Finite Group Databasebeta

← #29689129

Subgroups — #29689129

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×#16840342C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic, complemented
3#21448412C211yesmaximal, characteristic, complemented
4#21446256C211yesmaximal, characteristic, complemented
5#21446249C211yesmaximal, characteristic, complemented
6#21446246C211yesmaximal, characteristic, complemented
7#21446239C211yesmaximal, characteristic, complemented
8#21446139C211yesmaximal, characteristic, complemented
9#21446136C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21445908C211yesmaximal, characteristic, complemented
12#21445904C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#21445758C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840342—24no—
21#16840342C418yescomplemented
22C2×#14519755—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519752—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519751C2211yescharacteristic
27C2×#14519750—21no—
28C2×#14519750—21no—
29C2×#14519736C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37#16839727—24no—
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41#16839667—21no—
42#16839663—21no—
43#16839641—21no—
44#16839641—21no—
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C2×#11758226—22no—
63C2×#11758226—41no—
64C2×#11758226—41no—
65C2×#11758226—41no—
66C2×#11758226—41no—
67C2×#11758226C2×C414yescomplemented
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C2×#11758222C2×C414yes—
73C2×#11758222D414yes—
74C22×Dic122D411yescharacteristic
75C22×D244—21no—
76C22×D244—21no—
77C22×D244D411yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C22×C22⋊D61D411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—41no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—41no—
93C2×C8×D61—41no—
94#14519755—28no—
95#14519753—22no—
96#14519753C2×C414yescomplemented
97#14519752—28no—
98#14519752—22no—
99#14519752C2×C414yescomplemented
100#14519751—22no—
101#14519751C2×C414yes—
102#14519750—28no—
103#14519750—28no—
104#14519736—41no—
105#14519736—41no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C4⋊C4×D61—22no—
112C4⋊C4×D61C2×C414yescomplemented
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×C4×Dic61—21no—
122#14519701—41no—
123#14519701—41no—
124#14519699—41no—
125#14519699—41no—
126#14519697—41no—
127#14519697—41no—
128C22⋊#92418—22no—
129#14519689—22no—
130#14519689—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61C2×C414yes—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—41no—
145C2×C4⋊C4×C61—41no—
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150#103×C61—41no—
151#103×C61—41no—
152C22⋊C8×C61—22no—
153C24×C61C2×D411yescharacteristic
154C23×D61—21no—
155C23×D61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C22×C412yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—42no—
172C22×C4×C61—81no—
173C22×C4×C61—81no—
174C22×C4×C61C22×C412yes—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2411yescharacteristic
178C2×C22⋊D61—24no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C2×C22⋊D61—41no—
182C2×C22⋊D61—41no—
183C2×C22⋊D61—81no—
184C2×C22⋊D61—81no—
185C2×C22⋊D61C22⋊C414yes—
186C2×C22⋊D61C22⋊C414yes—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758226—44no—
193#11758226—44no—
194#11758226—44no—
195#11758226—44no—
196#11758222—44no—
197#11758222—44no—
198#11758222—44no—
199#11758222—44no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—24no—
205C2×D244—21no—
206C2×D244—24no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—42no—
210C2×D244—42no—
211C2×D244—81no—
212C2×D244—81no—
213C2×D244C22⋊C414yes—
214C2×D244C22×C412yes—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—81no—
228C2×C4×D61—81no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C22×C412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×Dic122—41no—
234C2×Dic122—41no—
235C2×Dic122C22⋊C414yes—
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—42no—
249C4⋊C4×C61C22×C412yes—
250C22⋊C4×C61—24no—
251C22⋊Dic61—42no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—81no—
256#11758198—81no—
257#11758198—81no—
258#11758198—81no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C412yes—
265#11758196—24no—
266#11758196—24no—
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—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—41no—
308Q8×C61—41no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
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—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—84no—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C23×C411yescharacteristic
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61H(5,𝔽2)11yescharacteristic
332C2×C4×C61H(5,𝔽2)11yescharacteristic
333C2×C4×C61H(5,𝔽2)11yescharacteristic
334C2×C4×C61H(5,𝔽2)11yescharacteristic
335C22⋊D61—44no—
336C22⋊D61—44no—
337C22⋊D61—84no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—22no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61C2×C22⋊C412yes—
352C2×Dic61C2×C22⋊C412yes—
353D244—22no—
354D244—22no—
355D244—44no—
356D244—48no—
357D244—41no—
358D244—41no—
359D244—84no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—48no—
369C4×D61—84no—
370Dic122—44no—
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#1872D6111yescharacteristic, complemented
436#1824—611no—
437#1823—611no—
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—1221no—
459C2×C22⋊Q8C2×D6111yescharacteristic
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×#103C2×D6111yescharacteristic
471C2×#103C2×D6111yescharacteristic
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#380—611no—
489#340—611no—
490#340—611no—
491#340—611no—
492#340—611no—
493#340—611no—
494#340—611no—
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×Q8C22×D6111yescharacteristic
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—22no—
536C22⋊Q8—614no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8C4×D6114yes—
540#121—614no—
541#121—614no—
542#121—1228no—
543#121—1228no—
544#121—1222no—
545#121—1228no—
546#121—1222no—
547#117—2441no—
548#117—2441no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
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—41no—
574#103—41no—
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—1221no—
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—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—614no—
607C2×Q8—2441no—
608C2×Q8—2441no—
609C2×Q8C2×C4×D6112yes—
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—2442no—
629C2×D4—2442no—
630C2×D4—2441no—
631C2×D4—2441no—
632C2×D4—2441no—
633C2×D4—2441no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
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—1224no—
652C22×C4—1224no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—4881no—
665C22×C4—4881no—
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—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—42no—
693C4⋊C4—612no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4C2×C4×D6112yes—
702C22⋊C4—24no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—4881no—
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—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—2444no—
746D4—1222no—
747D4—1222no—
748D4—4884no—
749D4—4884no—
750D4—2444no—
751D4—2448no—
752D4—2444no—
753D4—2444no—
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#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
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#1684032211yescharacteristic
841C22#1684032311yescharacteristic
842C22#1684056611yescharacteristic
843C22#1684056811yescharacteristic
844C22#1684057111yescharacteristic
845C22#1684057511yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—81no—
851C4—1222no—
852C4—1222no—
853C4—4881no—
854C4—4881no—
855C4—2442no—
856C4#1684023411yescharacteristic
857C4#1684023411yescharacteristic
858C4#1684032011yescharacteristic
859C4#1684032011yescharacteristic
860C2—42no—
861C2—4882no—
862C2—2442no—
863C2—2442no—
864C2#2144839311yescharacteristic
865C2#2145434311yescharacteristic
866C2#2145434711yescharacteristic
867C2#2145667511yescharacteristic
868C2#2145670511yescharacteristic
869C2#2145672311yescharacteristic
870C2#2145672911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC2×#16840342C2
cosocleC22×C4×C61C24
hypercenter#1872D61
hypocenterC61#21772
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21448412C2semidirect
4. #21446256C2semidirect
5. #21446249C2semidirect
6. #21446246C2semidirect
7. #21446239C2semidirect
8. #21446139C2semidirect
9. #21446136C2semidirect
10. #21446132C2semidirect
11. #21445908C2semidirect
12. #21445904C2semidirect
13. #21445758C2semidirect
14. #21445758C2semidirect
15. C61×#1872C2semidirect
21. #16840342C4semidirect
67. C2×#11758226C2×C4semidirect
96. #14519753C2×C4semidirect
99. #14519752C2×C4semidirect
112. C4⋊C4×D61C2×C4semidirect
435. #1872D61semidirect
497. C61#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168403422
C2×#168397272
#214484122
#214462562
#214462492
#214462462
#214462392
#214461392
#214461362
#214461322
#214459082
#214459042
#214457582
C61×#18722
#2177261