Finite Group Databasebeta

← C4×#16811614 #28318219

Subgroups — C4×#16811614 #28318219

Order 13568.

1706 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811614C212yesmaximal
2C4×D53⋊M16C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊#6157C211yesmaximal, characteristic, complemented
4#20290487C212yesmaximal, complemented
5#20290485C212yesmaximal, complemented
6C4×#13133280C212yesmaximal, complemented
7C4×#13133279C212yesmaximal, complemented
8#20290404C212yesmaximal, complemented
9C4×#41×D53C211yesmaximal, characteristic
10C2×D53⋊M16C2212yes—
11C22×C4⋊#6157C2212yes—
12C22×C4×#6157—21no—
13#16811614C4116yesdirect product factor
14C2×#13133280C2214yes—
15C2×#13133279C2214yes—
16C4×#11719936—21no—
17C4×#11719936—21no—
18C4×#11719940—21no—
19C4×#11719940—21no—
20#16811582C2212yes—
21C4×D53⋊C8C2212yes—
22C4×C4⋊#6157—21no—
23C4×C4⋊#6157—21no—
24C4×C4⋊#6157C2212yes—
25C4×C4⋊#6157C2212yes—
26C2×(C2×#6157)⋊C4—21no—
27#16811496C2214yes—
28#16811496C2214yes—
29C2×#41×D53C2211yescharacteristic
30#41×Dic53C411yescharacteristic, complemented
31C4×#11719949C411yescharacteristic, complemented
32C4×#11719949C411yescharacteristic, complemented
33C4×#11719945—21no—
34C4×#11719945C411yescharacteristic, complemented
35#16811091—21no—
36#16811091C411yescharacteristic, complemented
37C4×#11719947—21no—
38C4×#11719947—21no—
39C4×#11719947C411yescharacteristic, complemented
40C4×#11719947C411yescharacteristic, complemented
41C4×Q8×D53C2211yescharacteristic
42C4×Q8×D53C2211yescharacteristic
43C4×D4×D53—21no—
44C4×D4×D53—21no—
45C4×D4×D53C2211yescharacteristic
46C4×D4×D53C2211yescharacteristic
47#117×D53—21no—
48#117×D53C2211yescharacteristic
49C2×C42×D53—21no—
50C2×C42×D53C2211yescharacteristic
51C4×#41×C53C411yescharacteristic, complemented
52C23×#6157—22no—
53C2×#11719936—22no—
54D53⋊M16—24no—
55D53⋊M16C2×C418yescomplemented
56C2×#11719940—22no—
57C2×D53⋊C8C2314yes—
58C2×C4⋊#6157—22no—
59C2×C4⋊#6157—24no—
60C2×C4⋊#6157C2×C418yescomplemented
61C2×C4⋊#6157C2314yes—
62C2×C4×#6157—22no—
63C2×C4×#6157—22no—
64C2×C4×#6157—44no—
65#13133280C2×C4116yescomplemented
66#13133279C2×C4116yescomplemented
67#13133272—22no—
68#13133272—22no—
69C4×#88324—22no—
70C4×#88324—22no—
71(C2×#6157)⋊C4—22no—
72(C2×#6157)⋊C4—22no—
73C2×#11719949C2×C411yescharacteristic
74C2×#11719945—21no—
75C2×#11719945C2×C411yescharacteristic
76C2×#11719947—21no—
77C2×#11719947C2×C411yescharacteristic
78#41×D53—24no—
79#41×D53C2×C418yes—
80C2×Q8×D53C2311yescharacteristic
81C2×D4×D53—21no—
82C2×D4×D53C2311yescharacteristic
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C22×C4×D53D411yescharacteristic
87C22×C4×D53D411yescharacteristic
88C22×C4×D53C2311yescharacteristic
89Q8×Dic53C2×C411yescharacteristic, complemented
90Q8×Dic53C2×C411yescharacteristic, complemented
91C4×Dic106—21no—
92C4×Dic106—21no—
93C4×Dic106C2×C411yescharacteristic, complemented
94C4×Dic106C2×C411yescharacteristic, complemented
95#13133182—21no—
96#13133182—21no—
97#13133182C2×C411yescharacteristic, complemented
98#13133182C2×C411yescharacteristic, complemented
99C4×D212—21no—
100C4×D212—21no—
101C4×D212C2×C411yescharacteristic, complemented
102C4×D212C2×C411yescharacteristic, complemented
103D4×Dic53—21no—
104D4×Dic53—21no—
105D4×Dic53C2×C411yescharacteristic, complemented
106D4×Dic53C2×C411yescharacteristic, complemented
107#13133179—21no—
108#13133179—21no—
109#13133179C2×C411yescharacteristic, complemented
110#13133179C2×C411yescharacteristic, complemented
111C4×C22⋊D53—21no—
112C4×C22⋊D53—21no—
113C4×C22⋊D53—21no—
114C4×C22⋊D53—21no—
115C4×C22⋊D53—21no—
116C4×C22⋊D53—21no—
117#13133177—21no—
118#13133177—21no—
119#13133177—21no—
120#13133177—21no—
121#13133177—21no—
122#13133177—21no—
123#13133176—21no—
124#13133176C2×C411yescharacteristic
125#13133175—21no—
126#13133175—21no—
127#13133175C2×C411yescharacteristic
128#13133175C2×C411yescharacteristic
129#13133174—21no—
130#13133174—21no—
131#13133174—21no—
132#13133173—21no—
133#13133173—21no—
134#13133173—21no—
135C4⋊C4×D53—21no—
136C4⋊C4×D53—21no—
137C4⋊C4×D53C2311yescharacteristic
138C4⋊C4×D53C2311yescharacteristic
139C22⋊C4×D53—21no—
140C22⋊C4×D53—21no—
141C22⋊C4×D53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53C2×C411yescharacteristic
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53D411yescharacteristic
148C42×D53—21no—
149C42×D53—21no—
150C42×D53—21no—
151C42×D53—21no—
152C42×D53—21no—
153C42×D53—21no—
154C42×D53—21no—
155C42×D53C2×C411yescharacteristic
156C42×D53C2×C411yescharacteristic
157C42×D53D411yescharacteristic
158C42×D53D411yescharacteristic
159C42×D53D411yescharacteristic
160C42×D53D411yescharacteristic
161C42×D53C2311yescharacteristic
162C42×D53C2311yescharacteristic
163C2×#41×C53C2×C411yescharacteristic
164C4×Q8×C53C2×C411yescharacteristic, complemented
165C4×Q8×C53C2×C411yescharacteristic, complemented
166C4×D4×C53—21no—
167C4×D4×C53—21no—
168C4×D4×C53C2×C411yescharacteristic, complemented
169C4×D4×C53C2×C411yescharacteristic, complemented
170#117×C53—21no—
171#117×C53C2×C411yescharacteristic
172C2×C42×C53—21no—
173C2×C42×C53C2×C411yescharacteristic
174C23×D53—21no—
175C23×D53C2×D411yescharacteristic
176C22×#6157—28no—
177C22×#6157—24no—
178C22×#6157—44no—
179C22×#6157—44no—
180#41×C53—22no—
181#41×C53C4214yescomplemented
182C2×Q8×C53C22×C411yescharacteristic
183C2×D4×C53—21no—
184C2×D4×C53C22×C411yescharacteristic
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53C22⋊C411yescharacteristic
189C22×C4×C53C22⋊C411yescharacteristic
190C22×C4×C53C22×C411yescharacteristic
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53C22⋊C411yescharacteristic
198C22×Dic53C22⋊C411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200#11719949—22no—
201#11719949C4214yescomplemented
202Q8×D53—22no—
203Q8×D53C22×C414yes—
204#11719947—28no—
205#11719947—22no—
206#11719947C4214yescomplemented
207D4×D53—28no—
208D4×D53—22no—
209D4×D53C22×C414yes—
210#11719945—22no—
211#11719945—28no—
212#11719945C4214yescomplemented
213C2×D212—21no—
214C2×D212C22×C411yescharacteristic
215C2×C4×D53—21no—
216C2×C4×D53—21no—
217C2×C4×D53—21no—
218C2×C4×D53—28no—
219C2×C4×D53—22no—
220C2×C4×D53—22no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—21no—
224C2×C4×D53—21no—
225C2×C4×D53—21no—
226C2×C4×D53—21no—
227C2×C4×D53—42no—
228C2×C4×D53—44no—
229C2×C4×D53—42no—
230C2×C4×D53—42no—
231C2×C4×D53C22⋊C411yescharacteristic
232C2×C4×D53C22⋊C411yescharacteristic
233C2×C4×D53C22⋊C411yescharacteristic
234C2×C4×D53C22⋊C411yescharacteristic
235C2×C4×D53C22×C411yescharacteristic
236C2×C4×D53C22×C414yes—
237C2×C4×D53C2×D411yescharacteristic
238C2×C4×D53C2×D411yescharacteristic
239C2×C4×D53C2×D411yescharacteristic
240C2×C4×D53C2×D411yescharacteristic
241C2×C4×D53C2×D411yescharacteristic
242C2×C4×D53C2×D411yescharacteristic
243C2×C4×D53#4114yes—
244C2×C4×D53C2411yescharacteristic
245C2×Dic106—21no—
246C2×Dic106C22×C411yescharacteristic
247#11719940—28no—
248C2×#88324—24no—
249C4⋊#6157—28no—
250C4⋊#6157—24no—
251C4⋊#6157C22×C418yes—
252C4×#6157—44no—
253C4×#6157—44no—
254#11719936—28no—
255D53⋊C8—24no—
256D53⋊C8C22×C418yes—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53C22×C411yescharacteristic
260C4⋊C4×C53C22×C411yescharacteristic
261C22⋊C4×C53—21no—
262C22⋊C4×C53—21no—
263C22⋊C4×C53—21no—
264C42×C53—21no—
265C42×C53—21no—
266C42×C53—21no—
267C42×C53C22⋊C411yescharacteristic
268C42×C53C22⋊C411yescharacteristic
269C42×C53C22×C411yescharacteristic
270C42×C53C22×C411yescharacteristic
271C22⋊Dic53—21no—
272C22⋊Dic53—21no—
273C22⋊Dic53—21no—
274#11719921—21no—
275#11719921—21no—
276#11719921—21no—
277#11719921—21no—
278#11719921—21no—
279#11719921—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53—21no—
282C4⋊Dic53C22×C411yescharacteristic
283C4⋊Dic53C22×C411yescharacteristic
284#11719919—21no—
285#11719919—21no—
286#11719919—21no—
287#11719919—21no—
288#11719919—21no—
289#11719919—21no—
290C4×Dic53—21no—
291C4×Dic53—21no—
292C4×Dic53—21no—
293C4×Dic53—21no—
294C4×Dic53—21no—
295C4×Dic53—21no—
296C4×Dic53—21no—
297C4×Dic53—21no—
298C4×Dic53—21no—
299C4×Dic53C22⋊C411yescharacteristic
300C4×Dic53C22⋊C411yescharacteristic
301C4×Dic53C22⋊C411yescharacteristic
302C4×Dic53C22⋊C411yescharacteristic
303C4×Dic53C22⋊C411yescharacteristic
304C4×Dic53C22⋊C411yescharacteristic
305C4×Dic53C22×C411yescharacteristic
306C4×Dic53C22×C411yescharacteristic
307C4×Dic53C2×D411yescharacteristic
308C4×Dic53C2×D411yescharacteristic
309C4×Dic53C2×D411yescharacteristic
310C4×Dic53C2×D411yescharacteristic
311C23×C53—21no—
312C23×C53C2×C22⋊C411yescharacteristic
313C22×D53—21no—
314C22×D53—21no—
315C22×D53—22no—
316C22×D53—21no—
317C22×D53—24no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—42no—
321C22×D53C2×C22⋊C411yescharacteristic
322C22×D53C4×D414yes—
323C22×D53C22×D411yescharacteristic
324C2×#6157—28no—
325C2×#6157—416no—
326C2×#6157—44no—
327C2×#6157—44no—
328Q8×C53—21no—
329Q8×C53C2×C4212yescomplemented
330D4×C53—24no—
331D4×C53—21no—
332D4×C53C2×C4212yescomplemented
333C2×C4×C53—21no—
334C2×C4×C53—24no—
335C2×C4×C53—22no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—41no—
339C2×C4×C53—42no—
340C2×C4×C53—42no—
341C2×C4×C53C2×C4212yes—
342C2×C4×C53C2×C22⋊C411yescharacteristic
343C2×C4×C53C2×C22⋊C411yescharacteristic
344C2×C4×C53C2×C22⋊C411yescharacteristic
345C2×C4×C53C2×C22⋊C411yescharacteristic
346C2×C4×C53C2×C22⋊C411yescharacteristic
347C2×C4×C53#11712yes—
348C2×C4×C53C23×C411yescharacteristic
349C22⋊D53—24no—
350C22⋊D53—24no—
351C22⋊D53—24no—
352C2×Dic53—21no—
353C2×Dic53—24no—
354C2×Dic53—22no—
355C2×Dic53—21no—
356C2×Dic53—21no—
357C2×Dic53—41no—
358C2×Dic53—42no—
359C2×Dic53—42no—
360C2×Dic53C2×C22⋊C411yescharacteristic
361C2×Dic53C2×C22⋊C411yescharacteristic
362C2×Dic53C2×C22⋊C411yescharacteristic
363C2×Dic53C2×C22⋊C411yescharacteristic
364C2×Dic53C2×C22⋊C411yescharacteristic
365C2×Dic53C4×D414yes—
366C2×Dic53C22×D411yescharacteristic
367D212—24no—
368D212—21no—
369D212C2×C4212yescomplemented
370C4×D53—24no—
371C4×D53—21no—
372C4×D53—21no—
373C4×D53—22no—
374C4×D53—22no—
375C4×D53—24no—
376C4×D53—22no—
377C4×D53—24no—
378C4×D53—22no—
379C4×D53—41no—
380C4×D53—41no—
381C4×D53—42no—
382C4×D53—42no—
383C4×D53—41no—
384C4×D53—41no—
385C4×D53—42no—
386C4×D53—42no—
387C4×D53—42no—
388C4×D53C2×C4212yes—
389C4×D53#11712yes—
390C4×D53C4×D414yes—
391C4×D53C4×D414yes—
392C4×D53AGL(1,ℤ/8)12yes—
393C4×D53#13712yes—
394C4×D53C23×C412yes—
395C4×D53C2×#4112yes—
396Dic106—21no—
397Dic106—24no—
398Dic106C2×C4212yescomplemented
399#88324—28no—
400C4×#417—531nomaximal, Sylow
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—22no—
404C22×C53—41no—
405C22×C53—41no—
406C22×C53C4×C22⋊C412yes—
407C22×C53C22×C22⋊C411yescharacteristic
408C2×D53—21no—
409C2×D53—21no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—22no—
413C2×D53—41no—
414C2×D53—41no—
415C2×D53—44no—
416C2×D53—44no—
417C2×D53C4×C22⋊C412yes—
418C2×D53C2×C4×D412yes—
419C2×D53C2×AGL(1,ℤ/8)11yescharacteristic
420C2×D53C2×#13711yescharacteristic
421C2×D53#57512yes—
422#6157—48no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—22no—
427C4×C53—41no—
428C4×C53—41no—
429C4×C53C4×C22⋊C412yes—
430C4×C53#41712yescomplemented
431C4×C53C22×C4211yescharacteristic
432C4×C53C2×#11711yescharacteristic
433Dic53—21no—
434Dic53—21no—
435Dic53—21no—
436Dic53—22no—
437Dic53—41no—
438Dic53—41no—
439Dic53C4×C22⋊C412yes—
440Dic53#41712yescomplemented
441Dic53C2×C4×D412yes—
442C2×C4×#41—531no—
443C2×#417—532no—
444C2×C4×M16—531no—
445C2×C4×C4⋊C4—531no—
446#1763—532no—
447#1762—532no—
448C4×#103—532no—
449C4×#102—532no—
450#1736—532no—
451C2×C53—22no—
452C2×C53—42no—
453C2×C53C2×C4×C22⋊C411yescharacteristic
454C2×C53C2×#41711yescharacteristic
455C2×C53#289611yescharacteristic
456D53—22no—
457D53—42no—
458D53C4×AGL(1,ℤ/8)12yes—
459D53C4×#13712yes—
460C22×#41—531no—
461C22×M16—532no—
462C4×#41—531no—
463C4×#41—531no—
464C4×#41—531no—
465C4×#41—531no—
466C4×#41—531no—
467C4×#41—531no—
468C4×#41—531no—
469C4×#41—1061no—
470C4×#41—1061no—
471C4×#41—1061no—
472C4×#41—1061no—
473C4×#41#615711yescharacteristic, complemented
474C2×C4×Q8—531no—
475C2×C4×Q8—531no—
476C2×C4×D4—531no—
477C2×C4×D4—531no—
478C2×C4×D4—1061no—
479C2×C4×D4—1061no—
480C2×#117—531no—
481C2×#117—1061no—
482C22×C4⋊C4—532no—
483C22×C42—531no—
484C22×C42—1061no—
485C22×C42—1061no—
486#417—5316no—
487C2×#103—534no—
488C2×#102—534no—
489C4×M16—1061no—
490C4×M16—1061no—
491C4×M16—1061no—
492C4×M16—1061no—
493C2×#97—532no—
494C2×C4×C8—532no—
495C4×C4⋊C4—532no—
496C4×C4⋊C4—532no—
497C4×C4⋊C4—1061no—
498C4×C4⋊C4—1061no—
499C2×#95—1061no—
500#340—534no—
501#340—534no—
502C53C4×#41711yescharacteristic, complemented, Sylow
503C2×#41—538no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—1061no—
508C2×#41—1061no—
509C2×#41—1064no—
510C2×#41C2×#615711yescharacteristic
511C22×Q8—531no—
512C22×D4—531no—
513C22×D4—1061no—
514C23×C4—531no—
515C23×C4—531no—
516C23×C4—531no—
517C23×C4—1061no—
518C23×C4—1061no—
519C23×C4—1061no—
520C23×C4—1062no—
521C2×M16—538no—
522C2×M16—1062no—
523C2×M16—1062no—
524C2×M16—1064no—
525C22×C8—534no—
526C4×Q8—531no—
527C4×Q8—531no—
528C4×Q8—531no—
529C4×Q8—531no—
530C4×Q8—531no—
531C4×Q8—531no—
532C4×Q8—1061no—
533C4×Q8—1061no—
534C4×Q8—1061no—
535C4×Q8—1061no—
536C4×Q8C2×#615711yescharacteristic, complemented
537C4×Q8C2×#615711yescharacteristic, complemented
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—531no—
541C4×D4—531no—
542C4×D4—531no—
543C4×D4—531no—
544C4×D4—531no—
545C4×D4—531no—
546C4×D4—1061no—
547C4×D4—1061no—
548C4×D4—1061no—
549C4×D4—1061no—
550C4×D4—1061no—
551C4×D4—1061no—
552C4×D4—1061no—
553C4×D4—1061no—
554C4×D4—1061no—
555C4×D4—1061no—
556C4×D4—1061no—
557C4×D4—1061no—
558C4×D4—1061no—
559C4×D4—1061no—
560C4×D4—1061no—
561C4×D4—1061no—
562C4×D4—1061no—
563C4×D4—1061no—
564C4×D4C2×#615711yescharacteristic, complemented
565C4×D4C2×#615711yescharacteristic, complemented
566#117—21no—
567#117—531no—
568#117—531no—
569#117—531no—
570#117—1061no—
571#117—1061no—
572#117—1061no—
573#117—1061no—
574#117—1061no—
575#117—1061no—
576#117—1061no—
577#117—1061no—
578#117—1061no—
579#117C2×#615711yescharacteristic
580C2×C4⋊C4—534no—
581C2×C4⋊C4—538no—
582C2×C4⋊C4—531no—
583C2×C4⋊C4—531no—
584C2×C4⋊C4—1061no—
585C2×C4⋊C4—1061no—
586C2×C4⋊C4—1062no—
587C2×C4⋊C4—1064no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C42—21no—
592C2×C42—531no—
593C2×C42—531no—
594C2×C42—531no—
595C2×C42—531no—
596C2×C42—531no—
597C2×C42—531no—
598C2×C42—531no—
599C2×C42—531no—
600C2×C42—531no—
601C2×C42—531no—
602C2×C42—531no—
603C2×C42—1061no—
604C2×C42—1061no—
605C2×C42—1061no—
606C2×C42—1061no—
607C2×C42—1061no—
608C2×C42—1061no—
609C2×C42—1061no—
610C2×C42—1061no—
611C2×C42—1061no—
612C2×C42—1061no—
613C2×C42—1062no—
614C2×C42—1062no—
615C2×C42—2124no—
616C2×C42C2×#615711yescharacteristic
617#103—5316no—
618#102—5316no—
619#97—1062no—
620#97—1062no—
621C4×C8—1062no—
622C4×C8—1062no—
623#95—1062no—
624#95—1062no—
625C24—531no—
626C24—1061no—
627#41—22no—
628#41—534no—
629#41—534no—
630#41—534no—
631#41—1068no—
632#41—1068no—
633#41—1062no—
634#41—1062no—
635#41—1062no—
636#41C4×#615714yescomplemented
637C2×Q8—534no—
638C2×Q8—531no—
639C2×Q8—1061no—
640C2×Q8—1062no—
641C2×Q8C22×#615711yescharacteristic
642C2×D4—21no—
643C2×D4—534no—
644C2×D4—531no—
645C2×D4—1061no—
646C2×D4—1062no—
647C2×D4—1061no—
648C2×D4—1068no—
649C2×D4—1061no—
650C2×D4—1061no—
651C2×D4C22×#615711yescharacteristic
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—531no—
656C22×C4—534no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—534no—
661C22×C4—531no—
662C22×C4—531no—
663C22×C4—531no—
664C22×C4—531no—
665C22×C4—531no—
666C22×C4—531no—
667C22×C4—531no—
668C22×C4—531no—
669C22×C4—531no—
670C22×C4—531no—
671C22×C4—531no—
672C22×C4—1061no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—1068no—
676C22×C4—1061no—
677C22×C4—1061no—
678C22×C4—1061no—
679C22×C4—1061no—
680C22×C4—1061no—
681C22×C4—1061no—
682C22×C4—1061no—
683C22×C4—1061no—
684C22×C4—1061no—
685C22×C4—1064no—
686C22×C4—1068no—
687C22×C4—1061no—
688C22×C4—1061no—
689C22×C4—2122no—
690C22×C4—2122no—
691C22×C4—2122no—
692C22×C4—2124no—
693C22×C4—2124no—
694C22×C4—2124no—
695C22×C4C22⋊#615711yescharacteristic
696C22×C4C22⋊#615711yescharacteristic
697C22×C4C22×#615711yescharacteristic
698M16—1068no—
699M16—1068no—
700C2×C8—538no—
701C2×C8—1064no—
702C2×C8—1064no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—538no—
706C4⋊C4—531no—
707C4⋊C4—531no—
708C4⋊C4—1061no—
709C4⋊C4—1061no—
710C4⋊C4—1061no—
711C4⋊C4—1061no—
712C4⋊C4—1061no—
713C4⋊C4—1061no—
714C4⋊C4—1068no—
715C4⋊C4—1064no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4C22×#615711yescharacteristic
719C4⋊C4C22×#615711yescharacteristic
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C22⋊C4—1061no—
728C22⋊C4—1061no—
729C22⋊C4—1061no—
730C22⋊C4—1061no—
731C22⋊C4—1061no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—531no—
736C42—531no—
737C42—531no—
738C42—531no—
739C42—531no—
740C42—531no—
741C42—531no—
742C42—531no—
743C42—531no—
744C42—531no—
745C42—531no—
746C42—531no—
747C42—1061no—
748C42—1061no—
749C42—1061no—
750C42—1061no—
751C42—1061no—
752C42—1061no—
753C42—1061no—
754C42—1061no—
755C42—1061no—
756C42—2124no—
757C42—2124no—
758C42C22⋊#615711yescharacteristic
759C42C22⋊#615711yescharacteristic
760C42C22×#615711yescharacteristic
761C42C22×#615711yescharacteristic
762C23—21no—
763C23—531no—
764C23—534no—
765C23—531no—
766C23—1061no—
767C23—1061no—
768C23—1062no—
769C23—1064no—
770C23—1061no—
771C23—2121no—
772C23—2121no—
773C23—2122no—
774C23C2×C22⋊#615711yescharacteristic
775Q8—21no—
776Q8—532no—
777Q8—1064no—
778Q8—1061no—
779Q8C2×C4×#615712yescomplemented
780D4—24no—
781D4—21no—
782D4—532no—
783D4—1064no—
784D4—1064no—
785D4—1064no—
786D4—1064no—
787D4—1061no—
788D4C2×C4×#615712yescomplemented
789C2×C4—21no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—534no—
798C2×C4—531no—
799C2×C4—531no—
800C2×C4—531no—
801C2×C4—534no—
802C2×C4—534no—
803C2×C4—532no—
804C2×C4—532no—
805C2×C4—532no—
806C2×C4—532no—
807C2×C4—532no—
808C2×C4—532no—
809C2×C4—531no—
810C2×C4—531no—
811C2×C4—531no—
812C2×C4—1062no—
813C2×C4—1064no—
814C2×C4—1061no—
815C2×C4—1061no—
816C2×C4—1062no—
817C2×C4—1062no—
818C2×C4—1064no—
819C2×C4—1062no—
820C2×C4—1064no—
821C2×C4—1061no—
822C2×C4—1064no—
823C2×C4—1062no—
824C2×C4—1068no—
825C2×C4—1061no—
826C2×C4—1061no—
827C2×C4—2121no—
828C2×C4—2121no—
829C2×C4—2122no—
830C2×C4—2122no—
831C2×C4—2122no—
832C2×C4—2121no—
833C2×C4—2121no—
834C2×C4—2122no—
835C2×C4—2122no—
836C2×C4—2121no—
837C2×C4—2122no—
838C2×C4—2124no—
839C2×C4—2124no—
840C2×C4—21216no—
841C2×C4—2122no—
842C2×C4C2×C4×#615712yes—
843C2×C4C2×C22⋊#615711yescharacteristic
844C2×C4C2×C22⋊#615711yescharacteristic
845C2×C4C2×C22⋊#615711yescharacteristic
846C2×C4C2×C22⋊#615711yescharacteristic
847C2×C4C2×C22⋊#615711yescharacteristic
848C2×C4#1313329612yes—
849C2×C4C23×#615711yescharacteristic
850C8—1068no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—531no—
857C22—531no—
858C22—532no—
859C22—532no—
860C22—532no—
861C22—1064no—
862C22—1064no—
863C22—1061no—
864C22—1061no—
865C22—1062no—
866C22—2124no—
867C22—2124no—
868C22—2121no—
869C22—2121no—
870C22C4×C22⋊#615712yes—
871C22C22×C22⋊#615711yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—532no—
879C4—532no—
880C4—532no—
881C4—1061no—
882C4—1061no—
883C4—1061no—
884C4—1062no—
885C4—2128no—
886C4—2121no—
887C4—2121no—
888C4C4×C22⋊#615712yes—
889C4#1681161412yesdirect product factor
890C4C22×C4×#615711yescharacteristic
891C4C2×#1313329611yescharacteristic
892C2—22no—
893C2—42no—
894C2—532no—
895C2—532no—
896C2—1062no—
897C2—2122no—
898C2C2×C4×C22⋊#615711yescharacteristic
899C2C2×#1681161411yescharacteristic
900C2#2029133511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6157
commutatorC4×C53C22×C42
FrattiniC2×C4C23×#6157
FittingC4×#41×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC2×#41×D53C22
cosocleC2×C4×D53C24
hypercenterC4×#41#6157
hypocenterC53C4×#417
LCSG ▷ 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
2. C4×D53⋊M16C2semidirect
3. C2×C4×C4⋊#6157C2semidirect
4. #20290487C2semidirect
5. #20290485C2semidirect
6. C4×#13133280C2semidirect
7. C4×#13133279C2semidirect
8. #20290404C2semidirect
13. #16811614C4direct (N × H)
30. #41×Dic53C4semidirect
31. C4×#11719949C4semidirect
32. C4×#11719949C4semidirect
34. C4×#11719945C4semidirect
36. #16811091C4semidirect
39. C4×#11719947C4semidirect
40. C4×#11719947C4semidirect
51. C4×#41×C53C4semidirect
55. D53⋊M16C2×C4semidirect
60. C2×C4⋊#6157C2×C4semidirect
65. #13133280C2×C4semidirect
66. #13133279C2×C4semidirect
89. Q8×Dic53C2×C4semidirect
90. Q8×Dic53C2×C4semidirect
93. C4×Dic106C2×C4semidirect
94. C4×Dic106C2×C4semidirect
97. #13133182C2×C4semidirect
98. #13133182C2×C4semidirect
101. C4×D212C2×C4semidirect
102. C4×D212C2×C4semidirect
105. D4×Dic53C2×C4semidirect
106. D4×Dic53C2×C4semidirect
109. #13133179C2×C4semidirect
110. #13133179C2×C4semidirect
164. C4×Q8×C53C2×C4semidirect
165. C4×Q8×C53C2×C4semidirect
168. C4×D4×C53C2×C4semidirect
169. C4×D4×C53C2×C4semidirect
181. #41×C53C42semidirect
201. #11719949C42semidirect
206. #11719947C42semidirect
212. #11719945C42semidirect
329. Q8×C53C2×C42semidirect
332. D4×C53C2×C42semidirect
369. D212C2×C42semidirect
398. Dic106C2×C42semidirect
430. C4×C53#417semidirect
440. Dic53#417semidirect
473. C4×#41#6157semidirect
502. C53C4×#417semidirect
536. C4×Q8C2×#6157semidirect
537. C4×Q8C2×#6157semidirect
564. C4×D4C2×#6157semidirect
565. C4×D4C2×#6157semidirect
636. #41C4×#6157semidirect
779. Q8C2×C4×#6157semidirect
788. D4C2×C4×#6157semidirect
889. C4#16811614direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168116142
C4×D53⋊M162
C2×C4×C4⋊#61572
#202904872
#202904852
C4×#131332802
C4×#131332792
#202904042
C4×#41×D532
C4×#41753