Finite Group Databasebeta

← #10726759

Subgroups — #10726759

Order 768.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D12C211yesmaximal, characteristic
2C2×#4994C211yesmaximal, characteristic, complemented
3C2×#4668C211yesmaximal, characteristic, complemented
4C2×#4668C211yesmaximal, characteristic, complemented
5C2×#4667C211yesmaximal, characteristic, complemented
6C2×#4661C211yesmaximal, characteristic, complemented
7C3×#1436C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71536C211yesmaximal, 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#14733—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C2×C4×D12—24no—
39C2×C4×D12—24no—
40C2×C4×D12—24no—
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
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55#4994—24no—
56#4668—24no—
57#4668—24no—
58#4667—24no—
59#4661—24no—
60C22×C4×D4—31no—
61C2×#398—31no—
62C2×#396—31no—
63C2×#385—31no—
64C2×#385—31no—
65C2×#380—31no—
66#1441—31no—
67#1439—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1438—31no—
72#1436—31no—
73#1436D311yescharacteristic, complemented
74C22⋊#95—31no—
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12Q814yes—
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—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—41no—
107C22×C4×D3—41no—
108C22×C4×D3—41no—
109C22×C4×D3—41no—
110C22×C4×D3D414yes—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C42—22no—
115C2×C3×C42—22no—
116C2×C3×C42—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—22no—
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)⋊C4—41no—
146C2×(C2×D3)⋊C4D414yes—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—22no—
149C2×C4⋊Dic3—22no—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—41no—
155C2×C4⋊Dic3D414yes—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—41no—
164C2×Dic3⋊C4—41no—
165C4×D12—232no—
166C3×#95—22no—
167C3×#95—22no—
168C3×#95—22no—
169C3×#95—41no—
170C3×#95D414yescomplemented
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—41no—
180C23×D4—31no—
181C24×C4—31no—
182C24×C4—31no—
183C2×C4×D4—64no—
184C2×C4×D4—64no—
185C2×C4×D4—64no—
186C22×C4⋊C4—31no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4C2×D311yescharacteristic
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C42C2×D311yescharacteristic
204#398—64no—
205#396—64no—
206#385—64no—
207#385—64no—
208#380—64no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95C2×D311yescharacteristic
219C2×#95C2×D311yescharacteristic
220C2×#95C2×D311yescharacteristic
221C2×#95C2×D311yescharacteristic
222C2×#95C2×D311yescharacteristic
223C24×C3C2411yescharacteristic
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—
250C23×D3C2×Q812yes—
251C23×D3C2×Q812yes—
252C23×D3#4112yes—
253C23×D3#4112yes—
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×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×Q812yes—
300C22×C3×C4#4112yes—
301C22×C3×C4#4112yes—
302C22×C3×C4#4112yes—
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×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3C2×D412yes—
341C22×Dic3C2×D412yes—
342C22×Dic3C2×D412yes—
343C22×Dic3C2×D412yes—
344C22×Dic3#4112yes—
345C2×D12—28no—
346C2×D12—28no—
347C2×D12—28no—
348C2×D12—28no—
349C2×D12—28no—
350C2×D12—28no—
351C2×D12—28no—
352C2×C4×D3—28no—
353C2×C4×D3—28no—
354C2×C4×D3—28no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C3×C4⋊C4—44no—
367C3×C42—28no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4—28no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377(C2×D3)⋊C4—44no—
378C4⋊Dic3—28no—
379C4⋊Dic3—44no—
380C4⋊Dic3—44no—
381Dic3⋊C4—44no—
382Dic3⋊C4—44no—
383Dic3⋊C4—44no—
384C25—31no—
385C25—31no—
386C22×D4—34no—
387C22×D4—62no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C22×D4—62no—
392C22×D4—62no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—34no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—121no—
410C23×C4—121no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4C22×D311yescharacteristic
414C23×C4C22×D311yescharacteristic
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C4×D4—632no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—34no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—62no—
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4—62no—
436C2×C4⋊C4—62no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—121no—
440C2×C4⋊C4—121no—
441C2×C4⋊C4—121no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—121no—
465C2×C22⋊C4—121no—
466C2×C22⋊C4—121no—
467C2×C22⋊C4—121no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—41no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—121no—
488#95D1214yescomplemented
489C23×C3C22×D411yescharacteristic
490C23×C3C22×D411yescharacteristic
491C23×C3C22×D411yescharacteristic
492C23×C3C22×D411yescharacteristic
493C23×C3C22×Q811yescharacteristic
494C23×C3C2×#4111yescharacteristic
495C23×C3C2×#4111yescharacteristic
496C23×C3C2×#4111yescharacteristic
497C23×C3C2×#4111yescharacteristic
498C23×C3C2×#4111yescharacteristic
499C23×C3C2×#4111yescharacteristic
500C23×C3H(5,𝔽2)11yescharacteristic
501C23×C3H(5,𝔽2)11yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C32−1+411yescharacteristic
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—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—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—
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×D3C22⋊Q814yes—
573C22×D3C22⋊Q814yes—
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—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
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—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4#12114yes—
622C2×C3×C4C22⋊Q814yes—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
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—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3#12014yes—
665D12—232no—
666C4×D3—416no—
667C4×D3—416no—
668C24—32no—
669C24—32no—
670C24—32no—
671C24—32no—
672C24—32no—
673C24—32no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24C23×D311yescharacteristic
699C2×D4—68no—
700C2×D4—68no—
701C2×D4—68no—
702C2×D4—68no—
703C2×D4—68no—
704C2×D4—68no—
705C2×D4—68no—
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—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—32no—
750C22×C4—68no—
751C22×C4—68no—
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—68no—
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×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
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—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4C2×D1212yes—
802C22×C4C2×D1212yes—
803C22×C4C2×D1212yes—
804C22×C4#23512yes—
805C22×C4#23512yes—
806C22×C4D3×D412yes—
807C22×C4D3×D412yes—
808C22×C4D3×D412yes—
809C22×C4D3×Q812yes—
810C22×C4#23912yes—
811C4⋊C4—44no—
812C4⋊C4—68no—
813C4⋊C4—124no—
814C4⋊C4—124no—
815C4⋊C4—124no—
816C4⋊C4—124no—
817C4⋊C4—124no—
818C22⋊C4—68no—
819C22⋊C4—68no—
820C22⋊C4—68no—
821C22⋊C4—68no—
822C22⋊C4—124no—
823C22⋊C4—124no—
824C22⋊C4—124no—
825C22⋊C4—124no—
826C22⋊C4—124no—
827C22⋊C4—124no—
828C42—28no—
829C22×C3C2×#12011yescharacteristic
830C22×C3C2×#12111yescharacteristic
831C22×C3C2×C22⋊Q811yescharacteristic
832C22×C3C2×C22⋊Q811yescharacteristic
833C22×C3C2×C22⋊Q811yescharacteristic
834C22×C3#52511yescharacteristic
835C22×C3#52511yescharacteristic
836C22×C3#52511yescharacteristic
837C22×C3#52511yescharacteristic
838C22×C3#52511yescharacteristic
839C22×C3#52911yescharacteristic
840C22×C3#52911yescharacteristic
841C22×C3#53211yescharacteristic
842C22×C3#53411yescharacteristic
843C22×C3#53711yescharacteristic
844C22×C3#53811yescharacteristic
845C22×C3#53911yescharacteristic
846C22×C3#54011yescharacteristic
847C22×C3#54211yescharacteristic
848C22×C3D4211yescharacteristic
849C22×C3D4211yescharacteristic
850C22×C3#54611yescharacteristic
851C22×C3#54611yescharacteristic
852C22×C3#54611yescharacteristic
853C22×C3#54611yescharacteristic
854C22×C3#54711yescharacteristic
855C22×C3#54811yescharacteristic
856C22×C3D4×Q811yescharacteristic
857C22×C3#55011yescharacteristic
858C22×C3#55211yescharacteristic
859C22×C3#55311yescharacteristic
860C22×C3#55311yescharacteristic
861C22×C3#55411yescharacteristic
862C22×C3#55411yescharacteristic
863C22×C3#55411yescharacteristic
864C2×D3—24no—
865C2×D3—24no—
866C2×D3—24no—
867C2×D3—24no—
868C2×D3—24no—
869C2×D3—24no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C3×C4—24no—
895C3×C4—24no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—42no—
900C3×C4—81no—
901Dic3—24no—
902Dic3—42no—
903Dic3—42no—
904Dic3—81no—
905Dic3—81no—
906Dic3—81no—
907C23—34no—
908C23—34no—
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—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
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—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23C22×D1211yescharacteristic
978C23C2×#23511yescharacteristic
979C23C2×#23511yescharacteristic
980C23C2×D3×D411yescharacteristic
981C23C2×D3×D411yescharacteristic
982C23C2×D3×D411yescharacteristic
983C23#100411yescharacteristic
984C23C2×D3×Q811yescharacteristic
985C23C2×#23911yescharacteristic
986C23D3×#4111yescharacteristic
987C23D3×#4111yescharacteristic
988C23D3×#4111yescharacteristic
989C23#100911yescharacteristic
990C23#100911yescharacteristic
991C23#101011yescharacteristic
992D4—632no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—34no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—1216no—
1054C2×C4—1216no—
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—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4#89514yes—
1085C2×C4#89614yes—
1086C2×C3#239211yescharacteristic
1087C2×C3#240711yescharacteristic
1088C2×C3#241011yescharacteristic
1089C2×C3#241711yescharacteristic
1090C2×C3#244911yescharacteristic
1091C2×C3#245011yescharacteristic
1092C2×C3#245211yescharacteristic
1093C2×C3#245411yescharacteristic
1094C2×C3#245611yescharacteristic
1095C2×C3#246011yescharacteristic
1096C2×C3#246411yescharacteristic
1097C2×C3#246811yescharacteristic
1098C2×C3#257911yescharacteristic
1099C2×C3#263011yescharacteristic
1100C2×C3#284811yescharacteristic
1101D3—44no—
1102D3—44no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—64no—
1107C22—64no—
1108C22—64no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—122no—
1126C22—122no—
1127C22—122no—
1128C22—122no—
1129C22—122no—
1130C22—122no—
1131C22—122no—
1132C22—122no—
1133C22#547711yescharacteristic
1134C22#549011yescharacteristic
1135C22C2×#89511yescharacteristic
1136C22C2×#89611yescharacteristic
1137C22#552411yescharacteristic
1138C22#553011yescharacteristic
1139C22#553411yescharacteristic
1140C22#554711yescharacteristic
1141C22#554711yescharacteristic
1142C22#554711yescharacteristic
1143C22D4×D1211yescharacteristic
1144C22D4×D1211yescharacteristic
1145C22#555211yescharacteristic
1146C22#555411yescharacteristic
1147C22#556211yescharacteristic
1148C22Q8×D1211yescharacteristic
1149C22#557911yescharacteristic
1150C22#558011yescharacteristic
1151C22#558011yescharacteristic
1152C22D3×#12011yescharacteristic
1153C22#559911yescharacteristic
1154C22#560811yescharacteristic
1155C22D3×C22⋊Q811yescharacteristic
1156C22D3×C22⋊Q811yescharacteristic
1157C22#563011yescharacteristic
1158C22#563011yescharacteristic
1159C22#565311yescharacteristic
1160C22#565511yescharacteristic
1161C22#565611yescharacteristic
1162C22#567811yescharacteristic
1163C22#569011yescharacteristic
1164C22#569411yescharacteristic
1165C22#570711yescharacteristic
1166C22#570911yescharacteristic
1167C22#573011yescharacteristic
1168C4—24no—
1169C4—24no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—64no—
1175C4—81no—
1176C4—122no—
1177C4—122no—
1178C4—241no—
1179C4—241no—
1180C4—241no—
1181C3#1473311yescharacteristic, complemented, Sylow
1182C2—124no—
1183C2—124no—
1184C2#7359111yescharacteristic
1185C2#7367511yescharacteristic
1186C2#7377611yescharacteristic
1187C2#7460111yescharacteristic
1188C2#7465511yescharacteristic
1189C2#7468811yescharacteristic
1190C2#7499211yescharacteristic
1191C2#7500311yescharacteristic
1192C2#7532111yescharacteristic
1193C2#7537011yescharacteristic
1194C2#7550311yescharacteristic
1195C2#7590111yescharacteristic
1196C2#7601511yescharacteristic
1197C2#7621211yescharacteristic
1198C2#7662811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14733
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4994C2semidirect
3. C2×#4668C2semidirect
4. C2×#4668C2semidirect
5. C2×#4667C2semidirect
6. C2×#4661C2semidirect
7. C3×#1436C2semidirect
8. #71570C2semidirect
9. #71536C2semidirect
10. #69428C2semidirect
11. #69427C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69411C2semidirect
73. #1436D3semidirect
170. C3×#95D4semidirect
488. #95D12semidirect
1181. C3#14733semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D122
C2×#49942
C2×#46682
C2×#46672
C2×#46612
C3×#14362
#715702
#715362
#694282
#694272
#694262
(C2×D3)⋊#952
#694112
#147333