Finite Group Databasebeta

← #29689136

Subgroups — #29689136

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840343C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic, complemented
3#21448408C211yesmaximal, characteristic, complemented
4#21446256C211yesmaximal, characteristic, complemented
5#21446251C211yesmaximal, characteristic, complemented
6#21446246C211yesmaximal, characteristic, complemented
7#21446241C211yesmaximal, characteristic, complemented
8#21446140C211yesmaximal, characteristic, complemented
9#21446135C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21445909C211yesmaximal, characteristic, complemented
13#21445760C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#1823C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840343—24no—
21#16840343C418yescomplemented
22C2×#14519757—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519757C2211yescharacteristic
25C2×#14519752—21no—
26C2×#14519752C2211yescharacteristic
27C2×#14519752C2211yescharacteristic
28C2×#14519751—21no—
29C2×#14519751—21no—
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40#16839727—24no—
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44#16839666—21no—
45#16839662—21no—
46#16839640—21no—
47#16839638—21no—
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C2×#11758222C2×C414yes—
72C2×#11758222C2×C414yescomplemented
73C2×#11758222D414yes—
74C22×Dic122D411yescharacteristic
75C22×Dic122C2311yescharacteristic
76C22×D244—21no—
77C22×D244—21no—
78C22×D244D411yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61D411yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—41no—
89C2×#11758189—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94C2×C8×D61—41no—
95#14519757—22no—
96#14519757—22no—
97#14519757—28no—
98#14519757C2×C414yes—
99#14519757C2×C414yescomplemented
100#14519752—28no—
101#14519752—22no—
102#14519752—22no—
103#14519752C2×C414yes—
104#14519752C2×C414yescomplemented
105#14519751—28no—
106#14519751—28no—
107#14519735—41no—
108#14519735—41no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C4⋊C4×D61—41no—
115C4⋊C4×D61—41no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×C4×Dic61—21no—
125#14519702—41no—
126#14519702—41no—
127#14519700—41no—
128#14519700—41no—
129#14519699—41no—
130#14519699—41no—
131#14519697—41no—
132#14519697—41no—
133C22⋊#92418—22no—
134#14519689—22no—
135#14519689—22no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61C2×C414yescomplemented
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—24no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—81no—
167C22×C4×C61—81no—
168C22×C4×C61C22×C412yes—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2411yescharacteristic
172C2×C22⋊D61—24no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61—41no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61C22⋊C414yes—
180C2×C22⋊D61C22⋊C414yes—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186#11758222—44no—
187#11758222—44no—
188#11758222—44no—
189#11758222—44no—
190#11758222—44no—
191#11758222—44no—
192#11758222—44no—
193#11758222—44no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—24no—
200C2×D244—24no—
201C2×D244—41no—
202C2×D244—41no—
203C2×D244—81no—
204C2×D244—81no—
205C2×D244—81no—
206C2×D244—81no—
207C2×D244C22⋊C414yes—
208C2×D244C22×C412yes—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—24no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—81no—
222C2×C4×D61—81no—
223C2×C4×D61C22×C412yes—
224C2×C4×D61C22×C412yes—
225C2×C4×D61C2×D412yes—
226C2×C4×D61C2×D412yes—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—41no—
233C2×Dic122—41no—
234C2×Dic122C22⋊C414yes—
235C2×Dic122C22×C412yes—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C22×C412yes—
250C4⋊C4×C61C22×C412yes—
251C22⋊C4×C61—81no—
252C22⋊Dic61—81no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—42no—
258#11758198—81no—
259#11758198—81no—
260C4⋊Dic61—24no—
261C4⋊Dic61—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266#11758196—42no—
267C4×Dic61—42no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274#11758189—44no—
275C8×D61—44no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61C2×C22⋊C412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—22no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C2×C22⋊C412yes—
304C22×D61C2×C22⋊C412yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—84no—
324C2×C4×C61C2×C22⋊C412yes—
325C2×C4×C61C23×C411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61H(5,𝔽2)11yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C2×C4×C61H(5,𝔽2)11yescharacteristic
331C22⋊D61—44no—
332C22⋊D61—44no—
333C22⋊D61—48no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—22no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61C2×C22⋊C412yes—
348C2×Dic61C2×C22⋊C412yes—
349D244—22no—
350D244—22no—
351D244—44no—
352D244—41no—
353D244—41no—
354D244—84no—
355D244—84no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—48no—
365C4×D61—84no—
366Dic122—22no—
367Dic122—22no—
368Dic122—44no—
369Dic122—41no—
370Dic122—41no—
371C8×C61—41no—
372C8×C61—41no—
373#92418—41no—
374#92418—41no—
375#21772—611nomaximal, Sylow
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61C22×C22⋊C411yescharacteristic
384C22×C61#53411yescharacteristic
385C22×C61#53411yescharacteristic
386C22×C61#57611yescharacteristic
387C22×C61#57711yescharacteristic
388C22×C61#57711yescharacteristic
389C22×C61#57811yescharacteristic
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C4×C61—22no—
412C4×C61—42no—
413C4×C61—42no—
414C4×C61—81no—
415C4×C61—81no—
416C4×C61#51811yescharacteristic
417C4×C61#51811yescharacteristic
418C4×C61#53411yescharacteristic
419C4×C61#53411yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—42no—
423Dic61—81no—
424Dic61—81no—
425C2×#537—611no—
426C2×#408—611no—
427#2311—611no—
428#1895—611no—
429#1894—611no—
430#1893—611no—
431#1892—611no—
432#1875—611no—
433#1874—611no—
434#1873—611no—
435#1872—611no—
436#1824—611no—
437#1823D6111yescharacteristic, complemented
438#1788—611no—
439#1788—611no—
440C2×C61—42no—
441C2×C61#230811yescharacteristic
442C2×C61#289711yescharacteristic
443C2×C61#289811yescharacteristic
444C2×C61#319811yescharacteristic
445C2×C61#320111yescharacteristic
446C2×C61#320311yescharacteristic
447C2×C61#320411yescharacteristic
448D61—42no—
449D61—42no—
450D61—82no—
451C22×#41—611no—
452C22×#41—611no—
453C22×M16—611no—
454C23×C8—611no—
455#537—618no—
456#537—1224no—
457C2×C22⋊Q8—611no—
458C2×C22⋊Q8—611no—
459C2×C22⋊Q8—1221no—
460C2×#121—611no—
461C2×#121—611no—
462C2×#121—1221no—
463C2×#121—1221no—
464C2×#121—1221no—
465C2×#117—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4C2×D6111yescharacteristic
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476#408—1224no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8C2×D6111yescharacteristic
481#391—1221no—
482#390—1221no—
483#386—1221no—
484#386—1221no—
485#380—611no—
486#380—611no—
487#380—611no—
488#380C2×D6111yescharacteristic
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340C2×D6111yescharacteristic
494#340C2×D6111yescharacteristic
495#340C2×D6111yescharacteristic
496#340C2×D6111yescharacteristic
497C61#2177211yescharacteristic, complemented, Sylow
498C2×#41—614no—
499C2×#41—614no—
500C2×#41—614no—
501C2×#41—1222no—
502C2×#41—2441no—
503C2×#41—2441no—
504C2×#41—2441no—
505C2×#41—2441no—
506C2×#41—2441no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41—2441no—
510C22×Q8—611no—
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—611no—
514C22×D4—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C22×D4—1221no—
518C22×D4—1221no—
519C23×C4—21no—
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—1221no—
523C23×C4—1221no—
524C23×C4C22×D6111yescharacteristic
525C2×M16—1222no—
526C2×M16—2441no—
527C2×M16—2441no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—2441no—
532C22×C8—2441no—
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22⋊Q8—614no—
536C22⋊Q8—614no—
537C22⋊Q8—1222no—
538C22⋊Q8—1222no—
539C22⋊Q8—1228no—
540#121—614no—
541#121—614no—
542#121—1222no—
543#121—1222no—
544#121—1228no—
545#121—1228no—
546#121—1228no—
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—2441no—
557C2×C4⋊C4—2441no—
558C2×C4⋊C4C4×D6114yescomplemented
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573#103—2441no—
574#103—2441no—
575#103—2441no—
576#103—2441no—
577#102—2441no—
578#102—2441no—
579#102—2441no—
580#102—2441no—
581C22⋊C8—22no—
582C22⋊C8—1222no—
583C22⋊C8—1222no—
584C22⋊C8—1222no—
585#95—21no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—611no—
590C24—611no—
591C24—1221no—
592C24D4×D6111yescharacteristic
593#41—2444no—
594#41—2444no—
595#41—2444no—
596#41—2444no—
597#41—2444no—
598#41—2444no—
599#41—2444no—
600#41—2444no—
601C2×Q8—614no—
602C2×Q8—612no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—2441no—
609C2×Q8—2441no—
610C2×D4—614no—
611C2×D4—614no—
612C2×D4—612no—
613C2×D4—614no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—1221no—
622C2×D4—4881no—
623C2×D4—4881no—
624C2×D4—4881no—
625C2×D4—4881no—
626C2×D4—2441no—
627C2×D4—2441no—
628C2×D4—2441no—
629C2×D4—2441no—
630C2×D4—2441no—
631C2×D4—2441no—
632C2×D4—2442no—
633C2×D4—2442no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—4881no—
664C22×C4—4881no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6112yes—
669C22×C4D4×D6112yes—
670C22×C4D4×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672M16—2444no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—2444no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—2442no—
700C4⋊C4C2×C4×D6112yes—
701C4⋊C4C2×C4×D6112yes—
702C22⋊C4—81no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—4881no—
708C22⋊C4—4881no—
709C22⋊C4—4881no—
710C22⋊C4—2442no—
711C42—2442no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—612no—
719C23—612no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23—1222no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23C22⋊C4×D6112yes—
740C23C2×D4×D6111yescharacteristic
741Q8—1222no—
742Q8—1222no—
743Q8—2444no—
744Q8—2441no—
745Q8—2441no—
746D4—1222no—
747D4—1222no—
748D4—4884no—
749D4—4884no—
750D4—2444no—
751D4—2444no—
752D4—2444no—
753D4—2448no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—4884no—
791C2×C4—2448no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4C22⋊C4×D6112yes—
801C2×C4C22×C4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4#1451982311yescharacteristic
804C2×C4#1451982311yescharacteristic
805C2×C4#1451982311yescharacteristic
806C2×C4#1451982311yescharacteristic
807C8—41no—
808C8—41no—
809C8—2441no—
810C8—2441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—1222no—
819C22—1222no—
820C22—1222no—
821C22—1222no—
822C22—1222no—
823C22—1222no—
824C22—4881no—
825C22—4881no—
826C22—4881no—
827C22—4881no—
828C22—2442no—
829C22—2442no—
830C22—2442no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22C2×C22⋊C4×D6111yescharacteristic
840C22#1684032311yescharacteristic
841C22#1684032311yescharacteristic
842C22#1684056311yescharacteristic
843C22#1684056811yescharacteristic
844C22#1684057111yescharacteristic
845C22#1684057811yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—81no—
851C4—1222no—
852C4—1222no—
853C4—4881no—
854C4—4881no—
855C4—2442no—
856C4#1684023611yescharacteristic
857C4#1684023611yescharacteristic
858C4#1684032311yescharacteristic
859C4#1684032311yescharacteristic
860C2—42no—
861C2—4882no—
862C2—2442no—
863C2—2442no—
864C2#2144839611yescharacteristic
865C2#2145434011yescharacteristic
866C2#2145435111yescharacteristic
867C2#2145667811yescharacteristic
868C2#2145670811yescharacteristic
869C2#2145671911yescharacteristic
870C2#2145672911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1823C2
socleC23×C61C22×D4
prime radicalC2×#16840343C2
cosocleC22×C4×C61C24
hypercenter#1823D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21448408C2semidirect
4. #21446256C2semidirect
5. #21446251C2semidirect
6. #21446246C2semidirect
7. #21446241C2semidirect
8. #21446140C2semidirect
9. #21446135C2semidirect
10. #21446130C2semidirect
11. #21446125C2semidirect
12. #21445909C2semidirect
13. #21445760C2semidirect
14. #21445757C2semidirect
15. C61×#1823C2semidirect
21. #16840343C4semidirect
72. C2×#11758222C2×C4semidirect
99. #14519757C2×C4semidirect
104. #14519752C2×C4semidirect
145. C2×C4⋊C4×C61C2×C4semidirect
437. #1823D61semidirect
497. C61#21772semidirect
558. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403432
C2×#168397272
#214484082
#214462562
#214462512
#214462462
#214462412
#214461402
#214461352
#214461302
#214461252
#214459092
#214457602
#214457572
C61×#18232
#2177261