Finite Group Databasebeta

← C101×#25088 #38807239

Subgroups — C101×#25088 #38807239

Order 25856.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C101C211yesmaximal, characteristic, complemented
2C2×#463×C101C211yesmaximal, characteristic, complemented
3C2×#447×C101C211yesmaximal, characteristic
4C22×#102×C101C211yesmaximal, characteristic, complemented
5C101×#2435C211yesmaximal, characteristic, complemented
6C101×#2361C211yesmaximal, characteristic, complemented
7C101×#2065C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2042C211yesmaximal, characteristic, complemented
10C101×#2012C211yesmaximal, characteristic, complemented
11C101×#1983C211yesmaximal, characteristic, complemented
12C101×#1926C211yesmaximal, characteristic, complemented
13C101×#1879C211yesmaximal, characteristic, complemented
14C101×#1872C211yesmaximal, characteristic, complemented
15C101×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic, complemented
18C22×D8×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C23×C8×C101C2211yescharacteristic
21C2×#124×C101C2211yescharacteristic
22C2×#124×C101C2211yescharacteristic
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×C4×D4×C101—21no—
26C2×C4×D4×C101C2211yescharacteristic, complemented
27C22×C4⋊C4×C101C2211yescharacteristic
28#465×C101—24no—
29#463×C101—24no—
30#447×C101—24no—
31C2×#106×C101C2211yescharacteristic, complemented
32C2×C4⋊C8×C101C2211yescharacteristic, complemented
33C2×C4⋊C8×C101C2211yescharacteristic, complemented
34C2×#103×C101C2211yescharacteristic, complemented
35C2×#103×C101C2211yescharacteristic, complemented
36C2×#103×C101C2211yescharacteristic, complemented
37C2×#102×C101—24no—
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic, complemented
45C2×C22⋊C8×C101C2211yescharacteristic
46#394×C101—21no—
47#394×C101—21no—
48#390×C101C2211yescharacteristic
49#390×C101C2211yescharacteristic
50#390×C101C2211yescharacteristic, complemented
51#389×C101C2211yescharacteristic, complemented
52#388×C101—21no—
53#386×C101—21no—
54#385×C101—21no—
55#379×C101—21no—
56#379×C101—21no—
57C4×C4⋊C4×C101C2211yescharacteristic, complemented
58C4×C22⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#336×C101C2211yescharacteristic, complemented
62#336×C101C2211yescharacteristic, complemented
63C25×C101—21no—
64C22×Q8×C101C2311yescharacteristic
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—21no—
68C22×D4×C101—22no—
69C22×D4×C101—21no—
70C22×D4×C101—22no—
71C22×D4×C101—41no—
72C22×D4×C101—41no—
73C22×D4×C101C2311yescharacteristic
74C22×D4×C101C2311yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C23×C4×C101—21no—
77C23×C4×C101—21no—
78C23×C4×C101C2311yescharacteristic
79C2×SD16×C101—22no—
80C2×SD16×C101—22no—
81C2×SD16×C101—41no—
82C2×D8×C101—22no—
83C2×D8×C101—22no—
84C2×D8×C101—22no—
85C2×D8×C101—22no—
86C2×D8×C101—41no—
87C2×D8×C101—41no—
88C22×C8×C101—22no—
89C22×C8×C101—22no—
90C22×C8×C101—41no—
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95#124×C101—22no—
96#124×C101—22no—
97#124×C101—41no—
98#124×C101—41no—
99C22⋊Q8×C101—22no—
100C22⋊Q8×C101—22no—
101#121×C101—22no—
102#121×C101D414yes—
103C4×D4×C101—22no—
104C4×D4×C101—41no—
105C4×D4×C101—44no—
106C2×C4⋊C4×C101—22no—
107C2×C4⋊C4×C101—21no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—41no—
111C2×C4⋊C4×C101C2311yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101D411yescharacteristic
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132C2×C42×C101C2311yescharacteristic
133#106×C101—22no—
134C4⋊C8×C101—22no—
135C4⋊C8×C101—41no—
136#103×C101—22no—
137#103×C101—22no—
138#103×C101—41no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—22no—
144#102×C101—22no—
145#102×C101D414yescomplemented
146C22⋊C8×C101—22no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101D411yescharacteristic
150#95×C101D411yescharacteristic
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101—42no—
155C24×C101—42no—
156C24×C101—42no—
157C24×C101—42no—
158C24×C101—42no—
159C24×C101—81no—
160C24×C101—81no—
161C24×C101C2×D411yescharacteristic
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×D4×C101—28no—
169C2×D4×C101—24no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—21no—
182C2×D4×C101—21no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—44no—
186C2×D4×C101—44no—
187C2×D4×C101—42no—
188C2×D4×C101—42no—
189C2×D4×C101—44no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—42no—
193C2×D4×C101C2×D412yes—
194C2×D4×C101C2×D412yes—
195C2×D4×C101#4112yes—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—42no—
206C22×C4×C101—42no—
207C22×C4×C101—42no—
208C22×C4×C101—42no—
209C22×C4×C101—81no—
210C22×C4×C101—81no—
211C22×C4×C101C2×D411yescharacteristic
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D412yes—
217C22×C4×C101#4112yes—
218C22×C4×C101C2411yescharacteristic
219SD16×C101—44no—
220D8×C101—44no—
221D8×C101—44no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—44no—
234C2×C8×C101C2×D412yes—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—42no—
242C4⋊C4×C101—42no—
243C4⋊C4×C101—42no—
244C4⋊C4×C101C2×D412yes—
245C4⋊C4×C101C2×D412yes—
246C22⋊C4×C101—22no—
247C22⋊C4×C101—22no—
248C22⋊C4×C101—24no—
249C22⋊C4×C101—42no—
250C22⋊C4×C101—42no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—81no—
257C22⋊C4×C101—81no—
258C22⋊C4×C101—81no—
259C22⋊C4×C101—81no—
260C22⋊C4×C101—81no—
261C42×C101—21no—
262C42×C101—21no—
263C42×C101—21no—
264C42×C101—21no—
265C42×C101—42no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—22no—
271C23×C101—22no—
272C23×C101—22no—
273C23×C101—48no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—84no—
293C23×C101—84no—
294C23×C101—84no—
295C23×C101—84no—
296C23×C101—84no—
297C23×C101—84no—
298C23×C101#12112yes—
299C23×C101#13512yes—
300C23×C101AGL(1,ℤ/8)12yes—
301C23×C101C22×D411yescharacteristic
302Q8×C101—41no—
303Q8×C101—41no—
304Q8×C101—41no—
305Q8×C101—41no—
306D4×C101—22no—
307D4×C101—22no—
308D4×C101—22no—
309D4×C101—22no—
310D4×C101—22no—
311D4×C101—22no—
312D4×C101—48no—
313D4×C101—48no—
314D4×C101—41no—
315D4×C101—41no—
316D4×C101—41no—
317D4×C101—41no—
318D4×C101—41no—
319D4×C101—41no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—22no—
323C2×C4×C101—22no—
324C2×C4×C101—22no—
325C2×C4×C101—22no—
326C2×C4×C101—22no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—22no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—84no—
354C2×C4×C101—84no—
355C2×C4×C101#12112yes—
356C2×C4×C101C22×D411yescharacteristic
357C2×C4×C101C22×D411yescharacteristic
358C2×C4×C101C2×#4111yescharacteristic
359C2×C4×C101C2×#4111yescharacteristic
360C2×C4×C101H(5,𝔽2)11yescharacteristic
361C2×C4×C101H(5,𝔽2)11yescharacteristic
362C8×C101—22no—
363C8×C101—41no—
364C8×C101—41no—
365C8×C101—41no—
366C22×C101—22no—
367C22×C101—22no—
368C22×C101—22no—
369C22×C101—22no—
370C22×C101—22no—
371C22×C101—22no—
372C22×C101—42no—
373C22×C101—42no—
374C22×C101—42no—
375C22×C101—42no—
376C22×C101—42no—
377C22×C101—42no—
378C22×C101—42no—
379C22×C101—42no—
380C22×C101—42no—
381C22×C101—816no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101—81no—
393C22×C101—81no—
394C22×C101#46314yescomplemented
395C22×C101C2×#12111yescharacteristic
396C22×C101D4211yescharacteristic
397C22×C101#54611yescharacteristic
398C22×C101C2×#13511yescharacteristic
399C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C101#57611yescharacteristic
401C22×C101#57711yescharacteristic
402C4×C101—22no—
403C4×C101—41no—
404C4×C101—42no—
405C4×C101—41no—
406C4×C101—42no—
407C4×C101—41no—
408C4×C101—41no—
409C4×C101—81no—
410C4×C101—81no—
411C4×C101—81no—
412C4×C101#52511yescharacteristic
413C4×C101#53811yescharacteristic
414C4×C101D4211yescharacteristic
415C4×C101#54611yescharacteristic
416#25088C10111yesmaximal, characteristic, direct product factor, Sylow
417C2×C101—24no—
418C2×C101—82no—
419C2×C101—82no—
420C2×C101—82no—
421C2×C101#242411yescharacteristic
422C2×C101C2×#46311yescharacteristic
423C2×C101#304511yescharacteristic
424C2×C101#326411yescharacteristic
425C2×C101#328211yescharacteristic
426C2×C101#329711yescharacteristic
427C2×C101#330611yescharacteristic
428C2×#465C2×C10111yescharacteristic, complemented
429C2×#463C2×C10111yescharacteristic, complemented
430C2×#447C2×C10111yescharacteristic
431C22×#102C2×C10111yescharacteristic, complemented
432#2435C2×C10111yescharacteristic, complemented
433#2361C2×C10111yescharacteristic, complemented
434#2065C2×C10111yescharacteristic, complemented
435#2054C2×C10111yescharacteristic, complemented
436#2042C2×C10111yescharacteristic, complemented
437#2012C2×C10111yescharacteristic, complemented
438#1983C2×C10111yescharacteristic, complemented
439#1926C2×C10111yescharacteristic, complemented
440#1879C2×C10111yescharacteristic, complemented
441#1872C2×C10111yescharacteristic, complemented
442#1850C2×C10111yescharacteristic, complemented
443C101#2508811yescharacteristic, direct product factor, Sylow
444C23×D4C22×C10111yescharacteristic
445C22×SD16C22×C10111yescharacteristic, complemented
446C22×D8C22×C10111yescharacteristic
447C22×D8C22×C10111yescharacteristic
448C23×C8C22×C10111yescharacteristic
449C2×#124C22×C10111yescharacteristic
450C2×#124C22×C10111yescharacteristic
451C2×C22⋊Q8C22×C10111yescharacteristic
452C2×#121C22×C10111yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C10111yescharacteristic, complemented
455C22×C4⋊C4C22×C10111yescharacteristic
456#465—24no—
457#463—24no—
458#447—24no—
459C2×#106C22×C10111yescharacteristic, complemented
460C2×C4⋊C8C22×C10111yescharacteristic, complemented
461C2×C4⋊C8C22×C10111yescharacteristic, complemented
462C2×#103C22×C10111yescharacteristic, complemented
463C2×#103C22×C10111yescharacteristic, complemented
464C2×#103C22×C10111yescharacteristic, complemented
465C2×#102—24no—
466C2×#102C22×C10111yescharacteristic
467C2×#102C22×C10111yescharacteristic
468C2×#102C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×#102C22×C10111yescharacteristic
471C2×#102C22×C10111yescharacteristic
472C2×#102C22×C10111yescharacteristic, complemented
473C2×C22⋊C8C22×C10111yescharacteristic
474#394—21no—
475#394—21no—
476#390C22×C10111yescharacteristic
477#390C22×C10111yescharacteristic
478#390C22×C10111yescharacteristic, complemented
479#389C22×C10111yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#385—21no—
483#379—21no—
484#379—21no—
485C4×C4⋊C4C22×C10111yescharacteristic, complemented
486C4×C22⋊C4C22×C10111yescharacteristic
487#340C22×C10111yescharacteristic, complemented
488#340C22×C10111yescharacteristic, complemented
489#336C22×C10111yescharacteristic, complemented
490#336C22×C10111yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C10111yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C10111yescharacteristic
502C22×D4C23×C10111yescharacteristic
503C22×D4C23×C10111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C10111yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—41no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8C23×C10111yescharacteristic
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522C22×C8C23×C10111yescharacteristic
523#124—22no—
524#124—22no—
525#124—41no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529#121—22no—
530#121D4×C10114yes—
531C4×D4—22no—
532C4×D4—41no—
533C4×D4—44no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C4⋊C4C23×C10111yescharacteristic
541C2×C4⋊C4C23×C10111yescharacteristic
542C2×C4⋊C4C23×C10111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4D4×C10111yescharacteristic
557C2×C22⋊C4D4×C10111yescharacteristic
558C2×C42—21no—
559C2×C42C23×C10111yescharacteristic
560C2×C42C23×C10111yescharacteristic
561#106—22no—
562C4⋊C8—22no—
563C4⋊C8—41no—
564#103—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102D4×C10114yescomplemented
574C22⋊C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C10111yescharacteristic
578#95D4×C10111yescharacteristic
579C24—21no—
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C10111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×D4—28no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C10112yes—
622C2×D4C2×D4×C10112yes—
623C2×D4#41×C10112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4C2×D4×C10111yescharacteristic
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4C2×D4×C10111yescharacteristic
642C22×C4C2×D4×C10111yescharacteristic
643C22×C4C2×D4×C10111yescharacteristic
644C22×C4C2×D4×C10112yes—
645C22×C4#41×C10112yes—
646C22×C4C24×C10111yescharacteristic
647SD16—44no—
648D8—44no—
649D8—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×D4×C10112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C10112yes—
673C4⋊C4C2×D4×C10112yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—48no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C10112yes—
727C23#135×C10112yes—
728C23AGL(1,ℤ/8)×C10112yes—
729C23C22×D4×C10111yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4#121×C10112yes—
784C2×C4C22×D4×C10111yescharacteristic
785C2×C4C22×D4×C10111yescharacteristic
786C2×C4C2×#41×C10111yescharacteristic
787C2×C4C2×#41×C10111yescharacteristic
788C2×C4H(5,𝔽2)×C10111yescharacteristic
789C2×C4H(5,𝔽2)×C10111yescharacteristic
790C8—22no—
791C8—41no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—816no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22#463×C10114yescomplemented
823C22C2×#121×C10111yescharacteristic
824C22D42×C10111yescharacteristic
825C22#546×C10111yescharacteristic
826C22C2×#135×C10111yescharacteristic
827C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
828C22#576×C10111yescharacteristic
829C22#577×C10111yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4#525×C10111yescharacteristic
841C4#538×C10111yescharacteristic
842C4D42×C10111yescharacteristic
843C4#546×C10111yescharacteristic
844C2—24no—
845C2—82no—
846C2—82no—
847C2—82no—
848C2C101×#242411yescharacteristic
849C2C2×#463×C10111yescharacteristic
850C2C101×#304511yescharacteristic
851C2C101×#326411yescharacteristic
852C2C101×#328211yescharacteristic
853C2C101×#329711yescharacteristic
854C2C101×#330611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#465×C101C2semidirect
2. C2×#463×C101C2semidirect
4. C22×#102×C101C2semidirect
5. C101×#2435C2semidirect
6. C101×#2361C2semidirect
7. C101×#2065C2semidirect
8. C101×#2054C2semidirect
9. C101×#2042C2semidirect
10. C101×#2012C2semidirect
11. C101×#1983C2semidirect
12. C101×#1926C2semidirect
13. C101×#1879C2semidirect
14. C101×#1872C2semidirect
15. C101×#1850C2semidirect
17. C22×SD16×C101C22semidirect
26. C2×C4×D4×C101C22semidirect
31. C2×#106×C101C22semidirect
32. C2×C4⋊C8×C101C22semidirect
33. C2×C4⋊C8×C101C22semidirect
34. C2×#103×C101C22semidirect
35. C2×#103×C101C22semidirect
36. C2×#103×C101C22semidirect
44. C2×#102×C101C22semidirect
50. #390×C101C22semidirect
51. #389×C101C22semidirect
57. C4×C4⋊C4×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #336×C101C22semidirect
62. #336×C101C22semidirect
145. #102×C101D4semidirect
394. C22×C101#463semidirect
416. #25088C101direct (N × H)
428. C2×#465C2×C101semidirect
429. C2×#463C2×C101semidirect
431. C22×#102C2×C101semidirect
432. #2435C2×C101semidirect
433. #2361C2×C101semidirect
434. #2065C2×C101semidirect
435. #2054C2×C101semidirect
436. #2042C2×C101semidirect
437. #2012C2×C101semidirect
438. #1983C2×C101semidirect
439. #1926C2×C101semidirect
440. #1879C2×C101semidirect
441. #1872C2×C101semidirect
442. #1850C2×C101semidirect
443. C101#25088direct (N × H)
445. C22×SD16C22×C101semidirect
454. C2×C4×D4C22×C101semidirect
459. C2×#106C22×C101semidirect
460. C2×C4⋊C8C22×C101semidirect
461. C2×C4⋊C8C22×C101semidirect
462. C2×#103C22×C101semidirect
463. C2×#103C22×C101semidirect
464. C2×#103C22×C101semidirect
472. C2×#102C22×C101semidirect
478. #390C22×C101semidirect
479. #389C22×C101semidirect
485. C4×C4⋊C4C22×C101semidirect
487. #340C22×C101semidirect
488. #340C22×C101semidirect
489. #336C22×C101semidirect
490. #336C22×C101semidirect
573. #102D4×C101semidirect
822. C22#463×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1012
C2×#463×C1012
C2×#447×C1012
C22×#102×C1012
C101×#24352
C101×#23612
C101×#20652
C101×#20542
C101×#20422
C101×#20122
C101×#19832
C101×#19262
C101×#18792
C101×#18722
C101×#18502
#25088101