Finite Group Databasebeta

← #11824437

Subgroups — #11824437

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×#63980C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63979C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63885C211yesmaximal, characteristic, complemented
9C3×#5223C211yesmaximal, characteristic, complemented
10#10591724C211yesmaximal, characteristic, complemented
11#10591723C211yesmaximal, characteristic, complemented
12#10591707C211yesmaximal, characteristic, complemented
13#10591391C211yesmaximal, characteristic, complemented
14#10591383C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#83177—31nomaximal
17#76688—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×D12C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36#64148—24no—
37C2×#3752C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C3×#940—24no—
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44#63980—24no—
45#63979—24no—
46#63979—24no—
47#67⋊Dic3—24no—
48#63971—24no—
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57C2×Dic32C2211yescharacteristic
58#63885—24no—
59C3×C3⋊#95C2211yescharacteristic
60#63579C2211yescharacteristic
61C2×C3×#127—31no—
62C2×#940—31no—
63C2×#940—31no—
64C2×#940—31no—
65C2×#940—31no—
66C2×#940D311yescharacteristic, complemented
67C2×#939—31no—
68C2×#939—31no—
69C2×#939—31no—
70C2×#939—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—61no—
74C2×D4×Dic3—31no—
75C2×#884—31no—
76C2×#884—31no—
77C2×#67⋊C4—31no—
78C3×#392—31no—
79#5223—31no—
80#5223—31no—
81#5223—31no—
82#5223—31no—
83#5223D311yescharacteristic, complemented
84#5221—31no—
85#4960—31no—
86#4957—31no—
87#4957—31no—
88#4939—31no—
89C4×Dic3⋊C4—31no—
90#4671—31no—
91#4649—31no—
92C24×C32C2311yescharacteristic
93C24×C32C2311yescharacteristic
94C23×C3⋊D3C2311yescharacteristic
95C23×C3×D3C2311yescharacteristic
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C2×C32×D4—22no—
99C2×C32×D4—22no—
100C2×C32×D4—41no—
101C22×C32×C4C2311yescharacteristic
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—22no—
105C2×#638—22no—
106C2×#638—22no—
107C2×#638—41no—
108C22×C3⋊Dic3—22no—
109C22×C3⋊Dic3—22no—
110C22×C3⋊Dic3—22no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
119C2×C3×#67—22no—
120C2×C3×#67—22no—
121C2×C3×#67—22no—
122C2×C3×#67—22no—
123C2×C3×#67—22no—
124C2×C3×#67—22no—
125C2×C3×#67—22no—
126C2×C3×#67—41no—
127C2×C3×#67—41no—
128C2×C3×#67—41no—
129C2×C3×#67—41no—
130C2×C3×#67—41no—
131C2×C3×#67D414yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×D12—22no—
138C2×C3×D12—22no—
139C2×C3×D12—41no—
140C2×#626—22no—
141C2×#626—22no—
142C2×#626—22no—
143C2×#626—22no—
144C2×#626—22no—
145C2×#626—22no—
146C2×#626—41no—
147C2×#626—41no—
148C2×#626—41no—
149C2×#625—22no—
150C2×#625—22no—
151C2×#625—22no—
152C2×#625—22no—
153C2×#625—22no—
154C2×#625—41no—
155C2×D3×Dic3—22no—
156C2×D3×Dic3—22no—
157C2×D3×Dic3—22no—
158#3757—22no—
159#3752—22no—
160#3750D414yescomplemented
161C3×#217—22no—
162C3×#217—22no—
163C3×(C2×D3)⋊C4—22no—
164C3×C4×Dic3—22no—
165#3724D414yescomplemented
166Dic3⋊Dic3—22no—
167#3722—22no—
168(C2×D3)⋊Dic3—22no—
169(C2×D3)⋊Dic3—22no—
170(C2×D3)⋊Dic3—22no—
171(C2×D3)⋊Dic3—22no—
172Dic32—22no—
173Dic32D414yescomplemented
174#2541—91noSylow
175C22×C3×D4—21no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4C2×D311yescharacteristic
184C22×C3×D4C2×D311yescharacteristic
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—61no—
197C22×#67—61no—
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic
201C22×#67C2×D311yescharacteristic
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—61no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12C2×D311yescharacteristic
212C22×C4×D3—31no—
213C3×#127—64no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C42—31no—
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—61no—
225C2×#217C2×D311yescharacteristic
226C2×#217C2×D311yescharacteristic
227#940—24no—
228#940—64no—
229#940—64no—
230#940—64no—
231#940—64no—
232#939—64no—
233#939—64no—
234#939—64no—
235#939—64no—
236#939—64no—
237#939—64no—
238#939—68no—
239D4×Dic3—64no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—61no—
249C2×(C2×D3)⋊C4C2×D311yescharacteristic
250C2×C4⋊Dic3—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—61no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3C2×D311yescharacteristic
262#884—64no—
263#884—64no—
264#67⋊C4—64no—
265C3×#95—31no—
266C3⋊#95—31no—
267C3⋊#95—31no—
268C3⋊#95C2×D311yescharacteristic
269C23×C32—21no—
270C23×C32—21no—
271C23×C32—21no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—21no—
275C23×C32—21no—
276C23×C32—21no—
277C23×C32—21no—
278C23×C32—21no—
279C23×C32—21no—
280C23×C32—21no—
281C23×C32—21no—
282C23×C32C2×D412yes—
283C23×C32C2411yescharacteristic
284C22×C3⋊D3—21no—
285C22×C3⋊D3—21no—
286C22×C3⋊D3—21no—
287C22×C3⋊D3—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—21no—
290C22×C3⋊D3—21no—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—21no—
298C22×C3×D3—21no—
299C22×C3×D3—21no—
300C22×C3×D3—21no—
301C22×C3×D3—21no—
302C22×C3×D3—21no—
303C22×C3×D3—21no—
304C22×C3×D3—21no—
305C22×C3×D3—21no—
306C22×C3×D3—21no—
307C22×C3×D3—21no—
308C22×C3×D3—21no—
309C22×C3×D3—21no—
310C22×C3×D3—21no—
311C22×C3×D3C2×D412yes—
312C32×D4—44no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4C2×D412yes—
316#638—44no—
317#638—44no—
318C2×C3⋊Dic3—21no—
319C2×C3⋊Dic3—21no—
320C2×C3⋊Dic3—21no—
321C2×C3⋊Dic3—21no—
322C2×C3⋊Dic3—21no—
323C2×C3⋊Dic3—44no—
324C2×C3⋊Dic3C2×D412yes—
325C2×C3⋊Dic3C2×D412yes—
326C2×C3⋊Dic3C2×D412yes—
327C2×C3⋊Dic3C2×D412yes—
328C3×#67—28no—
329C3×#67—44no—
330C3×#67—44no—
331C3×#67—44no—
332C3×#67—44no—
333C3×#67—44no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—21no—
338C2×C3×Dic3—21no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—21no—
343C2×C3×Dic3C2×D412yes—
344C2×C3×Dic3C2×D412yes—
345C2×C3×Dic3C2×D412yes—
346C2×C3×Dic3C2×D412yes—
347C2×C3×Dic3C2×D412yes—
348C2×C3×Dic3#4112yes—
349C3×D12—44no—
350#626—44no—
351#626—44no—
352#626—44no—
353#625—44no—
354#625—44no—
355D3×Dic3—44no—
356C2×#127—31no—
357C2×#127—91no—
358C2×#127—91no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×#121—91no—
363C2×C4×D4—91no—
364#392—31no—
365#392—91no—
366#392—91no—
367#392—91no—
368#390—91no—
369#390—91no—
370C4×C4⋊C4—91no—
371C24×C3—21no—
372C24×C3—21no—
373C24×C3—31no—
374C24×C3—31no—
375C24×C3—31no—
376C24×C3C22×D311yescharacteristic
377C24×C3C22×D311yescharacteristic
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—61no—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C2×C3×D4—24no—
387C2×C3×D4—22no—
388C2×C3×D4—22no—
389C2×C3×D4—22no—
390C2×C3×D4—22no—
391C2×C3×D4—34no—
392C2×C3×D4—42no—
393C2×C3×D4—41no—
394C2×C3×D4—41no—
395C2×C3×D4—42no—
396C2×C3×D4—62no—
397C2×C3×D4—62no—
398C2×C3×D4—62no—
399C2×C3×D4—62no—
400C2×C3×D4—62no—
401C2×C3×D4—62no—
402C2×C3×D4—62no—
403C2×C3×D4—62no—
404C2×C3×D4—62no—
405C2×C3×D4—62no—
406C2×C3×D4—62no—
407C2×C3×D4—62no—
408C2×C3×D4—62no—
409C2×C3×D4—62no—
410C2×C3×D4—121no—
411C2×C3×D4—121no—
412C2×C3×D4—121no—
413C2×C3×D4—121no—
414C2×C3×D4—121no—
415C2×C3×D4—121no—
416C22×C3×C4—21no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C2×#67—22no—
425C2×#67—22no—
426C2×#67—22no—
427C2×#67—22no—
428C2×#67—22no—
429C2×#67—22no—
430C2×#67—22no—
431C2×#67—22no—
432C2×#67—22no—
433C2×#67—22no—
434C2×#67—22no—
435C2×#67—22no—
436C2×#67—41no—
437C2×#67—41no—
438C2×#67—41no—
439C2×#67—41no—
440C2×#67—41no—
441C2×#67—62no—
442C2×#67—62no—
443C2×#67—62no—
444C2×#67—62no—
445C2×#67—62no—
446C2×#67—62no—
447C2×#67—62no—
448C2×#67—62no—
449C2×#67—62no—
450C2×#67—62no—
451C2×#67—62no—
452C2×#67—62no—
453C2×#67—62no—
454C2×#67—62no—
455C2×#67—62no—
456C2×#67—62no—
457C2×#67—62no—
458C2×#67—62no—
459C2×#67—64no—
460C2×#67—64no—
461C2×#67—62no—
462C2×#67—62no—
463C2×#67—62no—
464C2×#67—62no—
465C2×#67—62no—
466C2×#67—62no—
467C2×#67—62no—
468C2×#67—62no—
469C2×#67—122no—
470C2×#67—122no—
471C2×#67—122no—
472C2×#67—121no—
473C2×#67—121no—
474C2×#67—121no—
475C2×#67—121no—
476C2×#67—121no—
477C2×#67—121no—
478C2×#67—121no—
479C2×#67—122no—
480C2×#67#6714yescomplemented
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—31no—
486C22×Dic3—31no—
487C22×Dic3—61no—
488C22×Dic3—61no—
489C22×Dic3—61no—
490C22×Dic3—62no—
491C22×Dic3—62no—
492C22×Dic3—62no—
493C22×Dic3—62no—
494C22×Dic3—62no—
495C22×Dic3—62no—
496C22×Dic3—62no—
497C22×Dic3—62no—
498C22×Dic3—62no—
499C22×Dic3—64no—
500C22×Dic3—122no—
501C22×Dic3—122no—
502C22×Dic3C22×D311yescharacteristic
503C22×Dic3C22×D311yescharacteristic
504C22×Dic3C22×D311yescharacteristic
505C22×Dic3C22×D311yescharacteristic
506C22×Dic3C22×D311yescharacteristic
507C2×D12—22no—
508C2×D12—22no—
509C2×D12—41no—
510C2×D12—62no—
511C2×D12—62no—
512C2×D12—62no—
513C2×D12—62no—
514C2×D12—62no—
515C2×D12—62no—
516C2×D12—121no—
517C2×D12—121no—
518C2×D12—121no—
519C2×C4×D3—62no—
520C2×C4×D3—62no—
521C2×C4×D3—62no—
522C3×C22⋊C4—62no—
523C3×C22⋊C4—62no—
524C3×C22⋊C4—62no—
525C3×C42—62no—
526#217—22no—
527#217—22no—
528#217—62no—
529#217—62no—
530#217—62no—
531#217—64no—
532#217—62no—
533#217—62no—
534#217—62no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—62no—
537(C2×D3)⋊C4—62no—
538(C2×D3)⋊C4—64no—
539(C2×D3)⋊C4—62no—
540(C2×D3)⋊C4—62no—
541(C2×D3)⋊C4—62no—
542(C2×D3)⋊C4—62no—
543(C2×D3)⋊C4—62no—
544(C2×D3)⋊C4—62no—
545C4⋊Dic3—62no—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—64no—
551Dic3⋊C4—62no—
552C4×Dic3—22no—
553C4×Dic3—34no—
554C4×Dic3—34no—
555C4×Dic3—62no—
556C4×Dic3—62no—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—41no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32C22×D411yescharacteristic
572C22×C32C22×D411yescharacteristic
573C22×C32C22×D411yescharacteristic
574C22×C32C22×D411yescharacteristic
575C22×C32C2×#4111yescharacteristic
576C22×C32H(5,𝔽2)11yescharacteristic
577C22×C32H(5,𝔽2)11yescharacteristic
578C2×C3⋊D3—41no—
579C2×C3⋊D3—41no—
580C2×C3⋊D3—41no—
581C2×C3⋊D3—41no—
582C2×C3⋊D3—41no—
583C2×C3⋊D3—41no—
584C2×C3⋊D3—41no—
585C2×C3×D3—22no—
586C2×C3×D3—22no—
587C2×C3×D3—22no—
588C2×C3×D3—41no—
589C2×C3×D3—41no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C2×C3×D3—41no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—41no—
596C2×C3×D3—41no—
597C2×C3×D3—41no—
598C2×C3×D3—41no—
599C2×C3×D3—41no—
600C2×C3×D3—41no—
601C2×C3×D3—41no—
602C2×C3×D3—41no—
603C2×C3×D3—41no—
604C2×C3×D3—41no—
605C2×C3×D3—41no—
606C32×C4—22no—
607C3⋊Dic3—22no—
608C3⋊Dic3—41no—
609C3⋊Dic3#12714yescomplemented
610C3×Dic3—22no—
611C3×Dic3—22no—
612C3×Dic3—22no—
613C3×Dic3—41no—
614C3×Dic3#12114yescomplemented
615C22×D4—31no—
616C22×D4—31no—
617C22×D4—31no—
618C22×D4—31no—
619C22×D4—31no—
620C22×D4—31no—
621C22×D4—31no—
622C22×D4—91no—
623C22×D4—91no—
624C22×D4—91no—
625C22×D4—91no—
626C22×D4—91no—
627C22×D4—91no—
628C22×D4—91no—
629C22×D4D3211yescharacteristic
630C23×C4—91no—
631C23×C4—91no—
632#127—64no—
633#127—184no—
634#127—184no—
635#121—184no—
636#121—184no—
637#121—184no—
638#121—184no—
639C4×D4—184no—
640C2×C4⋊C4—91no—
641C2×C4⋊C4—91no—
642C2×C4⋊C4—91no—
643C2×C22⋊C4—31no—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4—91no—
650C2×C22⋊C4—91no—
651C2×C22⋊C4—91no—
652C2×C22⋊C4—91no—
653C2×C42—31no—
654C2×C42—91no—
655C2×C42—91no—
656#95—31no—
657#95—91no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3—21no—
661C23×C3—21no—
662C23×C3—21no—
663C23×C3—21no—
664C23×C3—21no—
665C23×C3—21no—
666C23×C3—21no—
667C23×C3—21no—
668C23×C3—21no—
669C23×C3—21no—
670C23×C3—21no—
671C23×C3—21no—
672C23×C3—22no—
673C23×C3—21no—
674C23×C3—21no—
675C23×C3—21no—
676C23×C3—21no—
677C23×C3—21no—
678C23×C3—21no—
679C23×C3—21no—
680C23×C3—21no—
681C23×C3—21no—
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—22no—
689C23×C3—32no—
690C23×C3—41no—
691C23×C3—41no—
692C23×C3—41no—
693C23×C3—41no—
694C23×C3—41no—
695C23×C3—41no—
696C23×C3—41no—
697C23×C3—41no—
698C23×C3—41no—
699C23×C3—41no—
700C23×C3—61no—
701C23×C3—61no—
702C23×C3—61no—
703C23×C3—61no—
704C23×C3—61no—
705C23×C3—61no—
706C23×C3—61no—
707C23×C3—61no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—61no—
711C23×C3—61no—
712C23×C3—61no—
713C23×C3—61no—
714C23×C3—61no—
715C23×C3—61no—
716C23×C3—61no—
717C23×C3—61no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3D3×D412yes—
721C23×C3C2×#6712yes—
722C23×C3C23×D311yescharacteristic
723C23×C3C23×D311yescharacteristic
724C22×D3—21no—
725C22×D3—21no—
726C22×D3—21no—
727C22×D3—21no—
728C22×D3—21no—
729C22×D3—21no—
730C22×D3—21no—
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—21no—
734C22×D3—21no—
735C22×D3—21no—
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—21no—
740C22×D3—21no—
741C22×D3—21no—
742C22×D3—21no—
743C22×D3—21no—
744C22×D3—62no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—61no—
748C22×D3—61no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—61no—
753C22×D3—61no—
754C22×D3—61no—
755C22×D3—61no—
756C22×D3—61no—
757C22×D3—61no—
758C22×D3—61no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—121no—
763C22×D3—121no—
764C22×D3—121no—
765C22×D3C2×#6712yes—
766C3×D4—44no—
767C3×D4—44no—
768C3×D4—48no—
769C3×D4—68no—
770C3×D4—124no—
771C3×D4—124no—
772C3×D4—124no—
773C3×D4—124no—
774C3×D4—124no—
775C3×D4—124no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—22no—
781C2×C3×C4—32no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—32no—
785C2×C3×C4—32no—
786C2×C3×C4—32no—
787C2×C3×C4—41no—
788C2×C3×C4—41no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—61no—
797C2×C3×C4—61no—
798C2×C3×C4D3×D412yes—
799C2×C3×C4D3×D412yes—
800#67—28no—
801#67—44no—
802#67—44no—
803#67—44no—
804#67—44no—
805#67—44no—
806#67—124no—
807#67—124no—
808#67—124no—
809#67—124no—
810#67—124no—
811#67—124no—
812#67—124no—
813#67—124no—
814#67—124no—
815#67—124no—
816#67—128no—
817#67—128no—
818#67—124no—
819C2×Dic3—21no—
820C2×Dic3—21no—
821C2×Dic3—21no—
822C2×Dic3—21no—
823C2×Dic3—21no—
824C2×Dic3—21no—
825C2×Dic3—21no—
826C2×Dic3—21no—
827C2×Dic3—21no—
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—32no—
831C2×Dic3—32no—
832C2×Dic3—32no—
833C2×Dic3—32no—
834C2×Dic3—32no—
835C2×Dic3—32no—
836C2×Dic3—62no—
837C2×Dic3—62no—
838C2×Dic3—62no—
839C2×Dic3—62no—
840C2×Dic3—61no—
841C2×Dic3—61no—
842C2×Dic3—61no—
843C2×Dic3—61no—
844C2×Dic3—62no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—121no—
852C2×Dic3—121no—
853C2×Dic3—121no—
854C2×Dic3—121no—
855C2×Dic3—124no—
856C2×Dic3—124no—
857C2×Dic3—124no—
858C2×Dic3—128no—
859C2×Dic3D3×D412yes—
860C2×Dic3D3×D412yes—
861C2×Dic3D3×D412yes—
862C2×Dic3D3×D412yes—
863C2×Dic3#23712yes—
864C2×Dic3C2×#6712yes—
865D12—44no—
866D12—124no—
867D12—124no—
868D12—124no—
869C4×D3—124no—
870C2×C32—42no—
871C2×C32—81no—
872C2×C32C2×#12111yescharacteristic
873C2×C32C2×#12711yescharacteristic
874C2×C32#53511yescharacteristic
875C2×C32D4211yescharacteristic
876C2×C32D4211yescharacteristic
877C2×C32#55011yescharacteristic
878C2×C32#55011yescharacteristic
879C3⋊D3—81no—
880C3×D3—42no—
881C3×D3—81no—
882C3×D3—81no—
883C24—31no—
884C24—31no—
885C24—31no—
886C24—91no—
887C24C2×D3211yescharacteristic
888C24C2×D3211yescharacteristic
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—34no—
892C2×D4—41no—
893C2×D4—62no—
894C2×D4—62no—
895C2×D4—62no—
896C2×D4—62no—
897C2×D4—62no—
898C2×D4—62no—
899C2×D4—62no—
900C2×D4—62no—
901C2×D4—62no—
902C2×D4—62no—
903C2×D4—62no—
904C2×D4—62no—
905C2×D4—62no—
906C2×D4—62no—
907C2×D4—121no—
908C2×D4—121no—
909C2×D4—121no—
910C2×D4—121no—
911C2×D4—121no—
912C2×D4—121no—
913C2×D4—182no—
914C2×D4—182no—
915C2×D4—182no—
916C2×D4—182no—
917C2×D4—182no—
918C2×D4—182no—
919C2×D4—182no—
920C2×D4—182no—
921C2×D4—182no—
922C2×D4—182no—
923C2×D4—182no—
924C2×D4—182no—
925C2×D4—182no—
926C2×D4—182no—
927C2×D4—182no—
928C2×D4—182no—
929C2×D4—361no—
930C2×D4—361no—
931C2×D4—361no—
932C2×D4—361no—
933C2×D4—361no—
934C22×C4—31no—
935C22×C4—31no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—91no—
942C22×C4—182no—
943C22×C4—182no—
944C22×C4—182no—
945C22×C4—182no—
946C22×C4—182no—
947C22×C4—182no—
948C22×C4C2×D3211yescharacteristic
949C4⋊C4—94no—
950C4⋊C4—94no—
951C4⋊C4—182no—
952C22⋊C4—62no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—182no—
956C22⋊C4—182no—
957C22⋊C4—182no—
958C22⋊C4—182no—
959C22⋊C4—182no—
960C22⋊C4—182no—
961C22⋊C4—182no—
962C42—62no—
963C42—94no—
964C42—182no—
965C22×C3—24no—
966C22×C3—22no—
967C22×C3—22no—
968C22×C3—22no—
969C22×C3—22no—
970C22×C3—22no—
971C22×C3—22no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—42no—
982C22×C3—42no—
983C22×C3—42no—
984C22×C3—42no—
985C22×C3—42no—
986C22×C3—42no—
987C22×C3—42no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—41no—
1005C22×C3—41no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—41no—
1009C22×C3—41no—
1010C22×C3—62no—
1011C22×C3—62no—
1012C22×C3—62no—
1013C22×C3—81no—
1014C22×C3—81no—
1015C22×C3—81no—
1016C22×C3—81no—
1017C22×C3—121no—
1018C22×C3—121no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—121no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—121no—
1031C22×C3—121no—
1032C22×C3—121no—
1033C22×C3—121no—
1034C22×C3—121no—
1035C22×C3C2×D3×D411yescharacteristic
1036C22×C3C2×D3×D411yescharacteristic
1037C22×C3C2×D3×D411yescharacteristic
1038C22×C3C2×D3×D411yescharacteristic
1039C22×C3C2×D3×D411yescharacteristic
1040C22×C3C2×D3×D411yescharacteristic
1041C22×C3C2×D3×D411yescharacteristic
1042C22×C3C2×#23711yescharacteristic
1043C22×C3#100411yescharacteristic
1044C22×C3#100411yescharacteristic
1045C22×C3#100411yescharacteristic
1046C22×C3#100411yescharacteristic
1047C22×C3D3×#4111yescharacteristic
1048C22×C3C22×#6711yescharacteristic
1049C2×D3—22no—
1050C2×D3—22no—
1051C2×D3—22no—
1052C2×D3—41no—
1053C2×D3—41no—
1054C2×D3—41no—
1055C2×D3—41no—
1056C2×D3—41no—
1057C2×D3—41no—
1058C2×D3—41no—
1059C2×D3—41no—
1060C2×D3—41no—
1061C2×D3—41no—
1062C2×D3—41no—
1063C2×D3—41no—
1064C2×D3—41no—
1065C2×D3—41no—
1066C2×D3—41no—
1067C2×D3—41no—
1068C2×D3—41no—
1069C2×D3—41no—
1070C2×D3—122no—
1071C2×D3—122no—
1072C2×D3—122no—
1073C2×D3—121no—
1074C2×D3—121no—
1075C2×D3—121no—
1076C2×D3—121no—
1077C2×D3—121no—
1078C2×D3—121no—
1079C2×D3—121no—
1080C2×D3—121no—
1081C2×D3—121no—
1082C2×D3—121no—
1083C2×D3—121no—
1084C2×D3—121no—
1085C2×D3—121no—
1086C2×D3—121no—
1087C2×D3—241no—
1088C2×D3—241no—
1089C2×D3—241no—
1090C2×D3—241no—
1091C3×C4—22no—
1092C3×C4—22no—
1093C3×C4—34no—
1094C3×C4—42no—
1095C3×C4—62no—
1096C3×C4—62no—
1097C3×C4—62no—
1098C3×C4—121no—
1099Dic3—22no—
1100Dic3—22no—
1101Dic3—22no—
1102Dic3—34no—
1103Dic3—34no—
1104Dic3—41no—
1105Dic3—64no—
1106Dic3—62no—
1107Dic3—62no—
1108Dic3—122no—
1109Dic3—122no—
1110Dic3—121no—
1111Dic3—121no—
1112Dic3#93914yescomplemented
1113C32#254111yescharacteristic, complemented, Sylow
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—32no—
1128C23—61no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23—61no—
1137C23—61no—
1138C23—61no—
1139C23—61no—
1140C23—61no—
1141C23—61no—
1142C23—61no—
1143C23—61no—
1144C23—61no—
1145C23—61no—
1146C23—61no—
1147C23—61no—
1148C23—181no—
1149C23—181no—
1150C23—181no—
1151C23—181no—
1152C23—181no—
1153C23—181no—
1154C23—181no—
1155C23D3×#6712yes—
1156C23C22×D3211yescharacteristic
1157D4—44no—
1158D4—68no—
1159D4—124no—
1160D4—124no—
1161D4—124no—
1162D4—124no—
1163D4—124no—
1164D4—124no—
1165D4—364no—
1166D4—364no—
1167D4—364no—
1168D4—364no—
1169D4—364no—
1170D4—364no—
1171D4—364no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—92no—
1190C2×C4—92no—
1191C2×C4—92no—
1192C2×C4—92no—
1193C2×C4—181no—
1194C2×C4—181no—
1195C2×C4—181no—
1196C2×C4—181no—
1197C2×C4—181no—
1198C2×C4—364no—
1199C2×C4—364no—
1200C2×C4#381112yes—
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—21no—
1204C2×C3—21no—
1205C2×C3—21no—
1206C2×C3—21no—
1207C2×C3—21no—
1208C2×C3—44no—
1209C2×C3—42no—
1210C2×C3—42no—
1211C2×C3—82no—
1212C2×C3—81no—
1213C2×C3—81no—
1214C2×C3—122no—
1215C2×C3—241no—
1216C2×C3—241no—
1217C2×C3#559011yescharacteristic
1218C2×C3#559011yescharacteristic
1219C2×C3#559211yescharacteristic
1220C2×C3#559911yescharacteristic
1221C2×C3#559911yescharacteristic
1222C2×C3D3×#12111yescharacteristic
1223C2×C3D3×#12711yescharacteristic
1224C2×C3D3×#12711yescharacteristic
1225C2×C3#571511yescharacteristic
1226C2×C3#571811yescharacteristic
1227C2×C3#571811yescharacteristic
1228C2×C3D4×#6711yescharacteristic
1229C2×C3D4×#6711yescharacteristic
1230C2×C3C2×#93911yescharacteristic
1231D3—42no—
1232D3—81no—
1233D3—81no—
1234D3—242no—
1235D3—241no—
1236D3—241no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—62no—
1252C22—62no—
1253C22—62no—
1254C22—121no—
1255C22—121no—
1256C22—121no—
1257C22—121no—
1258C22—121no—
1259C22—121no—
1260C22—121no—
1261C22—121no—
1262C22—121no—
1263C22—121no—
1264C22—121no—
1265C22—121no—
1266C22—121no—
1267C22—121no—
1268C22—121no—
1269C22—121no—
1270C22—121no—
1271C22—121no—
1272C22—361no—
1273C22—361no—
1274C22—361no—
1275C22—361no—
1276C22—361no—
1277C22—361no—
1278C22—361no—
1279C22D32×D411yescharacteristic
1280C22D32×D411yescharacteristic
1281C22D3×#23711yescharacteristic
1282C22#6431311yescharacteristic
1283C22C2×D3×#6711yescharacteristic
1284C22C2×#381111yescharacteristic
1285C22#6433011yescharacteristic
1286C4—22no—
1287C4—34no—
1288C4—62no—
1289C4—62no—
1290C4—62no—
1291C4—94no—
1292C4—121no—
1293C4—182no—
1294C4—361no—
1295C3—21no—
1296C3#7668811yescharacteristic, complemented
1297C3#8317711yescharacteristic, complemented
1298C2—42no—
1299C2—81no—
1300C2—122no—
1301C2—241no—
1302C2—241no—
1303C2—721no—
1304C2#1059516411yescharacteristic
1305C2#1059522711yescharacteristic
1306C2D3×#93911yescharacteristic
1307C2#1059528611yescharacteristic
1308C2#1059528711yescharacteristic
1309C2#1059530011yescharacteristic
1310C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64148C2semidirect
2. C2×C3×#940C2semidirect
3. C2×#63980C2semidirect
4. C2×#63979C2semidirect
5. C2×#63979C2semidirect
6. C2×#67⋊Dic3C2semidirect
7. C2×#63971C2semidirect
8. C2×#63885C2semidirect
9. C3×#5223C2semidirect
10. #10591724C2semidirect
11. #10591723C2semidirect
12. #10591707C2semidirect
13. #10591391C2semidirect
14. #10591383C2semidirect
15. #10591243C2semidirect
66. C2×#940D3semidirect
83. #5223D3semidirect
131. C2×C3×#67D4semidirect
160. #3750D4semidirect
165. #3724D4semidirect
173. Dic32D4semidirect
480. C2×#67#67semidirect
609. C3⋊Dic3#127semidirect
614. C3×Dic3#121semidirect
1112. Dic3#939semidirect
1113. C32#2541semidirect
1296. C3#76688semidirect
1297. C3#83177semidirect

Maximal subgroups

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

subgroupindex
C2×#641482
C2×C3×#9402
C2×#639802
C2×#639792
C2×#67⋊Dic32
C2×#639712
C2×#638852
C3×#52232
#105917242
#105917232
#105917072
#105913912
#105913832
#105912432
#831773
#766883