Finite Group Databasebeta

← #10726641

Subgroups — #10726641

Order 768.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#896C211yesmaximal, characteristic, complemented
2C22×C4×D12C211yesmaximal, characteristic
3C2×#4989C211yesmaximal, characteristic, complemented
4C2×#4673C211yesmaximal, characteristic, complemented
5C2×#4668C211yesmaximal, characteristic, complemented
6C2×#4656C211yesmaximal, characteristic, complemented
7C3×#1436C211yesmaximal, characteristic, complemented
8#71536C211yesmaximal, characteristic, complemented
9#69428C211yesmaximal, characteristic, complemented
10#69428C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic
13#69426C211yesmaximal, characteristic
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69411C211yesmaximal, characteristic, complemented
16#14723—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×Dic6C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C2×#896—24no—
39C2×#896—24no—
40C2×#896—24no—
41C2×C4×D12—24no—
42C2×C4×D12—24no—
43C2×C4×D12—24no—
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
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
57C2×C3⋊#95C2211yescharacteristic
58#4989—24no—
59#4673—24no—
60#4668—24no—
61#4656—24no—
62C22×C22⋊Q8—31no—
63C22×C4×D4—31no—
64C2×#395—31no—
65C2×#393—31no—
66C2×#385—31no—
67C2×#385—31no—
68#1441—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1438—31no—
73#1438—31no—
74#1436—31no—
75#1436D311yescharacteristic, complemented
76C22⋊#95—31no—
77C24×D3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12Q814yescomplemented
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3D414yes—
113C22×Dic6—22no—
114C22×Dic6—22no—
115C22×Dic6—22no—
116C22×Dic6—22no—
117C22×Dic6—22no—
118C22×Dic6—41no—
119C22×Dic6—41no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4D414yescomplemented
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C2×C3×C42—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—22no—
138C2×(C2×D3)⋊C4—22no—
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—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4D414yes—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3—41no—
161C2×C4⋊Dic3D414yes—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—41no—
170C2×Dic3⋊C4D414yescomplemented
171#896—232no—
172C4×D12—232no—
173C3×#95—22no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95—22no—
177C3×#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C23×Q8—31no—
188C23×D4—31no—
189C24×C4—31no—
190C24×C4—31no—
191C2×C22⋊Q8—64no—
192C2×C22⋊Q8—64no—
193C2×C22⋊Q8—64no—
194C2×C4×D4—64no—
195C2×C4×D4—64no—
196C2×C4×D4—64no—
197C22×C4⋊C4—31no—
198C22×C4⋊C4—31no—
199C22×C4⋊C4—31no—
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4C2×D311yescharacteristic
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C42C2×D311yescharacteristic
214#395—64no—
215#393—64no—
216#385—64no—
217#385—64no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95—31no—
226C2×#95—31no—
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C2×#95C2×D311yescharacteristic
232C24×C3C2411yescharacteristic
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×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3C2×D412yes—
258C23×D3C2×D412yes—
259C23×D3C2×Q812yes—
260C23×D3C2×Q812yes—
261C23×D3#4112yes—
262C23×D3#4112yes—
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×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2×Q812yes—
310C22×C3×C4#4112yes—
311C22×C3×C4#4112yes—
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×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3C2×D412yes—
351C22×Dic3C2×D412yes—
352C22×Dic3C2×D412yes—
353C22×Dic3#4112yes—
354C2×D12—28no—
355C2×D12—28no—
356C2×D12—28no—
357C2×D12—28no—
358C2×D12—28no—
359C2×D12—28no—
360C2×D12—28no—
361C2×C4×D3—28no—
362C2×C4×D3—28no—
363C2×C4×D3—28no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C2×Dic6—28no—
376C2×Dic6—44no—
377C2×Dic6—44no—
378C2×Dic6—44no—
379C2×Dic6—44no—
380C2×Dic6—44no—
381C2×Dic6—44no—
382C3×C4⋊C4—28no—
383C3×C42—28no—
384(C2×D3)⋊C4—28no—
385(C2×D3)⋊C4—28no—
386(C2×D3)⋊C4—28no—
387(C2×D3)⋊C4—28no—
388(C2×D3)⋊C4—28no—
389(C2×D3)⋊C4—28no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394C4⋊Dic3—28no—
395C4⋊Dic3—44no—
396Dic3⋊C4—28no—
397Dic3⋊C4—28no—
398Dic3⋊C4—44no—
399C25—31no—
400C25—31no—
401C22×Q8—62no—
402C22×Q8—62no—
403C22×Q8—62no—
404C22×Q8—62no—
405C22×Q8—62no—
406C22×Q8—121no—
407C22×Q8—121no—
408C22×D4—34no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—62no—
414C22×D4—62no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—31no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—34no—
421C23×C4—31no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—121no—
432C23×C4—121no—
433C23×C4—121no—
434C23×C4—121no—
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C23×C4C22×D311yescharacteristic
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442C22⋊Q8—632no—
443C4×D4—632no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—34no—
447C2×C4⋊C4—34no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—62no—
453C2×C4⋊C4—62no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—121no—
460C2×C4⋊C4—121no—
461C2×C4⋊C4D1214yescomplemented
462C2×C22⋊C4—34no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—62no—
501#95—62no—
502#95—62no—
503#95—62no—
504#95—62no—
505#95—62no—
506#95—62no—
507#95—62no—
508#95—62no—
509C23×C3C22×D411yescharacteristic
510C23×C3C22×D411yescharacteristic
511C23×C3C22×D411yescharacteristic
512C23×C3C22×D411yescharacteristic
513C23×C3C22×D411yescharacteristic
514C23×C3C22×Q811yescharacteristic
515C23×C3C2×#4111yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3H(5,𝔽2)11yescharacteristic
521C23×C3H(5,𝔽2)11yescharacteristic
522C23×C32−1+411yescharacteristic
523C23×C32−1+411yescharacteristic
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—41no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—41no—
581C22×D3—41no—
582C22×D3—41no—
583C22×D3—41no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3—41no—
587C22×D3—41no—
588C22×D3—41no—
589C22×D3—41no—
590C22×D3—41no—
591C22×D3—41no—
592C22×D3C22⋊Q814yes—
593C22×D3C22⋊Q814yescomplemented
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4#12014yes—
642C2×C3×C4C22⋊Q814yescomplemented
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—22no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3#12014yes—
685D12—232no—
686C4×D3—416no—
687C4×D3—416no—
688Dic6—416no—
689C24—32no—
690C24—32no—
691C24—32no—
692C24—32no—
693C24—32no—
694C24—32no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24—61no—
717C24—61no—
718C24—61no—
719C24C23×D311yescharacteristic
720C2×Q8—68no—
721C2×Q8—124no—
722C2×Q8—124no—
723C2×Q8—124no—
724C2×Q8—124no—
725C2×Q8—124no—
726C2×Q8—124no—
727C2×D4—68no—
728C2×D4—68no—
729C2×D4—68no—
730C2×D4—68no—
731C2×D4—68no—
732C2×D4—68no—
733C2×D4—68no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—32no—
774C22×C4—32no—
775C22×C4—32no—
776C22×C4—32no—
777C22×C4—32no—
778C22×C4—32no—
779C22×C4—32no—
780C22×C4—68no—
781C22×C4—68no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—68no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—61no—
814C22×C4—61no—
815C22×C4—61no—
816C22×C4—61no—
817C22×C4—61no—
818C22×C4—124no—
819C22×C4—124no—
820C22×C4—124no—
821C22×C4—124no—
822C22×C4—124no—
823C22×C4—124no—
824C22×C4—124no—
825C22×C4—124no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4—124no—
829C22×C4C2×D1212yes—
830C22×C4C2×D1212yes—
831C22×C4C2×D1212yes—
832C22×C4#23512yes—
833C22×C4#23512yes—
834C22×C4D3×D412yes—
835C22×C4D3×D412yes—
836C22×C4D3×D412yes—
837C22×C4D3×D412yes—
838C22×C4D3×Q812yes—
839C4⋊C4—28no—
840C4⋊C4—68no—
841C4⋊C4—68no—
842C4⋊C4—68no—
843C4⋊C4—124no—
844C4⋊C4—124no—
845C22⋊C4—68no—
846C22⋊C4—68no—
847C22⋊C4—68no—
848C22⋊C4—68no—
849C22⋊C4—68no—
850C22⋊C4—68no—
851C22⋊C4—124no—
852C22⋊C4—124no—
853C22⋊C4—124no—
854C22⋊C4—124no—
855C42—28no—
856C22×C3C2×#12011yescharacteristic
857C22×C3C2×#12011yescharacteristic
858C22×C3C2×C22⋊Q811yescharacteristic
859C22×C3C2×C22⋊Q811yescharacteristic
860C22×C3C2×C22⋊Q811yescharacteristic
861C22×C3#52511yescharacteristic
862C22×C3#52511yescharacteristic
863C22×C3#52511yescharacteristic
864C22×C3#52511yescharacteristic
865C22×C3#52511yescharacteristic
866C22×C3#53211yescharacteristic
867C22×C3#53211yescharacteristic
868C22×C3#53211yescharacteristic
869C22×C3#53411yescharacteristic
870C22×C3#53611yescharacteristic
871C22×C3#53911yescharacteristic
872C22×C3#53911yescharacteristic
873C22×C3#54211yescharacteristic
874C22×C3#54211yescharacteristic
875C22×C3D4211yescharacteristic
876C22×C3D4211yescharacteristic
877C22×C3D4211yescharacteristic
878C22×C3D4211yescharacteristic
879C22×C3#54711yescharacteristic
880C22×C3#54711yescharacteristic
881C22×C3#54811yescharacteristic
882C22×C3#54811yescharacteristic
883C22×C3#54811yescharacteristic
884C22×C3#54811yescharacteristic
885C22×C3D4×Q811yescharacteristic
886C22×C3D4×Q811yescharacteristic
887C22×C3#55111yescharacteristic
888C22×C3#55111yescharacteristic
889C22×C3#55411yescharacteristic
890C22×C3#55411yescharacteristic
891C2×D3—24no—
892C2×D3—24no—
893C2×D3—24no—
894C2×D3—24no—
895C2×D3—24no—
896C2×D3—24no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—42no—
903C2×D3—42no—
904C2×D3—42no—
905C2×D3—42no—
906C2×D3—42no—
907C2×D3—42no—
908C2×D3—42no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3—42no—
912C2×D3—42no—
913C2×D3—42no—
914C2×D3—42no—
915C2×D3—42no—
916C2×D3—42no—
917C2×D3—42no—
918C2×D3—42no—
919C2×D3—42no—
920C2×D3—42no—
921C3×C4—24no—
922C3×C4—24no—
923C3×C4—42no—
924C3×C4—42no—
925C3×C4—42no—
926C3×C4—42no—
927C3×C4—81no—
928Dic3—24no—
929Dic3—42no—
930Dic3—42no—
931Dic3—42no—
932Dic3—42no—
933Dic3—81no—
934C23—34no—
935C23—34no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—62no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23—121no—
986C23—121no—
987C23—121no—
988C23—121no—
989C23—121no—
990C23—121no—
991C23—121no—
992C23—121no—
993C23—121no—
994C23—121no—
995C23—121no—
996C23—121no—
997C23—121no—
998C23—121no—
999C23—121no—
1000C23—121no—
1001C23—121no—
1002C23—121no—
1003C23—121no—
1004C23C22×D1211yescharacteristic
1005C23C2×#23511yescharacteristic
1006C23C2×#23511yescharacteristic
1007C23C2×D3×D411yescharacteristic
1008C23C2×D3×D411yescharacteristic
1009C23C2×D3×D411yescharacteristic
1010C23C2×D3×D411yescharacteristic
1011C23C2×D3×Q811yescharacteristic
1012C23#100711yescharacteristic
1013C23D3×#4111yescharacteristic
1014C23D3×#4111yescharacteristic
1015C23D3×#4111yescharacteristic
1016C23#100911yescharacteristic
1017C23#100911yescharacteristic
1018C23#101011yescharacteristic
1019Q8—1216no—
1020D4—632no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—34no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—62no—
1070C2×C4—62no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—62no—
1080C2×C4—62no—
1081C2×C4—62no—
1082C2×C4—62no—
1083C2×C4—62no—
1084C2×C4—62no—
1085C2×C4—62no—
1086C2×C4—62no—
1087C2×C4—1216no—
1088C2×C4—1216no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C4—121no—
1107C2×C4—121no—
1108C2×C4—121no—
1109C2×C4—121no—
1110C2×C4—121no—
1111C2×C4—121no—
1112C2×C4#88214yes—
1113C2×C4#89614yescomplemented
1114C2×C3#238811yescharacteristic
1115C2×C3#240311yescharacteristic
1116C2×C3#240911yescharacteristic
1117C2×C3#243211yescharacteristic
1118C2×C3#244911yescharacteristic
1119C2×C3#244911yescharacteristic
1120C2×C3#245211yescharacteristic
1121C2×C3#245211yescharacteristic
1122C2×C3#246111yescharacteristic
1123C2×C3#246111yescharacteristic
1124C2×C3#246311yescharacteristic
1125C2×C3#246311yescharacteristic
1126C2×C3#256411yescharacteristic
1127C2×C3#263811yescharacteristic
1128C2×C3#284811yescharacteristic
1129D3—44no—
1130D3—44no—
1131C22—64no—
1132C22—64no—
1133C22—64no—
1134C22—64no—
1135C22—64no—
1136C22—64no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22—122no—
1144C22—122no—
1145C22—122no—
1146C22—122no—
1147C22—122no—
1148C22—122no—
1149C22—122no—
1150C22—122no—
1151C22—122no—
1152C22—122no—
1153C22—122no—
1154C22—122no—
1155C22—122no—
1156C22—122no—
1157C22—122no—
1158C22—122no—
1159C22—122no—
1160C22—122no—
1161C22#547711yescharacteristic
1162C22C2×#88211yescharacteristic
1163C22#550711yescharacteristic
1164C22C2×#89611yescharacteristic
1165C22#552411yescharacteristic
1166C22#552711yescharacteristic
1167C22#553411yescharacteristic
1168C22#554711yescharacteristic
1169C22#554711yescharacteristic
1170C22#554711yescharacteristic
1171C22#554811yescharacteristic
1172C22#554811yescharacteristic
1173C22D4×D1211yescharacteristic
1174C22D4×D1211yescharacteristic
1175C22#555211yescharacteristic
1176C22Q8×D1211yescharacteristic
1177C22#557611yescharacteristic
1178C22#557911yescharacteristic
1179C22#558211yescharacteristic
1180C22D3×#12011yescharacteristic
1181C22#560911yescharacteristic
1182C22#560911yescharacteristic
1183C22D3×C22⋊Q811yescharacteristic
1184C22D3×C22⋊Q811yescharacteristic
1185C22#562811yescharacteristic
1186C22#563311yescharacteristic
1187C22#565311yescharacteristic
1188C22#565511yescharacteristic
1189C22#565611yescharacteristic
1190C22#567711yescharacteristic
1191C22#569011yescharacteristic
1192C22#569211yescharacteristic
1193C22#570511yescharacteristic
1194C22#570711yescharacteristic
1195C22#572711yescharacteristic
1196C4—24no—
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—64no—
1203C4—81no—
1204C4—122no—
1205C4—122no—
1206C4—122no—
1207C4—122no—
1208C4—241no—
1209C3#1472311yescharacteristic, complemented, Sylow
1210C2—124no—
1211C2—124no—
1212C2#7358011yescharacteristic
1213C2#7367511yescharacteristic
1214C2#7378211yescharacteristic
1215C2#7441111yescharacteristic
1216C2#7465511yescharacteristic
1217C2#7488411yescharacteristic
1218C2#7532111yescharacteristic
1219C2#7532711yescharacteristic
1220C2#7536011yescharacteristic
1221C2#7537911yescharacteristic
1222C2#7551211yescharacteristic
1223C2#7585611yescharacteristic
1224C2#7601011yescharacteristic
1225C2#7622511yescharacteristic
1226C2#7661911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14723
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#896C2semidirect
3. C2×#4989C2semidirect
4. C2×#4673C2semidirect
5. C2×#4668C2semidirect
6. C2×#4656C2semidirect
7. C3×#1436C2semidirect
8. #71536C2semidirect
9. #69428C2semidirect
10. #69428C2semidirect
11. #69427C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69411C2semidirect
75. #1436D3semidirect
98. C22×D12Q8semidirect
122. C2×C3×C4⋊C4D4semidirect
170. C2×Dic3⋊C4D4semidirect
461. C2×C4⋊C4D12semidirect
593. C22×D3C22⋊Q8semidirect
642. C2×C3×C4C22⋊Q8semidirect
1113. C2×C4#896semidirect
1209. C3#14723semidirect

Maximal subgroups

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

subgroupindex
C22×#8962
C22×C4×D122
C2×#49892
C2×#46732
C2×#46682
C2×#46562
C3×#14362
#715362
#694282
#694272
#694262
(C2×D3)⋊#952
#694112
#147233