Finite Group Databasebeta

← D53⋊#1806 #28319083

Subgroups — D53⋊#1806 #28319083

Order 13568.

1618 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D53⋊#423C211yesmaximal, characteristic, complemented
2C2×D53⋊#104C212yesmaximal
3C2×C4×C4⋊#6157C211yesmaximal, characteristic, complemented
4#20290590C212yesmaximal, complemented
5#20290589C212yesmaximal, complemented
6#20290588C212yesmaximal, complemented
7#20290587C212yesmaximal, complemented
8#20290391C212yesmaximal, complemented
9C4×#41×D53C211yesmaximal, characteristic
10C2×D53⋊M16C2212yes—
11C22×C4⋊#6157—21no—
12C22×C4×#6157C2212yes—
13#16811628C2212yescomplemented
14#16811627C2212yescomplemented
15#16811626—21no—
16#16811626—21no—
17D53⋊(C4⋊C8)—21no—
18D53⋊(C4⋊C8)—21no—
19C2×#13133282C2214yes—
20D53⋊#104—28no—
21C2×#13133281C2214yes—
22C4×C4⋊#6157—21no—
23C4×C4⋊#6157—21no—
24C4×C4⋊#6157C2212yescomplemented
25C4×C4⋊#6157C2212yescomplemented
26C2×(C2×#6157)⋊C4—21no—
27#16811493C2214yescomplemented
28#16811493C2214yescomplemented
29C2×#41×D53C2211yescharacteristic
30#41×Dic53C411yescharacteristic, complemented
31C4×#11719949C2211yescharacteristic
32C4×#11719949C2211yescharacteristic
33C4×#11719945—21no—
34C4×#11719945C411yescharacteristic, complemented
35#16811091—21no—
36#16811091C411yescharacteristic, complemented
37C4×#11719947—21no—
38C4×#11719947—21no—
39C4×#11719947C2211yescharacteristic
40C4×#11719947C2211yescharacteristic
41C4×Q8×D53C411yescharacteristic, complemented
42C4×Q8×D53C411yescharacteristic, complemented
43C4×D4×D53—21no—
44C4×D4×D53—21no—
45C4×D4×D53C411yescharacteristic, complemented
46C4×D4×D53C411yescharacteristic, complemented
47#117×D53—21no—
48#117×D53C2211yescharacteristic
49C2×C42×D53—21no—
50C2×C42×D53C2211yescharacteristic
51C4×#41×C53C411yescharacteristic, complemented
52C23×#6157—22no—
53C2×#11719936C2314yes—
54D53⋊M16—24no—
55D53⋊M16—24no—
56C2×#11719940—22no—
57C2×D53⋊C8—22no—
58C2×C4⋊#6157—28no—
59C2×C4⋊#6157—22no—
60C2×C4⋊#6157—22no—
61C2×C4×#6157—24no—
62C2×C4×#6157—24no—
63C2×C4×#6157—22no—
64C2×C4×#6157C2314yes—
65#13133284—22no—
66#13133284—22no—
67C4⋊#88324—22no—
68C4⋊#88324—22no—
69#13133282—28no—
70#13133281—28no—
71(C2×#6157)⋊C4—22no—
72(C2×#6157)⋊C4—22no—
73C2×#11719949C2311yescharacteristic
74C2×#11719945—21no—
75C2×#11719945C2×C411yescharacteristic
76C2×#11719947—21no—
77C2×#11719947C2311yescharacteristic
78#41×D53—22no—
79#41×D53—22no—
80#41×D53D414yes—
81#41×D53Q814yes—
82C2×Q8×D53C2×C411yescharacteristic
83C2×D4×D53—21no—
84C2×D4×D53C2×C411yescharacteristic
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91Q8×Dic53C2×C411yescharacteristic, complemented
92Q8×Dic53C2×C411yescharacteristic, complemented
93C4×Dic106—21no—
94C4×Dic106—21no—
95C4×Dic106C2×C411yescharacteristic, complemented
96C4×Dic106C2×C411yescharacteristic, complemented
97#13133182—21no—
98#13133182—21no—
99#13133182C2×C411yescharacteristic, complemented
100#13133182C2×C411yescharacteristic, complemented
101C4×D212—21no—
102C4×D212—21no—
103C4×D212C2×C411yescharacteristic, complemented
104C4×D212C2×C411yescharacteristic, complemented
105D4×Dic53—21no—
106D4×Dic53—21no—
107D4×Dic53C2×C411yescharacteristic, complemented
108D4×Dic53C2×C411yescharacteristic, complemented
109#13133179—21no—
110#13133179—21no—
111#13133179C2×C411yescharacteristic, complemented
112#13133179C2×C411yescharacteristic, complemented
113C4×C22⋊D53—21no—
114C4×C22⋊D53—21no—
115C4×C22⋊D53—21no—
116C4×C22⋊D53—21no—
117C4×C22⋊D53—21no—
118C4×C22⋊D53—21no—
119#13133177—21no—
120#13133177—21no—
121#13133177—21no—
122#13133177—21no—
123#13133177—21no—
124#13133177—21no—
125#13133176—21no—
126#13133176C2×C411yescharacteristic
127#13133175—21no—
128#13133175—21no—
129#13133175C2311yescharacteristic
130#13133175C2311yescharacteristic
131#13133174—21no—
132#13133174—21no—
133#13133174—21no—
134#13133173—21no—
135#13133173—21no—
136#13133173—21no—
137C4⋊C4×D53—21no—
138C4⋊C4×D53—21no—
139C4⋊C4×D53C2×C411yescharacteristic
140C4⋊C4×D53C2×C411yescharacteristic
141C22⋊C4×D53—21no—
142C22⋊C4×D53—21no—
143C22⋊C4×D53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2×C411yescharacteristic
148C2×C4×Dic53D411yescharacteristic
149C2×C4×Dic53D411yescharacteristic
150C42×D53—21no—
151C42×D53—21no—
152C42×D53—21no—
153C42×D53—21no—
154C42×D53—21no—
155C42×D53—21no—
156C42×D53—21no—
157C42×D53C2×C411yescharacteristic
158C42×D53C2×C411yescharacteristic
159C42×D53D411yescharacteristic
160C42×D53D411yescharacteristic
161C42×D53D411yescharacteristic
162C42×D53D411yescharacteristic
163C42×D53C2311yescharacteristic
164C42×D53C2311yescharacteristic
165C2×#41×C53C2×C411yescharacteristic
166C4×Q8×C53C2×C411yescharacteristic, complemented
167C4×Q8×C53C2×C411yescharacteristic, complemented
168C4×D4×C53—21no—
169C4×D4×C53—21no—
170C4×D4×C53C2×C411yescharacteristic, complemented
171C4×D4×C53C2×C411yescharacteristic, complemented
172#117×C53—21no—
173#117×C53C2×C411yescharacteristic
174C2×C42×C53—21no—
175C2×C42×C53C2×C411yescharacteristic
176C23×D53—21no—
177C23×D53C2×D411yescharacteristic
178C22×#6157—28no—
179C22×#6157—24no—
180C22×#6157—44no—
181C22×#6157—44no—
182#41×C53—22no—
183#41×C53C4⋊C414yescomplemented
184C2×Q8×C53C22×C411yescharacteristic
185C2×D4×C53—21no—
186C2×D4×C53C22×C411yescharacteristic
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C22⋊C411yescharacteristic
191C22×C4×C53C22⋊C411yescharacteristic
192C22×C4×C53C22×C411yescharacteristic
193C2×C22⋊D53—21no—
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53C22⋊C411yescharacteristic
200C22×Dic53C22⋊C411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202#11719949—21no—
203#11719949—21no—
204#11719949C2×D412yes—
205#11719949C2×Q812yes—
206Q8×D53—22no—
207Q8×D53C4⋊C414yescomplemented
208#11719947—24no—
209#11719947—24no—
210#11719947—21no—
211#11719947—21no—
212#11719947C2×D412yes—
213#11719947C2×Q812yes—
214D4×D53—24no—
215D4×D53—24no—
216D4×D53—22no—
217D4×D53C4⋊C414yescomplemented
218#11719945—22no—
219#11719945—24no—
220#11719945—24no—
221#11719945C4⋊C414yescomplemented
222C2×D212—21no—
223C2×D212C22×C411yescharacteristic
224C2×C4×D53—21no—
225C2×C4×D53—21no—
226C2×C4×D53—21no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—21no—
231C2×C4×D53—21no—
232C2×C4×D53—21no—
233C2×C4×D53—21no—
234C2×C4×D53—21no—
235C2×C4×D53—21no—
236C2×C4×D53—42no—
237C2×C4×D53—44no—
238C2×C4×D53—44no—
239C2×C4×D53C22⋊C411yescharacteristic
240C2×C4×D53C22⋊C411yescharacteristic
241C2×C4×D53C22⋊C411yescharacteristic
242C2×C4×D53C22⋊C411yescharacteristic
243C2×C4×D53C22×C411yescharacteristic
244C2×C4×D53C2×D411yescharacteristic
245C2×C4×D53C2×D411yescharacteristic
246C2×C4×D53C2×D411yescharacteristic
247C2×C4×D53C2×D411yescharacteristic
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2×D411yescharacteristic
250C2×C4×D53C2×D411yescharacteristic
251C2×C4×D53C2×Q812yes—
252C2×C4×D53#4112yes—
253C2×C4×D53#4112yes—
254C2×C4×D53C2411yescharacteristic
255C2×Dic106—21no—
256C2×Dic106C22×C411yescharacteristic
257#11719940—44no—
258C2×#88324—24no—
259C4⋊#6157—28no—
260C4⋊#6157—28no—
261C4×#6157—24no—
262C4×#6157—24no—
263C4×#6157—44no—
264#11719936—24no—
265#11719936—24no—
266D53⋊C8—44no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53C22×C411yescharacteristic
270C4⋊C4×C53C22×C411yescharacteristic
271C22⋊C4×C53—21no—
272C22⋊C4×C53—21no—
273C22⋊C4×C53—21no—
274C42×C53—21no—
275C42×C53—21no—
276C42×C53—21no—
277C42×C53C22⋊C411yescharacteristic
278C42×C53C22⋊C411yescharacteristic
279C42×C53C22×C411yescharacteristic
280C42×C53C22×C411yescharacteristic
281C22⋊Dic53—21no—
282C22⋊Dic53—21no—
283C22⋊Dic53—21no—
284#11719921—21no—
285#11719921—21no—
286#11719921—21no—
287#11719921—21no—
288#11719921—21no—
289#11719921—21no—
290C4⋊Dic53—21no—
291C4⋊Dic53—21no—
292C4⋊Dic53C22×C411yescharacteristic
293C4⋊Dic53C22×C411yescharacteristic
294#11719919—21no—
295#11719919—21no—
296#11719919—21no—
297#11719919—21no—
298#11719919—21no—
299#11719919—21no—
300C4×Dic53—21no—
301C4×Dic53—21no—
302C4×Dic53—21no—
303C4×Dic53—21no—
304C4×Dic53—21no—
305C4×Dic53—21no—
306C4×Dic53—21no—
307C4×Dic53—21no—
308C4×Dic53—21no—
309C4×Dic53C22⋊C411yescharacteristic
310C4×Dic53C22⋊C411yescharacteristic
311C4×Dic53C22⋊C411yescharacteristic
312C4×Dic53C22⋊C411yescharacteristic
313C4×Dic53C22⋊C411yescharacteristic
314C4×Dic53C22⋊C411yescharacteristic
315C4×Dic53C22×C411yescharacteristic
316C4×Dic53C22×C411yescharacteristic
317C4×Dic53C2×D411yescharacteristic
318C4×Dic53C2×D411yescharacteristic
319C4×Dic53C2×D411yescharacteristic
320C4×Dic53C2×D411yescharacteristic
321C23×C53—21no—
322C23×C53C2×C22⋊C411yescharacteristic
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—21no—
326C22×D53—24no—
327C22×D53—42no—
328C22×D53—42no—
329C22×D53C2×C22⋊C411yescharacteristic
330C22×D53#12112yes—
331C22×D53C22⋊Q812yes—
332C22×D53C22×D411yescharacteristic
333C2×#6157—28no—
334C2×#6157—44no—
335C2×#6157—416no—
336C2×#6157—44no—
337Q8×C53—21no—
338Q8×C53C2×C4⋊C412yescomplemented
339D4×C53—24no—
340D4×C53—21no—
341D4×C53C2×C4⋊C412yescomplemented
342C2×C4×C53—21no—
343C2×C4×C53—24no—
344C2×C4×C53—22no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—41no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53C2×C22⋊C411yescharacteristic
351C2×C4×C53C2×C22⋊C411yescharacteristic
352C2×C4×C53C2×C22⋊C411yescharacteristic
353C2×C4×C53C2×C22⋊C411yescharacteristic
354C2×C4×C53C2×C22⋊C411yescharacteristic
355C2×C4×C53C2×C4⋊C412yes—
356C2×C4×C53#11712yes—
357C2×C4×C53C23×C411yescharacteristic
358C22⋊D53—24no—
359C22⋊D53—22no—
360C22⋊D53—22no—
361C22⋊D53—24no—
362C2×Dic53—21no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—21no—
367C2×Dic53—21no—
368C2×Dic53—41no—
369C2×Dic53—42no—
370C2×Dic53—42no—
371C2×Dic53C2×C22⋊C411yescharacteristic
372C2×Dic53C2×C22⋊C411yescharacteristic
373C2×Dic53C2×C22⋊C411yescharacteristic
374C2×Dic53C2×C22⋊C411yescharacteristic
375C2×Dic53C2×C22⋊C411yescharacteristic
376C2×Dic53#12112yes—
377C2×Dic53C22⋊Q812yes—
378C2×Dic53C22×D411yescharacteristic
379D212—22no—
380D212—22no—
381D212—21no—
382D212C2×C4⋊C412yescomplemented
383C4×D53—24no—
384C4×D53—22no—
385C4×D53—22no—
386C4×D53—22no—
387C4×D53—24no—
388C4×D53—22no—
389C4×D53—22no—
390C4×D53—22no—
391C4×D53—22no—
392C4×D53—41no—
393C4×D53—41no—
394C4×D53—42no—
395C4×D53—42no—
396C4×D53—42no—
397C4×D53—42no—
398C4×D53—42no—
399C4×D53—42no—
400C4×D53#10414yescomplemented
401C4×D53C2×C4⋊C412yes—
402C4×D53#11712yes—
403C4×D53#12112yes—
404C4×D53#12112yes—
405C4×D53C22⋊Q812yes—
406C4×D53C22⋊Q812yes—
407C4×D53C22×D411yescharacteristic
408C4×D53C22×Q811yescharacteristic
409C4×D53C2×#4111yescharacteristic
410C4×D53C2×#4111yescharacteristic
411Dic106—21no—
412Dic106—24no—
413Dic106C2×C4⋊C412yescomplemented
414#88324—44no—
415C2×#1806—531nomaximal, Sylow
416C22×C53—21no—
417C22×C53—21no—
418C22×C53—22no—
419C22×C53—41no—
420C22×C53—41no—
421C22×C53#38012yes—
422C22×C53C22×C22⋊C411yescharacteristic
423C2×D53—21no—
424C2×D53—21no—
425C2×D53—24no—
426C2×D53—24no—
427C2×D53—22no—
428C2×D53—41no—
429C2×D53—41no—
430C2×D53—48no—
431C2×D53#38012yes—
432C2×D53C2×#10412yes—
433C2×D53#42112yes—
434C2×D53C2×#12111yescharacteristic
435C2×D53C2×C22⋊Q811yescharacteristic
436#6157—48no—
437C4×C53—21no—
438C4×C53—21no—
439C4×C53—21no—
440C4×C53—22no—
441C4×C53—41no—
442C4×C53—41no—
443C4×C53#38012yes—
444C4×C53C2×#10412yescomplemented
445C4×C53C22×C4⋊C411yescharacteristic
446C4×C53C2×#11711yescharacteristic
447Dic53—21no—
448Dic53—21no—
449Dic53—21no—
450Dic53—22no—
451Dic53—41no—
452Dic53—41no—
453Dic53#38012yes—
454Dic53C2×#10412yescomplemented
455Dic53C2×#12111yescharacteristic
456Dic53C2×C22⋊Q811yescharacteristic
457C2×C4×#41—531no—
458C2×#423—531no—
459C22×#104—532no—
460C2×C4×C4⋊C4—531no—
461#1806—532no—
462#1806—532no—
463#1806—532no—
464#1806—532no—
465C2×#339—532no—
466C2×C53—22no—
467C2×C53—42no—
468C2×C53C2×#38011yescharacteristic
469C2×C53C22×#10411yescharacteristic
470C2×C53C2×#42111yescharacteristic
471D53—21no—
472D53—21no—
473D53—42no—
474D53#180614yescomplemented
475C22×#41—531no—
476C22×M16—532no—
477C4×#41—531no—
478C4×#41—531no—
479C4×#41—531no—
480C4×#41—531no—
481C4×#41—531no—
482C4×#41—531no—
483C4×#41—531no—
484C4×#41—1061no—
485C4×#41—1061no—
486C4×#41—1061no—
487C4×#41—1061no—
488C4×#41#615711yescharacteristic, complemented
489C2×C4×Q8—531no—
490C2×C4×Q8—531no—
491C2×C4×D4—531no—
492C2×C4×D4—531no—
493C2×C4×D4—1061no—
494C2×C4×D4—1061no—
495C2×#117—531no—
496C2×#117—1061no—
497C22×C4⋊C4—1061no—
498C22×C42—531no—
499C22×C42—532no—
500C22×C42—1061no—
501#423—532no—
502#423—532no—
503#423—1061no—
504#423—1061no—
505C2×C4⋊C8—1061no—
506C2×C4⋊C8—1061no—
507C2×#104—534no—
508C2×#104—534no—
509C2×#104—1068no—
510C4×C4⋊C4—532no—
511C4×C4⋊C4—532no—
512C4×C4⋊C4—1061no—
513C4×C4⋊C4—1061no—
514C2×#95—1061no—
515#339—534no—
516#339—534no—
517C53C2×#180611yescharacteristic, complemented, Sylow
518C2×#41—534no—
519C2×#41—534no—
520C2×#41—531no—
521C2×#41—531no—
522C2×#41—531no—
523C2×#41—1061no—
524C2×#41—1061no—
525C2×#41—1062no—
526C2×#41—1062no—
527C2×#41C2×#615711yescharacteristic
528C22×Q8—531no—
529C22×D4—531no—
530C22×D4—1061no—
531C23×C4—531no—
532C23×C4—531no—
533C23×C4—531no—
534C23×C4—1061no—
535C23×C4—1061no—
536C23×C4—1061no—
537C23×C4—1062no—
538C2×M16—534no—
539C2×M16—1062no—
540C2×M16—1064no—
541C2×M16—1064no—
542C22×C8—1062no—
543C4×Q8—531no—
544C4×Q8—531no—
545C4×Q8—531no—
546C4×Q8—531no—
547C4×Q8—531no—
548C4×Q8—531no—
549C4×Q8—1061no—
550C4×Q8—1061no—
551C4×Q8—1061no—
552C4×Q8—1061no—
553C4×Q8C2×#615711yescharacteristic, complemented
554C4×Q8C2×#615711yescharacteristic, complemented
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—531no—
558C4×D4—531no—
559C4×D4—531no—
560C4×D4—531no—
561C4×D4—531no—
562C4×D4—531no—
563C4×D4—1061no—
564C4×D4—1061no—
565C4×D4—1061no—
566C4×D4—1061no—
567C4×D4—1061no—
568C4×D4—1061no—
569C4×D4—1061no—
570C4×D4—1061no—
571C4×D4—1061no—
572C4×D4—1061no—
573C4×D4—1061no—
574C4×D4—1061no—
575C4×D4—1061no—
576C4×D4—1061no—
577C4×D4—1061no—
578C4×D4—1061no—
579C4×D4—1061no—
580C4×D4—1061no—
581C4×D4C2×#615711yescharacteristic, complemented
582C4×D4C2×#615711yescharacteristic, complemented
583#117—21no—
584#117—531no—
585#117—531no—
586#117—531no—
587#117—1061no—
588#117—1061no—
589#117—1061no—
590#117—1061no—
591#117—1061no—
592#117—1061no—
593#117—1061no—
594#117—1061no—
595#117—1061no—
596#117C2×#615711yescharacteristic
597C2×C4⋊C4—531no—
598C2×C4⋊C4—531no—
599C2×C4⋊C4—1061no—
600C2×C4⋊C4—1061no—
601C2×C4⋊C4—1062no—
602C2×C4⋊C4—1062no—
603C2×C4⋊C4—1068no—
604C2×C22⋊C4—1061no—
605C2×C22⋊C4—1061no—
606C2×C22⋊C4—1061no—
607C2×C42—21no—
608C2×C42—531no—
609C2×C42—531no—
610C2×C42—531no—
611C2×C42—531no—
612C2×C42—531no—
613C2×C42—531no—
614C2×C42—531no—
615C2×C42—531no—
616C2×C42—531no—
617C2×C42—531no—
618C2×C42—531no—
619C2×C42—534no—
620C2×C42—1061no—
621C2×C42—1061no—
622C2×C42—1061no—
623C2×C42—1061no—
624C2×C42—1061no—
625C2×C42—1061no—
626C2×C42—1061no—
627C2×C42—1061no—
628C2×C42—1061no—
629C2×C42—1061no—
630C2×C42—1064no—
631C2×C42—1064no—
632C2×C42—1062no—
633C2×C42C2×#615711yescharacteristic
634C4⋊C8—1062no—
635C4⋊C8—1062no—
636C4⋊C8—1062no—
637C4⋊C8—1062no—
638#104—1068no—
639#104—1068no—
640#95—1062no—
641#95—1062no—
642C24—531no—
643C24—1061no—
644#41—22no—
645#41—532no—
646#41—532no—
647#41—532no—
648#41—532no—
649#41—534no—
650#41—1064no—
651#41—1064no—
652#41—1064no—
653#41—1064no—
654#41—1061no—
655#41—1061no—
656#41—1061no—
657#41—1061no—
658#41—1062no—
659#41C4⋊#615714yescomplemented
660C2×Q8—534no—
661C2×Q8—531no—
662C2×Q8—1061no—
663C2×Q8—1062no—
664C2×Q8C22×#615711yescharacteristic
665C2×D4—21no—
666C2×D4—534no—
667C2×D4—531no—
668C2×D4—1061no—
669C2×D4—1062no—
670C2×D4—1061no—
671C2×D4—1064no—
672C2×D4—1064no—
673C2×D4—1061no—
674C2×D4—1061no—
675C2×D4C22×#615711yescharacteristic
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—531no—
680C22×C4—531no—
681C22×C4—531no—
682C22×C4—531no—
683C22×C4—532no—
684C22×C4—532no—
685C22×C4—532no—
686C22×C4—532no—
687C22×C4—531no—
688C22×C4—531no—
689C22×C4—531no—
690C22×C4—531no—
691C22×C4—531no—
692C22×C4—531no—
693C22×C4—531no—
694C22×C4—531no—
695C22×C4—531no—
696C22×C4—531no—
697C22×C4—531no—
698C22×C4—1061no—
699C22×C4—1064no—
700C22×C4—1064no—
701C22×C4—1064no—
702C22×C4—1061no—
703C22×C4—1061no—
704C22×C4—1061no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1064no—
712C22×C4—1068no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—2124no—
716C22×C4—2122no—
717C22×C4—2124no—
718C22×C4—2124no—
719C22×C4—2124no—
720C22×C4C22⋊#615711yescharacteristic
721C22×C4C22⋊#615711yescharacteristic
722C22×C4C22×#615711yescharacteristic
723M16—1064no—
724M16—1064no—
725M16—2124no—
726C2×C8—1064no—
727C2×C8—2124no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—531no—
731C4⋊C4—531no—
732C4⋊C4—1061no—
733C4⋊C4—1061no—
734C4⋊C4—1061no—
735C4⋊C4—1061no—
736C4⋊C4—1061no—
737C4⋊C4—1061no—
738C4⋊C4—1068no—
739C4⋊C4—1068no—
740C4⋊C4—1061no—
741C4⋊C4—1061no—
742C4⋊C4C22×#615711yescharacteristic
743C4⋊C4C22×#615711yescharacteristic
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—1061no—
748C22⋊C4—1061no—
749C22⋊C4—1061no—
750C22⋊C4—1061no—
751C22⋊C4—1061no—
752C22⋊C4—1061no—
753C22⋊C4—1061no—
754C22⋊C4—1061no—
755C22⋊C4—1061no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—531no—
760C42—531no—
761C42—531no—
762C42—531no—
763C42—531no—
764C42—531no—
765C42—531no—
766C42—531no—
767C42—531no—
768C42—531no—
769C42—531no—
770C42—531no—
771C42—1061no—
772C42—1061no—
773C42—1061no—
774C42—1061no—
775C42—1061no—
776C42—1061no—
777C42—1064no—
778C42—1064no—
779C42—1061no—
780C42—1061no—
781C42—1061no—
782C42—2124no—
783C42C22⋊#615711yescharacteristic
784C42C22⋊#615711yescharacteristic
785C42C22×#615711yescharacteristic
786C42C22×#615711yescharacteristic
787C23—21no—
788C23—531no—
789C23—532no—
790C23—532no—
791C23—531no—
792C23—1062no—
793C23—1062no—
794C23—1064no—
795C23—1061no—
796C23—2122no—
797C23—2122no—
798C23C2×C22⋊#615711yescharacteristic
799Q8—21no—
800Q8—532no—
801Q8—1064no—
802Q8—1061no—
803Q8C2×C4⋊#615712yescomplemented
804D4—24no—
805D4—21no—
806D4—532no—
807D4—1062no—
808D4—1062no—
809D4—1064no—
810D4—1062no—
811D4—1062no—
812D4—1064no—
813D4—1061no—
814D4C2×C4⋊#615712yescomplemented
815C2×C4—21no—
816C2×C4—24no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—532no—
824C2×C4—532no—
825C2×C4—531no—
826C2×C4—531no—
827C2×C4—531no—
828C2×C4—532no—
829C2×C4—532no—
830C2×C4—532no—
831C2×C4—532no—
832C2×C4—534no—
833C2×C4—532no—
834C2×C4—531no—
835C2×C4—531no—
836C2×C4—532no—
837C2×C4—531no—
838C2×C4—531no—
839C2×C4—531no—
840C2×C4—531no—
841C2×C4—531no—
842C2×C4—1062no—
843C2×C4—1062no—
844C2×C4—1062no—
845C2×C4—1062no—
846C2×C4—1062no—
847C2×C4—1062no—
848C2×C4—1064no—
849C2×C4—1062no—
850C2×C4—1062no—
851C2×C4—1062no—
852C2×C4—1061no—
853C2×C4—1064no—
854C2×C4—1062no—
855C2×C4—1068no—
856C2×C4—1061no—
857C2×C4—1061no—
858C2×C4—2121no—
859C2×C4—2121no—
860C2×C4—2122no—
861C2×C4—2122no—
862C2×C4—2122no—
863C2×C4—2122no—
864C2×C4—2122no—
865C2×C4—2122no—
866C2×C4—2121no—
867C2×C4—2122no—
868C2×C4—2124no—
869C2×C4—21216no—
870C2×C4—2124no—
871C2×C4—2122no—
872C2×C4C2×C22⋊#615711yescharacteristic
873C2×C4C2×C22⋊#615711yescharacteristic
874C2×C4C2×C22⋊#615711yescharacteristic
875C2×C4C2×C22⋊#615711yescharacteristic
876C2×C4C2×C22⋊#615711yescharacteristic
877C2×C4C2×C4⋊#615712yes—
878C2×C4#1313329612yes—
879C2×C4C23×#615711yescharacteristic
880C8—2124no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—41no—
885C22—41no—
886C22—532no—
887C22—532no—
888C22—532no—
889C22—531no—
890C22—531no—
891C22—1064no—
892C22—1064no—
893C22—1061no—
894C22—1061no—
895C22—1062no—
896C22—2128no—
897C22—2121no—
898C22—2121no—
899C22#1681156512yes—
900C22C22×C22⋊#615711yescharacteristic
901C4—21no—
902C4—21no—
903C4—21no—
904C4—22no—
905C4—41no—
906C4—41no—
907C4—532no—
908C4—531no—
909C4—531no—
910C4—532no—
911C4—1061no—
912C4—1061no—
913C4—1061no—
914C4—1062no—
915C4—2128no—
916C4—2121no—
917C4—2121no—
918C4#1681156512yes—
919C4D53⋊#10412yescomplemented
920C4C22×C4⋊#615711yescharacteristic
921C4C2×#1313329611yescharacteristic
922C2—22no—
923C2—42no—
924C2—534no—
925C2—1061no—
926C2—1061no—
927C2—2122no—
928C2C2×#1681156511yescharacteristic
929C2C2×D53⋊#10411yescharacteristic
930C2D53⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC4×#41×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC2×#41×D53C22
cosocleC2×C4×D53C24
hypercenterC4×#41#6157
hypocenterC53C2×#1806
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. D53⋊#423C2semidirect
3. C2×C4×C4⋊#6157C2semidirect
4. #20290590C2semidirect
5. #20290589C2semidirect
6. #20290588C2semidirect
7. #20290587C2semidirect
8. #20290391C2semidirect
13. #16811628C22semidirect
14. #16811627C22semidirect
24. C4×C4⋊#6157C22semidirect
25. C4×C4⋊#6157C22semidirect
27. #16811493C22semidirect
28. #16811493C22semidirect
30. #41×Dic53C4semidirect
34. C4×#11719945C4semidirect
36. #16811091C4semidirect
41. C4×Q8×D53C4semidirect
42. C4×Q8×D53C4semidirect
45. C4×D4×D53C4semidirect
46. C4×D4×D53C4semidirect
51. C4×#41×C53C4semidirect
91. Q8×Dic53C2×C4semidirect
92. Q8×Dic53C2×C4semidirect
95. C4×Dic106C2×C4semidirect
96. C4×Dic106C2×C4semidirect
99. #13133182C2×C4semidirect
100. #13133182C2×C4semidirect
103. C4×D212C2×C4semidirect
104. C4×D212C2×C4semidirect
107. D4×Dic53C2×C4semidirect
108. D4×Dic53C2×C4semidirect
111. #13133179C2×C4semidirect
112. #13133179C2×C4semidirect
166. C4×Q8×C53C2×C4semidirect
167. C4×Q8×C53C2×C4semidirect
170. C4×D4×C53C2×C4semidirect
171. C4×D4×C53C2×C4semidirect
183. #41×C53C4⋊C4semidirect
207. Q8×D53C4⋊C4semidirect
217. D4×D53C4⋊C4semidirect
221. #11719945C4⋊C4semidirect
338. Q8×C53C2×C4⋊C4semidirect
341. D4×C53C2×C4⋊C4semidirect
382. D212C2×C4⋊C4semidirect
400. C4×D53#104semidirect
413. Dic106C2×C4⋊C4semidirect
444. C4×C53C2×#104semidirect
454. Dic53C2×#104semidirect
474. D53#1806semidirect
488. C4×#41#6157semidirect
517. C53C2×#1806semidirect
553. C4×Q8C2×#6157semidirect
554. C4×Q8C2×#6157semidirect
581. C4×D4C2×#6157semidirect
582. C4×D4C2×#6157semidirect
659. #41C4⋊#6157semidirect
803. Q8C2×C4⋊#6157semidirect
814. D4C2×C4⋊#6157semidirect
919. C4D53⋊#104semidirect

Maximal subgroups

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

subgroupindex
D53⋊#4232
C2×D53⋊#1042
C2×C4×C4⋊#61572
#202905902
#202905892
#202905882
#202905872
#202903912
C4×#41×D532
C2×#180653