Finite Group Databasebeta

← C101×#23881 #38806032

Subgroups — C101×#23881 #38806032

Order 25856.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C101C211yesmaximal, characteristic, complemented
2C101×#3489C211yesmaximal, characteristic, complemented
3C2×#456×C101C211yesmaximal, characteristic, complemented
4C2×#454×C101C211yesmaximal, characteristic, complemented
5C101×#3005C211yesmaximal, characteristic, complemented
6C101×#2432C211yesmaximal, characteristic, complemented
7C101×#2007C211yesmaximal, characteristic, complemented
8C101×#2006C211yesmaximal, characteristic, complemented
9C101×#2005C211yesmaximal, characteristic, complemented
10C101×#2003C211yesmaximal, characteristic, complemented
11C101×#1901C211yesmaximal, characteristic, complemented
12C101×#1883C211yesmaximal, characteristic, complemented
13C101×#1882C211yesmaximal, characteristic, complemented
14C101×#1871C211yesmaximal, characteristic, complemented
15C101×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×#41×C101C2211yescharacteristic
19#575×C101—24no—
20#575×C101—24no—
21C2×#137×C101—21no—
22C2×#137×C101C2211yescharacteristic
23C2×#137×C101C2211yescharacteristic
24C2×#137×C101C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C101—21no—
26C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C101C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
29C2×#135×C101—21no—
30C2×#135×C101—21no—
31C22×M16×C101C2211yescharacteristic
32D4×Q8×C101—21no—
33#548×C101—21no—
34#547×C101—21no—
35#547×C101—22no—
36#546×C101—21no—
37#546×C101—22no—
38#537×C101—21no—
39#537×C101C2211yescharacteristic
40#536×C101—21no—
41#536×C101C2211yescharacteristic
42C2×C4⋊Q8×C101C2211yescharacteristic, complemented
43C2×#124×C101C2211yescharacteristic, complemented
44#525×C101—21no—
45#525×C101C2211yescharacteristic
46C2×C22⋊Q8×C101—21no—
47C2×C22⋊Q8×C101C2211yescharacteristic
48#520×C101C2211yescharacteristic
49#456×C101—24no—
50#454×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
58C2×#104×C101C2211yescharacteristic
59C2×#104×C101C2211yescharacteristic, complemented
60C2×#104×C101C2211yescharacteristic, complemented
61#419×C101C2211yescharacteristic, complemented
62#418×C101C2211yescharacteristic, complemented
63C2×#101×C101C2211yescharacteristic, complemented
64C2×#101×C101C2211yescharacteristic, complemented
65#407×C101C2211yescharacteristic
66#394×C101—22no—
67#391×C101C2211yescharacteristic, complemented
68#390×C101C2211yescharacteristic, complemented
69#385×C101—22no—
70C4×C22⋊C4×C101C2211yescharacteristic
71#343×C101C2211yescharacteristic, complemented
72#343×C101C2211yescharacteristic, complemented
73#339×C101C2211yescharacteristic, complemented
74#339×C101C2211yescharacteristic, complemented
752−1+4×C101—22no—
762−1+4×C101—22no—
772−1+4×C101—41no—
782−1+4×C101—41no—
79C2×#41×C101—21no—
80C2×#41×C101—21no—
81C2×#41×C101—21no—
82C2×#41×C101—22no—
83C2×#41×C101—21no—
84C2×#41×C101—22no—
85C2×#41×C101—22no—
86C2×#41×C101—22no—
87C2×#41×C101—22no—
88C2×#41×C101—21no—
89C2×#41×C101—21no—
90C2×#41×C101—21no—
91C2×#41×C101—21no—
92C2×#41×C101—41no—
93C2×#41×C101—41no—
94C2×#41×C101—41no—
95C2×#41×C101—41no—
96C2×#41×C101D411yescharacteristic
97C2×#41×C101D411yescharacteristic
98C2×#41×C101C2311yescharacteristic
99C2×#41×C101C2311yescharacteristic
100C2×#41×C101C2311yescharacteristic
101C22×Q8×C101—21no—
102C22×Q8×C101—21no—
103C22×Q8×C101D411yescharacteristic
104C22×Q8×C101C2311yescharacteristic
105C22×Q8×C101C2311yescharacteristic
106C22×D4×C101—21no—
107C22×D4×C101—21no—
108C22×D4×C101D411yescharacteristic
109C22×D4×C101C2311yescharacteristic
110C23×C4×C101—21no—
111C23×C4×C101—21no—
112C23×C4×C101C2311yescharacteristic
113#137×C101—28no—
114#137×C101—22no—
115#137×C101—22no—
116#137×C101—22no—
117#137×C101—22no—
118#137×C101—41no—
119#137×C101D414yescomplemented
120AGL(1,ℤ/8)×C101—28no—
121AGL(1,ℤ/8)×C101—22no—
122AGL(1,ℤ/8)×C101—22no—
123AGL(1,ℤ/8)×C101—22no—
124AGL(1,ℤ/8)×C101—22no—
125AGL(1,ℤ/8)×C101—41no—
126AGL(1,ℤ/8)×C101D414yescomplemented
127#135×C101—28no—
128#135×C101—28no—
129C2×Q16×C101—21no—
130C2×Q16×C101—21no—
131C2×Q16×C101—21no—
132C2×SD16×C101—21no—
133C2×SD16×C101—21no—
134C2×SD16×C101—21no—
135C2×SD16×C101—21no—
136C2×SD16×C101—21no—
137C2×SD16×C101—21no—
138C2×D8×C101—21no—
139C2×D8×C101—21no—
140C2×D8×C101—21no—
141C2×M16×C101—21no—
142C2×M16×C101—22no—
143C2×M16×C101—22no—
144C2×M16×C101C2311yescharacteristic
145C2×M16×C101C2311yescharacteristic
146C2×M16×C101C2311yescharacteristic
147C2×M16×C101C2311yescharacteristic
148C22×C8×C101—21no—
149C4⋊Q8×C101—22no—
150C4⋊Q8×C101—21no—
151C4⋊Q8×C101—22no—
152C4⋊Q8×C101—41no—
153#124×C101—22no—
154#124×C101—21no—
155#124×C101—22no—
156#124×C101—41no—
157#123×C101—22no—
158#123×C101—22no—
159#123×C101—22no—
160#123×C101—21no—
161#123×C101—22no—
162C22⋊Q8×C101—22no—
163C22⋊Q8×C101—22no—
164C22⋊Q8×C101—22no—
165C22⋊Q8×C101—21no—
166C22⋊Q8×C101—21no—
167C22⋊Q8×C101—21no—
168C22⋊Q8×C101—21no—
169C22⋊Q8×C101—21no—
170C22⋊Q8×C101—21no—
171C22⋊Q8×C101—21no—
172C22⋊Q8×C101—21no—
173C22⋊Q8×C101D411yescharacteristic
174C22⋊Q8×C101D411yescharacteristic
175#121×C101—22no—
176#121×C101—22no—
177#121×C101—22no—
178#121×C101—21no—
179#121×C101—21no—
180#121×C101—22no—
181#121×C101D411yescharacteristic
182#121×C101D411yescharacteristic
183#120×C101—22no—
184#120×C101—21no—
185C4×Q8×C101—21no—
186C4×D4×C101—22no—
187C4×D4×C101—22no—
188C4×D4×C101—21no—
189C4×D4×C101—22no—
190C4×D4×C101—21no—
191C4×D4×C101—21no—
192#117×C101—21no—
193#117×C101C2311yescharacteristic
194C2×C4⋊C4×C101—22no—
195C2×C4⋊C4×C101—21no—
196C2×C4⋊C4×C101—22no—
197C2×C4⋊C4×C101D412yes—
198C2×C4⋊C4×C101C2311yescharacteristic
199C2×C22⋊C4×C101—22no—
200C2×C22⋊C4×C101—21no—
201C2×C22⋊C4×C101—22no—
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#101×C101—22no—
217#101×C101—22no—
218C22⋊C8×C101—21no—
219C22⋊C8×C101—21no—
220#95×C101—21no—
221#95×C101—22no—
222C24×C101—21no—
223C24×C101—21no—
224C24×C101C2×D411yescharacteristic
225#41×C101—21no—
226#41×C101—21no—
227#41×C101—24no—
228#41×C101—24no—
229#41×C101—22no—
230#41×C101—22no—
231#41×C101—21no—
232#41×C101—21no—
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—42no—
240#41×C101—42no—
241#41×C101—41no—
242#41×C101—41no—
243#41×C101—42no—
244#41×C101—42no—
245#41×C101—42no—
246#41×C101—42no—
247#41×C101—42no—
248#41×C101—42no—
249#41×C101—44no—
250#41×C101—44no—
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—22no—
260C2×Q8×C101—21no—
261C2×Q8×C101—21no—
262C2×Q8×C101—21no—
263C2×Q8×C101—21no—
264C2×Q8×C101—21no—
265C2×Q8×C101—21no—
266C2×Q8×C101—21no—
267C2×Q8×C101—21no—
268C2×Q8×C101—22no—
269C2×Q8×C101—21no—
270C2×Q8×C101—21no—
271C2×Q8×C101—21no—
272C2×Q8×C101—21no—
273C2×Q8×C101—41no—
274C2×Q8×C101—42no—
275C2×Q8×C101—42no—
276C2×Q8×C101—42no—
277C2×Q8×C101—42no—
278C2×Q8×C101C2×D411yescharacteristic
279C2×Q8×C101C2×D411yescharacteristic
280C2×Q8×C101C2×D412yes—
281C2×Q8×C101C2×D411yescharacteristic
282C2×D4×C101—21no—
283C2×D4×C101—22no—
284C2×D4×C101—22no—
285C2×D4×C101—21no—
286C2×D4×C101—21no—
287C2×D4×C101—21no—
288C2×D4×C101—21no—
289C2×D4×C101—21no—
290C2×D4×C101—22no—
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—42no—
303C2×D4×C101—41no—
304C2×D4×C101—41no—
305C2×D4×C101C2×D411yescharacteristic
306C2×D4×C101C2×D411yescharacteristic
307C2×D4×C101C2×D412yes—
308C2×D4×C101C2×D411yescharacteristic
309C22×C4×C101—21no—
310C22×C4×C101—21no—
311C22×C4×C101—21no—
312C22×C4×C101—21no—
313C22×C4×C101—21no—
314C22×C4×C101—22no—
315C22×C4×C101—22no—
316C22×C4×C101—21no—
317C22×C4×C101—21no—
318C22×C4×C101—21no—
319C22×C4×C101—22no—
320C22×C4×C101—21no—
321C22×C4×C101—21no—
322C22×C4×C101—21no—
323C22×C4×C101—21no—
324C22×C4×C101—21no—
325C22×C4×C101—42no—
326C22×C4×C101—42no—
327C22×C4×C101—42no—
328C22×C4×C101—42no—
329C22×C4×C101—41no—
330C22×C4×C101—41no—
331C22×C4×C101C2×D412yes—
332C22×C4×C101C2×D411yescharacteristic
333C22×C4×C101C2×D411yescharacteristic
334C22×C4×C101C2×D411yescharacteristic
335C22×C4×C101C2×D411yescharacteristic
336C22×C4×C101C2×D411yescharacteristic
337C22×C4×C101C2×D412yes—
338C22×C4×C101C2411yescharacteristic
339Q16×C101—24no—
340Q16×C101—24no—
341Q16×C101—42no—
342SD16×C101—24no—
343SD16×C101—24no—
344SD16×C101—24no—
345SD16×C101—24no—
346SD16×C101—42no—
347SD16×C101—42no—
348D8×C101—24no—
349D8×C101—24no—
350D8×C101—42no—
351M16×C101—24no—
352M16×C101—21no—
353M16×C101—21no—
354M16×C101—21no—
355M16×C101—21no—
356M16×C101—21no—
357M16×C101—21no—
358M16×C101C2×D412yes—
359M16×C101C2×D412yes—
360C2×C8×C101—24no—
361C2×C8×C101—21no—
362C2×C8×C101—21no—
363C2×C8×C101—21no—
364C2×C8×C101—21no—
365C4⋊C4×C101—22no—
366C4⋊C4×C101—22no—
367C4⋊C4×C101—22no—
368C4⋊C4×C101—22no—
369C4⋊C4×C101—21no—
370C4⋊C4×C101—22no—
371C4⋊C4×C101—22no—
372C4⋊C4×C101—21no—
373C4⋊C4×C101—21no—
374C4⋊C4×C101—21no—
375C4⋊C4×C101—44no—
376C4⋊C4×C101C2×D411yescharacteristic
377C4⋊C4×C101C2×D411yescharacteristic
378C22⋊C4×C101—22no—
379C22⋊C4×C101—22no—
380C22⋊C4×C101—22no—
381C22⋊C4×C101—22no—
382C22⋊C4×C101—22no—
383C22⋊C4×C101—21no—
384C22⋊C4×C101—22no—
385C22⋊C4×C101—22no—
386C22⋊C4×C101—21no—
387C22⋊C4×C101—21no—
388C22⋊C4×C101—21no—
389C22⋊C4×C101—21no—
390C22⋊C4×C101—44no—
391C22⋊C4×C101—44no—
392C22⋊C4×C101—42no—
393C42×C101—22no—
394C42×C101—21no—
395C42×C101—21no—
396C42×C101—21no—
397C42×C101—21no—
398C42×C101—21no—
399C23×C101—21no—
400C23×C101—21no—
401C23×C101—21no—
402C23×C101—21no—
403C23×C101—21no—
404C23×C101—22no—
405C23×C101—41no—
406C23×C101—41no—
407C23×C101—42no—
408C23×C101—42no—
409C23×C101—42no—
410C23×C101—42no—
411C23×C101—41no—
412C23×C101—41no—
413C23×C101—81no—
414C23×C101#12011yescharacteristic
415C23×C101#12011yescharacteristic
416C23×C101C22×D411yescharacteristic
417Q8×C101—21no—
418Q8×C101—21no—
419Q8×C101—22no—
420Q8×C101—21no—
421Q8×C101—21no—
422Q8×C101—22no—
423Q8×C101—21no—
424Q8×C101—42no—
425Q8×C101—44no—
426Q8×C101—41no—
427Q8×C101—41no—
428Q8×C101—41no—
429Q8×C101—41no—
430Q8×C101—41no—
431Q8×C101—41no—
432Q8×C101#12012yes—
433D4×C101—22no—
434D4×C101—22no—
435D4×C101—21no—
436D4×C101—22no—
437D4×C101—21no—
438D4×C101—21no—
439D4×C101—21no—
440D4×C101—22no—
441D4×C101—21no—
442D4×C101—42no—
443D4×C101—42no—
444D4×C101—42no—
445D4×C101—42no—
446D4×C101—44no—
447D4×C101—44no—
448D4×C101—44no—
449D4×C101—41no—
450D4×C101—41no—
451D4×C101—41no—
452D4×C101—41no—
453D4×C101—41no—
454D4×C101—41no—
455D4×C101—81no—
456D4×C101—82no—
457D4×C101#12012yes—
458C2×C4×C101—21no—
459C2×C4×C101—21no—
460C2×C4×C101—21no—
461C2×C4×C101—21no—
462C2×C4×C101—21no—
463C2×C4×C101—21no—
464C2×C4×C101—21no—
465C2×C4×C101—21no—
466C2×C4×C101—21no—
467C2×C4×C101—21no—
468C2×C4×C101—21no—
469C2×C4×C101—22no—
470C2×C4×C101—22no—
471C2×C4×C101—22no—
472C2×C4×C101—21no—
473C2×C4×C101—22no—
474C2×C4×C101—21no—
475C2×C4×C101—21no—
476C2×C4×C101—22no—
477C2×C4×C101—21no—
478C2×C4×C101—22no—
479C2×C4×C101—22no—
480C2×C4×C101—22no—
481C2×C4×C101—42no—
482C2×C4×C101—42no—
483C2×C4×C101—42no—
484C2×C4×C101—44no—
485C2×C4×C101—44no—
486C2×C4×C101—44no—
487C2×C4×C101—41no—
488C2×C4×C101—44no—
489C2×C4×C101—41no—
490C2×C4×C101—41no—
491C2×C4×C101—41no—
492C2×C4×C101—41no—
493C2×C4×C101—41no—
494C2×C4×C101—41no—
495C2×C4×C101—41no—
496C2×C4×C101—42no—
497C2×C4×C101—41no—
498C2×C4×C101—41no—
499C2×C4×C101—41no—
500C2×C4×C101—82no—
501C2×C4×C101#12011yescharacteristic
502C2×C4×C101#12011yescharacteristic
503C2×C4×C101C22×D411yescharacteristic
504C2×C4×C101C22×D411yescharacteristic
505C2×C4×C101C22×D411yescharacteristic
506C2×C4×C101C22×D411yescharacteristic
507C2×C4×C101H(5,𝔽2)11yescharacteristic
508C2×C4×C101H(5,𝔽2)11yescharacteristic
509C8×C101—22no—
510C8×C101—22no—
511C8×C101—41no—
512C8×C101—41no—
513C22×C101—21no—
514C22×C101—21no—
515C22×C101—21no—
516C22×C101—21no—
517C22×C101—22no—
518C22×C101—21no—
519C22×C101—21no—
520C22×C101—21no—
521C22×C101—21no—
522C22×C101—44no—
523C22×C101—41no—
524C22×C101—41no—
525C22×C101—41no—
526C22×C101—41no—
527C22×C101—42no—
528C22×C101—41no—
529C22×C101—41no—
530C22×C101—41no—
531C22×C101—41no—
532C22×C101—81no—
533C22×C101—81no—
534C22×C101—82no—
535C22×C101—84no—
536C22×C101—81no—
537C22×C101—81no—
538C22×C101C2×#12011yescharacteristic
539C22×C101D4211yescharacteristic
540C22×C101D4211yescharacteristic
541C4×C101—21no—
542C4×C101—21no—
543C4×C101—22no—
544C4×C101—42no—
545C4×C101—42no—
546C4×C101—41no—
547C4×C101—42no—
548C4×C101—41no—
549C4×C101—42no—
550C4×C101—41no—
551C4×C101—41no—
552C4×C101—81no—
553C4×C101C2×#12011yescharacteristic
554C4×C101#53411yescharacteristic
555C4×C101D4211yescharacteristic
556C4×C101D4211yescharacteristic
557#23881C10111yesmaximal, characteristic, direct product factor, Sylow
558C2×C101—21no—
559C2×C101—21no—
560C2×C101—41no—
561C2×C101—41no—
562C2×C101—42no—
563C2×C101—81no—
564C2×C101—82no—
565C2×C101—81no—
566C2×C101#240311yescharacteristic
567C2×C101#301811yescharacteristic
568C2×C101#302011yescharacteristic
569C2×#575C2×C10111yescharacteristic, complemented
570#3489C2×C10111yescharacteristic, complemented
571C2×#456C2×C10111yescharacteristic, complemented
572C2×#454C2×C10111yescharacteristic, complemented
573#3005C2×C10111yescharacteristic, complemented
574#2432C2×C10111yescharacteristic, complemented
575#2007C2×C10111yescharacteristic, complemented
576#2006C2×C10111yescharacteristic, complemented
577#2005C2×C10111yescharacteristic, complemented
578#2003C2×C10111yescharacteristic, complemented
579#1901C2×C10111yescharacteristic, complemented
580#1883C2×C10111yescharacteristic, complemented
581#1882C2×C10111yescharacteristic, complemented
582#1871C2×C10111yescharacteristic, complemented
583#1789C2×C10111yescharacteristic, complemented
584C101#2388111yescharacteristic, direct product factor, Sylow
585C2×2−1+4C22×C10111yescharacteristic
586C22×#41C22×C10111yescharacteristic
587C22×#41C22×C10111yescharacteristic
588#575—24no—
589#575—24no—
590C2×#137—21no—
591C2×#137C22×C10111yescharacteristic
592C2×#137C22×C10111yescharacteristic
593C2×#137C22×C10111yescharacteristic, complemented
594C2×AGL(1,ℤ/8)—21no—
595C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
596C2×AGL(1,ℤ/8)C22×C10111yescharacteristic
597C2×AGL(1,ℤ/8)C22×C10111yescharacteristic, complemented
598C2×#135—21no—
599C2×#135—21no—
600C22×M16C22×C10111yescharacteristic
601D4×Q8—21no—
602#548—21no—
603#547—21no—
604#547—22no—
605#546—21no—
606#546—22no—
607#537—21no—
608#537C22×C10111yescharacteristic
609#536—21no—
610#536C22×C10111yescharacteristic
611C2×C4⋊Q8C22×C10111yescharacteristic, complemented
612C2×#124C22×C10111yescharacteristic, complemented
613#525—21no—
614#525C22×C10111yescharacteristic
615C2×C22⋊Q8—21no—
616C2×C22⋊Q8C22×C10111yescharacteristic
617#520C22×C10111yescharacteristic
618#456—24no—
619#454—24no—
620#452—21no—
621#452—21no—
622#449—21no—
623#449—21no—
624C2×#104C22×C10111yescharacteristic
625C2×#104C22×C10111yescharacteristic
626C2×#104C22×C10111yescharacteristic
627C2×#104C22×C10111yescharacteristic
628C2×#104C22×C10111yescharacteristic, complemented
629C2×#104C22×C10111yescharacteristic, complemented
630#419C22×C10111yescharacteristic, complemented
631#418C22×C10111yescharacteristic, complemented
632C2×#101C22×C10111yescharacteristic, complemented
633C2×#101C22×C10111yescharacteristic, complemented
634#407C22×C10111yescharacteristic
635#394—22no—
636#391C22×C10111yescharacteristic, complemented
637#390C22×C10111yescharacteristic, complemented
638#385—22no—
639C4×C22⋊C4C22×C10111yescharacteristic
640#343C22×C10111yescharacteristic, complemented
641#343C22×C10111yescharacteristic, complemented
642#339C22×C10111yescharacteristic, complemented
643#339C22×C10111yescharacteristic, complemented
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C10111yescharacteristic
666C2×#41D4×C10111yescharacteristic
667C2×#41C23×C10111yescharacteristic
668C2×#41C23×C10111yescharacteristic
669C2×#41C23×C10111yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C10111yescharacteristic
673C22×Q8C23×C10111yescharacteristic
674C22×Q8C23×C10111yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C10111yescharacteristic
678C22×D4C23×C10111yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C10111yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C10114yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C10114yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C10111yescharacteristic
714C2×M16C23×C10111yescharacteristic
715C2×M16C23×C10111yescharacteristic
716C2×M16C23×C10111yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C10111yescharacteristic
743C22⋊Q8D4×C10111yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C10111yescharacteristic
751#121D4×C10111yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C10111yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C10112yes—
767C2×C4⋊C4C23×C10111yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C10112yes—
773C2×C42C23×C10111yescharacteristic
774C2×C42C23×C10111yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C10111yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C10112yes—
827#41C2×D4×C10112yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C10111yescharacteristic
848C2×Q8C2×D4×C10111yescharacteristic
849C2×Q8C2×D4×C10112yes—
850C2×Q8C2×D4×C10111yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C10111yescharacteristic
875C2×D4C2×D4×C10111yescharacteristic
876C2×D4C2×D4×C10112yes—
877C2×D4C2×D4×C10111yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C10112yes—
901C22×C4C2×D4×C10111yescharacteristic
902C22×C4C2×D4×C10111yescharacteristic
903C22×C4C2×D4×C10111yescharacteristic
904C22×C4C2×D4×C10111yescharacteristic
905C22×C4C2×D4×C10111yescharacteristic
906C22×C4C2×D4×C10112yes—
907C22×C4C24×C10111yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C10112yes—
928M16C2×D4×C10112yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C10111yescharacteristic
946C4⋊C4C2×D4×C10111yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C10111yescharacteristic
984C23#120×C10111yescharacteristic
985C23C22×D4×C10111yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C10112yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—44no—
1015D4—42no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C10112yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C10111yescharacteristic
1071C2×C4#120×C10111yescharacteristic
1072C2×C4C22×D4×C10111yescharacteristic
1073C2×C4C22×D4×C10111yescharacteristic
1074C2×C4C22×D4×C10111yescharacteristic
1075C2×C4C22×D4×C10111yescharacteristic
1076C2×C4H(5,𝔽2)×C10111yescharacteristic
1077C2×C4H(5,𝔽2)×C10111yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C10111yescharacteristic
1108C22D42×C10111yescharacteristic
1109C22D42×C10111yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—42no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C10111yescharacteristic
1123C4#534×C10111yescharacteristic
1124C4D42×C10111yescharacteristic
1125C4D42×C10111yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C101×#240311yescharacteristic
1135C2C101×#301811yescharacteristic
1136C2C101×#302011yescharacteristic
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×#3489C2semidirect
3. C2×#456×C101C2semidirect
4. C2×#454×C101C2semidirect
5. C101×#3005C2semidirect
6. C101×#2432C2semidirect
7. C101×#2007C2semidirect
8. C101×#2006C2semidirect
9. C101×#2005C2semidirect
10. C101×#2003C2semidirect
11. C101×#1901C2semidirect
12. C101×#1883C2semidirect
13. C101×#1882C2semidirect
14. C101×#1871C2semidirect
15. C101×#1789C2semidirect
24. C2×#137×C101C22semidirect
28. C2×AGL(1,ℤ/8)×C101C22semidirect
42. C2×C4⋊Q8×C101C22semidirect
43. C2×#124×C101C22semidirect
59. C2×#104×C101C22semidirect
60. C2×#104×C101C22semidirect
61. #419×C101C22semidirect
62. #418×C101C22semidirect
63. C2×#101×C101C22semidirect
64. C2×#101×C101C22semidirect
67. #391×C101C22semidirect
68. #390×C101C22semidirect
71. #343×C101C22semidirect
72. #343×C101C22semidirect
73. #339×C101C22semidirect
74. #339×C101C22semidirect
119. #137×C101D4semidirect
126. AGL(1,ℤ/8)×C101D4semidirect
557. #23881C101direct (N × H)
569. C2×#575C2×C101semidirect
570. #3489C2×C101semidirect
571. C2×#456C2×C101semidirect
572. C2×#454C2×C101semidirect
573. #3005C2×C101semidirect
574. #2432C2×C101semidirect
575. #2007C2×C101semidirect
576. #2006C2×C101semidirect
577. #2005C2×C101semidirect
578. #2003C2×C101semidirect
579. #1901C2×C101semidirect
580. #1883C2×C101semidirect
581. #1882C2×C101semidirect
582. #1871C2×C101semidirect
583. #1789C2×C101semidirect
584. C101#23881direct (N × H)
593. C2×#137C22×C101semidirect
597. C2×AGL(1,ℤ/8)C22×C101semidirect
611. C2×C4⋊Q8C22×C101semidirect
612. C2×#124C22×C101semidirect
628. C2×#104C22×C101semidirect
629. C2×#104C22×C101semidirect
630. #419C22×C101semidirect
631. #418C22×C101semidirect
632. C2×#101C22×C101semidirect
633. C2×#101C22×C101semidirect
636. #391C22×C101semidirect
637. #390C22×C101semidirect
640. #343C22×C101semidirect
641. #343C22×C101semidirect
642. #339C22×C101semidirect
643. #339C22×C101semidirect
688. #137D4×C101semidirect
695. AGL(1,ℤ/8)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×#34892
C2×#456×C1012
C2×#454×C1012
C101×#30052
C101×#24322
C101×#20072
C101×#20062
C101×#20052
C101×#20032
C101×#19012
C101×#18832
C101×#18822
C101×#18712
C101×#17892
#23881101