Finite Group Databasebeta

← #10733722

Subgroups — #10733722

Order 768.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#895C211yesmaximal, characteristic
2C2×C3×#398C211yesmaximal, characteristic, complemented
3C2×#4991C211yesmaximal, characteristic, complemented
4C2×#4991C211yesmaximal, characteristic, complemented
5C2×#4988C211yesmaximal, characteristic, complemented
6C2×#4990C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71564C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69426C211yesmaximal, characteristic, complemented
12#69426C211yesmaximal, characteristic, complemented
13#69426C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
16#15319—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊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×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#895—24no—
41C2×#895—24no—
42C2×#895—24no—
43C3×#398—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
56#4991—24no—
57#4991—24no—
58#4990—24no—
59#4988—24no—
60C22×#121—31no—
61C2×#398D311yescharacteristic, complemented
62C2×#394—31no—
63C2×#394—31no—
64C2×#390—31no—
65C2×#388—31no—
66#1440—31no—
67#1439—31no—
68#1439—31no—
69#1438—31no—
70#1438—31no—
71#1438—31no—
72#1436—31no—
73C22⋊#95—31no—
74C22⋊#95—31no—
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—22no—
104C22×D12—41no—
105C22×D12—41no—
106C22×D12—41no—
107C22×D12—41no—
108C22×D12—41no—
109C22×D12—41no—
110C22×D12D414yes—
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—41no—
117C22×C4×D3—41no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—41no—
128C2×C3×C4⋊C4—41no—
129C2×C3×C4⋊C4D414yes—
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—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
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×(C2×D3)⋊C4—41no—
163C2×(C2×D3)⋊C4—41no—
164C2×(C2×D3)⋊C4—41no—
165C2×(C2×D3)⋊C4—41no—
166C2×(C2×D3)⋊C4—41no—
167C2×(C2×D3)⋊C4—41no—
168C2×(C2×D3)⋊C4—41no—
169C2×(C2×D3)⋊C4—41no—
170C2×(C2×D3)⋊C4D414yes—
171C2×(C2×D3)⋊C4D414yescomplemented
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—41no—
175#895—232no—
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—41no—
186C3⋊#95—41no—
187C3⋊#95—41no—
188C23×D4—31no—
189C23×D4—31no—
190C23×D4—31no—
191C24×C4—31no—
192C2×#121—64no—
193C2×#121—64no—
194C2×#121—64no—
195C22×C4⋊C4C2×D311yescharacteristic
196C22×C4⋊C4C2×D311yescharacteristic
197C22×C4⋊C4C2×D311yescharacteristic
198C22×C4⋊C4C2×D311yescharacteristic
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×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4—31no—
213C22×C42—31no—
214#398—24no—
215#394—64no—
216#394—64no—
217#390—64no—
218#388—64no—
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×#95—31no—
228C2×#95C2×D311yescharacteristic
229C2×#95C2×D311yescharacteristic
230C2×#95C2×D311yescharacteristic
231C24×C3C2411yescharacteristic
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×D3C2×D412yes—
273C23×D3C2×D412yes—
274C23×D3C2×D412yes—
275C23×D3C2×D412yes—
276C23×D3#4112yes—
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×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
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×C4#4112yes—
324C22×C3×C4#4112yes—
325C22×C3×C4#4112yes—
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×Dic3—21no—
358C22×Dic3C2×D412yes—
359C22×Dic3C2×D412yes—
360C22×Dic3#4112yes—
361C2×D12—28no—
362C2×D12—28no—
363C2×D12—28no—
364C2×D12—28no—
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—
381C2×D12—44no—
382C2×C4×D3—28no—
383C2×C4×D3—44no—
384C2×C4×D3—44no—
385C2×C4×D3—44no—
386C2×C4×D3—44no—
387C2×C4×D3—44no—
388C2×C4×D3—44no—
389C3×C4⋊C4—28no—
390C3×C4⋊C4—44no—
391C3×C4⋊C4—44no—
392C3×C4⋊C4—44no—
393(C2×D3)⋊C4—28no—
394(C2×D3)⋊C4—28no—
395(C2×D3)⋊C4—28no—
396(C2×D3)⋊C4—44no—
397(C2×D3)⋊C4—44no—
398(C2×D3)⋊C4—44no—
399(C2×D3)⋊C4—44no—
400(C2×D3)⋊C4—44no—
401(C2×D3)⋊C4—44no—
402(C2×D3)⋊C4—44no—
403(C2×D3)⋊C4—44no—
404(C2×D3)⋊C4—44no—
405(C2×D3)⋊C4—44no—
406(C2×D3)⋊C4—44no—
407C4×Dic3—44no—
408C25—31no—
409C25—31no—
410C25—31no—
411C22×D4—34no—
412C22×D4—62no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—62no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—62no—
419C22×D4—62no—
420C22×D4—62no—
421C22×D4—62no—
422C22×D4—62no—
423C22×D4—62no—
424C22×D4—62no—
425C22×D4—62no—
426C22×D4—121no—
427C22×D4—121no—
428C22×D4—121no—
429C22×D4—121no—
430C22×D4—121no—
431C22×D4—121no—
432C23×C4—31no—
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—62no—
438C23×C4—62no—
439C23×C4—62no—
440C23×C4—62no—
441C23×C4—62no—
442C23×C4—121no—
443C23×C4—121no—
444C23×C4C22×D311yescharacteristic
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C23×C4C22×D311yescharacteristic
451#121—632no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4#6714yes—
464C2×C22⋊C4—34no—
465C2×C22⋊C4—34no—
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—62no—
489C2×C22⋊C4—62no—
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×C22⋊C4—121no—
500C2×C22⋊C4—121no—
501C2×C22⋊C4—121no—
502C2×C22⋊C4—121no—
503C2×C22⋊C4—121no—
504C2×C22⋊C4—121no—
505C2×C22⋊C4—121no—
506C2×C42—62no—
507C2×C42—62no—
508C2×C42—121no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—62no—
513#95—62no—
514#95—62no—
515#95—62no—
516#95—62no—
517#95—62no—
518#95—121no—
519#95—121no—
520#95—121no—
521C23×C3C22×D411yescharacteristic
522C23×C3C22×D411yescharacteristic
523C23×C3C22×D411yescharacteristic
524C23×C3C22×D411yescharacteristic
525C23×C3C2×#4111yescharacteristic
526C23×C3C2×#4111yescharacteristic
527C23×C3C2×#4111yescharacteristic
528C23×C3C2×#4111yescharacteristic
529C23×C3C2×#4111yescharacteristic
530C23×C3H(5,𝔽2)11yescharacteristic
531C23×C3H(5,𝔽2)11yescharacteristic
532C23×C3H(5,𝔽2)11yescharacteristic
533C23×C3H(5,𝔽2)11yescharacteristic
534C23×C3H(5,𝔽2)11yescharacteristic
535C23×C32−1+411yescharacteristic
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—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
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—
635C22×D3—41no—
636C22×D3—41no—
637C22×D3—41no—
638C22×D3—41no—
639C22×D3—41no—
640C22×D3#12114yes—
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—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4#12014yes—
689C2×C3×C4#12414yes—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
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—
719C2×Dic3—41no—
720C2×Dic3—41no—
721C2×Dic3—41no—
722C2×Dic3—41no—
723C2×Dic3—41no—
724C2×Dic3—41no—
725D12—416no—
726D12—416no—
727D12—416no—
728C4×D3—416no—
729C24—32no—
730C24—32no—
731C24—32no—
732C24—32no—
733C24—32no—
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—
767C24—61no—
768C24—61no—
769C24—61no—
770C24—61no—
771C24—61no—
772C24—61no—
773C24—61no—
774C24C23×D311yescharacteristic
775C2×D4—68no—
776C2×D4—68no—
777C2×D4—68no—
778C2×D4—68no—
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—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—124no—
793C2×D4—124no—
794C2×D4—124no—
795C2×D4—124no—
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—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—32no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—68no—
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×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4—61no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—124no—
873C22×C4—124no—
874C22×C4—124no—
875C22×C4—124no—
876C22×C4—124no—
877C22×C4—124no—
878C22×C4D3×D412yes—
879C22×C4D3×D412yes—
880C22×C4D3×D412yes—
881C22×C4#23912yes—
882C22×C4#23912yes—
883C22×C4#23912yes—
884C22×C4C2×#6712yes—
885C22×C4C2×#6712yes—
886C22×C4C2×#6712yes—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—68no—
892C22⋊C4—68no—
893C22⋊C4—68no—
894C22⋊C4—124no—
895C22⋊C4—124no—
896C22⋊C4—124no—
897C22⋊C4—124no—
898C22⋊C4—124no—
899C22⋊C4—124no—
900C22⋊C4—124no—
901C22⋊C4—124no—
902C22⋊C4—124no—
903C22⋊C4—124no—
904C22⋊C4—124no—
905C42—124no—
906C22×C3C2×#12011yescharacteristic
907C22×C3C2×#12111yescharacteristic
908C22×C3#52511yescharacteristic
909C22×C3C2×#12411yescharacteristic
910C22×C3#52911yescharacteristic
911C22×C3#53211yescharacteristic
912C22×C3#53411yescharacteristic
913C22×C3#53411yescharacteristic
914C22×C3#53511yescharacteristic
915C22×C3#53711yescharacteristic
916C22×C3#53911yescharacteristic
917C22×C3#54011yescharacteristic
918C22×C3#54011yescharacteristic
919C22×C3#54011yescharacteristic
920C22×C3#54211yescharacteristic
921C22×C3D4211yescharacteristic
922C22×C3D4211yescharacteristic
923C22×C3#54611yescharacteristic
924C22×C3#54611yescharacteristic
925C22×C3#54611yescharacteristic
926C22×C3#54611yescharacteristic
927C22×C3#54611yescharacteristic
928C22×C3#54611yescharacteristic
929C22×C3#54611yescharacteristic
930C22×C3#54611yescharacteristic
931C22×C3#54711yescharacteristic
932C22×C3#54711yescharacteristic
933C22×C3#54811yescharacteristic
934C22×C3#55011yescharacteristic
935C22×C3#55311yescharacteristic
936C22×C3#55311yescharacteristic
937C22×C3#55311yescharacteristic
938C22×C3#55511yescharacteristic
939C22×C3#56011yescharacteristic
940C22×C3#56211yescharacteristic
941C2×D3—24no—
942C2×D3—24no—
943C2×D3—24no—
944C2×D3—42no—
945C2×D3—42no—
946C2×D3—42no—
947C2×D3—42no—
948C2×D3—42no—
949C2×D3—42no—
950C2×D3—42no—
951C2×D3—42no—
952C2×D3—42no—
953C2×D3—42no—
954C2×D3—42no—
955C2×D3—42no—
956C2×D3—42no—
957C2×D3—42no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—42no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—42no—
965C2×D3—42no—
966C2×D3—42no—
967C2×D3—42no—
968C2×D3—42no—
969C2×D3—42no—
970C2×D3—81no—
971C2×D3—81no—
972C2×D3—81no—
973C2×D3—81no—
974C2×D3—81no—
975C2×D3—81no—
976C2×D3—81no—
977C2×D3—81no—
978C2×D3—81no—
979C2×D3—81no—
980C2×D3—81no—
981C2×D3—81no—
982C2×D3—81no—
983C2×D3—81no—
984C2×D3—81no—
985C2×D3—81no—
986C3×C4—24no—
987C3×C4—24no—
988C3×C4—42no—
989C3×C4—42no—
990C3×C4—42no—
991C3×C4—81no—
992C3×C4—81no—
993Dic3—42no—
994Dic3—42no—
995Dic3—42no—
996Dic3—81no—
997Dic3—81no—
998C23—34no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—62no—
1003C23—62no—
1004C23—62no—
1005C23—62no—
1006C23—62no—
1007C23—62no—
1008C23—62no—
1009C23—62no—
1010C23—62no—
1011C23—62no—
1012C23—62no—
1013C23—62no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
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—
1092C23—121no—
1093C23—121no—
1094C23—121no—
1095C23—121no—
1096C23—121no—
1097C23—121no—
1098C23—121no—
1099C23—121no—
1100C23—121no—
1101C23—121no—
1102C23—121no—
1103C23C2×D3×D411yescharacteristic
1104C23C2×D3×D411yescharacteristic
1105C23C2×D3×D411yescharacteristic
1106C23#100411yescharacteristic
1107C23C2×#23911yescharacteristic
1108C23C2×#23911yescharacteristic
1109C23C2×#23911yescharacteristic
1110C23#100711yescharacteristic
1111C23D3×#4111yescharacteristic
1112C23D3×#4111yescharacteristic
1113C23#100911yescharacteristic
1114C23#100911yescharacteristic
1115C23#100911yescharacteristic
1116C23#100911yescharacteristic
1117C23C22×#6711yescharacteristic
1118D4—1216no—
1119D4—1216no—
1120D4—1216no—
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—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
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—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
1173C2×C4—62no—
1174C2×C4—62no—
1175C2×C4—62no—
1176C2×C4—62no—
1177C2×C4—1216no—
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—121no—
1193C2×C4—121no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—121no—
1200C2×C4—121no—
1201C2×C4—121no—
1202C2×C4—121no—
1203C2×C4—121no—
1204C2×C4#93714yes—
1205C2×C4#94714yes—
1206C2×C3#240711yescharacteristic
1207C2×C3#241011yescharacteristic
1208C2×C3#242511yescharacteristic
1209C2×C3#243511yescharacteristic
1210C2×C3#246411yescharacteristic
1211C2×C3#247611yescharacteristic
1212C2×C3#249011yescharacteristic
1213C2×C3#249111yescharacteristic
1214C2×C3#254311yescharacteristic
1215C2×C3#267111yescharacteristic
1216C2×C3#267311yescharacteristic
1217C2×C3#269111yescharacteristic
1218C2×C3#269911yescharacteristic
1219C2×C3#270111yescharacteristic
1220C2×C3#271111yescharacteristic
1221D3—44no—
1222D3—82no—
1223D3—82no—
1224C22—64no—
1225C22—64no—
1226C22—64no—
1227C22—122no—
1228C22—122no—
1229C22—122no—
1230C22—122no—
1231C22—122no—
1232C22—122no—
1233C22—122no—
1234C22—122no—
1235C22—122no—
1236C22—122no—
1237C22—122no—
1238C22—122no—
1239C22—122no—
1240C22—122no—
1241C22—122no—
1242C22—122no—
1243C22—122no—
1244C22—122no—
1245C22—122no—
1246C22—122no—
1247C22—122no—
1248C22—122no—
1249C22—122no—
1250C22—122no—
1251C22—122no—
1252C22—122no—
1253C22—241no—
1254C22—241no—
1255C22—241no—
1256C22—241no—
1257C22—241no—
1258C22—241no—
1259C22—241no—
1260C22—241no—
1261C22—241no—
1262C22—241no—
1263C22—241no—
1264C22—241no—
1265C22—241no—
1266C22—241no—
1267C22—241no—
1268C22—241no—
1269C22D3×#12111yescharacteristic
1270C22#560511yescharacteristic
1271C22#560911yescharacteristic
1272C22#561011yescharacteristic
1273C22#562711yescharacteristic
1274C22#562911yescharacteristic
1275C22#563011yescharacteristic
1276C22#563011yescharacteristic
1277C22#563011yescharacteristic
1278C22#563011yescharacteristic
1279C22#563011yescharacteristic
1280C22#563111yescharacteristic
1281C22#565311yescharacteristic
1282C22#565411yescharacteristic
1283C22#566311yescharacteristic
1284C22#566611yescharacteristic
1285C22#569111yescharacteristic
1286C22#569211yescharacteristic
1287C22#569511yescharacteristic
1288C22#569511yescharacteristic
1289C22#569511yescharacteristic
1290C22#569711yescharacteristic
1291C22#569711yescharacteristic
1292C22#570011yescharacteristic
1293C22#572511yescharacteristic
1294C22#572611yescharacteristic
1295C22#573311yescharacteristic
1296C22#573411yescharacteristic
1297C22C2×#93711yescharacteristic
1298C22D4×#6711yescharacteristic
1299C22C2×#94711yescharacteristic
1300C22#581711yescharacteristic
1301C22#582911yescharacteristic
1302C22#583011yescharacteristic
1303C22#583411yescharacteristic
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—81no—
1310C4—81no—
1311C4—122no—
1312C4—122no—
1313C4—122no—
1314C4—241no—
1315C4—241no—
1316C3#1531911yescharacteristic, complemented, Sylow
1317C2—124no—
1318C2—242no—
1319C2—242no—
1320C2#7775311yescharacteristic
1321C2#7776011yescharacteristic
1322C2#7784711yescharacteristic
1323C2#7794811yescharacteristic
1324C2#7795711yescharacteristic
1325C2#7796711yescharacteristic
1326C2#7797811yescharacteristic
1327C2#7797911yescharacteristic
1328C2#8270211yescharacteristic
1329C2#8276111yescharacteristic
1330C2#8281211yescharacteristic
1331C2#8290611yescharacteristic
1332C2#8306111yescharacteristic
1333C2#8307011yescharacteristic
1334C2#8325711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#398C2
prime radicalC22×#895C2
hypercenterC2×#398D3
hypocenterC3#15319
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C2×C3×#398C2semidirect
3. C2×#4991C2semidirect
4. C2×#4991C2semidirect
5. C2×#4988C2semidirect
6. C2×#4990C2semidirect
7. #71570C2semidirect
8. #71570C2semidirect
9. #71564C2semidirect
10. #69429C2semidirect
11. #69426C2semidirect
12. #69426C2semidirect
13. #69426C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. (C2×D3)⋊#95C2semidirect
61. C2×#398D3semidirect
171. C2×(C2×D3)⋊C4D4semidirect
1316. C3#15319semidirect

Maximal subgroups

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

subgroupindex
C22×#8952
C2×C3×#3982
C2×#49912
C2×#49882
C2×#49902
#715702
#715642
#694292
#694262
(C2×D3)⋊#952
#153193