Finite Group Databasebeta

← #10702104

Subgroups — #10702104

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊C8C211yesmaximal, characteristic
2C2×C4×#217C211yesmaximal, characteristic
3C22×#830C211yesmaximal, characteristic
4C22×Dic3⋊C8C211yesmaximal, characteristic, complemented
5C2×#4550C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7C2×#4550C211yesmaximal, characteristic, complemented
8#11042—31nomaximal, Sylow
9C24×C3×C4C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×#217C411yescharacteristic
13C22×#217C411yescharacteristic
14C22×C4×Dic3C2211yescharacteristic
15C22×C4×Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C2×C3×C22⋊C8—22no—
19C2×C3×C22⋊C8—22no—
20C2×C3×C22⋊C8—22no—
21C4×#217—22no—
22C4×#217—22no—
23C2×C3⋊#95C411yescharacteristic
24C2×C3⋊#95C411yescharacteristic
25C2×#830—22no—
26C2×#830—22no—
27C2×#830—22no—
28C2×Dic3⋊C8—22no—
29C2×Dic3⋊C8—22no—
30C2×Dic3⋊C8—22no—
31#4550—22no—
32#4550—22no—
33#4550—22no—
34C22×C4⋊C8—31no—
35C22×C22⋊C8—31no—
36C22×C22⋊C8D311yescharacteristic
37C2×C4×C22⋊C4—31no—
38C2×#336—31no—
39C2×#336—31no—
40C2×#336—31no—
41C25×C3C2×C411yescharacteristic
42C23×C3×C4—21no—
43C23×C3×C4—21no—
44C23×C3×C4—21no—
45C23×C3×C4—21no—
46C23×C3×C4—21no—
47C23×C3×C4—21no—
48C23×C3×C4—21no—
49C23×C3×C4—21no—
50C23×C3×C4—21no—
51C23×C3×C4—21no—
52C23×C3×C4—21no—
53C23×C3×C4—21no—
54C23×C3×C4C2×C411yescharacteristic
55C23×C3×C4D412yes—
56C23×C3×C4Q812yes—
57C23×C3×C4C2311yescharacteristic
58C23×Dic3C2×C411yescharacteristic
59C23×Dic3C2×C411yescharacteristic
60C23×Dic3C2×C411yescharacteristic
61C23×Dic3C2×C411yescharacteristic
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—21no—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8—21no—
74C22×C3×C8D412yes—
75C22×C3×C8D412yes—
76C2×#217—22no—
77C2×#217—22no—
78C2×#217—22no—
79C2×#217—22no—
80C2×#217—22no—
81C2×#217C814yescomplemented
82C2×C4×Dic3—21no—
83C2×C4×Dic3—21no—
84C2×C4×Dic3—21no—
85C2×C4×Dic3—21no—
86C2×C4×Dic3—21no—
87C2×C4×Dic3—21no—
88C2×C4×Dic3—21no—
89C2×C4×Dic3—21no—
90C2×C4×Dic3—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3D412yes—
93C2×C4×Dic3D412yes—
94C22×C3⋊C8—21no—
95C22×C3⋊C8—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8—21no—
101C22×C3⋊C8—21no—
102C22×C3⋊C8—21no—
103C22×C3⋊C8—21no—
104C22×C3⋊C8—21no—
105C22×C3⋊C8—21no—
106C22×C3⋊C8D412yes—
107C22×C3⋊C8D412yes—
108C3×C22⋊C8—28no—
109C3⋊#95—22no—
110C3⋊#95—22no—
111#830—28no—
112Dic3⋊C8—28no—
113C24×C4C2×D311yescharacteristic
114C23×C8—31no—
115C23×C8—31no—
116C23×C8C2×D311yescharacteristic
117C23×C8C2×D311yescharacteristic
118C22×C22⋊C4—31no—
119C22×C22⋊C4—31no—
120C22×C42—31no—
121C22×C42—31no—
122C2×C4⋊C8—62no—
123C2×C4⋊C8—62no—
124C2×C4⋊C8—62no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—62no—
129C2×C22⋊C8—62no—
130C2×C22⋊C8—62no—
131C4×C22⋊C4—62no—
132C4×C22⋊C4—62no—
133C2×#95—31no—
134C2×#95—31no—
135#336—62no—
136#336—62no—
137#336—62no—
138C24×C3—21no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3—21no—
142C24×C3—21no—
143C24×C3—21no—
144C24×C3—21no—
145C24×C3—21no—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—21no—
150C24×C3C4⋊C412yes—
151C24×C3C2×C812yes—
152C24×C3M1612yes—
153C24×C3C22×C411yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4—41no—
175C22×C3×C4—41no—
176C22×C3×C4—41no—
177C22×C3×C4—41no—
178C22×C3×C4—41no—
179C22×C3×C4—41no—
180C22×C3×C4—41no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—41no—
184C22×C3×C4—41no—
185C22×C3×C4—41no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4C4⋊C412yes—
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2×D411yescharacteristic
194C22×C3×C4C2×D411yescharacteristic
195C22×C3×C4C2×D411yescharacteristic
196C22×C3×C4C2×Q811yescharacteristic
197C22×C3×C4#4111yescharacteristic
198C22×C3×C4#4111yescharacteristic
199C22×C3×C4#4111yescharacteristic
200C22×C3×C4#4111yescharacteristic
201C22×C3×C4#4111yescharacteristic
202C22×C3×C4#4111yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3C22⋊C412yes—
226C22×Dic3C22⋊C412yes—
227C22×Dic3C2×C812yes—
228C22×Dic3C2×C812yes—
229C22×Dic3M1612yes—
230C22×Dic3M1612yes—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—22no—
236C2×C3×C8—22no—
237C2×C3×C8—41no—
238C2×C3×C8—41no—
239C2×C3×C8—41no—
240C2×C3×C8—41no—
241C2×C3×C8—41no—
242C2×C3×C8—41no—
243C2×C3×C8—41no—
244C2×C3×C8—41no—
245#217—28no—
246#217—28no—
247C4×Dic3—22no—
248C4×Dic3—22no—
249C4×Dic3—22no—
250C4×Dic3—22no—
251C4×Dic3—41no—
252C4×Dic3—41no—
253C4×Dic3—41no—
254C4×Dic3—41no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8—22no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8—41no—
262C2×C3⋊C8—41no—
263C2×C3⋊C8—41no—
264C2×C3⋊C8—41no—
265C2×C3⋊C8—41no—
266C2×C3⋊C8—41no—
267C2×C3⋊C8—41no—
268C2×C3⋊C8—41no—
269C25C4×D311yescharacteristic
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—31no—
283C23×C4—31no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4Dic612yes—
287C23×C4C4×D311yescharacteristic
288C23×C4#6712yes—
289C23×C4C22×D311yescharacteristic
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—32no—
303C22×C8—32no—
304C22×C8—61no—
305C22×C8—61no—
306C22×C8—61no—
307C22×C8—61no—
308C22×C8—61no—
309C22×C8—61no—
310C22×C8—61no—
311C22×C8—61no—
312C22×C8—61no—
313C22×C8—61no—
314C22×C8—61no—
315C22×C8—61no—
316C22×C8#6712yes—
317C22×C8#6712yes—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—62no—
324C2×C42—32no—
325C2×C42—32no—
326C2×C42—61no—
327C2×C42—61no—
328C2×C42—61no—
329C2×C42—61no—
330C2×C42—61no—
331C2×C42—61no—
332C2×C42—61no—
333C2×C42—61no—
334C2×C42—61no—
335C2×C42—61no—
336C4⋊C8—68no—
337C22⋊C8—28no—
338C22⋊C8—68no—
339#95—62no—
340#95—62no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3C4⋊C814yescomplemented
376C23×C3C2×C22⋊C411yescharacteristic
377C23×C3C2×C4⋊C411yescharacteristic
378C23×C3#11711yescharacteristic
379C23×C3C4×D411yescharacteristic
380C23×C3C4×D411yescharacteristic
381C23×C3C4×D411yescharacteristic
382C23×C3C4×D411yescharacteristic
383C23×C3C22×C811yescharacteristic
384C23×C3C2×M1611yescharacteristic
385C23×C3C2×M1611yescharacteristic
386C23×C3C2×M1611yescharacteristic
387C23×C3#13111yescharacteristic
388C23×C3#13111yescharacteristic
389C23×C3#13111yescharacteristic
390C23×C3#13111yescharacteristic
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4#12011yescharacteristic
407C2×C3×C4#12011yescharacteristic
408C2×C3×C4#12011yescharacteristic
409C2×C3×C4#12111yescharacteristic
410C2×C3×C4#12111yescharacteristic
411C2×C3×C4#12111yescharacteristic
412C2×C3×C4#12111yescharacteristic
413C2×C3×C4#12111yescharacteristic
414C2×C3×C4#12111yescharacteristic
415C2×C3×C4#12111yescharacteristic
416C2×C3×C4#12111yescharacteristic
417C2×C3×C4C22⋊Q811yescharacteristic
418C2×C3×C4C22⋊Q811yescharacteristic
419C2×C3×C4C22⋊Q811yescharacteristic
420C2×C3×C4C22⋊Q811yescharacteristic
421C2×C3×C4C22⋊Q811yescharacteristic
422C2×C3×C4C22⋊Q811yescharacteristic
423C2×C3×C4#12311yescharacteristic
424C2×C3×C4#12311yescharacteristic
425C2×C3×C4#12311yescharacteristic
426C2×C3×C4#12311yescharacteristic
427C2×C3×C4#12311yescharacteristic
428C2×C3×C4#12411yescharacteristic
429C2×C3×C4#12411yescharacteristic
430C2×C3×C4#12411yescharacteristic
431C2×C3×C4#12611yescharacteristic
432C2×C3×C4#12611yescharacteristic
433C2×C3×C4#12711yescharacteristic
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3C22⋊C814yescomplemented
462C3×C8—42no—
463C3×C8—42no—
464C3⋊C8—42no—
465C3⋊C8—42no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24D3×C812yes—
479C24ΓL(1,𝔽25)12yes—
480C24Dic3⋊C412yes—
481C24C2×C4×D311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—32no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—32no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4Dic3⋊C412yes—
545C22×C4C2×Dic611yescharacteristic
546C22×C4#23511yescharacteristic
547C22×C4#23511yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4D3×D411yescharacteristic
550C22×C4D3×D411yescharacteristic
551C22×C4D3×D411yescharacteristic
552C22×C4#23711yescharacteristic
553C22×C4#23711yescharacteristic
554C22×C4#23711yescharacteristic
555C22×C4#23711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—62no—
574C2×C8—62no—
575C2×C8—62no—
576C2×C8—62no—
577C2×C8—62no—
578C2×C8—62no—
579C2×C8—121no—
580C2×C8—121no—
581C2×C8—121no—
582C2×C8—121no—
583C2×C8—121no—
584C2×C8—121no—
585C2×C8—121no—
586C2×C8—121no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C42—62no—
590C42—62no—
591C42—62no—
592C42—62no—
593C42—121no—
594C42—121no—
595C42—121no—
596C42—121no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3#38011yescharacteristic
613C22×C3#38511yescharacteristic
614C22×C3#38511yescharacteristic
615C22×C3#38611yescharacteristic
616C22×C3#38811yescharacteristic
617C22×C3#38811yescharacteristic
618C22×C3#39011yescharacteristic
619C22×C3C2×C22⋊C811yescharacteristic
620C22×C3#40711yescharacteristic
621C22×C3#40811yescharacteristic
622C22×C3#40811yescharacteristic
623C22×C3C2×C4⋊C811yescharacteristic
624C22×C3#42311yescharacteristic
625C22×C3#42411yescharacteristic
626C22×C3#42411yescharacteristic
627C22×C3#43111yescharacteristic
628C22×C3#43211yescharacteristic
629C22×C3#43311yescharacteristic
630C22×C3#43311yescharacteristic
631C22×C3C8×D411yescharacteristic
632C22×C3C8×D411yescharacteristic
633C22×C3C8×D411yescharacteristic
634C22×C3C8×D411yescharacteristic
635C22×C3#43511yescharacteristic
636C22×C3#43511yescharacteristic
637C22×C3#43511yescharacteristic
638C22×C3#43511yescharacteristic
639C22×C3#43511yescharacteristic
640C22×C3#43511yescharacteristic
641C22×C3#43511yescharacteristic
642C22×C3#43511yescharacteristic
643C22×C3#43611yescharacteristic
644C22×C3#43611yescharacteristic
645C22×C3#43611yescharacteristic
646C22×C3#43611yescharacteristic
647C3×C4—42no—
648C3×C4#39211yescharacteristic
649C3×C4#39311yescharacteristic
650C3×C4#39411yescharacteristic
651C3×C4#39411yescharacteristic
652C3×C4#39611yescharacteristic
653C3×C4#39611yescharacteristic
654C3×C4#39711yescharacteristic
655C3×C4#39911yescharacteristic
656Dic3—24no—
657Dic3—42no—
658Dic3—42no—
659Dic3—42no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23Dic3⋊C814yescomplemented
695C23#87711yescharacteristic
696C23D3×C22⋊C411yescharacteristic
697C23#67⋊C411yescharacteristic
698C23#67⋊C411yescharacteristic
699C23C2×D3×C811yescharacteristic
700C23C2×ΓL(1,𝔽25)11yescharacteristic
701C23#90111yescharacteristic
702C23#90111yescharacteristic
703C23D3×M1611yescharacteristic
704C23D3×M1611yescharacteristic
705C23#90711yescharacteristic
706C23#90711yescharacteristic
707C23C2×Dic3⋊C411yescharacteristic
708C23C4×#6711yescharacteristic
709C23C4×#6711yescharacteristic
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—34no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4#87811yescharacteristic
754C2×C4#87811yescharacteristic
755C2×C4#87811yescharacteristic
756C2×C4#87811yescharacteristic
757C2×C4#87911yescharacteristic
758C2×C4#87911yescharacteristic
759C2×C4#88311yescharacteristic
760C2×C4#88311yescharacteristic
761C2×C4#88411yescharacteristic
762C2×C4#88411yescharacteristic
763C2×C4#88511yescharacteristic
764C2×C4#88511yescharacteristic
765C2×C4#92411yescharacteristic
766C2×C4#92411yescharacteristic
767C2×C4#92911yescharacteristic
768C2×C4#93511yescharacteristic
769C2×C4#93511yescharacteristic
770C2×C4#93611yescharacteristic
771C2×C4#93711yescharacteristic
772C2×C4#93711yescharacteristic
773C2×C4#93811yescharacteristic
774C2×C4#93811yescharacteristic
775C2×C4#93911yescharacteristic
776C2×C4#93911yescharacteristic
777C2×C4#93911yescharacteristic
778C2×C4#93911yescharacteristic
779C2×C4#94011yescharacteristic
780C2×C4#95311yescharacteristic
781C8—42no—
782C8—42no—
783C8—122no—
784C8—122no—
785C2×C3—44no—
786C2×C3#143911yescharacteristic
787C2×C3#179711yescharacteristic
788C2×C3#179811yescharacteristic
789C2×C3#185011yescharacteristic
790C2×C3#185011yescharacteristic
791C2×C3#185111yescharacteristic
792C2×C3#185111yescharacteristic
793C2×C3#186911yescharacteristic
794C2×C3#187011yescharacteristic
795C2×C3#192311yescharacteristic
796C2×C3#192311yescharacteristic
797C2×C3#192411yescharacteristic
798C2×C3#192411yescharacteristic
799C2×C3#195411yescharacteristic
800C2×C3#195511yescharacteristic
801C22—24no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22#471811yescharacteristic
817C22#471911yescharacteristic
818C22#472011yescharacteristic
819C22#472011yescharacteristic
820C22D3×C22⋊C811yescharacteristic
821C22#67⋊C811yescharacteristic
822C22#67⋊C811yescharacteristic
823C22#472611yescharacteristic
824C22#472711yescharacteristic
825C22#472711yescharacteristic
826C22#472811yescharacteristic
827C22#472811yescharacteristic
828C22#472911yescharacteristic
829C22#472911yescharacteristic
830C22#473011yescharacteristic
831C22#473011yescharacteristic
832C22#494211yescharacteristic
833C22#494411yescharacteristic
834C22#494511yescharacteristic
835C22#494611yescharacteristic
836C22#495611yescharacteristic
837C22#495711yescharacteristic
838C22C2×Dic3⋊C811yescharacteristic
839C22#510211yescharacteristic
840C22C8×#6711yescharacteristic
841C22C8×#6711yescharacteristic
842C22#511111yescharacteristic
843C22#511111yescharacteristic
844C22#511811yescharacteristic
845C22#511911yescharacteristic
846C22#512711yescharacteristic
847C22#512711yescharacteristic
848C22#512811yescharacteristic
849C22#512811yescharacteristic
850C22#521011yescharacteristic
851C4—42no—
852C4—64no—
853C4—122no—
854C4—122no—
855C4—122no—
856C4#494711yescharacteristic
857C4#494811yescharacteristic
858C4#494811yescharacteristic
859C4#494911yescharacteristic
860C4#495211yescharacteristic
861C4#495911yescharacteristic
862C4#522211yescharacteristic
863C4#522311yescharacteristic
864C3#1104211yescharacteristic, complemented, Sylow
865C2—44no—
866C2#6990811yescharacteristic
867C2#6990911yescharacteristic
868C2#6991211yescharacteristic
869C2#6991311yescharacteristic
870C2#6991411yescharacteristic
871C2#6991511yescharacteristic
872C2#6991611yescharacteristic
873C2#6991711yescharacteristic
874C2#6995011yescharacteristic
875C2#6995111yescharacteristic
876C2#6995711yescharacteristic
877C2#6995811yescharacteristic
878C2#7154711yescharacteristic
879C2#7197411yescharacteristic
880C2#7199511yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D3
commutatorC23×C3C22×C8
FittingC22×C3×C22⋊C8C2
socleC24×C3C22×C4
prime radicalC25×C3C2×C4
cosocleC23×C3×C4C23
hypercenterC22×C22⋊C8D3
hypocenterC3#11042
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊C8C2semidirect
5. C2×#4550C2semidirect
6. C2×#4550C2semidirect
7. C2×#4550C2semidirect
81. C2×#217C8semidirect
375. C23×C3C4⋊C8semidirect
461. C2×Dic3C22⋊C8semidirect
694. C23Dic3⋊C8semidirect
864. C3#11042semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊C82
C2×C4×#2172
C22×#8302
C22×Dic3⋊C82
C2×#45502
#110423