Finite Group Databasebeta

← #10801296

Subgroups — #10801296

Order 768.

1058 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×C3×#435C211yesmaximal, characteristic, complemented
2C2×#5127C211yesmaximal, characteristic, complemented
3C2×#5122C211yesmaximal, characteristic, complemented
4C2×C8×#67C211yesmaximal, characteristic, complemented
5#82345C211yesmaximal, characteristic
6#71967C211yesmaximal, characteristic, complemented
7#71610C211yesmaximal, characteristic, complemented
8#70452C211yesmaximal, characteristic, complemented
9#70449C211yesmaximal, characteristic, complemented
10#69952C211yesmaximal, characteristic, complemented
11#69917C211yesmaximal, characteristic, complemented
12#69913C211yesmaximal, characteristic, complemented
13#69909C211yesmaximal, characteristic, complemented
14#69833C211yesmaximal, characteristic, complemented
15#69831C211yesmaximal, characteristic, complemented
16#21492—31nomaximal, Sylow
17C22×C3×M16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C2×C4×#67C2211yescharacteristic
22C2×#926C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C3×#435—24no—
26C2×C3×C4⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C2×C3×C22⋊C8C2211yescharacteristic
29C2×C3×#97C2211yescharacteristic
30#5223C411yescharacteristic
31#5222C411yescharacteristic
32C4×#217C2211yescharacteristic
33C2×#830C2211yescharacteristic
34C2×#830C2211yescharacteristic
35C2×#830C2211yescharacteristic
36#5127—24no—
37#5122—24no—
38C8×#67—24no—
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×#815C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×#815C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46C2×Dic3⋊C8C2211yescharacteristic
47C2×Dic3⋊C8C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50#4994C411yescharacteristic
51#4982C411yescharacteristic
52#4961C411yescharacteristic
53#4959C411yescharacteristic
54#4952C411yescharacteristic
55#4948C411yescharacteristic
56C4×(C2×D3)⋊C4C2211yescharacteristic
57C4×Dic3⋊C4C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#435—31no—
65C2×#435D311yescharacteristic, complemented
66C2×C8×D4—31no—
67C2×#405—31no—
68#2392—31no—
69#1955—31no—
70#1940—31no—
71#1923—31no—
72#1923—31no—
73#1869—31no—
74#1869—31no—
75#1798—31no—
76#1770—31no—
77#1752—31no—
78#1752—31no—
79C22×C3×D4C2×C411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67C2×C411yescharacteristic
83C22×#67C2×C411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C2×C3×M16—22no—
86C2×C3×M16—22no—
87C2×C3×M16D414yescomplemented
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8—22no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C2×C3×C4⋊C4C2×C411yescharacteristic
98C2×C3×C22⋊C4C2×C411yescharacteristic
99C2×C3×C22⋊C4C2×C411yescharacteristic
100C2×C3×C42C2311yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104C2×#217C2×C411yescharacteristic
105C2×#217C2×C411yescharacteristic
106C2×#217C2×C411yescharacteristic
107C4×#67—22no—
108C4×#67—22no—
109C4×#67—22no—
110C4×#67—22no—
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112C2×(C2×D3)⋊C4C2×C411yescharacteristic
113C2×(C2×D3)⋊C4C2×C411yescharacteristic
114C2×(C2×D3)⋊C4C2×C411yescharacteristic
115#926—22no—
116#926—22no—
117C2×C4⋊Dic3C2×C411yescharacteristic
118C2×C4⋊Dic3C2×C411yescharacteristic
119C2×Dic3⋊C4C2×C411yescharacteristic
120C2×Dic3⋊C4C2×C411yescharacteristic
121C2×Dic3⋊C4C2×C411yescharacteristic
122C2×Dic3⋊C4C2×C411yescharacteristic
123C2×C4×Dic3C2311yescharacteristic
124C2×C4×Dic3C2311yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8—22no—
127C22×C3⋊C8—22no—
128C22×C3⋊C8—22no—
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×C4⋊C8—22no—
137C3×C22⋊C8—22no—
138C3×C22⋊C8—22no—
139C3×#97—22no—
140C3⋊#95C2×C411yescharacteristic
141C3⋊#95C2×C411yescharacteristic
142C3⋊#95C2×C411yescharacteristic
143C3⋊#95C2×C411yescharacteristic
144C3⋊#95C2×C411yescharacteristic
145C3⋊#95C2×C411yescharacteristic
146#830—22no—
147#830—22no—
148#830—22no—
149(C2×D3)⋊C8—22no—
150(C2×D3)⋊C8—22no—
151(C2×D3)⋊C8—22no—
152#815—22no—
153#815—22no—
154#815—22no—
155Dic3⋊C8—22no—
156Dic3⋊C8—22no—
157Dic3⋊C8—22no—
158C8×Dic3—22no—
159C8×Dic3D414yescomplemented
160C22×M16C2×D311yescharacteristic
161C23×C8—31no—
162C23×C8—31no—
163C23×C8C2×D311yescharacteristic
164C2×C4×D4—31no—
165C2×C4×D4—31no—
166C2×C4×D4C2×D311yescharacteristic
167C2×#117—31no—
168#435—24no—
169#435—64no—
170C8×D4—64no—
171C2×C4⋊C8—31no—
172C2×C4⋊C8—31no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8C2×D311yescharacteristic
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—31no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—31no—
181C2×C22⋊C8C2×D311yescharacteristic
182C2×C22⋊C8C2×D311yescharacteristic
183#405—64no—
184C2×#97—31no—
185C2×#97—31no—
186C2×#97—31no—
187C2×#97C2×D311yescharacteristic
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#336—31no—
206#336—31no—
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—22no—
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—
249C3×M16—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—44no—
259C2×C3×C8C2×D412yes—
260C2×C3×C8C2×D412yes—
261C2×C3×C8C2×D412yes—
262C2×C3×C8#4112yes—
263C3×C4⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C42—21no—
267C3×C42—21no—
268#217—22no—
269#217—22no—
270#217—22no—
271#217—22no—
272#217—22no—
273#217—41no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—41no—
278C4⋊Dic3—22no—
279C4⋊Dic3—22no—
280Dic3⋊C4—22no—
281Dic3⋊C4—22no—
282Dic3⋊C4—41no—
283Dic3⋊C4—41no—
284C4×Dic3—21no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3C2×D412yes—
289C4×Dic3#4112yes—
290C2×C3⋊C8—28no—
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⋊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—22no—
311C2×M16—22no—
312C2×M16#6714yescomplemented
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—31no—
317C22×C8—31no—
318C22×C8—31no—
319C22×C8—31no—
320C22×C8—62no—
321C22×C8—62no—
322C22×C8—62no—
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—22no—
362C4⋊C8—62no—
363C4⋊C8—62no—
364C4⋊C8—62no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367C22⋊C8—62no—
368C22⋊C8—62no—
369C22⋊C8—62no—
370C22⋊C8—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373#97—22no—
374#97—62no—
375#97—62no—
376#97—62no—
377C4×C8—34no—
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×C3C4×D412yes—
398C23×C3#13112yes—
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—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
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—21no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4C4×D412yes—
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—28no—
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—41no—
463C3×C8—41no—
464C3×C8#12114yes—
465C3⋊C8—22no—
466C3⋊C8—22no—
467C3⋊C8—41no—
468C3⋊C8—41no—
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—62no—
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×C4#23512yes—
509C22×C4C2×#6712yes—
510C22×C4C23×D311yescharacteristic
511M16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—32no—
521C2×C8—32no—
522C2×C8—44no—
523C2×C8—68no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—124no—
535C2×C8D3×D412yes—
536C2×C8#23712yes—
537C2×C8C2×#6712yes—
538C2×C8C2×#6712yes—
539C4⋊C4—22no—
540C4⋊C4—62no—
541C4⋊C4—62no—
542C4⋊C4—62no—
543C4⋊C4—62no—
544C4⋊C4—121no—
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—22no—
570C22×C3—22no—
571C22×C3—22no—
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—41no—
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—32no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23#90712yes—
629C23C4×#6712yes—
630C23C22×C4×D311yescharacteristic
631D4—44no—
632D4—68no—
633D4—124no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—32no—
650C2×C4—32no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
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—61no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4C4×#6712yes—
679C2×C4C2×#23511yescharacteristic
680C2×C4C2×D3×D411yescharacteristic
681C2×C4C2×#23711yescharacteristic
682C2×C4D3×#4111yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4C22×#6711yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—62no—
689C8—62no—
690C8—121no—
691C8—121no—
692C8#93914yes—
693C2×C3—42no—
694C2×C3—42no—
695C2×C3C4×#12111yescharacteristic
696C2×C3#292911yescharacteristic
697C2×C3#293211yescharacteristic
698C2×C3#293311yescharacteristic
699C2×C3#293311yescharacteristic
700C2×C3#296811yescharacteristic
701C2×C3#296811yescharacteristic
702D3—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
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—
724C22C4×#23711yescharacteristic
725C22C4×D3×D411yescharacteristic
726C22C2×#90711yescharacteristic
727C22#574511yescharacteristic
728C22D3×#13111yescharacteristic
729C22#575011yescharacteristic
730C22C2×C4×#6711yescharacteristic
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—62no—
736C4—62no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4#553811yescharacteristic
743C4#554711yescharacteristic
744C4C2×#93911yescharacteristic
745C4#583211yescharacteristic
746C3#2149211yescharacteristic, complemented, Sylow
747C2—42no—
748C2—42no—
749C2—122no—
750C2#7945711yescharacteristic
751C2#7945811yescharacteristic
752C2#7947811yescharacteristic
753C2#7948011yescharacteristic
754C2C4×#93911yescharacteristic
755C2#8375711yescharacteristic
756C2#8379611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC2×C3×#435C2
prime radical#5223C4
cosocleC22×C3×C4C24
hypercenterC2×#435D3
hypocenterC3#21492
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#435C2semidirect
2. C2×#5127C2semidirect
3. C2×#5122C2semidirect
4. C2×C8×#67C2semidirect
6. #71967C2semidirect
7. #71610C2semidirect
8. #70452C2semidirect
9. #70449C2semidirect
10. #69952C2semidirect
11. #69917C2semidirect
12. #69913C2semidirect
13. #69909C2semidirect
14. #69833C2semidirect
15. #69831C2semidirect
65. C2×#435D3semidirect
87. C2×C3×M16D4semidirect
159. C8×Dic3D4semidirect
312. C2×M16#67semidirect
746. C3#21492semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4352
C2×#51272
C2×#51222
C2×C8×#672
#823452
#719672
#716102
#704522
#704492
#699522
#699172
#699132
#699092
#698332
#698312
#214923