Finite Group Databasebeta

← C2×#21457335 #30555000

Subgroups — C2×#21457335 #30555000

Order 15616.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic, complemented
2C22×SD16×D61C211yesmaximal, characteristic, complemented
3C2×#16840427C211yesmaximal, characteristic, complemented
4C2×#16840407C211yesmaximal, characteristic
5#21457335C2116yesmaximal, direct product factor
6C2×#16840154C211yesmaximal, characteristic, complemented
7C2×#16840011C211yesmaximal, characteristic, complemented
8C2×#16840002C211yesmaximal, characteristic, complemented
9C2×#16839985C211yesmaximal, characteristic, complemented
10C2×#16839921C211yesmaximal, characteristic, complemented
11C2×#16839919C211yesmaximal, characteristic, complemented
12C2×#16839902C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839862C211yesmaximal, characteristic, complemented
15C2×#16839832C211yesmaximal, characteristic, complemented
16C2×C61×#461C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic, complemented
20C22×D4×D61C2211yescharacteristic
21C2×#14519806—28no—
22C2×#14519806C2218yescomplemented
23C22×Dic244C2211yescharacteristic, complemented
24C22×#11758202C2211yescharacteristic, complemented
25C22×#11758202C2211yescharacteristic, complemented
26C22×#11758190C2211yescharacteristic
27C22×#11758200C2211yescharacteristic
28C22×#11758201C2211yescharacteristic
29C22×#11758201C2211yescharacteristic
30C2×SD16×D61—28no—
31C2×SD16×D61C2218yescomplemented
32C22×#11758189C2211yescharacteristic, complemented
33C22×C8×D61C2211yescharacteristic
34#16840427—24no—
35#16840427C2218yescomplemented
36#16840407—24no—
37#16840407C2218yes—
38C2×#14519776—21no—
39C2×#14519765C2211yescharacteristic
40C2×#14519761—21no—
41C2×#14519757C2211yescharacteristic
42C2×#14519755—21no—
43C2×#14519755—21no—
44C2×#14519753C2211yescharacteristic
45C2×#14519753C2211yescharacteristic, complemented
46C2×#14519752C2211yescharacteristic
47C2×#14519751—21no—
48C2×#14519747—21no—
49C2×C4×Dic122C2211yescharacteristic, complemented
50C2×C4×D244C2211yescharacteristic
51C2×#14519739—21no—
52C22×#11758198—21no—
53#16840154C2218yescomplemented
54#16840011C2218yescomplemented
55#16840002C2218yescomplemented
56#16839985C2218yescomplemented
57#16839921C2218yescomplemented
58#16839919C2218yescomplemented
59#16839911C2218yescomplemented
60#16839902C2218yescomplemented
61#16839862C2218yescomplemented
62#16839832C2218yescomplemented
63C2×#14519710C2211yescharacteristic, complemented
64C2×#14519702C2211yescharacteristic, complemented
65C2×#14519700C2211yescharacteristic, complemented
66C2×#14519699C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#14519689C2211yescharacteristic, complemented
70C2×#14519688C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C2×C4⋊Q8×C61C2211yescharacteristic, complemented
74C2×C4×D4×C61C2211yescharacteristic
75C61×#461C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#103×C61C2211yescharacteristic, complemented
79C24×D61—21no—
80C2×#11758224—24no—
81C2×#11758224—22no—
82C2×#11758224—42no—
83C2×#11758224C2314yes—
84C22×Dic122—21no—
85C22×Dic122—21no—
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C2×Q8×D61—22no—
89C2×Q8×D61—22no—
90C2×Q8×D61—24no—
91C2×Q8×D61—24no—
92C2×Q8×D61—42no—
93C2×Q8×D61—42no—
94C2×Q8×D61C2314yes—
95C2×Q8×D61C2314yescomplemented
96C22×D244—21no—
97C22×D244D411yescharacteristic
98C22×D244C2311yescharacteristic
99C22×C22⋊D61—21no—
100C22×C22⋊D61—21no—
101C2×D4×D61—24no—
102C2×D4×D61—22no—
103C2×D4×D61—42no—
104C2×D4×D61C2314yes—
105C23×Dic61—21no—
106C22×C4×D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C2311yescharacteristic
110#14519806—232no—
111C2×Dic244—24no—
112C2×Dic244C2314yescomplemented
113C2×#11758202—24no—
114C2×#11758202—42no—
115C2×#11758202C2314yescomplemented
116C2×#11758202C2314yescomplemented
117C2×#11758190—24no—
118C2×#11758190C2314yes—
119C2×#11758200D418yescomplemented
120C2×#11758200C2314yes—
121C2×#11758201—24no—
122C2×#11758201—42no—
123C2×#11758201C2314yes—
124C2×#11758201C2314yes—
125SD16×D61—232no—
126C2×#11758189—24no—
127C2×#11758189C2314yescomplemented
128C22×#92418C2311yescharacteristic
129C22×#92418C2311yescharacteristic
130C2×C8×D61—24no—
131C2×C8×D61C2314yes—
132#14519776—28no—
133#14519765—22no—
134#14519765C2314yes—
135#14519761—28no—
136#14519757—22no—
137#14519757C2314yes—
138#14519755—28no—
139#14519755—28no—
140#14519753—22no—
141#14519753—22no—
142#14519753C2314yes—
143#14519753C2314yescomplemented
144#14519752—22no—
145#14519752C2314yes—
146#14519751—28no—
147#14519747—28no—
148C4×Dic122—22no—
149C4×Dic122C2314yescomplemented
150C4×D244D414yes—
151C4×D244C2314yes—
152#14519739—28no—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61D411yescharacteristic
155C2×C4⋊Dic61C2311yescharacteristic
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—28no—
166C2×#11758198D411yescharacteristic
167C2×#11758198D411yescharacteristic
168C2×C4×Dic61—21no—
169#14519710C2314yescomplemented
170#14519702C2314yescomplemented
171#14519700C2314yescomplemented
172#14519699C2314yes—
173#14519698C2314yes—
174#14519689C2314yes—
175#14519689C2314yescomplemented
176#14519688C2314yescomplemented
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2311yescharacteristic
179C22×D4×C61C2311yescharacteristic
180C23×C4×C61—21no—
181C2×SD16×C61—24no—
182C2×SD16×C61—24no—
183C2×SD16×C61C2314yes—
184C2×SD16×C61C2314yes—
185C22×C8×C61C2311yescharacteristic
186C22×C8×C61C2311yescharacteristic
187C4⋊Q8×C61—22no—
188C4⋊Q8×C61C2314yescomplemented
189C4×D4×C61—22no—
190C4×D4×C61C2314yes—
191C2×C4⋊C4×C61—21no—
192C2×C4⋊C4×C61—21no—
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61—21no—
195C2×C42×C61C2311yescharacteristic
196C4⋊C8×C61C2314yescomplemented
197#103×C61C2314yescomplemented
198#103×C61C2314yescomplemented
199C24×C61—21no—
200C23×D61—21no—
201C23×D61—24no—
202C23×D61—44no—
203C23×D61—44no—
204C23×D61—82no—
205C23×D61C2×D411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—22no—
210C2×Q8×C61—22no—
211C2×Q8×C61—22no—
212C2×Q8×C61—22no—
213C2×Q8×C61C2412yes—
214C2×Q8×C61C2412yes—
215C2×D4×C61—21no—
216C2×D4×C61—22no—
217C2×D4×C61C2×D414yes—
218C2×D4×C61C2412yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
223C22×C4×C61—82no—
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—44no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238Q8×D61—28no—
239Q8×D61—28no—
240Q8×D61—44no—
241Q8×D61—44no—
242Q8×D61—48no—
243Q8×D61—48no—
244#11758224—28no—
245#11758224—44no—
246#11758224—48no—
247D4×D61—28no—
248D4×D61—44no—
249D4×D61—48no—
250C2×D244—24no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—21no—
254C2×D244—24no—
255C2×D244—82no—
256C2×D244C2×D414yes—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—44no—
265C2×C4×D61—44no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—21no—
271C2×Dic122—22no—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—21no—
275C2×Dic122—24no—
276C2×Dic122—24no—
277C2×Dic122—44no—
278C2×Dic122—44no—
279C2×Dic122C2×D414yes—
280C2×Dic122C2412yes—
281C2×Dic122C2412yes—
282SD16×C61—28no—
283SD16×C61—28no—
284C2×C8×C61—22no—
285C2×C8×C61—22no—
286C2×C8×C61C2412yes—
287C2×C8×C61C2412yes—
288C4⋊C4×C61—24no—
289C4⋊C4×C61—24no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61C2412yes—
292C22⋊C4×C61—24no—
293C42×C61C2×D412yes—
294C42×C61C2412yes—
295#11758202—28no—
296#11758202—44no—
297#11758201—28no—
298#11758201—44no—
299#11758200C2×D4116yescomplemented
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303#11758198—24no—
304#11758198—24no—
305#11758198—24no—
306#11758198C2×D414yes—
307#11758198C2×D414yes—
308C4⋊Dic61—21no—
309C4⋊Dic61—24no—
310C4⋊Dic61C2×D414yes—
311C4⋊Dic61C2412yes—
312#11758196—24no—
313#11758196—24no—
314#11758196—24no—
315C4×Dic61—24no—
316C2×#92418—22no—
317C2×#92418C2×D414yes—
318C2×#92418C2412yes—
319C2×#92418C2412yes—
320Dic244—28no—
321#11758190—28no—
322#11758189—28no—
323C8×D61—28no—
324C23×C61—24no—
325C23×C61—22no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—48no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61—42no—
339C22×D61—48no—
340C22×D61—84no—
341C22×D61—816no—
342C22×D61#13714yescomplemented
343C22×D61C22×D412yes—
344C22×D61C22×D412yes—
345Q8×C61—22no—
346Q8×C61—22no—
347Q8×C61—22no—
348Q8×C61—22no—
349Q8×C61—42no—
350Q8×C61—42no—
351D4×C61—24no—
352D4×C61—22no—
353D4×C61C22×D414yes—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—84no—
363C2×C4×C61C22×D412yes—
364C2×C4×C61C22×D412yes—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D412yes—
367C2×C4×C61H(5,𝔽2)12yes—
368C2×C4×C61C2511yescharacteristic
369C22⋊D61—48no—
370C22⋊D61—48no—
371C2×Dic61—24no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—48no—
378C2×Dic61—42no—
379C2×Dic61—42no—
380C2×Dic61C22×D412yes—
381C2×Dic61C22×D412yes—
382D244—28no—
383D244—22no—
384D244—22no—
385D244—42no—
386D244—84no—
387C4×D61—24no—
388C4×D61—24no—
389C4×D61—22no—
390C4×D61—22no—
391C4×D61—22no—
392C4×D61—22no—
393C4×D61—48no—
394C4×D61—48no—
395Dic122—24no—
396Dic122—22no—
397Dic122—22no—
398Dic122—22no—
399Dic122—48no—
400Dic122—48no—
401Dic122—42no—
402Dic122C22×D414yes—
403C8×C61—22no—
404C8×C61—22no—
405#92418—22no—
406#92418C22×D414yes—
407C2×#3266—611nomaximal, Sylow
408C22×C61—24no—
409C22×C61—48no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61D4212yes—
413C22×C61C2×#13712yes—
414C22×C61#57712yes—
415C22×C61C23×D411yescharacteristic
416C2×D61—22no—
417C2×D61—28no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—44no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—816no—
427C2×D61—84no—
428C2×D61C2×#13714yescomplemented
429C4×C61—22no—
430C4×C61—22no—
431C4×C61—42no—
432C4×C61—42no—
433C4×C61—42no—
434C4×C61D4212yes—
435C4×C61C23×D411yescharacteristic
436C4×C61C2×H(5,𝔽2)11yescharacteristic
437Dic61—24no—
438Dic61—22no—
439Dic61—22no—
440Dic61—42no—
441Dic61—42no—
442C22×#137—611no—
443C23×SD16—611no—
444C2×D4×Q8—611no—
445C2×#546—611no—
446#3266—6116no—
447C2×#497—611no—
448C2×#468—611no—
449C2×#467—611no—
450C2×#464—611no—
451C2×#461D6111yescharacteristic, complemented
452C2×#452—611no—
453C2×#451—611no—
454C2×#448—611no—
455C2×#450—611no—
456C2×#440—611no—
457C2×#435—611no—
458C2×C61—44no—
459C2×C61#326614yescomplemented
460C2×C61C2×D4211yescharacteristic
461C2×C61C22×#13711yescharacteristic
462C2×C61C2×#57711yescharacteristic
463D61—24no—
464D61—42no—
465D61—82no—
466C22×#41—611no—
467C23×Q8—611no—
468C23×Q8—611no—
469C23×D4—611no—
470C2×#137—618no—
471C2×#137—1228no—
472C22×Q16—611no—
473C22×Q16—611no—
474C22×Q16—611no—
475C22×SD16—611no—
476C22×SD16—611no—
477C22×SD16—611no—
478C22×SD16—618no—
479C22×SD16—611no—
480C22×SD16—1228no—
481C22×SD16C2×D6111yescharacteristic
482C22×SD16C2×D6111yescharacteristic
483C22×M16—611no—
484C23×C8—611no—
485D4×Q8—618no—
486D4×Q8—1224no—
487#546—618no—
488#546—1224no—
489C2×C4⋊Q8—1221no—
490C2×C4⋊Q8C2×D6111yescharacteristic, complemented
491C2×#124—611no—
492C2×#123—1221no—
493C2×C22⋊Q8—611no—
494C2×C22⋊Q8—611no—
495C2×C22⋊Q8—611no—
496C2×C22⋊Q8—1221no—
497C2×C22⋊Q8—1221no—
498C2×#121—611no—
499C2×#121—1221no—
500C2×#120—1221no—
501C2×C4×Q8—611no—
502C2×C4×D4—611no—
503C2×C4×D4—1221no—
504C2×C4×D4C2×D6111yescharacteristic
505C22×C22⋊C4—1221no—
506#497—618no—
507#468—618no—
508#467—618no—
509#464—618no—
510#461C2×D6118yescomplemented
511#452—618no—
512#451—618no—
513#450—618no—
514#448—618no—
515#440—618no—
516#435—618no—
517C2×#107—611no—
518C2×C4⋊C8C2×D6111yescharacteristic, complemented
519C2×#103—611no—
520C2×#103—611no—
521C2×#103C2×D6111yescharacteristic, complemented
522C2×#103C2×D6111yescharacteristic, complemented
523C2×#102—611no—
524C2×#102—611no—
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×#97—611no—
528C61C2×#326611yescharacteristic, complemented, Sylow
529C25—1221no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—2442no—
534C22×Q8—614no—
535C22×Q8—614no—
536C22×Q8—611no—
537C22×Q8—611no—
538C22×Q8—1221no—
539C22×Q8—1221no—
540C22×Q8—1222no—
541C22×Q8—1222no—
542C22×Q8—1224no—
543C22×Q8—1224no—
544C22×Q8—2442no—
545C22×Q8—2442no—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6111yescharacteristic
548C22×D4—614no—
549C22×D4—611no—
550C22×D4—611no—
551C22×D4—1221no—
552C22×D4—1222no—
553C22×D4—1221no—
554C22×D4—1224no—
555C22×D4—1221no—
556C22×D4—2442no—
557C22×D4C22×D6111yescharacteristic
558C23×C4—21no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—1221no—
562C23×C4—1221no—
563C23×C4—1221no—
564#137—12232no—
565C2×Q16—614no—
566C2×Q16—614no—
567C2×Q16—614no—
568C2×Q16—1224no—
569C2×Q16—1224no—
570C2×Q16—2442no—
571C2×SD16—24no—
572C2×SD16—24no—
573C2×SD16—618no—
574C2×SD16—614no—
575C2×SD16—614no—
576C2×SD16—614no—
577C2×SD16—614no—
578C2×SD16—1224no—
579C2×SD16—1224no—
580C2×SD16—12232no—
581C2×SD16—2442no—
582C2×SD16C22×D6114yes—
583C2×SD16C22×D6114yes—
584C2×M16—614no—
585C2×M16—1224no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—614no—
589C22×C8—1224no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—1228no—
594C4⋊Q8C22×D6114yescomplemented
595#124—614no—
596#124—1222no—
597#123—1228no—
598C22⋊Q8—614no—
599C22⋊Q8—614no—
600C22⋊Q8—614no—
601C22⋊Q8—1228no—
602C22⋊Q8—1228no—
603C22⋊Q8—1222no—
604C22⋊Q8—1222no—
605C22⋊Q8—1222no—
606#121—614no—
607#121—1228no—
608#121—1222no—
609#120—1228no—
610C4×Q8—614no—
611C4×Q8—1222no—
612C4×D4—22no—
613C4×D4—614no—
614C4×D4—614no—
615C4×D4—1228no—
616C4×D4C22×D6114yes—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4C22×D6111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—1228no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—1221no—
637C2×C42C22×D6111yescharacteristic
638#107—614no—
639C4⋊C8C22×D6114yescomplemented
640#103—614no—
641#103—614no—
642#103C22×D6114yescomplemented
643#103C22×D6114yescomplemented
644#102—614no—
645#102—614no—
646C22⋊C8—614no—
647C22⋊C8—614no—
648#97—614no—
649C24—21no—
650C24—611no—
651C24—611no—
652C24—1224no—
653C24—1221no—
654C24—4882no—
655C24—2444no—
656C24—2444no—
657#41—1228no—
658#41—2444no—
659#41—2448no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—614no—
667C2×Q8—612no—
668C2×Q8—612no—
669C2×Q8—1224no—
670C2×Q8—1224no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1222no—
674C2×Q8—1228no—
675C2×Q8—1228no—
676C2×Q8—1222no—
677C2×Q8—1222no—
678C2×Q8—2444no—
679C2×Q8—2444no—
680C2×Q8—2444no—
681C2×Q8—2444no—
682C2×Q8—2448no—
683C2×Q8—2448no—
684C2×Q8C23×D6112yes—
685C2×Q8C23×D6112yes—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—614no—
689C2×D4—612no—
690C2×D4—1224no—
691C2×D4—1224no—
692C2×D4—1224no—
693C2×D4—1228no—
694C2×D4—1224no—
695C2×D4—1222no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—4882no—
699C2×D4—2444no—
700C2×D4—2448no—
701C2×D4—2444no—
702C2×D4—2444no—
703C2×D4D4×D6114yes—
704C2×D4C23×D6112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—24no—
709C22×C4—82no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—1224no—
717C22×C4—1224no—
718C22×C4—1224no—
719C22×C4—1221no—
720C22×C4—1222no—
721C22×C4—1222no—
722C22×C4—1222no—
723C22×C4—1222no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—2444no—
727C22×C4—2444no—
728C22×C4—2444no—
729C22×C4D4×D6111yescharacteristic
730C22×C4D4×D6111yescharacteristic
731C22×C4C23×D6111yescharacteristic
732Q16—1228no—
733Q16—1228no—
734Q16—2444no—
735SD16—28no—
736SD16—28no—
737SD16—6116no—
738SD16—1228no—
739SD16—1228no—
740SD16—2444no—
741M16—1228no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—614no—
745C2×C8—612no—
746C2×C8—612no—
747C2×C8—1228no—
748C2×C8—1222no—
749C2×C8C23×D6112yes—
750C2×C8C23×D6112yes—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—21no—
754C4⋊C4—614no—
755C4⋊C4—612no—
756C4⋊C4—1224no—
757C4⋊C4—1224no—
758C4⋊C4—1224no—
759C4⋊C4—1221no—
760C4⋊C4—1224no—
761C4⋊C4C23×D6112yes—
762C22⋊C4—24no—
763C22⋊C4—614no—
764C22⋊C4—614no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—1224no—
768C22⋊C4—1224no—
769C22⋊C4—1224no—
770C22⋊C4—1224no—
771C42—1224no—
772C42D4×D6112yes—
773C42C23×D6112yes—
774C23—22no—
775C23—24no—
776C23—42no—
777C23—42no—
778C23—614no—
779C23—612no—
780C23—612no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1222no—
787C23—48816no—
788C23—4884no—
789C23—2448no—
790C23—2448no—
791C23—2442no—
792C23—2442no—
793C23—2442no—
794C23C2×D4×D6111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—42no—
800Q8—42no—
801Q8—614no—
802Q8—1222no—
803Q8—1224no—
804Q8—1222no—
805Q8—1222no—
806Q8—2448no—
807Q8—2448no—
808Q8—2442no—
809D4—22no—
810D4—24no—
811D4—1228no—
812D4—1222no—
813D4—1222no—
814D4—4884no—
815D4—2448no—
816D4—2448no—
817D4—2442no—
818D4C2×D4×D6114yes—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—84no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1224no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1224no—
839C2×C4—1224no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—2448no—
843C2×C4—2448no—
844C2×C4—2448no—
845C2×C4—2442no—
846C2×C4—2442no—
847C2×C4C2×D4×D6112yes—
848C2×C4C2×D4×D6112yes—
849C2×C4C2×D4×D6112yes—
850C2×C4C2×D4×D6111yescharacteristic
851C2×C4#1451982312yes—
852C2×C4C24×D6111yescharacteristic
853C8—22no—
854C8—22no—
855C8—614no—
856C8—1222no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—48no—
861C22—614no—
862C22—1222no—
863C22—1222no—
864C22—1228no—
865C22—1222no—
866C22—1222no—
867C22—1222no—
868C22—48816no—
869C22—4884no—
870C22—2442no—
871C22—2442no—
872C22—2442no—
873C22—2444no—
874C22#1684039612yes—
875C22#137×D6112yes—
876C22#1684056812yes—
877C22C22×D4×D6111yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—1222no—
884C4—1222no—
885C4—1224no—
886C4—2442no—
887C4—2442no—
888C4#1684039612yes—
889C4C22×D4×D6111yescharacteristic
890C4C2×#1451982311yescharacteristic
891C2—44no—
892C2—1224no—
893C2—4882no—
894C2—2442no—
895C2#2145733514yesdirect product factor
896C2C2×#1684039611yescharacteristic
897C2C2×#137×D6111yescharacteristic
898C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#461C2
socleC23×C61C22×D4
prime radicalC2×#16840407C2
hypercenterC2×#461D61
hypocenterC61C2×#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C22×#14519806C2semidirect
2. C22×SD16×D61C2semidirect
3. C2×#16840427C2semidirect
5. #21457335C2direct (N × H)
6. C2×#16840154C2semidirect
7. C2×#16840011C2semidirect
8. C2×#16840002C2semidirect
9. C2×#16839985C2semidirect
10. C2×#16839921C2semidirect
11. C2×#16839919C2semidirect
12. C2×#16839902C2semidirect
13. C2×#16839911C2semidirect
14. C2×#16839862C2semidirect
15. C2×#16839832C2semidirect
16. C2×C61×#461C2semidirect
19. C22×Q8×D61C22semidirect
22. C2×#14519806C22semidirect
23. C22×Dic244C22semidirect
24. C22×#11758202C22semidirect
25. C22×#11758202C22semidirect
31. C2×SD16×D61C22semidirect
32. C22×#11758189C22semidirect
35. #16840427C22semidirect
45. C2×#14519753C22semidirect
49. C2×C4×Dic122C22semidirect
53. #16840154C22semidirect
54. #16840011C22semidirect
55. #16840002C22semidirect
56. #16839985C22semidirect
57. #16839921C22semidirect
58. #16839919C22semidirect
59. #16839911C22semidirect
60. #16839902C22semidirect
61. #16839862C22semidirect
62. #16839832C22semidirect
63. C2×#14519710C22semidirect
64. C2×#14519702C22semidirect
65. C2×#14519700C22semidirect
69. C2×#14519689C22semidirect
70. C2×#14519688C22semidirect
73. C2×C4⋊Q8×C61C22semidirect
75. C61×#461C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#103×C61C22semidirect
95. C2×Q8×D61C23semidirect
112. C2×Dic244C23semidirect
115. C2×#11758202C23semidirect
116. C2×#11758202C23semidirect
119. C2×#11758200D4semidirect
127. C2×#11758189C23semidirect
143. #14519753C23semidirect
149. C4×Dic122C23semidirect
169. #14519710C23semidirect
170. #14519702C23semidirect
171. #14519700C23semidirect
175. #14519689C23semidirect
176. #14519688C23semidirect
188. C4⋊Q8×C61C23semidirect
196. C4⋊C8×C61C23semidirect
197. #103×C61C23semidirect
198. #103×C61C23semidirect
299. #11758200C2×D4semidirect
342. C22×D61#137semidirect
428. C2×D61C2×#137semidirect
451. C2×#461D61semidirect
459. C2×C61#3266semidirect
490. C2×C4⋊Q8C2×D61semidirect
510. #461C2×D61semidirect
518. C2×C4⋊C8C2×D61semidirect
521. C2×#103C2×D61semidirect
522. C2×#103C2×D61semidirect
528. C61C2×#3266semidirect
594. C4⋊Q8C22×D61semidirect
639. C4⋊C8C22×D61semidirect
642. #103C22×D61semidirect
643. #103C22×D61semidirect
895. C2#21457335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198062
C22×SD16×D612
C2×#168404272
C2×#168404072
#214573352
C2×#168401542
C2×#168400112
C2×#168400022
C2×#168399852
C2×#168399212
C2×#168399192
C2×#168399022
C2×#168399112
C2×#168398622
C2×#168398322
C2×C61×#4612
C2×#326661