Finite Group Databasebeta

← #10733788

Subgroups — #10733788

Order 768.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4994C211yesmaximal, characteristic, complemented
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C211yesmaximal, characteristic
5C2×#4668C211yesmaximal, characteristic, complemented
6C2×#4668C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13#69423C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69410C211yesmaximal, characteristic, complemented
16#15324—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4994—24no—
53#4987—24no—
54#4668—24no—
55#4668—24no—
56#4665—24no—
57#4665—24no—
58C2×#396—31no—
59C2×#386—31no—
60C2×#386—31no—
61C2×#385—31no—
62C2×#385—31no—
63C2×#380—31no—
64#1445—31no—
65#1442D311yescharacteristic, complemented
66#1441—31no—
67#1441—31no—
68#1439—31no—
69#1439—31no—
70#1439—31no—
71#1438—31no—
72C22⋊#95—31no—
73C24×D3C2311yescharacteristic
74C24×D3C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C22×D12—22no—
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—41no—
93C22×D12—41no—
94C22×D12Q814yes—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3—41no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—41no—
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—41no—
131C2×(C2×D3)⋊C4—41no—
132C2×(C2×D3)⋊C4—41no—
133C2×(C2×D3)⋊C4—41no—
134C2×(C2×D3)⋊C4—41no—
135C2×(C2×D3)⋊C4—41no—
136C2×(C2×D3)⋊C4—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4D414yes—
141C2×(C2×D3)⋊C4D414yes—
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—22no—
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—41no—
149C2×C4⋊Dic3—41no—
150C2×C4⋊Dic3—41no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—22no—
153C2×Dic3⋊C4—22no—
154C2×Dic3⋊C4—22no—
155C2×Dic3⋊C4—41no—
156C2×Dic3⋊C4—41no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—41no—
160C3×#95—41no—
161C3×#95—41no—
162C3×#95D414yescomplemented
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95—41no—
173C23×D4—31no—
174C24×C4—31no—
175C24×C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181C22×C4⋊C4C2×D311yescharacteristic
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192#396—64no—
193#386—64no—
194#386—64no—
195#385—64no—
196#385—64no—
197#380—64no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C24×C3C2411yescharacteristic
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
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×D3C2×D412yes—
240C23×D3C2×D412yes—
241C23×D3C2×Q812yes—
242C23×D3C2×Q812yes—
243C23×D3#4112yes—
244C23×D3#4112yes—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
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×C4C2×D412yes—
288C22×C3×C4C2×D412yes—
289C22×C3×C4C2×D412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×Q812yes—
293C22×C3×C4#4112yes—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
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×Dic3C2×D412yes—
333C22×Dic3C2×D412yes—
334C22×Dic3#4112yes—
335C22×Dic3#4112yes—
336C2×D12—28no—
337C2×D12—28no—
338C2×D12—44no—
339C2×D12—44no—
340C2×D12—44no—
341C2×D12—44no—
342C2×D12—44no—
343C2×C4×D3—28no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C3×C4⋊C4—44no—
358(C2×D3)⋊C4—28no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—44no—
361(C2×D3)⋊C4—44no—
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—
368C4⋊Dic3—44no—
369C4⋊Dic3—44no—
370C4⋊Dic3—44no—
371Dic3⋊C4—44no—
372Dic3⋊C4—44no—
373C25—31no—
374C25—31no—
375C22×D4—34no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—121no—
381C22×D4—121no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—62no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—62no—
392C23×C4—62no—
393C23×C4—62no—
394C23×C4—62no—
395C23×C4—62no—
396C23×C4—121no—
397C23×C4—121no—
398C23×C4—121no—
399C23×C4—121no—
400C23×C4—121no—
401C23×C4—121no—
402C23×C4C22×D311yescharacteristic
403C23×C4C22×D311yescharacteristic
404C23×C4C22×D311yescharacteristic
405C23×C4C22×D311yescharacteristic
406C23×C4C22×D311yescharacteristic
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—62no—
414C2×C4⋊C4—62no—
415C2×C4⋊C4—62no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—62no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—121no—
423C2×C4⋊C4—121no—
424C2×C4⋊C4—121no—
425C2×C4⋊C4—121no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
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×C22⋊C4—121no—
456C2×C22⋊C4—121no—
457#95—22no—
458#95—22no—
459#95—41no—
460#95—41no—
461#95—41no—
462#95—62no—
463#95—62no—
464#95—62no—
465#95—62no—
466#95—62no—
467#95—62no—
468#95—62no—
469#95—121no—
470#95—121no—
471#95—121no—
472#95D1214yescomplemented
473C23×C3C22×D411yescharacteristic
474C23×C3C22×D411yescharacteristic
475C23×C3C22×D411yescharacteristic
476C23×C3C22×Q811yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C23×C3C2×#4111yescharacteristic
481C23×C3C2×#4111yescharacteristic
482C23×C3H(5,𝔽2)11yescharacteristic
483C23×C3H(5,𝔽2)11yescharacteristic
484C23×C3H(5,𝔽2)11yescharacteristic
485C23×C3H(5,𝔽2)11yescharacteristic
486C23×C3H(5,𝔽2)11yescharacteristic
487C23×C32−1+411yescharacteristic
488C22×D3—22no—
489C22×D3—22no—
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—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
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×D3C22⋊Q814yes—
557C22×D3C22⋊Q814yes—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
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—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
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#12114yes—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
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—41no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—41no—
624C2×Dic3—41no—
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—
649D12—416no—
650C4×D3—416no—
651C4×D3—416no—
652C24—32no—
653C24—32no—
654C24—32no—
655C24—32no—
656C24—32no—
657C24—32no—
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—
682C24C23×D311yescharacteristic
683C2×D4—68no—
684C2×D4—68no—
685C2×D4—124no—
686C2×D4—124no—
687C2×D4—124no—
688C2×D4—124no—
689C2×D4—124no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
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—32no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—68no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—61no—
741C22×C4—61no—
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—124no—
776C22×C4—124no—
777C22×C4—124no—
778C22×C4—124no—
779C22×C4—124no—
780C22×C4—124no—
781C22×C4—124no—
782C22×C4—124no—
783C22×C4—124no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4C2×D1212yes—
789C22×C4C2×D1212yes—
790C22×C4C2×D1212yes—
791C22×C4D3×D412yes—
792C22×C4D3×D412yes—
793C22×C4D3×Q812yes—
794C22×C4#23912yes—
795C4⋊C4—44no—
796C4⋊C4—124no—
797C4⋊C4—124no—
798C4⋊C4—124no—
799C4⋊C4—124no—
800C4⋊C4—124no—
801C22⋊C4—68no—
802C22⋊C4—68no—
803C22⋊C4—124no—
804C22⋊C4—124no—
805C22⋊C4—124no—
806C22⋊C4—124no—
807C22⋊C4—124no—
808C22⋊C4—124no—
809C22⋊C4—124no—
810C22⋊C4—124no—
811C22×C3C2×#12111yescharacteristic
812C22×C3C2×C22⋊Q811yescharacteristic
813C22×C3C2×C22⋊Q811yescharacteristic
814C22×C3#52511yescharacteristic
815C22×C3#52511yescharacteristic
816C22×C3#52911yescharacteristic
817C22×C3#53411yescharacteristic
818C22×C3#53511yescharacteristic
819C22×C3#53711yescharacteristic
820C22×C3#53811yescharacteristic
821C22×C3#53811yescharacteristic
822C22×C3#53911yescharacteristic
823C22×C3#54011yescharacteristic
824C22×C3#54211yescharacteristic
825C22×C3#54311yescharacteristic
826C22×C3D4211yescharacteristic
827C22×C3D4211yescharacteristic
828C22×C3#54611yescharacteristic
829C22×C3#54611yescharacteristic
830C22×C3#54611yescharacteristic
831C22×C3#54611yescharacteristic
832C22×C3#54611yescharacteristic
833C22×C3#54611yescharacteristic
834C22×C3#54711yescharacteristic
835C22×C3D4×Q811yescharacteristic
836C22×C3#55111yescharacteristic
837C22×C3#55211yescharacteristic
838C22×C3#55311yescharacteristic
839C22×C3#55311yescharacteristic
840C22×C3#55311yescharacteristic
841C22×C3#55411yescharacteristic
842C22×C3#55411yescharacteristic
843C22×C3#55411yescharacteristic
844C22×C3#56011yescharacteristic
845C22×C3#56211yescharacteristic
846C2×D3—24no—
847C2×D3—24no—
848C2×D3—24no—
849C2×D3—24no—
850C2×D3—24no—
851C2×D3—24no—
852C2×D3—42no—
853C2×D3—42no—
854C2×D3—42no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C3×C4—24no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—42no—
881C3×C4—81no—
882C3×C4—81no—
883Dic3—42no—
884Dic3—42no—
885Dic3—42no—
886Dic3—42no—
887Dic3—81no—
888Dic3—81no—
889C23—34no—
890C23—34no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
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—
956C23—121no—
957C23—121no—
958C23—121no—
959C23C22×D1211yescharacteristic
960C23C2×D3×D411yescharacteristic
961C23C2×D3×D411yescharacteristic
962C23#100411yescharacteristic
963C23#100411yescharacteristic
964C23C2×D3×Q811yescharacteristic
965C23C2×#23911yescharacteristic
966C23D3×#4111yescharacteristic
967C23D3×#4111yescharacteristic
968C23D3×#4111yescharacteristic
969C23D3×#4111yescharacteristic
970C23#100911yescharacteristic
971C23#100911yescharacteristic
972C23#100911yescharacteristic
973C23#101011yescharacteristic
974D4—1216no—
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—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
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—41no—
1021C2×C4—41no—
1022C2×C4—41no—
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—1216no—
1036C2×C4—1216no—
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—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4#89514yes—
1068C2×C3#241711yescharacteristic
1069C2×C3#242411yescharacteristic
1070C2×C3#243711yescharacteristic
1071C2×C3#244911yescharacteristic
1072C2×C3#245011yescharacteristic
1073C2×C3#245711yescharacteristic
1074C2×C3#247011yescharacteristic
1075C2×C3#253511yescharacteristic
1076C2×C3#257911yescharacteristic
1077C2×C3#267111yescharacteristic
1078C2×C3#267811yescharacteristic
1079C2×C3#269111yescharacteristic
1080C2×C3#269211yescharacteristic
1081C2×C3#275011yescharacteristic
1082C2×C3#278011yescharacteristic
1083D3—44no—
1084D3—44no—
1085C22—64no—
1086C22—64no—
1087C22—64no—
1088C22—64no—
1089C22—64no—
1090C22—64no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22C2×#89511yescharacteristic
1116C22#552411yescharacteristic
1117C22#552511yescharacteristic
1118C22D4×D1211yescharacteristic
1119C22#555411yescharacteristic
1120C22#555411yescharacteristic
1121C22Q8×D1211yescharacteristic
1122C22#559011yescharacteristic
1123C22#560511yescharacteristic
1124C22#560811yescharacteristic
1125C22#561511yescharacteristic
1126C22D3×C22⋊Q811yescharacteristic
1127C22D3×C22⋊Q811yescharacteristic
1128C22#562711yescharacteristic
1129C22#563411yescharacteristic
1130C22#564411yescharacteristic
1131C22#565411yescharacteristic
1132C22#565511yescharacteristic
1133C22#566111yescharacteristic
1134C22#566611yescharacteristic
1135C22#566711yescharacteristic
1136C22#567611yescharacteristic
1137C22#567611yescharacteristic
1138C22#567611yescharacteristic
1139C22#567911yescharacteristic
1140C22#569011yescharacteristic
1141C22#569011yescharacteristic
1142C22#569411yescharacteristic
1143C22#569511yescharacteristic
1144C22#569511yescharacteristic
1145C22#570411yescharacteristic
1146C22#570611yescharacteristic
1147C22#570711yescharacteristic
1148C22#571011yescharacteristic
1149C22#573011yescharacteristic
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—81no—
1156C4—81no—
1157C4—122no—
1158C4—122no—
1159C4—122no—
1160C4—122no—
1161C4—241no—
1162C4—241no—
1163C3#1532411yescharacteristic, complemented, Sylow
1164C2—124no—
1165C2—124no—
1166C2#7423911yescharacteristic
1167C2#7460511yescharacteristic
1168C2#7532111yescharacteristic
1169C2#7539411yescharacteristic
1170C2#7585111yescharacteristic
1171C2#7591611yescharacteristic
1172C2#7621211yescharacteristic
1173C2#7686511yescharacteristic
1174C2#7713111yescharacteristic
1175C2#7769511yescharacteristic
1176C2#7796011yescharacteristic
1177C2#7800011yescharacteristic
1178C2#7814011yescharacteristic
1179C2#7834411yescharacteristic
1180C2#7839211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1442C2
prime radicalC23×D12C22
hypercenter#1442D3
hypocenterC3#15324
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#4994C2semidirect
2. C2×#4987C2semidirect
5. C2×#4668C2semidirect
6. C2×#4668C2semidirect
7. C3×#1442C2semidirect
8. #69428C2semidirect
9. #69427C2semidirect
10. #69427C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. #69423C2semidirect
14. #69411C2semidirect
15. #69410C2semidirect
65. #1442D3semidirect
162. C3×#95D4semidirect
472. #95D12semidirect
1163. C3#15324semidirect

Maximal subgroups

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

subgroupindex
C2×#49942
C2×#49872
C2×#46652
C2×#46682
C3×#14422
#694282
#694272
#694262
(C2×D3)⋊#952
#694232
#694112
#694102
#153243