Finite Group Databasebeta

← #10728007

Subgroups — #10728007

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3⋊#95C211yesmaximal, characteristic
2C2×C3⋊#401C211yesmaximal, characteristic, complemented
3C3×C22⋊#95C211yesmaximal, characteristic
4#72127C211yesmaximal, characteristic
5#71544C211yesmaximal, characteristic
6#71544C211yesmaximal, characteristic
7#71544C211yesmaximal, characteristic
8#71544C211yesmaximal, characteristic
9#69418C211yesmaximal, characteristic, complemented
10#69418C211yesmaximal, characteristic, complemented
11#69418C211yesmaximal, characteristic, complemented
12#69417C211yesmaximal, characteristic, complemented
13#69417C211yesmaximal, characteristic, complemented
14#69417C211yesmaximal, characteristic, complemented
15#69416C211yesmaximal, characteristic, complemented
16C22⋊#401—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C24×Dic3C2211yescharacteristic
19C24×Dic3C2211yescharacteristic
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C2×C3×#95C2211yescharacteristic
25C2×C3×#95C2211yescharacteristic
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3⋊#95—24no—
29C2×C3⋊#95C2211yescharacteristic
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2211yescharacteristic
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
53C3⋊#401—24no—
54C2×#401—31no—
55C22×#95—31no—
56#1443—31no—
57#1443—31no—
58#1443—31no—
59#1443—31no—
60#1443—31no—
61#1443—31no—
62#1443—31no—
63C22⋊#95—31no—
64C22⋊#95—31no—
65C22⋊#95—31no—
66C22⋊#95—31no—
67C22⋊#95—31no—
68C22⋊#95D311yescharacteristic
69C25×C3C2311yescharacteristic
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4—22no—
75C23×C3×C4—41no—
76C23×C3×C4—41no—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—22no—
84C23×Dic3—22no—
85C23×Dic3—22no—
86C23×Dic3—22no—
87C23×Dic3—22no—
88C23×Dic3—22no—
89C23×Dic3—22no—
90C23×Dic3—22no—
91C23×Dic3—22no—
92C23×Dic3—22no—
93C23×Dic3—41no—
94C23×Dic3—41no—
95C23×Dic3—41no—
96C23×Dic3—41no—
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×#217—22no—
112C2×#217—22no—
113C2×#217—22no—
114C2×#217—22no—
115C2×#217—22no—
116C2×#217—22no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—41no—
120C3×#95—41no—
121C3⋊#95—22no—
122C3⋊#95—22no—
123C3⋊#95—22no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95—22no—
129C3⋊#95—22no—
130C3⋊#95—22no—
131C3⋊#95—22no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—41no—
135C3⋊#95—41no—
136C3⋊#95—41no—
137C3⋊#95—41no—
138C3⋊#95—41no—
139C3⋊#95—41no—
140C3⋊#95—41no—
141C3⋊#95—41no—
142C3⋊#95—41no—
143C3⋊#95—41no—
144C3⋊#95D414yes—
145C24×C4—31no—
146C24×C4—31no—
147C24×C4C2×D311yescharacteristic
148C22×C22⋊C4—31no—
149C22×C22⋊C4—31no—
150C22×C22⋊C4C2×D311yescharacteristic
151C22×C22⋊C4C2×D311yescharacteristic
152#401—64no—
153C2×#95—31no—
154C2×#95—31no—
155C2×#95—31no—
156C2×#95—31no—
157C2×#95—31no—
158C2×#95—31no—
159C2×#95—31no—
160C2×#95—31no—
161C2×#95—31no—
162C2×#95—31no—
163C2×#95—31no—
164C2×#95—31no—
165C2×#95—31no—
166C2×#95—31no—
167C2×#95—31no—
168C2×#95—31no—
169C2×#95—31no—
170C2×#95—31no—
171C2×#95—31no—
172C2×#95—31no—
173C2×#95—31no—
174C2×#95—31no—
175C2×#95—31no—
176C2×#95—31no—
177C2×#95—64no—
178C2×#95C2×D311yescharacteristic
179C2×#95C2×D311yescharacteristic
180C2×#95C2×D311yescharacteristic
181C2×#95C2×D311yescharacteristic
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—21no—
187C24×C3—21no—
188C24×C3—21no—
189C24×C3—21no—
190C24×C3#4112yes—
191C24×C3#4112yes—
192C24×C3#4112yes—
193C24×C3#4112yes—
194C24×C3#4112yes—
195C24×C3#4112yes—
196C24×C3#4112yes—
197C24×C3C2411yescharacteristic
198C22×C3×C4—28no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
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—44no—
240C22×C3×C4—44no—
241C22×C3×C4—44no—
242C22×C3×C4—44no—
243C22×C3×C4—44no—
244C22×C3×C4—44no—
245C22×C3×C4C2×D412yes—
246C22×C3×C4#4112yes—
247C22×Dic3—28no—
248C22×Dic3—28no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
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—44no—
302C22×Dic3—44no—
303C22×Dic3—44no—
304C22×Dic3—44no—
305C22×Dic3—44no—
306C22×Dic3—44no—
307C22×Dic3—44no—
308C22×Dic3—44no—
309C22×Dic3—44no—
310C22×Dic3—44no—
311C22×Dic3—44no—
312C22×Dic3—44no—
313C22×Dic3C2×D412yes—
314C22×Dic3C2×D412yes—
315C22×Dic3#4112yes—
316C22×Dic3#4112yes—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319#217—44no—
320#217—44no—
321C25C22×D311yescharacteristic
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—41no—
336C23×C4—41no—
337C23×C4—62no—
338C23×C4—62no—
339C23×C4—62no—
340C23×C4—62no—
341C23×C4—62no—
342C23×C4—62no—
343C23×C4—62no—
344C23×C4—62no—
345C23×C4—62no—
346C23×C4—62no—
347C23×C4—121no—
348C23×C4—121no—
349C23×C4—121no—
350C23×C4—121no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C23×C4C22×D311yescharacteristic
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—62no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—62no—
369#95—22no—
370#95—22no—
371#95—34no—
372#95—41no—
373#95—41no—
374#95—62no—
375#95—62no—
376#95—62no—
377#95—62no—
378#95—62no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383#95—62no—
384#95—62no—
385#95—62no—
386#95—62no—
387#95—121no—
388#95—121no—
389#95—121no—
390#95—121no—
391#95—121no—
392#95—121no—
393#95—121no—
394#95—121no—
395#95—121no—
396#95—121no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3#12614yes—
426C23×C3#12614yes—
427C23×C3#12614yes—
428C23×C3#12614yes—
429C23×C3#12614yes—
430C23×C3#12614yes—
431C23×C3#12614yes—
432C23×C3C22×D411yescharacteristic
433C23×C3C2×#4111yescharacteristic
434C23×C3C2×#4111yescharacteristic
435C23×C3C2×#4111yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3C2×#4111yescharacteristic
439C23×C3C2×#4111yescharacteristic
440C23×C3C2×#4111yescharacteristic
441C23×C3C2×#4111yescharacteristic
442C23×C3C2×#4111yescharacteristic
443C23×C3H(5,𝔽2)11yescharacteristic
444C23×C3H(5,𝔽2)11yescharacteristic
445C23×C3H(5,𝔽2)11yescharacteristic
446C23×C32−1+411yescharacteristic
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—416no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—416no—
503C2×Dic3—416no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24#23512yes—
557C24#23512yes—
558C24#23512yes—
559C24#23712yes—
560C24#23712yes—
561C24#23712yes—
562C24#23912yes—
563C24C23×D311yescharacteristic
564C22×C4—28no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—68no—
616C22×C4—68no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—124no—
670C22×C4—124no—
671C22×C4—124no—
672C22×C4—124no—
673C22×C4—124no—
674C22×C4—124no—
675C22×C4—124no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4—124no—
680C22×C4—124no—
681C22×C4D3×D412yes—
682C22×C4#23712yes—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—124no—
686C22⋊C4—124no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—24no—
691C22×C3—24no—
692C22×C3—24no—
693C22×C3—24no—
694C22×C3—24no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—24no—
701C22×C3#40118yescomplemented
702C22×C3#52511yescharacteristic
703C22×C3#52511yescharacteristic
704C22×C3#52511yescharacteristic
705C22×C3C2×#12611yescharacteristic
706C22×C3C2×#12611yescharacteristic
707C22×C3C2×#12611yescharacteristic
708C22×C3C2×#12611yescharacteristic
709C22×C3C2×#12611yescharacteristic
710C22×C3C2×#12611yescharacteristic
711C22×C3C2×#12611yescharacteristic
712C22×C3#52911yescharacteristic
713C22×C3#52911yescharacteristic
714C22×C3#52911yescharacteristic
715C22×C3#53811yescharacteristic
716C22×C3#53811yescharacteristic
717C22×C3#53811yescharacteristic
718C22×C3#53911yescharacteristic
719C22×C3#53911yescharacteristic
720C22×C3#53911yescharacteristic
721C22×C3#54611yescharacteristic
722C22×C3#54611yescharacteristic
723C22×C3#54611yescharacteristic
724C22×C3#54811yescharacteristic
725C22×C3#55111yescharacteristic
726C22×C3#55111yescharacteristic
727C22×C3#55111yescharacteristic
728C22×C3#55111yescharacteristic
729C22×C3#55111yescharacteristic
730C22×C3#55111yescharacteristic
731C22×C3#55211yescharacteristic
732C22×C3#55211yescharacteristic
733C22×C3#55211yescharacteristic
734C22×C3#55311yescharacteristic
735C22×C3#55311yescharacteristic
736C22×C3#55311yescharacteristic
737C3×C4—42no—
738C3×C4—42no—
739C3×C4—81no—
740C3×C4—81no—
741C3×C4—81no—
742C3×C4—81no—
743Dic3—42no—
744Dic3—42no—
745Dic3—42no—
746Dic3—42no—
747Dic3—81no—
748Dic3—81no—
749Dic3—81no—
750Dic3—81no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23#87614yes—
780C23#87914yes—
781C23#87914yes—
782C23#87914yes—
783C23#89814yes—
784C23#89814yes—
785C23#89814yes—
786C23C2×#23511yescharacteristic
787C23C2×#23511yescharacteristic
788C23C2×#23511yescharacteristic
789C23C2×D3×D411yescharacteristic
790C23C2×#23711yescharacteristic
791C23C2×#23711yescharacteristic
792C23C2×#23711yescharacteristic
793C23C2×#23711yescharacteristic
794C23#100411yescharacteristic
795C23#100411yescharacteristic
796C23C2×#23911yescharacteristic
797C23D3×#4111yescharacteristic
798C23D3×#4111yescharacteristic
799C23#100911yescharacteristic
800C23#101011yescharacteristic
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—416no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—62no—
851C2×C4—62no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—1216no—
857C2×C4—1216no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—121no—
888C2×C4—121no—
889C2×C4—121no—
890C2×C4—121no—
891C2×C4—121no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C3—28no—
903C2×C3C2×#40111yescharacteristic
904C2×C3#248011yescharacteristic
905C2×C3#248011yescharacteristic
906C2×C3#248011yescharacteristic
907C2×C3#248111yescharacteristic
908C2×C3#248111yescharacteristic
909C2×C3#248111yescharacteristic
910C2×C3#249311yescharacteristic
911C2×C3#249311yescharacteristic
912C2×C3#249311yescharacteristic
913C2×C3#251011yescharacteristic
914C2×C3#251011yescharacteristic
915C2×C3#251011yescharacteristic
916C2×C3#264311yescharacteristic
917C2×C3#285211yescharacteristic
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22C3⋊#40118yescomplemented
933C22C2×#87611yescharacteristic
934C22C2×#87911yescharacteristic
935C22C2×#87911yescharacteristic
936C22C2×#87911yescharacteristic
937C22#549011yescharacteristic
938C22#549511yescharacteristic
939C22C2×#89811yescharacteristic
940C22C2×#89811yescharacteristic
941C22C2×#89811yescharacteristic
942C22#552711yescharacteristic
943C22#553111yescharacteristic
944C22#553811yescharacteristic
945C22#554011yescharacteristic
946C22#554011yescharacteristic
947C22#554711yescharacteristic
948C22#555211yescharacteristic
949C22#556011yescharacteristic
950C22#556411yescharacteristic
951C22#556511yescharacteristic
952C22#558611yescharacteristic
953C22#558711yescharacteristic
954C22#559111yescharacteristic
955C22#559311yescharacteristic
956C22#560011yescharacteristic
957C22#560211yescharacteristic
958C22#560611yescharacteristic
959C22#561711yescharacteristic
960C22#563011yescharacteristic
961C22#563711yescharacteristic
962C22#563711yescharacteristic
963C22#564211yescharacteristic
964C22#564911yescharacteristic
965C22#565011yescharacteristic
966C22#565811yescharacteristic
967C22#566511yescharacteristic
968C4—42no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4—81no—
974C4—122no—
975C4—122no—
976C4—122no—
977C4—122no—
978C4—241no—
979C4—241no—
980C4—241no—
981C4—241no—
982C3C22⋊#40111yescharacteristic, complemented, Sylow
983C2—28no—
984C2C2×C3⋊#40111yescharacteristic
985C2#7350311yescharacteristic
986C2#7352111yescharacteristic
987C2#7383111yescharacteristic
988C2#7390911yescharacteristic
989C2#7391711yescharacteristic
990C2#7407711yescharacteristic
991C2#7445211yescharacteristic
992C2#7445411yescharacteristic
993C2#7445811yescharacteristic
994C2#7446511yescharacteristic
995C2#7473611yescharacteristic
996C2#7474311yescharacteristic
997C2#7478611yescharacteristic
998C2#7487011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×C22⋊#95C2
prime radicalC25×C3C23
hypercenterC22⋊#95D3
hypocenterC3C22⋊#401
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊#401C2semidirect
9. #69418C2semidirect
10. #69418C2semidirect
11. #69418C2semidirect
12. #69417C2semidirect
13. #69417C2semidirect
14. #69417C2semidirect
15. #69416C2semidirect
701. C22×C3#401semidirect
932. C22C3⋊#401semidirect
982. C3C22⋊#401semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊#952
C2×C3⋊#4012
C3×C22⋊#952
#721272
#715442
#694182
#694172
#694162
C22⋊#4013