Finite Group Databasebeta

← #10740291

Subgroups — #10740291

Order 768.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4994C211yesmaximal, characteristic, complemented
2C2×#4988C211yesmaximal, characteristic, complemented
3C2×#4939C211yesmaximal, characteristic, complemented
4C2×#4677C211yesmaximal, characteristic, complemented
5C2×#4671C211yesmaximal, characteristic
6C2×#4672C211yesmaximal, characteristic, complemented
7C2×#4670C211yesmaximal, characteristic, complemented
8C2×#4653C211yesmaximal, characteristic, complemented
9C3×#1436C211yesmaximal, characteristic, complemented
10#71537C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14#69426C211yesmaximal, characteristic, complemented
15#69426C211yesmaximal, characteristic, complemented
16#15776—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
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#4988—24no—
54#4939—24no—
55#4677—24no—
56#4672—24no—
57#4671—24no—
58#4670—24no—
59#4653—24no—
60C2×#399—31no—
61C2×#396—31no—
62C2×#394—31no—
63C2×#392—31no—
64C2×#390—31no—
65C2×#390—31no—
66C2×#388—31no—
67C2×#387—31no—
68#1439—31no—
69#1439—31no—
70#1438—31no—
71#1438—31no—
72#1438—31no—
73#1437—31no—
74#1436D311yescharacteristic, complemented
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
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×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—22no—
103C22×D12—41no—
104C22×D12—41no—
105C22×D12—41no—
106C22×D12—41no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12—41no—
110C22×D12—41no—
111C2×C3×C4⋊C4—41no—
112C2×C3×C4⋊C4—41no—
113C2×C3×C4⋊C4D414yescomplemented
114C2×C3×C42—22no—
115C2×C3×C42—41no—
116C2×C3×C42—41no—
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—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—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4—41no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4—41no—
158C2×(C2×D3)⋊C4—41no—
159C2×(C2×D3)⋊C4—41no—
160C2×(C2×D3)⋊C4—41no—
161C2×(C2×D3)⋊C4—41no—
162C2×C4⋊Dic3—22no—
163C2×C4⋊Dic3—22no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3—22no—
167C2×C4⋊Dic3—22no—
168C2×C4⋊Dic3—41no—
169C2×C4⋊Dic3—41no—
170C2×C4⋊Dic3D414yescomplemented
171C2×Dic3⋊C4—22no—
172C2×Dic3⋊C4—22no—
173C2×Dic3⋊C4—22no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—22no—
176C2×C4×Dic3—22no—
177C3×#95—22no—
178C3×#95—41no—
179C3×#95—41no—
180C3×#95D414yes—
181C3×#95D414yescomplemented
182C3⋊#95—22no—
183C3⋊#95—22no—
184C3⋊#95—22no—
185C3⋊#95—22no—
186C3⋊#95—22no—
187C23×D4—31no—
188C23×D4—31no—
189C23×D4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4C2×D311yescharacteristic
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×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×C42—31no—
211C22×C42C2×D311yescharacteristic
212#399—64no—
213#396—64no—
214#394—64no—
215#392—64no—
216#390—64no—
217#390—64no—
218#388—64no—
219#387—64no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—31no—
224C2×#95—31no—
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C24×C3C2411yescharacteristic
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×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×D3—21no—
258C23×D3—21no—
259C23×D3—21no—
260C23×D3—21no—
261C23×D3—21no—
262C23×D3—21no—
263C23×D3—21no—
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—21no—
269C23×D3—21no—
270C23×D3—21no—
271C23×D3—21no—
272C23×D3—21no—
273C23×D3#4112yes—
274C23×D3#4112yes—
275C23×D3#4112yes—
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×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2×D412yes—
320C22×C3×C4C2×D412yes—
321C22×C3×C4C2×D412yes—
322C22×C3×C4C2×D412yes—
323C22×C3×C4C2×D412yes—
324C22×C3×C4#4112yes—
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×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3C2×D412yes—
358C22×Dic3C2×D412yes—
359C22×Dic3#4112yes—
360C2×D12—28no—
361C2×D12—28no—
362C2×D12—44no—
363C2×D12—44no—
364C2×D12—44no—
365C2×D12—44no—
366C2×D12—44no—
367C2×D12—44no—
368C2×D12—44no—
369C2×D12—44no—
370C2×D12—44no—
371C2×D12—44no—
372C2×D12—44no—
373C2×D12—44no—
374C2×D12—44no—
375C2×D12—44no—
376C2×D12—44no—
377C2×D12—44no—
378C2×D12—44no—
379C2×D12—44no—
380C2×D12—44no—
381C3×C4⋊C4—44no—
382C3×C42—44no—
383(C2×D3)⋊C4—28no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386(C2×D3)⋊C4—44no—
387(C2×D3)⋊C4—44no—
388(C2×D3)⋊C4—44no—
389(C2×D3)⋊C4—44no—
390(C2×D3)⋊C4—44no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395(C2×D3)⋊C4—44no—
396(C2×D3)⋊C4—44no—
397(C2×D3)⋊C4—44no—
398C4⋊Dic3—28no—
399C4⋊Dic3—44no—
400C4⋊Dic3—44no—
401Dic3⋊C4—44no—
402C4×Dic3—44no—
403C25—31no—
404C25—31no—
405C25—31no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—62no—
409C22×D4—62no—
410C22×D4—62no—
411C22×D4—62no—
412C22×D4—62no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—62no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—121no—
420C22×D4—121no—
421C22×D4—121no—
422C22×D4—121no—
423C22×D4—121no—
424C22×D4—121no—
425C22×D4—121no—
426C22×D4—121no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4C22×D311yescharacteristic
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C2×C4⋊C4—34no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—62no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—121no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4D1214yescomplemented
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—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—121no—
486C2×C22⋊C4—121no—
487C2×C22⋊C4—121no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×C22⋊C4—121no—
493C2×C22⋊C4—121no—
494C2×C22⋊C4—121no—
495C2×C22⋊C4—121no—
496C2×C22⋊C4—121no—
497C2×C22⋊C4—121no—
498C2×C22⋊C4—121no—
499C2×C42—22no—
500C2×C42—41no—
501C2×C42—41no—
502C2×C42—62no—
503C2×C42—62no—
504C2×C42—62no—
505#95—22no—
506#95—41no—
507#95—41no—
508#95—62no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95D1214yes—
514#95D1214yescomplemented
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C22×D411yescharacteristic
518C23×C3C22×D411yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3H(5,𝔽2)11yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C3H(5,𝔽2)11yescharacteristic
527C23×C3H(5,𝔽2)11yescharacteristic
528C23×C3H(5,𝔽2)11yescharacteristic
529C23×C32−1+411yescharacteristic
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—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×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×D3—41no—
593C22×D3—41no—
594C22×D3—41no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C22×D3—41no—
613C22×D3—41no—
614C22×D3—41no—
615C22×D3—41no—
616C22×D3—41no—
617C22×D3—41no—
618C22×D3—41no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—41no—
622C22×D3—41no—
623C22×D3—41no—
624C22×D3—41no—
625C22×D3—41no—
626C22×D3—41no—
627C22×D3—41no—
628C22×D3—41no—
629C22×D3—41no—
630C22×D3—41no—
631C22×D3—41no—
632C22×D3—41no—
633C22×D3—41no—
634C22×D3—41no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4#12114yes—
683C2×C3×C4#12714yes—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—41no—
694C2×Dic3—41no—
695C2×Dic3—41no—
696C2×Dic3—41no—
697C2×Dic3—41no—
698C2×Dic3—41no—
699C2×Dic3—41no—
700C2×Dic3—41no—
701C2×Dic3—41no—
702C2×Dic3—41no—
703C2×Dic3—41no—
704C2×Dic3—41no—
705C2×Dic3—41no—
706C2×Dic3—41no—
707C2×Dic3—41no—
708C2×Dic3—41no—
709C2×Dic3—41no—
710C2×Dic3—41no—
711C2×Dic3—41no—
712C2×Dic3—41no—
713C2×Dic3—41no—
714C2×Dic3—41no—
715C2×Dic3—41no—
716C2×Dic3—41no—
717C2×Dic3—41no—
718C2×Dic3—41no—
719D12—416no—
720D12—416no—
721D12—416no—
722C24—32no—
723C24—32no—
724C24—32no—
725C24—61no—
726C24—61no—
727C24—61no—
728C24—61no—
729C24—61no—
730C24—61no—
731C24—61no—
732C24—61no—
733C24—61no—
734C24—61no—
735C24—61no—
736C24—61no—
737C24—61no—
738C24—61no—
739C24—61no—
740C24—61no—
741C24—61no—
742C24—61no—
743C24—61no—
744C24—61no—
745C24—61no—
746C24—61no—
747C24—61no—
748C24—61no—
749C24—61no—
750C24—61no—
751C24—61no—
752C24—61no—
753C24—61no—
754C24—61no—
755C24—61no—
756C24—61no—
757C24—61no—
758C24—61no—
759C24—61no—
760C24—61no—
761C24—61no—
762C24—61no—
763C24—61no—
764C24—61no—
765C24—61no—
766C24—61no—
767C24C23×D311yescharacteristic
768C2×D4—68no—
769C2×D4—68no—
770C2×D4—124no—
771C2×D4—124no—
772C2×D4—124no—
773C2×D4—124no—
774C2×D4—124no—
775C2×D4—124no—
776C2×D4—124no—
777C2×D4—124no—
778C2×D4—124no—
779C2×D4—124no—
780C2×D4—124no—
781C2×D4—124no—
782C2×D4—124no—
783C2×D4—124no—
784C2×D4—124no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—124no—
788C2×D4—124no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—32no—
828C22×C4—32no—
829C22×C4—32no—
830C22×C4—61no—
831C22×C4—61no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—61no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—61no—
848C22×C4—61no—
849C22×C4—61no—
850C22×C4—61no—
851C22×C4—61no—
852C22×C4—61no—
853C22×C4—61no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4C2×D1212yes—
863C22×C4C2×D1212yes—
864C22×C4C2×D1212yes—
865C22×C4C2×D1212yes—
866C22×C4C2×D1212yes—
867C22×C4C2×D1212yes—
868C22×C4C2×D1212yes—
869C22×C4C2×D1212yes—
870C22×C4C2×D1212yes—
871C22×C4D3×D412yes—
872C22×C4#23912yes—
873C4⋊C4—44no—
874C4⋊C4—68no—
875C4⋊C4—124no—
876C4⋊C4—124no—
877C4⋊C4—124no—
878C22⋊C4—68no—
879C22⋊C4—124no—
880C22⋊C4—124no—
881C22⋊C4—124no—
882C22⋊C4—124no—
883C22⋊C4—124no—
884C22⋊C4—124no—
885C22⋊C4—124no—
886C22⋊C4—124no—
887C22⋊C4—124no—
888C22⋊C4—124no—
889C22⋊C4—124no—
890C22⋊C4—124no—
891C22⋊C4—124no—
892C22⋊C4—124no—
893C42—44no—
894C42—124no—
895C22×C3C2×#12111yescharacteristic
896C22×C3#52511yescharacteristic
897C22×C3#52511yescharacteristic
898C22×C3#52511yescharacteristic
899C22×C3#52911yescharacteristic
900C22×C3C2×#12711yescharacteristic
901C22×C3#53411yescharacteristic
902C22×C3#53511yescharacteristic
903C22×C3#53511yescharacteristic
904C22×C3#53711yescharacteristic
905C22×C3#53811yescharacteristic
906C22×C3#53811yescharacteristic
907C22×C3#53911yescharacteristic
908C22×C3#54011yescharacteristic
909C22×C3#54211yescharacteristic
910C22×C3D4211yescharacteristic
911C22×C3D4211yescharacteristic
912C22×C3#54611yescharacteristic
913C22×C3#54611yescharacteristic
914C22×C3#54611yescharacteristic
915C22×C3#54611yescharacteristic
916C22×C3#54611yescharacteristic
917C22×C3#54611yescharacteristic
918C22×C3#54811yescharacteristic
919C22×C3#54811yescharacteristic
920C22×C3#54811yescharacteristic
921C22×C3#55011yescharacteristic
922C22×C3#55011yescharacteristic
923C22×C3#55011yescharacteristic
924C22×C3#55111yescharacteristic
925C22×C3#55111yescharacteristic
926C22×C3#55111yescharacteristic
927C22×C3#55311yescharacteristic
928C22×C3#56011yescharacteristic
929C22×C3#56211yescharacteristic
930C2×D3—42no—
931C2×D3—42no—
932C2×D3—42no—
933C2×D3—42no—
934C2×D3—42no—
935C2×D3—42no—
936C2×D3—42no—
937C2×D3—42no—
938C2×D3—42no—
939C2×D3—42no—
940C2×D3—42no—
941C2×D3—42no—
942C2×D3—42no—
943C2×D3—42no—
944C2×D3—42no—
945C2×D3—42no—
946C2×D3—42no—
947C2×D3—42no—
948C2×D3—42no—
949C2×D3—42no—
950C2×D3—42no—
951C2×D3—81no—
952C2×D3—81no—
953C2×D3—81no—
954C2×D3—81no—
955C2×D3—81no—
956C2×D3—81no—
957C2×D3—81no—
958C2×D3—81no—
959C2×D3—81no—
960C2×D3—81no—
961C2×D3—81no—
962C2×D3—81no—
963C2×D3—81no—
964C2×D3—81no—
965C2×D3—81no—
966C2×D3—81no—
967C2×D3—81no—
968C2×D3—81no—
969C2×D3—81no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C3×C4—24no—
976C3×C4—24no—
977C3×C4—42no—
978C3×C4—42no—
979C3×C4—42no—
980C3×C4—42no—
981C3×C4—42no—
982Dic3—42no—
983Dic3—42no—
984Dic3—42no—
985Dic3—81no—
986Dic3—81no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—62no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—62no—
1003C23—62no—
1004C23—62no—
1005C23—62no—
1006C23—62no—
1007C23—62no—
1008C23—121no—
1009C23—121no—
1010C23—121no—
1011C23—121no—
1012C23—121no—
1013C23—121no—
1014C23—121no—
1015C23—121no—
1016C23—121no—
1017C23—121no—
1018C23—121no—
1019C23—121no—
1020C23—121no—
1021C23—121no—
1022C23—121no—
1023C23—121no—
1024C23—121no—
1025C23—121no—
1026C23—121no—
1027C23—121no—
1028C23—121no—
1029C23—121no—
1030C23—121no—
1031C23—121no—
1032C23—121no—
1033C23—121no—
1034C23—121no—
1035C23—121no—
1036C23—121no—
1037C23—121no—
1038C23—121no—
1039C23—121no—
1040C23—121no—
1041C23—121no—
1042C23—121no—
1043C23—121no—
1044C23—121no—
1045C23—121no—
1046C23—121no—
1047C23—121no—
1048C23—121no—
1049C23—121no—
1050C23—121no—
1051C23—121no—
1052C23—121no—
1053C23—121no—
1054C23—121no—
1055C23—121no—
1056C23—121no—
1057C23—121no—
1058C23—121no—
1059C23—121no—
1060C23—121no—
1061C23—121no—
1062C23—121no—
1063C23—121no—
1064C23—121no—
1065C23—121no—
1066C23—121no—
1067C23—121no—
1068C23—121no—
1069C23—121no—
1070C23—121no—
1071C23—121no—
1072C23—121no—
1073C23—121no—
1074C23—121no—
1075C23—121no—
1076C23—121no—
1077C23—121no—
1078C23—121no—
1079C23—121no—
1080C23—121no—
1081C23—121no—
1082C23—121no—
1083C23—121no—
1084C23—121no—
1085C23—121no—
1086C23—121no—
1087C23—121no—
1088C23—121no—
1089C23—121no—
1090C23—121no—
1091C23—121no—
1092C23C22×D1211yescharacteristic
1093C23C22×D1211yescharacteristic
1094C23C22×D1211yescharacteristic
1095C23C2×D3×D411yescharacteristic
1096C23#100411yescharacteristic
1097C23#100411yescharacteristic
1098C23#100411yescharacteristic
1099C23C2×#23911yescharacteristic
1100C23#100711yescharacteristic
1101C23D3×#4111yescharacteristic
1102C23D3×#4111yescharacteristic
1103C23D3×#4111yescharacteristic
1104C23D3×#4111yescharacteristic
1105C23#100911yescharacteristic
1106C23#100911yescharacteristic
1107D4—1216no—
1108D4—1216no—
1109D4—1216no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—62no—
1158C2×C4—62no—
1159C2×C4—62no—
1160C2×C4—62no—
1161C2×C4—62no—
1162C2×C4—62no—
1163C2×C4—62no—
1164C2×C4—62no—
1165C2×C4—62no—
1166C2×C4—121no—
1167C2×C4—121no—
1168C2×C4—121no—
1169C2×C4—121no—
1170C2×C4—121no—
1171C2×C4—121no—
1172C2×C4—121no—
1173C2×C4—121no—
1174C2×C4—121no—
1175C2×C4—121no—
1176C2×C4—121no—
1177C2×C4—121no—
1178C2×C4—121no—
1179C2×C4—121no—
1180C2×C4—121no—
1181C2×C4—121no—
1182C2×C4—121no—
1183C2×C4—121no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—121no—
1191C2×C4—121no—
1192C2×C4#87414yes—
1193C2×C4#89514yes—
1194C2×C3#241111yescharacteristic
1195C2×C3#242611yescharacteristic
1196C2×C3#245611yescharacteristic
1197C2×C3#246311yescharacteristic
1198C2×C3#246711yescharacteristic
1199C2×C3#247111yescharacteristic
1200C2×C3#253911yescharacteristic
1201C2×C3#254011yescharacteristic
1202C2×C3#254111yescharacteristic
1203C2×C3#267311yescharacteristic
1204C2×C3#267611yescharacteristic
1205C2×C3#268511yescharacteristic
1206C2×C3#270511yescharacteristic
1207C2×C3#271111yescharacteristic
1208C2×C3#273011yescharacteristic
1209D3—82no—
1210D3—82no—
1211D3—82no—
1212C22—122no—
1213C22—122no—
1214C22—122no—
1215C22—122no—
1216C22—122no—
1217C22—122no—
1218C22—122no—
1219C22—122no—
1220C22—122no—
1221C22—122no—
1222C22—122no—
1223C22—122no—
1224C22—122no—
1225C22—122no—
1226C22—122no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—122no—
1233C22—241no—
1234C22—241no—
1235C22—241no—
1236C22—241no—
1237C22—241no—
1238C22—241no—
1239C22—241no—
1240C22—241no—
1241C22—241no—
1242C22—241no—
1243C22—241no—
1244C22—241no—
1245C22—241no—
1246C22—241no—
1247C22—241no—
1248C22—241no—
1249C22—241no—
1250C22—241no—
1251C22—241no—
1252C22—241no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22C2×#87411yescharacteristic
1258C22#549311yescharacteristic
1259C22C2×#89511yescharacteristic
1260C22#551011yescharacteristic
1261C22#552411yescharacteristic
1262C22#552411yescharacteristic
1263C22#552511yescharacteristic
1264C22D4×D1211yescharacteristic
1265C22D4×D1211yescharacteristic
1266C22#555411yescharacteristic
1267C22#555411yescharacteristic
1268C22#555411yescharacteristic
1269C22#555411yescharacteristic
1270C22#555411yescharacteristic
1271C22#555411yescharacteristic
1272C22#557611yescharacteristic
1273C22#557611yescharacteristic
1274C22#557711yescharacteristic
1275C22#557711yescharacteristic
1276C22#559211yescharacteristic
1277C22#559911yescharacteristic
1278C22#562011yescharacteristic
1279C22#563311yescharacteristic
1280C22#563711yescharacteristic
1281C22#563711yescharacteristic
1282C22#564711yescharacteristic
1283C22#565611yescharacteristic
1284C22#565711yescharacteristic
1285C22#566311yescharacteristic
1286C22#567811yescharacteristic
1287C22#569111yescharacteristic
1288C22#569211yescharacteristic
1289C22#570511yescharacteristic
1290C22#570911yescharacteristic
1291C22#573311yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—122no—
1300C4—122no—
1301C4—122no—
1302C4—241no—
1303C4—241no—
1304C3#1577611yescharacteristic, complemented, Sylow
1305C2—242no—
1306C2—242no—
1307C2—242no—
1308C2#7359711yescharacteristic
1309C2#7379811yescharacteristic
1310C2#7379911yescharacteristic
1311C2#7450911yescharacteristic
1312C2#7460211yescharacteristic
1313C2#7479211yescharacteristic
1314C2#7500111yescharacteristic
1315C2#7515511yescharacteristic
1316C2#7532711yescharacteristic
1317C2#7533211yescharacteristic
1318C2#7550311yescharacteristic
1319C2#7591811yescharacteristic
1320C2#7611311yescharacteristic
1321C2#7621811yescharacteristic
1322C2#7657111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC2×#4671C2
hypercenter#1436D3
hypocenterC3#15776
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C2×#4994C2semidirect
2. C2×#4988C2semidirect
3. C2×#4939C2semidirect
4. C2×#4677C2semidirect
6. C2×#4672C2semidirect
7. C2×#4670C2semidirect
8. C2×#4653C2semidirect
9. C3×#1436C2semidirect
10. #71537C2semidirect
11. #69427C2semidirect
12. #69427C2semidirect
13. #69426C2semidirect
14. #69426C2semidirect
15. #69426C2semidirect
74. #1436D3semidirect
113. C2×C3×C4⋊C4D4semidirect
170. C2×C4⋊Dic3D4semidirect
181. C3×#95D4semidirect
453. C2×C4⋊C4D12semidirect
514. #95D12semidirect
1304. C3#15776semidirect

Maximal subgroups

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

subgroupindex
C2×#49942
C2×#49882
C2×#49392
C2×#46772
C2×#46712
C2×#46722
C2×#46702
C2×#46532
C3×#14362
#715372
#694272
#694262
#157763