Finite Group Databasebeta

← C2×#21457901 #30556540

Subgroups — C2×#21457901 #30556540

Order 15616.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840400C211yesmaximal, characteristic
3#21457901C2116yesmaximal, direct product factor
4C2×#16840123C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840075C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16840002C211yesmaximal, characteristic, complemented
10C2×#16839987C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839914C211yesmaximal, characteristic, complemented
13C2×#16839859C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840467—24no—
23#16840467C2218yescomplemented
24#16840400—24no—
25#16840400C2218yes—
26C2×#14519776C2211yescharacteristic, complemented
27C2×#14519767—21no—
28C2×#14519766C2211yescharacteristic
29C2×#14519760—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519756—21no—
32C2×#14519756C2211yescharacteristic, complemented
33C2×#14519755—21no—
34C2×#14519753C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519749—21no—
37C2×#14519745—21no—
38C2×#14519742C2211yescharacteristic, complemented
39C2×D4×Dic61C2211yescharacteristic
40C2×C4×C22⋊D61—21no—
41C2×C4×C22⋊D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43C22×#11758198—21no—
44#16840123C2218yescomplemented
45#16840096C2218yescomplemented
46#16840075C2218yescomplemented
47#16840040C2218yescomplemented
48#16840008C2218yescomplemented
49#16840002C2218yescomplemented
50#16839987C2218yescomplemented
51#16839924C2218yescomplemented
52#16839914C2218yescomplemented
53#16839859C2218yescomplemented
54#16839831C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519701C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#102×D61C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic, 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×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61D411yescharacteristic
84C2×D4×D61—24no—
85C2×D4×D61—22no—
86C2×D4×D61—42no—
87C2×D4×D61C2314yes—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758202—42no—
92C2×#11758202C2314yescomplemented
93C2×#11758190—42no—
94C2×#11758190C2314yes—
95C2×#11758200—24no—
96C2×#11758200C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C2×C8×D61—42no—
100C2×C8×D61C2314yes—
101#14519776—22no—
102#14519776C2314yescomplemented
103#14519767—28no—
104#14519766—22no—
105#14519766C2314yes—
106#14519760—28no—
107#14519757—22no—
108#14519757C2314yes—
109#14519756—22no—
110#14519756—28no—
111#14519756C2314yescomplemented
112#14519755—28no—
113#14519753—22no—
114#14519753C2314yes—
115#14519751—22no—
116#14519751C2314yes—
117#14519749—28no—
118#14519745—28no—
119#14519742—22no—
120#14519742C2314yescomplemented
121D4×Dic61—22no—
122D4×Dic61C2314yes—
123C4×C22⋊D61—28no—
124C4×C22⋊D61D414yes—
125C4×C22⋊D61C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196D411yescharacteristic
135C4⋊C4×D61—22no—
136C4⋊C4×D61C2314yes—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61D411yescharacteristic
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—28no—
146C2×#11758198D411yescharacteristic
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yescomplemented
150#14519710C2314yescomplemented
151#14519710C2314yescomplemented
152#14519706C2314yescomplemented
153#14519702C2314yescomplemented
154#14519701C2314yescomplemented
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yescomplemented
160#14519689C2314yes—
161#14519687C2314yescomplemented
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—22no—
177C2×C4⋊C4×C61—21no—
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—21no—
211C22×C4×C61—24no—
212C22×C4×C61—24no—
213C22×C4×C61—44no—
214C22×C4×C61—82no—
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—24no—
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×D61—24no—
243C2×C4×D61—82no—
244C2×C4×D61C2×D412yes—
245C2×C4×D61C2412yes—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—21no—
249C2×Dic122—24no—
250C2×Dic122—82no—
251C2×Dic122C2412yes—
252M16×C61—44no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61C2412yes—
256C2×C8×C61C2412yes—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—24no—
260C4⋊C4×C61C2412yes—
261C4⋊C4×C61C2412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61C2×D414yes—
265#11758202—44no—
266#11758200—28no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198C2×D414yes—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61C2412yes—
277C4⋊Dic61C2412yes—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196C2×D414yes—
284C4×Dic61—24no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2412yes—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291#11758190—44no—
292C8×D61—44no—
293C23×C61—24no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D412yes—
301C23×C61C22×D411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—48no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—48no—
310C22×D61—84no—
311C22×D61—816no—
312C22×D61#13714yes—
313C22×D61C22×D412yes—
314Q8×C61—22no—
315Q8×C61—22no—
316Q8×C61—42no—
317D4×C61—24no—
318D4×C61—22no—
319D4×C61—48no—
320D4×C61C2×#4114yes—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—42no—
332C2×C4×C61—84no—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4112yes—
336C2×C4×C61H(5,𝔽2)12yes—
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—28no—
339C22⋊D61—48no—
340C22⋊D61—84no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—42no—
350C2×Dic61—84no—
351C2×Dic61C22×D412yes—
352C2×Dic61C22×D412yes—
353C2×Dic61C22×D412yes—
354D244—22no—
355D244—22no—
356D244—42no—
357C4×D61—24no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—84no—
361Dic122—22no—
362Dic122—22no—
363Dic122—42no—
364Dic122—84no—
365C8×C61—22no—
366C8×C61—22no—
367#92418—22no—
368#92418—22no—
369C2×#3314—611nomaximal, Sylow
370C22×C61—24no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—48no—
375C22×C61—44no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61#54612yes—
379C22×C61C2×#13712yes—
380C22×C61#57612yes—
381C22×C61C23×D411yescharacteristic
382C2×D61—22no—
383C2×D61—28no—
384C2×D61—22no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—816no—
389C2×D61—84no—
390C2×D61C2×#13714yes—
391C4×C61—22no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61#54612yes—
396C4×C61C22×#4111yescharacteristic
397C4×C61C2×H(5,𝔽2)11yescharacteristic
398Dic61—22no—
399Dic61—22no—
400Dic61—22no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C2×#554—611no—
405C2×#546—611no—
406#3314—6116no—
407C2×#489—611no—
408C2×#484—611no—
409C2×#480—611no—
410C2×#474—611no—
411C2×#468—611no—
412C2×#467—611no—
413C2×#464—611no—
414C2×#452—611no—
415C2×#450—611no—
416C2×#440—611no—
417C2×#435—611no—
418C2×#417D6111yescharacteristic, complemented
419C22×#102—611no—
420C2×C61—44no—
421C2×C61—42no—
422C2×C61#331414yescomplemented
423C2×C61C2×#54611yescharacteristic
424C2×C61C22×#13711yescharacteristic
425C2×C61C2×#57611yescharacteristic
426D61—24no—
427D61—82no—
428C22×#41C2×D6111yescharacteristic
429C23×D4—611no—
430C22×Q16—611no—
431C22×SD16—611no—
432C22×SD16—611no—
433C22×M16C2×D6111yescharacteristic, complemented
434C23×C8—611no—
435#554—618no—
436#554—1224no—
437#546—618no—
438#546—1224no—
439C2×C4⋊Q8—611no—
440C2×#125—1221no—
441C2×#124—611no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—1221no—
447C2×C22⋊Q8—1221no—
448C2×#121—611no—
449C2×#121—1221no—
450C2×#120—1221no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—1221no—
455C22×C4⋊C4—611no—
456C22×C4⋊C4C2×D6111yescharacteristic, complemented
457C22×C22⋊C4—1221no—
458#489—618no—
459#484—618no—
460#480—618no—
461#474—618no—
462#468—618no—
463#467—618no—
464#464—618no—
465#452—618no—
466#450—618no—
467#440—618no—
468#435—618no—
469C2×#107—611no—
470C2×#107—611no—
471C2×#107—611no—
472C2×C4⋊C8—611no—
473#417C2×D6118yescomplemented
474C2×#103—611no—
475C2×#103—611no—
476C2×#103C2×D6111yescharacteristic, complemented
477C2×#103C2×D6111yescharacteristic, complemented
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—618no—
483C2×#102C2×D6111yescharacteristic
484C2×#102C2×D6111yescharacteristic
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×#97—611no—
488C61C2×#331411yescharacteristic, complemented, Sylow
489C25—1221no—
490C2×#41—22no—
491C2×#41—24no—
492C2×#41—42no—
493C2×#41C22×D6114yes—
494C22×Q8—611no—
495C22×Q8—1221no—
496C22×Q8C22×D6111yescharacteristic
497C22×D4—21no—
498C22×D4—611no—
499C22×D4—614no—
500C22×D4—611no—
501C22×D4—1222no—
502C22×D4—1221no—
503C22×D4—1224no—
504C22×D4—1221no—
505C22×D4—2442no—
506C22×D4C22×D6111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—611no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4C22×D6111yescharacteristic
513C2×Q16—614no—
514C2×Q16—2442no—
515C2×SD16—614no—
516C2×SD16—614no—
517C2×SD16—1224no—
518C2×SD16—2442no—
519C2×M16—42no—
520C2×M16C22×D6114yescomplemented
521C22×C8—611no—
522C22×C8—611no—
523C22×C8—614no—
524C22×C8—2442no—
525C22×C8C22×D6111yescharacteristic
526C22×C8C22×D6111yescharacteristic
527C4⋊Q8—614no—
528C4⋊Q8—1222no—
529#125—1228no—
530#124—614no—
531#124—1222no—
532#123—1228no—
533C22⋊Q8—614no—
534C22⋊Q8—614no—
535C22⋊Q8—614no—
536C22⋊Q8—1228no—
537C22⋊Q8—1228no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541#121—614no—
542#121—1228no—
543#121—1222no—
544#120—1228no—
545C4×Q8—614no—
546C4×Q8—1222no—
547C4×D4—614no—
548C4×D4—614no—
549C4×D4—614no—
550C4×D4—1222no—
551C4×D4—1228no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—614no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6114yescomplemented
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—1228no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C42—611no—
579C2×C42—1221no—
580#107—614no—
581#107—614no—
582#107—614no—
583C4⋊C8—614no—
584#103—614no—
585#103—614no—
586#103C22×D6114yescomplemented
587#103C22×D6114yescomplemented
588#102—614no—
589#102—614no—
590#102—614no—
591#102—614no—
592#102C22×D6114yes—
593#102C22×D6114yes—
594C22⋊C8—614no—
595C22⋊C8—614no—
596#97—614no—
597C24—21no—
598C24—611no—
599C24—1224no—
600C24—1221no—
601C24—4882no—
602C24—2444no—
603C24—2444no—
604C24D4×D6111yescharacteristic
605#41—28no—
606#41—44no—
607#41—48no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—612no—
612C2×Q8—1224no—
613C2×Q8—1221no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—4882no—
617C2×Q8C23×D6112yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—44no—
622C2×D4—614no—
623C2×D4—612no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1228no—
627C2×D4—1224no—
628C2×D4—1221no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—4882no—
632C2×D4—2444no—
633C2×D4—2448no—
634C2×D4—2444no—
635C2×D4#1175822214yes—
636C2×D4C23×D6112yes—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—82no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—1224no—
652C22×C4—1224no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—4882no—
659C22×C4—4882no—
660C22×C4D4×D6112yes—
661C22×C4D4×D6111yescharacteristic
662C22×C4C23×D6112yes—
663C22×C4C23×D6111yescharacteristic
664Q16—2444no—
665SD16—1228no—
666SD16—2444no—
667M16—44no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—612no—
671C2×C8—612no—
672C2×C8—1222no—
673C2×C8—1222no—
674C2×C8—2444no—
675C2×C8C23×D6112yes—
676C2×C8C23×D6112yes—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—24no—
680C4⋊C4—614no—
681C4⋊C4—612no—
682C4⋊C4—612no—
683C4⋊C4—1224no—
684C4⋊C4—1224no—
685C4⋊C4—1224no—
686C4⋊C4—1224no—
687C4⋊C4—1224no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1224no—
691C4⋊C4C23×D6112yes—
692C4⋊C4C23×D6112yes—
693C22⋊C4—614no—
694C22⋊C4—614no—
695C22⋊C4—1224no—
696C22⋊C4—1224no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C42—612no—
703C42—612no—
704C42—1224no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—42no—
711C23—42no—
712C23—614no—
713C23—612no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—48816no—
718C23—4884no—
719C23—2448no—
720C23—2448no—
721C23—2442no—
722C23—2442no—
723C23—2442no—
724C23C2×D4×D6112yes—
725C23C2×D4×D6111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—1222no—
730Q8—1222no—
731Q8—4884no—
732Q8—2442no—
733D4—22no—
734D4—24no—
735D4—48no—
736D4—1228no—
737D4—1222no—
738D4—1222no—
739D4—4884no—
740D4—2448no—
741D4—2442no—
742D4C2×#1175822214yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—4884no—
768C2×C4—4884no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4C2×D4×D6112yes—
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×#1175822212yes—
775C2×C4#1451982212yes—
776C2×C4C24×D6111yescharacteristic
777C8—22no—
778C8—22no—
779C8—1222no—
780C8—1222no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—44no—
788C22—48no—
789C22—614no—
790C22—1222no—
791C22—1222no—
792C22—1228no—
793C22—48816no—
794C22—4884no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22#1684040212yes—
799C22#137×D6112yes—
800C22#1684056612yes—
801C22C22×D4×D6111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—1222no—
807C4—1222no—
808C4—1222no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4#1684040212yes—
813C4C22×#1175822211yescharacteristic
814C4C2×#1451982211yescharacteristic
815C2—42no—
816C2—44no—
817C2—1224no—
818C2—4882no—
819C2#2145790114yesdirect product factor
820C2C2×#1684040211yescharacteristic
821C2C2×#137×D6111yescharacteristic
822C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840400C2
hypercenterC2×#417D61
hypocenterC61C2×#3314
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×#16840467C2semidirect
3. #21457901C2direct (N × H)
4. C2×#16840123C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840075C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16840002C2semidirect
10. C2×#16839987C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839914C2semidirect
13. C2×#16839859C2semidirect
14. C2×#16839831C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#417C2semidirect
18. C22×#11758202C22semidirect
23. #16840467C22semidirect
26. C2×#14519776C22semidirect
32. C2×#14519756C22semidirect
38. C2×#14519742C22semidirect
44. #16840123C22semidirect
45. #16840096C22semidirect
46. #16840075C22semidirect
47. #16840040C22semidirect
48. #16840008C22semidirect
49. #16840002C22semidirect
50. #16839987C22semidirect
51. #16839924C22semidirect
52. #16839914C22semidirect
53. #16839859C22semidirect
54. #16839831C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519710C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519701C22semidirect
65. #102×D61C22semidirect
66. C2×C22⋊#92418C22semidirect
68. C2×#14519687C22semidirect
70. C22×M16×C61C22semidirect
71. C22×C4⋊C4×C61C22semidirect
72. C61×#417C22semidirect
73. C2×#103×C61C22semidirect
74. C2×#103×C61C22semidirect
92. C2×#11758202C23semidirect
102. #14519776C23semidirect
111. #14519756C23semidirect
120. #14519742C23semidirect
149. #14519711C23semidirect
150. #14519710C23semidirect
151. #14519710C23semidirect
152. #14519706C23semidirect
153. #14519702C23semidirect
154. #14519701C23semidirect
159. C22⋊#92418C23semidirect
161. #14519687C23semidirect
173. C2×M16×C61C23semidirect
180. C2×C4⋊C4×C61C23semidirect
181. #103×C61C23semidirect
182. #103×C61C23semidirect
418. C2×#417D61semidirect
422. C2×C61#3314semidirect
433. C22×M16C2×D61semidirect
456. C22×C4⋊C4C2×D61semidirect
473. #417C2×D61semidirect
476. C2×#103C2×D61semidirect
477. C2×#103C2×D61semidirect
488. C61C2×#3314semidirect
520. C2×M16C22×D61semidirect
567. C2×C4⋊C4C22×D61semidirect
586. #103C22×D61semidirect
587. #103C22×D61semidirect
819. C2#21457901direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168404002
#214579012
C2×#168401232
C2×#168400962
C2×#168400752
C2×#168400402
C2×#168400082
C2×#168400022
C2×#168399872
C2×#168399242
C2×#168399142
C2×#168398592
C2×#168398312
C2×#102×D612
C2×C61×#4172
C2×#331461