no—
38#4987—31no—
39C2×#807—31no—
40#4551—31no—
41#4529—31no—
42C24×C32—21no—
43C23×C3⋊D3D411yescharacteristic
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D412yes—
50C22×C32×C4C2311yescharacteristic
51C2×#638—24no—
52C2×#638—42no—
53C2×#638—42no—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64#3757—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
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#3722—42no—
78#2033—91noSylow
79C22×C3×D4—21no—
80C22×C3×D4C2×D311yescharacteristic
81C22×C3×D4C2×D311yescharacteristic
82C22×#67—61no—
83C22×#67—61no—
84C22×#67—62no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93C2×#217—61no—
94C2×#217—62no—
95#938—62no—
96#938—62no—
97#938—64no—
98#938—64no—
99#938—62no—
100#938—62no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110C3×#102—62no—
111C3×#102—62no—
112#832—22no—
113#832—22no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116(C2×D3)⋊C8—62no—
117(C2×D3)⋊C8—62no—
118#818—62no—
119#807—62no—
120C23×C32—22no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—21no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—21no—
133C22×C3⋊D3—21no—
134C22×C3⋊D3D812yes—
135C32×D4—22no—
136C32×D4—22no—
137C32×D4—41no—
138C32×D4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145#638—48no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3—41no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154C4×C3⋊D3—41no—
155C4×C3⋊D3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—41no—
164C2×#121—91no—
165C2×#107—91no—
166C2×#102—31no—
167C2×#102—31no—
168C2×C22⋊C8—91no—
169#380—91no—
170#340—91no—
171C24×C3—22no—
172C24×C3—21no—
173C24×C3—21no—
174C23×D3—31no—
175C23×D3—31no—
176C23×D3—61no—
177C2×C3×D4—22no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4—41no—
192C2×C3×D4—41no—
193C2×C3×D4D1212yes—
194C2×C3×D4#6712yes—
195C22×C3×C4—21no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C2×#67—68no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—122no—
204C2×#67—122no—
205C2×#67—124no—
206C2×#67—124no—
207C2×#67—122no—
208C2×#67—122no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—61no—
214C22×Dic3—62no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—121no—
232C2×C4×D3—121no—
233C2×C4×D3—121no—
234C2×C4×D3—121no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245#217—68no—
246#217—64no—
247#217—64no—
248(C2×D3)⋊C4—122no—
249(C2×D3)⋊C4—122no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—61no—
259C4⋊Dic3—61no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8#6712yescomplemented
266C22×C32—42no—
267C22×C32—42no—
268C22×C32—42no—
269C22×C32—81no—
270C22×C32—81no—
271C22×C32—81no—
272C22×C32—81no—
273C22×C32#12011yescharacteristic
274C22×C32#12111yescharacteristic
275C22×C32#12311yescharacteristic
276C22×C32C2×D811yescharacteristic
277C22×C32#13511yescharacteristic
278C22×C32AGL(1,ℤ/8)11yescharacteristic
279C22×C32#13711yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—22no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C32×C4#12111yescharacteristic
288C32×C4#12111yescharacteristic
289C32×C4#12311yescharacteristic
290C32×C4#12411yescharacteristic
291C3⋊Dic3—41no—
292C3⋊Dic3—42no—
293C3×Dic3—81no—
294C3×Dic3—81no—
295C22×D4—181no—
296C22×D4D3211yescharacteristic
297C23×C4—91no—
298C22×C8—31no—
299C22×C8—31no—
300#121—182no—
301#121—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—181no—
306C2×C22⋊C4—181no—
307#107—182no—
308#102—62no—
309#102—62no—
310C22⋊C8—182no—
311#95—181no—
312C23×C3—24no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—21no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—41no—
323C23×C3—41no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3D3×D411yescharacteristic
335C23×C3D3×D411yescharacteristic
336C22×D3—32no—
337C22×D3—32no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C22×D3—121no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—42no—
362C3×D4—42no—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—41no—
366C3×D4—41no—
367C3×D4—41no—
368C3×D4—41no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4—121no—
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4#23711yescharacteristic
389C2×C3×C4#23711yescharacteristic
390C2×C3×C4#23711yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393#67—1216no—
394#67—128no—
395#67—128no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—64no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C4×D3—122no—
421C4×D3—122no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—121no—
428C4×D3—121no—
429C4×D3—121no—
430C4×D3—121no—
431C4×D3—121no—
432C3×C8—62no—
433C3×C8—121no—
434C3⋊C8—22no—
435C3⋊C8—41no—
436C2×C32—82no—
437C2×C32#39411yescharacteristic
438C2×C32#44711yescharacteristic
439C2×C32#45211yescharacteristic
440C2×C32#46611yescharacteristic
441C2×C32#46811yescharacteristic
442C2×C32#48011yescharacteristic
443C2×C32#48211yescharacteristic
444C3⋊D3—42no—
445C24—21no—
446C24—91no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—184no—
453C2×D4—362no—
454C2×D4—362no—
455C2×D4#62612yes—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—91no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4C2×D3211yescharacteristic
467C2×C8—32no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8—61no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C4⋊C4—92no—
478C4⋊C4—181no—
479C22⋊C4—184no—
480C22⋊C4—362no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—44no—
489C22×C3—44no—
490C22×C3—44no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—82no—
501C22×C3—81no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—81no—
505C22×C3—81no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3#88211yescharacteristic
510C22×C3#88311yescharacteristic
511C22×C3#88311yescharacteristic
512C22×C3#88411yescharacteristic
513C22×C3D3×D811yescharacteristic
514C22×C3D3×D811yescharacteristic
515C22×C3#91111yescharacteristic
516C22×C3#91211yescharacteristic
517C22×C3#91411yescharacteristic
518C22×C3#91511yescharacteristic
519C22×C3#91511yescharacteristic
520C22×C3#91611yescharacteristic
521C22×C3#93711yescharacteristic
522C22×C3#93811yescharacteristic
523C2×D3—64no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—121no—
541C2×D3—121no—
542C2×D3—121no—
543C2×D3—121no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—241no—
549C3×C4—241no—
550C3×C4#88411yescharacteristic
551C3×C4#88511yescharacteristic
552C3×C4#88511yescharacteristic
553C3×C4#88611yescharacteristic
554C3×C4#92911yescharacteristic
555C3×C4#93011yescharacteristic
556C3×C4#93911yescharacteristic
557C3×C4#93911yescharacteristic
558Dic3—81no—
559Dic3—81no—
560Dic3—122no—
561Dic3—124no—
562Dic3—122no—
563Dic3—121no—
564Dic3—121no—
565Dic3—122no—
566C32#203311yescharacteristic, complemented, Sylow
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—92no—
575C23—181no—
576C23—181no—
577C23—181no—
578C23—181no—
579C23—181no—
580C23—181no—
581C23#381111yescharacteristic
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586D4—368no—
587C2×C4—121no—
588C2×C4—121no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—121no—
592C2×C4—121no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—182no—
597C2×C4—361no—
598C2×C4—361no—
599C2×C4—361no—
600C2×C4—361no—
601C2×C4—361no—
602C2×C4—361no—
603C2×C4#380411yescharacteristic
604C2×C4#380411yescharacteristic
605C2×C4#380411yescharacteristic
606C2×C4C2×#62611yescharacteristic
607C2×C4D3×#6711yescharacteristic
608C2×C4#381111yescharacteristic
609C8—62no—
610C8—121no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—84no—
619C2×C3—82no—
620C2×C3—82no—
621C2×C3#477311yescharacteristic
622C2×C3#477411yescharacteristic
623C2×C3#477411yescharacteristic
624C2×C3#477511yescharacteristic
625C2×C3#477911yescharacteristic
626C2×C3#478011yescharacteristic
627C2×C3#478311yescharacteristic
628C2×C3#478411yescharacteristic
629C2×C3#495911yescharacteristic
630C2×C3#496111yescharacteristic
631C2×C3#515611yescharacteristic
632C2×C3#515711yescharacteristic
633C2×C3#517311yescharacteristic
634C2×C3#517411yescharacteristic
635D3—124no—
636D3—122no—
637D3—122no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—182no—
646C22—182no—
647C22—182no—
648C22—361no—
649C22—361no—
650C22—361no—
651C22—361no—
652C22#6392611yescharacteristic
653C22#6393111yescharacteristic
654C22#6393611yescharacteristic
655C22#6393711yescharacteristic
656C22#6395811yescharacteristic
657C22#6397511yescharacteristic
658C22#6398111yescharacteristic
659C4—241no—
660C4—241no—
661C4—362no—
662C4—361no—
663C4#6395311yescharacteristic
664C4#6396611yescharacteristic
665C4#6397111yescharacteristic
666C4#6397811yescharacteristic
667C3—21no—
668C3#7017511yescharacteristic, complemented
669C3#7020611yescharacteristic, complemented
670C2—82no—
671C2—362no—
672C2#1059141711yescharacteristic
673C2#1059142511yescharacteristic
674C2#1059145511yescharacteristic
675C2#1059145611yescharacteristic
676C2#1059146411yescharacteristic
677C2#1059146611yescharacteristic
678C2#1059171211yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64147C2
hypercenterC22×D4D32
hypocenterC32#2033
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#832C2semidirect
3. C2×C3×#832C2semidirect
4. #10591325C2semidirect
5. C2×#63575C2semidirect
6. C2×#63557C2semidirect
7. #10589164C2semidirect
32. C2×#832D3semidirect
33. C2×#832D3semidirect
76. C2×C3×C3⋊C8D4semidirect
265. C2×C3⋊C8#67semidirect
566. C32#2033semidirect
668. C3#70175semidirect
669. C3#70206semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C3×#8322
#105913252
C2×#635752
C2×#635572
#105891642
#702063
#701753