Finite Group Databasebeta

← #28312903

Subgroups — #28312903

Order 13568.

1486 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811572C212yesmaximal
2C2×#16811569C211yesmaximal, characteristic
3C2×C4×C4⋊#6157C211yesmaximal, characteristic
4#20289901C212yesmaximal
5#20289900C212yesmaximal
6#20289895C212yesmaximal
7#20289893C211yesmaximal, characteristic
8#20289893C211yesmaximal, characteristic
9#20289893C211yesmaximal, characteristic
10#20289893C211yesmaximal, characteristic
11C4×C4⋊C4×D53C211yesmaximal, characteristic
12C22×C4⋊#6157C2211yescharacteristic
13C22×C4⋊#6157C2211yescharacteristic
14C22×C4⋊#6157C2212yes—
15C22×C4⋊#6157C2212yes—
16C22×C4⋊#6157C2211yescharacteristic
17C22×C4⋊#6157C2211yescharacteristic
18C22×C4×#6157C2212yes—
19#16811572—28no—
20#16811569—24no—
21C4×C4⋊#6157—24no—
22C2×(C2×#6157)⋊C4C2212yes—
23C2×(C2×#6157)⋊C4C2212yes—
24C2×(C2×#6157)⋊C4C2212yes—
25C2×(C2×#6157)⋊C4C2212yes—
26C2×(C2×#6157)⋊C4C2212yes—
27C2×(C2×#6157)⋊C4C2212yes—
28C2×(C2×#6157)⋊C4C2212yes—
29C2×(C2×#6157)⋊C4C2212yes—
30C2×(C2×#6157)⋊C4C2212yes—
31C2×C4⋊C4×D53C2211yescharacteristic
32C2×C4⋊C4×D53C2211yescharacteristic
33C2×C42×D53C2211yescharacteristic
34C2×C42×D53C2211yescharacteristic
35C2×C42×D53C2211yescharacteristic
36C4⋊C4×Dic53C411yescharacteristic, complemented
37C4⋊C4×Dic53C411yescharacteristic, complemented
38C4×#11719919C411yescharacteristic, complemented
39C4×#11719919C411yescharacteristic, complemented
40C4×C4⋊Dic53C411yescharacteristic, complemented
41#16810474C411yescharacteristic, complemented
42#16810474C411yescharacteristic, complemented
43#95×D53C2211yescharacteristic
44#95×D53C2211yescharacteristic
45C4×C4⋊C4×C53C411yescharacteristic, complemented
46C23×#6157C2312yes—
47C23×#6157C2312yes—
48C23×#6157C2312yes—
49C23×#6157C2312yes—
50C2×C4⋊#6157—22no—
51C2×C4⋊#6157—22no—
52C2×C4⋊#6157—22no—
53C2×C4⋊#6157—22no—
54C2×C4⋊#6157—24no—
55C2×C4⋊#6157—24no—
56C2×C4⋊#6157—22no—
57C2×C4⋊#6157—24no—
58C2×C4⋊#6157—24no—
59C2×C4⋊#6157—22no—
60C2×C4⋊#6157—22no—
61C2×C4⋊#6157—22no—
62C2×C4⋊#6157—22no—
63C2×C4⋊#6157—22no—
64C2×C4⋊#6157—42no—
65C2×C4⋊#6157—42no—
66C2×C4⋊#6157D414yes—
67C2×C4⋊#6157Q814yes—
68C2×C4×#6157—24no—
69C2×C4×#6157—24no—
70C2×C4×#6157—42no—
71(C2×#6157)⋊C4—24no—
72(C2×#6157)⋊C4—24no—
73(C2×#6157)⋊C4—24no—
74(C2×#6157)⋊C4—24no—
75(C2×#6157)⋊C4—24no—
76(C2×#6157)⋊C4—24no—
77(C2×#6157)⋊C4—42no—
78(C2×#6157)⋊C4—42no—
79(C2×#6157)⋊C4—42no—
80C22×C4×D53C2311yescharacteristic
81C22×C4×D53C2311yescharacteristic
82C22×C4×D53C2311yescharacteristic
83C22×C4×D53C2311yescharacteristic
84C22×C4×D53C2311yescharacteristic
85C22×C4×D53C2311yescharacteristic
86C22×C4×D53C2311yescharacteristic
87C2×C4⋊Dic53C2×C411yescharacteristic
88C2×C4⋊Dic53C2×C411yescharacteristic
89C2×#11719919C2×C411yescharacteristic
90C2×#11719919C2×C411yescharacteristic
91C2×#11719919C2×C411yescharacteristic
92C2×#11719919C2×C411yescharacteristic
93C4⋊C4×D53—22no—
94C4⋊C4×D53—22no—
95C4⋊C4×D53D414yes—
96C4⋊C4×D53Q814yes—
97C2×C4×Dic53C2×C411yescharacteristic
98C2×C4×Dic53C2×C411yescharacteristic
99C2×C4×Dic53C2×C411yescharacteristic
100C2×C4×Dic53C2×C411yescharacteristic
101C2×C4×Dic53C2×C411yescharacteristic
102C2×C4×Dic53C2×C411yescharacteristic
103C2×C4×Dic53C2×C411yescharacteristic
104C2×C4×Dic53C2×C411yescharacteristic
105C2×C4×Dic53C2×C411yescharacteristic
106C42×D53—22no—
107C42×D53—22no—
108C42×D53—22no—
109C42×D53—22no—
110C42×D53—22no—
111C42×D53—22no—
112#13133124C2×C411yescharacteristic
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118C2×C4⋊C4×C53C2×C411yescharacteristic
119C2×C4⋊C4×C53C2×C411yescharacteristic
120C2×C42×C53C2×C411yescharacteristic
121C2×C42×C53C2×C411yescharacteristic
122C2×C42×C53C2×C411yescharacteristic
123#95×C53C2×C411yescharacteristic
124#95×C53C2×C411yescharacteristic
125C23×D53C2411yescharacteristic
126C22×#6157—22no—
127C22×#6157—22no—
128C22×#6157—22no—
129C22×#6157—22no—
130C22×#6157—22no—
131C22×#6157—22no—
132C22×#6157—22no—
133C22×#6157—22no—
134C22×#6157—22no—
135C22×#6157—22no—
136C22×#6157—22no—
137C22×#6157—22no—
138C22×#6157—22no—
139C22×#6157—22no—
140C22×#6157—22no—
141C22×#6157—22no—
142C22×#6157—22no—
143C22×#6157—22no—
144C22×#6157—22no—
145C22×#6157—22no—
146C22×#6157—22no—
147C22×#6157—22no—
148C22×#6157—22no—
149C22×#6157—22no—
150C22×#6157—22no—
151C22×#6157—22no—
152C22×#6157C2×D414yes—
153C22×#6157C2×Q814yes—
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C22×C411yescharacteristic
157C22×C4×C53C22×C411yescharacteristic
158C22×C4×C53C22×C411yescharacteristic
159C22×C4×C53C22×C411yescharacteristic
160C22×C4×C53C22×C411yescharacteristic
161C22×Dic53C22×C411yescharacteristic
162C22×Dic53C22×C411yescharacteristic
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—21no—
196C2×C4×D53C2×D412yes—
197C2×C4×D53C2×D412yes—
198C2×C4×D53C2×D412yes—
199C2×C4×D53C2×D412yes—
200C2×C4×D53C2×Q812yes—
201C2×C4×D53C2×Q812yes—
202C2×C4×D53C2×Q812yes—
203C2×C4×D53C2×Q812yes—
204C2×C4×D53#4112yes—
205C2×C4×D53#4112yes—
206C2×C4×D53#4112yes—
207C2×C4×D53#4112yes—
208C2×C4×D53#4112yes—
209C2×C4×D53#4112yes—
210C4⋊#6157—28no—
211C4⋊#6157—28no—
212C4⋊#6157—48no—
213C4⋊#6157—48no—
214C4⋊#6157—44no—
215C4⋊#6157—44no—
216C4×#6157—48no—
217C4⋊C4×C53—22no—
218C4⋊C4×C53C4⋊C414yescomplemented
219C42×C53—22no—
220C42×C53—22no—
221C42×C53—22no—
222C4⋊Dic53—22no—
223C4⋊Dic53C4⋊C414yescomplemented
224#11719919—22no—
225#11719919—22no—
226#11719919C4⋊C414yescomplemented
227#11719919C4⋊C414yescomplemented
228C4×Dic53—22no—
229C4×Dic53—22no—
230C4×Dic53—22no—
231C4×Dic53—22no—
232C4×Dic53—22no—
233C4×Dic53—22no—
234C4×Dic53—22no—
235C4×Dic53—22no—
236C4×Dic53—22no—
237C23×C53C23×C411yescharacteristic
238C22×D53C22×D411yescharacteristic
239C22×D53C22×D411yescharacteristic
240C22×D53C22×Q811yescharacteristic
241C22×D53C22×Q811yescharacteristic
242C22×D53C2×#4111yescharacteristic
243C22×D53C2×#4111yescharacteristic
244C22×D53C2×#4111yescharacteristic
245C22×D53C2×#4111yescharacteristic
246C22×D53C2×#4111yescharacteristic
247C22×D53C2×#4111yescharacteristic
248C22×D53H(5,𝔽2)11yescharacteristic
249C22×D53H(5,𝔽2)11yescharacteristic
250C22×D532−1+411yescharacteristic
251C22×D532−1+411yescharacteristic
252C2×#6157—24no—
253C2×#6157—24no—
254C2×#6157—24no—
255C2×#6157—24no—
256C2×#6157—24no—
257C2×#6157—24no—
258C2×#6157—42no—
259C2×#6157—42no—
260C2×#6157—42no—
261C2×#6157—42no—
262C2×#6157—42no—
263C2×#6157—42no—
264C2×#6157—42no—
265C2×#6157—42no—
266C2×#6157—42no—
267C2×#6157—42no—
268C2×#6157—42no—
269C2×#6157—42no—
270C2×#6157—42no—
271C2×#6157—42no—
272C2×#6157—42no—
273C2×#6157—42no—
274C2×#6157—42no—
275C2×#6157—42no—
276C2×#6157—42no—
277C2×#6157—42no—
278C2×#6157—42no—
279C2×#6157—42no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53C2×C4⋊C412yes—
295C2×C4×C53C2×C4⋊C412yes—
296C2×C4×C53C2×C4⋊C412yes—
297C2×C4×C53#11712yes—
298C2×C4×C53#11712yes—
299C2×C4×C53C4×D412yes—
300C2×C4×C53C4×Q812yes—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53C2×C4⋊C412yes—
316C2×Dic53C2×C4⋊C412yes—
317C2×Dic53C2×C4⋊C412yes—
318C2×Dic53#11712yes—
319C2×Dic53#11712yes—
320C2×Dic53C4×D412yes—
321C2×Dic53C4×Q812yes—
322C4×D53—22no—
323C4×D53—22no—
324C4×D53—22no—
325C4×D53—22no—
326C4×D53—22no—
327C4×D53—22no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—22no—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—22no—
336C4×D53—22no—
337C4×D53—22no—
338C4×D53—41no—
339C4×D53—41no—
340C4×D53—41no—
341C4×D53—41no—
342C4×D53—41no—
343C4×D53—41no—
344C4×D53—41no—
345C4×D53—41no—
346C4×D53C22⋊Q814yes—
347C4×D53#12314yes—
348C4×D53#12514yes—
349C4×D53#12614yes—
350#13884—531nomaximal, Sylow
351C22×C53C22×C4⋊C411yescharacteristic
352C22×C53C2×#11711yescharacteristic
353C22×C53C2×#11711yescharacteristic
354C22×C53C2×C4×D411yescharacteristic
355C22×C53C2×C4×Q811yescharacteristic
356C22×C53#52011yescharacteristic
357C22×C53#52011yescharacteristic
358C2×D53C2×C22⋊Q811yescharacteristic
359C2×D53C2×#12311yescharacteristic
360C2×D53C2×#12511yescharacteristic
361C2×D53C2×#12611yescharacteristic
362C2×D53#53211yescharacteristic
363C2×D53#53211yescharacteristic
364C2×D53#53311yescharacteristic
365C2×D53#53311yescharacteristic
366C2×D53#54011yescharacteristic
367C2×D53#54111yescharacteristic
368C2×D53#54211yescharacteristic
369C2×D53#54211yescharacteristic
370C2×D53D4211yescharacteristic
371C2×D53#54611yescharacteristic
372C2×D53#54711yescharacteristic
373C2×D53#54811yescharacteristic
374C2×D53D4×Q811yescharacteristic
375C2×D53D4×Q811yescharacteristic
376C2×D53#55011yescharacteristic
377C2×D53#55211yescharacteristic
378C2×D53#55311yescharacteristic
379C2×D53#55411yescharacteristic
380C2×D53#55411yescharacteristic
381C2×D53#55611yescharacteristic
382C2×D53#55711yescharacteristic
383C2×D53#55711yescharacteristic
384C2×D53Q8211yescharacteristic
385C2×D53#55911yescharacteristic
386#6157—44no—
387#6157—44no—
388#6157—82no—
389#6157—82no—
390C4×C53—22no—
391C4×C53—22no—
392C4×C53—22no—
393C4×C53—22no—
394C4×C53—41no—
395C4×C53—41no—
396C4×C53#38714yescomplemented
397Dic53—22no—
398Dic53—22no—
399Dic53—22no—
400Dic53—22no—
401Dic53—41no—
402Dic53—41no—
403Dic53#38714yescomplemented
404C2×#387—532no—
405C2×#384—531no—
406C2×C4×C4⋊C4—531no—
407C2×C4×C4⋊C4—531no—
408#1442—532no—
409#1441—532no—
410#1436—532no—
411C4⋊#95—531no—
412C4⋊#95—531no—
413C4⋊#95—531no—
414C4⋊#95—531no—
415C2×C53#228511yescharacteristic
416C2×C53C2×#38711yescharacteristic
417C2×C53#231411yescharacteristic
418C2×C53D4×C4⋊C411yescharacteristic
419C2×C53Q8×C4⋊C411yescharacteristic
420C2×C53#235211yescharacteristic
421C2×C53#235511yescharacteristic
422D53#244511yescharacteristic
423D53#244611yescharacteristic
424D53#245111yescharacteristic
425D53#245211yescharacteristic
426D53#250611yescharacteristic
427D53#250711yescharacteristic
428D53#251111yescharacteristic
429D53#251211yescharacteristic
430C22×C4⋊C4—531no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—531no—
433C22×C4⋊C4—531no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—531no—
436C22×C4⋊C4—532no—
437C22×C4⋊C4—532no—
438C22×C42—531no—
439C22×C42—531no—
440C22×C42—531no—
441C22×C42—532no—
442#387—1068no—
443#384—1064no—
444C4×C4⋊C4—531no—
445C4×C4⋊C4—531no—
446C4×C4⋊C4—531no—
447C4×C4⋊C4—531no—
448C4×C4⋊C4—531no—
449C4×C4⋊C4—531no—
450C4×C4⋊C4—531no—
451C4×C4⋊C4—1064no—
452C4×C4⋊C4#615711yescharacteristic, complemented
453C2×#95—531no—
454C2×#95—531no—
455C2×#95—532no—
456C2×#95—532no—
457C2×#95—532no—
458C2×#95—532no—
459C2×#95—532no—
460C2×#95—532no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C53#1388411yescharacteristic, complemented, Sylow
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—532no—
471C23×C4—532no—
472C23×C4—531no—
473C23×C4—531no—
474C23×C4—532no—
475C23×C4—532no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—534no—
482C2×C4⋊C4—534no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—1062no—
489C2×C4⋊C4—1062no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1062no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1064no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1062no—
497C2×C4⋊C4—1062no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—2122no—
503C2×C4⋊C4—2122no—
504C2×C4⋊C4C2×#615711yescharacteristic
505C2×C4⋊C4C2×#615711yescharacteristic
506C2×C42—531no—
507C2×C42—531no—
508C2×C42—531no—
509C2×C42—531no—
510C2×C42—531no—
511C2×C42—531no—
512C2×C42—531no—
513C2×C42—531no—
514C2×C42—531no—
515C2×C42—1062no—
516C2×C42—1062no—
517C2×C42—1062no—
518C2×C42—1062no—
519C2×C42—1062no—
520C2×C42—1062no—
521C2×C42—1064no—
522C2×C42—1064no—
523C2×C42—2122no—
524C2×C42C2×#615711yescharacteristic
525C2×C42C2×#615711yescharacteristic
526C2×C42C2×#615711yescharacteristic
527#95—531no—
528#95—531no—
529#95—531no—
530#95—531no—
531#95—531no—
532#95—531no—
533#95—1064no—
534#95—1064no—
535#95—1064no—
536#95—1064no—
537#95—1064no—
538#95—1064no—
539#95—2122no—
540#95—2122no—
541#95—2122no—
542#95C2×#615711yescharacteristic
543#95C2×#615711yescharacteristic
544C24—531no—
545C22×C4—531no—
546C22×C4—532no—
547C22×C4—532no—
548C22×C4—532no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—532no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—531no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—534no—
565C22×C4—534no—
566C22×C4—531no—
567C22×C4—531no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4C22×#615711yescharacteristic
623C22×C4C22×#615711yescharacteristic
624C22×C4C22×#615711yescharacteristic
625C22×C4C22×#615711yescharacteristic
626C22×C4C22×#615711yescharacteristic
627C22×C4C22×#615711yescharacteristic
628C22×C4C22×#615711yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—534no—
631C4⋊C4—534no—
632C4⋊C4—534no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C4⋊C4—1068no—
636C4⋊C4—1068no—
637C4⋊C4—1062no—
638C4⋊C4—2124no—
639C4⋊C4—2124no—
640C4⋊C4—2128no—
641C4⋊C4—2128no—
642C4⋊C4C4⋊#615714yescomplemented
643C42—22no—
644C42—22no—
645C42—22no—
646C42—1062no—
647C42—1062no—
648C42—1062no—
649C42—1062no—
650C42—1062no—
651C42—1062no—
652C42—1062no—
653C42—1062no—
654C42—1062no—
655C42—2128no—
656C23—531no—
657C23—531no—
658C23—531no—
659C23—531no—
660C23—531no—
661C23—531no—
662C23—531no—
663C23—531no—
664C23—531no—
665C23—531no—
666C23—531no—
667C23—531no—
668C23—531no—
669C23—531no—
670C23C23×#615711yescharacteristic
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—532no—
686C2×C4—532no—
687C2×C4—532no—
688C2×C4—534no—
689C2×C4—534no—
690C2×C4—534no—
691C2×C4—534no—
692C2×C4—532no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—1064no—
721C2×C4—1064no—
722C2×C4—1064no—
723C2×C4—1064no—
724C2×C4—1064no—
725C2×C4—1064no—
726C2×C4—1061no—
727C2×C4—1061no—
728C2×C4—1061no—
729C2×C4—1061no—
730C2×C4—1061no—
731C2×C4—1061no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2121no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4C2×C4⋊#615712yes—
763C2×C4C2×C4⋊#615712yes—
764C2×C4C2×C4⋊#615712yes—
765C2×C4#1313329612yes—
766C2×C4#1313329612yes—
767C2×C4D4×#615712yes—
768C2×C4Q8×#615712yes—
769C22—531no—
770C22—531no—
771C22—531no—
772C22—531no—
773C22—531no—
774C22—531no—
775C22—531no—
776C22—531no—
777C22—531no—
778C22—531no—
779C22—531no—
780C22—531no—
781C22—531no—
782C22—531no—
783C22—531no—
784C22—531no—
785C22—531no—
786C22—531no—
787C22—531no—
788C22—531no—
789C22—531no—
790C22—531no—
791C22—531no—
792C22—531no—
793C22—531no—
794C22—531no—
795C22—531no—
796C22—531no—
797C22C22×C4⋊#615711yescharacteristic
798C22C2×#1313329611yescharacteristic
799C22C2×#1313329611yescharacteristic
800C22C2×D4×#615711yescharacteristic
801C22C2×Q8×#615711yescharacteristic
802C22#1681169211yescharacteristic
803C22#1681169211yescharacteristic
804C4—22no—
805C4—22no—
806C4—22no—
807C4—22no—
808C4—41no—
809C4—41no—
810C4—534no—
811C4—1062no—
812C4—1062no—
813C4—1062no—
814C4—1062no—
815C4—4242no—
816C4—4242no—
817C4—2124no—
818C4—2124no—
819C4—2121no—
820C4—2121no—
821C4#1681157214yescomplemented
822C2—531no—
823C2—531no—
824C2—531no—
825C2—531no—
826C2—531no—
827C2—531no—
828C2—531no—
829C2—531no—
830C2#2029116411yescharacteristic
831C2C2×#1681157211yescharacteristic
832C2#2029119311yescharacteristic
833C2D4×C4⋊#615711yescharacteristic
834C2Q8×C4⋊#615711yescharacteristic
835C2#2029123111yescharacteristic
836C2#2029123411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
FittingC4×C4⋊C4×C53C4
prime radical, cosocleC23×D53C24
hypercenterC4×C4⋊C4#6157
hypocenterC53#13884
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. C4⋊C4×Dic53C4semidirect
37. C4⋊C4×Dic53C4semidirect
38. C4×#11719919C4semidirect
39. C4×#11719919C4semidirect
40. C4×C4⋊Dic53C4semidirect
41. #16810474C4semidirect
42. #16810474C4semidirect
45. C4×C4⋊C4×C53C4semidirect
218. C4⋊C4×C53C4⋊C4semidirect
223. C4⋊Dic53C4⋊C4semidirect
226. #11719919C4⋊C4semidirect
227. #11719919C4⋊C4semidirect
396. C4×C53#387semidirect
403. Dic53#387semidirect
452. C4×C4⋊C4#6157semidirect
464. C53#13884semidirect
642. C4⋊C4C4⋊#6157semidirect
821. C4#16811572semidirect

Maximal subgroups

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

subgroupindex
C2×#168115722
C2×#168115692
C2×C4×C4⋊#61572
#202899012
#202899002
#202898952
#202898932
C4×C4⋊C4×D532
#1388453