Finite Group Databasebeta

← #10724478

Subgroups — #10724478

Order 768.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5213C211yesmaximal, characteristic
2C3×C22⋊#95C211yesmaximal, characteristic, complemented
3#72127C211yesmaximal, characteristic, complemented
4#71550C211yesmaximal, characteristic
5#71550C211yesmaximal, characteristic
6#71545C211yesmaximal, characteristic, complemented
7#71545C211yesmaximal, characteristic, complemented
8#69429C211yesmaximal, characteristic, complemented
9#69429C211yesmaximal, characteristic, complemented
10#69418C211yesmaximal, characteristic, complemented
11#69417C211yesmaximal, characteristic, complemented
12#69408C211yesmaximal, characteristic, complemented
13#69408C211yesmaximal, characteristic, complemented
14#69403C211yesmaximal, characteristic, complemented
15#69402C211yesmaximal, characteristic, complemented
16#14516—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C23×#67C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C22×#217C2211yescharacteristic
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
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36#5213C418yescomplemented
37C2×C3⋊#95C2211yescharacteristic
38C2×C3⋊#95C2211yescharacteristic
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×#386—31no—
54#1443—31no—
55#1443—31no—
56#1440—31no—
57#1440—31no—
58#1438—31no—
59#1438—31no—
60#1437—31no—
61#1437—31no—
62#1437—31no—
63#1437—31no—
64#1434—31no—
65#1434—31no—
66C22⋊#95—31no—
67C22⋊#95D311yescharacteristic, complemented
68C25×C3C2311yescharacteristic
69C24×D3C2311yescharacteristic
70C23×C3×C4—41no—
71C23×C3×C4—41no—
72C23×C3×C4—41no—
73C23×C3×C4—41no—
74C23×C3×C4—41no—
75C23×C3×C4—41no—
76C23×C3×C4C2×C414yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—22no—
84C22×#67—22no—
85C22×#67—41no—
86C22×#67—41no—
87C22×#67—41no—
88C22×#67—41no—
89C22×#67C2×C414yes—
90C23×Dic3C2311yescharacteristic
91C23×Dic3C2311yescharacteristic
92C23×Dic3C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—22no—
100C2×C3×C22⋊C4—22no—
101C2×C3×C22⋊C4—41no—
102C2×C3×C22⋊C4—41no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—22no—
106C2×#217—22no—
107C2×#217—41no—
108C2×#217—41no—
109C2×#217—41no—
110C2×#217—41no—
111C2×#217C2×C414yes—
112C2×(C2×D3)⋊C4—22no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—41no—
117C2×(C2×D3)⋊C4—41no—
118C2×(C2×D3)⋊C4—41no—
119C2×(C2×D3)⋊C4—41no—
120C2×(C2×D3)⋊C4—41no—
121C2×(C2×D3)⋊C4—41no—
122C2×(C2×D3)⋊C4—41no—
123C2×(C2×D3)⋊C4—41no—
124C2×(C2×D3)⋊C4—41no—
125C2×(C2×D3)⋊C4—41no—
126C2×(C2×D3)⋊C4—41no—
127C2×(C2×D3)⋊C4—41no—
128C2×(C2×D3)⋊C4C2×C414yes—
129C2×(C2×D3)⋊C4C2×C414yes—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—41no—
133C2×C4×Dic3—41no—
134C2×C4×Dic3—41no—
135C2×C4×Dic3—41no—
136C3×#95—41no—
137C3×#95—41no—
138C3×#95—41no—
139C3×#95—41no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95—41no—
145C3⋊#95—41no—
146C3⋊#95—41no—
147C3⋊#95—41no—
148C3⋊#95—41no—
149C3⋊#95—41no—
150C3⋊#95—41no—
151C3⋊#95—41no—
152C3⋊#95—41no—
153C3⋊#95—41no—
154C3⋊#95C2×C414yes—
155C3⋊#95C2×C414yes—
156C23×D4—31no—
157C24×C4C2×D311yescharacteristic
158C22×C22⋊C4—31no—
159C22×C22⋊C4—31no—
160C22×C22⋊C4—31no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—31no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—31no—
165C22×C22⋊C4—31no—
166C22×C22⋊C4—31no—
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C22⋊C4C2×D311yescharacteristic
169C22×C42—31no—
170C22×C42—31no—
171#386—38no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—31no—
178C2×#95—31no—
179C2×#95—31no—
180C2×#95—31no—
181C2×#95—31no—
182C2×#95—31no—
183C2×#95—31no—
184C2×#95—31no—
185C2×#95—31no—
186C2×#95—31no—
187C2×#95—31no—
188C2×#95C2×D311yescharacteristic
189C2×#95C2×D311yescharacteristic
190C2×#95C2×D311yescharacteristic
191C2×#95C2×D311yescharacteristic
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3C22×C412yes—
205C24×C3#4112yes—
206C24×C3#4112yes—
207C24×C3C2411yescharacteristic
208C23×D3—21no—
209C23×D3—21no—
210C23×D3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—21no—
214C23×D3—21no—
215C23×D3—21no—
216C23×D3—21no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3C22×C412yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
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—44no—
262C22×C3×C4—44no—
263C22×C3×C4—44no—
264C22×C3×C4—44no—
265C22×C3×C4—44no—
266C22×C3×C4—44no—
267C22×C3×C4—44no—
268C22×C3×C4C22×C412yes—
269C22×C3×C4C22×C412yes—
270C22×C3×C4#4112yes—
271C22×C3×C4#4112yes—
272C2×#67—28no—
273C2×#67—44no—
274C2×#67—44no—
275C2×#67—44no—
276C2×#67—44no—
277C2×#67—44no—
278C2×#67—44no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
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×Dic3C22×C412yes—
324C22×Dic3C22×C412yes—
325C22×Dic3C22×C412yes—
326C22×Dic3#4112yes—
327C22×Dic3#4112yes—
328C3×C22⋊C4—44no—
329C3×C22⋊C4—44no—
330#217—44no—
331#217—44no—
332#217—44no—
333(C2×D3)⋊C4—44no—
334(C2×D3)⋊C4—44no—
335(C2×D3)⋊C4—44no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339C4×Dic3—44no—
340C4×Dic3—44no—
341C25—31no—
342C25C22×D311yescharacteristic
343C22×D4—34no—
344C22×D4—62no—
345C22×D4—62no—
346C22×D4—121no—
347C22×D4—121no—
348C22×D4—121no—
349C22×D4—121no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—41no—
358C23×C4—41no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4C4×D314yes—
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—34no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C22⋊C4—62no—
384C2×C22⋊C4—62no—
385C2×C22⋊C4—62no—
386C2×C22⋊C4—62no—
387C2×C22⋊C4—121no—
388C2×C22⋊C4—121no—
389C2×C22⋊C4—121no—
390C2×C22⋊C4—121no—
391C2×C22⋊C4—121no—
392C2×C22⋊C4—121no—
393C2×C22⋊C4—121no—
394C2×C22⋊C4—121no—
395C2×C22⋊C4—121no—
396C2×C22⋊C4—121no—
397C2×C22⋊C4—121no—
398C2×C22⋊C4—121no—
399C2×C22⋊C4—121no—
400C2×C22⋊C4—121no—
401C2×C22⋊C4—121no—
402C2×C22⋊C4—121no—
403C2×C42—62no—
404C2×C42—62no—
405C2×C42—121no—
406C2×C42—121no—
407C2×C42—121no—
408C2×C42—121no—
409#95—34no—
410#95—34no—
411#95—41no—
412#95—41no—
413#95—41no—
414#95—41no—
415#95—62no—
416#95—62no—
417#95—121no—
418#95—121no—
419#95—121no—
420#95—121no—
421#95—121no—
422#95—121no—
423#95—121no—
424#95—121no—
425#95—121no—
426#95—121no—
427#95—121no—
428#95—121no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3#11714yes—
464C23×C3C23×C411yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3C2×#4111yescharacteristic
468C23×C3C2×#4111yescharacteristic
469C23×C3C2×#4111yescharacteristic
470C23×C3C2×#4111yescharacteristic
471C23×C3H(5,𝔽2)11yescharacteristic
472C23×C3H(5,𝔽2)11yescharacteristic
473C23×C3H(5,𝔽2)11yescharacteristic
474C23×C3H(5,𝔽2)11yescharacteristic
475C23×C3H(5,𝔽2)11yescharacteristic
476C23×C3H(5,𝔽2)11yescharacteristic
477C23×C3H(5,𝔽2)11yescharacteristic
478C23×C3H(5,𝔽2)11yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3—41no—
505C22×D3—41no—
506C22×D3—41no—
507C22×D3—41no—
508C22×D3—41no—
509C22×D3—41no—
510C22×D3—41no—
511C22×D3—41no—
512C22×D3—41no—
513C22×D3—41no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—416no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557#67—416no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—41no—
574C2×Dic3—41no—
575C2×Dic3—41no—
576C2×Dic3—41no—
577C2×Dic3—41no—
578C2×Dic3—41no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—41no—
589C2×Dic3—41no—
590C2×Dic3—41no—
591C2×Dic3—41no—
592C2×Dic3—41no—
593C2×Dic3—41no—
594C2×Dic3—41no—
595C2×Dic3—41no—
596C2×Dic3—41no—
597C2×Dic3—41no—
598C2×Dic3—41no—
599C2×Dic3—41no—
600C2×Dic3—41no—
601C2×Dic3—41no—
602C2×Dic3—41no—
603C2×Dic3—41no—
604C2×Dic3—41no—
605C2×Dic3—41no—
606C2×Dic3—41no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—32no—
620C24—61no—
621C24—61no—
622C24—61no—
623C24—61no—
624C24—61no—
625C24—61no—
626C24—61no—
627C24—61no—
628C24—61no—
629C24—61no—
630C24—61no—
631C24—61no—
632C24—61no—
633C24—61no—
634C24C2×C4×D312yes—
635C24#23712yes—
636C24#23912yes—
637C24C23×D311yescharacteristic
638C2×D4—68no—
639C2×D4—124no—
640C2×D4—124no—
641C2×D4—124no—
642C2×D4—124no—
643C2×D4—124no—
644C2×D4—124no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—32no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—61no—
715C22×C4—61no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—61no—
722C22×C4—61no—
723C22×C4—61no—
724C22×C4—61no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4—61no—
730C22×C4—61no—
731C22×C4—61no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—61no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4C2×C4×D312yes—
740C22×C4C2×C4×D312yes—
741C22×C4#23512yes—
742C22×C4#23512yes—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—124no—
746C22⋊C4—124no—
747C22⋊C4—124no—
748C22⋊C4—124no—
749C22⋊C4—124no—
750C22⋊C4—124no—
751C22⋊C4—124no—
752C22⋊C4—124no—
753C22⋊C4—124no—
754C42—124no—
755C42—124no—
756C22×C3—24no—
757C22×C3—24no—
758C22×C3—24no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3C2×#11711yescharacteristic
772C22×C3C4×#4111yescharacteristic
773C22×C3C4×#4111yescharacteristic
774C22×C3#51811yescharacteristic
775C22×C3#51811yescharacteristic
776C22×C3#51811yescharacteristic
777C22×C3#51811yescharacteristic
778C22×C3#53811yescharacteristic
779C22×C3#53811yescharacteristic
780C22×C3#53811yescharacteristic
781C22×C3#53811yescharacteristic
782C22×C3#53811yescharacteristic
783C22×C3#53811yescharacteristic
784C22×C3#53811yescharacteristic
785C22×C3#53811yescharacteristic
786C22×C3#54011yescharacteristic
787C22×C3#54011yescharacteristic
788C22×C3#54011yescharacteristic
789C22×C3#54011yescharacteristic
790C22×C3#55111yescharacteristic
791C22×C3#55111yescharacteristic
792C22×C3#55111yescharacteristic
793C22×C3#55111yescharacteristic
794C22×C3#55111yescharacteristic
795C22×C3#55311yescharacteristic
796C22×C3#55311yescharacteristic
797C22×C3#55311yescharacteristic
798C22×C3#55311yescharacteristic
799C22×C3#55311yescharacteristic
800C22×C3#55311yescharacteristic
801C22×C3#55911yescharacteristic
802C22×C3#56011yescharacteristic
803C22×C3#56011yescharacteristic
804C22×C3#56011yescharacteristic
805C22×C3H(3,𝔽4)11yescharacteristic
806C2×D3—42no—
807C2×D3—42no—
808C2×D3—42no—
809C2×D3—42no—
810C2×D3—42no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—81no—
814C2×D3—81no—
815C2×D3—81no—
816C2×D3—81no—
817C2×D3—81no—
818C2×D3—81no—
819C2×D3—81no—
820C2×D3—81no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—81no—
826C3×C4—81no—
827Dic3—42no—
828Dic3—42no—
829Dic3—42no—
830Dic3—42no—
831Dic3—42no—
832Dic3—81no—
833Dic3—81no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—62no—
874C23—62no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23—121no—
879C23—121no—
880C23—121no—
881C23—121no—
882C23—121no—
883C23—121no—
884C23—121no—
885C23—121no—
886C23—121no—
887C23—121no—
888C23—121no—
889C23—121no—
890C23—121no—
891C23—121no—
892C23—121no—
893C23—121no—
894C23—121no—
895C23—121no—
896C23—121no—
897C23—121no—
898C23—121no—
899C23—121no—
900C23—121no—
901C23—121no—
902C23—121no—
903C23#89214yes—
904C23C22×C4×D311yescharacteristic
905C23C2×#23511yescharacteristic
906C23C2×#23511yescharacteristic
907C23C2×#23711yescharacteristic
908C23#100411yescharacteristic
909C23#100411yescharacteristic
910C23#100411yescharacteristic
911C23#100411yescharacteristic
912C23#100411yescharacteristic
913C23#100411yescharacteristic
914C23C2×#23911yescharacteristic
915C23D3×#4111yescharacteristic
916C23D3×#4111yescharacteristic
917C23#100911yescharacteristic
918C23#100911yescharacteristic
919D4—1216no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—416no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—121no—
987C2×C4—121no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—121no—
992C2×C4—121no—
993C2×C4—121no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—121no—
997C2×C4—121no—
998C2×C4—121no—
999C2×C4—121no—
1000C2×C4—121no—
1001C2×C4—121no—
1002C2×C4—121no—
1003C2×C4—121no—
1004C2×C4—121no—
1005C2×C4—121no—
1006C2×C4—121no—
1007C2×C4—121no—
1008C2×C4—121no—
1009C2×C4—121no—
1010C2×C4—121no—
1011C2×C4—121no—
1012C2×C3—44no—
1013C2×C3#231211yescharacteristic
1014C2×C3#233311yescharacteristic
1015C2×C3#233311yescharacteristic
1016C2×C3#235311yescharacteristic
1017C2×C3#235311yescharacteristic
1018C2×C3#237411yescharacteristic
1019C2×C3#237511yescharacteristic
1020C2×C3#274911yescharacteristic
1021C2×C3#274911yescharacteristic
1022C2×C3#275311yescharacteristic
1023C2×C3#275311yescharacteristic
1024C2×C3#277811yescharacteristic
1025C2×C3#277811yescharacteristic
1026C2×C3#279711yescharacteristic
1027C2×C3#279711yescharacteristic
1028D3—82no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—122no—
1045C22—122no—
1046C22—122no—
1047C22—122no—
1048C22—122no—
1049C22—122no—
1050C22—122no—
1051C22—241no—
1052C22—241no—
1053C22—241no—
1054C22—241no—
1055C22—241no—
1056C22—241no—
1057C22—241no—
1058C22—241no—
1059C22C4×#23511yescharacteristic
1060C22#548611yescharacteristic
1061C22#548611yescharacteristic
1062C22#548611yescharacteristic
1063C22#549511yescharacteristic
1064C22#549511yescharacteristic
1065C22C2×#89211yescharacteristic
1066C22#551411yescharacteristic
1067C22#551411yescharacteristic
1068C22#552111yescharacteristic
1069C22#552211yescharacteristic
1070C22#554011yescharacteristic
1071C22#555611yescharacteristic
1072C22#555811yescharacteristic
1073C22#555911yescharacteristic
1074C22#556011yescharacteristic
1075C22#556011yescharacteristic
1076C22#556211yescharacteristic
1077C22#556211yescharacteristic
1078C22#559411yescharacteristic
1079C22#559511yescharacteristic
1080C22#559511yescharacteristic
1081C22#559511yescharacteristic
1082C22#560111yescharacteristic
1083C22#560111yescharacteristic
1084C22#561711yescharacteristic
1085C22#561711yescharacteristic
1086C22#563711yescharacteristic
1087C22#563711yescharacteristic
1088C22#564411yescharacteristic
1089C22#564411yescharacteristic
1090C22#565711yescharacteristic
1091C22#565711yescharacteristic
1092C22#566311yescharacteristic
1093C22#566311yescharacteristic
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—81no—
1099C4—81no—
1100C4—122no—
1101C4—122no—
1102C4—122no—
1103C4—122no—
1104C4—122no—
1105C4—241no—
1106C4—241no—
1107C3#1451611yescharacteristic, complemented, Sylow
1108C2—44no—
1109C2—242no—
1110C2#7333611yescharacteristic
1111C2#7344911yescharacteristic
1112C2#7347811yescharacteristic
1113C2#7385111yescharacteristic
1114C2#7388411yescharacteristic
1115C2#7400411yescharacteristic
1116C2#7405811yescharacteristic
1117C2#7454911yescharacteristic
1118C2#7458011yescharacteristic
1119C2#7464611yescharacteristic
1120C2#7464911yescharacteristic
1121C2#7484111yescharacteristic
1122C2#7484611yescharacteristic
1123C2#7485411yescharacteristic
1124C2#7486411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×C22⋊#95C2
socle, cosocleC24×C3C24
prime radicalC23×#67C22
hypercenterC22⋊#95D3
hypocenterC3#14516
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C3×C22⋊#95C2semidirect
3. #72127C2semidirect
6. #71545C2semidirect
7. #71545C2semidirect
8. #69429C2semidirect
9. #69429C2semidirect
10. #69418C2semidirect
11. #69417C2semidirect
12. #69408C2semidirect
13. #69408C2semidirect
14. #69403C2semidirect
15. #69402C2semidirect
36. #5213C4semidirect
67. C22⋊#95D3semidirect
1107. C3#14516semidirect

Maximal subgroups

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

subgroupindex
C2×#52132
C3×C22⋊#952
#721272
#715502
#715452
#694292
#694182
#694172
#694082
#694032
#694022
#145163