Finite Group Databasebeta

← C2×#21458036 #30556827

Subgroups — C2×#21458036 #30556827

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840447C211yesmaximal, characteristic, complemented
2C2×#16840400C211yesmaximal, characteristic
3#21458036C2116yesmaximal, direct product factor
4C2×#16840118C211yesmaximal, characteristic, complemented
5C2×#16840080C211yesmaximal, characteristic, complemented
6C2×#16840102C211yesmaximal, characteristic, complemented
7C2×#16840060C211yesmaximal, characteristic, complemented
8C2×#16840019C211yesmaximal, characteristic, complemented
9C2×#16840008C211yesmaximal, characteristic, complemented
10C2×#16839987C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839914C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×#16839838C211yesmaximal, characteristic, complemented
15C2×#16839765C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22#16840447—24no—
23#16840447C2218yescomplemented
24#16840400—24no—
25#16840400C2218yes—
26C2×#14519772—21no—
27C2×#14519768C2211yescharacteristic, complemented
28C2×#14519767—21no—
29C2×#14519766C2211yescharacteristic
30C2×#14519760—21no—
31C2×#14519760—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519756C2211yescharacteristic, complemented
34C2×#14519753C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519749—21no—
37C2×#14519745—21no—
38C2×#14519742C2211yescharacteristic, complemented
39C2×D4×Dic61C2211yescharacteristic
40C2×C4×C22⋊D61C2211yescharacteristic
41C2×#14519736—21no—
42C2×#14519735C2211yescharacteristic
43C22×#11758198—21no—
44#16840118C2218yescomplemented
45#16840102C2218yescomplemented
46#16840080C2218yescomplemented
47#16840060C2218yescomplemented
48#16840019C2218yescomplemented
49#16840008C2218yescomplemented
50#16839987C2218yescomplemented
51#16839924C2218yescomplemented
52#16839914C2218yescomplemented
53#16839853C2218yescomplemented
54#16839838C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59#16839765C2218yescomplemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic, complemented
71C22×C4⋊C4×C61C2211yescharacteristic, complemented
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61D411yescharacteristic
83C2×D4×D61—24no—
84C2×D4×D61—22no—
85C2×D4×D61—42no—
86C2×D4×D61C2314yes—
87C23×Dic61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758202—42no—
90C2×#11758202C2314yescomplemented
91C2×#11758190—42no—
92C2×#11758190C2314yes—
93C2×#11758200—24no—
94C2×#11758200C2314yes—
95C2×#11758189—42no—
96C2×#11758189C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519772—28no—
100#14519768—22no—
101#14519768C2314yescomplemented
102#14519767—28no—
103#14519766—22no—
104#14519766C2314yes—
105#14519760—28no—
106#14519760—28no—
107#14519757—22no—
108#14519757C2314yes—
109#14519756—22no—
110#14519756C2314yescomplemented
111#14519753—22no—
112#14519753C2314yes—
113#14519751—22no—
114#14519751C2314yes—
115#14519749—28no—
116#14519745—28no—
117#14519742—22no—
118#14519742C2314yescomplemented
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121C4×C22⋊D61D414yes—
122C4×C22⋊D61C2314yes—
123#14519736—28no—
124#14519735—22no—
125#14519735C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—28no—
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yescomplemented
150#14519708C2314yescomplemented
151#14519708C2314yescomplemented
152#14519706C2314yescomplemented
153#14519702C2314yescomplemented
154#14519701C2314yescomplemented
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yescomplemented
160#14519689C2314yes—
161C8×Dic61C2314yescomplemented
162C2×#41×C61—22no—
163C2×#41×C61—24no—
164C2×#41×C61—42no—
165C2×#41×C61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×M16×C61—42no—
173C2×M16×C61C2314yescomplemented
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—22no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2314yescomplemented
181#103×C61C2314yescomplemented
182#103×C61C2314yescomplemented
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—24no—
189C23×D61—44no—
190C23×D61—44no—
191C23×D61—82no—
192C23×D61C2×D411yescharacteristic
193#41×C61—28no—
194#41×C61—44no—
195#41×C61—48no—
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61C2412yes—
200C2×D4×C61—24no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—44no—
204C2×D4×C61#4114yes—
205C2×D4×C61C2412yes—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—44no—
214C22×C4×C61—44no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2412yes—
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61C2×D414yes—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—24no—
229C22×Dic61—82no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233D4×D61—28no—
234D4×D61—44no—
235D4×D61—48no—
236C2×D244—22no—
237C2×D244—22no—
238C2×D244—21no—
239C2×D244C2412yes—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2412yes—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122C2412yes—
248M16×C61—44no—
249C2×C8×C61—22no—
250C2×C8×C61—22no—
251C2×C8×C61C2412yes—
252C2×C8×C61C2412yes—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61C2×D414yes—
261#11758202—44no—
262#11758200—28no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196C2×D414yes—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2412yes—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289#11758190—44no—
290#11758189—44no—
291C23×C61—24no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—84no—
310C22×D61—816no—
311C22×D61C22×D412yes—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—42no—
315D4×C61—24no—
316D4×C61—22no—
317D4×C61—48no—
318D4×C61C2×#4114yes—
319C2×C4×C61—22no—
320C2×C4×C61—24no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—48no—
327C2×C4×C61—48no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4112yes—
334C2×C4×C61H(5,𝔽2)12yes—
335C2×C4×C61C2511yescharacteristic
336C22⋊D61—44no—
337C22⋊D61—48no—
338C22⋊D61—84no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61—84no—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351C2×Dic61C22×D412yes—
352D244—22no—
353D244—22no—
354D244—42no—
355C4×D61—24no—
356C4×D61—22no—
357C4×D61—22no—
358Dic122—22no—
359Dic122—22no—
360Dic122—42no—
361C8×C61—22no—
362C8×C61—22no—
363#92418—22no—
364#92418—22no—
365C2×#3323—611nomaximal, Sylow
366C22×C61—24no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—48no—
371C22×C61—44no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61#54612yes—
375C22×C61#57512yes—
376C22×C61#57712yes—
377C22×C61C23×D411yescharacteristic
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—44no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—816no—
386C2×D61—84no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61#54612yes—
392C4×C61C22×#4111yescharacteristic
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394Dic61—22no—
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400C2×#552—611no—
401C2×#546—611no—
402#3323—6116no—
403C2×#488—611no—
404C2×#481—611no—
405C2×#485—611no—
406C2×#478—611no—
407C2×#470—611no—
408C2×#468—611no—
409C2×#464—611no—
410C2×#452—611no—
411C2×#450—611no—
412C2×C4×SD16—611no—
413C2×#436—611no—
414C2×#417D6111yescharacteristic, complemented
415C2×#418—611no—
416C2×C61—44no—
417C2×C61—42no—
418C2×C61#332314yescomplemented
419C2×C61C2×#54611yescharacteristic
420C2×C61C2×#57511yescharacteristic
421C2×C61C2×#57711yescharacteristic
422D61—42no—
423D61—82no—
424C22×#41C2×D6111yescharacteristic
425C23×D4—611no—
426C22×Q16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×M16—611no—
430C22×M16C2×D6111yescharacteristic, complemented
431#552—618no—
432#552—1224no—
433#546—618no—
434#546—1224no—
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#124—611no—
439C2×#123—1221no—
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—611no—
444C2×#121—611no—
445C2×#121—1221no—
446C2×#120—1221no—
447C2×C4×Q8—611no—
448C2×C4×D4—611no—
449C2×C4×D4—611no—
450C2×#117—611no—
451C2×#117—1221no—
452C22×C4⋊C4C2×D6111yescharacteristic, complemented
453C22×C22⋊C4—1221no—
454#488—618no—
455#485—618no—
456#481—618no—
457#478—618no—
458#470—618no—
459#468—618no—
460#464—618no—
461#452—618no—
462#450—618no—
463C4×SD16—618no—
464#436—618no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#106—611no—
468C2×C4⋊C8—611no—
469#418—618no—
470#417C2×D6118yescomplemented
471C2×#103—611no—
472C2×#103—611no—
473C2×#103C2×D6111yescharacteristic, complemented
474C2×#103C2×D6111yescharacteristic, complemented
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102C2×D6111yescharacteristic
480C2×#102C2×D6111yescharacteristic
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C4×C8—611no—
484C61C2×#332311yescharacteristic, complemented, Sylow
485C25—1221no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D6114yes—
490C22×Q8—611no—
491C22×Q8C22×D6111yescharacteristic
492C22×D4—21no—
493C22×D4—611no—
494C22×D4—614no—
495C22×D4—611no—
496C22×D4—1222no—
497C22×D4—1221no—
498C22×D4—1224no—
499C22×D4—1221no—
500C22×D4—2442no—
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—611no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C2×Q16—614no—
508C2×Q16—2442no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1224no—
512C2×SD16—2442no—
513C2×M16—42no—
514C2×M16—614no—
515C2×M16—2442no—
516C2×M16C22×D6114yescomplemented
517C22×C8—611no—
518C22×C8—611no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521#126—1228no—
522#125—614no—
523#125—1222no—
524#125—1228no—
525#124—614no—
526#124—1222no—
527#123—1228no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535#121—614no—
536#121—1228no—
537#121—1222no—
538#120—1228no—
539C4×Q8—614no—
540C4×Q8—1222no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1222no—
545#117—614no—
546#117—1228no—
547#117—1222no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C4⋊C4C22×D6111yescharacteristic
561C2×C4⋊C4C22×D6114yescomplemented
562C2×C22⋊C4—611no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—1228no—
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×C22⋊C4—1221no—
573C2×C42—611no—
574C2×C42—1221no—
575C2×C42—1221no—
576#107—614no—
577#106—614no—
578#106—614no—
579C4⋊C8—614no—
580#103—614no—
581#103—614no—
582#103C22×D6114yescomplemented
583#103C22×D6114yescomplemented
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588#102C22×D6114yes—
589#102C22×D6114yes—
590C22⋊C8—614no—
591C22⋊C8—614no—
592C4×C8—614no—
593C24—21no—
594C24—611no—
595C24—1224no—
596C24—1221no—
597C24—4882no—
598C24—2444no—
599C24—2444no—
600C24D4×D6111yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—612no—
608C2×Q8—1221no—
609C2×Q8—1222no—
610C2×Q8—1222no—
611C2×Q8C23×D6112yes—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—614no—
617C2×D4—612no—
618C2×D4—1224no—
619C2×D4—1228no—
620C2×D4—1224no—
621C2×D4—1221no—
622C2×D4—1222no—
623C2×D4—1222no—
624C2×D4—4882no—
625C2×D4—2444no—
626C2×D4—2448no—
627C2×D4—2442no—
628C2×D4—2444no—
629C2×D4#1175822214yes—
630C2×D4C23×D6112yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—612no—
644C22×C4—612no—
645C22×C4—1224no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—4882no—
652C22×C4D4×D6112yes—
653C22×C4D4×D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657SD16—1228no—
658SD16—2444no—
659M16—44no—
660M16—2444no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—612no—
664C2×C8—612no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—614no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1224no—
683C4⋊C4C23×D6112yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C42—612no—
696C42—612no—
697C42—1224no—
698C42—1224no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—42no—
705C23—42no—
706C23—612no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—4884no—
712C23—48816no—
713C23—2448no—
714C23—2448no—
715C23—2442no—
716C23—2442no—
717C23—2442no—
718C23C2×D4×D6112yes—
719C23C2×D4×D6111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1222no—
724Q8—1222no—
725Q8—2442no—
726D4—22no—
727D4—24no—
728D4—48no—
729D4—1222no—
730D4—1222no—
731D4—4884no—
732D4—2444no—
733D4—2448no—
734D4—2442no—
735D4C2×#1175822214yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—612no—
749C2×C4—612no—
750C2×C4—612no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1224no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—4884no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4—2442no—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4C2×#1175822212yes—
767C2×C4#1451982212yes—
768C2×C4C24×D6111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1222no—
772C8—1222no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—48816no—
785C22—4884no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2444no—
790C22#1684040212yes—
791C22#1684055812yes—
792C22#1684057112yes—
793C22C22×D4×D6111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—1222no—
799C4—1222no—
800C4—1222no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4#1684040212yes—
805C4C22×#1175822211yescharacteristic
806C4C2×#1451982211yescharacteristic
807C2—42no—
808C2—44no—
809C2—4882no—
810C2—2442no—
811C2#2145803614yesdirect product factor
812C2C2×#1684040211yescharacteristic
813C2C2×#1684055811yescharacteristic
814C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
hypercenterC2×#417D61
hypocenterC61C2×#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840447C2semidirect
3. #21458036C2direct (N × H)
4. C2×#16840118C2semidirect
5. C2×#16840080C2semidirect
6. C2×#16840102C2semidirect
7. C2×#16840060C2semidirect
8. C2×#16840019C2semidirect
9. C2×#16840008C2semidirect
10. C2×#16839987C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839914C2semidirect
13. C2×#16839853C2semidirect
14. C2×#16839838C2semidirect
15. C2×#16839765C2semidirect
16. C2×C61×#417C2semidirect
18. C22×#11758202C22semidirect
23. #16840447C22semidirect
27. C2×#14519768C22semidirect
33. C2×#14519756C22semidirect
38. C2×#14519742C22semidirect
44. #16840118C22semidirect
45. #16840102C22semidirect
46. #16840080C22semidirect
47. #16840060C22semidirect
48. #16840019C22semidirect
49. #16840008C22semidirect
50. #16839987C22semidirect
51. #16839924C22semidirect
52. #16839914C22semidirect
53. #16839853C22semidirect
54. #16839838C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519708C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. #16839765C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
66. C2×C22⋊#92418C22semidirect
68. C2×C8×Dic61C22semidirect
70. C22×M16×C61C22semidirect
71. C22×C4⋊C4×C61C22semidirect
72. C61×#417C22semidirect
73. C2×#103×C61C22semidirect
74. C2×#103×C61C22semidirect
90. C2×#11758202C23semidirect
101. #14519768C23semidirect
110. #14519756C23semidirect
118. #14519742C23semidirect
149. #14519711C23semidirect
150. #14519708C23semidirect
151. #14519708C23semidirect
152. #14519706C23semidirect
153. #14519702C23semidirect
154. #14519701C23semidirect
159. C22⋊#92418C23semidirect
161. C8×Dic61C23semidirect
173. C2×M16×C61C23semidirect
180. C2×C4⋊C4×C61C23semidirect
181. #103×C61C23semidirect
182. #103×C61C23semidirect
414. C2×#417D61semidirect
418. C2×C61#3323semidirect
430. C22×M16C2×D61semidirect
452. C22×C4⋊C4C2×D61semidirect
470. #417C2×D61semidirect
473. C2×#103C2×D61semidirect
474. C2×#103C2×D61semidirect
484. C61C2×#3323semidirect
516. C2×M16C22×D61semidirect
561. C2×C4⋊C4C22×D61semidirect
582. #103C22×D61semidirect
583. #103C22×D61semidirect
811. C2#21458036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404472
C2×#168404002
#214580362
C2×#168401182
C2×#168400802
C2×#168401022
C2×#168400602
C2×#168400192
C2×#168400082
C2×#168399872
C2×#168399242
C2×#168399142
C2×#168398532
C2×#168398382
C2×#168397652
C2×C61×#4172
C2×#332361