Finite Group Databasebeta

← C101×#23878 #38806029

Subgroups — C101×#23878 #38806029

Order 25856.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C101C211yesmaximal, characteristic, complemented
2C101×#3488C211yesmaximal, characteristic, complemented
3C2×#455×C101C211yesmaximal, characteristic, complemented
4C2×#453×C101C211yesmaximal, characteristic, complemented
5C101×#3005C211yesmaximal, characteristic, complemented
6C101×#2431C211yesmaximal, characteristic, complemented
7C101×#2007C211yesmaximal, characteristic, complemented
8C101×#2006C211yesmaximal, characteristic, complemented
9C101×#2004C211yesmaximal, characteristic, complemented
10C101×#2002C211yesmaximal, characteristic, complemented
11C101×#1900C211yesmaximal, characteristic, complemented
12C101×#1883C211yesmaximal, characteristic, complemented
13C101×#1882C211yesmaximal, characteristic, complemented
14C101×#1871C211yesmaximal, characteristic, complemented
15C101×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×#41×C101C2211yescharacteristic, complemented
19#575×C101—24no—
20#575×C101—24no—
21C2×#137×C101—21no—
22C2×#137×C101C2211yescharacteristic
23C2×#137×C101C2211yescharacteristic, complemented
24C2×#137×C101C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C101—21no—
26C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
29C2×#135×C101—21no—
30C2×#135×C101—21no—
31C22×M16×C101C2211yescharacteristic, complemented
32#550×C101—21no—
33#548×C101—21no—
34#546×C101—21no—
35#546×C101—22no—
36D42×C101—22no—
37D42×C101—21no—
38#537×C101—21no—
39#537×C101C2211yescharacteristic
40#535×C101—21no—
41#535×C101C2211yescharacteristic
42C2×#127×C101C2211yescharacteristic, complemented
43C2×#124×C101C2211yescharacteristic, complemented
44#525×C101—21no—
45#525×C101C2211yescharacteristic
46C2×#121×C101—21no—
47C2×#121×C101C2211yescharacteristic
48#520×C101C2211yescharacteristic
49#455×C101—24no—
50#453×C101—24no—
51#452×C101—21no—
52#452×C101—21no—
53#449×C101—21no—
54#449×C101—21no—
55C2×#104×C101C2211yescharacteristic
56C2×#104×C101C2211yescharacteristic
57C2×#104×C101C2211yescharacteristic, complemented
58C2×#104×C101C2211yescharacteristic, complemented
59C2×#104×C101C2211yescharacteristic, complemented
60C2×#104×C101C2211yescharacteristic, complemented
61#419×C101C2211yescharacteristic, complemented
62#418×C101C2211yescharacteristic, complemented
63C2×#100×C101C2211yescharacteristic, complemented
64C2×#100×C101C2211yescharacteristic, complemented
65#407×C101C2211yescharacteristic, complemented
66#392×C101—22no—
67#391×C101C2211yescharacteristic, complemented
68#390×C101C2211yescharacteristic, complemented
69#386×C101—22no—
70C4×C22⋊C4×C101C2211yescharacteristic, complemented
71#343×C101C2211yescharacteristic, complemented
72#343×C101C2211yescharacteristic, complemented
73#339×C101C2211yescharacteristic, complemented
74#339×C101C2211yescharacteristic, complemented
75H(5,𝔽2)×C101—22no—
76H(5,𝔽2)×C101—22no—
77H(5,𝔽2)×C101—41no—
78H(5,𝔽2)×C101—41no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—21no—
83C2×#41×C101—22no—
84C2×#41×C101—22no—
85C2×#41×C101—22no—
86C2×#41×C101—22no—
87C2×#41×C101—21no—
88C2×#41×C101—21no—
89C2×#41×C101—21no—
90C2×#41×C101—21no—
91C2×#41×C101—41no—
92C2×#41×C101—41no—
93C2×#41×C101—41no—
94C2×#41×C101—41no—
95C2×#41×C101D411yescharacteristic, complemented
96C2×#41×C101D411yescharacteristic, complemented
97C2×#41×C101C2311yescharacteristic
98C2×#41×C101C2311yescharacteristic
99C2×#41×C101C2311yescharacteristic
100C22×Q8×C101D411yescharacteristic, complemented
101C22×Q8×C101C2311yescharacteristic
102C22×D4×C101—21no—
103C22×D4×C101—22no—
104C22×D4×C101—22no—
105C22×D4×C101—21no—
106C22×D4×C101—21no—
107C22×D4×C101—21no—
108C22×D4×C101—22no—
109C22×D4×C101D412yes—
110C22×D4×C101D411yescharacteristic, complemented
111C22×D4×C101C2311yescharacteristic
112C22×D4×C101C2311yescharacteristic
113C23×C4×C101—21no—
114C23×C4×C101—21no—
115C23×C4×C101C2311yescharacteristic
116#137×C101—28no—
117#137×C101—22no—
118#137×C101—22no—
119#137×C101—22no—
120#137×C101—22no—
121#137×C101—41no—
122#137×C101D414yescomplemented
123AGL(1,ℤ/8)×C101—28no—
124AGL(1,ℤ/8)×C101—22no—
125AGL(1,ℤ/8)×C101—22no—
126AGL(1,ℤ/8)×C101—22no—
127AGL(1,ℤ/8)×C101—22no—
128AGL(1,ℤ/8)×C101—41no—
129AGL(1,ℤ/8)×C101D414yescomplemented
130#135×C101—28no—
131#135×C101—28no—
132C2×Q16×C101—21no—
133C2×Q16×C101—21no—
134C2×Q16×C101—21no—
135C2×SD16×C101—21no—
136C2×SD16×C101—21no—
137C2×SD16×C101—21no—
138C2×SD16×C101—21no—
139C2×SD16×C101—21no—
140C2×SD16×C101—21no—
141C2×D8×C101—21no—
142C2×D8×C101—21no—
143C2×D8×C101—21no—
144C2×M16×C101—21no—
145C2×M16×C101—22no—
146C2×M16×C101—22no—
147C2×M16×C101C2311yescharacteristic
148C2×M16×C101C2311yescharacteristic
149C2×M16×C101C2311yescharacteristic
150C2×M16×C101C2311yescharacteristic
151C22×C8×C101—21no—
152#127×C101—22no—
153#127×C101—21no—
154#127×C101—22no—
155#127×C101—41no—
156#124×C101—22no—
157#124×C101—21no—
158#124×C101—22no—
159#124×C101—41no—
160#123×C101—22no—
161#123×C101—21no—
162C22⋊Q8×C101—22no—
163C22⋊Q8×C101—21no—
164C22⋊Q8×C101—21no—
165C22⋊Q8×C101D411yescharacteristic, complemented
166C22⋊Q8×C101D411yescharacteristic, complemented
167#121×C101—22no—
168#121×C101—22no—
169#121×C101—22no—
170#121×C101—22no—
171#121×C101—22no—
172#121×C101—21no—
173#121×C101—21no—
174#121×C101—21no—
175#121×C101—21no—
176#121×C101—21no—
177#121×C101—21no—
178#121×C101—22no—
179#121×C101—21no—
180#121×C101—21no—
181#121×C101D411yescharacteristic, complemented
182#121×C101D411yescharacteristic, complemented
183#120×C101—22no—
184#120×C101—22no—
185#120×C101—22no—
186#120×C101—21no—
187#120×C101—22no—
188C4×Q8×C101—21no—
189C4×D4×C101—22no—
190C4×D4×C101—22no—
191C4×D4×C101—21no—
192C4×D4×C101—22no—
193C4×D4×C101—21no—
194C4×D4×C101—21no—
195#117×C101—21no—
196#117×C101C2311yescharacteristic
197C2×C4⋊C4×C101—21no—
198C2×C4⋊C4×C101C2311yescharacteristic
199C2×C22⋊C4×C101—22no—
200C2×C22⋊C4×C101—22no—
201C2×C22⋊C4×C101—21no—
202C2×C22⋊C4×C101—22no—
203C2×C22⋊C4×C101D412yes—
204C2×C42×C101C2311yescharacteristic
205C2×C42×C101C2311yescharacteristic
206#104×C101—22no—
207#104×C101—22no—
208#104×C101—22no—
209#104×C101—22no—
210#104×C101—41no—
211#104×C101—41no—
212#103×C101—21no—
213#103×C101—21no—
214#102×C101—21no—
215#102×C101—21no—
216#100×C101—22no—
217#100×C101—22no—
218C22⋊C8×C101—21no—
219C22⋊C8×C101—21no—
220#95×C101—21no—
221#95×C101—22no—
222C24×C101—22no—
223C24×C101—21no—
224C24×C101—21no—
225C24×C101C2×D412yes—
226C24×C101C2×D411yescharacteristic
227#41×C101—21no—
228#41×C101—21no—
229#41×C101—24no—
230#41×C101—24no—
231#41×C101—22no—
232#41×C101—22no—
233#41×C101—21no—
234#41×C101—21no—
235#41×C101—21no—
236#41×C101—21no—
237#41×C101—21no—
238#41×C101—21no—
239#41×C101—21no—
240#41×C101—21no—
241#41×C101—42no—
242#41×C101—42no—
243#41×C101—41no—
244#41×C101—41no—
245#41×C101—42no—
246#41×C101—42no—
247#41×C101—42no—
248#41×C101—42no—
249#41×C101—42no—
250#41×C101—42no—
251#41×C101—42no—
252#41×C101—42no—
253#41×C101—42no—
254#41×C101—42no—
255#41×C101—42no—
256#41×C101—42no—
257#41×C101C2×D412yes—
258#41×C101C2×D412yes—
259C2×Q8×C101—21no—
260C2×Q8×C101—21no—
261C2×Q8×C101—22no—
262C2×Q8×C101—21no—
263C2×Q8×C101—21no—
264C2×Q8×C101—21no—
265C2×Q8×C101—21no—
266C2×Q8×C101—41no—
267C2×Q8×C101C2×D411yescharacteristic
268C2×Q8×C101C2×D411yescharacteristic
269C2×Q8×C101C2×D411yescharacteristic
270C2×Q8×C101C2×D412yescomplemented
271C2×D4×C101—21no—
272C2×D4×C101—22no—
273C2×D4×C101—22no—
274C2×D4×C101—22no—
275C2×D4×C101—22no—
276C2×D4×C101—21no—
277C2×D4×C101—21no—
278C2×D4×C101—21no—
279C2×D4×C101—21no—
280C2×D4×C101—21no—
281C2×D4×C101—22no—
282C2×D4×C101—22no—
283C2×D4×C101—22no—
284C2×D4×C101—21no—
285C2×D4×C101—22no—
286C2×D4×C101—21no—
287C2×D4×C101—21no—
288C2×D4×C101—21no—
289C2×D4×C101—21no—
290C2×D4×C101—21no—
291C2×D4×C101—21no—
292C2×D4×C101—21no—
293C2×D4×C101—21no—
294C2×D4×C101—21no—
295C2×D4×C101—21no—
296C2×D4×C101—21no—
297C2×D4×C101—21no—
298C2×D4×C101—41no—
299C2×D4×C101—42no—
300C2×D4×C101—42no—
301C2×D4×C101—42no—
302C2×D4×C101—44no—
303C2×D4×C101—42no—
304C2×D4×C101—42no—
305C2×D4×C101—44no—
306C2×D4×C101—44no—
307C2×D4×C101—42no—
308C2×D4×C101—42no—
309C2×D4×C101—41no—
310C2×D4×C101—41no—
311C2×D4×C101—42no—
312C2×D4×C101—44no—
313C2×D4×C101—82no—
314C2×D4×C101—82no—
315C2×D4×C101—84no—
316C2×D4×C101C2×D411yescharacteristic
317C2×D4×C101C2×D411yescharacteristic
318C2×D4×C101C2×D411yescharacteristic
319C2×D4×C101C2×D412yescomplemented
320C22×C4×C101—21no—
321C22×C4×C101—21no—
322C22×C4×C101—21no—
323C22×C4×C101—21no—
324C22×C4×C101—21no—
325C22×C4×C101—22no—
326C22×C4×C101—21no—
327C22×C4×C101—21no—
328C22×C4×C101—21no—
329C22×C4×C101—22no—
330C22×C4×C101—21no—
331C22×C4×C101—21no—
332C22×C4×C101—21no—
333C22×C4×C101—21no—
334C22×C4×C101—21no—
335C22×C4×C101—42no—
336C22×C4×C101—42no—
337C22×C4×C101—42no—
338C22×C4×C101—42no—
339C22×C4×C101—41no—
340C22×C4×C101—41no—
341C22×C4×C101C2×D411yescharacteristic
342C22×C4×C101C2×D411yescharacteristic
343C22×C4×C101C2×D411yescharacteristic
344C22×C4×C101C2×D411yescharacteristic
345C22×C4×C101C2×D411yescharacteristic
346C22×C4×C101C2×D412yes—
347C22×C4×C101C2411yescharacteristic
348Q16×C101—24no—
349Q16×C101—24no—
350Q16×C101—42no—
351SD16×C101—24no—
352SD16×C101—24no—
353SD16×C101—24no—
354SD16×C101—24no—
355SD16×C101—42no—
356SD16×C101—42no—
357D8×C101—24no—
358D8×C101—24no—
359D8×C101—42no—
360M16×C101—24no—
361M16×C101—21no—
362M16×C101—21no—
363M16×C101—21no—
364M16×C101—21no—
365M16×C101—21no—
366M16×C101—21no—
367M16×C101C2×D412yescomplemented
368M16×C101C2×D412yescomplemented
369C2×C8×C101—24no—
370C2×C8×C101—21no—
371C2×C8×C101—21no—
372C2×C8×C101—21no—
373C2×C8×C101—21no—
374C4⋊C4×C101—22no—
375C4⋊C4×C101—22no—
376C4⋊C4×C101—21no—
377C4⋊C4×C101—21no—
378C4⋊C4×C101—21no—
379C4⋊C4×C101—21no—
380C4⋊C4×C101C2×D411yescharacteristic
381C4⋊C4×C101C2×D411yescharacteristic
382C22⋊C4×C101—22no—
383C22⋊C4×C101—22no—
384C22⋊C4×C101—22no—
385C22⋊C4×C101—22no—
386C22⋊C4×C101—22no—
387C22⋊C4×C101—21no—
388C22⋊C4×C101—21no—
389C22⋊C4×C101—21no—
390C22⋊C4×C101—21no—
391C22⋊C4×C101—22no—
392C22⋊C4×C101—22no—
393C22⋊C4×C101—21no—
394C22⋊C4×C101—44no—
395C22⋊C4×C101—42no—
396C22⋊C4×C101—82no—
397C42×C101—22no—
398C42×C101—21no—
399C42×C101—21no—
400C42×C101—21no—
401C42×C101—21no—
402C42×C101—21no—
403C23×C101—21no—
404C23×C101—21no—
405C23×C101—21no—
406C23×C101—22no—
407C23×C101—21no—
408C23×C101—21no—
409C23×C101—22no—
410C23×C101—22no—
411C23×C101—22no—
412C23×C101—41no—
413C23×C101—41no—
414C23×C101—42no—
415C23×C101—42no—
416C23×C101—42no—
417C23×C101—42no—
418C23×C101—44no—
419C23×C101—42no—
420C23×C101—42no—
421C23×C101—41no—
422C23×C101—41no—
423C23×C101—81no—
424C23×C101—82no—
425C23×C101—82no—
426C23×C101#12011yescharacteristic
427C23×C101#12011yescharacteristic
428C23×C101C22×D411yescharacteristic
429Q8×C101—21no—
430Q8×C101—21no—
431Q8×C101—22no—
432Q8×C101—21no—
433Q8×C101—21no—
434Q8×C101—22no—
435Q8×C101—21no—
436Q8×C101—42no—
437Q8×C101—41no—
438Q8×C101—41no—
439Q8×C101#12012yes—
440D4×C101—22no—
441D4×C101—22no—
442D4×C101—21no—
443D4×C101—22no—
444D4×C101—21no—
445D4×C101—21no—
446D4×C101—21no—
447D4×C101—22no—
448D4×C101—21no—
449D4×C101—42no—
450D4×C101—42no—
451D4×C101—44no—
452D4×C101—42no—
453D4×C101—44no—
454D4×C101—44no—
455D4×C101—42no—
456D4×C101—44no—
457D4×C101—44no—
458D4×C101—41no—
459D4×C101—41no—
460D4×C101—41no—
461D4×C101—41no—
462D4×C101—41no—
463D4×C101—41no—
464D4×C101—41no—
465D4×C101—41no—
466D4×C101—41no—
467D4×C101—41no—
468D4×C101—81no—
469D4×C101—82no—
470D4×C101—82no—
471D4×C101—82no—
472D4×C101—82no—
473D4×C101—88no—
474D4×C101#12012yes—
475C2×C4×C101—21no—
476C2×C4×C101—21no—
477C2×C4×C101—21no—
478C2×C4×C101—21no—
479C2×C4×C101—21no—
480C2×C4×C101—21no—
481C2×C4×C101—21no—
482C2×C4×C101—21no—
483C2×C4×C101—21no—
484C2×C4×C101—21no—
485C2×C4×C101—21no—
486C2×C4×C101—22no—
487C2×C4×C101—22no—
488C2×C4×C101—22no—
489C2×C4×C101—21no—
490C2×C4×C101—22no—
491C2×C4×C101—21no—
492C2×C4×C101—21no—
493C2×C4×C101—21no—
494C2×C4×C101—22no—
495C2×C4×C101—42no—
496C2×C4×C101—42no—
497C2×C4×C101—42no—
498C2×C4×C101—44no—
499C2×C4×C101—44no—
500C2×C4×C101—44no—
501C2×C4×C101—41no—
502C2×C4×C101—41no—
503C2×C4×C101—41no—
504C2×C4×C101—41no—
505C2×C4×C101—41no—
506C2×C4×C101—41no—
507C2×C4×C101—41no—
508C2×C4×C101—41no—
509C2×C4×C101—42no—
510C2×C4×C101—41no—
511C2×C4×C101—41no—
512C2×C4×C101—41no—
513C2×C4×C101—82no—
514C2×C4×C101#12011yescharacteristic
515C2×C4×C101#12011yescharacteristic
516C2×C4×C101C22×D411yescharacteristic
517C2×C4×C101C22×D411yescharacteristic
518C2×C4×C101C22×D411yescharacteristic
519C2×C4×C101C22×D411yescharacteristic
520C2×C4×C101H(5,𝔽2)11yescharacteristic
521C2×C4×C101H(5,𝔽2)11yescharacteristic
522C8×C101—22no—
523C8×C101—22no—
524C8×C101—41no—
525C8×C101—41no—
526C22×C101—21no—
527C22×C101—21no—
528C22×C101—21no—
529C22×C101—21no—
530C22×C101—22no—
531C22×C101—21no—
532C22×C101—21no—
533C22×C101—21no—
534C22×C101—21no—
535C22×C101—44no—
536C22×C101—41no—
537C22×C101—41no—
538C22×C101—41no—
539C22×C101—42no—
540C22×C101—41no—
541C22×C101—42no—
542C22×C101—41no—
543C22×C101—42no—
544C22×C101—41no—
545C22×C101—42no—
546C22×C101—41no—
547C22×C101—41no—
548C22×C101—81no—
549C22×C101—81no—
550C22×C101—82no—
551C22×C101—82no—
552C22×C101—82no—
553C22×C101—84no—
554C22×C101—81no—
555C22×C101—81no—
556C22×C101—164no—
557C22×C101C2×#12011yescharacteristic
558C22×C101D4211yescharacteristic
559C22×C101D4211yescharacteristic
560C4×C101—21no—
561C4×C101—21no—
562C4×C101—22no—
563C4×C101—42no—
564C4×C101—41no—
565C4×C101—41no—
566C4×C101—42no—
567C4×C101—41no—
568C4×C101—42no—
569C4×C101—41no—
570C4×C101—81no—
571C4×C101C2×#12011yescharacteristic
572C4×C101#53411yescharacteristic
573C4×C101D4211yescharacteristic
574C4×C101D4211yescharacteristic
575#23878C10111yesmaximal, characteristic, direct product factor, Sylow
576C2×C101—21no—
577C2×C101—21no—
578C2×C101—41no—
579C2×C101—41no—
580C2×C101—42no—
581C2×C101—82no—
582C2×C101—81no—
583C2×C101—82no—
584C2×C101—81no—
585C2×C101#240311yescharacteristic
586C2×C101#301811yescharacteristic
587C2×C101#301911yescharacteristic
588C2×#575C2×C10111yescharacteristic, complemented
589#3488C2×C10111yescharacteristic, complemented
590C2×#455C2×C10111yescharacteristic, complemented
591C2×#453C2×C10111yescharacteristic, complemented
592#3005C2×C10111yescharacteristic, complemented
593#2431C2×C10111yescharacteristic, complemented
594#2007C2×C10111yescharacteristic, complemented
595#2006C2×C10111yescharacteristic, complemented
596#2004C2×C10111yescharacteristic, complemented
597#2002C2×C10111yescharacteristic, complemented
598#1900C2×C10111yescharacteristic, complemented
599#1883C2×C10111yescharacteristic, complemented
600#1882C2×C10111yescharacteristic, complemented
601#1871C2×C10111yescharacteristic, complemented
602#1789C2×C10111yescharacteristic, complemented
603C101#2387811yescharacteristic, direct product factor, Sylow
604C2×H(5,𝔽2)C22×C10111yescharacteristic
605C22×#41C22×C10111yescharacteristic
606C22×#41C22×C10111yescharacteristic, complemented
607#575—24no—
608#575—24no—
609C2×#137—21no—
610C2×#137C22×C10111yescharacteristic
611C2×#137C22×C10111yescharacteristic, complemented
612C2×#137C22×C10111yescharacteristic, complemented
613C2×AGL(1,ℤ/8)—21no—
614C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
615C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
616C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
617C2×#135—21no—
618C2×#135—21no—
619C22×M16C22×C10111yescharacteristic, complemented
620#550—21no—
621#548—21no—
622#546—21no—
623#546—22no—
624D42—22no—
625D42—21no—
626#537—21no—
627#537C22×C10111yescharacteristic
628#535—21no—
629#535C22×C10111yescharacteristic
630C2×#127C22×C10111yescharacteristic, complemented
631C2×#124C22×C10111yescharacteristic, complemented
632#525—21no—
633#525C22×C10111yescharacteristic
634C2×#121—21no—
635C2×#121C22×C10111yescharacteristic
636#520C22×C10111yescharacteristic
637#455—24no—
638#453—24no—
639#452—21no—
640#452—21no—
641#449—21no—
642#449—21no—
643C2×#104C22×C10111yescharacteristic
644C2×#104C22×C10111yescharacteristic
645C2×#104C22×C10111yescharacteristic, complemented
646C2×#104C22×C10111yescharacteristic, complemented
647C2×#104C22×C10111yescharacteristic, complemented
648C2×#104C22×C10111yescharacteristic, complemented
649#419C22×C10111yescharacteristic, complemented
650#418C22×C10111yescharacteristic, complemented
651C2×#100C22×C10111yescharacteristic, complemented
652C2×#100C22×C10111yescharacteristic, complemented
653#407C22×C10111yescharacteristic, complemented
654#392—22no—
655#391C22×C10111yescharacteristic, complemented
656#390C22×C10111yescharacteristic, complemented
657#386—22no—
658C4×C22⋊C4C22×C10111yescharacteristic, complemented
659#343C22×C10111yescharacteristic, complemented
660#343C22×C10111yescharacteristic, complemented
661#339C22×C10111yescharacteristic, complemented
662#339C22×C10111yescharacteristic, complemented
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C10111yescharacteristic, complemented
684C2×#41D4×C10111yescharacteristic, complemented
685C2×#41C23×C10111yescharacteristic
686C2×#41C23×C10111yescharacteristic
687C2×#41C23×C10111yescharacteristic
688C22×Q8D4×C10111yescharacteristic, complemented
689C22×Q8C23×C10111yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C10112yes—
698C22×D4D4×C10111yescharacteristic, complemented
699C22×D4C23×C10111yescharacteristic
700C22×D4C23×C10111yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C10111yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C10114yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C10114yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C10111yescharacteristic
736C2×M16C23×C10111yescharacteristic
737C2×M16C23×C10111yescharacteristic
738C2×M16C23×C10111yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C10111yescharacteristic, complemented
754C22⋊Q8D4×C10111yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C10111yescharacteristic, complemented
770#121D4×C10111yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C10111yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C10111yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C10112yes—
792C2×C42C23×C10111yescharacteristic
793C2×C42C23×C10111yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C10112yes—
814C24C2×D4×C10111yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C10112yes—
846#41C2×D4×C10112yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C10111yescharacteristic
856C2×Q8C2×D4×C10111yescharacteristic
857C2×Q8C2×D4×C10111yescharacteristic
858C2×Q8C2×D4×C10112yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C10111yescharacteristic
905C2×D4C2×D4×C10111yescharacteristic
906C2×D4C2×D4×C10111yescharacteristic
907C2×D4C2×D4×C10112yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C10111yescharacteristic
930C22×C4C2×D4×C10111yescharacteristic
931C22×C4C2×D4×C10111yescharacteristic
932C22×C4C2×D4×C10111yescharacteristic
933C22×C4C2×D4×C10111yescharacteristic
934C22×C4C2×D4×C10112yes—
935C22×C4C24×C10111yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C10112yescomplemented
956M16C2×D4×C10112yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C10111yescharacteristic
969C4⋊C4C2×D4×C10111yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C10111yescharacteristic
1015C23#120×C10111yescharacteristic
1016C23C22×D4×C10111yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C10112yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C10112yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C10111yescharacteristic
1103C2×C4#120×C10111yescharacteristic
1104C2×C4C22×D4×C10111yescharacteristic
1105C2×C4C22×D4×C10111yescharacteristic
1106C2×C4C22×D4×C10111yescharacteristic
1107C2×C4C22×D4×C10111yescharacteristic
1108C2×C4H(5,𝔽2)×C10111yescharacteristic
1109C2×C4H(5,𝔽2)×C10111yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C10111yescharacteristic
1146C22D42×C10111yescharacteristic
1147C22D42×C10111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×#120×C10111yescharacteristic
1160C4#534×C10111yescharacteristic
1161C4D42×C10111yescharacteristic
1162C4D42×C10111yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C101×#240311yescharacteristic
1173C2C101×#301811yescharacteristic
1174C2C101×#301911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
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. C2×#575×C101C2semidirect
2. C101×#3488C2semidirect
3. C2×#455×C101C2semidirect
4. C2×#453×C101C2semidirect
5. C101×#3005C2semidirect
6. C101×#2431C2semidirect
7. C101×#2007C2semidirect
8. C101×#2006C2semidirect
9. C101×#2004C2semidirect
10. C101×#2002C2semidirect
11. C101×#1900C2semidirect
12. C101×#1883C2semidirect
13. C101×#1882C2semidirect
14. C101×#1871C2semidirect
15. C101×#1789C2semidirect
18. C22×#41×C101C22semidirect
23. C2×#137×C101C22semidirect
24. C2×#137×C101C22semidirect
27. C2×AGL(1,ℤ/8)×C101C22semidirect
28. C2×AGL(1,ℤ/8)×C101C22semidirect
31. C22×M16×C101C22semidirect
42. C2×#127×C101C22semidirect
43. C2×#124×C101C22semidirect
57. C2×#104×C101C22semidirect
58. C2×#104×C101C22semidirect
59. C2×#104×C101C22semidirect
60. C2×#104×C101C22semidirect
61. #419×C101C22semidirect
62. #418×C101C22semidirect
63. C2×#100×C101C22semidirect
64. C2×#100×C101C22semidirect
65. #407×C101C22semidirect
67. #391×C101C22semidirect
68. #390×C101C22semidirect
70. C4×C22⋊C4×C101C22semidirect
71. #343×C101C22semidirect
72. #343×C101C22semidirect
73. #339×C101C22semidirect
74. #339×C101C22semidirect
95. C2×#41×C101D4semidirect
96. C2×#41×C101D4semidirect
100. C22×Q8×C101D4semidirect
110. C22×D4×C101D4semidirect
122. #137×C101D4semidirect
129. AGL(1,ℤ/8)×C101D4semidirect
165. C22⋊Q8×C101D4semidirect
166. C22⋊Q8×C101D4semidirect
181. #121×C101D4semidirect
182. #121×C101D4semidirect
270. C2×Q8×C101C2×D4semidirect
319. C2×D4×C101C2×D4semidirect
367. M16×C101C2×D4semidirect
368. M16×C101C2×D4semidirect
575. #23878C101direct (N × H)
588. C2×#575C2×C101semidirect
589. #3488C2×C101semidirect
590. C2×#455C2×C101semidirect
591. C2×#453C2×C101semidirect
592. #3005C2×C101semidirect
593. #2431C2×C101semidirect
594. #2007C2×C101semidirect
595. #2006C2×C101semidirect
596. #2004C2×C101semidirect
597. #2002C2×C101semidirect
598. #1900C2×C101semidirect
599. #1883C2×C101semidirect
600. #1882C2×C101semidirect
601. #1871C2×C101semidirect
602. #1789C2×C101semidirect
603. C101#23878direct (N × H)
606. C22×#41C22×C101semidirect
611. C2×#137C22×C101semidirect
612. C2×#137C22×C101semidirect
615. C2×AGL(1,ℤ/8)C22×C101semidirect
616. C2×AGL(1,ℤ/8)C22×C101semidirect
619. C22×M16C22×C101semidirect
630. C2×#127C22×C101semidirect
631. C2×#124C22×C101semidirect
645. C2×#104C22×C101semidirect
646. C2×#104C22×C101semidirect
647. C2×#104C22×C101semidirect
648. C2×#104C22×C101semidirect
649. #419C22×C101semidirect
650. #418C22×C101semidirect
651. C2×#100C22×C101semidirect
652. C2×#100C22×C101semidirect
653. #407C22×C101semidirect
655. #391C22×C101semidirect
656. #390C22×C101semidirect
658. C4×C22⋊C4C22×C101semidirect
659. #343C22×C101semidirect
660. #343C22×C101semidirect
661. #339C22×C101semidirect
662. #339C22×C101semidirect
683. C2×#41D4×C101semidirect
684. C2×#41D4×C101semidirect
688. C22×Q8D4×C101semidirect
698. C22×D4D4×C101semidirect
710. #137D4×C101semidirect
717. AGL(1,ℤ/8)D4×C101semidirect
753. C22⋊Q8D4×C101semidirect
754. C22⋊Q8D4×C101semidirect
769. #121D4×C101semidirect
770. #121D4×C101semidirect
858. C2×Q8C2×D4×C101semidirect
907. C2×D4C2×D4×C101semidirect
955. M16C2×D4×C101semidirect
956. M16C2×D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1012
C101×#34882
C2×#455×C1012
C2×#453×C1012
C101×#30052
C101×#24312
C101×#20072
C101×#20062
C101×#20042
C101×#20022
C101×#19002
C101×#18832
C101×#18822
C101×#18712
C101×#17892
#23878101