Finite Group Databasebeta

← #10812221

Subgroups — #10812221

Order 768.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#408C211yesmaximal, characteristic
2#84086C211yesmaximal, characteristic
3C2×#4720C211yesmaximal, characteristic, complemented
4#72136C211yesmaximal, characteristic
5#71995C211yesmaximal, characteristic, complemented
6#71983C211yesmaximal, characteristic, complemented
7#71974C211yesmaximal, characteristic, complemented
8#71967C211yesmaximal, characteristic, complemented
9#69915C211yesmaximal, characteristic, complemented
10#69915C211yesmaximal, characteristic, complemented
11#69914C211yesmaximal, characteristic, complemented
12#69912C211yesmaximal, characteristic, complemented
13#69911C211yesmaximal, characteristic, complemented
14#69908C211yesmaximal, characteristic, complemented
15#69906C211yesmaximal, characteristic, complemented
16#22561—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C23×C3×C8C2211yescharacteristic
20C2×#926C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C3×#408—24no—
23C2×C3×C22⋊C8C2211yescharacteristic
24C2×C3×C22⋊C8C2211yescharacteristic
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27#5229C411yescharacteristic
28#5229C411yescharacteristic
29#5221C411yescharacteristic
30#5221C411yescharacteristic
31#5220C411yescharacteristic
32#5220C411yescharacteristic
33#5220C411yescharacteristic
34#5220C411yescharacteristic
35C4×#217C2211yescharacteristic
36C4×#217C2211yescharacteristic
37C4×#217C2211yescharacteristic
38C4×#217C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#815C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic
51C2×Dic3⋊C8C2211yescharacteristic
52C2×C8×Dic3C2211yescharacteristic
53#4720—24no—
54#4550C2211yescharacteristic
55#4550C2211yescharacteristic
56#4550C2211yescharacteristic
57#4550C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62C2×#433—31no—
63C2×#408D311yescharacteristic
64#2297—31no—
65#1924—31no—
66#1924—31no—
67#1924—31no—
68#1923—31no—
69#1851—31no—
70#1850—31no—
71#1818—31no—
72#1797—31no—
73#1780—31no—
74#1753—31no—
75#1752—31no—
76#1749—31no—
77C2×C3×#41—22no—
78C2×C3×#41—22no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C22×C3×Q8C2×C411yescharacteristic
84C22×C3×D4C2×C411yescharacteristic
85C22×C3×D4C2×C411yescharacteristic
86C22×C3×D4C2×C411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×Dic3C2×C411yescharacteristic
91C23×Dic3C2×C411yescharacteristic
92C2×C3×M16—22no—
93C2×C3×M16—22no—
94C2×C3×M16—41no—
95C22×C3×C8—22no—
96C22×C3×C8—22no—
97C22×C3×C8—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×#217C2×C411yescharacteristic
105C2×#217C2×C411yescharacteristic
106C2×#217C2×C411yescharacteristic
107C2×#217C2×C411yescharacteristic
108C2×#217C2×C411yescharacteristic
109C2×#217C2×C411yescharacteristic
110C2×#217C2×C411yescharacteristic
111C2×#217C2×C411yescharacteristic
112#926—22no—
113#926—22no—
114C2×C4⋊Dic3C2×C411yescharacteristic
115C2×C4⋊Dic3C2×C411yescharacteristic
116C2×C4×Dic3—41no—
117C2×C4×Dic3—41no—
118C2×C4×Dic3C2×C411yescharacteristic
119C2×C4×Dic3C2×C411yescharacteristic
120C2×C4×Dic3C2311yescharacteristic
121C2×C4×Dic3C2311yescharacteristic
122C2×C4×Dic3C2311yescharacteristic
123C2×C4×Dic3C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C3×C22⋊C8—22no—
129C3×C22⋊C8—22no—
130C3×C22⋊C8—22no—
131C3×C22⋊C8D414yes—
132C3⋊#95C2×C411yescharacteristic
133C3⋊#95C2×C411yescharacteristic
134C3⋊#95C2×C411yescharacteristic
135C3⋊#95C2×C411yescharacteristic
136C3⋊#95C2×C411yescharacteristic
137C3⋊#95C2×C411yescharacteristic
138C3⋊#95C2×C411yescharacteristic
139C3⋊#95C2×C411yescharacteristic
140#830—22no—
141#830—22no—
142#830—22no—
143#830—22no—
144#830—41no—
145#830—41no—
146#815—22no—
147#815—41no—
148#815—41no—
149Dic3⋊C8—22no—
150Dic3⋊C8—22no—
151Dic3⋊C8—41no—
152Dic3⋊C8—41no—
153C8×Dic3—22no—
154C22×#41C2×D311yescharacteristic
155C22×M16C2×D311yescharacteristic
156C23×C8C2×D311yescharacteristic
157C2×#117—31no—
158C22×C42—31no—
159#433—64no—
160C2×C4⋊C8—31no—
161C2×C4⋊C8—31no—
162C2×C4⋊C8—31no—
163C2×C4⋊C8—31no—
164#408—24no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—31no—
168C2×C22⋊C8—31no—
169C2×C22⋊C8—31no—
170C2×C22⋊C8—31no—
171C2×C22⋊C8C2×D311yescharacteristic
172C2×C22⋊C8C2×D311yescharacteristic
173C2×C22⋊C8C2×D311yescharacteristic
174C2×C22⋊C8C2×D311yescharacteristic
175C2×#97—31no—
176C2×#97—31no—
177C2×#97—31no—
178C2×C4×C8—31no—
179#391—31no—
180#391—31no—
181#390—31no—
182#390—31no—
183#386—31no—
184#386—31no—
185#386—31no—
186#386—31no—
187C4×C22⋊C4—31no—
188C4×C22⋊C4—31no—
189C4×C22⋊C4—31no—
190C4×C22⋊C4—31no—
191#336—31no—
192#336—31no—
193#336—31no—
194#336—31no—
195#336—31no—
196#336—31no—
197#336—31no—
198#336—31no—
199C24×C3C22×C411yescharacteristic
200C24×C3C22×C411yescharacteristic
201C24×C3C22×C411yescharacteristic
202C3×#41—44no—
203C3×#41—44no—
204C3×#41—44no—
205C3×#41—44no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—41no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
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×C4C22×C411yescharacteristic
233C22×C3×C4C22×C411yescharacteristic
234C22×C3×C4C22×C411yescharacteristic
235C22×C3×C4C2×D412yes—
236C22×C3×C4#4112yes—
237C22×C3×C4#4112yes—
238C22×C3×C4#4112yes—
239C22×C3×C4C2411yescharacteristic
240C22×Dic3—22no—
241C22×Dic3—41no—
242C22×Dic3—41no—
243C22×Dic3—41no—
244C22×Dic3—41no—
245C22×Dic3—41no—
246C22×Dic3C22×C411yescharacteristic
247C22×Dic3C22×C411yescharacteristic
248C22×Dic3C22×C411yescharacteristic
249C22×Dic3C22×C411yescharacteristic
250C22×Dic3C22×C411yescharacteristic
251C22×Dic3C22×C411yescharacteristic
252C22×Dic3C22×C411yescharacteristic
253C22×Dic3C22×C411yescharacteristic
254C3×M16—44no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—44no—
266C2×C3×C8C2×D412yes—
267C2×C3×C8C2×D412yes—
268#217—22no—
269#217—22no—
270#217—22no—
271#217—22no—
272#217—41no—
273#217—41no—
274#217—41no—
275#217—41no—
276#217—41no—
277#217—41no—
278C4⋊Dic3—22no—
279C4⋊Dic3—22no—
280C4×Dic3—21no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283C4×Dic3—21no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3—41no—
289C4×Dic3—41no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—41no—
307C2×#41—41no—
308C22×Q8C4×D311yescharacteristic
309C22×D4C4×D311yescharacteristic
310C22×D4C4×D311yescharacteristic
311C22×D4C4×D311yescharacteristic
312C23×C4—31no—
313C23×C4—31no—
314C23×C4C22×D311yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—41no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—31no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—41no—
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C22×C8C22×D311yescharacteristic
331#117—62no—
332#117—62no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C42—31no—
346C2×C42—31no—
347C2×C42—31no—
348C2×C42—31no—
349C2×C42—31no—
350C2×C42—31no—
351C2×C42—121no—
352C2×C42—121no—
353C4⋊C8—62no—
354C4⋊C8—62no—
355C4⋊C8—121no—
356C4⋊C8—121no—
357C22⋊C8—22no—
358C22⋊C8—22no—
359C22⋊C8—22no—
360C22⋊C8—62no—
361C22⋊C8—62no—
362C22⋊C8—62no—
363C22⋊C8—62no—
364C22⋊C8—121no—
365C22⋊C8—121no—
366C22⋊C8#6714yes—
367#97—62no—
368#97—121no—
369#97—121no—
370C4×C8—62no—
371#95—31no—
372#95—31no—
373#95—31no—
374#95—31no—
375#95—31no—
376#95—31no—
377#95—31no—
378#95—31no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3#11712yes—
399C23×C3C4×D412yes—
400C23×C3C23×C411yescharacteristic
401C3×Q8—44no—
402C3×D4—44no—
403C3×D4—44no—
404C3×D4—44no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4#11712yes—
425C2×C3×C4C4×D412yes—
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4H(5,𝔽2)11yescharacteristic
431C2×C3×C4H(5,𝔽2)11yescharacteristic
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—44no—
456C2×Dic3—44no—
457C2×Dic3#13112yes—
458C3×C8—22no—
459C3×C8—22no—
460C3×C8—41no—
461C3×C8—41no—
462C3⋊C8—41no—
463C3⋊C8—41no—
464C3⋊C8—41no—
465C3⋊C8—41no—
466C24C2×C4×D311yescharacteristic
467C24C2×C4×D311yescharacteristic
468C24C2×C4×D311yescharacteristic
469#41—44no—
470#41—44no—
471#41—44no—
472#41—44no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—41no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—31no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—62no—
508C22×C4—121no—
509C22×C4—121no—
510C22×C4—121no—
511C22×C4—121no—
512C22×C4—121no—
513C22×C4C2×C4×D311yescharacteristic
514C22×C4C2×C4×D311yescharacteristic
515C22×C4C2×C4×D311yescharacteristic
516C22×C4#23512yes—
517C22×C4#23712yes—
518C22×C4#23712yes—
519C22×C4C2×#6712yes—
520C22×C4C23×D311yescharacteristic
521M16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—44no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8C2×#6712yes—
546C2×C8C2×#6712yes—
547C4⋊C4—62no—
548C4⋊C4—62no—
549C22⋊C4—62no—
550C22⋊C4—62no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—121no—
554C22⋊C4—121no—
555C22⋊C4—121no—
556C22⋊C4—121no—
557C22⋊C4—121no—
558C22⋊C4—121no—
559C42—61no—
560C42—61no—
561C42—61no—
562C42—61no—
563C42—61no—
564C42—61no—
565C42—61no—
566C42—61no—
567C42—121no—
568C42—121no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C2×#11711yescharacteristic
591C22×C3C2×C4×D411yescharacteristic
592C22×C3#51811yescharacteristic
593C22×C3C2×#13111yescharacteristic
594C22×C3#56811yescharacteristic
595C22×C3#56811yescharacteristic
596C22×C3#56811yescharacteristic
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—41no—
600C3×C4#54611yescharacteristic
601C3×C4#54611yescharacteristic
602C3×C4#55111yescharacteristic
603C3×C4#55111yescharacteristic
604Dic3—22no—
605Dic3—41no—
606Dic3—41no—
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23#87712yes—
632C23C4×#6712yes—
633C23C22×C4×D311yescharacteristic
634Q8—44no—
635D4—44no—
636D4—44no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—32no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—124no—
682C2×C4—124no—
683C2×C4#87712yes—
684C2×C4C4×#6712yes—
685C2×C4C2×#23511yescharacteristic
686C2×C4C2×#23711yescharacteristic
687C2×C4C2×#23711yescharacteristic
688C2×C4#100411yescharacteristic
689C2×C4#100411yescharacteristic
690C2×C4C22×#6711yescharacteristic
691C8—22no—
692C8—22no—
693C8—41no—
694C8—41no—
695C8—121no—
696C8—121no—
697C8—121no—
698C8—121no—
699C2×C3—42no—
700C2×C3—42no—
701C2×C3—81no—
702C2×C3#234211yescharacteristic
703C2×C3#292311yescharacteristic
704C2×C3#292511yescharacteristic
705C2×C3#293211yescharacteristic
706C2×C3#293511yescharacteristic
707C2×C3#297611yescharacteristic
708C2×C3#297811yescharacteristic
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22C2×#87711yescharacteristic
731C22#548611yescharacteristic
732C22D3×#13111yescharacteristic
733C22#575011yescharacteristic
734C22#575011yescharacteristic
735C22#575011yescharacteristic
736C22C2×C4×#6711yescharacteristic
737C4—22no—
738C4—22no—
739C4—41no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4#549511yescharacteristic
749C4#549511yescharacteristic
750C4#580611yescharacteristic
751C4#580611yescharacteristic
752C3#2256111yescharacteristic, complemented, Sylow
753C2—42no—
754C2—42no—
755C2—81no—
756C2#7864911yescharacteristic
757C2#7865011yescharacteristic
758C2#7866411yescharacteristic
759C2#7866611yescharacteristic
760C2#8209811yescharacteristic
761C2#8378711yescharacteristic
762C2#8378811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC2×C3×#408C2
prime radicalC22×C3×#41C22
cosocleC22×C3×C4C24
hypercenterC2×#408D3
hypocenterC3#22561
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
3. C2×#4720C2semidirect
5. #71995C2semidirect
6. #71983C2semidirect
7. #71974C2semidirect
8. #71967C2semidirect
9. #69915C2semidirect
10. #69915C2semidirect
11. #69914C2semidirect
12. #69912C2semidirect
13. #69911C2semidirect
14. #69908C2semidirect
15. #69906C2semidirect
752. C3#22561semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4082
#840862
C2×#47202
#721362
#719952
#719832
#719742
#719672
#699152
#699142
#699122
#699112
#699082
#699062
#225613