Finite Group Databasebeta

← C2×#20291583 #28329821

Subgroups — C2×#20291583 #28329821

Order 13568.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291583C2116yesmaximal, direct product factor
2C2×#16811657C211yesmaximal, characteristic, complemented
3C2×#16811656C211yesmaximal, characteristic, complemented
4C2×#16811655C211yesmaximal, characteristic, complemented
5C2×#16811653C211yesmaximal, characteristic, complemented
6C2×#16811653C211yesmaximal, characteristic, complemented
7C2×#16811652C211yesmaximal, characteristic, complemented
8C2×#16811651C211yesmaximal, characteristic, complemented
9C2×#16811650C211yesmaximal, characteristic, complemented
10C2×#16811647C211yesmaximal, characteristic, complemented
11C2×#16811647C211yesmaximal, characteristic, complemented
12C2×#16811597C211yesmaximal, characteristic, complemented
13C2×#16811596C211yesmaximal, characteristic, complemented
14C2×#16811594C211yesmaximal, characteristic, complemented
15C2×D53⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
16C2×#16811131C211yesmaximal, characteristic
17C22×#11719936C2211yescharacteristic
18C22×#11719936C2211yescharacteristic
19C22×#11719936C2211yescharacteristic, complemented
20C22×#11719940C2211yescharacteristic, complemented
21C22×D53⋊C8C2211yescharacteristic
22C22×D53⋊C8C2211yescharacteristic
23C22×D53⋊C8C2211yescharacteristic, complemented
24C23×#88324C2211yescharacteristic, complemented
25#16811657C2218yescomplemented
26#16811656C2218yescomplemented
27#16811655C2218yescomplemented
28#16811653C2218yescomplemented
29#16811653C2218yescomplemented
30#16811652C2218yescomplemented
31#16811651C2218yescomplemented
32#16811650C2218yescomplemented
33#16811647C2218yescomplemented
34#16811647C2218yescomplemented
35C2×#13133284C2211yescharacteristic, complemented
36C2×#13133284C2211yescharacteristic, complemented
37C2×C4⋊#88324C2211yescharacteristic, complemented
38C2×C4⋊#88324C2211yescharacteristic, complemented
39#16811597C2218yescomplemented
40#16811596C2218yescomplemented
41#16811594C2218yescomplemented
42C2×#13133274C2211yescharacteristic
43C2×#13133274C2211yescharacteristic
44C2×#13133274C2211yescharacteristic
45C2×#13133274C2211yescharacteristic
46C2×#13133274C2211yescharacteristic, complemented
47C2×#13133274C2211yescharacteristic, complemented
48D53⋊(C22⋊C8)C2218yescomplemented
49C2×C22⋊#88324C2211yescharacteristic
50C2×C22⋊#88324C2211yescharacteristic
51C2×C22⋊#88324C2211yescharacteristic
52C2×C22⋊#88324C2211yescharacteristic
53C2×C22⋊#88324C2211yescharacteristic, complemented
54C2×C22⋊#88324C2211yescharacteristic, complemented
55C2×#13133272C2211yescharacteristic, complemented
56C2×#13133272C2211yescharacteristic, complemented
57C2×C4×#88324C2211yescharacteristic, complemented
58C2×C4×#88324C2211yescharacteristic, complemented
59C22×#11719947C2211yescharacteristic
60C23×C4×D53C2211yescharacteristic
61#16811131C418yes—
62#16811131C2218yes—
63C2×#13133200C411yescharacteristic
64C2×#13133195C411yescharacteristic
65C2×#13133195C411yescharacteristic
66C2×#13133190C411yescharacteristic
67C2×#13133190C411yescharacteristic
68C2×#13133187C411yescharacteristic
69C2×#13133185C411yescharacteristic
70C2×#13133179C2211yescharacteristic
71C2×#13133179C2211yescharacteristic
72C2×#13133177C2211yescharacteristic
73C2×#13133177C2211yescharacteristic
74C2×#13133173C2211yescharacteristic
75C2×#123×C53C411yescharacteristic
76C2×#11719936—42no—
77C2×#11719936—42no—
78C2×#11719936—42no—
79C2×#11719936C2314yes—
80C2×#11719936C2314yes—
81C2×#11719936C2314yescomplemented
82C2×#11719940—42no—
83C2×#11719940C2314yescomplemented
84C2×D53⋊C8—42no—
85C2×D53⋊C8—42no—
86C2×D53⋊C8—42no—
87C2×D53⋊C8C2314yes—
88C2×D53⋊C8C2314yes—
89C2×D53⋊C8C2314yescomplemented
90C22×#88324—42no—
91C22×#88324C2311yescharacteristic
92C22×#88324C2311yescharacteristic
93C22×#88324C2311yescharacteristic
94C22×#88324C2311yescharacteristic
95C22×#88324C2311yescharacteristic
96C22×#88324C2311yescharacteristic
97C22×#88324C2311yescharacteristic
98C22×#88324C2311yescharacteristic
99C22×#88324C2314yescomplemented
100#13133284C2314yescomplemented
101#13133284C2314yescomplemented
102C4⋊#88324C2314yescomplemented
103C4⋊#88324C2314yescomplemented
104#13133274C2314yes—
105#13133274C2314yes—
106#13133274C2314yes—
107#13133274C2314yes—
108#13133274C2314yescomplemented
109#13133274C2314yescomplemented
110C22⋊#88324C2314yes—
111C22⋊#88324C2314yes—
112C22⋊#88324C2314yes—
113C22⋊#88324C2314yes—
114C22⋊#88324C2314yescomplemented
115C22⋊#88324C2314yescomplemented
116#13133272C2314yescomplemented
117#13133272C2314yescomplemented
118C4×#88324C2314yescomplemented
119C4×#88324C2314yescomplemented
120C24×D53C2×C411yescharacteristic
121C2×#11719947—42no—
122C2×#11719947—42no—
123C2×#11719947C2×C414yes—
124C2×#11719947C2314yes—
125C22×Dic106C2×C411yescharacteristic
126C22×D212C2×C411yescharacteristic
127C22×D212C2×C411yescharacteristic
128C22×C22⋊D53C2×C411yescharacteristic
129C22×C22⋊D53C2×C411yescharacteristic
130C22×C22⋊D53C2×C411yescharacteristic
131C22×C22⋊D53C2×C411yescharacteristic
132C23×Dic53C2311yescharacteristic
133C23×Dic53C2311yescharacteristic
134C22×C4×D53—42no—
135C22×C4×D53—42no—
136C22×C4×D53C2×C411yescharacteristic
137C22×C4×D53C2×C411yescharacteristic
138C22×C4×D53C2×C414yes—
139C22×C4×D53C2311yescharacteristic
140C22×C4×D53C2311yescharacteristic
141C22×C4×D53C2311yescharacteristic
142C22×C4×D53C2314yes—
143#13133200C2×C418yes—
144#13133195C2×C418yes—
145#13133195C2×C418yes—
146#13133190C2×C418yes—
147#13133190C2×C418yes—
148#13133187C2×C418yes—
149#13133185C2×C418yes—
150#13133179C2×C414yes—
151#13133179C2×C414yes—
152#13133179C2314yes—
153#13133179C2314yes—
154#13133177C2×C414yes—
155#13133177C2×C414yes—
156#13133177C2314yes—
157#13133177C2314yes—
158#13133173C2×C414yes—
159#13133173C2314yes—
160C2×#11719919C2×C411yescharacteristic
161C2×#11719919C2×C411yescharacteristic
162C2×#11719919C2×C411yescharacteristic
163C2×#11719919C2×C411yescharacteristic
164C2×C22⋊Dic53C2×C411yescharacteristic
165C2×#11719921C2×C411yescharacteristic
166C2×#11719921C2×C411yescharacteristic
167C2×#11719921C2×C411yescharacteristic
168C2×#11719921C2×C411yescharacteristic
169C2×#11719921C2×C411yescharacteristic
170C2×#11719921C2×C411yescharacteristic
171C2×C4×Dic53C2311yescharacteristic
172C2×C4×Dic53C2311yescharacteristic
173C22×D4×C53C2×C411yescharacteristic
174C23×C4×C53C2×C411yescharacteristic
175#123×C53C2×C418yes—
176C2×C4⋊C4×C53C2×C411yescharacteristic
177C2×C4⋊C4×C53C2×C411yescharacteristic
178C2×C22⋊C4×C53C2×C411yescharacteristic
179C2×C22⋊C4×C53C2×C411yescharacteristic
180C2×C22⋊C4×C53C2×C411yescharacteristic
181C24×C53C22×C411yescharacteristic
182C24×C53C22×C411yescharacteristic
183C23×D53—24no—
184C23×D53—42no—
185C23×D53—42no—
186C23×D53C22×C411yescharacteristic
187C23×D53C22×C411yescharacteristic
188C23×D53C22×C411yescharacteristic
189C23×D53C22×C414yes—
190C2×D4×C53—42no—
191C2×D4×C53C22×C414yes—
192C22×C4×C53—42no—
193C22×C4×C53C22×C411yescharacteristic
194C22×C4×C53C22×C411yescharacteristic
195C22×C4×C53C22×C411yescharacteristic
196C22×C4×C53C22×C411yescharacteristic
197C22×C4×C53C22×C411yescharacteristic
198C22×C4×C53C22×C414yes—
199C2×C22⋊D53—24no—
200C2×C22⋊D53—42no—
201C2×C22⋊D53—42no—
202C2×C22⋊D53—42no—
203C2×C22⋊D53C22×C414yes—
204C2×C22⋊D53C22×C414yes—
205C2×C22⋊D53C22×C414yes—
206C2×C22⋊D53C22×C414yes—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53C22×C411yescharacteristic
212C22×Dic53C22×C411yescharacteristic
213C22×Dic53C22×C411yescharacteristic
214C22×Dic53C22×C411yescharacteristic
215C22×Dic53C22×C412yes—
216C22×Dic53C22×C412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C22×Dic53C2411yescharacteristic
220#11719947—48no—
221#11719947—44no—
222#11719947—44no—
223C2×D212—24no—
224C2×D212—42no—
225C2×D212C22×C414yes—
226C2×D212C22×C414yes—
227C2×C4×D53—22no—
228C2×C4×D53—22no—
229C2×C4×D53—22no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—22no—
233C2×C4×D53—48no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×C4×D53—42no—
237C2×C4×D53—42no—
238C2×C4×D53C22×C412yes—
239C2×C4×D53C22×C412yes—
240C2×C4×D53C22×C412yes—
241C2×C4×D53C22×C414yes—
242C2×C4×D53C22×C414yes—
243C2×C4×D53C2412yes—
244C2×C4×D53C2412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—42no—
247C2×Dic106C22×C414yes—
248#11719940—44no—
249C2×#88324—22no—
250C2×#88324—22no—
251C2×#88324—22no—
252C2×#88324—22no—
253C2×#88324—22no—
254C2×#88324—22no—
255C2×#88324—22no—
256C2×#88324—22no—
257C2×#88324—44no—
258C2×#88324C2412yes—
259C2×#88324C2412yes—
260C2×#88324C2412yes—
261C2×#88324C2412yes—
262C2×#88324C2412yes—
263C2×#88324C2412yes—
264C2×#88324C2412yes—
265C2×#88324C2412yes—
266#11719936—44no—
267#11719936—44no—
268#11719936—44no—
269D53⋊C8—44no—
270D53⋊C8—44no—
271D53⋊C8—44no—
272C4⋊C4×C53C22×C414yes—
273C4⋊C4×C53C22×C414yes—
274C22⋊C4×C53C22×C414yes—
275C22⋊C4×C53C22×C414yes—
276C22⋊C4×C53C22×C414yes—
277C22⋊Dic53C22×C414yes—
278#11719921C22×C414yes—
279#11719921C22×C414yes—
280#11719921C22×C414yes—
281#11719921C22×C414yes—
282#11719921C22×C414yes—
283#11719921C22×C414yes—
284#11719919C22×C414yes—
285#11719919C22×C414yes—
286#11719919C22×C414yes—
287#11719919C22×C414yes—
288C4×Dic53C22×C412yes—
289C4×Dic53C22×C412yes—
290C4×Dic53C2412yes—
291C4×Dic53C2412yes—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53C23×C412yes—
299C23×C53C23×C412yes—
300C23×C53C23×C411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—22no—
309C22×D53—28no—
310C22×D53—44no—
311C22×D53—44no—
312C22×D53—416no—
313C22×D53#13114yes—
314C22×D53C23×C412yes—
315C22×D53C23×C412yes—
316C22×D53C23×C412yes—
317D4×C53—44no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—44no—
324C2×C4×C53C23×C412yes—
325C2×C4×C53C23×C412yes—
326C2×C4×C53C23×C412yes—
327C2×C4×C53C23×C412yes—
328C2×C4×C53C23×C412yes—
329C22⋊D53—28no—
330C22⋊D53—44no—
331C22⋊D53—44no—
332C22⋊D53—44no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—24no—
338C2×Dic53—24no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53C23×C412yes—
344C2×Dic53C23×C412yes—
345C2×Dic53C23×C412yes—
346C2×Dic53C23×C412yes—
347C2×Dic53C23×C411yescharacteristic
348C2×Dic53H(5,𝔽2)12yes—
349C2×Dic53H(5,𝔽2)12yes—
350C2×Dic53C2511yescharacteristic
351D212—28no—
352D212—44no—
353C4×D53—24no—
354C4×D53—24no—
355C4×D53—24no—
356C4×D53—22no—
357C4×D53—22no—
358C4×D53—22no—
359C4×D53—22no—
360C4×D53—22no—
361C4×D53—22no—
362C4×D53—44no—
363C4×D53—44no—
364Dic106—44no—
365#88324—22no—
366#88324—22no—
367#88324—22no—
368#88324—22no—
369#88324—22no—
370#88324—22no—
371#88324—22no—
372#88324—22no—
373C2×#2976—531nomaximal, Sylow
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—44no—
381C22×C53—44no—
382C22×C53#51812yes—
383C22×C53C2×#13112yes—
384C22×C53#56812yes—
385C22×C53C24×C411yescharacteristic
386C2×D53—22no—
387C2×D53—28no—
388C2×D53—22no—
389C2×D53—22no—
390C2×D53—22no—
391C2×D53—22no—
392C2×D53—22no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—416no—
396C2×D53—44no—
397C2×D53—44no—
398C2×D53C2×#13114yes—
399C4×C53—22no—
400C4×C53—22no—
401C4×C53—22no—
402C4×C53—22no—
403C4×C53—22no—
404Dic53—22no—
405Dic53—22no—
406Dic53—22no—
407Dic53—22no—
408Dic53#51812yes—
409Dic53C2×H(5,𝔽2)11yescharacteristic
410Dic53C2×H(5,𝔽2)11yescharacteristic
411C2×#525—531no—
412#2976—5316no—
413C2×#436—531no—
414C2×#436—531no—
415C2×#435—531no—
416C2×#435—531no—
417C2×#435—531no—
418C2×#435—531no—
419C2×C8×D4—531no—
420C2×C8×D4—531no—
421C2×#433—531no—
422C2×#433—531no—
423C2×#408—531no—
424C2×#408—531no—
425C2×#407—531no—
426C22×C22⋊C8—531no—
427C2×C53—42no—
428C2×C53—42no—
429C2×C53#297614yescomplemented
430C2×C53C2×#51811yescharacteristic
431C2×C53C22×#13111yescharacteristic
432C2×C53C2×#56811yescharacteristic
433D53—24no—
434D53—42no—
435D53—42no—
436C22×#41—531no—
437C24×C4—531no—
438C22×M16—531no—
439C22×M16—531no—
440C22×M16—531no—
441C22×M16—531no—
442C23×C8—531no—
443C23×C8—531no—
444C23×C8—531no—
445C23×C8—531no—
446#525—538no—
447#525—538no—
448C2×#123—531no—
449C2×#123#615711yescharacteristic
450C2×C22⋊Q8—531no—
451C2×C22⋊Q8—531no—
452C2×#121—531no—
453C2×#121—531no—
454C2×#120—531no—
455C2×#120—531no—
456C2×C4×D4—531no—
457C2×C4×D4—531no—
458C2×C4×D4—531no—
459C2×C4×D4—531no—
460C2×#117—531no—
461#436—538no—
462#436—538no—
463#435—538no—
464#435—538no—
465#435—538no—
466#435—538no—
467C8×D4—538no—
468C8×D4—538no—
469#433—538no—
470#433—538no—
471C2×C4⋊C8—531no—
472C2×C4⋊C8—531no—
473C2×C4⋊C8—531no—
474C2×C4⋊C8—531no—
475#408—538no—
476#408—538no—
477#407—538no—
478C2×C22⋊C8—531no—
479C2×C22⋊C8—531no—
480C2×C22⋊C8—538no—
481C2×C22⋊C8—531no—
482C2×C22⋊C8—531no—
483C2×C22⋊C8—531no—
484C2×C22⋊C8—531no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×C22⋊C8—531no—
488C2×C22⋊C8—531no—
489C2×C22⋊C8—531no—
490C2×C22⋊C8—531no—
491C2×#97—531no—
492C2×#97—531no—
493C2×C4×C8—531no—
494C2×C4×C8—531no—
495C53C2×#297611yescharacteristic, complemented, Sylow
496C25—531no—
497C2×#41—534no—
498C2×#41—534no—
499C2×#41—2122no—
500C2×#41—2122no—
501C22×Q8—531no—
502C22×D4—531no—
503C22×D4—531no—
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—531no—
507C22×D4—531no—
508C22×D4C2×#615711yescharacteristic
509C23×C4—531no—
510C23×C4—531no—
511C23×C4—531no—
512C23×C4—531no—
513C23×C4—531no—
514C23×C4—531no—
515C23×C4—531no—
516C23×C4—534no—
517C23×C4—534no—
518C23×C4—2122no—
519C23×C4—2122no—
520C23×C4C2×#615711yescharacteristic
521C2×M16—534no—
522C2×M16—534no—
523C2×M16—534no—
524C2×M16—534no—
525C2×M16—2122no—
526C2×M16—2122no—
527C2×M16—2122no—
528C2×M16—2122no—
529C22×C8—531no—
530C22×C8—531no—
531C22×C8—531no—
532C22×C8—531no—
533C22×C8—531no—
534C22×C8—531no—
535C22×C8—531no—
536C22×C8—531no—
537C22×C8—534no—
538C22×C8—534no—
539C22×C8—534no—
540C22×C8—534no—
541C22×C8—2122no—
542C22×C8—2122no—
543C22×C8—2122no—
544C22×C8—2122no—
545#123—538no—
546#123C2×#615718yes—
547C22⋊Q8—538no—
548C22⋊Q8—538no—
549#121—538no—
550#121—538no—
551#120—538no—
552#120—538no—
553C4×D4—534no—
554C4×D4—534no—
555C4×D4—534no—
556C4×D4—534no—
557C4×D4—534no—
558C4×D4—534no—
559C4×D4—534no—
560C4×D4—534no—
561#117—534no—
562#117—534no—
563C2×C4⋊C4—531no—
564C2×C4⋊C4—531no—
565C2×C4⋊C4—531no—
566C2×C4⋊C4—531no—
567C2×C4⋊C4C2×#615711yescharacteristic
568C2×C4⋊C4C2×#615711yescharacteristic
569C2×C22⋊C4—531no—
570C2×C22⋊C4—531no—
571C2×C22⋊C4—531no—
572C2×C22⋊C4—531no—
573C2×C22⋊C4—531no—
574C2×C22⋊C4—531no—
575C2×C22⋊C4—531no—
576C2×C22⋊C4C2×#615711yescharacteristic
577C2×C22⋊C4C2×#615711yescharacteristic
578C2×C22⋊C4C2×#615711yescharacteristic
579C2×C42—531no—
580C2×C42—531no—
581C4⋊C8—534no—
582C4⋊C8—534no—
583C4⋊C8—534no—
584C4⋊C8—534no—
585C22⋊C8—534no—
586C22⋊C8—534no—
587C22⋊C8—534no—
588C22⋊C8—534no—
589C22⋊C8—534no—
590C22⋊C8—534no—
591C22⋊C8—534no—
592C22⋊C8—534no—
593C22⋊C8—534no—
594C22⋊C8—534no—
595C22⋊C8—534no—
596C22⋊C8—534no—
597#97—534no—
598#97—534no—
599C4×C8—534no—
600C4×C8—534no—
601C24—531no—
602C24—531no—
603C24—531no—
604C24—534no—
605C24—1064no—
606C24—2122no—
607C24—2122no—
608C24C22×#615711yescharacteristic
609C24C22×#615711yescharacteristic
610#41—2124no—
611#41—2124no—
612#41—2128no—
613C2×Q8—534no—
614C2×Q8—2122no—
615C2×D4—42no—
616C2×D4—534no—
617C2×D4—534no—
618C2×D4—534no—
619C2×D4—534no—
620C2×D4—534no—
621C2×D4—534no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—2122no—
625C2×D4—2122no—
626C2×D4—2122no—
627C2×D4—2122no—
628C2×D4C22×#615714yes—
629C22×C4—42no—
630C22×C4—531no—
631C22×C4—532no—
632C22×C4—532no—
633C22×C4—532no—
634C22×C4—532no—
635C22×C4—531no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—531no—
639C22×C4—532no—
640C22×C4—532no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—532no—
644C22×C4—532no—
645C22×C4—534no—
646C22×C4—534no—
647C22×C4—1062no—
648C22×C4—1062no—
649C22×C4—1062no—
650C22×C4—1062no—
651C22×C4—1062no—
652C22×C4—1062no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1062no—
656C22×C4—1062no—
657C22×C4—2122no—
658C22×C4—2122no—
659C22×C4—2124no—
660C22×C4—2124no—
661C22×C4—2128no—
662C22×C4C22×#615711yescharacteristic
663C22×C4C22×#615711yescharacteristic
664C22×C4C22×#615711yescharacteristic
665C22×C4C22×#615711yescharacteristic
666C22×C4C22×#615711yescharacteristic
667C22×C4C22×#615714yes—
668M16—2124no—
669M16—2124no—
670M16—2124no—
671M16—2124no—
672C2×C8—532no—
673C2×C8—532no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—532no—
677C2×C8—532no—
678C2×C8—532no—
679C2×C8—532no—
680C2×C8—1062no—
681C2×C8—1062no—
682C2×C8—1062no—
683C2×C8—1062no—
684C2×C8—1062no—
685C2×C8—1062no—
686C2×C8—1062no—
687C2×C8—1062no—
688C2×C8—2124no—
689C2×C8—2124no—
690C2×C8—2124no—
691C2×C8—2124no—
692C4⋊C4—534no—
693C4⋊C4—534no—
694C4⋊C4—534no—
695C4⋊C4—534no—
696C4⋊C4C22×#615714yes—
697C4⋊C4C22×#615714yes—
698C22⋊C4—534no—
699C22⋊C4—534no—
700C22⋊C4—534no—
701C22⋊C4—534no—
702C22⋊C4—534no—
703C22⋊C4—534no—
704C22⋊C4—534no—
705C22⋊C4C22×#615714yes—
706C22⋊C4C22×#615714yes—
707C22⋊C4C22×#615714yes—
708C42—532no—
709C42—532no—
710C42—532no—
711C42—532no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—534no—
719C23—532no—
720C23—532no—
721C23—532no—
722C23—1068no—
723C23—1062no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23—1062no—
728C23—1062no—
729C23—1062no—
730C23—1062no—
731C23—2124no—
732C23—2124no—
733C23—21216no—
734C23C23×#615712yes—
735C23C23×#615712yes—
736C23C23×#615711yescharacteristic
737Q8—2124no—
738D4—44no—
739D4—1068no—
740D4—1068no—
741D4—2124no—
742D4—2124no—
743D4—2124no—
744D4—2124no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—44no—
751C2×C4—532no—
752C2×C4—532no—
753C2×C4—531no—
754C2×C4—531no—
755C2×C4—532no—
756C2×C4—532no—
757C2×C4—532no—
758C2×C4—532no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1064no—
766C2×C4—1064no—
767C2×C4—1064no—
768C2×C4—1062no—
769C2×C4—1062no—
770C2×C4—1062no—
771C2×C4—1062no—
772C2×C4—1064no—
773C2×C4—1064no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—2124no—
779C2×C4—2124no—
780C2×C4C23×#615712yes—
781C2×C4C23×#615712yes—
782C2×C4C23×#615712yes—
783C2×C4C23×#615712yes—
784C2×C4C23×#615712yes—
785C8—1062no—
786C8—1062no—
787C8—1062no—
788C8—1062no—
789C8—1062no—
790C8—1062no—
791C8—1062no—
792C8—1062no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—534no—
802C22—1062no—
803C22—1062no—
804C22—1068no—
805C22—1062no—
806C22—1062no—
807C22—1062no—
808C22—1062no—
809C22—1062no—
810C22—1062no—
811C22—21216no—
812C22—2124no—
813C22—2124no—
814C22#1681169012yes—
815C22D53⋊#13112yes—
816C22#1681170212yes—
817C22C24×#615711yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—531no—
824C4—531no—
825C4—532no—
826C4—1062no—
827C4—1062no—
828C4—1062no—
829C4—1062no—
830C2—42no—
831C2—42no—
832C2—1064no—
833C2—2122no—
834C2—2122no—
835C2#2029158314yesdirect product factor
836C2C2×#1681169011yescharacteristic
837C2C2×D53⋊#13111yescharacteristic
838C2C2×#1681170211yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#123×C53C4
socleC23×C53C23×C4
prime radicalC2×#16811131C2
cosocleC2×Dic53C25
hypercenterC2×#123#6157
hypocenterC53C2×#2976
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #20291583C2direct (N × H)
2. C2×#16811657C2semidirect
3. C2×#16811656C2semidirect
4. C2×#16811655C2semidirect
5. C2×#16811653C2semidirect
6. C2×#16811653C2semidirect
7. C2×#16811652C2semidirect
8. C2×#16811651C2semidirect
9. C2×#16811650C2semidirect
10. C2×#16811647C2semidirect
11. C2×#16811647C2semidirect
12. C2×#16811597C2semidirect
13. C2×#16811596C2semidirect
14. C2×#16811594C2semidirect
15. C2×D53⋊(C22⋊C8)C2semidirect
19. C22×#11719936C22semidirect
20. C22×#11719940C22semidirect
23. C22×D53⋊C8C22semidirect
24. C23×#88324C22semidirect
25. #16811657C22semidirect
26. #16811656C22semidirect
27. #16811655C22semidirect
28. #16811653C22semidirect
29. #16811653C22semidirect
30. #16811652C22semidirect
31. #16811651C22semidirect
32. #16811650C22semidirect
33. #16811647C22semidirect
34. #16811647C22semidirect
35. C2×#13133284C22semidirect
36. C2×#13133284C22semidirect
37. C2×C4⋊#88324C22semidirect
38. C2×C4⋊#88324C22semidirect
39. #16811597C22semidirect
40. #16811596C22semidirect
41. #16811594C22semidirect
46. C2×#13133274C22semidirect
47. C2×#13133274C22semidirect
48. D53⋊(C22⋊C8)C22semidirect
53. C2×C22⋊#88324C22semidirect
54. C2×C22⋊#88324C22semidirect
55. C2×#13133272C22semidirect
56. C2×#13133272C22semidirect
57. C2×C4×#88324C22semidirect
58. C2×C4×#88324C22semidirect
81. C2×#11719936C23semidirect
83. C2×#11719940C23semidirect
89. C2×D53⋊C8C23semidirect
99. C22×#88324C23semidirect
100. #13133284C23semidirect
101. #13133284C23semidirect
102. C4⋊#88324C23semidirect
103. C4⋊#88324C23semidirect
108. #13133274C23semidirect
109. #13133274C23semidirect
114. C22⋊#88324C23semidirect
115. C22⋊#88324C23semidirect
116. #13133272C23semidirect
117. #13133272C23semidirect
118. C4×#88324C23semidirect
119. C4×#88324C23semidirect
429. C2×C53#2976semidirect
495. C53C2×#2976semidirect
835. C2#20291583direct (N × H)

Maximal subgroups

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

subgroupindex
#202915832
C2×#168116572
C2×#168116562
C2×#168116552
C2×#168116532
C2×#168116522
C2×#168116512
C2×#168116502
C2×#168116472
C2×#168115972
C2×#168115962
C2×#168115942
C2×D53⋊(C22⋊C8)2
C2×#168111312
C2×#297653