Finite Group Databasebeta

← #10801271

Subgroups — #10801271

Order 768.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×M16C211yesmaximal, characteristic, complemented
2C4×#939C211yesmaximal, characteristic
3C2×#5012C211yesmaximal, characteristic, complemented
4C2×#4728C211yesmaximal, characteristic, complemented
5C2×#4728C211yesmaximal, characteristic, complemented
6C3×#1870C211yesmaximal, characteristic, complemented
7#71996C211yesmaximal, characteristic, complemented
8#69949C211yesmaximal, characteristic, complemented
9#69917C211yesmaximal, characteristic, complemented
10#69912C211yesmaximal, characteristic, complemented
11#69908C211yesmaximal, characteristic, complemented
12#68653C211yesmaximal, characteristic, complemented
13#68647C211yesmaximal, characteristic, complemented
14#68618C211yesmaximal, characteristic, complemented
15#68615C211yesmaximal, characteristic, complemented
16#21490—31nomaximal, Sylow
17C22×C3×M16C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×#939C411yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C2×C4×#67C2211yescharacteristic
22C22×C4×Dic3C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C2×C3×C22⋊C8C2211yescharacteristic
29#5220C411yescharacteristic
30C4×#217C2211yescharacteristic
31C2×#830C2211yescharacteristic
32C2×#830C2211yescharacteristic
33Dic3×M16—24no—
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×(C2×D3)⋊C8C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
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#4990C411yescharacteristic
47#4976C411yescharacteristic
48#4958C411yescharacteristic
49#4957C411yescharacteristic
50#4945C411yescharacteristic
51#4942C411yescharacteristic
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×C4×M16—31no—
68C4×#121—31no—
69#1955—31no—
70#1940—31no—
71#1923—31no—
72#1923—31no—
73#1870—31no—
74#1870D311yescharacteristic, complemented
75#1797—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
84C23×Dic3C2×C411yescharacteristic
85C23×Dic3C2×C411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C2×C3×M16—22no—
88C2×C3×M16—22no—
89C2×C3×M16—22no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C2×C3×C4⋊C4C2×C411yescharacteristic
97C2×C3×C22⋊C4C2×C411yescharacteristic
98C2×C3×C22⋊C4C2×C411yescharacteristic
99C2×C3×C42C2311yescharacteristic
100C2×#217C2×C411yescharacteristic
101C2×#217C2×C411yescharacteristic
102C2×#217C2×C411yescharacteristic
103C2×#217C2×C411yescharacteristic
104#939—24no—
105C4×#67—22no—
106C4×#67—22no—
107C4×#67—22no—
108C4×#67—22no—
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×(C2×D3)⋊C4C2×C411yescharacteristic
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112C2×(C2×D3)⋊C4C2×C411yescharacteristic
113C2×Dic3⋊C4C2×C411yescharacteristic
114C2×Dic3⋊C4C2×C411yescharacteristic
115C2×Dic3⋊C4C2×C411yescharacteristic
116C2×Dic3⋊C4C2×C411yescharacteristic
117C2×C4×Dic3—22no—
118C2×C4×Dic3—22no—
119C2×C4×Dic3C2×C411yescharacteristic
120C2×C4×Dic3C2×C411yescharacteristic
121C2×C4×Dic3C2311yescharacteristic
122C2×C4×Dic3C2311yescharacteristic
123C2×C4×Dic3C2311yescharacteristic
124C2×#208—22no—
125C2×#208—22no—
126C2×#208—22no—
127C2×#208—22no—
128C2×#208—22no—
129C2×#208D414yescomplemented
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×D3×C8—22no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137C3×C22⋊C8—22no—
138C3×C22⋊C8—22no—
139C3×C22⋊C8—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(C2×D3)⋊C8—22no—
149(C2×D3)⋊C8—22no—
150(C2×D3)⋊C8—22no—
151#815—22no—
152#815—22no—
153#815D414yescomplemented
154Dic3⋊C8—22no—
155Dic3⋊C8—22no—
156Dic3⋊C8—22no—
157C8×Dic3—22no—
158C8×Dic3—22no—
159C4⋊(C3⋊C8)—22no—
160C4×C3⋊C8—22no—
161C22×M16—31no—
162C22×M16—31no—
163C22×M16C2×D311yescharacteristic
164C23×C8—31no—
165C2×#121—31no—
166C2×C4×D4—31no—
167C2×C4×D4—31no—
168C2×C4×D4C2×D311yescharacteristic
169C22×C42—31no—
170#436—64no—
171#435—64no—
172#435—64no—
173C2×C4⋊C8—31no—
174C2×C4⋊C8—31no—
175C2×C4⋊C8—31no—
176C2×C4⋊C8—31no—
177C2×C22⋊C8—31no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—31no—
180C2×C22⋊C8—31no—
181C2×C22⋊C8—31no—
182C2×C22⋊C8C2×D311yescharacteristic
183C2×C22⋊C8C2×D311yescharacteristic
184C2×C22⋊C8C2×D311yescharacteristic
185C4×M16—64no—
186C2×#97—31no—
187C2×#97—31no—
188C2×#97—31no—
189C2×C4×C8—31no—
190C2×C4×C8—31no—
191C2×C4×C8—31no—
192#390—31no—
193#389—31no—
194#388—31no—
195#388—31no—
196#386—31no—
197#386—31no—
198#380—31no—
199C4×C4⋊C4—31no—
200C4×C22⋊C4—31no—
201C4×C22⋊C4—31no—
202#336—31no—
203#336—31no—
204#336—31no—
205#336—31no—
206#336C2×D311yescharacteristic
207#336C2×D311yescharacteristic
208C24×C3C22×C411yescharacteristic
209C24×C3C22×C411yescharacteristic
210C23×D3C22×C411yescharacteristic
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—41no—
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×C4C22×C411yescharacteristic
225C22×C3×C4C22×C411yescharacteristic
226C22×C3×C4C22×C411yescharacteristic
227C22×C3×C4C22×C411yescharacteristic
228C22×C3×C4C2×D412yes—
229C22×C3×C4#4112yes—
230C22×C3×C4C2411yescharacteristic
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—22no—
235C2×#67—41no—
236C2×#67—41no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—41no—
242C22×Dic3—41no—
243C22×Dic3C22×C411yescharacteristic
244C22×Dic3C22×C411yescharacteristic
245C22×Dic3C22×C411yescharacteristic
246C22×Dic3C22×C411yescharacteristic
247C22×Dic3C22×C411yescharacteristic
248C22×Dic3C22×C411yescharacteristic
249C22×Dic3C22×C411yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C3×M16—28no—
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—21no—
266C2×C3×C8—21no—
267C2×C3×C8C2×D412yes—
268C2×C3×C8#4112yes—
269C3×C4⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—22no—
272C3×C42—21no—
273C3×C42—21no—
274#217—22no—
275#217—22no—
276#217—22no—
277#217—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—22no—
281(C2×D3)⋊C4M1614yescomplemented
282Dic3⋊C4—22no—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—41no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3—21no—
289C4×Dic3—21no—
290C4×Dic3—22no—
291C4×Dic3—22no—
292C4×Dic3C2×D412yes—
293C4×Dic3#4112yes—
294#208—28no—
295#208—44no—
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×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8C2×D412yes—
305C2×C3⋊C8C2×D412yes—
306C2×C3⋊C8C2×D412yes—
307C2×C3⋊C8#4112yes—
308D3×C8—44no—
309C22×D4—31no—
310C22×D4—31no—
311C22×D4C4×D311yescharacteristic
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—22no—
320C2×M16—34no—
321C2×M16—62no—
322C2×M16—62no—
323C2×M16—62no—
324C2×M16—62no—
325C2×M16—62no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—62no—
331C22×C8—62no—
332C22×C8—62no—
333C22×C8C22×D311yescharacteristic
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336C22×C8C22×D311yescharacteristic
337#121—64no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—62no—
341C4×D4—62no—
342C4×D4—62no—
343C4×D4—62no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4C4×D311yescharacteristic
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⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4C4×D311yescharacteristic
358C2×C22⋊C4C4×D311yescharacteristic
359C2×C42—31no—
360C2×C42—31no—
361C2×C42—31no—
362C2×C42—31no—
363C2×C42—31no—
364C2×C42—62no—
365C2×C42—62no—
366C2×C42C22×D311yescharacteristic
367C4⋊C8—62no—
368C4⋊C8—62no—
369C4⋊C8—62no—
370C4⋊C8—62no—
371C22⋊C8—22no—
372C22⋊C8—22no—
373C22⋊C8—22no—
374C22⋊C8—62no—
375C22⋊C8—62no—
376C22⋊C8—62no—
377C22⋊C8—62no—
378C22⋊C8—62no—
379#97—34no—
380#97—62no—
381#97—62no—
382C4×C8—62no—
383C4×C8—62no—
384C4×C8—62no—
385#95—31no—
386#95—31no—
387#95—31no—
388#95—31no—
389#95—31no—
390#95—31no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3C4×D412yes—
405C23×C3C23×C411yescharacteristic
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3C2×M1612yes—
413C3×D4—44no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4C4×D412yes—
433C2×C3×C4C2×M1612yes—
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440#67—44no—
441#67—44no—
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—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—44no—
460C2×Dic3—44no—
461C2×Dic3C4×D412yes—
462C2×Dic3C4×D412yes—
463C2×Dic3C2×M1612yes—
464C2×Dic3#13112yes—
465C4×D3—41no—
466C4×D3—41no—
467C4×D3—41no—
468C4×D3—41no—
469C3×C8—22no—
470C3×C8—22no—
471C3×C8—41no—
472C3×C8—41no—
473C3⋊C8—22no—
474C3⋊C8—41no—
475C3⋊C8—41no—
476C3⋊C8#12114yescomplemented
477C24—31no—
478C24C2×C4×D311yescharacteristic
479C24C2×C4×D311yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—121no—
488C2×D4—121no—
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—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—121no—
517C22×C4—121no—
518C22×C4C2×C4×D311yescharacteristic
519C22×C4C2×C4×D311yescharacteristic
520C22×C4C2×C4×D311yescharacteristic
521C22×C4C2×C4×D311yescharacteristic
522C22×C4D3×D412yes—
523C22×C4#23712yes—
524C22×C4C23×D311yescharacteristic
525M16—28no—
526M16—68no—
527M16—124no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—32no—
539C2×C8—32no—
540C2×C8—32no—
541C2×C8—32no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—124no—
551C2×C8D3×D412yes—
552C2×C8#23712yes—
553C4⋊C4—22no—
554C4⋊C4—62no—
555C4⋊C4—62no—
556C4⋊C4—62no—
557C4⋊C4—121no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—34no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C22⋊C4—62no—
564C22⋊C4—62no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—62no—
568C42—21no—
569C42—21no—
570C42—32no—
571C42—32no—
572C42—62no—
573C42—62no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42—61no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
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×C3—41no—
591C22×C3—41no—
592C22×C3C2×C4×D411yescharacteristic
593C22×C3C2×C4×D411yescharacteristic
594C22×C3C4×#4111yescharacteristic
595C22×C3C22×M1611yescharacteristic
596C22×C3C2×#13111yescharacteristic
597C22×C3#56811yescharacteristic
598C22×C3#56811yescharacteristic
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4C2×#12111yescharacteristic
611C3×C4#52511yescharacteristic
612C3×C4#52911yescharacteristic
613C3×C4#53211yescharacteristic
614Dic3—22no—
615Dic3—22no—
616Dic3—22no—
617Dic3—22no—
618Dic3—41no—
619Dic3—41no—
620Dic3—41no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—32no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23#67⋊C412yes—
642C23C22×C4×D311yescharacteristic
643D4—44no—
644D4—124no—
645D4—124no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
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—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—124no—
686C2×C4—124no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4#67⋊C412yes—
692C2×C4D3×M1612yes—
693C2×C4C2×D3×D411yescharacteristic
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×#23711yescharacteristic
696C2×C4C2×#23711yescharacteristic
697C2×C4D3×#4111yescharacteristic
698C2×C4D3×#4111yescharacteristic
699C8—22no—
700C8—22no—
701C8—34no—
702C8—41no—
703C8—41no—
704C8—62no—
705C8—121no—
706C8—121no—
707C2×C3—42no—
708C2×C3—81no—
709C2×C3C4×#12111yescharacteristic
710C2×C3#293311yescharacteristic
711C2×C3D4×M1611yescharacteristic
712C2×C3D4×M1611yescharacteristic
713C2×C3#293511yescharacteristic
714C2×C3#296511yescharacteristic
715C2×C3#296711yescharacteristic
716D3—42no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—62no—
732C22—62no—
733C22—62no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22C2×#67⋊C411yescharacteristic
739C22C4×#23711yescharacteristic
740C22C4×D3×D411yescharacteristic
741C22C2×D3×M1611yescharacteristic
742C22#574511yescharacteristic
743C22D3×#13111yescharacteristic
744C22#575011yescharacteristic
745C4—22no—
746C4—22no—
747C4—41no—
748C4—41no—
749C4—62no—
750C4—62no—
751C4—62no—
752C4—62no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4#558611yescharacteristic
757C4#559611yescharacteristic
758C4D3×#12111yescharacteristic
759C4#564911yescharacteristic
760C3#2149011yescharacteristic, complemented, Sylow
761C2—42no—
762C2—81no—
763C2—122no—
764C2#7466011yescharacteristic
765C2#7862811yescharacteristic
766C2#7866011yescharacteristic
767C2#7945511yescharacteristic
768C2#7948211yescharacteristic
769C2#7951711yescharacteristic
770C2#7954011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1870C2
prime radicalC2×#939C4
cosocleC22×C3×C4C24
hypercenter#1870D3
hypocenterC3#21490
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×M16C2semidirect
3. C2×#5012C2semidirect
4. C2×#4728C2semidirect
5. C2×#4728C2semidirect
6. C3×#1870C2semidirect
7. #71996C2semidirect
8. #69949C2semidirect
9. #69917C2semidirect
10. #69912C2semidirect
11. #69908C2semidirect
12. #68653C2semidirect
13. #68647C2semidirect
14. #68618C2semidirect
15. #68615C2semidirect
74. #1870D3semidirect
129. C2×#208D4semidirect
153. #815D4semidirect
281. (C2×D3)⋊C4M16semidirect
476. C3⋊C8#121semidirect
760. C3#21490semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×M162
C4×#9392
C2×#50122
C2×#47282
C3×#18702
#719962
#699492
#699172
#699122
#699082
#686532
#686472
#686182
#686152
#214903