Finite Group Databasebeta

← #10720210

Subgroups — #10720210

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic
2C22×C3⋊#95C211yesmaximal, characteristic, complemented
3C2×#4958C211yesmaximal, characteristic
4C2×#4958C211yesmaximal, characteristic
5C2×#4950C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
7C2×#4670C211yesmaximal, characteristic, complemented
8C3×C22⋊#95C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69427C211yesmaximal, characteristic, complemented
11#69418C211yesmaximal, characteristic, complemented
12#69415C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69407C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38#5213—24no—
39C2×C3⋊#95—24no—
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
54#4958—24no—
55#4958C418yescomplemented
56#4950—24no—
57Dic3×C22⋊C4—24no—
58#4670—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#385—31no—
64C2×C4×C22⋊C4—31no—
65C22×#95—31no—
66#1443—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1437—31no—
71#1436—31no—
72#1434—31no—
73C22⋊#95D311yescharacteristic, complemented
74C25×C3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—41no—
82C23×C3×C4—41no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—22no—
90C22×#67—22no—
91C22×#67—22no—
92C22×#67—22no—
93C22×#67—22no—
94C22×#67—22no—
95C22×#67C2×C414yes—
96C23×Dic3—22no—
97C23×Dic3—22no—
98C23×Dic3—22no—
99C23×Dic3—22no—
100C23×Dic3—22no—
101C23×Dic3—22no—
102C23×Dic3—22no—
103C23×Dic3—22no—
104C23×Dic3—22no—
105C23×Dic3—41no—
106C23×Dic3—41no—
107C23×Dic3—41no—
108C23×Dic3—41no—
109C23×Dic3C2×C414yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C22⋊C4—22no—
120C2×C3×C22⋊C4—22no—
121C2×C3×C22⋊C4C2×C414yes—
122C2×C3×C22⋊C4D414yes—
123C2×#217—22no—
124C2×#217—22no—
125C2×#217D414yes—
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—41no—
137C2×(C2×D3)⋊C4—41no—
138C2×(C2×D3)⋊C4—41no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4C2×C414yescomplemented
143C2×(C2×D3)⋊C4C2×C414yescomplemented
144C2×C4⋊Dic3—22no—
145C2×C4⋊Dic3—22no—
146C2×C4⋊Dic3—22no—
147C2×C4⋊Dic3—22no—
148C2×C4⋊Dic3—41no—
149C2×C4⋊Dic3—41no—
150C2×C4×Dic3—22no—
151C2×C4×Dic3—22no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—41no—
155C2×C4×Dic3—41no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—41no—
159C3×#95—41no—
160C3⋊#95—22no—
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95C2×C414yescomplemented
172C3⋊#95C2×C414yescomplemented
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4C2×D311yescharacteristic
178C22×C4⋊C4—31no—
179C22×C4⋊C4—31no—
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4C2×D311yescharacteristic
188C22×C22⋊C4C2×D311yescharacteristic
189C22×C42—31no—
190C22×C42—31no—
191#388—64no—
192#386—38no—
193#386—64no—
194#386—64no—
195#385—64no—
196C4×C22⋊C4—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
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—64no—
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3C22×C412yes—
225C24×C3C2×D412yes—
226C24×C3C2×D412yes—
227C24×C3#4112yes—
228C24×C3#4112yes—
229C24×C3#4112yes—
230C24×C3#4112yes—
231C24×C3C2411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3C22×C412yes—
247C22×C3×C4—28no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
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—44no—
285C22×C3×C4—44no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4—44no—
290C22×C3×C4C22×C412yes—
291C22×C3×C4C22×C412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4C2×D412yes—
294C22×C3×C4C2×D412yes—
295C22×C3×C4#4112yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—44no—
300C2×#67—44no—
301C2×#67—44no—
302C2×#67—44no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—28no—
308C22×Dic3—28no—
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—28no—
346C22×Dic3—44no—
347C22×Dic3—44no—
348C22×Dic3—44no—
349C22×Dic3—44no—
350C22×Dic3—44no—
351C22×Dic3—44no—
352C22×Dic3—44no—
353C22×Dic3—44no—
354C22×Dic3—44no—
355C22×Dic3—44no—
356C22×Dic3—44no—
357C22×Dic3C22×C412yes—
358C22×Dic3C22×C412yes—
359C22×Dic3C22×C412yes—
360C22×Dic3C2×D412yes—
361C22×Dic3C2×D412yes—
362C22×Dic3C2×D412yes—
363C22×Dic3C2×D412yes—
364C22×Dic3#4112yes—
365C22×Dic3#4112yes—
366C3×C22⋊C4—28no—
367C3×C22⋊C4—28no—
368#217—28no—
369(C2×D3)⋊C4—28no—
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—
377C4×Dic3—44no—
378C4×Dic3—44no—
379C25—31no—
380C25C22×D311yescharacteristic
381C22×D4—34no—
382C22×D4—62no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—31no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—31no—
399C23×C4—31no—
400C23×C4—34no—
401C23×C4—41no—
402C23×C4—41no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4—62no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4—121no—
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C2×C4⋊C4—62no—
423C2×C4⋊C4—62no—
424C2×C4⋊C4—62no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—121no—
427C2×C4⋊C4—121no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—34no—
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—121no—
448C2×C22⋊C4—121no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4C4×D314yes—
454C2×C22⋊C4D1214yes—
455C2×C42—62no—
456C2×C42—62no—
457C2×C42—62no—
458C2×C42—62no—
459C2×C42—121no—
460C2×C42—121no—
461#95—22no—
462#95—22no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—41no—
467#95—41no—
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—62no—
477#95—62no—
478#95—62no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3#11714yes—
508C23×C3C4×D414yes—
509C23×C3C4×D414yes—
510C23×C3#12114yes—
511C23×C3#12314yes—
512C23×C3#12414yes—
513C23×C3#12614yes—
514C23×C3C23×C411yescharacteristic
515C23×C3C22×D411yescharacteristic
516C23×C3C22×D411yescharacteristic
517C23×C3C22×D411yescharacteristic
518C23×C3C2×#4111yescharacteristic
519C23×C3C2×#4111yescharacteristic
520C23×C3C2×#4111yescharacteristic
521C23×C3C2×#4111yescharacteristic
522C23×C3C2×#4111yescharacteristic
523C23×C3C2×#4111yescharacteristic
524C23×C3C2×#4111yescharacteristic
525C23×C3H(5,𝔽2)11yescharacteristic
526C23×C3H(5,𝔽2)11yescharacteristic
527C23×C3H(5,𝔽2)11yescharacteristic
528C23×C32−1+411yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
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—
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—416no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
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—
607#67—416no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
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—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—416no—
633C2×Dic3—416no—
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—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3C4×D414yes—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—32no—
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—
682C24C2×C4×D312yes—
683C24C2×D1212yes—
684C24#23512yes—
685C24D3×D412yes—
686C24#23712yes—
687C24#23712yes—
688C24#23912yes—
689C24C23×D311yescharacteristic
690C2×D4—68no—
691C2×D4—68no—
692C2×D4—68no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
697C22×C4—28no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
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—32no—
735C22×C4—32no—
736C22×C4—32no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—68no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—68no—
755C22×C4—68no—
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—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4—124no—
801C22×C4—124no—
802C22×C4—124no—
803C22×C4C2×C4×D312yes—
804C22×C4C2×C4×D312yes—
805C22×C4C2×D1212yes—
806C22×C4C2×D1212yes—
807C22×C4D3×D412yes—
808C22×C4#23712yes—
809C4⋊C4—124no—
810C4⋊C4—124no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—68no—
814C22⋊C4—68no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—124no—
821C42—124no—
822C22×C3—24no—
823C22×C3—24no—
824C22×C3—24no—
825C22×C3—24no—
826C22×C3—24no—
827C22×C3—24no—
828C22×C3—24no—
829C22×C3—24no—
830C22×C3—24no—
831C22×C3—24no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—24no—
835C22×C3—24no—
836C22×C3#38818yescomplemented
837C22×C3C2×#11711yescharacteristic
838C22×C3C2×C4×D411yescharacteristic
839C22×C3C2×C4×D411yescharacteristic
840C22×C3C2×C4×D411yescharacteristic
841C22×C3C4×#4111yescharacteristic
842C22×C3#51811yescharacteristic
843C22×C3#52011yescharacteristic
844C22×C3C2×#12111yescharacteristic
845C22×C3C2×#12311yescharacteristic
846C22×C3#52511yescharacteristic
847C22×C3#52511yescharacteristic
848C22×C3C2×#12411yescharacteristic
849C22×C3C2×#12611yescharacteristic
850C22×C3#52911yescharacteristic
851C22×C3#52911yescharacteristic
852C22×C3#53811yescharacteristic
853C22×C3#53811yescharacteristic
854C22×C3#53911yescharacteristic
855C22×C3#53911yescharacteristic
856C22×C3D4211yescharacteristic
857C22×C3D4211yescharacteristic
858C22×C3#54611yescharacteristic
859C22×C3#54611yescharacteristic
860C22×C3#54611yescharacteristic
861C22×C3#54611yescharacteristic
862C22×C3#54611yescharacteristic
863C22×C3#54711yescharacteristic
864C22×C3#54711yescharacteristic
865C22×C3#54811yescharacteristic
866C22×C3#55111yescharacteristic
867C22×C3#55111yescharacteristic
868C22×C3#55211yescharacteristic
869C22×C3#55311yescharacteristic
870C22×C3#55311yescharacteristic
871C22×C3#55311yescharacteristic
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C2×D3—81no—
883C2×D3—81no—
884C2×D3—81no—
885C2×D3—81no—
886C2×D3—81no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893Dic3—24no—
894Dic3—42no—
895Dic3—42no—
896Dic3—42no—
897Dic3—42no—
898Dic3—42no—
899Dic3—42no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
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—
963C23C4×D1214yes—
964C23#67⋊C414yes—
965C23#88514yes—
966C23#88614yes—
967C23#89214yes—
968C23#89514yes—
969C23#89814yes—
970C23C22×C4×D311yescharacteristic
971C23C22×D1211yescharacteristic
972C23C2×#23511yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23C2×#23711yescharacteristic
976C23C2×#23711yescharacteristic
977C23C2×#23711yescharacteristic
978C23#100411yescharacteristic
979C23#100411yescharacteristic
980C23C2×#23911yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23#100911yescharacteristic
984C23#101011yescharacteristic
985D4—1216no—
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—22no—
1004C2×C4—34no—
1005C2×C4—416no—
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—41no—
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—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—1216no—
1055C2×C4—1216no—
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—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C3—28no—
1081C2×C3C2×#38811yescharacteristic
1082C2×C3#229011yescharacteristic
1083C2×C3#231811yescharacteristic
1084C2×C3#235811yescharacteristic
1085C2×C3#235911yescharacteristic
1086C2×C3#236111yescharacteristic
1087C2×C3#236411yescharacteristic
1088C2×C3#242411yescharacteristic
1089C2×C3#242511yescharacteristic
1090C2×C3#244311yescharacteristic
1091C2×C3#244411yescharacteristic
1092C2×C3#247211yescharacteristic
1093C2×C3#248111yescharacteristic
1094C2×C3#248811yescharacteristic
1095C2×C3#251011yescharacteristic
1096D3—82no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—122no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—241no—
1119C22—241no—
1120C22—241no—
1121C22—241no—
1122C22—241no—
1123C22—241no—
1124C22—241no—
1125C22—241no—
1126C22#467018yescomplemented
1127C22C2×C4×D1211yescharacteristic
1128C22C2×#67⋊C411yescharacteristic
1129C22#549011yescharacteristic
1130C22C2×#88511yescharacteristic
1131C22C2×#88611yescharacteristic
1132C22#549511yescharacteristic
1133C22C2×#89211yescharacteristic
1134C22C2×#89511yescharacteristic
1135C22C2×#89811yescharacteristic
1136C22#552711yescharacteristic
1137C22#553111yescharacteristic
1138C22C4×#23711yescharacteristic
1139C22C4×D3×D411yescharacteristic
1140C22#554511yescharacteristic
1141C22#554611yescharacteristic
1142C22D4×D1211yescharacteristic
1143C22#555411yescharacteristic
1144C22#555411yescharacteristic
1145C22#555511yescharacteristic
1146C22#558611yescharacteristic
1147C22#559011yescharacteristic
1148C22#559111yescharacteristic
1149C22#559311yescharacteristic
1150C22#559811yescharacteristic
1151C22#560111yescharacteristic
1152C22#560111yescharacteristic
1153C22#561811yescharacteristic
1154C22#562411yescharacteristic
1155C22#562711yescharacteristic
1156C22#564411yescharacteristic
1157C22#564511yescharacteristic
1158C22#564911yescharacteristic
1159C22#565411yescharacteristic
1160C22#565511yescharacteristic
1161C22#566511yescharacteristic
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—64no—
1169C4—122no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—122no—
1175C3#1414011yescharacteristic, complemented, Sylow
1176C2—28no—
1177C2—242no—
1178C2C2×#467011yescharacteristic
1179C2#7346411yescharacteristic
1180C2#7357711yescharacteristic
1181C2#7382911yescharacteristic
1182C2#7391011yescharacteristic
1183C2#7392811yescharacteristic
1184C2#7407611yescharacteristic
1185C2#7437711yescharacteristic
1186C2#7438311yescharacteristic
1187C2#7441011yescharacteristic
1188C2#7460511yescharacteristic
1189C2#7467611yescharacteristic
1190C2#7467811yescharacteristic
1191C2#7470311yescharacteristic
1192C2#7470611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊#95C2semidirect
5. C2×#4950C2semidirect
6. C2×Dic3×C22⋊C4C2semidirect
7. C2×#4670C2semidirect
8. C3×C22⋊#95C2semidirect
9. #69429C2semidirect
10. #69427C2semidirect
11. #69418C2semidirect
12. #69415C2semidirect
13. #69408C2semidirect
14. #69407C2semidirect
15. #69402C2semidirect
55. #4958C4semidirect
73. C22⋊#95D3semidirect
142. C2×(C2×D3)⋊C4C2×C4semidirect
143. C2×(C2×D3)⋊C4C2×C4semidirect
171. C3⋊#95C2×C4semidirect
172. C3⋊#95C2×C4semidirect
173. C3⋊#95D4semidirect
836. C22×C3#388semidirect
1126. C22#4670semidirect
1175. C3#14140semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C22×C3⋊#952
C2×#49582
C2×#49502
C2×Dic3×C22⋊C42
C2×#46702
C3×C22⋊#952
#694292
#694272
#694182
#694152
#694082
#694072
#694022
#141403