Finite Group Databasebeta

← #11793183

Subgroups — #11793183

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic, complemented
4C2×C3×#818C211yesmaximal, characteristic, complemented
5#10591325C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70634—31nomaximal
9#70175—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C22×C32×C8C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×#3722—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63916—22no—
21#63916—22no—
22#63647—22no—
23C3×#821—22no—
24C3×#818—22no—
25#63579—21no—
26#63562—22no—
27C2×#938—31no—
28C2×#895—31no—
29C2×C3×#107—31no—
30C2×C3×#102—31no—
31C2×#832—31no—
32C2×#821D311yescharacteristic, complemented
33C2×(C2×D3)⋊C8—31no—
34C2×(C2×D3)⋊C8—31no—
35C2×(C2×D3)⋊C8—61no—
36C2×#818D311yescharacteristic, complemented
37#4987—31no—
38#4987—31no—
39C2×#809—31no—
40#4529—31no—
41#4529—31no—
42C23×C3⋊D3D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
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⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—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—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8D412yescomplemented
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3D412yes—
76#3722—42no—
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—21no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
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×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—61no—
104#895—62no—
105#895—62no—
106C3×#107—62no—
107C3×#102—62no—
108#832—62no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#821—22no—
112(C2×D3)⋊C8—64no—
113(C2×D3)⋊C8—62no—
114(C2×D3)⋊C8—62no—
115#818—22no—
116#809—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3D812yes—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C4×C3⋊D3—41no—
142C4×C3⋊D3—41no—
143C4×C3⋊D3—41no—
144C4×C3⋊D3—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—41no—
157C3×D12—41no—
158#626—48no—
159C32×C8—22no—
160C3⋊(C3⋊C8)—41no—
161C2×#121—91no—
162C2×#107—31no—
163C2×#102—31no—
164C2×#102—91no—
165C2×C22⋊C8—91no—
166#380—91no—
167#340—91no—
168C24×C3—61no—
169C23×D3—21no—
170C23×D3—31no—
171C23×D3—31no—
172C23×D3—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—64no—
186C2×#67—122no—
187C2×#67—122no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—64no—
200C2×D12—122no—
201C2×D12—122no—
202C2×D12D1212yes—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
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—121no—
218C2×C4×D3—121no—
219C2×C4×D3—121no—
220C2×C4×D3—121no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C2×C3×C8D1212yescomplemented
229C2×C3×C8#6712yescomplemented
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236#217—64no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3#6712yes—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—121no—
254C2×C3⋊C8—121no—
255C22×C32#12011yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32#12311yescharacteristic
258C22×C32C2×D811yescharacteristic
259C22×C32#13511yescharacteristic
260C22×C32AGL(1,ℤ/8)11yescharacteristic
261C22×C32#13711yescharacteristic
262C2×C3⋊D3—22no—
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—41no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12311yescharacteristic
279C32×C4#12411yescharacteristic
280C3⋊Dic3—41no—
281C3×Dic3—42no—
282C3×Dic3—81no—
283C3×Dic3—81no—
284C22×D4—31no—
285C22×D4—181no—
286C23×C4—91no—
287C22×C8—91no—
288C22×C8D3211yescharacteristic
289#121—182no—
290#121—182no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C22⋊C4—181no—
295C2×C22⋊C4—181no—
296#107—62no—
297#102—62no—
298#102—182no—
299C22⋊C8—182no—
300#95—181no—
301C23×C3—21no—
302C23×C3—62no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3D3×D411yescharacteristic
310C23×C3D3×D411yescharacteristic
311C22×D3—22no—
312C22×D3—32no—
313C22×D3—32no—
314C22×D3—41no—
315C22×D3—41no—
316C22×D3—41no—
317C22×D3—41no—
318C22×D3—41no—
319C22×D3—41no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—61no—
324C22×D3—61no—
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—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—121no—
342C3×D4—121no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—62no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4—121no—
358C2×C3×C4C2×D1211yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4#23511yescharacteristic
361C2×C3×C4#23511yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4#23911yescharacteristic
367C2×C3×C4#23911yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C2×#6711yescharacteristic
370#67—128no—
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389D12—22no—
390D12—22no—
391D12—41no—
392D12—41no—
393D12—128no—
394C4×D3—122no—
395C4×D3—122no—
396C4×D3—122no—
397C4×D3—122no—
398C4×D3—121no—
399C4×D3—121no—
400C4×D3—121no—
401C4×D3—121no—
402C4×D3—121no—
403C4×D3—121no—
404C4×D3—121no—
405C4×D3—121no—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—42no—
409C3⋊C8—122no—
410C3⋊C8—121no—
411C3⋊C8—121no—
412C2×C32#39411yescharacteristic
413C2×C32#44711yescharacteristic
414C2×C32#45211yescharacteristic
415C2×C32#46611yescharacteristic
416C2×C32#46811yescharacteristic
417C2×C32#48011yescharacteristic
418C2×C32#48211yescharacteristic
419C3⋊D3—42no—
420C3×D3—82no—
421C24—61no—
422C24—91no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—184no—
430C2×D4—362no—
431C2×D4—362no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—91no—
436C22×C4—181no—
437C22×C4—181no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4—181no—
441C22×C4—181no—
442C22×C4C2×D3211yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—181no—
446C2×C8—181no—
447C2×C8—181no—
448C2×C8#62612yescomplemented
449C4⋊C4—32no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C22⋊C4—184no—
456C22⋊C4—362no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—241no—
468C22×C3—241no—
469C22×C3—241no—
470C22×C3—241no—
471C22×C3#88211yescharacteristic
472C22×C3#88311yescharacteristic
473C22×C3#89411yescharacteristic
474C22×C3#89511yescharacteristic
475C22×C3D3×D811yescharacteristic
476C22×C3D3×D811yescharacteristic
477C22×C3#91111yescharacteristic
478C22×C3#91211yescharacteristic
479C22×C3#91411yescharacteristic
480C22×C3#91511yescharacteristic
481C22×C3#91811yescharacteristic
482C22×C3#91911yescharacteristic
483C22×C3#93711yescharacteristic
484C22×C3#93811yescharacteristic
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—64no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—81no—
496C2×D3—81no—
497C2×D3—81no—
498C2×D3—81no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—122no—
518C3×C4—241no—
519C3×C4—241no—
520C3×C4#88511yescharacteristic
521C3×C4#88611yescharacteristic
522C3×C4#89411yescharacteristic
523C3×C4#89511yescharacteristic
524C3×C4#93011yescharacteristic
525C3×C4#93011yescharacteristic
526C3×C4#93911yescharacteristic
527C3×C4#94711yescharacteristic
528Dic3—42no—
529Dic3—81no—
530Dic3—81no—
531Dic3—122no—
532Dic3—121no—
533Dic3—121no—
534C32#203311yescharacteristic, complemented, Sylow
535C23—62no—
536C23—92no—
537C23—121no—
538C23—121no—
539C23—121no—
540C23—121no—
541C23—121no—
542C23—121no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23—181no—
549C23#380211yescharacteristic
550D4—62no—
551D4—62no—
552D4—121no—
553D4—121no—
554D4—368no—
555C2×C4—62no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4—121no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—361no—
568C2×C4—361no—
569C2×C4—361no—
570C2×C4—361no—
571C2×C4#379611yescharacteristic
572C2×C4#379911yescharacteristic
573C2×C4D3×D1211yescharacteristic
574C2×C4#380411yescharacteristic
575C2×C4C2×#62611yescharacteristic
576C2×C4D3×#6711yescharacteristic
577C8—22no—
578C8—361no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—242no—
587C2×C3#477311yescharacteristic
588C2×C3#477411yescharacteristic
589C2×C3#478311yescharacteristic
590C2×C3#478411yescharacteristic
591C2×C3#488211yescharacteristic
592C2×C3#488311yescharacteristic
593C2×C3#488511yescharacteristic
594C2×C3#488611yescharacteristic
595C2×C3#496111yescharacteristic
596C2×C3#499111yescharacteristic
597C2×C3#515611yescharacteristic
598C2×C3#515711yescharacteristic
599C2×C3#517411yescharacteristic
600C2×C3#518711yescharacteristic
601D3—82no—
602D3—124no—
603D3—122no—
604D3—122no—
605C22—122no—
606C22—122no—
607C22—122no—
608C22—182no—
609C22—182no—
610C22—182no—
611C22—241no—
612C22—241no—
613C22—241no—
614C22—241no—
615C22—361no—
616C22—361no—
617C22—361no—
618C22—361no—
619C22#6379711yescharacteristic
620C22#6379811yescharacteristic
621C22#6381011yescharacteristic
622C22#6381111yescharacteristic
623C22#6385411yescharacteristic
624C22#6391611yescharacteristic
625C22#6392211yescharacteristic
626C4—122no—
627C4—241no—
628C4—241no—
629C4—361no—
630C4#6389011yescharacteristic
631C4#6390711yescharacteristic
632C4#6390911yescharacteristic
633C4#6397811yescharacteristic
634C3—21no—
635C3#7017511yescharacteristic, complemented
636C3#7063411yescharacteristic, complemented
637C2—242no—
638C2—362no—
639C2#1059065011yescharacteristic
640C2#1059065111yescharacteristic
641C2#1059084411yescharacteristic
642C2#1059084511yescharacteristic
643C2#1059094511yescharacteristic
644C2#1059096511yescharacteristic
645C2#1059139211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×C8D32
hypocenterC32#2033
LCSG ▷ C22×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
2. C2×#63647C2semidirect
3. C2×C3×#821C2semidirect
4. C2×C3×#818C2semidirect
5. #10591325C2semidirect
6. C2×#63562C2semidirect
7. #10589163C2semidirect
32. C2×#821D3semidirect
36. C2×#818D3semidirect
66. C2×C32×C8D4semidirect
228. C2×C3×C8D12semidirect
229. C2×C3×C8#67semidirect
448. C2×C8#626semidirect
534. C32#2033semidirect
635. C3#70175semidirect
636. C3#70634semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
C2×#636472
C2×C3×#8212
C2×C3×#8182
#105913252
C2×#635622
#105891632
#706343
#701753