Finite Group Databasebeta

← #10718331

Subgroups — #10718331

Order 768.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#884C211yesmaximal, characteristic
2C2×#4957C211yesmaximal, characteristic, complemented
3C2×#4957C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic, complemented
5C2×#4939C211yesmaximal, characteristic, complemented
6C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C2×#4667C211yesmaximal, characteristic, complemented
8C2×#4647C211yesmaximal, characteristic, complemented
9C2×#4666C211yesmaximal, characteristic, complemented
10C3×#1437C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#71546C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#13998—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×C4⋊Dic3C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×C4×Dic3C2211yescharacteristic
44C2×#884—24no—
45C2×#884—24no—
46C2×#884C418yescomplemented
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4957—24no—
56#4957—24no—
57#4957—24no—
58#4939—24no—
59C4×Dic3⋊C4—24no—
60#4667—24no—
61#4666—24no—
62#4647—24no—
63C22×#121—31no—
64C2×#390—31no—
65C2×#390—31no—
66C2×#390—31no—
67C2×#390—31no—
68C2×#389—31no—
69C2×#380—31no—
70C2×C4×C4⋊C4—31no—
71C2×C4×C22⋊C4—31no—
72#1439—31no—
73#1439—31no—
74#1438—31no—
75#1438—31no—
76#1437—31no—
77#1437D311yescharacteristic, complemented
78C25×C3C2311yescharacteristic
79C24×D3C2311yescharacteristic
80C24×D3C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67—22no—
96C22×#67—22no—
97C22×#67—41no—
98C22×#67—41no—
99C22×#67C2×C414yes—
100C22×#67C2×C414yes—
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—22no—
110C22×D12—22no—
111C22×D12—41no—
112C22×D12—41no—
113C22×D12C2×C414yes—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—22no—
117C22×C4×D3—22no—
118C22×C4×D3—22no—
119C22×C4×D3—22no—
120C22×C4×D3C2×C414yes—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—41no—
129C2×C3×C22⋊C4C2×C414yes—
130C2×C3×C42—22no—
131C2×C3×C42—22no—
132C2×C3×C42—41no—
133C2×#217—22no—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—41no—
137C2×#217—41no—
138C2×#217—41no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—22no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4C2×C414yes—
165C2×(C2×D3)⋊C4D414yescomplemented
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3—22no—
168C2×C4⋊Dic3—41no—
169C2×Dic3⋊C4—22no—
170C2×Dic3⋊C4—22no—
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×Dic3⋊C4—22no—
175C2×Dic3⋊C4—22no—
176C2×Dic3⋊C4—41no—
177C2×Dic3⋊C4C2×C414yes—
178C2×Dic3⋊C4D414yes—
179C2×Dic3⋊C4D414yes—
180C2×Dic3⋊C4D414yescomplemented
181C2×C4×Dic3—22no—
182C2×C4×Dic3—22no—
183C2×C4×Dic3—22no—
184C2×C4×Dic3—22no—
185C2×C4×Dic3—22no—
186C2×C4×Dic3—22no—
187C2×C4×Dic3—22no—
188C2×C4×Dic3—41no—
189C2×C4×Dic3D414yescomplemented
190#884—232no—
191C3×#95—22no—
192C3×#95—22no—
193C3×#95—22no—
194C3⋊#95—22no—
195C3⋊#95—22no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198C3⋊#95—22no—
199C23×D4—31no—
200C23×D4—31no—
201C23×D4—31no—
202C24×C4—31no—
203C2×#121—38no—
204C2×#121—64no—
205C2×#121—64no—
206C22×C4⋊C4—31no—
207C22×C4⋊C4—31no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—31no—
210C22×C4⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C22⋊C4—31no—
214C22×C22⋊C4—31no—
215C22×C22⋊C4—31no—
216C22×C22⋊C4—31no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—31no—
220C22×C22⋊C4—31no—
221C22×C22⋊C4—31no—
222C22×C22⋊C4C2×D311yescharacteristic
223C22×C22⋊C4C2×D311yescharacteristic
224C22×C22⋊C4C2×D311yescharacteristic
225C22×C42—31no—
226C22×C42—31no—
227C22×C42—31no—
228C22×C42C2×D311yescharacteristic
229#390—64no—
230#390—64no—
231#390—64no—
232#390—64no—
233#389—64no—
234#380—64no—
235C4×C4⋊C4—64no—
236C4×C22⋊C4—64no—
237C2×#95—31no—
238C2×#95—31no—
239C2×#95—31no—
240C2×#95—31no—
241C2×#95—31no—
242C2×#95C2×D311yescharacteristic
243C2×#95C2×D311yescharacteristic
244C2×#95C2×D311yescharacteristic
245C24×C3—21no—
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—21no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—21no—
259C24×C3C22×C412yes—
260C24×C3C2411yescharacteristic
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3—21no—
274C23×D3—21no—
275C23×D3—21no—
276C23×D3—21no—
277C23×D3—21no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—21no—
283C23×D3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C23×D3—21no—
287C23×D3C22×C412yes—
288C23×D3C22×C412yes—
289C23×D3C2×D412yes—
290C23×D3#4112yes—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4C22×C412yes—
325C22×C3×C4C22×C412yes—
326C22×C3×C4C2×D412yes—
327C22×C3×C4C2×D412yes—
328C22×C3×C4C2×D412yes—
329C22×C3×C4C2×D412yes—
330C22×C3×C4C2×D412yes—
331C22×C3×C4#4112yes—
332C22×C3×C4#4112yes—
333C2×#67—28no—
334C2×#67—28no—
335C2×#67—28no—
336C2×#67—28no—
337C2×#67—28no—
338C2×#67—44no—
339C2×#67—44no—
340C2×#67—44no—
341C2×#67—44no—
342C2×#67—44no—
343C2×#67—44no—
344C2×#67—44no—
345C2×#67—44no—
346C2×#67—44no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369C22×Dic3—21no—
370C22×Dic3—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373C22×Dic3—21no—
374C22×Dic3—21no—
375C22×Dic3—21no—
376C22×Dic3C22×C412yes—
377C22×Dic3C22×C412yes—
378C22×Dic3C2×D412yes—
379C22×Dic3C2×D412yes—
380C22×Dic3C2×D412yes—
381C22×Dic3C2×D412yes—
382C22×Dic3C2×D412yes—
383C22×Dic3C2×D412yes—
384C22×Dic3C2×D412yes—
385C22×Dic3C2×D412yes—
386C22×Dic3C2×D412yes—
387C22×Dic3#4112yes—
388C22×Dic3#4112yes—
389C2×D12—28no—
390C2×D12—28no—
391C2×D12—44no—
392C2×D12—44no—
393C2×D12—44no—
394C2×D12—44no—
395C2×D12—44no—
396C2×C4×D3—28no—
397C2×C4×D3—28no—
398C2×C4×D3—28no—
399C2×C4×D3—44no—
400C2×C4×D3—44no—
401C2×C4×D3—44no—
402C2×C4×D3—44no—
403C3×C22⋊C4—28no—
404C3×C22⋊C4—44no—
405C3×C22⋊C4—44no—
406C3×C42—44no—
407#217—44no—
408#217—44no—
409(C2×D3)⋊C4—28no—
410(C2×D3)⋊C4—28no—
411(C2×D3)⋊C4—28no—
412(C2×D3)⋊C4—44no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415(C2×D3)⋊C4—44no—
416(C2×D3)⋊C4—44no—
417(C2×D3)⋊C4—44no—
418C4⋊Dic3—44no—
419Dic3⋊C4—28no—
420Dic3⋊C4—44no—
421Dic3⋊C4—44no—
422Dic3⋊C4C22⋊C4116yescomplemented
423C4×Dic3—28no—
424C4×Dic3—44no—
425C4×Dic3—44no—
426C25—31no—
427C25—31no—
428C25C22×D311yescharacteristic
429C22×D4—34no—
430C22×D4—34no—
431C22×D4—34no—
432C22×D4—62no—
433C22×D4—62no—
434C22×D4—62no—
435C22×D4—62no—
436C22×D4—62no—
437C22×D4—62no—
438C22×D4—62no—
439C22×D4—62no—
440C22×D4—62no—
441C22×D4—62no—
442C22×D4—62no—
443C22×D4—62no—
444C22×D4—62no—
445C22×D4—62no—
446C22×D4—121no—
447C22×D4—121no—
448C22×D4—121no—
449C22×D4—121no—
450C23×C4—31no—
451C23×C4—31no—
452C23×C4—31no—
453C23×C4—31no—
454C23×C4—31no—
455C23×C4—34no—
456C23×C4—31no—
457C23×C4—62no—
458C23×C4—62no—
459C23×C4—62no—
460C23×C4—62no—
461C23×C4—62no—
462C23×C4—62no—
463C23×C4C22×D311yescharacteristic
464C23×C4C22×D311yescharacteristic
465C23×C4C22×D311yescharacteristic
466C23×C4C22×D311yescharacteristic
467C23×C4C22×D311yescharacteristic
468C23×C4C22×D311yescharacteristic
469#121—632no—
470C2×C4⋊C4—34no—
471C2×C4⋊C4—34no—
472C2×C4⋊C4—34no—
473C2×C4⋊C4—34no—
474C2×C4⋊C4—62no—
475C2×C4⋊C4—62no—
476C2×C4⋊C4—62no—
477C2×C4⋊C4—62no—
478C2×C4⋊C4—62no—
479C2×C4⋊C4—62no—
480C2×C4⋊C4—62no—
481C2×C4⋊C4—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—121no—
484C2×C4⋊C4—121no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—34no—
493C2×C22⋊C4—34no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—62no—
497C2×C22⋊C4—62no—
498C2×C22⋊C4—62no—
499C2×C22⋊C4—62no—
500C2×C22⋊C4—62no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4—62no—
504C2×C22⋊C4—62no—
505C2×C22⋊C4—62no—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—62no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4—62no—
512C2×C22⋊C4—62no—
513C2×C22⋊C4—62no—
514C2×C22⋊C4—62no—
515C2×C22⋊C4—62no—
516C2×C22⋊C4—62no—
517C2×C22⋊C4—121no—
518C2×C22⋊C4—121no—
519C2×C22⋊C4—121no—
520C2×C22⋊C4—121no—
521C2×C22⋊C4—121no—
522C2×C22⋊C4—121no—
523C2×C22⋊C4—121no—
524C2×C22⋊C4—121no—
525C2×C22⋊C4—121no—
526C2×C22⋊C4C4×D314yes—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—34no—
530C2×C42—41no—
531C2×C42—62no—
532C2×C42—62no—
533C2×C42—62no—
534C2×C42—62no—
535C2×C42—62no—
536C2×C42—62no—
537C2×C42—62no—
538C2×C42—121no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—62no—
543#95—62no—
544#95—62no—
545#95—62no—
546#95—62no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3C23×C411yescharacteristic
583C23×C3C22×D411yescharacteristic
584C23×C3C22×D411yescharacteristic
585C23×C3C22×D411yescharacteristic
586C23×C3C22×D411yescharacteristic
587C23×C3C22×D411yescharacteristic
588C23×C3C2×#4111yescharacteristic
589C23×C3C2×#4111yescharacteristic
590C23×C3C2×#4111yescharacteristic
591C23×C3C2×#4111yescharacteristic
592C23×C3C2×#4111yescharacteristic
593C23×C3H(5,𝔽2)11yescharacteristic
594C23×C3H(5,𝔽2)11yescharacteristic
595C23×C3H(5,𝔽2)11yescharacteristic
596C23×C32−1+411yescharacteristic
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3—41no—
641C22×D3—41no—
642C22×D3—41no—
643C22×D3—41no—
644C22×D3—41no—
645C22×D3—41no—
646C22×D3—41no—
647C22×D3—41no—
648C22×D3—41no—
649C22×D3—41no—
650C22×D3—41no—
651C22×D3—41no—
652C22×D3—41no—
653C22×D3—41no—
654C22×D3—41no—
655C22×D3—41no—
656C22×D3—41no—
657C22×D3—41no—
658C22×D3—41no—
659C22×D3—41no—
660C22×D3—41no—
661C22×D3—41no—
662C22×D3—41no—
663C22×D3—41no—
664C22×D3—41no—
665C22×D3—41no—
666C22×D3C4×D414yes—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4C2×C22⋊C414yes—
708C2×C3×C4#12114yescomplemented
709#67—416no—
710#67—416no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—22no—
726C2×Dic3—41no—
727C2×Dic3—41no—
728C2×Dic3—41no—
729C2×Dic3—41no—
730C2×Dic3—41no—
731C2×Dic3—41no—
732C2×Dic3—41no—
733C2×Dic3—41no—
734C2×Dic3—41no—
735C2×Dic3—41no—
736C2×Dic3—41no—
737C2×Dic3—41no—
738C2×Dic3—41no—
739C2×Dic3—41no—
740C2×Dic3—41no—
741C2×Dic3—41no—
742C2×Dic3—41no—
743C2×Dic3—41no—
744C2×Dic3—41no—
745C2×Dic3C2×C22⋊C414yes—
746C2×Dic3C2×C22⋊C414yes—
747C2×Dic3C4×D414yes—
748C2×Dic3C4×D414yes—
749C2×Dic3#12114yes—
750C2×Dic3#12114yes—
751C2×Dic3#12414yes—
752C2×Dic3#12714yes—
753D12—416no—
754C4×D3—416no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—32no—
770C24—32no—
771C24—32no—
772C24—32no—
773C24—61no—
774C24—61no—
775C24—61no—
776C24—61no—
777C24—61no—
778C24—61no—
779C24—61no—
780C24—61no—
781C24—61no—
782C24—61no—
783C24—61no—
784C24—61no—
785C24—61no—
786C24—61no—
787C24—61no—
788C24—61no—
789C24—61no—
790C24—61no—
791C24—61no—
792C24—61no—
793C24—61no—
794C24—61no—
795C24—61no—
796C24—61no—
797C24—61no—
798C24—61no—
799C24C2×C4×D312yes—
800C24C23×D311yescharacteristic
801C2×D4—68no—
802C2×D4—68no—
803C2×D4—68no—
804C2×D4—68no—
805C2×D4—68no—
806C2×D4—68no—
807C2×D4—68no—
808C2×D4—124no—
809C2×D4—124no—
810C2×D4—124no—
811C2×D4—124no—
812C2×D4—124no—
813C2×D4—124no—
814C2×D4—124no—
815C2×D4—124no—
816C2×D4—124no—
817C2×D4—124no—
818C2×D4—124no—
819C2×D4—124no—
820C2×D4—124no—
821C2×D4—124no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—32no—
856C22×C4—32no—
857C22×C4—32no—
858C22×C4—32no—
859C22×C4—32no—
860C22×C4—32no—
861C22×C4—32no—
862C22×C4—32no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—32no—
866C22×C4—32no—
867C22×C4—32no—
868C22×C4—68no—
869C22×C4—68no—
870C22×C4—68no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4—61no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—61no—
877C22×C4—61no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—61no—
883C22×C4—61no—
884C22×C4—61no—
885C22×C4—61no—
886C22×C4—61no—
887C22×C4—61no—
888C22×C4—61no—
889C22×C4—61no—
890C22×C4—61no—
891C22×C4—61no—
892C22×C4—61no—
893C22×C4—61no—
894C22×C4—61no—
895C22×C4—61no—
896C22×C4—61no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4—61no—
900C22×C4—124no—
901C22×C4—124no—
902C22×C4—124no—
903C22×C4—124no—
904C22×C4C2×C4×D312yes—
905C22×C4C2×C4×D312yes—
906C22×C4#23512yes—
907C22×C4#23512yes—
908C22×C4D3×D412yes—
909C22×C4D3×D412yes—
910C22×C4D3×D412yes—
911C22×C4D3×D412yes—
912C22×C4D3×D412yes—
913C4⋊C4—316no—
914C4⋊C4—68no—
915C4⋊C4—124no—
916C4⋊C4—124no—
917C4⋊C4—124no—
918C22⋊C4—28no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—68no—
922C22⋊C4—68no—
923C22⋊C4—68no—
924C22⋊C4—124no—
925C22⋊C4—124no—
926C22⋊C4—124no—
927C22⋊C4—124no—
928C22⋊C4—124no—
929C22⋊C4—124no—
930C22⋊C4—124no—
931C22⋊C4—124no—
932C42—44no—
933C42—68no—
934C42—124no—
935C42—124no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—42no—
942C22×C3—42no—
943C22×C3—81no—
944C22×C3—81no—
945C22×C3—81no—
946C22×C3—81no—
947C22×C3—81no—
948C22×C3—81no—
949C22×C3—81no—
950C22×C3—81no—
951C22×C3C22×C22⋊C411yescharacteristic
952C22×C3C2×C4×D411yescharacteristic
953C22×C3C2×C4×D411yescharacteristic
954C22×C3C2×C4×D411yescharacteristic
955C22×C3C4×#4111yescharacteristic
956C22×C3#51811yescharacteristic
957C22×C3#52011yescharacteristic
958C22×C3C2×#12111yescharacteristic
959C22×C3C2×#12111yescharacteristic
960C22×C3C2×#12111yescharacteristic
961C22×C3#52511yescharacteristic
962C22×C3C2×#12411yescharacteristic
963C22×C3#52911yescharacteristic
964C22×C3C2×#12711yescharacteristic
965C22×C3#53211yescharacteristic
966C22×C3#53511yescharacteristic
967C22×C3#53711yescharacteristic
968C22×C3#54011yescharacteristic
969C22×C3#54211yescharacteristic
970C22×C3D4211yescharacteristic
971C22×C3D4211yescharacteristic
972C22×C3D4211yescharacteristic
973C22×C3#54611yescharacteristic
974C22×C3#54611yescharacteristic
975C22×C3#54611yescharacteristic
976C22×C3#54711yescharacteristic
977C22×C3#54811yescharacteristic
978C22×C3#54811yescharacteristic
979C22×C3#54811yescharacteristic
980C22×C3#55011yescharacteristic
981C22×C3#55011yescharacteristic
982C22×C3#55011yescharacteristic
983C22×C3#55311yescharacteristic
984C22×C3#55311yescharacteristic
985C22×C3#55511yescharacteristic
986C2×D3—24no—
987C2×D3—24no—
988C2×D3—24no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—42no—
994C2×D3—42no—
995C2×D3—42no—
996C2×D3—42no—
997C2×D3—42no—
998C2×D3—42no—
999C2×D3—42no—
1000C2×D3—42no—
1001C2×D3—42no—
1002C2×D3—42no—
1003C2×D3—42no—
1004C2×D3—42no—
1005C2×D3—42no—
1006C2×D3—42no—
1007C2×D3—42no—
1008C2×D3—81no—
1009C2×D3—81no—
1010C2×D3—81no—
1011C2×D3—81no—
1012C2×D3—81no—
1013C2×D3—81no—
1014C2×D3—81no—
1015C2×D3—81no—
1016C3×C4—24no—
1017C3×C4—24no—
1018C3×C4—42no—
1019C3×C4—42no—
1020C3×C4—42no—
1021C3×C4—81no—
1022Dic3—24no—
1023Dic3—42no—
1024Dic3—42no—
1025Dic3—42no—
1026Dic3—81no—
1027Dic3#39018yescomplemented
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—34no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—62no—
1065C23—62no—
1066C23—62no—
1067C23—62no—
1068C23—62no—
1069C23—62no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—62no—
1075C23—62no—
1076C23—62no—
1077C23—62no—
1078C23—62no—
1079C23—62no—
1080C23—62no—
1081C23—62no—
1082C23—62no—
1083C23—62no—
1084C23—62no—
1085C23—62no—
1086C23—62no—
1087C23—62no—
1088C23—62no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23—121no—
1104C23—121no—
1105C23—121no—
1106C23—121no—
1107C23—121no—
1108C23—121no—
1109C23—121no—
1110C23—121no—
1111C23—121no—
1112C23—121no—
1113C23—121no—
1114C23—121no—
1115C23—121no—
1116C23—121no—
1117C23—121no—
1118C23—121no—
1119C23—121no—
1120C23—121no—
1121C23—121no—
1122C23—121no—
1123C23—121no—
1124C23—121no—
1125C23—121no—
1126C23—121no—
1127C23—121no—
1128C23—121no—
1129C23—121no—
1130C23—121no—
1131C23—121no—
1132C23—121no—
1133C23C22×C4×D311yescharacteristic
1134C23C2×#23511yescharacteristic
1135C23C2×#23511yescharacteristic
1136C23C2×D3×D411yescharacteristic
1137C23C2×D3×D411yescharacteristic
1138C23C2×D3×D411yescharacteristic
1139C23C2×D3×D411yescharacteristic
1140C23C2×D3×D411yescharacteristic
1141C23#100411yescharacteristic
1142C23D3×#4111yescharacteristic
1143C23D3×#4111yescharacteristic
1144C23D3×#4111yescharacteristic
1145C23#100911yescharacteristic
1146C23#100911yescharacteristic
1147C23#101011yescharacteristic
1148D4—1216no—
1149D4—1216no—
1150D4—1216no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—34no—
1173C2×C4—34no—
1174C2×C4—34no—
1175C2×C4—34no—
1176C2×C4—34no—
1177C2×C4—34no—
1178C2×C4—34no—
1179C2×C4—34no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—62no—
1200C2×C4—62no—
1201C2×C4—62no—
1202C2×C4—62no—
1203C2×C4—62no—
1204C2×C4—62no—
1205C2×C4—62no—
1206C2×C4—62no—
1207C2×C4—62no—
1208C2×C4—62no—
1209C2×C4—62no—
1210C2×C4—62no—
1211C2×C4—62no—
1212C2×C4—62no—
1213C2×C4—62no—
1214C2×C4—1216no—
1215C2×C4—121no—
1216C2×C4—121no—
1217C2×C4—121no—
1218C2×C4—121no—
1219C2×C4—121no—
1220C2×C4—121no—
1221C2×C4—121no—
1222C2×C4—121no—
1223C2×C4—121no—
1224C2×C4—121no—
1225C2×C4—121no—
1226C2×C4—121no—
1227C2×C4—121no—
1228C2×C4—121no—
1229C2×C4—121no—
1230C2×C4—121no—
1231C2×C4—121no—
1232C2×C4—121no—
1233C2×C4—121no—
1234C2×C4D3×C22⋊C414yes—
1235C2×C4#88414yescomplemented
1236C2×C3—82no—
1237C2×C3C2×#39011yescharacteristic
1238C2×C3C4×#12111yescharacteristic
1239C2×C3#232411yescharacteristic
1240C2×C3D4×C22⋊C411yescharacteristic
1241C2×C3#234111yescharacteristic
1242C2×C3#236111yescharacteristic
1243C2×C3#236311yescharacteristic
1244C2×C3#241411yescharacteristic
1245C2×C3#241611yescharacteristic
1246C2×C3#242611yescharacteristic
1247C2×C3#242811yescharacteristic
1248C2×C3#249011yescharacteristic
1249C2×C3#249111yescharacteristic
1250C2×C3#254011yescharacteristic
1251C2×C3#254111yescharacteristic
1252D3—44no—
1253D3—82no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—64no—
1262C22—64no—
1263C22—64no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—122no—
1273C22—122no—
1274C22—122no—
1275C22—122no—
1276C22—122no—
1277C22—122no—
1278C22—122no—
1279C22—122no—
1280C22—122no—
1281C22—122no—
1282C22—122no—
1283C22—122no—
1284C22—122no—
1285C22—122no—
1286C22—122no—
1287C22—122no—
1288C22—122no—
1289C22—122no—
1290C22—122no—
1291C22—241no—
1292C22—241no—
1293C22—241no—
1294C22—241no—
1295C22—241no—
1296C22—241no—
1297C22—241no—
1298C22—241no—
1299C22C4×#23511yescharacteristic
1300C22C2×D3×C22⋊C411yescharacteristic
1301C22C2×#88411yescharacteristic
1302C22#549011yescharacteristic
1303C22#552311yescharacteristic
1304C22#552811yescharacteristic
1305C22#553211yescharacteristic
1306C22#554011yescharacteristic
1307C22C4×D3×D411yescharacteristic
1308C22C4×D3×D411yescharacteristic
1309C22C4×D3×D411yescharacteristic
1310C22#554511yescharacteristic
1311C22#554711yescharacteristic
1312C22#554811yescharacteristic
1313C22#555211yescharacteristic
1314C22#555211yescharacteristic
1315C22#555311yescharacteristic
1316C22#555311yescharacteristic
1317C22#555311yescharacteristic
1318C22#559011yescharacteristic
1319C22#559711yescharacteristic
1320C22D3×#12111yescharacteristic
1321C22D3×#12111yescharacteristic
1322C22#560911yescharacteristic
1323C22#560911yescharacteristic
1324C22#561011yescharacteristic
1325C22#565411yescharacteristic
1326C22#565511yescharacteristic
1327C22#566311yescharacteristic
1328C22D3×#12411yescharacteristic
1329C22#567411yescharacteristic
1330C22#567711yescharacteristic
1331C22#570911yescharacteristic
1332C22#571011yescharacteristic
1333C22D3×#12711yescharacteristic
1334C4—24no—
1335C4—24no—
1336C4—38no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—64no—
1341C4—81no—
1342C4—122no—
1343C4—122no—
1344C4—122no—
1345C4—241no—
1346C3#1399811yescharacteristic, complemented, Sylow
1347C2—82no—
1348C2—124no—
1349C2—242no—
1350C2#7345411yescharacteristic
1351C2#7347011yescharacteristic
1352C2C4×#88411yescharacteristic
1353C2#7469211yescharacteristic
1354C2#7469811yescharacteristic
1355C2#7487811yescharacteristic
1356C2#7546111yescharacteristic
1357C2#7547711yescharacteristic
1358C2#7549511yescharacteristic
1359C2#7549911yescharacteristic
1360C2#7554511yescharacteristic
1361C2#7554611yescharacteristic
1362C2#7634711yescharacteristic
1363C2#7634811yescharacteristic
1364C2D3×#39011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1437C2
socle, cosocleC24×C3C24
prime radicalC22×#884C2
hypercenter#1437D3
hypocenterC3#13998
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#4957C2semidirect
3. C2×#4957C2semidirect
4. C2×#4957C2semidirect
5. C2×#4939C2semidirect
6. C2×C4×Dic3⋊C4C2semidirect
7. C2×#4667C2semidirect
8. C2×#4647C2semidirect
9. C2×#4666C2semidirect
10. C3×#1437C2semidirect
11. #71550C2semidirect
12. #71546C2semidirect
13. #69428C2semidirect
14. #69426C2semidirect
15. #69408C2semidirect
46. C2×#884C4semidirect
77. #1437D3semidirect
165. C2×(C2×D3)⋊C4D4semidirect
180. C2×Dic3⋊C4D4semidirect
189. C2×C4×Dic3D4semidirect
422. Dic3⋊C4C22⋊C4semidirect
708. C2×C3×C4#121semidirect
1027. Dic3#390semidirect
1235. C2×C4#884semidirect
1346. C3#13998semidirect

Maximal subgroups

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

subgroupindex
C22×#8842
C2×#49572
C2×#49392
C2×C4×Dic3⋊C42
C2×#46672
C2×#46472
C2×#46662
C3×#14372
#715502
#715462
#694282
#694262
#694082
#139983