Finite Group Databasebeta

← #10718052

Subgroups — #10718052

Order 768.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D12C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4665C211yesmaximal, characteristic
5C2×#4668C211yesmaximal, characteristic, complemented
6C2×#4668C211yesmaximal, characteristic, complemented
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1436C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71536C211yesmaximal, characteristic, complemented
11#69427C211yesmaximal, characteristic, complemented
12(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
14#69419C211yesmaximal, characteristic, complemented
15#69415C211yesmaximal, characteristic, complemented
16#13975—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
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
36C2×C4×D12—24no—
37C2×C4×D12—24no—
38C2×C4×D12—24no—
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
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#4987—24no—
56#4668—24no—
57#4668—24no—
58#4665—24no—
59#4665C418yescomplemented
60D3×#95—24no—
61C22×C4×D4—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#385—31no—
65C2×#385—31no—
66C2×#380—31no—
67C22×#95—31no—
68#1444—31no—
69#1442—31no—
70#1439—31no—
71#1439—31no—
72#1436—31no—
73#1436D311yescharacteristic, complemented
74C22⋊#95—31no—
75C22⋊#95—31no—
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
90C23×Dic3C2311yescharacteristic
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12C2×C414yes—
96C22×D12D414yes—
97C22×D12Q814yes—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—22no—
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—
118C22×C4×D3—41no—
119C22×C4×D3—41no—
120C22×C4×D3—41no—
121C22×C4×D3—41no—
122C22×C4×D3—41no—
123C22×C4×D3—41no—
124C22×C4×D3C2×C414yescomplemented
125C22×C4×D3D414yes—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—41no—
129C2×C3×C42—22no—
130C2×C3×C42—22no—
131C2×C3×C42—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)⋊C4C2×C414yescomplemented
153C2×(C2×D3)⋊C4C2×C414yescomplemented
154C2×(C2×D3)⋊C4C2×C414yescomplemented
155C2×(C2×D3)⋊C4D414yes—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—22no—
160C2×C4⋊Dic3—22no—
161C2×C4⋊Dic3—22no—
162C2×C4⋊Dic3—41no—
163C2×C4⋊Dic3—41no—
164C2×C4⋊Dic3—41no—
165C2×Dic3⋊C4—22no—
166C2×Dic3⋊C4—22no—
167C2×Dic3⋊C4—22no—
168C4×D12—232no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—41no—
172C3×#95C2×C414yescomplemented
173C3×#95D414yescomplemented
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—41no—
184C3⋊#95C2×C414yescomplemented
185C23×D4—31no—
186C24×C4—31no—
187C24×C4—31no—
188C24×C4—31no—
189C24×C4—31no—
190C2×C4×D4—64no—
191C2×C4×D4—64no—
192C2×C4×D4—64no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4C2×D311yescharacteristic
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×C42C2×D311yescharacteristic
207#386—38no—
208#386—64no—
209#385—64no—
210#385—64no—
211#380—64no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C2×#95—64no—
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C2×#95C2×D311yescharacteristic
229C24×C3C2411yescharacteristic
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3C22×C412yes—
251C23×D3C22×C412yes—
252C23×D3C2×D412yes—
253C23×D3C2×D412yes—
254C23×D3C2×D412yes—
255C23×D3C2×D412yes—
256C23×D3C2×Q812yes—
257C23×D3C2×Q812yes—
258C23×D3#4112yes—
259C23×D3#4112yes—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4C22×C412yes—
298C22×C3×C4C22×C412yes—
299C22×C3×C4C22×C412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×Q812yes—
307C22×C3×C4#4112yes—
308C22×C3×C4#4112yes—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3C22×C412yes—
347C22×Dic3C22×C412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3C2×D412yes—
350C22×Dic3#4112yes—
351C2×D12—28no—
352C2×D12—28no—
353C2×D12—28no—
354C2×D12—28no—
355C2×D12—28no—
356C2×D12—28no—
357C2×D12C4⋊C4116yescomplemented
358C2×C4×D3—28no—
359C2×C4×D3—28no—
360C2×C4×D3—28no—
361C2×C4×D3—28no—
362C2×C4×D3—28no—
363C2×C4×D3—28no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C2×C4×D3—44no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C2×C4×D3—44no—
374C2×C4×D3—44no—
375C2×C4×D3—44no—
376C2×C4×D3—44no—
377C2×C4×D3—44no—
378C2×C4×D3—44no—
379C2×C4×D3—44no—
380C2×C4×D3—44no—
381C2×C4×D3—44no—
382C2×C4×D3—44no—
383C2×C4×D3—44no—
384C2×C4×D3—44no—
385C2×C4×D3—44no—
386C3×C4⋊C4—44no—
387C3×C42—28no—
388(C2×D3)⋊C4—28no—
389(C2×D3)⋊C4—28no—
390(C2×D3)⋊C4—28no—
391(C2×D3)⋊C4—28no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394(C2×D3)⋊C4—44no—
395(C2×D3)⋊C4—44no—
396C4⋊Dic3—28no—
397C4⋊Dic3—44no—
398C4⋊Dic3—44no—
399Dic3⋊C4—44no—
400C25—31no—
401C25—31no—
402C22×D4—34no—
403C22×D4—34no—
404C22×D4—34no—
405C22×D4—62no—
406C22×D4—62no—
407C22×D4—62no—
408C22×D4—62no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—34no—
415C23×C4—34no—
416C23×C4—31no—
417C23×C4—62no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—62no—
424C23×C4—62no—
425C23×C4—62no—
426C23×C4—62no—
427C23×C4—62no—
428C23×C4—62no—
429C23×C4—62no—
430C23×C4—62no—
431C23×C4—62no—
432C23×C4—62no—
433C23×C4—62no—
434C23×C4—62no—
435C23×C4—121no—
436C23×C4—121no—
437C23×C4—121no—
438C23×C4—121no—
439C23×C4—121no—
440C23×C4—121no—
441C23×C4—121no—
442C23×C4—121no—
443C23×C4C22×D311yescharacteristic
444C23×C4C22×D311yescharacteristic
445C23×C4C22×D311yescharacteristic
446C23×C4C22×D311yescharacteristic
447C23×C4C22×D311yescharacteristic
448C23×C4C22×D311yescharacteristic
449C23×C4C22×D311yescharacteristic
450C4×D4—632no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—62no—
455C2×C4⋊C4—62no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—62no—
459C2×C4⋊C4—62no—
460C2×C4⋊C4—62no—
461C2×C4⋊C4—62no—
462C2×C4⋊C4—62no—
463C2×C4⋊C4—121no—
464C2×C4⋊C4—121no—
465C2×C4⋊C4—121no—
466C2×C22⋊C4—34no—
467C2×C22⋊C4—34no—
468C2×C22⋊C4—34no—
469C2×C22⋊C4—34no—
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—121no—
487C2×C22⋊C4—121no—
488C2×C22⋊C4—121no—
489C2×C22⋊C4—121no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493#95—22no—
494#95—22no—
495#95—34no—
496#95—41no—
497#95—62no—
498#95—62no—
499#95—62no—
500#95—62no—
501#95—62no—
502#95—62no—
503#95—62no—
504#95—62no—
505#95—62no—
506#95—121no—
507#95C4×D314yescomplemented
508#95D1214yescomplemented
509C23×C3C23×C411yescharacteristic
510C23×C3C22×D411yescharacteristic
511C23×C3C22×D411yescharacteristic
512C23×C3C22×D411yescharacteristic
513C23×C3C22×D411yescharacteristic
514C23×C3C22×Q811yescharacteristic
515C23×C3C2×#4111yescharacteristic
516C23×C3C2×#4111yescharacteristic
517C23×C3C2×#4111yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3H(5,𝔽2)11yescharacteristic
521C23×C3H(5,𝔽2)11yescharacteristic
522C23×C3H(5,𝔽2)11yescharacteristic
523C23×C32−1+411yescharacteristic
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—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—22no—
569C22×D3—22no—
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×D3C2×C4⋊C414yes—
587C22×D3C2×C4⋊C414yes—
588C22×D3C4×D414yes—
589C22×D3C4×D414yes—
590C22×D3#12014yes—
591C22×D3C22⋊Q814yes—
592C22×D3C22⋊Q814yes—
593C22×D3#12314yes—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4C2×C4⋊C414yes—
641C2×C3×C4C4×D414yescomplemented
642C2×C3×C4#12114yes—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—22no—
655C2×Dic3—22no—
656C2×Dic3—22no—
657C2×Dic3—22no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C2×Dic3—41no—
673C2×Dic3—41no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676C2×Dic3—41no—
677C2×Dic3—41no—
678C2×Dic3—41no—
679C2×Dic3—41no—
680C2×Dic3—41no—
681C2×Dic3—41no—
682C2×Dic3—41no—
683C2×Dic3—41no—
684C2×Dic3—41no—
685D12—232no—
686C4×D3—416no—
687C4×D3—416no—
688C4×D3—416no—
689C4×D3—416no—
690C24—32no—
691C24—32no—
692C24—32no—
693C24—32no—
694C24—32no—
695C24—32no—
696C24—32no—
697C24—32no—
698C24—32no—
699C24—32no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24—61no—
705C24—61no—
706C24—61no—
707C24—61no—
708C24—61no—
709C24—61no—
710C24—61no—
711C24—61no—
712C24—61no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24—61no—
717C24—61no—
718C24—61no—
719C24—61no—
720C24C23×D311yescharacteristic
721C2×D4—316no—
722C2×D4—68no—
723C2×D4—68no—
724C2×D4—68no—
725C2×D4—68no—
726C2×D4—68no—
727C2×D4—68no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—68no—
771C22×C4—68no—
772C22×C4—68no—
773C22×C4—68no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—68no—
805C22×C4—68no—
806C22×C4—61no—
807C22×C4—61no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—61no—
812C22×C4—61no—
813C22×C4—124no—
814C22×C4—124no—
815C22×C4—124no—
816C22×C4—124no—
817C22×C4—124no—
818C22×C4—124no—
819C22×C4—124no—
820C22×C4—124no—
821C22×C4—124no—
822C22×C4—124no—
823C22×C4—124no—
824C22×C4—124no—
825C22×C4—124no—
826C22×C4—124no—
827C22×C4—124no—
828C22×C4—124no—
829C22×C4—124no—
830C22×C4—124no—
831C22×C4—124no—
832C22×C4—124no—
833C22×C4—124no—
834C22×C4—124no—
835C22×C4C2×C4×D312yes—
836C22×C4C2×C4×D312yes—
837C22×C4C2×C4×D312yes—
838C22×C4C2×D1212yes—
839C22×C4C2×D1212yes—
840C22×C4C2×D1212yes—
841C22×C4#23512yes—
842C22×C4D3×D412yes—
843C22×C4D3×D412yes—
844C22×C4D3×D412yes—
845C22×C4D3×Q812yes—
846C22×C4#23912yes—
847C4⋊C4—44no—
848C4⋊C4—68no—
849C4⋊C4—124no—
850C4⋊C4—124no—
851C4⋊C4—124no—
852C22⋊C4—68no—
853C22⋊C4—68no—
854C22⋊C4—68no—
855C22⋊C4—68no—
856C22⋊C4—124no—
857C22⋊C4—124no—
858C22⋊C4—124no—
859C22⋊C4—124no—
860C42—28no—
861C22×C3C22×C4⋊C411yescharacteristic
862C22×C3C2×C4×D411yescharacteristic
863C22×C3C2×C4×D411yescharacteristic
864C22×C3C2×C4×D411yescharacteristic
865C22×C3C4×#4111yescharacteristic
866C22×C3#51811yescharacteristic
867C22×C3#52011yescharacteristic
868C22×C3C2×#12011yescharacteristic
869C22×C3C2×#12111yescharacteristic
870C22×C3C2×C22⋊Q811yescharacteristic
871C22×C3C2×C22⋊Q811yescharacteristic
872C22×C3C2×#12311yescharacteristic
873C22×C3#52511yescharacteristic
874C22×C3#52911yescharacteristic
875C22×C3#53211yescharacteristic
876C22×C3#53411yescharacteristic
877C22×C3#53711yescharacteristic
878C22×C3#53811yescharacteristic
879C22×C3#53911yescharacteristic
880C22×C3D4211yescharacteristic
881C22×C3D4211yescharacteristic
882C22×C3#54611yescharacteristic
883C22×C3#54611yescharacteristic
884C22×C3#54611yescharacteristic
885C22×C3#54611yescharacteristic
886C22×C3#54611yescharacteristic
887C22×C3#54711yescharacteristic
888C22×C3#54711yescharacteristic
889C22×C3D4×Q811yescharacteristic
890C22×C3#55111yescharacteristic
891C22×C3#55111yescharacteristic
892C22×C3#55211yescharacteristic
893C22×C3#55411yescharacteristic
894C22×C3#55411yescharacteristic
895C22×C3#55411yescharacteristic
896C2×D3—24no—
897C2×D3—24no—
898C2×D3—24no—
899C2×D3—24no—
900C2×D3—24no—
901C2×D3—24no—
902C2×D3—24no—
903C2×D3—24no—
904C2×D3—24no—
905C2×D3—24no—
906C2×D3—24no—
907C2×D3—24no—
908C2×D3—24no—
909C2×D3—24no—
910C2×D3—24no—
911C2×D3—24no—
912C2×D3—24no—
913C2×D3—42no—
914C2×D3—42no—
915C2×D3—42no—
916C2×D3—42no—
917C2×D3—42no—
918C2×D3—42no—
919C2×D3—42no—
920C2×D3—42no—
921C2×D3—42no—
922C2×D3—42no—
923C2×D3—42no—
924C2×D3—42no—
925C2×D3#38518yescomplemented
926C3×C4—24no—
927C3×C4—24no—
928C3×C4—24no—
929C3×C4—42no—
930C3×C4—42no—
931C3×C4—42no—
932C3×C4—81no—
933Dic3—42no—
934Dic3—42no—
935Dic3—42no—
936Dic3—42no—
937Dic3—42no—
938Dic3—81no—
939C23—34no—
940C23—34no—
941C23—34no—
942C23—34no—
943C23—34no—
944C23—34no—
945C23—34no—
946C23—34no—
947C23—62no—
948C23—62no—
949C23—62no—
950C23—62no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—121no—
994C23—121no—
995C23—121no—
996C23—121no—
997C23—121no—
998C23—121no—
999C23—121no—
1000C23—121no—
1001C23—121no—
1002C23—121no—
1003C23—121no—
1004C23—121no—
1005C23—121no—
1006C23—121no—
1007C23—121no—
1008C23—121no—
1009C23C22×C4×D311yescharacteristic
1010C23C22×D1211yescharacteristic
1011C23C2×#23511yescharacteristic
1012C23C2×D3×D411yescharacteristic
1013C23C2×D3×D411yescharacteristic
1014C23C2×D3×D411yescharacteristic
1015C23#100411yescharacteristic
1016C23C2×D3×Q811yescharacteristic
1017C23C2×#23911yescharacteristic
1018C23D3×#4111yescharacteristic
1019C23D3×#4111yescharacteristic
1020C23D3×#4111yescharacteristic
1021C23#100911yescharacteristic
1022C23#100911yescharacteristic
1023C23#101011yescharacteristic
1024D4—632no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—62no—
1072C2×C4—62no—
1073C2×C4—62no—
1074C2×C4—62no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—62no—
1080C2×C4—62no—
1081C2×C4—62no—
1082C2×C4—62no—
1083C2×C4—62no—
1084C2×C4—62no—
1085C2×C4—62no—
1086C2×C4—1216no—
1087C2×C4—1216no—
1088C2×C4—1216no—
1089C2×C4—1216no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4—121no—
1095C2×C4—121no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—121no—
1099C2×C4—121no—
1100C2×C4—121no—
1101C2×C4—121no—
1102C2×C4—121no—
1103C2×C4—121no—
1104C2×C4—121no—
1105C2×C4—121no—
1106C2×C4—121no—
1107C2×C4—121no—
1108C2×C4—121no—
1109C2×C4—121no—
1110C2×C4—121no—
1111C2×C4—121no—
1112C2×C4—121no—
1113C2×C4—121no—
1114C2×C4—121no—
1115C2×C4—121no—
1116C2×C4—121no—
1117C2×C4C4×D1214yescomplemented
1118C2×C4D3×C4⋊C414yes—
1119C2×C4#89514yes—
1120C2×C3C2×#38511yescharacteristic
1121C2×C3C4×#12111yescharacteristic
1122C2×C3#232511yescharacteristic
1123C2×C3D4×C4⋊C411yescharacteristic
1124C2×C3#234911yescharacteristic
1125C2×C3#235811yescharacteristic
1126C2×C3#235911yescharacteristic
1127C2×C3#241011yescharacteristic
1128C2×C3#241711yescharacteristic
1129C2×C3#241811yescharacteristic
1130C2×C3#241911yescharacteristic
1131C2×C3#243011yescharacteristic
1132C2×C3#244911yescharacteristic
1133C2×C3#245011yescharacteristic
1134C2×C3#256411yescharacteristic
1135D3—28no—
1136D3—44no—
1137C22—38no—
1138C22—64no—
1139C22—64no—
1140C22—64no—
1141C22—64no—
1142C22—64no—
1143C22—64no—
1144C22—64no—
1145C22—64no—
1146C22—64no—
1147C22—64no—
1148C22—64no—
1149C22—64no—
1150C22—64no—
1151C22—64no—
1152C22—64no—
1153C22—64no—
1154C22—64no—
1155C22—122no—
1156C22—122no—
1157C22—122no—
1158C22—122no—
1159C22—122no—
1160C22—122no—
1161C22—122no—
1162C22—122no—
1163C22—122no—
1164C22—122no—
1165C22—122no—
1166C22—122no—
1167C22C2×C4×D1211yescharacteristic
1168C22#549011yescharacteristic
1169C22C2×D3×C4⋊C411yescharacteristic
1170C22C2×#89511yescharacteristic
1171C22#552311yescharacteristic
1172C22#552411yescharacteristic
1173C22#552711yescharacteristic
1174C22C4×D3×D411yescharacteristic
1175C22C4×D3×D411yescharacteristic
1176C22#554511yescharacteristic
1177C22#554811yescharacteristic
1178C22D4×D1211yescharacteristic
1179C22D4×D1211yescharacteristic
1180C22#555111yescharacteristic
1181C22#555411yescharacteristic
1182C22C4×#23911yescharacteristic
1183C22Q8×D1211yescharacteristic
1184C22#557911yescharacteristic
1185C22#558011yescharacteristic
1186C22D3×#12011yescharacteristic
1187C22#560811yescharacteristic
1188C22#561211yescharacteristic
1189C22D3×C22⋊Q811yescharacteristic
1190C22D3×C22⋊Q811yescharacteristic
1191C22#563011yescharacteristic
1192C22#563011yescharacteristic
1193C22D3×#12311yescharacteristic
1194C22#565311yescharacteristic
1195C22#565511yescharacteristic
1196C22#567811yescharacteristic
1197C22#569011yescharacteristic
1198C22#569411yescharacteristic
1199C22#570511yescharacteristic
1200C22#570711yescharacteristic
1201C22#573011yescharacteristic
1202C4—24no—
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—81no—
1209C4—122no—
1210C4—122no—
1211C4—122no—
1212C4—122no—
1213C4—122no—
1214C4—241no—
1215C3#1397511yescharacteristic, complemented, Sylow
1216C2—68no—
1217C2—124no—
1218C2#7357711yescharacteristic
1219C2C4×#89511yescharacteristic
1220C2C4⋊C4×D1211yescharacteristic
1221C2D3×#38511yescharacteristic
1222C2#7460111yescharacteristic
1223C2#7489611yescharacteristic
1224C2#7530811yescharacteristic
1225C2#7531611yescharacteristic
1226C2#7532111yescharacteristic
1227C2#7536011yescharacteristic
1228C2#7582911yescharacteristic
1229C2#7584411yescharacteristic
1230C2#7620311yescharacteristic
1231C2#7621211yescharacteristic
1232C2#7662811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#13975
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4987C2semidirect
5. C2×#4668C2semidirect
6. C2×#4668C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1436C2semidirect
9. #71570C2semidirect
10. #71536C2semidirect
11. #69427C2semidirect
12. (C2×D3)⋊#95C2semidirect
13. (C2×D3)⋊#95C2semidirect
14. #69419C2semidirect
15. #69415C2semidirect
59. #4665C4semidirect
73. #1436D3semidirect
124. C22×C4×D3C2×C4semidirect
152. C2×(C2×D3)⋊C4C2×C4semidirect
153. C2×(C2×D3)⋊C4C2×C4semidirect
154. C2×(C2×D3)⋊C4C2×C4semidirect
172. C3×#95C2×C4semidirect
173. C3×#95D4semidirect
184. C3⋊#95C2×C4semidirect
357. C2×D12C4⋊C4semidirect
507. #95C4×D3semidirect
508. #95D12semidirect
641. C2×C3×C4C4×D4semidirect
925. C2×D3#385semidirect
1117. C2×C4C4×D12semidirect
1215. C3#13975semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D122
C2×#49872
C2×#46652
C2×#46682
C2×D3×#952
C3×#14362
#715702
#715362
#694272
(C2×D3)⋊#952
#694192
#694152
#139753