Finite Group Databasebeta

← #27395519

Subgroups — #27395519

Order 13568.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283419C211yesmaximal, characteristic, complemented
2#20283160C211yesmaximal, characteristic, complemented
3#20275609C211yesmaximal, characteristic, complemented
4#20275604C211yesmaximal, characteristic, complemented
5#20275428C211yesmaximal, characteristic, complemented
6#20275421C211yesmaximal, characteristic, complemented
7#20275365C211yesmaximal, characteristic, complemented
8#20275365C211yesmaximal, characteristic, complemented
9#20275044C211yesmaximal, characteristic, complemented
10#20275044C211yesmaximal, characteristic, complemented
11#20275018C211yesmaximal, characteristic, complemented
12#20274922C211yesmaximal, characteristic, complemented
13#20274659C211yesmaximal, characteristic, complemented
14#20274501C211yesmaximal, characteristic, complemented
15C53×#3002C211yesmaximal, characteristic
16C2×#13133224C2211yescharacteristic, complemented
17C22×#11719917C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19#16810701—21no—
20#16810701—21no—
21#16810695—21no—
22#16810695—21no—
23C2×#13133153C2211yescharacteristic, complemented
24C2×#13133153C2211yescharacteristic, complemented
25#16810650C2211yescharacteristic, complemented
26C2×#13133144C2211yescharacteristic
27C2×#13133144C2211yescharacteristic
28C2×#13133144C2211yescharacteristic
29C2×#13133144C2211yescharacteristic
30C2×#13133144C2211yescharacteristic, complemented
31C2×#13133144C2211yescharacteristic, complemented
32#16810590—21no—
33#16810590—21no—
34#16810590C2211yescharacteristic
35#16810590C2211yescharacteristic
36#16810590C2211yescharacteristic
37#16810590C2211yescharacteristic
38#16810590C2211yescharacteristic, complemented
39#16810587—21no—
40#16810587—21no—
41#16810587C2211yescharacteristic
42#16810579C2211yescharacteristic, complemented
43C2×#13133127C2211yescharacteristic, complemented
44C2×C8×Dic53C2211yescharacteristic, complemented
45C4×C22⋊Dic53C2211yescharacteristic
46#16810388C2211yescharacteristic, complemented
47#16810388C2211yescharacteristic, complemented
48#16810382C2211yescharacteristic, complemented
49#16810382C2211yescharacteristic, complemented
50#16810377C2211yescharacteristic, complemented
51#16810377C2211yescharacteristic, complemented
52C22×#41×C53C2211yescharacteristic
53C2×#135×C53C2211yescharacteristic
54C2×#135×C53C2211yescharacteristic
55C53×#525C2211yescharacteristic
56C53×#452C411yescharacteristic, complemented
57C53×#452C411yescharacteristic, complemented
58C53×#451C411yescharacteristic, complemented
59C53×#450C411yescharacteristic, complemented
60C53×#449C411yescharacteristic, complemented
61C53×#449C411yescharacteristic, complemented
62C53×#448C411yescharacteristic, complemented
63C53×#447C411yescharacteristic, complemented
64C53×#416C2211yescharacteristic
65C53×#416C2211yescharacteristic
66C2×C22⋊C8×C53C2211yescharacteristic
67#13133224—41no—
68#13133224—41no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917—41no—
72C2×#11719917—41no—
73C2×#11719917—41no—
74C2×#11719917—41no—
75C2×#11719917D411yescharacteristic
76C2×#11719917D411yescharacteristic
77C2×#11719917D411yescharacteristic
78C2×#11719917D411yescharacteristic
79C2×#11719917C2311yescharacteristic
80C2×#11719917C2311yescharacteristic
81C2×#11719917C2311yescharacteristic
82C2×#11719917C2311yescharacteristic
83C22×#88322—21no—
84C22×#88322—21no—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C2×C22⋊Dic53—21no—
88C2×C4×Dic53C2311yescharacteristic
89C2×C4×Dic53C2311yescharacteristic
90#13133153—41no—
91#13133153—41no—
92C4⋊#88322—21no—
93C4⋊#88322—21no—
94#13133144—41no—
95#13133144—41no—
96#13133144—41no—
97#13133144—41no—
98#13133144—41no—
99#13133144—41no—
100C22⋊#88322—21no—
101C22⋊#88322—21no—
102C22⋊#88322—21no—
103C22⋊#88322—21no—
104C22⋊#88322—21no—
105C22⋊#88322—21no—
106C22⋊#88322—21no—
107C22⋊#88322—21no—
108C22⋊#88322—21no—
109C22⋊#88322—21no—
110C22⋊#88322—21no—
111C22⋊#88322—21no—
112#13133128—21no—
113#13133127—41no—
114C4×#88322—21no—
115C8×Dic53—41no—
116#13133124—21no—
117C2×#41×C53—21no—
118C2×#41×C53—21no—
119C2×#41×C53—41no—
120C2×#41×C53—41no—
121C2×#41×C53—41no—
122C2×#41×C53—41no—
123C2×#41×C53C2×C411yescharacteristic
124C2×#41×C53C2×C411yescharacteristic
125C2×#41×C53C2311yescharacteristic
126C2×#41×C53C2311yescharacteristic
127C2×#41×C53C2311yescharacteristic
128C22×Q8×C53C2×C411yescharacteristic
129C22×D4×C53—21no—
130C22×D4×C53C2×C411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133#135×C53—41no—
134#135×C53—41no—
135#135×C53—41no—
136#135×C53—41no—
137C2×Q16×C53C2×C411yescharacteristic
138C2×Q16×C53C2×C411yescharacteristic
139C2×SD16×C53C2×C411yescharacteristic
140C2×SD16×C53C2×C411yescharacteristic
141C2×SD16×C53C2×C411yescharacteristic
142C2×SD16×C53C2×C411yescharacteristic
143C2×D8×C53C2×C411yescharacteristic
144C2×D8×C53C2×C411yescharacteristic
145C22×C8×C53C2311yescharacteristic
146C22×C8×C53C2311yescharacteristic
147#123×C53—21no—
148C22⋊Q8×C53C2×C411yescharacteristic
149C22⋊Q8×C53C2×C411yescharacteristic
150#121×C53C2×C411yescharacteristic
151#121×C53C2×C411yescharacteristic
152#120×C53—21no—
153C4×D4×C53—21no—
154C4×D4×C53—21no—
155#117×C53C2311yescharacteristic
156#103×C53C2×C411yescharacteristic
157#103×C53C2×C411yescharacteristic
158#103×C53C2×C411yescharacteristic
159#103×C53C2×C411yescharacteristic
160#102×C53C2×C411yescharacteristic
161#102×C53C2×C411yescharacteristic
162#102×C53C2×C411yescharacteristic
163#102×C53C2×C411yescharacteristic
164C22⋊C8×C53C2×C411yescharacteristic
165C22⋊C8×C53C2×C411yescharacteristic
166C22⋊C8×C53C2×C411yescharacteristic
167C22⋊C8×C53C2×C411yescharacteristic
168C24×C53—21no—
169C24×C53#4111yescharacteristic
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173#41×C53—21no—
174#41×C53—21no—
175#41×C53—21no—
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—21no—
179#41×C53—21no—
180#41×C53—21no—
181#41×C53—21no—
182#41×C53—41no—
183#41×C53—41no—
184#41×C53—41no—
185#41×C53—41no—
186#41×C53—42no—
187#41×C53—42no—
188#41×C53—42no—
189#41×C53—42no—
190C2×Q8×C53—21no—
191C2×Q8×C53—41no—
192C2×Q8×C53—41no—
193C2×Q8×C53C22×C411yescharacteristic
194C2×Q8×C53C22×C411yescharacteristic
195C2×Q8×C53C22×C411yescharacteristic
196C2×D4×C53—21no—
197C2×D4×C53—21no—
198C2×D4×C53—21no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—21no—
204C2×D4×C53—41no—
205C2×D4×C53—41no—
206C2×D4×C53—42no—
207C2×D4×C53—42no—
208C2×D4×C53C22×C411yescharacteristic
209C2×D4×C53C22×C411yescharacteristic
210C2×D4×C53C22×C411yescharacteristic
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—42no—
222C22×C4×C53—42no—
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53#4111yescharacteristic
228C22×C4×C53C2411yescharacteristic
229C22×Dic53—21no—
230C22×Dic53—21no—
231Q16×C53—41no—
232Q16×C53—41no—
233SD16×C53—41no—
234SD16×C53—41no—
235SD16×C53—41no—
236SD16×C53—41no—
237D8×C53—41no—
238D8×C53—41no—
239C2×C8×C53—21no—
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53C22×C411yescharacteristic
244C2×C8×C53C22×C411yescharacteristic
245C2×C8×C53C22×C411yescharacteristic
246C2×C8×C53C22×C411yescharacteristic
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53C22×C411yescharacteristic
250C4⋊C4×C53C22×C411yescharacteristic
251C22⋊C4×C53—21no—
252C22⋊C4×C53—21no—
253C22⋊C4×C53—21no—
254C22⋊C4×C53—21no—
255C22⋊C4×C53—21no—
256C42×C53—21no—
257C22⋊Dic53—42no—
258C4×Dic53—21no—
259C4×Dic53—21no—
260C4×Dic53—21no—
261C4×Dic53—21no—
262#11719917—21no—
263#11719917—21no—
264#11719917—21no—
265#11719917—21no—
266#11719917—21no—
267#11719917—21no—
268#11719917—21no—
269#11719917—21no—
270#11719917—41no—
271#11719917—41no—
272#11719917—41no—
273#11719917—41no—
274#11719917—42no—
275#11719917—42no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—42no—
285C2×#88322—42no—
286C2×#88322C2×D411yescharacteristic
287C2×#88322C2×D411yescharacteristic
288C2×#88322C2×D411yescharacteristic
289C2×#88322C2×D411yescharacteristic
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—21no—
295C23×C53—41no—
296C23×C53—41no—
297C23×C53—42no—
298C23×C53—81no—
299C23×C53—81no—
300C23×C53C4×D411yescharacteristic
301C23×C53C4×D411yescharacteristic
302C23×C53C2×#4111yescharacteristic
303Q8×C53—21no—
304Q8×C53—21no—
305Q8×C53—21no—
306Q8×C53—21no—
307Q8×C53—21no—
308Q8×C53—21no—
309Q8×C53—42no—
310D4×C53—21no—
311D4×C53—21no—
312D4×C53—21no—
313D4×C53—21no—
314D4×C53—21no—
315D4×C53—21no—
316D4×C53—42no—
317D4×C53—42no—
318D4×C53—42no—
319D4×C53—41no—
320D4×C53—41no—
321D4×C53—41no—
322D4×C53—41no—
323D4×C53—41no—
324D4×C53—41no—
325D4×C53—81no—
326D4×C53—81no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—42no—
343C2×C4×C53—42no—
344C2×C4×C53—42no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53C4×D411yescharacteristic
352C2×C4×C53C4×D411yescharacteristic
353C2×C4×C53C23×C411yescharacteristic
354C2×C4×C53C22×D411yescharacteristic
355C2×C4×C53H(5,𝔽2)11yescharacteristic
356C2×C4×C53H(5,𝔽2)11yescharacteristic
357C2×C4×C53H(5,𝔽2)11yescharacteristic
358C2×C4×C53H(5,𝔽2)11yescharacteristic
359C2×Dic53—22no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C8×C53—21no—
366C8×C53—21no—
367C8×C53—21no—
368C8×C53—21no—
369#88322—21no—
370#88322—21no—
371#88322—21no—
372#88322—21no—
373#88322—41no—
374#88322—41no—
375#88322—41no—
376#88322—41no—
377#22062—531nomaximal, Sylow
378C22×C53—21no—
379C22×C53—21no—
380C22×C53—21no—
381C22×C53—21no—
382C22×C53—21no—
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—21no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—81no—
396C22×C53—81no—
397C22×C53—84no—
398C22×C53C2×C4×D411yescharacteristic
399C22×C53#53811yescharacteristic
400C22×C53#53811yescharacteristic
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—41no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53—41no—
407C4×C53—41no—
408C4×C53#51811yescharacteristic
409C4×C53#51811yescharacteristic
410C4×C53#53411yescharacteristic
411C4×C53#53511yescharacteristic
412Dic53—42no—
413Dic53—81no—
414#3002D5311yescharacteristic
415#2930—531no—
416#2879—531no—
417#1975—531no—
418#1974—531no—
419#1938—531no—
420#1937—531no—
421#1929—531no—
422#1929—531no—
423#1876—531no—
424#1876—531no—
425#1871—531no—
426#1855—531no—
427#1789—531no—
428#1753—531no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—41no—
432C2×C53—41no—
433C2×C53—81no—
434C2×C53—81no—
435C2×C53—81no—
436C2×C53#232111yescharacteristic
437C2×C53#295611yescharacteristic
438C2×C53#295711yescharacteristic
439C22×#41C2×D5311yescharacteristic
440C2×#135C2×D5311yescharacteristic
441C2×#135C2×D5311yescharacteristic
442C2×#131—531no—
443C22×M16—531no—
444C22×M16—531no—
445#525C2×D5311yescharacteristic
446#452Dic5311yescharacteristic, complemented
447#452Dic5311yescharacteristic, complemented
448#451Dic5311yescharacteristic, complemented
449#450Dic5311yescharacteristic, complemented
450#449Dic5311yescharacteristic, complemented
451#449Dic5311yescharacteristic, complemented
452#448Dic5311yescharacteristic, complemented
453#447Dic5311yescharacteristic, complemented
454#436—1061no—
455#436—1061no—
456#435—1061no—
457#435—1061no—
458C2×#108—531no—
459C2×#108—531no—
460#424—531no—
461C2×#104—531no—
462C2×#104—531no—
463C2×#104—531no—
464C2×#104—531no—
465C2×#104—531no—
466C2×#104—531no—
467#416C2×D5311yescharacteristic
468#416C2×D5311yescharacteristic
469#408—531no—
470#408—531no—
471#408—531no—
472#408—531no—
473#408—531no—
474#408—1061no—
475#408—1061no—
476#407—531no—
477#407—1061no—
478#407—1061no—
479C2×C22⋊C8C2×D5311yescharacteristic
480#405—531no—
481C2×#97—531no—
482C2×C4×C8—531no—
483C4×C22⋊C4—531no—
484#341—531no—
485#341—531no—
486#339—531no—
487#339—531no—
488#336—531no—
489#336—531no—
490C53#2206211yescharacteristic, complemented, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×Dic5311yescharacteristic
498C2×#41C2×Dic5311yescharacteristic
499C2×#41C22×D5311yescharacteristic
500C2×#41C22×D5311yescharacteristic
501C2×#41C22×D5311yescharacteristic
502C22×Q8C2×Dic5311yescharacteristic
503C22×D4—21no—
504C22×D4C2×Dic5311yescharacteristic
505C23×C4—21no—
506C23×C4C22×D5311yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×Dic5311yescharacteristic
512C2×Q16C2×Dic5311yescharacteristic
513C2×SD16C2×Dic5311yescharacteristic
514C2×SD16C2×Dic5311yescharacteristic
515C2×SD16C2×Dic5311yescharacteristic
516C2×SD16C2×Dic5311yescharacteristic
517C2×D8C2×Dic5311yescharacteristic
518C2×D8C2×Dic5311yescharacteristic
519#131—2121no—
520#131—2121no—
521C2×M16—531no—
522C2×M16—531no—
523C2×M16—531no—
524C2×M16—531no—
525C2×M16—531no—
526C2×M16—531no—
527C2×M16—531no—
528C2×M16—531no—
529C2×M16—1061no—
530C2×M16—1061no—
531C2×M16—2121no—
532C2×M16—2121no—
533C2×M16—2121no—
534C2×M16—2121no—
535C22×C8—531no—
536C22×C8—531no—
537C22×C8—1061no—
538C22×C8—1061no—
539C22×C8C22×D5311yescharacteristic
540C22×C8C22×D5311yescharacteristic
541#123—21no—
542C22⋊Q8C2×Dic5311yescharacteristic
543C22⋊Q8C2×Dic5311yescharacteristic
544#121C2×Dic5311yescharacteristic
545#121C2×Dic5311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C22×D5311yescharacteristic
550C2×C22⋊C4—1061no—
551C2×C42—531no—
552C2×C42—531no—
553#108—2121no—
554#108—2121no—
555C4⋊C8—1061no—
556C4⋊C8—1061no—
557#104—2121no—
558#104—2121no—
559#104—2121no—
560#104—2121no—
561#104—2121no—
562#104—2121no—
563#103C2×Dic5311yescharacteristic
564#103C2×Dic5311yescharacteristic
565#103C2×Dic5311yescharacteristic
566#103C2×Dic5311yescharacteristic
567#102C2×Dic5311yescharacteristic
568#102C2×Dic5311yescharacteristic
569#102C2×Dic5311yescharacteristic
570#102C2×Dic5311yescharacteristic
571C22⋊C8—1061no—
572C22⋊C8—1061no—
573C22⋊C8—1061no—
574C22⋊C8—1061no—
575C22⋊C8—1061no—
576C22⋊C8—1061no—
577C22⋊C8—1061no—
578C22⋊C8—1061no—
579C22⋊C8—1061no—
580C22⋊C8—1061no—
581C22⋊C8—1061no—
582C22⋊C8—1061no—
583C22⋊C8C2×Dic5311yescharacteristic
584C22⋊C8C2×Dic5311yescharacteristic
585C22⋊C8C2×Dic5311yescharacteristic
586C22⋊C8C2×Dic5311yescharacteristic
587#97—1061no—
588#97—2121no—
589C4×C8—1061no—
590C4×C8—2121no—
591#95—1061no—
592C24—21no—
593C24#1171994711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×Dic5311yescharacteristic
618C2×Q8C22×Dic5311yescharacteristic
619C2×Q8C22×Dic5311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×Dic5311yescharacteristic
633C2×D4C22×Dic5311yescharacteristic
634C2×D4C22×Dic5311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4D4×D5311yescharacteristic
650C22×C4D4×D5311yescharacteristic
651C22×C4#1171994711yescharacteristic
652C22×C4C22×Dic5311yescharacteristic
653C22×C4C22×Dic5311yescharacteristic
654C22×C4C23×D5311yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—1061no—
664M16—1061no—
665M16—1061no—
666M16—1061no—
667M16—1061no—
668M16—1061no—
669M16—1061no—
670M16—1061no—
671M16—2121no—
672M16—2121no—
673M16—2121no—
674M16—2121no—
675M16—2122no—
676M16—2122no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—531no—
682C2×C8—531no—
683C2×C8—531no—
684C2×C8—531no—
685C2×C8—1061no—
686C2×C8—1061no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—2122no—
694C2×C8—2122no—
695C2×C8C22×Dic5311yescharacteristic
696C2×C8C22×Dic5311yescharacteristic
697C2×C8C22×Dic5311yescharacteristic
698C2×C8C22×Dic5311yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×Dic5311yescharacteristic
702C4⋊C4C22×Dic5311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—2122no—
709C42—21no—
710C42—1061no—
711C42—1061no—
712C42—1061no—
713C42—1061no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23D4×Dic5311yescharacteristic
725C23D4×Dic5311yescharacteristic
726C23C2×#1171994711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—1062no—
776C2×C4—2121no—
777C2×C4—2121no—
778C2×C4—2121no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4D4×Dic5311yescharacteristic
782C2×C4D4×Dic5311yescharacteristic
783C2×C4C23×Dic5311yescharacteristic
784C2×C4C2×D4×D5311yescharacteristic
785C2×C4#1313326211yescharacteristic
786C2×C4#1313326211yescharacteristic
787C2×C4#1313326211yescharacteristic
788C2×C4#1313326211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—1061no—
794C8—1061no—
795C8—1061no—
796C8—1061no—
797C8—2121no—
798C8—2121no—
799C8—2121no—
800C8—2121no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×D4×Dic5311yescharacteristic
822C22#1681120811yescharacteristic
823C22#1681120811yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—4241no—
832C4—2122no—
833C4#1681109811yescharacteristic
834C4#1681109811yescharacteristic
835C4#1681118311yescharacteristic
836C4#1681118811yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#2027737611yescharacteristic
845C2#2028362511yescharacteristic
846C2#2028363211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#3002C2
socleC22×C53C2×C4×D4
cosocleC22×C4×C53C24
hypercenter#3002D53
hypocenterC53#22062
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #20283419C2semidirect
2. #20283160C2semidirect
3. #20275609C2semidirect
4. #20275604C2semidirect
5. #20275428C2semidirect
6. #20275421C2semidirect
7. #20275365C2semidirect
8. #20275365C2semidirect
9. #20275044C2semidirect
10. #20275044C2semidirect
11. #20275018C2semidirect
12. #20274922C2semidirect
13. #20274659C2semidirect
14. #20274501C2semidirect
16. C2×#13133224C22semidirect
23. C2×#13133153C22semidirect
24. C2×#13133153C22semidirect
25. #16810650C22semidirect
30. C2×#13133144C22semidirect
31. C2×#13133144C22semidirect
38. #16810590C22semidirect
42. #16810579C22semidirect
43. C2×#13133127C22semidirect
44. C2×C8×Dic53C22semidirect
46. #16810388C22semidirect
47. #16810388C22semidirect
48. #16810382C22semidirect
49. #16810382C22semidirect
50. #16810377C22semidirect
51. #16810377C22semidirect
56. C53×#452C4semidirect
57. C53×#452C4semidirect
58. C53×#451C4semidirect
59. C53×#450C4semidirect
60. C53×#449C4semidirect
61. C53×#449C4semidirect
62. C53×#448C4semidirect
63. C53×#447C4semidirect
446. #452Dic53semidirect
447. #452Dic53semidirect
448. #451Dic53semidirect
449. #450Dic53semidirect
450. #449Dic53semidirect
451. #449Dic53semidirect
452. #448Dic53semidirect
453. #447Dic53semidirect
490. C53#22062semidirect

Maximal subgroups

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

subgroupindex
#202834192
#202831602
#202756092
#202756042
#202754282
#202754212
#202753652
#202750442
#202750182
#202749222
#202746592
#202745012
C53×#30022
#2206253