Finite Group Databasebeta

← #29685366

Subgroups — #29685366

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840345C211yesmaximal, characteristic
2#21448414C211yesmaximal, characteristic, complemented
3#21448171C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446271C212yesmaximal, complemented
7#21446269C212yesmaximal, complemented
8C4×#14519691C211yesmaximal, characteristic, complemented
9C4×#14519691C211yesmaximal, characteristic, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C4×#99×C61C211yesmaximal, characteristic, complemented
12#16840345—22no—
13#16840345—22no—
14#16840345—22no—
15#16840345—22no—
16C2×#14519772C411yescharacteristic, complemented
17C2×#14519771C411yescharacteristic, complemented
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519763C411yescharacteristic, complemented
20C2×#14519762C411yescharacteristic, complemented
21C2×#14519760C411yescharacteristic, complemented
22C2×#14519754C2211yescharacteristic
23C2×#14519751C411yescharacteristic, complemented
24C2×#14519750C411yescharacteristic, complemented
25C2×#14519749C2211yescharacteristic
26C2×#14519747C2211yescharacteristic
27C2×#14519745C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C2×C22⋊C4×D61C2212yes—
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839653—22no—
35#16839651—22no—
36#16839620C2212yes—
37#16839617C2212yes—
38C22⋊C4×Dic61C2212yes—
39C4×#11758198—22no—
40C4×C22⋊Dic61C2211yescharacteristic
41C4×C22⋊Dic61C2211yescharacteristic
42#16839609—22no—
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2212yes—
48C4×C22⋊C4×C61C2211yescharacteristic
49C4×C22⋊C4×C61C2211yescharacteristic
50C61×#342C2212yes—
51C24×D61C2311yescharacteristic
52C22×Dic122C2×C411yescharacteristic, complemented
53C22×D244C2×C411yescharacteristic
54C22×D244C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic, complemented
58C22×C22⋊D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—22no—
61C22×C4×D61C2×C411yescharacteristic, complemented
62#14519772—22no—
63#14519772—22no—
64#14519771—22no—
65#14519771—22no—
66#14519765—22no—
67#14519765—22no—
68#14519763—22no—
69#14519763—22no—
70#14519762—22no—
71#14519762—22no—
72#14519760—22no—
73#14519760—22no—
74#14519754—22no—
75#14519754—22no—
76#14519751—22no—
77#14519751—22no—
78#14519750—22no—
79#14519750—22no—
80#14519749—22no—
81#14519749—22no—
82#14519747—22no—
83#14519747—22no—
84#14519745—22no—
85#14519745—22no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C2×C4⋊Dic61C2×C411yescharacteristic, complemented
91C2×#11758196—22no—
92C2×#11758196C2×C411yescharacteristic, complemented
93C2×#11758196C2×C411yescharacteristic, complemented
94C2×#11758196C2×C411yescharacteristic, complemented
95C2×#11758196C2×C411yescharacteristic, complemented
96C2×C22⋊Dic61C2×C411yescharacteristic, complemented
97C2×C22⋊Dic61C2312yes—
98C2×C22⋊Dic61C2311yescharacteristic
99C2×C22⋊Dic61C2312yes—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic, complemented
112C2×#11758198C2×C411yescharacteristic, complemented
113C2×#11758198D412yes—
114C2×#11758198D412yes—
115C2×#11758198D412yes—
116C2×#11758198D412yes—
117C22⋊C4×D61—24no—
118C22⋊C4×D61—24no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2×C411yescharacteristic, complemented
123#14519692—24no—
124#14519691—24no—
125#14519691—24no—
126#14519684—21no—
127#14519684—21no—
128#14519684—22no—
129#14519684—22no—
130C22×D4×C61C2311yescharacteristic
131C23×C4×C61C2×C411yescharacteristic, complemented
132C23×C4×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
138C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61C2312yes—
142C2×C42×C61—21no—
143C2×C42×C61—21no—
144C2×C42×C61C2×C411yescharacteristic, complemented
145#99×C61—24no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61C22×C411yescharacteristic
149C24×C61C2411yescharacteristic
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—81no—
153C23×D61—81no—
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C411yescharacteristic
156C23×D61C22×C411yescharacteristic
157C23×D61C2×D412yes—
158C23×D61C2×D412yes—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—22no—
167C22×C4×C61—81no—
168C22×C4×C61—81no—
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—22no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—81no—
186C2×C22⋊D61—81no—
187C2×C22⋊D61—81no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—81no—
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C22×Dic61C22×C411yescharacteristic
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C2×D412yes—
197C22×Dic61C2×D412yes—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—81no—
201C2×D244—81no—
202C2×C4×D61—28no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—82no—
206C2×C4×D61—82no—
207C2×C4×D61—81no—
208C2×Dic122—22no—
209C2×Dic122—81no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C22⋊C4×C61—21no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—21no—
216C22⋊C4×C61—21no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61#4114yes—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—81no—
223C42×C61—81no—
224C22⋊Dic61—21no—
225C22⋊Dic61—21no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61#4114yes—
231#11758198—28no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—21no—
237#11758198—21no—
238#11758198—22no—
239#11758198—82no—
240#11758198—82no—
241#11758198C22⋊C412yes—
242#11758198C22⋊C412yes—
243#11758198C22⋊C412yes—
244#11758198C22⋊C412yes—
245#11758198C22⋊C412yes—
246#11758198C22⋊C412yes—
247#11758198C22⋊C412yes—
248#11758198C22⋊C412yes—
249C4⋊Dic61—22no—
250#11758196—21no—
251#11758196—21no—
252#11758196—22no—
253#11758196—22no—
254#11758196—22no—
255#11758196—82no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—82no—
259C4×Dic61—81no—
260C4×Dic61—81no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61C23×C411yescharacteristic
269C23×C61C22×D411yescharacteristic
270C23×C61C22×D411yescharacteristic
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—24no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—84no—
294C22×D61—84no—
295C22×D61C2×C22⋊C412yes—
296C22×D61C2×C22⋊C412yes—
297D4×C61—42no—
298D4×C61—42no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—24no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—81no—
319C2×C4×C61—81no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—82no—
327C22⋊D61—82no—
328C22⋊D61—82no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—24no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61C2×C22⋊C412yes—
347C2×Dic61C2×C22⋊C412yes—
348D244—82no—
349D244—82no—
350C4×D61—81no—
351C4×D61—81no—
352C4×D61—88no—
353Dic122—82no—
354#21422—611nomaximal, Sylow
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61C4×#4111yescharacteristic
370C22×C61C4×#4111yescharacteristic
371C22×C61#52512yes—
372C22×C61#53212yes—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—84no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61—81no—
389C2×D61—81no—
390C2×D61—81no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—44no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—82no—
400Dic61—22no—
401Dic61—22no—
402Dic61—44no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61—82no—
407C2×#538—611no—
408#2312—611no—
409#2273—611no—
410#1996—612no—
411#1964—612no—
412#1898—612no—
413#1898—612no—
414C4×#99—611no—
415C4×#99—611no—
416C4×#99—611no—
417C4×#99D6111yescharacteristic, complemented
418C2×C61—22no—
419C2×C61—22no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—81no—
423C2×C61#229711yescharacteristic
424C2×C61#288311yescharacteristic
425C2×C61#288311yescharacteristic
426D61—42no—
427D61—42no—
428D61—81no—
429#538—1222no—
430#538—1222no—
431#538—1222no—
432#538—1222no—
433C2×#126—611no—
434C2×#126—611no—
435C2×#124—611no—
436C2×#124—611no—
437C2×#123—611no—
438C2×#123—611no—
439C2×C22⋊Q8—611no—
440C2×#121—611no—
441C2×#121—611no—
442C2×#121—611no—
443C2×#120—611no—
444C2×#120—611no—
445C2×C4×D4—611no—
446C2×C4×D4C2×D6111yescharacteristic
447C22×C22⋊C4—611no—
448C22×C22⋊C4—612no—
449C2×#99—612no—
450C2×#99—612no—
451C2×#99—612no—
452C2×#99C2×D6112yes—
453#388—1222no—
454#388—1222no—
455#380—612no—
456#379—612no—
457C4×C22⋊C4—611no—
458C4×C22⋊C4—611no—
459C4×C22⋊C4—612no—
460C4×C22⋊C4—1222no—
461C4×C22⋊C4—1222no—
462C4×C22⋊C4C2×D6111yescharacteristic
463C4×C22⋊C4C2×D6111yescharacteristic
464#342—612no—
465#342—612no—
466#342—612no—
467#342C2×D6112yes—
468C61#2142211yescharacteristic, complemented, Sylow
469C25—611no—
470C22×Q8—611no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—611no—
474C22×D4—611no—
475C22×D4—611no—
476C22×D4—611no—
477C22×D4C22×D6111yescharacteristic
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—1222no—
481C23×C4C4×D6111yescharacteristic, complemented
482C23×C4C22×D6111yescharacteristic
483#126—1222no—
484#126—1222no—
485#126—1222no—
486#126—1222no—
487#124—1222no—
488#124—1222no—
489#124—1222no—
490#124—1222no—
491#123—1222no—
492#123—1222no—
493#123—1222no—
494#123—1222no—
495C22⋊Q8—1222no—
496C22⋊Q8—1222no—
497#121—1222no—
498#121—1222no—
499#121—1222no—
500#121—1222no—
501#121—1222no—
502#121—1222no—
503#120—1222no—
504#120—1222no—
505#120—1222no—
506#120—1222no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—1221no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1221no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4C4×D6111yescharacteristic, complemented
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—612no—
527C2×C22⋊C4—612no—
528C2×C22⋊C4—612no—
529C2×C22⋊C4—612no—
530C2×C22⋊C4—612no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—611no—
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—612no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4—1222no—
542C2×C22⋊C4—1224no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1222no—
545C2×C22⋊C4C4×D6111yescharacteristic, complemented
546C2×C22⋊C4C22×D6112yes—
547C2×C22⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4C22×D6112yes—
549C2×C42—21no—
550C2×C42—21no—
551C2×C42—611no—
552C2×C42—1222no—
553C2×C42—1221no—
554C2×C42—1221no—
555C2×C42C4×D6111yescharacteristic, complemented
556#99—24no—
557#99—1224no—
558#99—1224no—
559#99—1224no—
560#95—21no—
561#95—21no—
562#95—1222no—
563#95—1222no—
564#95—1221no—
565#95—1221no—
566C24—611no—
567C24—611no—
568C24—612no—
569C24—612no—
570C24—611no—
571C24—1222no—
572C24—1222no—
573C24—4881no—
574C24—4881no—
575C24C2×C4×D6111yescharacteristic
576C24C23×D6111yescharacteristic
577C2×Q8—1222no—
578C2×Q8—4881no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—4881no—
593C2×D4—4881no—
594C2×D4—4881no—
595C2×D4—4881no—
596C2×D4—4881no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—1228no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1222no—
615C22×C4—4882no—
616C22×C4—4882no—
617C22×C4—4881no—
618C22×C4—4881no—
619C22×C4C2×C4×D6111yescharacteristic
620C22×C4C2×C4×D6111yescharacteristic
621C22×C4C2×C4×D6111yescharacteristic
622C22×C4C2×C4×D6111yescharacteristic
623C22×C4C2×C4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—4882no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—612no—
645C22⋊C4—612no—
646C22⋊C4—612no—
647C22⋊C4—612no—
648C22⋊C4—612no—
649C22⋊C4—612no—
650C22⋊C4—612no—
651C22⋊C4—612no—
652C22⋊C4—614no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1228no—
659C22⋊C4—1222no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1222no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1222no—
666C22⋊C4—1222no—
667C22⋊C4—4882no—
668C22⋊C4—4882no—
669C22⋊C4#1175822214yes—
670C42—21no—
671C42—21no—
672C42—81no—
673C42—81no—
674C42—1221no—
675C42—1221no—
676C42—4881no—
677C42—4881no—
678C42—4882no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—612no—
687C23—612no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1224no—
693C23—1222no—
694C23—1222no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—4884no—
699C23—4884no—
700C23—2442no—
701C23—2442no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2442no—
707C23—2442no—
708C23—2441no—
709C23—2441no—
710C23C22×C4×D6111yescharacteristic
711C23C2×D4×D6111yescharacteristic
712C23C2×D4×D6111yescharacteristic
713C23#41×D6112yes—
714C23C2×#1175822212yes—
715Q8—4882no—
716D4—42no—
717D4—42no—
718D4—4882no—
719D4—4882no—
720D4—4882no—
721D4—4882no—
722D4—4882no—
723D4—2442no—
724D4—2442no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1224no—
754C2×C4—4881no—
755C2×C4—4881no—
756C2×C4—4888no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2442no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4C22⋊C4×D6111yescharacteristic
769C2×C4C22⋊C4×D6111yescharacteristic
770C2×C4C22⋊C4×D6111yescharacteristic
771C2×C4C22⋊C4×D6111yescharacteristic
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—81no—
784C22—81no—
785C22—1222no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—1222no—
790C22—1222no—
791C22—4881no—
792C22—4881no—
793C22—4884no—
794C22—4881no—
795C22—4881no—
796C22—4881no—
797C22—4881no—
798C22—2444no—
799C22—2444no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22C2×C22⋊C4×D6111yescharacteristic
804C22#1684023011yescharacteristic
805C22C4×#1175822211yescharacteristic
806C22#1684027112yes—
807C22#1684030912yes—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—44no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—1222no—
818C4—1222no—
819C4—4882no—
820C4—2444no—
821C4—2441no—
822C4—2441no—
823C4—2441no—
824C2—22no—
825C2—22no—
826C2—21no—
827C2—21no—
828C2—81no—
829C2—4881no—
830C2—2442no—
831C2—2442no—
832C2#2144830511yescharacteristic
833C2#2145427711yescharacteristic
834C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840345C2
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#21422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448414C2semidirect
3. #21448171C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446271C2semidirect
7. #21446269C2semidirect
8. C4×#14519691C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C4×#99×C61C2semidirect
16. C2×#14519772C4semidirect
17. C2×#14519771C4semidirect
18. C2×#14519765C4semidirect
19. C2×#14519763C4semidirect
20. C2×#14519762C4semidirect
21. C2×#14519760C4semidirect
23. C2×#14519751C4semidirect
24. C2×#14519750C4semidirect
52. C22×Dic122C2×C4semidirect
57. C22×C22⋊D61C2×C4semidirect
61. C22×C4×D61C2×C4semidirect
90. C2×C4⋊Dic61C2×C4semidirect
92. C2×#11758196C2×C4semidirect
93. C2×#11758196C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
96. C2×C22⋊Dic61C2×C4semidirect
111. C2×#11758198C2×C4semidirect
112. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
131. C23×C4×C61C2×C4semidirect
137. C2×C4⋊C4×C61C2×C4semidirect
138. C2×C22⋊C4×C61C2×C4semidirect
144. C2×C42×C61C2×C4semidirect
417. C4×#99D61semidirect
468. C61#21422semidirect
481. C23×C4C4×D61semidirect
521. C2×C4⋊C4C4×D61semidirect
545. C2×C22⋊C4C4×D61semidirect
555. C2×C42C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403452
#214484142
#214481712
#214468022
#214466532
#214462712
#214462692
C4×#145196912
C4×#145196922
C4×#99×C612
#2142261