Finite Group Databasebeta

← #29688925

Subgroups — #29688925

Order 15616.

1802 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×#16839725C211yesmaximal, characteristic, complemented
3C2×#16839724C211yesmaximal, characteristic, complemented
4#21446117C211yesmaximal, characteristic, complemented
5#21446116C211yesmaximal, characteristic, complemented
6#21446115C212yesmaximal, complemented
7#21446114C211yesmaximal, characteristic, complemented
8#21446113C212yesmaximal, complemented
9#21445886C212yesmaximal, complemented
10#21445728C212yesmaximal, complemented
11C61×#1870C211yesmaximal, characteristic, complemented
12C22×D4×D61C411yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×C4×D61C2211yescharacteristic
15C22×#11758194C2211yescharacteristic, complemented
16C22×#11758189C2212yescomplemented
17C2×C4×D244C2211yescharacteristic
18C2×D4×Dic61C411yescharacteristic
19C2×#14519739C411yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×#14519737C411yescharacteristic
23C2×#14519737C411yescharacteristic
24C4×D4×D61—24no—
25C4×D4×D61—24no—
26C2×C4⋊C4×D61C411yescharacteristic
27C2×C22⋊C4×D61C411yescharacteristic
28C2×C22⋊C4×D61C411yescharacteristic
29C2×C42×D61C2211yescharacteristic
30#16839725—24no—
31#16839724—24no—
32C2×C22⋊#92418C2211yescharacteristic, complemented
33C2×C22⋊#92418C2212yescomplemented
34C2×#14519689C2212yes—
35C2×#14519689C2212yes—
36C2×#14519689C2212yescomplemented
37C2×#14519689C2212yescomplemented
38C2×#14519689C2212yescomplemented
39#16839517C2212yescomplemented
40#16839516C2212yescomplemented
41#16839516C2212yescomplemented
42C22×M16×C61C2211yescharacteristic, complemented
43C2×C4×D4×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic, complemented
45C2×C22⋊C8×C61C2212yescomplemented
46C61×#336C2212yescomplemented
47C24×D61C2×C411yescharacteristic
48C24×D61C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61C2×C411yescharacteristic
51C22×C22⋊D61C2×C411yescharacteristic
52C2×D4×D61—24no—
53C2×D4×D61—24no—
54C2×D4×D61—24no—
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—42no—
60C22×C4×D61—42no—
61C22×C4×D61—42no—
62C22×C4×D61—42no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61D414yes—
70C22×C4×D61D414yes—
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—22no—
75C2×#11758194—42no—
76C2×#11758189—24no—
77C2×#11758189—42no—
78C2×#11758189—42no—
79C22×#92418C2312yes—
80C22×#92418C2312yes—
81C4×D244—22no—
82C4×D244—22no—
83D4×Dic61—24no—
84#14519739—24no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89#14519737—24no—
90#14519737—24no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C4⋊C4×D61—24no—
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C22⋊C4×D61—24no—
102C22⋊C4×D61—24no—
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—22no—
107C42×D61—22no—
108C22⋊#92418—22no—
109C22⋊#92418—42no—
110#14519689—24no—
111#14519689—24no—
112#14519689—24no—
113#14519689—42no—
114#14519689—42no—
115C22×D4×C61C2×C411yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C2×M16×C61—22no—
119C2×M16×C61—42no—
120C22×C8×C61C2312yes—
121C22×C8×C61C2312yes—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C22⋊C8×C61—22no—
129C22⋊C8×C61—42no—
130C24×C61C22×C411yescharacteristic
131C24×C61C22×C411yescharacteristic
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61—42no—
139C23×D61—42no—
140C23×D61C22⋊C414yes—
141C23×D61M1614yescomplemented
142C23×D61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C22×Dic61—22no—
168C22×Dic61—42no—
169C22×Dic61—42no—
170C22×Dic61C22⋊C414yes—
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176D4×D61—232no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—48no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—48no—
197C2×C4×D61—44no—
198C2×C4×D61—44no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61C22⋊C414yes—
205C2×C4×D61C22⋊C414yes—
206C2×C4×D61M1614yescomplemented
207C2×C4×D61C2×D412yes—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×D412yes—
210C2×C4×D61C2×D412yes—
211M16×C61—44no—
212C2×C8×C61—22no—
213C2×C8×C61—22no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61—22no—
217C2×C8×C61—22no—
218C4⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C42×C61—21no—
222C42×C61—21no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229C4⋊Dic61—22no—
230#11758196—22no—
231#11758196—22no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236#11758194—44no—
237C2×#92418—22no—
238C2×#92418—22no—
239C2×#92418—22no—
240C2×#92418—22no—
241C2×#92418—22no—
242C2×#92418—22no—
243#11758189—48no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61C2×C22⋊C412yes—
253C23×C61C2×M1612yes—
254C23×C61C23×C411yescharacteristic
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—21no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—28no—
266C22×D61—28no—
267C22×D61—44no—
268C22×D61—44no—
269C22×D61—48no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—48no—
273C22×D61—48no—
274C22×D61—48no—
275C22×D61C2×C22⋊C412yes—
276C22×D61C2×C22⋊C412yes—
277C22×D61C2×M1612yes—
278C22×D61C2×M1612yes—
279C22×D61C2×M1612yes—
280D4×C61—28no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—42no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×M1612yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61H(5,𝔽2)12yes—
299C2×C4×C61H(5,𝔽2)12yes—
300C22⋊D61—28no—
301C22⋊D61—28no—
302C2×Dic61—21no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—44no—
311C2×Dic61—44no—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×M1612yes—
315D244—28no—
316C4×D61—28no—
317C4×D61—24no—
318C4×D61—24no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—44no—
324C4×D61—44no—
325C4×D61—44no—
326C4×D61—44no—
327C4×D61—44no—
328C4×D61—42no—
329C4×D61—41no—
330C4×D61—41no—
331C8×C61—42no—
332C8×C61—42no—
333#92418—42no—
334#92418—42no—
335#21742—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—24no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61C22×C22⋊C411yescharacteristic
347C22×C61#51812yes—
348C22×C61C22×M1611yescharacteristic
349C22×C61C22×M1611yescharacteristic
350C22×C61#56812yes—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—24no—
354C2×D61—24no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—24no—
360C2×D61—416no—
361C2×D61—416no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61#40714yes—
368C4×C61—22no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61#53412yes—
373C4×C61#53411yescharacteristic
374C4×C61#53411yescharacteristic
375Dic61—22no—
376Dic61—22no—
377Dic61—22no—
378Dic61—41no—
379Dic61—41no—
380C22×C4×D4—611no—
381C2×#407—611no—
382C2×#407—611no—
383#1870—612no—
384#1870—611no—
385#1870—612no—
386#1870—611no—
387#1870—611no—
388#1870D6111yescharacteristic, complemented
389#1817—612no—
390#1779—612no—
391C2×C61—42no—
392C2×C61—42no—
393C2×C61#230811yescharacteristic
394C2×C61C2×#40711yescharacteristic
395C2×C61#287911yescharacteristic
396C2×C61#297312yes—
397C2×C61#297512yes—
398D61—24no—
399D61—42no—
400D61—42no—
401C23×D4—611no—
402C24×C4—611no—
403C24×C4—611no—
404C22×M16—611no—
405C22×M16—612no—
406C22×M16C2×D6111yescharacteristic, complemented
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—1224no—
415C2×C4×D4—1224no—
416C2×C4×D4C2×D6111yescharacteristic
417C22×C4⋊C4—611no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4—611no—
420C22×C42—611no—
421#407—1224no—
422#407—1224no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—612no—
425C2×C22⋊C8—612no—
426C2×C22⋊C8—612no—
427C2×C22⋊C8—612no—
428C2×C22⋊C8—612no—
429C2×C22⋊C8—612no—
430C2×C22⋊C8C2×D6111yescharacteristic, complemented
431C2×C22⋊C8C2×D6112yescomplemented
432#336—612no—
433#336—612no—
434#336—612no—
435#336C2×D6112yescomplemented
436C61#2174211yescharacteristic, complemented, Sylow
437C25—611no—
438C25—611no—
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—611no—
442C22×D4—1224no—
443C22×D4—1224no—
444C22×D4—1224no—
445C22×D4C4×D6111yescharacteristic
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—614no—
453C23×C4—614no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—1222no—
460C23×C4—1222no—
461C23×C4—2442no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×M16—22no—
468C2×M16—42no—
469C2×M16—1224no—
470C2×M16—1222no—
471C2×M16—2442no—
472C2×M16—2442no—
473C2×M16—2442no—
474C22×C8—612no—
475C22×C8—612no—
476C22×C8C22×D6112yes—
477C22×C8C22×D6112yes—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1224no—
483C4×D4—1224no—
484C4×D4—1224no—
485C4×D4—1222no—
486C4×D4—1222no—
487C4×D4—1224no—
488C4×D4—1222no—
489C4×D4—1222no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1224no—
494C2×C4⋊C4C4×D6111yescharacteristic
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4C4×D6111yescharacteristic
504C2×C22⋊C4C4×D6111yescharacteristic
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—1222no—
509C2×C42—1222no—
510C2×C42C22×D6111yescharacteristic
511C22⋊C8—22no—
512C22⋊C8—42no—
513C22⋊C8—1224no—
514C22⋊C8—1224no—
515C22⋊C8—1224no—
516C22⋊C8—1222no—
517C22⋊C8—2442no—
518C22⋊C8—2442no—
519C22⋊C8—2442no—
520C24—611no—
521C24—611no—
522C24—611no—
523C24—614no—
524C24—614no—
525C24—1222no—
526C24—1222no—
527C24—1222no—
528C24—1222no—
529C24—2442no—
530C24—2442no—
531C24—2442no—
532C24—2442no—
533C24C2×C4×D6111yescharacteristic
534C24C2×C4×D6111yescharacteristic
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—12232no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—614no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—614no—
563C22×C4—614no—
564C22×C4—614no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—2448no—
582C22×C4—2444no—
583C22×C4—2444no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2448no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4D4×D6112yes—
599C22×C4D4×D6112yes—
600C22×C4C23×D6111yescharacteristic
601M16—44no—
602M16—2448no—
603M16—2444no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—1222no—
614C2×C8—1222no—
615C2×C8—1222no—
616C4⋊C4—22no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C42—21no—
629C42—21no—
630C42—1222no—
631C42—1222no—
632C42—1221no—
633C42—1221no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—612no—
643C23—612no—
644C23—612no—
645C23—612no—
646C23—612no—
647C23—1228no—
648C23—1228no—
649C23—1222no—
650C23—1222no—
651C23—1221no—
652C23—1222no—
653C23—1222no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—1222no—
658C23—1222no—
659C23—2444no—
660C23—2444no—
661C23—2448no—
662C23—2444no—
663C23—2448no—
664C23—2448no—
665C23—2444no—
666C23—2448no—
667C23C22⋊C4×D6112yes—
668C23M16×D6112yes—
669C23C22×C4×D6111yescharacteristic
670D4—28no—
671D4—1228no—
672D4—1228no—
673D4—1228no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—1228no—
691C2×C4—1221no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1221no—
695C2×C4—1224no—
696C2×C4—1224no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—2444no—
706C2×C4—2444no—
707C2×C4—2444no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—2442no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4C22⋊C4×D6112yes—
716C2×C4M16×D6112yes—
717C2×C4C2×D4×D6111yescharacteristic
718C2×C4C2×D4×D6111yescharacteristic
719C2×C4#1451982212yes—
720C2×C4#1451982312yes—
721C8—42no—
722C8—42no—
723C8—2442no—
724C8—2442no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—614no—
736C22—1224no—
737C22—1222no—
738C22—1222no—
739C22—1224no—
740C22—1222no—
741C22—1222no—
742C22—1222no—
743C22—1222no—
744C22—1224no—
745C22—24416no—
746C22—24416no—
747C22—2442no—
748C22—2442no—
749C22—2441no—
750C22—2441no—
751C22—2442no—
752C22C2×C22⋊C4×D6111yescharacteristic
753C22#1684023412yes—
754C22C2×M16×D6111yescharacteristic
755C22C2×M16×D6111yescharacteristic
756C22#1684052712yes—
757C4—22no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—1222no—
762C4—1222no—
763C4—1222no—
764C4—2441no—
765C4—2441no—
766C4#1684032012yes—
767C4#1684032211yescharacteristic
768C4#1684032311yescharacteristic
769C2—42no—
770C2—42no—
771C2—1224no—
772C2—2442no—
773C2—2442no—
774C2#2144839311yescharacteristic
775C2#407×D6111yescharacteristic
776C2#2145426111yescharacteristic
777C2#2145484412yes—
778C2#2145485712yes—
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC22×D4×D61C4
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#21742
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16839725C2semidirect
3. C2×#16839724C2semidirect
4. #21446117C2semidirect
5. #21446116C2semidirect
6. #21446115C2semidirect
7. #21446114C2semidirect
8. #21446113C2semidirect
9. #21445886C2semidirect
10. #21445728C2semidirect
11. C61×#1870C2semidirect
15. C22×#11758194C22semidirect
16. C22×#11758189C22semidirect
32. C2×C22⋊#92418C22semidirect
33. C2×C22⋊#92418C22semidirect
36. C2×#14519689C22semidirect
37. C2×#14519689C22semidirect
38. C2×#14519689C22semidirect
39. #16839517C22semidirect
40. #16839516C22semidirect
41. #16839516C22semidirect
42. C22×M16×C61C22semidirect
44. C2×C22⋊C8×C61C22semidirect
45. C2×C22⋊C8×C61C22semidirect
46. C61×#336C22semidirect
141. C23×D61M16semidirect
206. C2×C4×D61M16semidirect
388. #1870D61semidirect
406. C22×M16C2×D61semidirect
430. C2×C22⋊C8C2×D61semidirect
431. C2×C22⋊C8C2×D61semidirect
435. #336C2×D61semidirect
436. C61#21742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×#168397252
C2×#168397242
#214461172
#214461162
#214461152
#214461142
#214461132
#214458862
#214457282
C61×#18702
#2174261