Finite Group Databasebeta

← C101×#24283 #38806434

Subgroups — C101×#24283 #38806434

Order 25856.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C101C211yesmaximal, characteristic, complemented
2C2×#473×C101C211yesmaximal, characteristic, complemented
3C2×#471×C101C211yesmaximal, characteristic, complemented
4C101×#3005C211yesmaximal, characteristic
5C101×#3004C211yesmaximal, characteristic, complemented
6C101×#2930C211yesmaximal, characteristic, complemented
7C101×#2047C211yesmaximal, characteristic, complemented
8C101×#2046C211yesmaximal, characteristic, complemented
9C101×#2020C211yesmaximal, characteristic, complemented
10C101×#2019C211yesmaximal, characteristic, complemented
11C101×#1979C211yesmaximal, characteristic, complemented
12C101×#1977C211yesmaximal, characteristic, complemented
13C101×#1811C211yesmaximal, characteristic, complemented
14C101×#1785C211yesmaximal, characteristic, complemented
15C101×#1784C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C2×#137×C101—24no—
19C2×#137×C101—24no—
20C2×#137×C101—22no—
21C2×#137×C101—22no—
22C2×#137×C101C2211yescharacteristic
23C2×#137×C101C2211yescharacteristic
24C2×#137×C101C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
26C22×Q16×C101C2211yescharacteristic
27C22×Q16×C101C2211yescharacteristic
28C22×SD16×C101C2211yescharacteristic
29C22×SD16×C101C2211yescharacteristic
30C2×#131×C101C2211yescharacteristic
31C22×M16×C101C2211yescharacteristic
32#525×C101C2211yescharacteristic
33#473×C101—24no—
34#471×C101—24no—
35#452×C101—22no—
36#451×C101—22no—
37#449×C101—22no—
38#448×C101—22no—
39#436×C101—22no—
40#435×C101—22no—
41C2×#108×C101C2211yescharacteristic
42C2×#108×C101C2211yescharacteristic
43#424×C101C2211yescharacteristic
44#419×C101C2211yescharacteristic
45#419×C101C2211yescharacteristic
46#419×C101C2211yescharacteristic
47#418×C101C2211yescharacteristic
48C2×#101×C101C2211yescharacteristic
49C2×#101×C101C2211yescharacteristic
50C2×#101×C101C2211yescharacteristic
51C2×#101×C101C2211yescharacteristic
52C2×#101×C101C2211yescharacteristic
53C2×#101×C101C2211yescharacteristic
54C2×#100×C101C2211yescharacteristic
55C2×#100×C101C2211yescharacteristic
56#408×C101C2211yescharacteristic
57#407×C101C2211yescharacteristic
58#407×C101C2211yescharacteristic
59#407×C101C2211yescharacteristic
60#405×C101C2211yescharacteristic
61#341×C101C2211yescharacteristic
62#341×C101C2211yescharacteristic
63C2×#41×C101—22no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C2×#41×C101C2311yescharacteristic
70C22×Q8×C101—21no—
71C22×Q8×C101—22no—
72C22×Q8×C101—22no—
73C22×Q8×C101—22no—
74C22×Q8×C101—22no—
75C22×Q8×C101—41no—
76C22×Q8×C101—41no—
77C22×Q8×C101C2311yescharacteristic
78C22×Q8×C101C2311yescharacteristic
79C22×Q8×C101C2311yescharacteristic
80C22×D4×C101—21no—
81C22×D4×C101C2311yescharacteristic
82C23×C4×C101—21no—
83C23×C4×C101—21no—
84C23×C4×C101C2311yescharacteristic
85#137×C101—216no—
86#137×C101—216no—
87#137×C101—22no—
88#137×C101—22no—
89#137×C101—22no—
90#137×C101—41no—
91#137×C101—41no—
92#137×C101—41no—
93AGL(1,ℤ/8)×C101—22no—
94AGL(1,ℤ/8)×C101—41no—
95C2×Q16×C101—22no—
96C2×Q16×C101—22no—
97C2×Q16×C101—21no—
98C2×Q16×C101—21no—
99C2×Q16×C101—21no—
100C2×Q16×C101—22no—
101C2×Q16×C101—21no—
102C2×Q16×C101—21no—
103C2×Q16×C101—22no—
104C2×Q16×C101D414yescomplemented
105C2×SD16×C101—22no—
106C2×SD16×C101—22no—
107C2×SD16×C101—21no—
108C2×SD16×C101—21no—
109C2×SD16×C101—21no—
110C2×SD16×C101—21no—
111C2×SD16×C101—22no—
112C2×SD16×C101—21no—
113C2×SD16×C101—21no—
114C2×SD16×C101—22no—
115C2×SD16×C101D414yescomplemented
116C2×D8×C101—21no—
117#131×C101—22no—
118#131×C101—22no—
119C2×M16×C101—22no—
120C2×M16×C101—22no—
121C2×M16×C101—21no—
122C2×M16×C101D412yes—
123C2×M16×C101D412yes—
124C2×M16×C101C2311yescharacteristic
125C2×M16×C101C2311yescharacteristic
126C2×M16×C101C2311yescharacteristic
127C2×M16×C101C2311yescharacteristic
128C2×M16×C101C2311yescharacteristic
129C2×M16×C101C2311yescharacteristic
130C22×C8×C101—21no—
131C22×C8×C101C2311yescharacteristic
132C22×C8×C101C2311yescharacteristic
133#123×C101—21no—
134C22⋊Q8×C101D412yes—
135#121×C101D412yes—
136#120×C101—21no—
137C4×D4×C101—22no—
138#117×C101C2311yescharacteristic
139#108×C101—22no—
140#108×C101—22no—
141C4⋊C8×C101—22no—
142#103×C101—22no—
143#103×C101—22no—
144#103×C101—22no—
145#102×C101—22no—
146#101×C101—22no—
147#101×C101—22no—
148#101×C101—22no—
149#101×C101—41no—
150#101×C101—41no—
151#101×C101—41no—
152#100×C101—22no—
153#100×C101—41no—
154C22⋊C8×C101—22no—
155C22⋊C8×C101—22no—
156C22⋊C8×C101—22no—
157C22⋊C8×C101—22no—
158#97×C101—21no—
159C4×C8×C101—21no—
160C24×C101—21no—
161C24×C101#4111yescharacteristic
162#41×C101—28no—
163#41×C101—21no—
164#41×C101—21no—
165#41×C101—21no—
166#41×C101—21no—
167#41×C101—44no—
168#41×C101—44no—
169#41×C101—44no—
170C2×Q8×C101—21no—
171C2×Q8×C101—21no—
172C2×Q8×C101—21no—
173C2×Q8×C101—28no—
174C2×Q8×C101—21no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—42no—
187C2×Q8×C101—42no—
188C2×Q8×C101—44no—
189C2×Q8×C101—44no—
190C2×Q8×C101—44no—
191C2×Q8×C101—42no—
192C2×Q8×C101C2×D412yes—
193C2×Q8×C101C2×D412yes—
194C2×Q8×C101C2×D412yes—
195C2×Q8×C101C2×D411yescharacteristic
196C2×D4×C101—21no—
197C2×D4×C101—22no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—42no—
204C2×D4×C101—42no—
205C2×D4×C101—42no—
206C2×D4×C101C2×D412yes—
207C2×D4×C101C2×D411yescharacteristic
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—42no—
217C22×C4×C101—42no—
218C22×C4×C101—42no—
219C22×C4×C101—42no—
220C22×C4×C101—42no—
221C22×C4×C101—42no—
222C22×C4×C101C2×D412yes—
223C22×C4×C101C2×D412yes—
224C22×C4×C101#4111yescharacteristic
225C22×C4×C101C2411yescharacteristic
226Q16×C101—28no—
227Q16×C101—24no—
228Q16×C101—24no—
229Q16×C101—42no—
230Q16×C101—42no—
231Q16×C101—42no—
232SD16×C101—28no—
233SD16×C101—24no—
234SD16×C101—24no—
235SD16×C101—42no—
236SD16×C101—42no—
237SD16×C101—42no—
238SD16×C101—42no—
239D8×C101—42no—
240M16×C101—24no—
241M16×C101—24no—
242M16×C101—21no—
243M16×C101—21no—
244M16×C101—21no—
245M16×C101—21no—
246M16×C101—21no—
247M16×C101—21no—
248M16×C101—21no—
249M16×C101—21no—
250M16×C101—21no—
251M16×C101—21no—
252M16×C101—21no—
253M16×C101—21no—
254M16×C101—42no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—42no—
264C2×C8×C101C2×D412yes—
265C2×C8×C101C2×D411yescharacteristic
266C2×C8×C101C2×D411yescharacteristic
267C2×C8×C101C2×D412yes—
268C2×C8×C101C2×D412yes—
269C4⋊C4×C101—22no—
270C4⋊C4×C101C2×D412yes—
271C22⋊C4×C101—22no—
272C22⋊C4×C101—21no—
273C22⋊C4×C101—22no—
274C42×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—22no—
279C23×C101—42no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—82no—
283C23×C101#12112yes—
284C23×C101C2×#4111yescharacteristic
285Q8×C101—22no—
286Q8×C101—22no—
287Q8×C101—22no—
288Q8×C101—21no—
289Q8×C101—22no—
290Q8×C101—22no—
291Q8×C101—22no—
292Q8×C101—21no—
293Q8×C101—48no—
294Q8×C101—41no—
295Q8×C101—41no—
296Q8×C101—41no—
297Q8×C101—41no—
298Q8×C101—41no—
299Q8×C101—41no—
300D4×C101—22no—
301D4×C101—21no—
302D4×C101—22no—
303D4×C101—21no—
304D4×C101—48no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—82no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—22no—
313C2×C4×C101—22no—
314C2×C4×C101—22no—
315C2×C4×C101—22no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—22no—
319C2×C4×C101—22no—
320C2×C4×C101—22no—
321C2×C4×C101—48no—
322C2×C4×C101—48no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101#12112yes—
332C2×C4×C101C22×D411yescharacteristic
333C2×C4×C101C22×D411yescharacteristic
334C2×C4×C101C22×D411yescharacteristic
335C2×C4×C101C22×D411yescharacteristic
336C2×C4×C101H(5,𝔽2)11yescharacteristic
337C2×C4×C101H(5,𝔽2)11yescharacteristic
338C8×C101—22no—
339C8×C101—41no—
340C8×C101—41no—
341C8×C101—41no—
342C8×C101—41no—
343C8×C101—41no—
344C8×C101—41no—
345C8×C101#12012yes—
346C8×C101#12012yes—
347C22×C101—22no—
348C22×C101—22no—
349C22×C101—22no—
350C22×C101—22no—
351C22×C101—42no—
352C22×C101—42no—
353C22×C101—42no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—82no—
357C22×C101—82no—
358C22×C101—82no—
359C22×C101C2×#12111yescharacteristic
360C22×C101#54611yescharacteristic
361C22×C101#54611yescharacteristic
362C4×C101—22no—
363C4×C101—42no—
364C4×C101—42no—
365C4×C101—42no—
366C4×C101—41no—
367C4×C101—42no—
368C4×C101C2×#12011yescharacteristic
369C4×C101#53511yescharacteristic
370C4×C101D4211yescharacteristic
371C4×C101D4211yescharacteristic
372#24283C10111yesmaximal, characteristic, direct product factor, Sylow
373C2×C101—21no—
374C2×C101—21no—
375C2×C101—42no—
376C2×C101—81no—
377C2×C101—82no—
378C2×C101#240811yescharacteristic
379C2×C101#306912yes—
380C22×#137C2×C10111yescharacteristic, complemented
381C2×#473C2×C10111yescharacteristic, complemented
382C2×#471C2×C10111yescharacteristic, complemented
383#3005C2×C10111yescharacteristic
384#3004C2×C10111yescharacteristic, complemented
385#2930C2×C10111yescharacteristic, complemented
386#2047C2×C10111yescharacteristic, complemented
387#2046C2×C10111yescharacteristic, complemented
388#2020C2×C10111yescharacteristic, complemented
389#2019C2×C10111yescharacteristic, complemented
390#1979C2×C10111yescharacteristic, complemented
391#1977C2×C10111yescharacteristic, complemented
392#1811C2×C10111yescharacteristic, complemented
393#1785C2×C10111yescharacteristic, complemented
394#1784C2×C10111yescharacteristic, complemented
395C101#2428311yescharacteristic, direct product factor, Sylow
396C22×#41C22×C10111yescharacteristic
397C23×Q8C22×C10111yescharacteristic
398C2×#137—24no—
399C2×#137—24no—
400C2×#137—22no—
401C2×#137—22no—
402C2×#137C22×C10111yescharacteristic
403C2×#137C22×C10111yescharacteristic
404C2×#137C22×C10111yescharacteristic
405C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
406C22×Q16C22×C10111yescharacteristic
407C22×Q16C22×C10111yescharacteristic
408C22×SD16C22×C10111yescharacteristic
409C22×SD16C22×C10111yescharacteristic
410C2×#131C22×C10111yescharacteristic
411C22×M16C22×C10111yescharacteristic
412#525C22×C10111yescharacteristic
413#473—24no—
414#471—24no—
415#452—22no—
416#451—22no—
417#449—22no—
418#448—22no—
419#436—22no—
420#435—22no—
421C2×#108C22×C10111yescharacteristic
422C2×#108C22×C10111yescharacteristic
423#424C22×C10111yescharacteristic
424#419C22×C10111yescharacteristic
425#419C22×C10111yescharacteristic
426#419C22×C10111yescharacteristic
427#418C22×C10111yescharacteristic
428C2×#101C22×C10111yescharacteristic
429C2×#101C22×C10111yescharacteristic
430C2×#101C22×C10111yescharacteristic
431C2×#101C22×C10111yescharacteristic
432C2×#101C22×C10111yescharacteristic
433C2×#101C22×C10111yescharacteristic
434C2×#100C22×C10111yescharacteristic
435C2×#100C22×C10111yescharacteristic
436#408C22×C10111yescharacteristic
437#407C22×C10111yescharacteristic
438#407C22×C10111yescharacteristic
439#407C22×C10111yescharacteristic
440#405C22×C10111yescharacteristic
441#341C22×C10111yescharacteristic
442#341C22×C10111yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41C23×C10111yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C10111yescharacteristic
458C22×Q8C23×C10111yescharacteristic
459C22×Q8C23×C10111yescharacteristic
460C22×D4—21no—
461C22×D4C23×C10111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C10111yescharacteristic
465#137—216no—
466#137—216no—
467#137—22no—
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—41no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—22no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16D4×C10114yescomplemented
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16D4×C10114yescomplemented
496C2×D8—21no—
497#131—22no—
498#131—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—21no—
502C2×M16D4×C10112yes—
503C2×M16D4×C10112yes—
504C2×M16C23×C10111yescharacteristic
505C2×M16C23×C10111yescharacteristic
506C2×M16C23×C10111yescharacteristic
507C2×M16C23×C10111yescharacteristic
508C2×M16C23×C10111yescharacteristic
509C2×M16C23×C10111yescharacteristic
510C22×C8—21no—
511C22×C8C23×C10111yescharacteristic
512C22×C8C23×C10111yescharacteristic
513#123—21no—
514C22⋊Q8D4×C10112yes—
515#121D4×C10112yes—
516#120—21no—
517C4×D4—22no—
518#117C23×C10111yescharacteristic
519#108—22no—
520#108—22no—
521C4⋊C8—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#101—22no—
527#101—22no—
528#101—22no—
529#101—41no—
530#101—41no—
531#101—41no—
532#100—22no—
533#100—41no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538#97—21no—
539C4×C8—21no—
540C24—21no—
541C24#41×C10111yescharacteristic
542#41—28no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C10112yes—
573C2×Q8C2×D4×C10112yes—
574C2×Q8C2×D4×C10112yes—
575C2×Q8C2×D4×C10111yescharacteristic
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×D4×C10112yes—
587C2×D4C2×D4×C10111yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C10112yes—
603C22×C4C2×D4×C10112yes—
604C22×C4#41×C10111yescharacteristic
605C22×C4C24×C10111yescharacteristic
606Q16—28no—
607Q16—24no—
608Q16—24no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612SD16—28no—
613SD16—24no—
614SD16—24no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619D8—42no—
620M16—24no—
621M16—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C2×C8C2×D4×C10112yes—
645C2×C8C2×D4×C10111yescharacteristic
646C2×C8C2×D4×C10111yescharacteristic
647C2×C8C2×D4×C10112yes—
648C2×C8C2×D4×C10112yes—
649C4⋊C4—22no—
650C4⋊C4C2×D4×C10112yes—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C42—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23#121×C10112yes—
664C23C2×#41×C10111yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#121×C10112yes—
712C2×C4C22×D4×C10111yescharacteristic
713C2×C4C22×D4×C10111yescharacteristic
714C2×C4C22×D4×C10111yescharacteristic
715C2×C4C22×D4×C10111yescharacteristic
716C2×C4H(5,𝔽2)×C10111yescharacteristic
717C2×C4H(5,𝔽2)×C10111yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8#120×C10112yes—
726C8#120×C10112yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×#121×C10111yescharacteristic
740C22#546×C10111yescharacteristic
741C22#546×C10111yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—41no—
747C4—42no—
748C4C2×#120×C10111yescharacteristic
749C4#535×C10111yescharacteristic
750C4D42×C10111yescharacteristic
751C4D42×C10111yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2C101×#240811yescharacteristic
758C2C101×#306912yes—
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3005C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C101C2semidirect
2. C2×#473×C101C2semidirect
3. C2×#471×C101C2semidirect
5. C101×#3004C2semidirect
6. C101×#2930C2semidirect
7. C101×#2047C2semidirect
8. C101×#2046C2semidirect
9. C101×#2020C2semidirect
10. C101×#2019C2semidirect
11. C101×#1979C2semidirect
12. C101×#1977C2semidirect
13. C101×#1811C2semidirect
14. C101×#1785C2semidirect
15. C101×#1784C2semidirect
104. C2×Q16×C101D4semidirect
115. C2×SD16×C101D4semidirect
372. #24283C101direct (N × H)
380. C22×#137C2×C101semidirect
381. C2×#473C2×C101semidirect
382. C2×#471C2×C101semidirect
384. #3004C2×C101semidirect
385. #2930C2×C101semidirect
386. #2047C2×C101semidirect
387. #2046C2×C101semidirect
388. #2020C2×C101semidirect
389. #2019C2×C101semidirect
390. #1979C2×C101semidirect
391. #1977C2×C101semidirect
392. #1811C2×C101semidirect
393. #1785C2×C101semidirect
394. #1784C2×C101semidirect
395. C101#24283direct (N × H)
484. C2×Q16D4×C101semidirect
495. C2×SD16D4×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1012
C2×#473×C1012
C2×#471×C1012
C101×#30052
C101×#30042
C101×#29302
C101×#20472
C101×#20462
C101×#20202
C101×#20192
C101×#19792
C101×#19772
C101×#18112
C101×#17852
C101×#17842
#24283101