Finite Group Databasebeta

← #29685358

Subgroups — #29685358

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840289C211yesmaximal, characteristic
2#21448210C211yesmaximal, characteristic, complemented
3#117×Dic61C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446278C211yesmaximal, characteristic, complemented
7#21446277C211yesmaximal, characteristic, complemented
8#21446275C211yesmaximal, characteristic, complemented
9#99×Dic61C212yesmaximal, complemented
10#21445606C212yesmaximal, complemented
11C61×#1899C211yesmaximal, characteristic, complemented
12#16840289—21no—
13#16840289—21no—
14#16840289—21no—
15#16840289—21no—
16#16840289—21no—
17#16840289—21no—
18#16840289—21no—
19#16840289—21no—
20C2×#14519772C411yescharacteristic, complemented
21C2×#14519770C411yescharacteristic, complemented
22C2×#14519767C411yescharacteristic, complemented
23C2×#14519763C411yescharacteristic, complemented
24C2×#14519760C2211yescharacteristic
25C2×#14519754C2211yescharacteristic
26C2×#14519749C2211yescharacteristic
27C2×#14519742C411yescharacteristic, complemented
28C2×D4×Dic61C2211yescharacteristic
29C2×#14519737C411yescharacteristic, complemented
30C2×#14519737C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519735C411yescharacteristic, complemented
33C2×#14519733C411yescharacteristic, complemented
34C22×C4×Dic61C2211yescharacteristic
35C2×#14519692C2212yes—
36C2×#14519691C2212yes—
37C2×#14519691C2212yes—
38#16839629—21no—
39#16839626—21no—
40#16839625C2211yescharacteristic
41#16839620C2212yes—
42C4⋊C4×Dic61—21no—
43C4⋊C4×Dic61—21no—
44#16839613—21no—
45C22⋊C4×Dic61C2212yes—
46C22⋊C4×Dic61C2212yes—
47C22⋊C4×Dic61C2212yes—
48#16839608—21no—
49#16839607—21no—
50C42×Dic61—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×#123×C61C2211yescharacteristic
55C2×#117×C61C2211yescharacteristic
56C2×#99×C61C2212yes—
57C61×#381C2211yescharacteristic
58C61×#342C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2311yescharacteristic
62C23×Dic61C2×C411yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66#14519772—21no—
67#14519772—21no—
68#14519772—21no—
69#14519772—21no—
70#14519770—21no—
71#14519770—21no—
72#14519770—21no—
73#14519770—21no—
74#14519767—21no—
75#14519767—21no—
76#14519767—21no—
77#14519767—21no—
78#14519763—21no—
79#14519763—21no—
80#14519763—21no—
81#14519763—21no—
82#14519760—21no—
83#14519760—21no—
84#14519760—21no—
85#14519760—21no—
86#14519754—21no—
87#14519754—21no—
88#14519754—21no—
89#14519754—21no—
90#14519749—21no—
91#14519749—21no—
92#14519749—21no—
93#14519749—21no—
94#14519742—21no—
95#14519742—21no—
96#14519742—21no—
97#14519742—21no—
98D4×Dic61—21no—
99D4×Dic61—21no—
100D4×Dic61—21no—
101D4×Dic61—21no—
102#14519737—21no—
103#14519737—21no—
104#14519737—21no—
105#14519737—21no—
106#14519737—21no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519736—24no—
111#14519735—21no—
112#14519735—21no—
113#14519735—21no—
114#14519735—21no—
115#14519733—21no—
116#14519733—21no—
117#14519733—21no—
118#14519733—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196—22no—
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2312yes—
132C2×C22⋊Dic61C2311yescharacteristic
133C2×C22⋊Dic61C2312yes—
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×C4×Dic61—21no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61C2×C411yescharacteristic
147C2×C4×Dic61C2×C411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C2×C4×Dic61D411yescharacteristic
150C2×C4×Dic61D411yescharacteristic
151C2×C4×Dic61D411yescharacteristic
152C2×C4×Dic61D411yescharacteristic
153C2×C4×Dic61D411yescharacteristic
154C2×C4×Dic61D411yescharacteristic
155C2×C4×Dic61D411yescharacteristic
156#14519692—24no—
157#14519691—24no—
158#14519691—24no—
159#14519684—21no—
160#14519684—21no—
161#14519684—22no—
162#14519684—22no—
163#14519684—22no—
164#14519684—22no—
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167#123×C61—21no—
168#123×C61—21no—
169#123×C61—21no—
170#123×C61—21no—
171#117×C61—24no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2×C411yescharacteristic
174C2×C4⋊C4×C61C2×C411yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2312yes—
178C2×C22⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61C2312yes—
180C2×C42×C61—21no—
181#99×C61—24no—
182#95×C61—21no—
183#95×C61—21no—
184C24×C61C22×C411yescharacteristic
185C24×C61C2411yescharacteristic
186C23×D61C22×C411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—42no—
211C22×Dic61—22no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61—42no—
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—42no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—42no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61#4114yes—
254C42×C61—24no—
255C22⋊Dic61—21no—
256C22⋊Dic61—21no—
257C22⋊Dic61—22no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—22no—
263C22⋊Dic61—22no—
264C22⋊Dic61#4114yes—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273C4⋊Dic61—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—44no—
291C4×Dic61—24no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—44no—
297C4×Dic61—44no—
298C4×Dic61—44no—
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22⋊C411yescharacteristic
304C4×Dic61C22⋊C411yescharacteristic
305C4×Dic61C22⋊C411yescharacteristic
306C4×Dic61C22⋊C411yescharacteristic
307C4×Dic61C22⋊C411yescharacteristic
308C4×Dic61C22⋊C411yescharacteristic
309C4×Dic61C22⋊C411yescharacteristic
310C4×Dic61C22⋊C411yescharacteristic
311C4×Dic61C22⋊C411yescharacteristic
312C4×Dic61C22⋊C411yescharacteristic
313C4×Dic61C22⋊C411yescharacteristic
314C4×Dic61C22⋊C411yescharacteristic
315C23×C61—21no—
316C23×C61—22no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61C23×C411yescharacteristic
322C23×C61C22×D411yescharacteristic
323C23×C61C22×D411yescharacteristic
324C23×C61C2×#4112yes—
325C23×C61C2×#4112yes—
326C22×D61—21no—
327C22×D61—22no—
328C22×D61—41no—
329C22×D61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—42no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—24no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C22⋊D61—42no—
358C22⋊D61—41no—
359C22⋊D61—41no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—22no—
372C2×Dic61—24no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—42no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—42no—
386C2×Dic61—42no—
387C2×Dic61—42no—
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C4×D61—42no—
397C4×D61—42no—
398Dic122—42no—
399Dic122—42no—
400#21421—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—82no—
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61C4×#4112yes—
415C22×C61#52511yescharacteristic
416C22×C61#52511yescharacteristic
417C22×C61#53212yes—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—82no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—44no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—82no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—44no—
438Dic61—41no—
439Dic61—41no—
440Dic61—41no—
441Dic61—82no—
442Dic61#41012yes—
443Dic61#41012yes—
444C2×#529—611no—
445#2283—611no—
446C4×#117—611no—
447#1996—612no—
448#1964—612no—
449#1899—611no—
450#1899—611no—
451#1899—611no—
452#1899D6111yescharacteristic, complemented
453C4×#99—612no—
454C4×#99—612no—
455C2×C61—21no—
456C2×C61—22no—
457C2×C61—21no—
458C2×C61—22no—
459C2×C61—81no—
460C2×C61#229711yescharacteristic
461C2×C61C2×#41011yescharacteristic
462C2×C61C2×#41011yescharacteristic
463D61—81no—
464#529—1221no—
465#529—1221no—
466#529—1221no—
467#529—1221no—
468#529—1221no—
469#529—1221no—
470#529—1221no—
471#529—1221no—
472C2×#126—611no—
473C2×#126—611no—
474C2×#125—611no—
475C2×#124—611no—
476C2×#123—611no—
477C2×#123C2×D6111yescharacteristic
478C2×C22⋊Q8—611no—
479C2×#121—611no—
480C2×C4×Q8—611no—
481C2×C4×D4—611no—
482C2×C4×D4—611no—
483C2×C4×D4—611no—
484C2×#117—611no—
485C2×#117—611no—
486C2×#117—611no—
487C2×#117C2×D6111yescharacteristic
488C22×C42—611no—
489C2×#99—612no—
490C2×#99—612no—
491C2×#99—612no—
492C2×#99C2×D6112yes—
493#383—1221no—
494#382—1221no—
495#381—611no—
496#381C2×D6111yescharacteristic
497#380—612no—
498C4×C4⋊C4—1221no—
499C4×C4⋊C4—1221no—
500C4×C4⋊C4—1221no—
501C4×C22⋊C4—612no—
502C4×C22⋊C4—612no—
503C4×C22⋊C4—612no—
504#376—1221no—
505#376—1221no—
506C43—1221no—
507#342—612no—
508#342—612no—
509#342—612no—
510#342C2×D6112yes—
511C61#2142111yescharacteristic, complemented, Sylow
512C22×Q8—611no—
513C22×D4—611no—
514C22×D4—611no—
515C22×D4C22×D6111yescharacteristic
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4—611no—
520C23×C4C22×D6111yescharacteristic
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#126—1221no—
527#126—1221no—
528#126—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#124—1221no—
534#124—1221no—
535#124—1221no—
536#124—1221no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549#121—1221no—
550#121—1221no—
551#121—1221no—
552#121—1221no—
553C4×Q8—1221no—
554C4×Q8—1221no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569#117—24no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117—1221no—
575#117—1221no—
576#117—1221no—
577#117—1221no—
578#117—1224no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4C4×D6111yescharacteristic
591C2×C4⋊C4C4×D6111yescharacteristic
592C2×C22⋊C4—612no—
593C2×C22⋊C4—611no—
594C2×C22⋊C4—611no—
595C2×C22⋊C4—611no—
596C2×C22⋊C4—611no—
597C2×C22⋊C4—611no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—612no—
601C2×C22⋊C4C4×D6111yescharacteristic
602C2×C22⋊C4C4×D6111yescharacteristic
603C2×C22⋊C4C22×D6112yes—
604C2×C22⋊C4C22×D6111yescharacteristic
605C2×C22⋊C4C22×D6112yes—
606C2×C42—21no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—1221no—
622C2×C42—1222no—
623C2×C42—1222no—
624C2×C42—1222no—
625#99—24no—
626#99—1224no—
627#99—1224no—
628#99—1224no—
629#95—21no—
630#95—21no—
631#95—1222no—
632#95—1222no—
633#95—1222no—
634#95—1222no—
635#95—1221no—
636#95—1221no—
637C24—611no—
638C24C2×C4×D6111yescharacteristic
639C24C23×D6111yescharacteristic
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—2442no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1222no—
652C2×D4—1222no—
653C2×D4—2442no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4C2×C4×D6111yescharacteristic
684C22×C4C2×C4×D6111yescharacteristic
685C22×C4C2×C4×D6111yescharacteristic
686C22×C4C2×C4×D6111yescharacteristic
687C22×C4C2×C4×D6111yescharacteristic
688C22×C4D4×D6111yescharacteristic
689C22×C4D4×D6111yescharacteristic
690C22×C4D4×D6111yescharacteristic
691C22×C4D4×D6111yescharacteristic
692C4⋊C4—24no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1224no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—2444no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—22no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—614no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1222no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4#1175822414yes—
743C42—24no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1224no—
765C42—2444no—
766C42—2444no—
767C42—2444no—
768C23—21no—
769C23—22no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—1222no—
775C23—1221no—
776C23—2441no—
777C23—2441no—
778C23C22×C4×D6111yescharacteristic
779C23C2×D4×D6111yescharacteristic
780C23C2×D4×D6111yescharacteristic
781C23#41×D6112yes—
782C23C2×#1175822412yes—
783Q8—2442no—
784Q8—2442no—
785D4—41no—
786D4—41no—
787D4—42no—
788D4—2442no—
789D4—2442no—
790D4—2441no—
791D4—2441no—
792D4—2442no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1222no—
831C2×C4—1224no—
832C2×C4—2442no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2442no—
844C2×C4—2442no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4C22⋊C4×D6111yescharacteristic
850C2×C4C22⋊C4×D6111yescharacteristic
851C2×C4C22⋊C4×D6111yescharacteristic
852C2×C4C22⋊C4×D6111yescharacteristic
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—82no—
865C22—4882no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C2×C22⋊C4×D6111yescharacteristic
870C22C4×#1175822412yes—
871C22#1684026811yescharacteristic
872C22#1684027011yescharacteristic
873C22#1684030712yes—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—44no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—82no—
883C4—612no—
884C4—612no—
885C4—1221no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—1221no—
890C4—1221no—
891C4—4882no—
892C4—2444no—
893C4—2441no—
894C4—2441no—
895C4—2441no—
896C2—21no—
897C2—22no—
898C2—21no—
899C2—22no—
900C2—81no—
901C2—4881no—
902C2#2144830411yescharacteristic
903C2#410×D6111yescharacteristic
904C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1899C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenter#1899D61
hypocenterC61#21421
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. #21448210C2semidirect
3. #117×Dic61C2semidirect
4. #21446802C2semidirect
6. #21446278C2semidirect
7. #21446277C2semidirect
8. #21446275C2semidirect
9. #99×Dic61C2semidirect
10. #21445606C2semidirect
11. C61×#1899C2semidirect
20. C2×#14519772C4semidirect
21. C2×#14519770C4semidirect
22. C2×#14519767C4semidirect
23. C2×#14519763C4semidirect
27. C2×#14519742C4semidirect
29. C2×#14519737C4semidirect
32. C2×#14519735C4semidirect
33. C2×#14519733C4semidirect
452. #1899D61semidirect
511. C61#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#168402892
#214482102
#117×Dic612
#214468022
#214466532
#214462782
#214462772
#214462752
#99×Dic612
#214456062
C61×#18992
#2142161