Finite Group Databasebeta

← #10740302

Subgroups — #10740302

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×C3×#396C211yesmaximal, characteristic, complemented
2C2×#4993C211yesmaximal, characteristic, complemented
3C2×#4991C211yesmaximal, characteristic, complemented
4C2×#4988C211yesmaximal, characteristic, complemented
5C2×#4978C211yesmaximal, characteristic, complemented
6C2×#4960C211yesmaximal, characteristic
7C2×#4957C211yesmaximal, characteristic, complemented
8C2×#4944C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71564C211yesmaximal, characteristic, complemented
11#71550C211yesmaximal, characteristic, complemented
12#71550C211yesmaximal, characteristic, complemented
13#71550C211yesmaximal, characteristic, complemented
14#69428C211yesmaximal, characteristic, complemented
15#69408C211yesmaximal, characteristic, complemented
16#15776—31nomaximal, Sylow
17C23×#67C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C23×D12C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
39C22×Dic3⋊C4C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C22×C4×Dic3C2211yescharacteristic
42C3×#396—24no—
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
53#4993—24no—
54#4991—24no—
55#4988—24no—
56#4978—24no—
57#4960—24no—
58#4957—24no—
59#4944—24no—
60C2×#399—31no—
61C2×#396D311yescharacteristic, complemented
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#1436—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C24×D3C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—22no—
85C22×#67—22no—
86C22×#67—22no—
87C22×#67—22no—
88C22×#67—22no—
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—41no—
93C22×#67—41no—
94C22×#67—41no—
95C22×#67—41no—
96C22×#67—41no—
97C22×#67—41no—
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C22×D12—22no—
105C22×D12—22no—
106C22×D12—22no—
107C22×D12—22no—
108C22×D12—22no—
109C22×D12—41no—
110C22×D12—41no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—41no—
117C2×C3×C4⋊C4—41no—
118C2×C3×C4⋊C4—41no—
119C2×C3×C4⋊C4D414yescomplemented
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4—22no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C22⋊C4—41no—
127C2×C3×C22⋊C4—41no—
128C2×C3×C22⋊C4—41no—
129C2×#217—22no—
130C2×#217—22no—
131C2×#217—22no—
132C2×#217—22no—
133C2×#217—22no—
134C2×#217—41no—
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—22no—
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×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4—41no—
170C2×Dic3⋊C4D414yescomplemented
171C2×C4×Dic3—22no—
172C2×C4×Dic3—22no—
173C2×C4×Dic3—22no—
174C2×C4×Dic3—22no—
175C2×C4×Dic3—41no—
176C2×C4×Dic3—41no—
177C3×#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—41no—
184C3⋊#95—41no—
185C3⋊#95D414yes—
186C3⋊#95D414yescomplemented
187C23×D4—31no—
188C23×D4—31no—
189C23×D4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4C2×D311yescharacteristic
193C22×C4⋊C4C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C42—31no—
211C22×C42—31no—
212#399—64no—
213#396—24no—
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×#95—31no—
226C2×#95—31no—
227C2×#95—31no—
228C2×#95—31no—
229C2×#95C2×D311yescharacteristic
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3—21no—
236C24×C3—21no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—21no—
240C24×C3—21no—
241C24×C3—21no—
242C24×C3—21no—
243C24×C3—21no—
244C24×C3#4112yes—
245C24×C3C2411yescharacteristic
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—21no—
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×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×D412yes—
317C22×C3×C4C2×D412yes—
318C2×#67—28no—
319C2×#67—44no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—44no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—44no—
330C2×#67—44no—
331C2×#67—44no—
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×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366C22×Dic3C2×D412yes—
367C22×Dic3C2×D412yes—
368C22×Dic3C2×D412yes—
369C22×Dic3C2×D412yes—
370C22×Dic3C2×D412yes—
371C22×Dic3C2×D412yes—
372C22×Dic3#4112yes—
373C22×Dic3#4112yes—
374C2×D12—28no—
375C2×D12—44no—
376C2×D12—44no—
377C2×D12—44no—
378C2×D12—44no—
379C2×D12—44no—
380C2×D12—44no—
381C3×C4⋊C4—44no—
382C3×C4⋊C4—44no—
383C3×C4⋊C4—44no—
384C3×C22⋊C4—44no—
385C3×C22⋊C4—44no—
386C3×C22⋊C4—44no—
387#217—28no—
388#217—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—
398(C2×D3)⋊C4—44no—
399Dic3⋊C4—28no—
400Dic3⋊C4—44no—
401C4×Dic3—44no—
402C4×Dic3—44no—
403C25—31no—
404C25—31no—
405C25C22×D311yescharacteristic
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×C4—31no—
433C23×C4C22×D311yescharacteristic
434C23×C4C22×D311yescharacteristic
435C23×C4C22×D311yescharacteristic
436C23×C4C22×D311yescharacteristic
437C23×C4C22×D311yescharacteristic
438C23×C4C22×D311yescharacteristic
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—34no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—62no—
449C2×C4⋊C4—62no—
450C2×C4⋊C4—62no—
451C2×C4⋊C4—62no—
452C2×C4⋊C4—121no—
453C2×C4⋊C4#6714yescomplemented
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—62no—
469C2×C22⋊C4—62no—
470C2×C22⋊C4—62no—
471C2×C22⋊C4—62no—
472C2×C22⋊C4—62no—
473C2×C22⋊C4—62no—
474C2×C22⋊C4—62no—
475C2×C22⋊C4—62no—
476C2×C22⋊C4—62no—
477C2×C22⋊C4—62no—
478C2×C22⋊C4—62no—
479C2×C22⋊C4—62no—
480C2×C22⋊C4—62no—
481C2×C22⋊C4—62no—
482C2×C22⋊C4—62no—
483C2×C22⋊C4—62no—
484C2×C22⋊C4—62no—
485C2×C22⋊C4—62no—
486C2×C22⋊C4—62no—
487C2×C22⋊C4—62no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C22⋊C4—121no—
491C2×C22⋊C4—121no—
492C2×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—62no—
500C2×C42—62no—
501C2×C42—62no—
502C2×C42—62no—
503C2×C42—121no—
504C2×C42—121no—
505#95—22no—
506#95—34no—
507#95—34no—
508#95—62no—
509#95—62no—
510#95—62no—
511#95—62no—
512#95—62no—
513#95—121no—
514#95—121no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—22no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3C22×D411yescharacteristic
551C23×C3C22×D411yescharacteristic
552C23×C3C22×D411yescharacteristic
553C23×C3C22×D411yescharacteristic
554C23×C3C2×#4111yescharacteristic
555C23×C3C2×#4111yescharacteristic
556C23×C3C2×#4111yescharacteristic
557C23×C3C2×#4111yescharacteristic
558C23×C3C2×#4111yescharacteristic
559C23×C3H(5,𝔽2)11yescharacteristic
560C23×C3H(5,𝔽2)11yescharacteristic
561C23×C3H(5,𝔽2)11yescharacteristic
562C23×C3H(5,𝔽2)11yescharacteristic
563C23×C3H(5,𝔽2)11yescharacteristic
564C23×C32−1+411yescharacteristic
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
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—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
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#12714yes—
677#67—416no—
678#67—416no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
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—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
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#12114yes—
721D12—416no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—32no—
737C24—32no—
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#23912yes—
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—32no—
826C22×C4—32no—
827C22×C4—32no—
828C22×C4—32no—
829C22×C4—32no—
830C22×C4—32no—
831C22×C4—32no—
832C22×C4—32no—
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×C4—61no—
863C22×C4—61no—
864C22×C4—61no—
865C22×C4—61no—
866C22×C4—61no—
867C22×C4D3×D412yes—
868C22×C4D3×D412yes—
869C22×C4D3×D412yes—
870C22×C4C2×#6712yes—
871C22×C4C2×#6712yes—
872C22×C4C2×#6712yes—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—68no—
877C4⋊C4—124no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—68no—
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—124no—
894C42—124no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—42no—
900C22×C3—42no—
901C22×C3—42no—
902C22×C3—81no—
903C22×C3—81no—
904C22×C3—81no—
905C22×C3—81no—
906C22×C3—81no—
907C22×C3—81no—
908C22×C3—81no—
909C22×C3—81no—
910C22×C3C2×#12111yescharacteristic
911C22×C3#52511yescharacteristic
912C22×C3#52511yescharacteristic
913C22×C3#52511yescharacteristic
914C22×C3#52911yescharacteristic
915C22×C3C2×#12711yescharacteristic
916C22×C3#53411yescharacteristic
917C22×C3#53511yescharacteristic
918C22×C3#53511yescharacteristic
919C22×C3#53711yescharacteristic
920C22×C3#53811yescharacteristic
921C22×C3#53811yescharacteristic
922C22×C3#53911yescharacteristic
923C22×C3#54011yescharacteristic
924C22×C3#54211yescharacteristic
925C22×C3D4211yescharacteristic
926C22×C3D4211yescharacteristic
927C22×C3#54611yescharacteristic
928C22×C3#54611yescharacteristic
929C22×C3#54611yescharacteristic
930C22×C3#54611yescharacteristic
931C22×C3#54611yescharacteristic
932C22×C3#54611yescharacteristic
933C22×C3#54811yescharacteristic
934C22×C3#54811yescharacteristic
935C22×C3#54811yescharacteristic
936C22×C3#55011yescharacteristic
937C22×C3#55011yescharacteristic
938C22×C3#55011yescharacteristic
939C22×C3#55111yescharacteristic
940C22×C3#55111yescharacteristic
941C22×C3#55111yescharacteristic
942C22×C3#55311yescharacteristic
943C22×C3#56011yescharacteristic
944C22×C3#56211yescharacteristic
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—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—42no—
977C3×C4—42no—
978C3×C4—42no—
979C3×C4—81no—
980C3×C4—81no—
981Dic3—24no—
982Dic3—42no—
983Dic3—42no—
984Dic3—42no—
985Dic3—42no—
986Dic3—42no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—62no—
1028C23—62no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
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—
1092C23C2×D3×D411yescharacteristic
1093C23C2×D3×D411yescharacteristic
1094C23C2×D3×D411yescharacteristic
1095C23#100411yescharacteristic
1096C23#100411yescharacteristic
1097C23#100411yescharacteristic
1098C23C2×#23911yescharacteristic
1099C23#100711yescharacteristic
1100C23D3×#4111yescharacteristic
1101C23D3×#4111yescharacteristic
1102C23D3×#4111yescharacteristic
1103C23D3×#4111yescharacteristic
1104C23#100911yescharacteristic
1105C23#100911yescharacteristic
1106C23C22×#6711yescharacteristic
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—34no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
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—62no—
1153C2×C4—62no—
1154C2×C4—62no—
1155C2×C4—62no—
1156C2×C4—62no—
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—62no—
1167C2×C4—62no—
1168C2×C4—62no—
1169C2×C4—62no—
1170C2×C4—62no—
1171C2×C4—62no—
1172C2×C4—62no—
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—121no—
1193C2×C4#94014yes—
1194C2×C3—82no—
1195C2×C3#241111yescharacteristic
1196C2×C3#242611yescharacteristic
1197C2×C3#245611yescharacteristic
1198C2×C3#246311yescharacteristic
1199C2×C3#246711yescharacteristic
1200C2×C3#247111yescharacteristic
1201C2×C3#253911yescharacteristic
1202C2×C3#254011yescharacteristic
1203C2×C3#254111yescharacteristic
1204C2×C3#267311yescharacteristic
1205C2×C3#267611yescharacteristic
1206C2×C3#268511yescharacteristic
1207C2×C3#270511yescharacteristic
1208C2×C3#271111yescharacteristic
1209C2×C3#273011yescharacteristic
1210D3—82no—
1211D3—82no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
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—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—
1257C22#559911yescharacteristic
1258C22#559911yescharacteristic
1259C22D3×#12111yescharacteristic
1260C22#560711yescharacteristic
1261C22#560711yescharacteristic
1262C22#560911yescharacteristic
1263C22#561011yescharacteristic
1264C22#561011yescharacteristic
1265C22#561011yescharacteristic
1266C22#561011yescharacteristic
1267C22#561511yescharacteristic
1268C22#562011yescharacteristic
1269C22#562711yescharacteristic
1270C22#562711yescharacteristic
1271C22#562911yescharacteristic
1272C22#563011yescharacteristic
1273C22#563311yescharacteristic
1274C22#563311yescharacteristic
1275C22#563711yescharacteristic
1276C22#563711yescharacteristic
1277C22#563811yescharacteristic
1278C22#564011yescharacteristic
1279C22#564411yescharacteristic
1280C22#564711yescharacteristic
1281C22#570411yescharacteristic
1282C22#570511yescharacteristic
1283C22#570611yescharacteristic
1284C22#570911yescharacteristic
1285C22D4×#6711yescharacteristic
1286C22C2×#94011yescharacteristic
1287C22#580411yescharacteristic
1288C22#581711yescharacteristic
1289C22#582811yescharacteristic
1290C22#582911yescharacteristic
1291C22#583411yescharacteristic
1292C4—24no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—64no—
1297C4—81no—
1298C4—81no—
1299C4—122no—
1300C4—122no—
1301C4—122no—
1302C4—122no—
1303C4—122no—
1304C3#1577611yescharacteristic, complemented, Sylow
1305C2—82no—
1306C2—242no—
1307C2—242no—
1308C2#7728611yescharacteristic
1309C2#7729211yescharacteristic
1310C2#7730011yescharacteristic
1311C2#7735311yescharacteristic
1312C2#7735911yescharacteristic
1313C2#7741411yescharacteristic
1314C2#7742911yescharacteristic
1315C2#7743411yescharacteristic
1316C2#8266911yescharacteristic
1317C2#8268311yescharacteristic
1318C2#8270811yescharacteristic
1319C2#8277911yescharacteristic
1320C2#8280611yescharacteristic
1321C2#8281811yescharacteristic
1322C2#8310611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC2×C3×#396C2
prime radicalC2×#4960C2
hypercenterC2×#396D3
hypocenterC3#15776
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C2×C3×#396C2semidirect
2. C2×#4993C2semidirect
3. C2×#4991C2semidirect
4. C2×#4988C2semidirect
5. C2×#4978C2semidirect
7. C2×#4957C2semidirect
8. C2×#4944C2semidirect
9. #71570C2semidirect
10. #71564C2semidirect
11. #71550C2semidirect
12. #71550C2semidirect
13. #71550C2semidirect
14. #69428C2semidirect
15. #69408C2semidirect
61. C2×#396D3semidirect
119. C2×C3×C4⋊C4D4semidirect
170. C2×Dic3⋊C4D4semidirect
186. C3⋊#95D4semidirect
453. C2×C4⋊C4#67semidirect
1304. C3#15776semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3962
C2×#49932
C2×#49912
C2×#49882
C2×#49782
C2×#49602
C2×#49572
C2×#49442
#715702
#715642
#715502
#694282
#694082
#157763