Finite Group Databasebeta

← #29683765

Subgroups — #29683765

Order 15616.

1858 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840321C211yesmaximal, characteristic
2C22×#14519692C211yesmaximal, characteristic, complemented
3C22×#14519691C211yesmaximal, characteristic, complemented
4C22×#14519691C211yesmaximal, characteristic, complemented
5#21448431C211yesmaximal, characteristic, complemented
6#21448172C211yesmaximal, characteristic, complemented
7#21446653C218yesmaximal, complemented
8C22×#99×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10#16840321—22no—
11#16840321—22no—
12#16840321—22no—
13#16840321—22no—
14C2×#14519760C412yescomplemented
15C2×#14519758C412yescomplemented
16C2×#14519749C2214yes—
17C2×#14519746C412yescomplemented
18C2×#14519745C412yescomplemented
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C2×#14519692—24no—
23C2×#14519692C2214yescomplemented
24C2×#14519691—24no—
25C2×#14519691—24no—
26C2×#14519691C2214yescomplemented
27C2×#14519691C2214yescomplemented
28#16839635—22no—
29#16839634—22no—
30#16839620C2214yescomplemented
31C22⋊C4×Dic61—22no—
32C22⋊C4×Dic61C2214yescomplemented
33C4×C22⋊Dic61—22no—
34C23×D4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic
36C22×C22⋊C4×C61C2211yescharacteristic
37C2×#99×C61—24no—
38C2×#99×C61C2214yescomplemented
39C24×D61C2×C411yescharacteristic
40C22×C22⋊D61—22no—
41C22×C22⋊D61—22no—
42C22×C22⋊D61—21no—
43C22×C22⋊D61—21no—
44C22×C22⋊D61—21no—
45C22×C22⋊D61—21no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—22no—
48C22×C22⋊D61C2×C412yes—
49C22×C22⋊D61C2×C414yescomplemented
50C22×C22⋊D61C2312yes—
51C23×Dic61—21no—
52C23×Dic61—21no—
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2312yes—
55#14519760—24no—
56#14519760—24no—
57#14519758—24no—
58#14519758—24no—
59#14519749—28no—
60#14519749—28no—
61#14519746—24no—
62#14519746—24no—
63#14519745—24no—
64#14519745—24no—
65C2×#11758196—24no—
66C2×#11758196C2×C414yescomplemented
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—22no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61C2×C412yes—
73C2×C22⋊Dic61C2×C412yes—
74C2×C22⋊Dic61C2×C414yescomplemented
75C2×C22⋊Dic61D412yes—
76C2×C22⋊Dic61D412yes—
77C2×C22⋊Dic61D412yes—
78C2×C22⋊Dic61D412yes—
79C2×C22⋊Dic61D414yescomplemented
80C2×C22⋊Dic61C2312yes—
81C2×C22⋊Dic61C2312yes—
82C2×#11758198C2×C414yescomplemented
83C2×C4×Dic61—24no—
84#14519692—28no—
85#14519691—28no—
86#14519691—28no—
87#14519684—24no—
88#14519684—24no—
89C25×C61C2×C411yescharacteristic
90C25×C61C2311yescharacteristic
91C22×D4×C61—22no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—22no—
97C22×D4×C61—22no—
98C22×D4×C61—22no—
99C22×D4×C61C2×C412yes—
100C22×D4×C61C2312yes—
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103C23×C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61D414yescomplemented
110C2×C22⋊C4×C61C2312yes—
111C2×C22⋊C4×C61C2312yes—
112#99×C61—28no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—22no—
117C24×C61—82no—
118C24×C61—82no—
119C24×C61C22×C412yes—
120C24×C61C22×C411yescharacteristic
121C24×C61C22×C411yescharacteristic
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D411yescharacteristic
124C24×C61C2×D411yescharacteristic
125C24×C61C2×D411yescharacteristic
126C24×C61C2×D412yes—
127C24×C61C2×D412yes—
128C24×C61#4112yes—
129C24×C61#4112yes—
130C24×C61C2411yescharacteristic
131C23×D61—21no—
132C23×D61—21no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—82no—
136C23×D61C22×C412yes—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—24no—
140C2×D4×C61—24no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—42no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61—42no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—24no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61—82no—
164C22×C4×C61—82no—
165C22×C4×C61C22×C412yes—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—28no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61—84no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—24no—
192C22×Dic61—22no—
193C22×Dic61—42no—
194C22×Dic61—82no—
195C22×Dic61—82no—
196C22×Dic61—82no—
197C22×Dic61C22×C412yes—
198C22×Dic61C22×C414yes—
199C22×Dic61C2×D414yes—
200C22×Dic61C2×D414yes—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—42no—
206C22⋊C4×C61C2×D414yes—
207C22⋊Dic61—24no—
208C22⋊Dic61—22no—
209C22⋊Dic61—28no—
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212C22⋊Dic61—42no—
213C22⋊Dic61C22⋊C414yes—
214C22⋊Dic61C22⋊C414yes—
215C22⋊Dic61C22⋊C414yes—
216C22⋊Dic61C22⋊C414yes—
217C22⋊Dic61C2×D414yes—
218#11758198—28no—
219#11758196—28no—
220#11758196—84no—
221C4×Dic61—84no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—42no—
231C23×C61—42no—
232C23×C61—44no—
233C23×C61—42no—
234C23×C61—42no—
235C23×C61—82no—
236C23×C61—82no—
237C23×C61—82no—
238C23×C61—82no—
239C23×C61—82no—
240C23×C61—82no—
241C23×C61—84no—
242C23×C61—84no—
243C23×C61C2×C22⋊C411yescharacteristic
244C23×C61C2×C22⋊C411yescharacteristic
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C4×D412yes—
248C23×C61C4×D412yes—
249C23×C61C4×D412yes—
250C23×C61C4×D412yes—
251C23×C61#12112yes—
252C23×C61#12112yes—
253C23×C61#12112yes—
254C23×C61#12112yes—
255C23×C61#12412yes—
256C23×C61#12412yes—
257C23×C61#12712yes—
258C23×C61#12712yes—
259C23×C61C23×C411yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C23×C61C22×D411yescharacteristic
263C23×C61C22×D411yescharacteristic
264C23×C61C2×#4111yescharacteristic
265C23×C61C2×#4111yescharacteristic
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—44no—
272C22×D61—82no—
273C22×D61—82no—
274C22×D61—84no—
275C22×D61—84no—
276D4×C61—42no—
277D4×C61—42no—
278D4×C61—42no—
279D4×C61—42no—
280D4×C61—44no—
281D4×C61—44no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—44no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—44no—
290C2×C4×C61—42no—
291C2×C4×C61—84no—
292C2×C4×C61—84no—
293C22⋊D61—42no—
294C22⋊D61—42no—
295C22⋊D61—42no—
296C22⋊D61—42no—
297C22⋊D61—44no—
298C22⋊D61—44no—
299C22⋊D61—88no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—44no—
305C2×Dic61—44no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—44no—
311C2×Dic61—42no—
312C2×Dic61—84no—
313C2×Dic61—84no—
314C2×Dic61C2×C22⋊C418yes—
315#21213—611nomaximal, Sylow
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—44no—
340C22×C61—42no—
341C22×C61—82no—
342C22×C61—82no—
343C22×C61—84no—
344C22×C61—84no—
345C22×C61#39012yes—
346C22×C61#39012yes—
347C22×C61#39012yes—
348C22×C61#39012yes—
349C22×C61C22×C22⋊C411yescharacteristic
350C22×C61C2×C4×D411yescharacteristic
351C22×C61C2×C4×D411yescharacteristic
352C22×C61C2×#12111yescharacteristic
353C22×C61C2×#12111yescharacteristic
354C22×C61C2×#12411yescharacteristic
355C22×C61C2×#12711yescharacteristic
356C2×D61—44no—
357C2×D61—42no—
358C2×D61—84no—
359C2×D61—84no—
360C2×D61—82no—
361C2×D61—82no—
362C4×C61—44no—
363C4×C61—42no—
364C4×C61—82no—
365Dic61—28no—
366Dic61—44no—
367Dic61—42no—
368Dic61—82no—
369C2×#534—611no—
370C22×#99—611no—
371C22×#99—611no—
372C22×#99—611no—
373C22×#99D6111yescharacteristic, complemented
374#2315—611no—
375#2273—611no—
376#1964—618no—
377C2×C61—21no—
378C2×C61—21no—
379C2×C61—21no—
380C2×C61—21no—
381C2×C61—21no—
382C2×C61—22no—
383C2×C61—22no—
384C2×C61—22no—
385C2×C61—22no—
386C2×C61—21no—
387C2×C61—82no—
388C2×C61C2×#39011yescharacteristic
389C2×C61#288312yes—
390D61—82no—
391C23×D4—611no—
392C23×D4C2×D6111yescharacteristic
393#534—1222no—
394#534—1222no—
395#534—1222no—
396#534—1222no—
397C2×#123—612no—
398C2×#123—612no—
399C2×#121—614no—
400C2×#120—612no—
401C2×#120—612no—
402C22×C22⋊C4—611no—
403C22×C22⋊C4—611no—
404C22×C22⋊C4—611no—
405C22×C22⋊C4C2×D6111yescharacteristic
406C22×C22⋊C4C2×D6111yescharacteristic
407C2×#99—24no—
408C2×#99—614no—
409C2×#99—614no—
410C2×#99—614no—
411C2×#99—1224no—
412C2×#99—1224no—
413C2×#99—1224no—
414C2×#99C2×D6114yescomplemented
415#385—1222no—
416#385—1222no—
417#380—614no—
418C4×C22⋊C4—614no—
419C4×C22⋊C4—1222no—
420C4×C22⋊C4—1222no—
421C61#2121311yescharacteristic, complemented, Sylow
422C25—611no—
423C25C4×D6111yescharacteristic
424C25C22×D6111yescharacteristic
425C22×D4—22no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—612no—
434C22×D4—612no—
435C22×D4—614no—
436C22×D4—1222no—
437C22×D4—1221no—
438C22×D4—1221no—
439C22×D4—1221no—
440C22×D4—1221no—
441C22×D4—1222no—
442C22×D4—1222no—
443C22×D4—1222no—
444C22×D4C4×D6112yes—
445C22×D4C22×D6112yes—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—612no—
449C23×C4—611no—
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4C4×D6111yescharacteristic
453#123—1224no—
454#123—1224no—
455#123—1224no—
456#123—1224no—
457#121—1228no—
458#121—1228no—
459#120—1224no—
460#120—1224no—
461#120—1224no—
462#120—1224no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—1224no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—612no—
471C2×C22⋊C4—612no—
472C2×C22⋊C4—612no—
473C2×C22⋊C4—612no—
474C2×C22⋊C4—612no—
475C2×C22⋊C4—612no—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—612no—
478C2×C22⋊C4—614no—
479C2×C22⋊C4—614no—
480C2×C22⋊C4—612no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1222no—
484C2×C22⋊C4—1222no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4C22⋊D6114yescomplemented
487C2×C22⋊C4C22×D6112yes—
488C2×C22⋊C4C22×D6112yes—
489C2×C42—1224no—
490#99—28no—
491#99—1228no—
492#99—1228no—
493#99—1228no—
494#95—1224no—
495#95—1224no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—82no—
501C24—82no—
502C24—612no—
503C24—1221no—
504C24—1221no—
505C24—1222no—
506C24—1222no—
507C24—4882no—
508C24C2×C4×D6112yes—
509C24C2×C4×D6111yescharacteristic
510C24C2×C4×D6111yescharacteristic
511C24#1175822212yes—
512C24D4×D6111yescharacteristic
513C24D4×D6111yescharacteristic
514C24D4×D6111yescharacteristic
515C24D4×D6111yescharacteristic
516C24D4×D6112yes—
517C24#1175822412yes—
518C24C2×C22⋊D6112yes—
519C24C23×D6111yescharacteristic
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—1228no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1224no—
548C2×D4—1224no—
549C2×D4—4884no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4—2442no—
555C2×D4—2442no—
556C2×D4—2442no—
557C2×D4—2442no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—42no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—614no—
569C22×C4—614no—
570C22×C4—614no—
571C22×C4—612no—
572C22×C4—1224no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—4882no—
580C22×C4—4882no—
581C22×C4—4882no—
582C22×C4—2442no—
583C22×C4C2×C4×D6112yes—
584C4⋊C4—1228no—
585C4⋊C4—4884no—
586C22⋊C4—22no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—42no—
591C22⋊C4—614no—
592C22⋊C4—614no—
593C22⋊C4—614no—
594C22⋊C4—614no—
595C22⋊C4—614no—
596C22⋊C4—1228no—
597C22⋊C4—1228no—
598C22⋊C4—1222no—
599C22⋊C4—1224no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—2442no—
603C22⋊C4C2×C22⋊D6114yes—
604C42—4884no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—44no—
616C23—42no—
617C23—42no—
618C23—82no—
619C23—82no—
620C23—82no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—84no—
625C23—84no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—4882no—
630C23—4882no—
631C23—4884no—
632C23—4884no—
633C23—2444no—
634C23—2442no—
635C23—2442no—
636C23C22⋊C4×D6111yescharacteristic
637C23C22⋊C4×D6111yescharacteristic
638C23C22⋊C4×D6111yescharacteristic
639C23C22⋊C4×D6111yescharacteristic
640C23#1451973712yes—
641C23#1451973712yes—
642C23C4×C22⋊D6112yes—
643C23C4×C22⋊D6112yes—
644C23#1451974912yes—
645C23#1451974912yes—
646C23#1451975012yes—
647C23#1451975012yes—
648C23#1451976312yes—
649C23#1451976312yes—
650C23#1451977312yes—
651C23#1451977312yes—
652C23C22×C4×D6111yescharacteristic
653C23C2×D4×D6111yescharacteristic
654C23C2×D4×D6111yescharacteristic
655C23C2×D4×D6111yescharacteristic
656C23C22×C22⋊D6111yescharacteristic
657C23C2×#1175822411yescharacteristic
658C23C2×#1175822211yescharacteristic
659D4—42no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—44no—
664D4—44no—
665D4—4888no—
666D4—2442no—
667D4—2442no—
668D4—2442no—
669D4—2442no—
670D4—2444no—
671D4—2444no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—44no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—618no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—4884no—
689C2×C4—4884no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4—2442no—
695C2×C4—2444no—
696C2×C4—2442no—
697C2×C4—2442no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—82no—
724C22—82no—
725C22—84no—
726C22—84no—
727C22—4882no—
728C22—4882no—
729C22—4884no—
730C22—4884no—
731C22—2442no—
732C22—2444no—
733C22#1683966212yes—
734C22#1683966212yes—
735C22#1683966212yes—
736C22#1683966212yes—
737C22C2×C22⋊C4×D6111yescharacteristic
738C22C2×#1451973711yescharacteristic
739C22C2×C4×C22⋊D6111yescharacteristic
740C22C2×#1451974911yescharacteristic
741C22C2×#1451975011yescharacteristic
742C22C2×#1451976311yescharacteristic
743C22C2×#1451977311yescharacteristic
744C4—44no—
745C4—42no—
746C4—82no—
747C4—1228no—
748C4—4882no—
749C4—2444no—
750C4—2442no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—22no—
760C2—21no—
761C2—82no—
762C2—4882no—
763C2C2×#1683966211yescharacteristic
764C2#2145427712yes—
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC22×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840321C2
cosocleC24×C61C24
hypercenterC22×#99D61
hypocenterC61#21213
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C22×#14519692C2semidirect
3. C22×#14519691C2semidirect
4. C22×#14519691C2semidirect
5. #21448431C2semidirect
6. #21448172C2semidirect
7. #21446653C2semidirect
8. C22×#99×C61C2semidirect
14. C2×#14519760C4semidirect
15. C2×#14519758C4semidirect
17. C2×#14519746C4semidirect
18. C2×#14519745C4semidirect
23. C2×#14519692C22semidirect
26. C2×#14519691C22semidirect
27. C2×#14519691C22semidirect
30. #16839620C22semidirect
32. C22⋊C4×Dic61C22semidirect
38. C2×#99×C61C22semidirect
49. C22×C22⋊D61C2×C4semidirect
66. C2×#11758196C2×C4semidirect
74. C2×C22⋊Dic61C2×C4semidirect
79. C2×C22⋊Dic61D4semidirect
82. C2×#11758198C2×C4semidirect
109. C2×C22⋊C4×C61D4semidirect
373. C22×#99D61semidirect
414. C2×#99C2×D61semidirect
421. C61#21213semidirect
486. C2×C22⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403212
C22×#145196922
C22×#145196912
#214484312
#214481722
#214466532
C22×#99×C612
#2121361