Finite Group Databasebeta

← #10733746

Subgroups — #10733746

Order 768.

1982 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic
2C2×C3×#391C211yesmaximal, characteristic, complemented
3C2×#5230C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×#4940C211yesmaximal, characteristic, complemented
6C2×#4672C211yesmaximal, characteristic
7#71570C211yesmaximal, characteristic, complemented
8#71537C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69428C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic
14#69407C211yesmaximal, characteristic, complemented
15#69405C211yesmaximal, characteristic, complemented
16#15321—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C2×#947—24no—
22C2×#947—24no—
23C2×#947—24no—
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic
41C3×#391—24no—
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46#5230—24no—
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4994—24no—
58#4940—24no—
59#4672—24no—
60C22×#124—31no—
61C2×#396—31no—
62C2×#395—31no—
63C2×#394—31no—
64C2×#391D311yescharacteristic, complemented
65C2×#388—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1438—31no—
72#1437—31no—
73#1436—31no—
74#1436—31no—
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8D414yes—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—41no—
103C22×D12—41no—
104C2×C3×C4⋊C4—22no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—41no—
107C2×C3×C42—22no—
108C2×C3×C42—22no—
109C2×C3×C42—41no—
110#947—232no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4D414yes—
146C2×(C2×D3)⋊C4D414yes—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—41no—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—41no—
158C2×Dic3⋊C4—41no—
159C2×C4×Dic3—22no—
160C2×C4×Dic3—22no—
161C2×C4×Dic3—22no—
162C3×#95—22no—
163C3×#95—22no—
164C3×#95—22no—
165C3×#95D414yes—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C23×Q8C2×D311yescharacteristic
177C23×D4—31no—
178C2×#124—64no—
179C2×#124—64no—
180C2×#124—64no—
181C22×C4⋊C4—31no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C42—31no—
199C22×C42C2×D311yescharacteristic
200#396—64no—
201#395—64no—
202#394—64no—
203#391—24no—
204#388—64no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3C2411yescharacteristic
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3C2×D412yes—
249C23×D3C2×D412yes—
250C2×C3×Q8—28no—
251C2×C3×Q8—28no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4#4112yes—
305C22×C3×C4#4112yes—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3#4112yes—
346C22×Dic3#4112yes—
347C22×Dic3#4112yes—
348C2×D12—28no—
349C2×D12—44no—
350C2×D12—44no—
351C2×D12—44no—
352C2×D12—44no—
353C2×D12—44no—
354C2×D12—44no—
355C3×C4⋊C4—44no—
356C3×C42—44no—
357(C2×D3)⋊C4—28no—
358(C2×D3)⋊C4—28no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—28no—
362(C2×D3)⋊C4—44no—
363(C2×D3)⋊C4—44no—
364(C2×D3)⋊C4—44no—
365(C2×D3)⋊C4—44no—
366(C2×D3)⋊C4—44no—
367(C2×D3)⋊C4—44no—
368(C2×D3)⋊C4—44no—
369C4⋊Dic3—44no—
370Dic3⋊C4—44no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373C4×Dic3—28no—
374C25—31no—
375C25—31no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—41no—
381C22×Q8—41no—
382C22×Q8D1214yes—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C22×D4—121no—
389C22×D4—121no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C23×C4C22×D311yescharacteristic
400C23×C4C22×D311yescharacteristic
401C23×C4C22×D311yescharacteristic
402C23×C4C22×D311yescharacteristic
403#124—632no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—121no—
417C2×C4⋊C4—121no—
418C2×C4⋊C4—121no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—62no—
427C2×C22⋊C4—62no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—121no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4—121no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—41no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—62no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—121no—
474#95#6714yes—
475C23×C3C22×D411yescharacteristic
476C23×C3C22×D411yescharacteristic
477C23×C3C22×D411yescharacteristic
478C23×C3C22×D411yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C32−1+411yescharacteristic
488C23×C32−1+411yescharacteristic
489C23×C32−1+411yescharacteristic
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C22×D3—41no—
515C22×D3—41no—
516C22×D3—41no—
517C22×D3—41no—
518C22×D3—41no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3—41no—
558C22×D3—41no—
559C22×D3—41no—
560C3×Q8—416no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4#12014yes—
609C2×C3×C4#12114yes—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652D12—416no—
653C24—32no—
654C24—32no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24C23×D311yescharacteristic
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×D4—68no—
692C2×D4—124no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
697C2×D4—124no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—61no—
743C22×C4—61no—
744C22×C4—61no—
745C22×C4—61no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4C2×D1212yes—
780C22×C4C2×D1212yes—
781C22×C4C2×D1212yes—
782C22×C4#23512yes—
783C22×C4D3×D412yes—
784C22×C4D3×D412yes—
785C22×C4#23912yes—
786C22×C4C2×#6712yes—
787C22×C4C2×#6712yes—
788C22×C4C2×#6712yes—
789C4⋊C4—44no—
790C4⋊C4—124no—
791C4⋊C4—124no—
792C4⋊C4—124no—
793C4⋊C4—124no—
794C22⋊C4—68no—
795C22⋊C4—68no—
796C22⋊C4—68no—
797C22⋊C4—68no—
798C22⋊C4—68no—
799C22⋊C4—124no—
800C22⋊C4—124no—
801C22⋊C4—124no—
802C22⋊C4—124no—
803C22⋊C4—124no—
804C22⋊C4—124no—
805C22⋊C4—124no—
806C42—44no—
807C42—68no—
808C22×C3C2×#12011yescharacteristic
809C22×C3C2×#12111yescharacteristic
810C22×C3#52511yescharacteristic
811C22×C3#52911yescharacteristic
812C22×C3#53211yescharacteristic
813C22×C3#53211yescharacteristic
814C22×C3#53411yescharacteristic
815C22×C3#53611yescharacteristic
816C22×C3#53611yescharacteristic
817C22×C3#53711yescharacteristic
818C22×C3#53811yescharacteristic
819C22×C3#54211yescharacteristic
820C22×C3#54211yescharacteristic
821C22×C3#54211yescharacteristic
822C22×C3#54211yescharacteristic
823C22×C3D4211yescharacteristic
824C22×C3D4211yescharacteristic
825C22×C3#54611yescharacteristic
826C22×C3#54611yescharacteristic
827C22×C3#54611yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#54711yescharacteristic
830C22×C3#54711yescharacteristic
831C22×C3#54711yescharacteristic
832C22×C3#54811yescharacteristic
833C22×C3#54811yescharacteristic
834C22×C3#54811yescharacteristic
835C22×C3#54811yescharacteristic
836C22×C3#55011yescharacteristic
837C22×C3#55111yescharacteristic
838C22×C3#55511yescharacteristic
839C22×C3#55611yescharacteristic
840C22×C3#55611yescharacteristic
841C22×C3#56211yescharacteristic
842C22×C3#56311yescharacteristic
843C2×D3—42no—
844C2×D3—42no—
845C2×D3—42no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—42no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—42no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—81no—
858C2×D3—81no—
859C2×D3—81no—
860C2×D3—81no—
861C2×D3—81no—
862C2×D3—81no—
863C2×D3—81no—
864C2×D3—81no—
865C2×D3—81no—
866C2×D3—81no—
867C2×D3—81no—
868C2×D3—81no—
869C2×D3—81no—
870C2×D3—81no—
871C2×D3—81no—
872C2×D3—81no—
873C3×C4—24no—
874C3×C4—24no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—81no—
880Dic3—42no—
881Dic3—42no—
882Dic3—42no—
883Dic3—42no—
884Dic3—42no—
885Dic3—81no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23—121no—
904C23—121no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—121no—
914C23—121no—
915C23—121no—
916C23—121no—
917C23—121no—
918C23—121no—
919C23—121no—
920C23—121no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23C22×D1211yescharacteristic
957C23C2×#23511yescharacteristic
958C23C2×D3×D411yescharacteristic
959C23C2×D3×D411yescharacteristic
960C23#100411yescharacteristic
961C23#100411yescharacteristic
962C23C2×#23911yescharacteristic
963C23#100711yescharacteristic
964C23#100711yescharacteristic
965C23#100711yescharacteristic
966C23D3×#4111yescharacteristic
967C23D3×#4111yescharacteristic
968C23D3×#4111yescharacteristic
969C23#100911yescharacteristic
970C23C22×#6711yescharacteristic
971Q8—416no—
972D4—1216no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—62no—
1021C2×C4—62no—
1022C2×C4—62no—
1023C2×C4—62no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—121no—
1039C2×C4—121no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4#88214yes—
1063C2×C4#93014yes—
1064C2×C3#240711yescharacteristic
1065C2×C3#241011yescharacteristic
1066C2×C3#242611yescharacteristic
1067C2×C3#243211yescharacteristic
1068C2×C3#246111yescharacteristic
1069C2×C3#247411yescharacteristic
1070C2×C3#252111yescharacteristic
1071C2×C3#254511yescharacteristic
1072C2×C3#255511yescharacteristic
1073C2×C3#267211yescharacteristic
1074C2×C3#267411yescharacteristic
1075C2×C3#270011yescharacteristic
1076C2×C3#271511yescharacteristic
1077C2×C3#273011yescharacteristic
1078C2×C3#273111yescharacteristic
1079D3—82no—
1080D3—82no—
1081C22—122no—
1082C22—122no—
1083C22—122no—
1084C22—122no—
1085C22—122no—
1086C22—122no—
1087C22—122no—
1088C22—122no—
1089C22—122no—
1090C22—122no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—241no—
1096C22—241no—
1097C22—241no—
1098C22—241no—
1099C22—241no—
1100C22—241no—
1101C22—241no—
1102C22—241no—
1103C22—241no—
1104C22—241no—
1105C22—241no—
1106C22—241no—
1107C22—241no—
1108C22—241no—
1109C22—241no—
1110C22—241no—
1111C22C2×#88211yescharacteristic
1112C22#549011yescharacteristic
1113C22#549011yescharacteristic
1114C22#549311yescharacteristic
1115C22#556811yescharacteristic
1116C22#556811yescharacteristic
1117C22#557611yescharacteristic
1118C22#557611yescharacteristic
1119C22#557611yescharacteristic
1120C22#557711yescharacteristic
1121C22#558011yescharacteristic
1122C22#558211yescharacteristic
1123C22#562711yescharacteristic
1124C22#562911yescharacteristic
1125C22#563111yescharacteristic
1126C22#563111yescharacteristic
1127C22#563711yescharacteristic
1128C22#564011yescharacteristic
1129C22#564011yescharacteristic
1130C22#564711yescharacteristic
1131C22#566811yescharacteristic
1132C22#567011yescharacteristic
1133C22#567611yescharacteristic
1134C22#567811yescharacteristic
1135C22#572411yescharacteristic
1136C22#572611yescharacteristic
1137C22#573311yescharacteristic
1138C22#573511yescharacteristic
1139C22C2×#93011yescharacteristic
1140C22D4×#6711yescharacteristic
1141C22D4×#6711yescharacteristic
1142C22#581611yescharacteristic
1143C22#581711yescharacteristic
1144C22#582911yescharacteristic
1145C22#583211yescharacteristic
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—81no—
1153C4—122no—
1154C4—122no—
1155C4—122no—
1156C4—122no—
1157C4—122no—
1158C4—241no—
1159C3#1532111yescharacteristic, complemented, Sylow
1160C2—242no—
1161C2—242no—
1162C2#7649811yescharacteristic
1163C2#7651511yescharacteristic
1164C2#7657111yescharacteristic
1165C2#7657211yescharacteristic
1166C2#7661811yescharacteristic
1167C2#7663511yescharacteristic
1168C2#7664911yescharacteristic
1169C2#7665311yescharacteristic
1170C2#8212711yescharacteristic
1171C2#8247411yescharacteristic
1172C2#8249511yescharacteristic
1173C2#8276711yescharacteristic
1174C2#8282611yescharacteristic
1175C2#8297511yescharacteristic
1176C2#8326511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#391C2
prime radicalC23×D12C22
hypercenterC2×#391D3
hypocenterC3#15321
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×C3×#391C2semidirect
3. C2×#5230C2semidirect
4. C2×#4994C2semidirect
5. C2×#4940C2semidirect
7. #71570C2semidirect
8. #71537C2semidirect
9. #69429C2semidirect
10. #69428C2semidirect
11. #69428C2semidirect
12. #69427C2semidirect
14. #69407C2semidirect
15. #69405C2semidirect
64. C2×#391D3semidirect
1159. C3#15321semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C2×C3×#3912
C2×#52302
C2×#49942
C2×#49402
C2×#46722
#715702
#715372
#694292
#694282
#694272
#694262
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