Finite Group Databasebeta

← #10733603

Subgroups — #10733603

Order 768.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#875C211yesmaximal, characteristic
2C2×#4987C211yesmaximal, characteristic, complemented
3C2×#4665C211yesmaximal, characteristic
4C2×#4674C211yesmaximal, characteristic, complemented
5C2×#4656C211yesmaximal, characteristic, complemented
6C2×#4672C211yesmaximal, characteristic
7C3×#1436C211yesmaximal, characteristic, complemented
8#71570C211yesmaximal, characteristic, complemented
9#71536C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11#69429C211yesmaximal, characteristic, complemented
12#69427C211yesmaximal, characteristic, complemented
13#69427C211yesmaximal, characteristic, complemented
14(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
15#69424C211yesmaximal, characteristic, complemented
16#15311—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×Dic6C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C2×#875—24no—
37C2×#875—24no—
38C2×#875—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#4674—24no—
57#4672—24no—
58#4665—24no—
59#4656—24no—
60C22×#124—31no—
61C2×#397—31no—
62C2×#395—31no—
63C2×#394—31no—
64C2×#386—31no—
65C2×#380—31no—
66#1446—31no—
67#1440—31no—
68#1440—31no—
69#1439—31no—
70#1439—31no—
71#1439—31no—
72#1436—31no—
73#1436D311yescharacteristic, complemented
74C22⋊#95—31no—
75C24×D3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C23×Dic3C2311yescharacteristic
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—41no—
95C22×D12—41no—
96C22×D12D414yes—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—41no—
103C22×C4×D3—41no—
104C22×Dic6—22no—
105C22×Dic6—22no—
106C22×Dic6—22no—
107C22×Dic6—22no—
108C22×Dic6—22no—
109C22×Dic6—41no—
110C22×Dic6—41no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—41no—
114C2×C3×C42—22no—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4—22no—
122C2×(C2×D3)⋊C4—22no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—22no—
140C2×(C2×D3)⋊C4—22no—
141C2×(C2×D3)⋊C4—22no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4—41no—
146C2×(C2×D3)⋊C4—41no—
147C2×(C2×D3)⋊C4—41no—
148C2×(C2×D3)⋊C4D414yes—
149C2×(C2×D3)⋊C4D414yes—
150C2×C4⋊Dic3—22no—
151C2×C4⋊Dic3—22no—
152C2×C4⋊Dic3—22no—
153C2×C4⋊Dic3—22no—
154C2×C4⋊Dic3—41no—
155C2×C4⋊Dic3—41no—
156C2×Dic3⋊C4—22no—
157C2×Dic3⋊C4—22no—
158C2×Dic3⋊C4—22no—
159#875—232no—
160C3×#95—22no—
161C3×#95—22no—
162C3×#95—22no—
163C3×#95—41no—
164C3×#95D414yes—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—41no—
175C3⋊#95—41no—
176C23×Q8—31no—
177C23×D4—31no—
178C24×C4—31no—
179C2×#124—64no—
180C2×#124—64no—
181C2×#124—64no—
182C22×C4⋊C4—31no—
183C22×C4⋊C4—31no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4C2×D311yescharacteristic
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C22⋊C4—31no—
190C22×C22⋊C4—31no—
191C22×C22⋊C4—31no—
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C42C2×D311yescharacteristic
198#397—64no—
199#395—64no—
200#394—64no—
201#386—64no—
202#380—64no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C2×#95C2×D311yescharacteristic
217C2×#95C2×D311yescharacteristic
218C2×#95C2×D311yescharacteristic
219C24×C3C2411yescharacteristic
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
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×D3C2×D412yes—
247C23×D3C2×D412yes—
248C23×D3C2×D412yes—
249C23×D3C2×D412yes—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
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×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4C2×D412yes—
296C22×C3×C4#4112yes—
297C22×C3×C4#4112yes—
298C22×C3×C4#4112yes—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
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×Dic3C2×D412yes—
338C22×Dic3C2×D412yes—
339C22×Dic3#4112yes—
340C22×Dic3#4112yes—
341C2×D12—28no—
342C2×D12—28no—
343C2×D12—44no—
344C2×D12—44no—
345C2×D12—44no—
346C2×D12—44no—
347C2×D12—44no—
348C2×C4×D3—28no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×Dic6—28no—
356C2×Dic6—44no—
357C2×Dic6—44no—
358C2×Dic6—44no—
359C2×Dic6—44no—
360C2×Dic6—44no—
361C2×Dic6—44no—
362C3×C4⋊C4—44no—
363C3×C42—28no—
364(C2×D3)⋊C4—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—28no—
367(C2×D3)⋊C4—28no—
368(C2×D3)⋊C4—44no—
369(C2×D3)⋊C4—44no—
370(C2×D3)⋊C4—44no—
371(C2×D3)⋊C4—44no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375C4⋊Dic3—44no—
376C4⋊Dic3—44no—
377Dic3⋊C4—44no—
378C25—31no—
379C25—31no—
380C22×Q8—62no—
381C22×Q8—62no—
382C22×Q8—62no—
383C22×Q8—62no—
384C22×Q8—62no—
385C22×Q8—121no—
386C22×Q8—121no—
387C22×D4—34no—
388C22×D4—62no—
389C22×D4—62no—
390C22×D4—62no—
391C22×D4—62no—
392C22×D4—121no—
393C22×D4—121no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—121no—
406C23×C4—121no—
407C23×C4C22×D311yescharacteristic
408C23×C4C22×D311yescharacteristic
409C23×C4C22×D311yescharacteristic
410C23×C4C22×D311yescharacteristic
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414#124—632no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—62no—
419C2×C4⋊C4—62no—
420C2×C4⋊C4—62no—
421C2×C4⋊C4—62no—
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—121no—
426C2×C4⋊C4—121no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—62no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—62no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—62no—
450C2×C22⋊C4—62no—
451C2×C22⋊C4—62no—
452C2×C22⋊C4—62no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—121no—
455C2×C22⋊C4—121no—
456C2×C22⋊C4—121no—
457C2×C22⋊C4—121no—
458C2×C22⋊C4—121no—
459C2×C22⋊C4—121no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—41no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—121no—
477#95—121no—
478#95D1214yes—
479C23×C3C22×D411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C22×D411yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3H(5,𝔽2)11yescharacteristic
489C23×C3H(5,𝔽2)11yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C32−1+411yescharacteristic
492C23×C32−1+411yescharacteristic
493C23×C32−1+411yescharacteristic
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
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—41no—
520C22×D3—41no—
521C22×D3—41no—
522C22×D3—41no—
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
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#12014yes—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
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#12114yes—
612C2×C3×C4#12414yescomplemented
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—41no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—41no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655D12—416no—
656C4×D3—416no—
657Dic6—416no—
658C24—32no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—61no—
663C24—61no—
664C24—61no—
665C24—61no—
666C24—61no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24C23×D311yescharacteristic
689C2×Q8—68no—
690C2×Q8—124no—
691C2×Q8—124no—
692C2×Q8—124no—
693C2×Q8—124no—
694C2×Q8—124no—
695C2×Q8—124no—
696C2×D4—68no—
697C2×D4—68no—
698C2×D4—124no—
699C2×D4—124no—
700C2×D4—124no—
701C2×D4—124no—
702C2×D4—124no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
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—32no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—68no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
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—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4C2×D1212yes—
793C22×C4C2×D1212yes—
794C22×C4C2×D1212yes—
795C22×C4#23512yes—
796C22×C4#23512yes—
797C22×C4D3×D412yes—
798C22×C4D3×D412yes—
799C22×C4D3×D412yes—
800C22×C4#23912yes—
801C4⋊C4—44no—
802C4⋊C4—124no—
803C4⋊C4—124no—
804C4⋊C4—124no—
805C22⋊C4—68no—
806C22⋊C4—68no—
807C22⋊C4—68no—
808C22⋊C4—68no—
809C22⋊C4—124no—
810C22⋊C4—124no—
811C22⋊C4—124no—
812C22⋊C4—124no—
813C22⋊C4—124no—
814C22⋊C4—124no—
815C22⋊C4—124no—
816C42—28no—
817C22×C3C2×#12011yescharacteristic
818C22×C3C2×#12111yescharacteristic
819C22×C3#52511yescharacteristic
820C22×C3C2×#12411yescharacteristic
821C22×C3#52911yescharacteristic
822C22×C3#53211yescharacteristic
823C22×C3#53411yescharacteristic
824C22×C3#53611yescharacteristic
825C22×C3#53611yescharacteristic
826C22×C3#53711yescharacteristic
827C22×C3#53811yescharacteristic
828C22×C3#54211yescharacteristic
829C22×C3#54211yescharacteristic
830C22×C3#54211yescharacteristic
831C22×C3#54211yescharacteristic
832C22×C3D4211yescharacteristic
833C22×C3D4211yescharacteristic
834C22×C3#54611yescharacteristic
835C22×C3#54611yescharacteristic
836C22×C3#54611yescharacteristic
837C22×C3#54611yescharacteristic
838C22×C3#54611yescharacteristic
839C22×C3#54711yescharacteristic
840C22×C3#54711yescharacteristic
841C22×C3#54711yescharacteristic
842C22×C3#54711yescharacteristic
843C22×C3#54711yescharacteristic
844C22×C3#54711yescharacteristic
845C22×C3#54811yescharacteristic
846C22×C3#55111yescharacteristic
847C22×C3#55511yescharacteristic
848C22×C3#55611yescharacteristic
849C22×C3#55611yescharacteristic
850C22×C3#56211yescharacteristic
851C22×C3#56311yescharacteristic
852C2×D3—24no—
853C2×D3—24no—
854C2×D3—24no—
855C2×D3—42no—
856C2×D3—42no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—42no—
862C2×D3—42no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—42no—
866C2×D3—42no—
867C2×D3—42no—
868C2×D3—42no—
869C2×D3—42no—
870C2×D3—42no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—81no—
875C2×D3—81no—
876C2×D3—81no—
877C2×D3—81no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C3×C4—24no—
883C3×C4—24no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—42no—
887C3×C4—81no—
888C3×C4—81no—
889Dic3—42no—
890Dic3—42no—
891Dic3—42no—
892Dic3—42no—
893Dic3—81no—
894Dic3—81no—
895C23—34no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—62no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—121no—
922C23—121no—
923C23—121no—
924C23—121no—
925C23—121no—
926C23—121no—
927C23—121no—
928C23—121no—
929C23—121no—
930C23—121no—
931C23—121no—
932C23—121no—
933C23—121no—
934C23—121no—
935C23—121no—
936C23—121no—
937C23—121no—
938C23—121no—
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—
965C23C22×D1211yescharacteristic
966C23C2×#23511yescharacteristic
967C23C2×#23511yescharacteristic
968C23C2×D3×D411yescharacteristic
969C23C2×D3×D411yescharacteristic
970C23C2×D3×D411yescharacteristic
971C23#100411yescharacteristic
972C23C2×#23911yescharacteristic
973C23#100711yescharacteristic
974C23D3×#4111yescharacteristic
975C23D3×#4111yescharacteristic
976C23#100911yescharacteristic
977C23#100911yescharacteristic
978C23#101011yescharacteristic
979C23#101011yescharacteristic
980Q8—1216no—
981D4—1216no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
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—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—1216no—
1042C2×C4—121no—
1043C2×C4—121no—
1044C2×C4—121no—
1045C2×C4—121no—
1046C2×C4—121no—
1047C2×C4—121no—
1048C2×C4—121no—
1049C2×C4—121no—
1050C2×C4—121no—
1051C2×C4—121no—
1052C2×C4—121no—
1053C2×C4—121no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4#87514yescomplemented
1073C2×C4#89514yes—
1074C2×C3#240611yescharacteristic
1075C2×C3#241011yescharacteristic
1076C2×C3#242711yescharacteristic
1077C2×C3#243011yescharacteristic
1078C2×C3#247211yescharacteristic
1079C2×C3#247411yescharacteristic
1080C2×C3#249111yescharacteristic
1081C2×C3#252111yescharacteristic
1082C2×C3#254711yescharacteristic
1083C2×C3#267211yescharacteristic
1084C2×C3#267411yescharacteristic
1085C2×C3#268611yescharacteristic
1086C2×C3#270011yescharacteristic
1087C2×C3#271511yescharacteristic
1088C2×C3#271711yescharacteristic
1089D3—44no—
1090D3—82no—
1091C22—64no—
1092C22—64no—
1093C22—64no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—122no—
1102C22—122no—
1103C22—122no—
1104C22—122no—
1105C22—122no—
1106C22—122no—
1107C22—122no—
1108C22—122no—
1109C22—122no—
1110C22—122no—
1111C22—122no—
1112C22—122no—
1113C22—241no—
1114C22—241no—
1115C22—241no—
1116C22—241no—
1117C22—241no—
1118C22—241no—
1119C22—241no—
1120C22—241no—
1121C22C2×#87511yescharacteristic
1122C22#549011yescharacteristic
1123C22C2×#89511yescharacteristic
1124C22#550711yescharacteristic
1125C22#552611yescharacteristic
1126C22#552711yescharacteristic
1127C22#553211yescharacteristic
1128C22#554711yescharacteristic
1129C22#554811yescharacteristic
1130C22D4×D1211yescharacteristic
1131C22D4×D1211yescharacteristic
1132C22#555111yescharacteristic
1133C22#555111yescharacteristic
1134C22#555411yescharacteristic
1135C22#556011yescharacteristic
1136C22#557611yescharacteristic
1137C22#558211yescharacteristic
1138C22#558411yescharacteristic
1139C22#558411yescharacteristic
1140C22D3×#12011yescharacteristic
1141C22#560811yescharacteristic
1142C22#561211yescharacteristic
1143C22#562811yescharacteristic
1144C22#563011yescharacteristic
1145C22#563011yescharacteristic
1146C22#563111yescharacteristic
1147C22#565311yescharacteristic
1148C22#565511yescharacteristic
1149C22#565511yescharacteristic
1150C22#568411yescharacteristic
1151C22#569111yescharacteristic
1152C22#569911yescharacteristic
1153C22#571011yescharacteristic
1154C22#571011yescharacteristic
1155C22#573311yescharacteristic
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—81no—
1163C4—122no—
1164C4—122no—
1165C4—122no—
1166C4—122no—
1167C4—241no—
1168C4—241no—
1169C3#1531111yescharacteristic, complemented, Sylow
1170C2—124no—
1171C2—242no—
1172C2#7359411yescharacteristic
1173C2#7378811yescharacteristic
1174C2#7380211yescharacteristic
1175C2#7460011yescharacteristic
1176C2#7460111yescharacteristic
1177C2#7489611yescharacteristic
1178C2#7501011yescharacteristic
1179C2#7504411yescharacteristic
1180C2#7538811yescharacteristic
1181C2#7539811yescharacteristic
1182C2#7566511yescharacteristic
1183C2#7592111yescharacteristic
1184C2#7611611yescharacteristic
1185C2#7621911yescharacteristic
1186C2#7665011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1436C2
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#15311
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#4987C2semidirect
4. C2×#4674C2semidirect
5. C2×#4656C2semidirect
7. C3×#1436C2semidirect
8. #71570C2semidirect
9. #71536C2semidirect
10. #69429C2semidirect
11. #69429C2semidirect
12. #69427C2semidirect
13. #69427C2semidirect
14. (C2×D3)⋊#95C2semidirect
15. #69424C2semidirect
73. #1436D3semidirect
612. C2×C3×C4#124semidirect
1072. C2×C4#875semidirect
1169. C3#15311semidirect

Maximal subgroups

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

subgroupindex
C22×#8752
C2×#49872
C2×#46652
C2×#46742
C2×#46562
C2×#46722
C3×#14362
#715702
#715362
#694292
#694272
(C2×D3)⋊#952
#694242
#153113