Finite Group Databasebeta

← #27404834

Subgroups — #27404834

Order 13568.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283937C211yesmaximal, characteristic
2C2×#16810746C211yesmaximal, characteristic, complemented
3#20283436C211yesmaximal, characteristic, complemented
4C22×#13133145C211yesmaximal, characteristic, complemented
5#20283161C211yesmaximal, characteristic, complemented
6#20275608C211yesmaximal, characteristic, complemented
7#20275426C211yesmaximal, characteristic, complemented
8#20275364C211yesmaximal, characteristic, complemented
9#20275158C211yesmaximal, characteristic, complemented
10#20275041C211yesmaximal, characteristic, complemented
11#20275041C211yesmaximal, characteristic, complemented
12#20274993C211yesmaximal, characteristic, complemented
13#20274922C211yesmaximal, characteristic, complemented
14#20274559C211yesmaximal, characteristic, complemented
15C53×#1749C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133239C2211yescharacteristic
18C2×#13133239C2211yescharacteristic
19C2×#13133223C2211yescharacteristic
20C2×#13133223C2211yescharacteristic
21C2×#13133223C2211yescharacteristic, complemented
22C22×#11719917C2211yescharacteristic
23#16811134C2211yescharacteristic
24#16810787C411yescharacteristic, complemented
25#16810787C411yescharacteristic, complemented
26#16810781C411yescharacteristic, complemented
27#16810776C411yescharacteristic, complemented
28#16810770C411yescharacteristic, complemented
29#16810770C411yescharacteristic, complemented
30#16810764C411yescharacteristic, complemented
31#16810759C411yescharacteristic, complemented
32#16810746—24no—
33#16810698—21no—
34#16810697—21no—
35#16810691—21no—
36#16810686—21no—
37C2×#13133153C2211yescharacteristic, complemented
38C2×#13133153C2211yescharacteristic, complemented
39#16810649C2211yescharacteristic, complemented
40C2×#13133145—24no—
41C2×#13133145C2211yescharacteristic
42C2×#13133145C2211yescharacteristic
43C2×#13133145C2211yescharacteristic
44C2×#13133145C2211yescharacteristic
45C2×#13133145C2211yescharacteristic, complemented
46C2×#13133145C2211yescharacteristic, complemented
47#16810620C2211yescharacteristic
48#16810620C2211yescharacteristic
49#16810589C2211yescharacteristic
50#16810589C2211yescharacteristic
51#16810589C2211yescharacteristic, complemented
52#16810588—21no—
53#16810588—21no—
54#16810587C2211yescharacteristic
55#16810585—21no—
56C22⋊C8×D53—21no—
57#16810578C2211yescharacteristic, complemented
58#16810388C2211yescharacteristic, complemented
59#16810388C2211yescharacteristic, complemented
60#16810383C2211yescharacteristic, complemented
61#16810383C2211yescharacteristic, complemented
62C22×C42×C53C2211yescharacteristic
63C2×C22⋊C8×C53C2211yescharacteristic
64C2×C22⋊C8×C53C2211yescharacteristic
65C2×#97×C53C2211yescharacteristic, complemented
66C2×#97×C53C2211yescharacteristic, complemented
67C53×#336C2211yescharacteristic, complemented
68C53×#336C2211yescharacteristic, complemented
69C2×#11719945—21no—
70C2×#11719945—21no—
71C2×#11719945—22no—
72C2×#11719945—22no—
73C2×#11719945—41no—
74C2×#11719945—41no—
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C2×#11719945C2311yescharacteristic
78C2×#11719945C2311yescharacteristic
79C2×#11719945C2311yescharacteristic
80C22×Dic106C2×C411yescharacteristic
81C22×D212C2×C411yescharacteristic
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84#13133239—22no—
85#13133239—22no—
86#13133239—41no—
87#13133239—41no—
88C2×Dic212C2×C411yescharacteristic, complemented
89C2×Dic212C2×C411yescharacteristic, complemented
90C2×#11719913C2×C411yescharacteristic, complemented
91C2×#11719913C2×C411yescharacteristic, complemented
92C2×#11719913C2×C411yescharacteristic, complemented
93C2×#11719913C2×C411yescharacteristic, complemented
94C2×D424C2×C411yescharacteristic, complemented
95C2×D424C2×C411yescharacteristic, complemented
96#13133223—22no—
97#13133223—22no—
98#13133223—22no—
99#13133223—41no—
100#13133223—41no—
101#13133223—41no—
102C2×#11719917—22no—
103C2×#11719917—21no—
104C2×#11719917—41no—
105C2×#11719917C2311yescharacteristic
106C2×#11719917C2311yescharacteristic
107C2×#11719917C2311yescharacteristic
108C2×#11719917C2311yescharacteristic
109C2×#11719912—21no—
110C2×#11719912—21no—
111C2×#11719912—21no—
112C22×#88322—21no—
113C2×C8×D53—21no—
114C2×C8×D53—21no—
115C2×C8×D53—21no—
116#13133200—21no—
117#13133196C2×C411yescharacteristic
118#13133196C2×C411yescharacteristic
119#13133191C2×C411yescharacteristic
120#13133191C2×C411yescharacteristic
121#13133186—21no—
122C4×C22⋊D53—21no—
123C4×C22⋊D53—21no—
124#13133176C2311yescharacteristic
125#13133153—22no—
126#13133153—41no—
127#13133146—21no—
128#13133146—21no—
129#13133145—22no—
130#13133145—22no—
131#13133145—22no—
132#13133145—22no—
133#13133145—41no—
134#13133145D414yescomplemented
135#13133142C2×C411yescharacteristic, complemented
136#13133142C2×C411yescharacteristic, complemented
137#13133142C2×C411yescharacteristic, complemented
138#13133142C2×C411yescharacteristic, complemented
139#13133139C2×C411yescharacteristic, complemented
140#13133139C2×C411yescharacteristic, complemented
141#13133139C2×C411yescharacteristic, complemented
142#13133139C2×C411yescharacteristic, complemented
143C22⋊#88322—21no—
144C22⋊#88322—21no—
145#13133129—21no—
146#13133129—21no—
147#13133129—21no—
148#13133129—21no—
149#13133129—21no—
150#13133129—21no—
151#13133127—21no—
152C8×Dic53—21no—
153C23×C4×C53—21no—
154C23×C4×C53C2311yescharacteristic
155C22×C8×C53C2311yescharacteristic
156C22×C8×C53C2311yescharacteristic
157C22×C8×C53C2311yescharacteristic
158C22×C8×C53C2311yescharacteristic
159C2×C42×C53—21no—
160C2×C42×C53—22no—
161C2×C42×C53—41no—
162C2×C42×C53C2311yescharacteristic
163C2×C42×C53C2311yescharacteristic
164C22⋊C8×C53C2×C411yescharacteristic
165C22⋊C8×C53C2×C411yescharacteristic
166C22⋊C8×C53C2×C411yescharacteristic
167C22⋊C8×C53C2×C411yescharacteristic
168C22⋊C8×C53D411yescharacteristic
169C22⋊C8×C53D411yescharacteristic
170C22⋊C8×C53D411yescharacteristic
171C22⋊C8×C53D411yescharacteristic
172#97×C53—22no—
173#97×C53—41no—
174C24×C53#4111yescharacteristic
175C23×D53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—42no—
183C22×C4×C53—42no—
184C22×C4×C53—42no—
185C22×C4×C53C22×C411yescharacteristic
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53#4111yescharacteristic
190C22×C4×C53C2411yescharacteristic
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C2×C22⋊D53—21no—
197C2×C22⋊D53—21no—
198C2×C22⋊D53—42no—
199C2×C22⋊D53—42no—
200C22×Dic53—21no—
201#11719945—21no—
202#11719945—21no—
203#11719945—21no—
204#11719945—21no—
205#11719945—21no—
206#11719945—21no—
207#11719945—21no—
208#11719945—21no—
209#11719945—21no—
210#11719945—21no—
211#11719945—22no—
212#11719945—22no—
213#11719945—41no—
214#11719945—41no—
215#11719945—42no—
216#11719945—42no—
217#11719945—42no—
218#11719945—42no—
219#11719945C2×D412yes—
220#11719945#4112yes—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212—41no—
224C2×D212C22×C411yescharacteristic
225C2×D212C22×C411yescharacteristic
226C2×D212C22×C411yescharacteristic
227C2×C4×D53—21no—
228C2×C4×D53—21no—
229C2×C4×D53—21no—
230C2×C4×D53—21no—
231C2×C4×D53—21no—
232C2×C4×D53—42no—
233C2×C4×D53—42no—
234C2×Dic106—22no—
235C2×Dic106—21no—
236C2×Dic106—41no—
237C2×Dic106C22×C411yescharacteristic
238C2×Dic106C22×C411yescharacteristic
239C2×Dic106C22×C411yescharacteristic
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53C22×C411yescharacteristic
249C2×C8×C53C22×C411yescharacteristic
250C2×C8×C53C22×C411yescharacteristic
251C2×C8×C53C22×C411yescharacteristic
252C2×C8×C53C2×D411yescharacteristic
253C2×C8×C53C2×D411yescharacteristic
254C2×C8×C53C2×D411yescharacteristic
255C2×C8×C53C2×D411yescharacteristic
256C42×C53—21no—
257C42×C53—21no—
258C42×C53—21no—
259C42×C53—42no—
260C42×C53C2×D412yes—
261C22⋊Dic53—21no—
262C22⋊Dic53—21no—
263C22⋊Dic53—21no—
264#11719921—21no—
265#11719921—21no—
266C4⋊Dic53C22×C411yescharacteristic
267C4⋊Dic53C22×C411yescharacteristic
268#11719919—21no—
269#11719919—21no—
270C4×Dic53—21no—
271#11719917—21no—
272#11719917—21no—
273#11719917—21no—
274#11719917—21no—
275#11719917—21no—
276#11719917—21no—
277#11719917—21no—
278#11719917—42no—
279#11719917C2×D412yes—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—42no—
285Dic212—22no—
286Dic212—41no—
287D424—22no—
288D424—41no—
289#11719913—22no—
290#11719913—22no—
291#11719913—41no—
292#11719913—41no—
293#11719912—42no—
294#11719912—42no—
295#11719912—42no—
296C8×D53—42no—
297C8×D53—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—22no—
302C23×C53—41no—
303C23×C53C4×D411yescharacteristic
304C23×C53C4×D411yescharacteristic
305C23×C53C2×#4111yescharacteristic
306C22×D53—21no—
307C22×D53—21no—
308C22×D53—21no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—81no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—48no—
328C2×C4×C53—41no—
329C2×C4×C53C4×D411yescharacteristic
330C2×C4×C53C4×D411yescharacteristic
331C2×C4×C53C23×C411yescharacteristic
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C2×#4111yescharacteristic
335C2×C4×C53H(5,𝔽2)11yescharacteristic
336C2×C4×C53H(5,𝔽2)11yescharacteristic
337C22⋊D53—22no—
338C22⋊D53—22no—
339C22⋊D53—42no—
340C22⋊D53—42no—
341C22⋊D53—41no—
342C22⋊D53—41no—
343C22⋊D53—41no—
344C22⋊D53—41no—
345C22⋊D53—42no—
346C22⋊D53—81no—
347C2×Dic53—21no—
348C2×Dic53—21no—
349C2×Dic53—21no—
350C2×Dic53—21no—
351C2×Dic53—21no—
352C2×Dic53—42no—
353D212—21no—
354D212—21no—
355D212—21no—
356D212—21no—
357D212—21no—
358D212—42no—
359D212C4×D412yes—
360C4×D53—22no—
361C4×D53—22no—
362C4×D53—42no—
363C4×D53—42no—
364C4×D53—41no—
365C4×D53—41no—
366C4×D53—41no—
367C4×D53—41no—
368Dic106—21no—
369Dic106—21no—
370Dic106—21no—
371Dic106—21no—
372Dic106—21no—
373Dic106—42no—
374Dic106C4×D412yes—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—21no—
378C8×C53—21no—
379C8×C53—21no—
380C8×C53—21no—
381C8×C53—21no—
382C8×C53—21no—
383#88322—22no—
384#88322—41no—
385#88322—41no—
386#88322—41no—
387#22886—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—21no—
394C22×C53—21no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53#44412yescomplemented
398C22×C53C2×C4×D411yescharacteristic
399C22×C53#54611yescharacteristic
400C22×C53#55111yescharacteristic
401C2×D53—22no—
402C2×D53—41no—
403C2×D53—41no—
404C2×D53—41no—
405C2×D53—41no—
406C2×D53—41no—
407C2×D53—41no—
408C2×D53—41no—
409C2×D53—41no—
410C2×D53—84no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—42no—
414C4×C53—42no—
415C4×C53C2×C4×D411yescharacteristic
416C4×C53#51811yescharacteristic
417C4×C53D4211yescharacteristic
418C4×C53#54611yescharacteristic
419Dic53—22no—
420Dic53—41no—
421Dic53—41no—
422Dic53—41no—
423Dic53—41no—
424#3002—531no—
425C2×#444—531no—
426#2933—531no—
427C22×#104—531no—
428#2880—531no—
429#1975—531no—
430#1938—531no—
431#1929—531no—
432#1896—531no—
433#1876—531no—
434#1876—531no—
435#1866—531no—
436#1855—531no—
437#1765—531no—
438#1749D5311yescharacteristic, complemented
439C2×C53—21no—
440C2×C53—22no—
441C2×C53—21no—
442C2×C53—41no—
443C2×C53#235811yescharacteristic
444C2×C53C2×#44411yescharacteristic
445C2×C53#295611yescharacteristic
446D53—42no—
447D53—81no—
448D53—81no—
449C22×#41—531no—
450C2×#135—531no—
451C2×#135—531no—
452C2×#131—531no—
453C2×#131—531no—
454C2×#131—531no—
455C22×M16—531no—
456#525—531no—
457C22×C42C2×D5311yescharacteristic
458#452—531no—
459#452—531no—
460#451—531no—
461#450—531no—
462#449—531no—
463#449—531no—
464#448—531no—
465#447—531no—
466#444—1064no—
467#436—1061no—
468#435—1061no—
469#435—1061no—
470C8×D4—1061no—
471C2×#108—531no—
472C2×#108—531no—
473#424—531no—
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—531no—
479C2×#104—531no—
480C2×#104—1064no—
481#416—531no—
482#416—531no—
483#408—531no—
484#408—531no—
485#408—531no—
486#408—1061no—
487#408—1061no—
488#407—531no—
489#407—1061no—
490C2×C22⋊C8—1061no—
491C2×C22⋊C8C2×D5311yescharacteristic
492C2×C22⋊C8C2×D5311yescharacteristic
493#405—531no—
494C2×#97C2×D5311yescharacteristic, complemented
495C2×#97C2×D5311yescharacteristic, complemented
496#341—531no—
497#341—531no—
498#339—531no—
499#339—531no—
500#336C2×D5311yescharacteristic, complemented
501#336C2×D5311yescharacteristic, complemented
502C53#2288611yescharacteristic, complemented, Sylow
503C2×#41—531no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—531no—
508C2×#41—1062no—
509C2×#41—1062no—
510C2×#41—1061no—
511C2×#41—1061no—
512C2×#41—2121no—
513C2×#41—2121no—
514C22×Q8—531no—
515C22×D4—531no—
516C22×D4—1061no—
517C23×C4—21no—
518C23×C4—1061no—
519C23×C4C22×D5311yescharacteristic
520#135—1062no—
521#135—1062no—
522#135—2121no—
523#135—2121no—
524C2×Q16—531no—
525C2×Q16—531no—
526C2×SD16—531no—
527C2×SD16—531no—
528C2×SD16—531no—
529C2×SD16—531no—
530C2×D8—531no—
531C2×D8—531no—
532#131—1062no—
533#131—1062no—
534#131—1062no—
535#131—2121no—
536#131—2121no—
537#131—2121no—
538C2×M16—531no—
539C2×M16—531no—
540C2×M16—531no—
541C2×M16—531no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16—1061no—
545C2×M16—1061no—
546C2×M16—1062no—
547C2×M16—2121no—
548C22×C8—1061no—
549C22×C8—1061no—
550C22×C8—1061no—
551C22×C8—1061no—
552C22×C8C22×D5311yescharacteristic
553C22×C8C22×D5311yescharacteristic
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
556#123—1061no—
557C22⋊Q8—531no—
558C22⋊Q8—531no—
559#121—531no—
560#121—531no—
561#120—1061no—
562C4×D4—1061no—
563C4×D4—1061no—
564#117—531no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D5311yescharacteristic
569C2×C42C22×D5311yescharacteristic
570#108—1062no—
571#108—2121no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
574#104—534no—
575#104—1062no—
576#104—1062no—
577#104—1062no—
578#104—1062no—
579#104—2121no—
580#103—531no—
581#103—531no—
582#103—531no—
583#103—531no—
584#102—531no—
585#102—531no—
586#102—531no—
587#102—531no—
588C22⋊C8—1061no—
589C22⋊C8—1061no—
590C22⋊C8—1061no—
591C22⋊C8—1061no—
592C22⋊C8—1061no—
593C22⋊C8—1061no—
594C22⋊C8—1061no—
595C22⋊C8—1061no—
596C22⋊C8C4×D5311yescharacteristic
597C22⋊C8C4×D5311yescharacteristic
598C22⋊C8C4×D5311yescharacteristic
599C22⋊C8C4×D5311yescharacteristic
600C22⋊C8D21211yescharacteristic
601C22⋊C8D21211yescharacteristic
602C22⋊C8D21211yescharacteristic
603C22⋊C8D21211yescharacteristic
604#97—22no—
605#97—41no—
606#97—1061no—
607C4×C8—1061no—
608C24—1061no—
609C24#1171994511yescharacteristic
610#41—532no—
611#41—532no—
612#41—1062no—
613#41—1062no—
614#41—1061no—
615#41—1061no—
616#41—1061no—
617#41—1061no—
618#41—1061no—
619#41—1061no—
620#41—1061no—
621#41—1061no—
622#41—1061no—
623#41—1061no—
624#41—2122no—
625#41—2122no—
626#41—2121no—
627#41—2121no—
628#41—2122no—
629#41—2122no—
630C2×Q8—531no—
631C2×Q8—531no—
632C2×Q8—531no—
633C2×Q8—1062no—
634C2×Q8—1061no—
635C2×Q8—2121no—
636C2×D4—531no—
637C2×D4—531no—
638C2×D4—531no—
639C2×D4—1062no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—2121no—
649C2×D4—2122no—
650C2×D4—2122no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—2122no—
667C22×C4—2122no—
668C22×C4C2×C4×D5311yescharacteristic
669C22×C4C2×C4×D5311yescharacteristic
670C22×C4C2×D21211yescharacteristic
671C22×C4C2×D21211yescharacteristic
672C22×C4#1171994511yescharacteristic
673C22×C4C23×D5311yescharacteristic
674Q16—1062no—
675Q16—2121no—
676SD16—1062no—
677SD16—1062no—
678SD16—2121no—
679SD16—2121no—
680D8—1062no—
681D8—2121no—
682M16—532no—
683M16—1061no—
684M16—1061no—
685M16—1061no—
686M16—1061no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—2122no—
691M16—2122no—
692M16—2122no—
693M16—2122no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—1061no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—2122no—
707C2×C8—2122no—
708C2×C8—2122no—
709C2×C8—2122no—
710C2×C8C2×C4×D5311yescharacteristic
711C2×C8C2×C4×D5311yescharacteristic
712C2×C8C2×C4×D5311yescharacteristic
713C2×C8C2×C4×D5311yescharacteristic
714C2×C8C2×D21211yescharacteristic
715C2×C8C2×D21211yescharacteristic
716C2×C8C2×D21211yescharacteristic
717C2×C8C2×D21211yescharacteristic
718C4⋊C4—531no—
719C4⋊C4—531no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C22⋊C4—1061no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1061no—
732C42D4×D5312yes—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—41no—
737C23—1061no—
738C23—1061no—
739C23—1061no—
740C23—4241no—
741C23—2122no—
742C23—2122no—
743C23C4×D21211yescharacteristic
744C23C4×D21211yescharacteristic
745C23C2×#1171994511yescharacteristic
746Q8—532no—
747Q8—1061no—
748Q8—1061no—
749Q8—1061no—
750Q8—1061no—
751Q8—1061no—
752Q8—2122no—
753D4—532no—
754D4—1062no—
755D4—1062no—
756D4—1061no—
757D4—1061no—
758D4—1061no—
759D4—1061no—
760D4—1061no—
761D4—4241no—
762D4—2122no—
763D4—2122no—
764D4—2122no—
765D4—2121no—
766D4—2121no—
767D4—2122no—
768D4—2121no—
769D4—2121no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—1061no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1061no—
791C2×C4—1061no—
792C2×C4—1061no—
793C2×C4—1061no—
794C2×C4—2122no—
795C2×C4—2122no—
796C2×C4—2122no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4C4×D21211yescharacteristic
802C2×C4C4×D21211yescharacteristic
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C22×D21211yescharacteristic
806C2×C4#41×D5311yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—1062no—
818C8—2121no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—1062no—
831C22—4244no—
832C22—2121no—
833C22—2121no—
834C22—2121no—
835C22—2121no—
836C22—2121no—
837C22—2121no—
838C22—2121no—
839C22—2121no—
840C22#1681074612yescomplemented
841C22C2×C4×D21211yescharacteristic
842C22#1681126311yescharacteristic
843C22#1681129711yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—1062no—
849C4—2121no—
850C4—2121no—
851C4—2121no—
852C4—2121no—
853C4C4×D4×D5311yescharacteristic
854C4#1681109511yescharacteristic
855C4D4×D21211yescharacteristic
856C4#1681126811yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—4241no—
862C2—4241no—
863C2—2122no—
864C2#2027769711yescharacteristic
865C2C2×#1681074611yescharacteristic
866C2#2028362611yescharacteristic
subgroupG/H
centerC2×C4C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1749C2
socleC22×C53C2×C4×D4
prime radical#20283937C2
cosocleC22×C4×C53C24
hypercenter#1749D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#16810746C2semidirect
3. #20283436C2semidirect
4. C22×#13133145C2semidirect
5. #20283161C2semidirect
6. #20275608C2semidirect
7. #20275426C2semidirect
8. #20275364C2semidirect
9. #20275158C2semidirect
10. #20275041C2semidirect
11. #20275041C2semidirect
12. #20274993C2semidirect
13. #20274922C2semidirect
14. #20274559C2semidirect
15. C53×#1749C2semidirect
21. C2×#13133223C22semidirect
24. #16810787C4semidirect
25. #16810787C4semidirect
26. #16810781C4semidirect
27. #16810776C4semidirect
28. #16810770C4semidirect
29. #16810770C4semidirect
30. #16810764C4semidirect
31. #16810759C4semidirect
37. C2×#13133153C22semidirect
38. C2×#13133153C22semidirect
39. #16810649C22semidirect
45. C2×#13133145C22semidirect
46. C2×#13133145C22semidirect
51. #16810589C22semidirect
57. #16810578C22semidirect
58. #16810388C22semidirect
59. #16810388C22semidirect
60. #16810383C22semidirect
61. #16810383C22semidirect
65. C2×#97×C53C22semidirect
66. C2×#97×C53C22semidirect
67. C53×#336C22semidirect
68. C53×#336C22semidirect
88. C2×Dic212C2×C4semidirect
89. C2×Dic212C2×C4semidirect
90. C2×#11719913C2×C4semidirect
91. C2×#11719913C2×C4semidirect
92. C2×#11719913C2×C4semidirect
93. C2×#11719913C2×C4semidirect
94. C2×D424C2×C4semidirect
95. C2×D424C2×C4semidirect
134. #13133145D4semidirect
135. #13133142C2×C4semidirect
136. #13133142C2×C4semidirect
137. #13133142C2×C4semidirect
138. #13133142C2×C4semidirect
139. #13133139C2×C4semidirect
140. #13133139C2×C4semidirect
141. #13133139C2×C4semidirect
142. #13133139C2×C4semidirect
397. C22×C53#444semidirect
438. #1749D53semidirect
494. C2×#97C2×D53semidirect
495. C2×#97C2×D53semidirect
500. #336C2×D53semidirect
501. #336C2×D53semidirect
502. C53#22886semidirect
840. C22#16810746semidirect

Maximal subgroups

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

subgroupindex
#202839372
C2×#168107462
#202834362
C22×#131331452
#202831612
#202756082
#202754262
#202753642
#202751582
#202750412
#202749932
#202749222
#202745592
C53×#17492
#2288653