Finite Group Databasebeta

← #10746866

Subgroups — #10746866

Order 768.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#894C211yesmaximal, characteristic
2C22×#896C211yesmaximal, characteristic, complemented
3C2×#4991C211yesmaximal, characteristic
4C2×#4979C211yesmaximal, characteristic, complemented
5C2×#4673C211yesmaximal, characteristic, complemented
6C2×#4672C211yesmaximal, characteristic
7C3×#1444C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71568C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69428C211yesmaximal, characteristic, complemented
13#69428C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69409C211yesmaximal, characteristic, complemented
16#16251—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊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×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C2×#896—24no—
39C2×#896—24no—
40C2×#896—24no—
41C2×#894—24no—
42C2×#894—24no—
43C2×#894—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
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4991—24no—
59#4979—24no—
60#4673—24no—
61#4672—24no—
62C22×#123—31no—
63C22×C22⋊Q8—31no—
64C2×#395—31no—
65C2×#394—31no—
66C2×#394—31no—
67C2×#393—31no—
68#1444—31no—
69#1444D311yescharacteristic, complemented
70#1441—31no—
71#1440—31no—
72#1440—31no—
73#1439—31no—
74#1439—31no—
75#1439—31no—
76C22⋊#95—31no—
77C24×D3C2311yescharacteristic
78C24×D3C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—41no—
98C22×D12—41no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—41no—
104C22×C4×D3—41no—
105C22×C4×D3D414yes—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—22no—
110C22×Dic6—22no—
111C22×Dic6—41no—
112C22×Dic6—41no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—41no—
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—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4—41no—
149C2×(C2×D3)⋊C4—41no—
150C2×(C2×D3)⋊C4—41no—
151C2×(C2×D3)⋊C4—41no—
152C2×(C2×D3)⋊C4D414yes—
153C2×(C2×D3)⋊C4D414yes—
154C2×(C2×D3)⋊C4D414yes—
155C2×Dic3⋊C4—22no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×Dic3⋊C4—22no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4—22no—
165C2×Dic3⋊C4—41no—
166C2×Dic3⋊C4D414yes—
167#896—232no—
168#894—232no—
169C3×#95—22no—
170C3×#95—22no—
171C3×#95—22no—
172C3×#95—41no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95—41no—
181C3⋊#95—41no—
182C3⋊#95—41no—
183C23×Q8—31no—
184C23×D4—31no—
185C24×C4—31no—
186C2×#123—64no—
187C2×#123—64no—
188C2×#123—64no—
189C2×C22⋊Q8—64no—
190C2×C22⋊Q8—64no—
191C2×C22⋊Q8—64no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
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—
210#395—64no—
211#394—64no—
212#394—64no—
213#393—64no—
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—31no—
224C2×#95C2×D311yescharacteristic
225C2×#95C2×D311yescharacteristic
226C2×#95C2×D311yescharacteristic
227C2×#95C2×D311yescharacteristic
228C24×C3C2411yescharacteristic
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×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×D3C2×D412yes—
256C23×D3C2×D412yes—
257C23×D3C2×D412yes—
258C23×D3C2×D412yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×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×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4#4112yes—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×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×Dic3C2×D412yes—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C22×Dic3C2×D412yes—
348C22×Dic3C2×D412yes—
349C22×Dic3#4112yes—
350C2×D12—28no—
351C2×D12—44no—
352C2×D12—44no—
353C2×D12—44no—
354C2×D12—44no—
355C2×D12—44no—
356C2×D12—44no—
357C2×C4×D3—28no—
358C2×C4×D3—28no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×Dic6—28no—
365C2×Dic6—44no—
366C2×Dic6—44no—
367C2×Dic6—44no—
368C2×Dic6—44no—
369C2×Dic6—44no—
370C2×Dic6—44no—
371C3×C4⋊C4—28no—
372C3×C4⋊C4—28no—
373C3×C4⋊C4—44no—
374(C2×D3)⋊C4—28no—
375(C2×D3)⋊C4—28no—
376(C2×D3)⋊C4—28no—
377(C2×D3)⋊C4—28no—
378(C2×D3)⋊C4—28no—
379(C2×D3)⋊C4—44no—
380(C2×D3)⋊C4—44no—
381(C2×D3)⋊C4—44no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385Dic3⋊C4—28no—
386Dic3⋊C4—28no—
387Dic3⋊C4—28no—
388Dic3⋊C4—44no—
389C25—31no—
390C25—31no—
391C22×Q8—62no—
392C22×Q8—62no—
393C22×Q8—62no—
394C22×Q8—62no—
395C22×Q8—62no—
396C22×Q8—121no—
397C22×Q8—121no—
398C22×D4—62no—
399C22×D4—62no—
400C22×D4—62no—
401C22×D4—62no—
402C22×D4—62no—
403C22×D4—121no—
404C22×D4—121no—
405C23×C4—31no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—34no—
411C23×C4—31no—
412C23×C4—62no—
413C23×C4—62no—
414C23×C4—62no—
415C23×C4—62no—
416C23×C4—121no—
417C23×C4—121no—
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C23×C4C22×D311yescharacteristic
423C23×C4C22×D311yescharacteristic
424C23×C4C22×D311yescharacteristic
425#123—632no—
426C22⋊Q8—632no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—62no—
438C2×C4⋊C4—62no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—62no—
443C2×C4⋊C4—62no—
444C2×C4⋊C4—62no—
445C2×C4⋊C4—62no—
446C2×C4⋊C4—62no—
447C2×C4⋊C4—121no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
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—121no—
476C2×C22⋊C4—121no—
477C2×C22⋊C4—121no—
478C2×C22⋊C4—121no—
479C2×C22⋊C4—121no—
480C2×C22⋊C4—121no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—41no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—121no—
493#95—121no—
494#95—121no—
495C23×C3C22×D411yescharacteristic
496C23×C3C22×D411yescharacteristic
497C23×C3C22×D411yescharacteristic
498C23×C3C22×D411yescharacteristic
499C23×C3C22×D411yescharacteristic
500C23×C3C2×#4111yescharacteristic
501C23×C3C2×#4111yescharacteristic
502C23×C3H(5,𝔽2)11yescharacteristic
503C23×C3H(5,𝔽2)11yescharacteristic
504C23×C3H(5,𝔽2)11yescharacteristic
505C23×C32−1+411yescharacteristic
506C23×C32−1+411yescharacteristic
507C23×C32−1+411yescharacteristic
508C23×C32−1+411yescharacteristic
509C23×C32−1+411yescharacteristic
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
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—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
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#12014yes—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
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×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
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#12014yes—
671D12—416no—
672C4×D3—416no—
673Dic6—416no—
674C24—32no—
675C24—32no—
676C24—32no—
677C24—32no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24—61no—
701C24—61no—
702C24—61no—
703C24—61no—
704C24C23×D311yescharacteristic
705C2×Q8—68no—
706C2×Q8—124no—
707C2×Q8—124no—
708C2×Q8—124no—
709C2×Q8—124no—
710C2×Q8—124no—
711C2×Q8—124no—
712C2×D4—68no—
713C2×D4—124no—
714C2×D4—124no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C2×D4—124no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
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—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—68no—
770C22×C4—68no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
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—61no—
805C22×C4—61no—
806C22×C4—124no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4#23512yes—
812C22×C4D3×D412yes—
813C22×C4D3×D412yes—
814C22×C4D3×D412yes—
815C22×C4D3×D412yes—
816C22×C4D3×D412yes—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—44no—
820C4⋊C4—68no—
821C4⋊C4—68no—
822C4⋊C4—68no—
823C4⋊C4—124no—
824C22⋊C4—68no—
825C22⋊C4—68no—
826C22⋊C4—68no—
827C22⋊C4—68no—
828C22⋊C4—68no—
829C22⋊C4—124no—
830C22⋊C4—124no—
831C22⋊C4—124no—
832C22⋊C4—124no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C22×C3C2×#12011yescharacteristic
836C22×C3C2×#12011yescharacteristic
837C22×C3#53211yescharacteristic
838C22×C3#53411yescharacteristic
839C22×C3#53611yescharacteristic
840C22×C3#53611yescharacteristic
841C22×C3#53611yescharacteristic
842C22×C3#53611yescharacteristic
843C22×C3#53611yescharacteristic
844C22×C3#53611yescharacteristic
845C22×C3#53611yescharacteristic
846C22×C3#53611yescharacteristic
847C22×C3#53711yescharacteristic
848C22×C3#53711yescharacteristic
849C22×C3#53711yescharacteristic
850C22×C3#53911yescharacteristic
851C22×C3#53911yescharacteristic
852C22×C3#54211yescharacteristic
853C22×C3#54211yescharacteristic
854C22×C3D4211yescharacteristic
855C22×C3D4211yescharacteristic
856C22×C3D4211yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54711yescharacteristic
861C22×C3#54711yescharacteristic
862C22×C3#54711yescharacteristic
863C22×C3#54711yescharacteristic
864C22×C3#54811yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#56211yescharacteristic
867C22×C3#56211yescharacteristic
868C22×C3#56311yescharacteristic
869C22×C3#56311yescharacteristic
870C2×D3—24no—
871C2×D3—24no—
872C2×D3—24no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C2×D3—42no—
886C2×D3—42no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—42no—
891C2×D3—42no—
892C2×D3—81no—
893C2×D3—81no—
894C2×D3—81no—
895C2×D3—81no—
896C2×D3—81no—
897C2×D3—81no—
898C2×D3—81no—
899C2×D3—81no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—42no—
903C3×C4—42no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—81no—
907Dic3—24no—
908Dic3—42no—
909Dic3—42no—
910Dic3—42no—
911Dic3—42no—
912Dic3—81no—
913C23—34no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—121no—
940C23—121no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23C2×#23511yescharacteristic
984C23C2×D3×D411yescharacteristic
985C23C2×D3×D411yescharacteristic
986C23C2×D3×D411yescharacteristic
987C23C2×D3×D411yescharacteristic
988C23C2×D3×D411yescharacteristic
989C23#100411yescharacteristic
990C23#100711yescharacteristic
991C23#100711yescharacteristic
992C23#100711yescharacteristic
993C23#100711yescharacteristic
994C23D3×#4111yescharacteristic
995C23#100911yescharacteristic
996C23#100911yescharacteristic
997C23#101011yescharacteristic
998Q8—1216no—
999D4—1216no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—34no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—62no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—62no—
1066C2×C4—62no—
1067C2×C4—62no—
1068C2×C4—1216no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C3#240311yescharacteristic
1093C2×C3#243011yescharacteristic
1094C2×C3#243211yescharacteristic
1095C2×C3#261411yescharacteristic
1096C2×C3#261611yescharacteristic
1097C2×C3#266311yescharacteristic
1098C2×C3#267211yescharacteristic
1099C2×C3#267211yescharacteristic
1100C2×C3#267411yescharacteristic
1101C2×C3#267411yescharacteristic
1102C2×C3#268011yescharacteristic
1103C2×C3#268011yescharacteristic
1104C2×C3#268111yescharacteristic
1105C2×C3#268111yescharacteristic
1106C2×C3#281411yescharacteristic
1107D3—44no—
1108D3—82no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—122no—
1120C22—122no—
1121C22—122no—
1122C22—122no—
1123C22—122no—
1124C22—122no—
1125C22—122no—
1126C22—122no—
1127C22—122no—
1128C22—122no—
1129C22—122no—
1130C22—122no—
1131C22—241no—
1132C22—241no—
1133C22—241no—
1134C22—241no—
1135C22—241no—
1136C22—241no—
1137C22—241no—
1138C22—241no—
1139C22#550711yescharacteristic
1140C22#550711yescharacteristic
1141C22#551511yescharacteristic
1142C22#554811yescharacteristic
1143C22#555011yescharacteristic
1144C22#555211yescharacteristic
1145C22#558211yescharacteristic
1146C22D3×#12011yescharacteristic
1147C22D3×#12011yescharacteristic
1148C22#559011yescharacteristic
1149C22#560511yescharacteristic
1150C22#560911yescharacteristic
1151C22#560911yescharacteristic
1152C22#562811yescharacteristic
1153C22#562811yescharacteristic
1154C22#562811yescharacteristic
1155C22#562911yescharacteristic
1156C22#562911yescharacteristic
1157C22#562911yescharacteristic
1158C22#563111yescharacteristic
1159C22#563311yescharacteristic
1160C22#564011yescharacteristic
1161C22#565411yescharacteristic
1162C22#565511yescharacteristic
1163C22#566711yescharacteristic
1164C22#569211yescharacteristic
1165C22#569911yescharacteristic
1166C22#570011yescharacteristic
1167C22#571711yescharacteristic
1168C22#572411yescharacteristic
1169C22#572411yescharacteristic
1170C22#572411yescharacteristic
1171C22#572411yescharacteristic
1172C22#572411yescharacteristic
1173C22#573511yescharacteristic
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—64no—
1181C4—81no—
1182C4—122no—
1183C4—122no—
1184C4—122no—
1185C4—122no—
1186C4—241no—
1187C3#1625111yescharacteristic, complemented, Sylow
1188C2—124no—
1189C2—242no—
1190C2#7437111yescharacteristic
1191C2#7441111yescharacteristic
1192C2#7460611yescharacteristic
1193C2#7463211yescharacteristic
1194C2#7625511yescharacteristic
1195C2#7625711yescharacteristic
1196C2#7625811yescharacteristic
1197C2#7675311yescharacteristic
1198C2#7720111yescharacteristic
1199C2#7725611yescharacteristic
1200C2#7726011yescharacteristic
1201C2#7796911yescharacteristic
1202C2#7797011yescharacteristic
1203C2#7800511yescharacteristic
1204C2#7811411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1444C2
prime radicalC23×D12C22
hypercenter#1444D3
hypocenterC3#16251
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
2. C22×#896C2semidirect
4. C2×#4979C2semidirect
5. C2×#4673C2semidirect
7. C3×#1444C2semidirect
8. #71570C2semidirect
9. #71568C2semidirect
10. #69429C2semidirect
11. #69429C2semidirect
12. #69428C2semidirect
13. #69428C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69409C2semidirect
69. #1444D3semidirect
1187. C3#16251semidirect

Maximal subgroups

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

subgroupindex
C22×#8942
C22×#8962
C2×#49912
C2×#49792
C2×#46732
C2×#46722
C3×#14442
#715702
#715682
#694292
#694282
(C2×D3)⋊#952
#694092
#162513