Finite Group Databasebeta

← #10801345

Subgroups — #10801345

Order 768.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5101C211yesmaximal, characteristic, complemented
2#82345C211yesmaximal, characteristic
3C2×#5012C211yesmaximal, characteristic, complemented
4C2×#4728C211yesmaximal, characteristic, complemented
5C2×#4728C211yesmaximal, characteristic, complemented
6C3×#1869C211yesmaximal, characteristic, complemented
7#71975C211yesmaximal, characteristic, complemented
8#69949C211yesmaximal, characteristic, complemented
9#69916C211yesmaximal, characteristic, complemented
10#69914C211yesmaximal, characteristic, complemented
11#69909C211yesmaximal, characteristic, complemented
12#68653C211yesmaximal, characteristic, complemented
13#68647C211yesmaximal, characteristic, complemented
14#68617C211yesmaximal, characteristic, complemented
15#68616C211yesmaximal, characteristic, complemented
16#21496—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C4×#67C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C2×#926C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28#5223C411yescharacteristic
29#5222C411yescharacteristic
30C4×#217C2211yescharacteristic
31C2×#830C2211yescharacteristic
32C2×#830C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36#5101—24no—
37C2×#815C2211yescharacteristic
38C2×#815C2211yescharacteristic
39C2×#815C2211yescharacteristic
40C2×Dic3⋊C8C2211yescharacteristic
41C2×Dic3⋊C8C2211yescharacteristic
42C2×Dic3⋊C8C2211yescharacteristic
43C2×C8×Dic3C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#5012—24no—
46#4994C411yescharacteristic
47#4982C411yescharacteristic
48#4961C411yescharacteristic
49#4959C411yescharacteristic
50#4952C411yescharacteristic
51#4948C411yescharacteristic
52C4×(C2×D3)⋊C4C2211yescharacteristic
53C4×Dic3⋊C4C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55C2×C4×C3⋊C8C2211yescharacteristic
56#4728—24no—
57#4728—24no—
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#436—31no—
65C2×#435—31no—
66C2×#435—31no—
67C2×#405—31no—
68#2392—31no—
69#1954—31no—
70#1939—31no—
71#1924—31no—
72#1924—31no—
73#1869—31no—
74#1869D311yescharacteristic, complemented
75#1798—31no—
76#1771—31no—
77#1753—31no—
78C8×C22⋊C4—31no—
79C22×C3×D4C2×C411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67C2×C411yescharacteristic
83C22×#67C2×C411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×C3×C8—22no—
86C22×C3×C8—22no—
87C22×C3×C8—22no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C2×C3×C4⋊C4C2×C411yescharacteristic
95C2×C3×C22⋊C4C2×C411yescharacteristic
96C2×C3×C22⋊C4C2×C411yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×#217C2×C411yescharacteristic
99C2×#217C2×C411yescharacteristic
100C2×#217C2×C411yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C4×#67—22no—
105C4×#67—22no—
106C4×#67—22no—
107C4×#67—22no—
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×(C2×D3)⋊C4C2×C411yescharacteristic
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112#926—22no—
113#926—22no—
114C2×C4⋊Dic3C2×C411yescharacteristic
115C2×C4⋊Dic3C2×C411yescharacteristic
116C2×Dic3⋊C4C2×C411yescharacteristic
117C2×Dic3⋊C4C2×C411yescharacteristic
118C2×Dic3⋊C4C2×C411yescharacteristic
119C2×Dic3⋊C4C2×C411yescharacteristic
120C2×C4×Dic3C2311yescharacteristic
121C2×C4×Dic3C2311yescharacteristic
122C2×C4×Dic3C2311yescharacteristic
123C2×#208—22no—
124C2×#208—22no—
125C2×#208—22no—
126C2×#208—22no—
127C2×#208—22no—
128C2×#208D414yescomplemented
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C2×D3×C8—22no—
134C2×D3×C8—22no—
135C2×D3×C8—22no—
136C3×C22⋊C8—22no—
137C3×C22⋊C8—22no—
138C3×C22⋊C8—22no—
139C3⋊#95C2×C411yescharacteristic
140C3⋊#95C2×C411yescharacteristic
141C3⋊#95C2×C411yescharacteristic
142C3⋊#95C2×C411yescharacteristic
143C3⋊#95C2×C411yescharacteristic
144C3⋊#95C2×C411yescharacteristic
145#830—22no—
146#830—22no—
147(C2×D3)⋊C8—22no—
148(C2×D3)⋊C8—22no—
149(C2×D3)⋊C8—22no—
150#815—22no—
151#815—22no—
152#815D414yescomplemented
153Dic3⋊C8—22no—
154Dic3⋊C8—22no—
155Dic3⋊C8—22no—
156C8×Dic3—22no—
157C8×Dic3—22no—
158C4⋊(C3⋊C8)—22no—
159C4×C3⋊C8—22no—
160C22×M16—31no—
161C22×M16—31no—
162C23×C8—31no—
163C23×C8C2×D311yescharacteristic
164C2×C4×D4—31no—
165C2×C4×D4—31no—
166C2×C4×D4C2×D311yescharacteristic
167C2×#117—31no—
168#436—64no—
169#435—64no—
170#435—64no—
171C2×C4⋊C8—31no—
172C2×C4⋊C8—31no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8—31no—
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—31no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8C2×D311yescharacteristic
181C2×C22⋊C8C2×D311yescharacteristic
182C2×C22⋊C8C2×D311yescharacteristic
183#405—64no—
184C2×#97—31no—
185C2×#97—31no—
186C2×#97—31no—
187C2×C4×C8—31no—
188C2×C4×C8—31no—
189C2×C4×C8—31no—
190#398—31no—
191#397—31no—
192#396—31no—
193#396—31no—
194#394—31no—
195#394—31no—
196#394—31no—
197#392—31no—
198C4×C4⋊C4—31no—
199C4×C22⋊C4—31no—
200C4×C22⋊C4—31no—
201#336—31no—
202#336—31no—
203#336—31no—
204#336—31no—
205#336C2×D311yescharacteristic
206#336C2×D311yescharacteristic
207C24×C3C22×C411yescharacteristic
208C24×C3C22×C411yescharacteristic
209C23×D3C22×C411yescharacteristic
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—41no—
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×C4C22×C411yescharacteristic
224C22×C3×C4C22×C411yescharacteristic
225C22×C3×C4C22×C411yescharacteristic
226C22×C3×C4C22×C411yescharacteristic
227C22×C3×C4C2×D412yes—
228C22×C3×C4#4112yes—
229C22×C3×C4C2411yescharacteristic
230C2×#67—22no—
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—41no—
235C2×#67—41no—
236C22×Dic3C22×C411yescharacteristic
237C22×Dic3C22×C411yescharacteristic
238C22×Dic3C22×C411yescharacteristic
239C22×Dic3C22×C411yescharacteristic
240C22×Dic3C22×C411yescharacteristic
241C22×Dic3C22×C411yescharacteristic
242C22×Dic3C22×C411yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C3×C8—28no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8C2×D412yes—
261C2×C3×C8#4112yes—
262C3×C4⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C42—21no—
266C3×C42—21no—
267#217—22no—
268#217—22no—
269#217—22no—
270#217—22no—
271#217—41no—
272#217—41no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277C4⋊Dic3—22no—
278C4⋊Dic3—22no—
279Dic3⋊C4—22no—
280Dic3⋊C4—22no—
281Dic3⋊C4—22no—
282Dic3⋊C4—41no—
283C4×Dic3—21no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3C2×D412yes—
288C4×Dic3#4112yes—
289#208—28no—
290#208—44no—
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⋊C8C2×D412yes—
300C2×C3⋊C8C2×D412yes—
301C2×C3⋊C8C2×D412yes—
302C2×C3⋊C8#4112yes—
303D3×C8—44no—
304C22×D4—31no—
305C22×D4—31no—
306C22×D4C4×D311yescharacteristic
307C23×C4—31no—
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C2×M16—34no—
311C2×M16—62no—
312C2×M16—62no—
313C2×M16—62no—
314C2×M16—62no—
315C2×M16—62no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—31no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8—31no—
323C22×C8—62no—
324C22×C8—62no—
325C22×C8—62no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—62no—
333C4×D4—62no—
334C4×D4—62no—
335C4×D4—62no—
336#117—62no—
337#117—62no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4C4×D311yescharacteristic
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—31no—
353C2×C22⋊C4—31no—
354C2×C22⋊C4—31no—
355C2×C22⋊C4C4×D311yescharacteristic
356C2×C22⋊C4C4×D311yescharacteristic
357C2×C42—31no—
358C2×C42—31no—
359C2×C42—31no—
360C2×C42C22×D311yescharacteristic
361C4⋊C8—62no—
362C4⋊C8—62no—
363C4⋊C8—62no—
364C4⋊C8—62no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C22⋊C8—62no—
369C22⋊C8—62no—
370C22⋊C8—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373#97—34no—
374#97—62no—
375#97—62no—
376C4×C8—62no—
377C4×C8—62no—
378C4×C8—62no—
379#95—31no—
380#95—31no—
381#95—31no—
382#95—31no—
383#95—31no—
384#95—31no—
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×C3C4×D412yes—
399C23×C3C23×C411yescharacteristic
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3#13112yes—
407C3×D4—44no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4C4×D412yes—
427C2×C3×C4#13112yes—
428C2×C3×C4C22×D411yescharacteristic
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4C2×#4111yescharacteristic
433C2×C3×C4C2×#4111yescharacteristic
434#67—44no—
435#67—44no—
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×Dic3C4×D412yes—
456C2×Dic3C4×D412yes—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C3×C8—22no—
462C3×C8—22no—
463C3×C8—41no—
464C3×C8—41no—
465C3⋊C8—22no—
466C3⋊C8—41no—
467C3⋊C8—41no—
468C3⋊C8#12114yes—
469C24—31no—
470C24C2×C4×D311yescharacteristic
471C24C2×C4×D311yescharacteristic
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—41no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—121no—
480C2×D4—121no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—31no—
492C22×C4—31no—
493C22×C4—31no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4C2×C4×D311yescharacteristic
505C22×C4C2×C4×D311yescharacteristic
506C22×C4C2×C4×D311yescharacteristic
507C22×C4C2×C4×D311yescharacteristic
508C22×C4D3×D412yes—
509C22×C4#23712yes—
510C22×C4C23×D311yescharacteristic
511M16—68no—
512M16—124no—
513C2×C8—28no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—32no—
525C2×C8—32no—
526C2×C8—32no—
527C2×C8—32no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—124no—
537C2×C8D3×D412yes—
538C2×C8#23712yes—
539C4⋊C4—22no—
540C4⋊C4—62no—
541C4⋊C4—62no—
542C4⋊C4—62no—
543C4⋊C4—62no—
544C4⋊C4—62no—
545C4⋊C4—121no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—62no—
549C22⋊C4—62no—
550C22⋊C4—62no—
551C22⋊C4—62no—
552C22⋊C4—62no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—62no—
556C22⋊C4—121no—
557C22⋊C4—121no—
558C42—21no—
559C42—21no—
560C42—32no—
561C42—32no—
562C42—61no—
563C42—61no—
564C42—61no—
565C42—61no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×C4×D411yescharacteristic
581C22×C3C2×C4×D411yescharacteristic
582C22×C3C4×#4111yescharacteristic
583C22×C3C2×#13111yescharacteristic
584C22×C3C2×#13111yescharacteristic
585C22×C3#56811yescharacteristic
586C22×C3#56811yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4C2×#12111yescharacteristic
599C3×C4#52511yescharacteristic
600C3×C4#52911yescharacteristic
601C3×C4#53211yescharacteristic
602Dic3—22no—
603Dic3—22no—
604Dic3—41no—
605Dic3—41no—
606Dic3—41no—
607Dic3—41no—
608Dic3—41no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—32no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23#67⋊C412yes—
630C23C22×C4×D311yescharacteristic
631D4—44no—
632D4—124no—
633D4—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—32no—
649C2×C4—32no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
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—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4#67⋊C412yes—
678C2×C4#90112yes—
679C2×C4C2×D3×D411yescharacteristic
680C2×C4C2×D3×D411yescharacteristic
681C2×C4C2×#23711yescharacteristic
682C2×C4C2×#23711yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C8—22no—
686C8—22no—
687C8—34no—
688C8—41no—
689C8—41no—
690C8—62no—
691C8—121no—
692C8—121no—
693C2×C3—42no—
694C2×C3—81no—
695C2×C3C4×#12111yescharacteristic
696C2×C3#293311yescharacteristic
697C2×C3#293311yescharacteristic
698C2×C3#293311yescharacteristic
699C2×C3#293511yescharacteristic
700C2×C3#296611yescharacteristic
701C2×C3#296711yescharacteristic
702D3—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22C2×#67⋊C411yescharacteristic
725C22C4×#23711yescharacteristic
726C22C4×D3×D411yescharacteristic
727C22C2×#90111yescharacteristic
728C22#574511yescharacteristic
729C22D3×#13111yescharacteristic
730C22#575011yescharacteristic
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—62no—
736C4—62no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4#558611yescharacteristic
743C4#559611yescharacteristic
744C4D3×#12111yescharacteristic
745C4#564911yescharacteristic
746C3#2149611yescharacteristic, complemented, Sylow
747C2—42no—
748C2—81no—
749C2—122no—
750C2#7466011yescharacteristic
751C2#7859611yescharacteristic
752C2#7865911yescharacteristic
753C2#7940111yescharacteristic
754C2#7942511yescharacteristic
755C2#7945511yescharacteristic
756C2#7948211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1869C2
prime radical#5223C4
cosocleC22×C3×C4C24
hypercenter#1869D3
hypocenterC3#21496
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#5101C2semidirect
3. C2×#5012C2semidirect
4. C2×#4728C2semidirect
5. C2×#4728C2semidirect
6. C3×#1869C2semidirect
7. #71975C2semidirect
8. #69949C2semidirect
9. #69916C2semidirect
10. #69914C2semidirect
11. #69909C2semidirect
12. #68653C2semidirect
13. #68647C2semidirect
14. #68617C2semidirect
15. #68616C2semidirect
74. #1869D3semidirect
128. C2×#208D4semidirect
152. #815D4semidirect
746. C3#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#51012
#823452
C2×#50122
C2×#47282
C3×#18692
#719752
#699492
#699162
#699142
#699092
#686532
#686472
#686172
#686162
#214963