Finite Group Databasebeta

← #10729243

Subgroups — #10729243

Order 768.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#898C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic, complemented
3C2×#4939C211yesmaximal, characteristic
4C2×#4670C211yesmaximal, characteristic, complemented
5C3×#1436C211yesmaximal, characteristic, complemented
6C4×C3⋊#95C211yesmaximal, characteristic, complemented
7#69429C211yesmaximal, characteristic, complemented
8#69428C211yesmaximal, characteristic, complemented
9#69427C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic
12#69426C211yesmaximal, characteristic
13#69419C211yesmaximal, characteristic, complemented
14#69411C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#14930—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×(C2×D3)⋊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×(C2×D3)⋊C4C2211yescharacteristic
32C22×C4⋊Dic3C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C2×#898—24no—
39C2×#898—24no—
40C2×#898—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#4990—24no—
56#4939—24no—
57#4670—24no—
58C22×#126—31no—
59C2×#390—31no—
60C2×#388—31no—
61C2×#388—31no—
62#1444—31no—
63#1441—31no—
64#1440—31no—
65#1439—31no—
66#1439—31no—
67#1439—31no—
68#1438—31no—
69#1438—31no—
70#1437—31no—
71#1436D311yescharacteristic, complemented
72C4×#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—22no—
93C22×D12—41no—
94C22×D12—41no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4D414yescomplemented
98C2×C3×C42—22no—
99C2×C3×C42—22no—
100C2×C3×C42—41no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4—22no—
103C2×(C2×D3)⋊C4—22no—
104C2×(C2×D3)⋊C4—22no—
105C2×(C2×D3)⋊C4—22no—
106C2×(C2×D3)⋊C4—22no—
107C2×(C2×D3)⋊C4—22no—
108C2×(C2×D3)⋊C4—22no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
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—41no—
129C2×(C2×D3)⋊C4—41no—
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)⋊C4D414yes—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3—22no—
139C2×C4⋊Dic3—22no—
140C2×C4⋊Dic3—22no—
141C2×C4⋊Dic3—22no—
142C2×C4⋊Dic3—22no—
143C2×C4⋊Dic3—41no—
144C2×C4⋊Dic3—41no—
145C2×C4⋊Dic3—41no—
146C2×Dic3⋊C4—22no—
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4—22no—
149C2×C4×Dic3—22no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—41no—
154C2×C4×Dic3D414yescomplemented
155#898—232no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95—41no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—41no—
169C3⋊#95—41no—
170C23×D4—31no—
171C2×#126—64no—
172C2×#126—64no—
173C2×#126—64no—
174C22×C4⋊C4—31no—
175C22×C4⋊C4—31no—
176C22×C4⋊C4—31no—
177C22×C4⋊C4—31no—
178C22×C4⋊C4C2×D311yescharacteristic
179C22×C22⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
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×C42—31no—
192C22×C42—31no—
193C22×C42C2×D311yescharacteristic
194#390—64no—
195#388—64no—
196#388—64no—
197C2×#95—31no—
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×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3C2411yescharacteristic
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
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×D3—21no—
240C23×D3C2×D412yes—
241C23×D3#4112yes—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
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×C4C2×D412yes—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D412yes—
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D412yes—
286C22×C3×C4#4112yes—
287C22×C3×C4#4112yes—
288C22×C3×C4#4112yes—
289C22×C3×C4#4112yes—
290C22×C3×C4#4112yes—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
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×Dic3C2×D412yes—
329C22×Dic3C2×D412yes—
330C22×Dic3C2×D412yes—
331C22×Dic3#4112yes—
332C22×Dic3#4112yes—
333C2×D12—28no—
334C2×D12—44no—
335C2×D12—44no—
336C2×D12—44no—
337C2×D12—44no—
338C2×D12—44no—
339C2×D12—44no—
340C3×C4⋊C4—28no—
341C3×C42—44no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354C4⋊Dic3—28no—
355C4⋊Dic3—44no—
356C4⋊Dic3—44no—
357Dic3⋊C4—28no—
358C4×Dic3—28no—
359C4×Dic3—44no—
360C25—31no—
361C25—31no—
362C22×D4—62no—
363C22×D4—62no—
364C22×D4—62no—
365C22×D4—62no—
366C22×D4—62no—
367C22×D4—121no—
368C22×D4—121no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382#126—632no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—121no—
395C2×C4⋊C4—121no—
396C2×C4⋊C4—121no—
397C2×C4⋊C4D1214yescomplemented
398C2×C22⋊C4—34no—
399C2×C22⋊C4—62no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—62no—
411C2×C22⋊C4—62no—
412C2×C22⋊C4—62no—
413C2×C22⋊C4—62no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—62no—
419C2×C22⋊C4—62no—
420C2×C22⋊C4—62no—
421C2×C22⋊C4—62no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—62no—
425C2×C22⋊C4—62no—
426C2×C22⋊C4—121no—
427C2×C22⋊C4—121no—
428C2×C22⋊C4—121no—
429C2×C22⋊C4—121no—
430C2×C22⋊C4—121no—
431C2×C22⋊C4—121no—
432C2×C22⋊C4—121no—
433C2×C22⋊C4—121no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—34no—
437C2×C42—41no—
438C2×C42—62no—
439C2×C42—62no—
440C2×C42—62no—
441C2×C42—62no—
442C2×C42—121no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—41no—
448#95—62no—
449#95—62no—
450#95—62no—
451#95—62no—
452#95—62no—
453#95—62no—
454#95—62no—
455#95—121no—
456#95—121no—
457C23×C3C22×D411yescharacteristic
458C23×C3C22×D411yescharacteristic
459C23×C3C22×D411yescharacteristic
460C23×C3C2×#4111yescharacteristic
461C23×C3C2×#4111yescharacteristic
462C23×C3C2×#4111yescharacteristic
463C23×C3C2×#4111yescharacteristic
464C23×C3C2×#4111yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3H(5,𝔽2)11yescharacteristic
469C23×C3H(5,𝔽2)11yescharacteristic
470C23×C3H(5,𝔽2)11yescharacteristic
471C23×C32−1+411yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
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—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
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—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
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#12014yes—
590C2×C3×C4#12614yescomplemented
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—41no—
607C2×Dic3—41no—
608C2×Dic3—41no—
609C2×Dic3—41no—
610C2×Dic3—41no—
611C2×Dic3—41no—
612C2×Dic3—41no—
613C2×Dic3—41no—
614C2×Dic3—41no—
615C2×Dic3—41no—
616C2×Dic3—41no—
617C2×Dic3—41no—
618C2×Dic3—41no—
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—
633D12—416no—
634C24—32no—
635C24—32no—
636C24—61no—
637C24—61no—
638C24—61no—
639C24—61no—
640C24—61no—
641C24—61no—
642C24—61no—
643C24—61no—
644C24—61no—
645C24—61no—
646C24—61no—
647C24—61no—
648C24—61no—
649C24—61no—
650C24—61no—
651C24—61no—
652C24—61no—
653C24—61no—
654C24—61no—
655C24—61no—
656C24—61no—
657C24—61no—
658C24—61no—
659C24—61no—
660C24—61no—
661C24—61no—
662C24—61no—
663C24—61no—
664C24C23×D311yescharacteristic
665C2×D4—68no—
666C2×D4—124no—
667C2×D4—124no—
668C2×D4—124no—
669C2×D4—124no—
670C2×D4—124no—
671C2×D4—124no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
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—32no—
712C22×C4—32no—
713C22×C4—32no—
714C22×C4—32no—
715C22×C4—32no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
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×C4C2×D1212yes—
754C22×C4C2×D1212yes—
755C22×C4C2×D1212yes—
756C22×C4#23512yes—
757C22×C4#23512yes—
758C22×C4D3×D412yes—
759C22×C4D3×D412yes—
760C22×C4#23712yes—
761C22×C4#23912yes—
762C22×C4#23912yes—
763C4⋊C4—28no—
764C4⋊C4—68no—
765C4⋊C4—68no—
766C4⋊C4—124no—
767C4⋊C4—124no—
768C22⋊C4—68no—
769C22⋊C4—68no—
770C22⋊C4—68no—
771C22⋊C4—68no—
772C22⋊C4—68no—
773C22⋊C4—124no—
774C22⋊C4—124no—
775C22⋊C4—124no—
776C22⋊C4—124no—
777C22⋊C4—124no—
778C22⋊C4—124no—
779C22⋊C4—124no—
780C42—44no—
781C42—68no—
782C42—124no—
783C22×C3C2×#12011yescharacteristic
784C22×C3#52511yescharacteristic
785C22×C3#52511yescharacteristic
786C22×C3#52511yescharacteristic
787C22×C3C2×#12611yescharacteristic
788C22×C3#52911yescharacteristic
789C22×C3#52911yescharacteristic
790C22×C3#52911yescharacteristic
791C22×C3#53211yescharacteristic
792C22×C3#53211yescharacteristic
793C22×C3#53211yescharacteristic
794C22×C3#53211yescharacteristic
795C22×C3#53211yescharacteristic
796C22×C3#53511yescharacteristic
797C22×C3#53711yescharacteristic
798C22×C3#53811yescharacteristic
799C22×C3#53811yescharacteristic
800C22×C3#54211yescharacteristic
801C22×C3#54211yescharacteristic
802C22×C3#54611yescharacteristic
803C22×C3#54611yescharacteristic
804C22×C3#54611yescharacteristic
805C22×C3#54611yescharacteristic
806C22×C3#54711yescharacteristic
807C22×C3#54711yescharacteristic
808C22×C3#55011yescharacteristic
809C22×C3#55011yescharacteristic
810C22×C3#55111yescharacteristic
811C22×C3#55111yescharacteristic
812C22×C3#55111yescharacteristic
813C22×C3#55211yescharacteristic
814C22×C3#55311yescharacteristic
815C22×C3#55311yescharacteristic
816C22×C3#55311yescharacteristic
817C22×C3#55611yescharacteristic
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C2×D3—42no—
824C2×D3—42no—
825C2×D3—42no—
826C2×D3—42no—
827C2×D3—42no—
828C2×D3—42no—
829C2×D3—42no—
830C2×D3—42no—
831C2×D3—42no—
832C2×D3—81no—
833C2×D3—81no—
834C2×D3—81no—
835C2×D3—81no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C2×D3—81no—
840C2×D3—81no—
841C2×D3—81no—
842C2×D3—81no—
843C2×D3—81no—
844C2×D3—81no—
845C2×D3—81no—
846C2×D3—81no—
847C2×D3—81no—
848C3×C4—24no—
849C3×C4—24no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4—81no—
855Dic3—42no—
856Dic3—42no—
857Dic3—42no—
858Dic3—42no—
859Dic3—42no—
860Dic3—81no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—62no—
865C23—62no—
866C23—62no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
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—
931C23C22×D1211yescharacteristic
932C23C2×#23511yescharacteristic
933C23C2×#23511yescharacteristic
934C23C2×D3×D411yescharacteristic
935C23C2×D3×D411yescharacteristic
936C23C2×#23711yescharacteristic
937C23#100411yescharacteristic
938C23C2×#23911yescharacteristic
939C23C2×#23911yescharacteristic
940C23D3×#4111yescharacteristic
941C23D3×#4111yescharacteristic
942C23D3×#4111yescharacteristic
943C23#100911yescharacteristic
944C23#100911yescharacteristic
945C23#101011yescharacteristic
946D4—1216no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—62no—
1002C2×C4—62no—
1003C2×C4—62no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C4—121no—
1013C2×C4—121no—
1014C2×C4—121no—
1015C2×C4—121no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—121no—
1020C2×C4—121no—
1021C2×C4—121no—
1022C2×C4—121no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—121no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—121no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4#88214yes—
1037C2×C4#89814yescomplemented
1038C2×C3#238811yescharacteristic
1039C2×C3#243011yescharacteristic
1040C2×C3#243111yescharacteristic
1041C2×C3#246711yescharacteristic
1042C2×C3#246811yescharacteristic
1043C2×C3#247911yescharacteristic
1044C2×C3#248011yescharacteristic
1045C2×C3#251211yescharacteristic
1046C2×C3#252111yescharacteristic
1047C2×C3#255411yescharacteristic
1048C2×C3#255911yescharacteristic
1049C2×C3#260111yescharacteristic
1050C2×C3#260311yescharacteristic
1051C2×C3#266211yescharacteristic
1052C2×C3#286011yescharacteristic
1053D3—82no—
1054D3—82no—
1055C22—122no—
1056C22—122no—
1057C22—122no—
1058C22—122no—
1059C22—122no—
1060C22—122no—
1061C22—122no—
1062C22—122no—
1063C22—122no—
1064C22—122no—
1065C22—122no—
1066C22—122no—
1067C22—122no—
1068C22—122no—
1069C22—241no—
1070C22—241no—
1071C22—241no—
1072C22—241no—
1073C22—241no—
1074C22—241no—
1075C22—241no—
1076C22—241no—
1077C22—241no—
1078C22—241no—
1079C22—241no—
1080C22—241no—
1081C22—241no—
1082C22—241no—
1083C22—241no—
1084C22—241no—
1085C22#547711yescharacteristic
1086C22C2×#88211yescharacteristic
1087C22C2×#89811yescharacteristic
1088C22#551411yescharacteristic
1089C22#552411yescharacteristic
1090C22#552711yescharacteristic
1091C22#553411yescharacteristic
1092C22#554711yescharacteristic
1093C22#554711yescharacteristic
1094C22#554811yescharacteristic
1095C22#554811yescharacteristic
1096C22#555411yescharacteristic
1097C22#555511yescharacteristic
1098C22#556011yescharacteristic
1099C22#556511yescharacteristic
1100C22#557711yescharacteristic
1101C22#557711yescharacteristic
1102C22#558011yescharacteristic
1103C22#558411yescharacteristic
1104C22#559111yescharacteristic
1105C22#559611yescharacteristic
1106C22#559711yescharacteristic
1107C22#562411yescharacteristic
1108C22#563011yescharacteristic
1109C22#563011yescharacteristic
1110C22#563711yescharacteristic
1111C22#565511yescharacteristic
1112C22#565711yescharacteristic
1113C22#565811yescharacteristic
1114C22#567411yescharacteristic
1115C22#569111yescharacteristic
1116C22#569411yescharacteristic
1117C22#570911yescharacteristic
1118C22#571011yescharacteristic
1119C22#572511yescharacteristic
1120C4—24no—
1121C4—24no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—81no—
1127C4—122no—
1128C4—122no—
1129C4—122no—
1130C4—122no—
1131C4—122no—
1132C4—241no—
1133C3#1493011yescharacteristic, complemented, Sylow
1134C2—242no—
1135C2—242no—
1136C2#7358011yescharacteristic
1137C2#7369211yescharacteristic
1138C2#7380311yescharacteristic
1139C2#7445211yescharacteristic
1140C2#7447611yescharacteristic
1141C2#7469911yescharacteristic
1142C2#7500111yescharacteristic
1143C2#7500311yescharacteristic
1144C2#7501811yescharacteristic
1145C2#7504411yescharacteristic
1146C2#7564711yescharacteristic
1147C2#7566311yescharacteristic
1148C2#7609511yescharacteristic
1149C2#7619111yescharacteristic
1150C2#7662611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14930
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#898C2semidirect
2. C2×#4990C2semidirect
4. C2×#4670C2semidirect
5. C3×#1436C2semidirect
6. C4×C3⋊#95C2semidirect
7. #69429C2semidirect
8. #69428C2semidirect
9. #69427C2semidirect
10. #69427C2semidirect
13. #69419C2semidirect
14. #69411C2semidirect
15. #69408C2semidirect
71. #1436D3semidirect
97. C2×C3×C4⋊C4D4semidirect
154. C2×C4×Dic3D4semidirect
397. C2×C4⋊C4D12semidirect
590. C2×C3×C4#126semidirect
1037. C2×C4#898semidirect
1133. C3#14930semidirect

Maximal subgroups

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

subgroupindex
C22×#8982
C2×#49902
C2×#49392
C2×#46702
C3×#14362
C4×C3⋊#952
#694292
#694282
#694272
#694262
#694192
#694112
#694082
#149303