Finite Group Databasebeta

← C101×#25575 #38807726

Subgroups — C101×#25575 #38807726

Order 25856.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C101C211yesmaximal, characteristic, complemented
2C2×#488×C101C211yesmaximal, characteristic, complemented
3C2×#463×C101C211yesmaximal, characteristic, complemented
4C101×#2540C211yesmaximal, characteristic, complemented
5C101×#2000C211yesmaximal, characteristic, complemented
6C101×#2000C211yesmaximal, characteristic, complemented
7C101×#1999C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1989C211yesmaximal, characteristic, complemented
10C101×#1954C211yesmaximal, characteristic, complemented
11C101×#1875C211yesmaximal, characteristic, complemented
12C101×#1874C211yesmaximal, characteristic, complemented
13C101×#1873C211yesmaximal, characteristic, complemented
14C101×#1872C211yesmaximal, characteristic, complemented
15C4×#102×C101C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18#553×C101—24no—
19#553×C101—24no—
20C2×#126×C101—21no—
21C2×#125×C101C2211yescharacteristic
22C2×#124×C101C2211yescharacteristic
23C2×#123×C101—21no—
24C2×C22⋊Q8×C101C2211yescharacteristic
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101C2211yescharacteristic
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×C4×D4×C101—21no—
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C2×#117×C101C2211yescharacteristic
35C22×C4⋊C4×C101C2211yescharacteristic
36#488×C101—24no—
37#463×C101—24no—
38C2×C4⋊C8×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#103×C101C2211yescharacteristic
41C2×#103×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×C22⋊C8×C101C2211yescharacteristic
49C2×C22⋊C8×C101C2211yescharacteristic
50C2×C22⋊C8×C101C2211yescharacteristic
51C2×C4×C8×C101C2211yescharacteristic
52#399×C101—21no—
53#392×C101—21no—
54#390×C101—21no—
55#390×C101—21no—
56C4×C4⋊C4×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63C22×Q8×C101C2311yescharacteristic
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101D411yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
71C23×C4×C101—21no—
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C2×SD16×C101—22no—
76C2×SD16×C101—41no—
77C2×SD16×C101—41no—
78C2×D8×C101—22no—
79C2×D8×C101—41no—
80C2×D8×C101—41no—
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85#126×C101—28no—
86#125×C101—22no—
87#125×C101D414yescomplemented
88#124×C101—22no—
89#124×C101—22no—
90#123×C101—28no—
91C22⋊Q8×C101—22no—
92C22⋊Q8×C101—22no—
93C22⋊Q8×C101—41no—
94C22⋊Q8×C101—41no—
95#121×C101—28no—
96#121×C101—22no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—41no—
103#121×C101—41no—
104C4×D4×C101—28no—
105C4×D4×C101—22no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108C4×D4×C101D414yescomplemented
109#117×C101—22no—
110#117×C101—22no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101—21no—
114C2×C4⋊C4×C101—22no—
115C2×C4⋊C4×C101—22no—
116C2×C4⋊C4×C101—21no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101D411yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
120C2×C4⋊C4×C101C2311yescharacteristic
121C2×C4⋊C4×C101C2311yescharacteristic
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C4⋊C4×C101C2311yescharacteristic
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101D411yescharacteristic
135C2×C22⋊C4×C101D411yescharacteristic
136C2×C42×C101—21no—
137C2×C42×C101—21no—
138C2×C42×C101C2311yescharacteristic
139C4⋊C8×C101—22no—
140#103×C101—22no—
141#103×C101—22no—
142#103×C101—22no—
143#102×C101—22no—
144#102×C101—22no—
145#102×C101—22no—
146#102×C101—22no—
147#102×C101—22no—
148C22⋊C8×C101—41no—
149C22⋊C8×C101—41no—
150C22⋊C8×C101—41no—
151C22⋊C8×C101—41no—
152C4×C8×C101—22no—
153#95×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101C2×D411yescharacteristic
157C24×C101C2×D411yescharacteristic
158C2×Q8×C101—21no—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×Q8×C101—21no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×D4×C101—24no—
165C2×D4×C101—22no—
166C2×D4×C101—24no—
167C2×D4×C101—22no—
168C2×D4×C101—21no—
169C2×D4×C101—21no—
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—41no—
180C2×D4×C101—42no—
181C2×D4×C101—42no—
182C2×D4×C101—42no—
183C2×D4×C101—42no—
184C2×D4×C101—42no—
185C2×D4×C101—42no—
186C2×D4×C101—81no—
187C2×D4×C101—81no—
188C2×D4×C101—81no—
189C2×D4×C101—81no—
190C2×D4×C101C2×D412yes—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—24no—
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—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—24no—
210C22×C4×C101—21no—
211C22×C4×C101—81no—
212C22×C4×C101—81no—
213C22×C4×C101—81no—
214C22×C4×C101—81no—
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2411yescharacteristic
220SD16×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—21no—
234C4⋊C4×C101—24no—
235C4⋊C4×C101—24no—
236C4⋊C4×C101—24no—
237C4⋊C4×C101—22no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—42no—
244C4⋊C4×C101—42no—
245C4⋊C4×C101C2×D412yes—
246C4⋊C4×C101C2×D412yes—
247C4⋊C4×C101C2×D412yes—
248C4⋊C4×C101#4112yes—
249C4⋊C4×C101#4112yes—
250C22⋊C4×C101—24no—
251C22⋊C4×C101—24no—
252C22⋊C4×C101—24no—
253C22⋊C4×C101—24no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—42no—
258C22⋊C4×C101—42no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—42no—
261C22⋊C4×C101—42no—
262C42×C101—24no—
263C42×C101—81no—
264C42×C101C2×D412yes—
265C42×C101C2×D412yes—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—22no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
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—41no—
293C23×C101#13512yes—
294C23×C101C22×D411yescharacteristic
295Q8×C101—41no—
296Q8×C101—41no—
297Q8×C101—41no—
298Q8×C101—41no—
299D4×C101—22no—
300D4×C101—22no—
301D4×C101—44no—
302D4×C101—48no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—84no—
310D4×C101—84no—
311D4×C101—84no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—21no—
317C2×C4×C101—22no—
318C2×C4×C101—22no—
319C2×C4×C101—21no—
320C2×C4×C101—22no—
321C2×C4×C101—22no—
322C2×C4×C101—22no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
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—84no—
349C2×C4×C101—84no—
350C2×C4×C101#12012yes—
351C2×C4×C101#12012yes—
352C2×C4×C101C22×D411yescharacteristic
353C2×C4×C101C22×D411yescharacteristic
354C2×C4×C101C2×#4111yescharacteristic
355C2×C4×C101C2×#4111yescharacteristic
356C2×C4×C101H(5,𝔽2)11yescharacteristic
357C2×C4×C101H(5,𝔽2)11yescharacteristic
358C8×C101—41no—
359C8×C101—41no—
360C8×C101—41no—
361C8×C101—41no—
362C22×C101—22no—
363C22×C101—22no—
364C22×C101—22no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—42no—
371C22×C101—41no—
372C22×C101—42no—
373C22×C101—42no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—41no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
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×C101C2×#12011yescharacteristic
391C22×C101#54611yescharacteristic
392C22×C101#54611yescharacteristic
393C22×C101C2×#13511yescharacteristic
394C22×C101#57511yescharacteristic
395C22×C101#57611yescharacteristic
396C22×C101#57711yescharacteristic
397C4×C101—22no—
398C4×C101—22no—
399C4×C101—41no—
400C4×C101—41no—
401C4×C101—42no—
402C4×C101—42no—
403C4×C101—42no—
404C4×C101—42no—
405C4×C101—42no—
406C4×C101—81no—
407C4×C101#53211yescharacteristic
408C4×C101#53511yescharacteristic
409C4×C101#55011yescharacteristic
410C4×C101#55011yescharacteristic
411#25575C10111yesmaximal, characteristic, direct product factor, Sylow
412C2×C101—42no—
413C2×C101—81no—
414C2×C101—82no—
415C2×C101—161no—
416C2×C101#243111yescharacteristic
417C2×C101#300211yescharacteristic
418C2×C101#301211yescharacteristic
419C2×C101#329711yescharacteristic
420C2×C101#330111yescharacteristic
421C2×C101#332211yescharacteristic
422C2×C101#332611yescharacteristic
423C2×#553C2×C10111yescharacteristic, complemented
424C2×#488C2×C10111yescharacteristic, complemented
425C2×#463C2×C10111yescharacteristic, complemented
426#2540C2×C10111yescharacteristic, complemented
427#2000C2×C10111yescharacteristic, complemented
428#2000C2×C10111yescharacteristic, complemented
429#1999C2×C10111yescharacteristic, complemented
430#1999C2×C10111yescharacteristic, complemented
431#1989C2×C10111yescharacteristic, complemented
432#1954C2×C10111yescharacteristic, complemented
433#1875C2×C10111yescharacteristic, complemented
434#1874C2×C10111yescharacteristic, complemented
435#1873C2×C10111yescharacteristic, complemented
436#1872C2×C10111yescharacteristic, complemented
437C4×#102C2×C10111yescharacteristic, complemented
438C101#2557511yescharacteristic, direct product factor, Sylow
439C22×SD16C22×C10111yescharacteristic
440C22×D8C22×C10111yescharacteristic
441#553—24no—
442#553—24no—
443C2×#126—21no—
444C2×#125C22×C10111yescharacteristic
445C2×#124C22×C10111yescharacteristic
446C2×#123—21no—
447C2×C22⋊Q8C22×C10111yescharacteristic
448C2×C22⋊Q8C22×C10111yescharacteristic
449C2×#121—21no—
450C2×#121C22×C10111yescharacteristic
451C2×#121C22×C10111yescharacteristic
452C2×#121C22×C10111yescharacteristic
453C2×#121C22×C10111yescharacteristic
454C2×C4×D4—21no—
455C2×C4×D4C22×C10111yescharacteristic
456C2×C4×D4C22×C10111yescharacteristic
457C2×#117C22×C10111yescharacteristic
458C22×C4⋊C4C22×C10111yescharacteristic
459#488—24no—
460#463—24no—
461C2×C4⋊C8C22×C10111yescharacteristic
462C2×#103C22×C10111yescharacteristic
463C2×#103C22×C10111yescharacteristic
464C2×#103C22×C10111yescharacteristic
465C2×#102C22×C10111yescharacteristic
466C2×#102C22×C10111yescharacteristic
467C2×#102C22×C10111yescharacteristic
468C2×#102C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×C22⋊C8C22×C10111yescharacteristic
471C2×C22⋊C8C22×C10111yescharacteristic
472C2×C22⋊C8C22×C10111yescharacteristic
473C2×C22⋊C8C22×C10111yescharacteristic
474C2×C4×C8C22×C10111yescharacteristic
475#399—21no—
476#392—21no—
477#390—21no—
478#390—21no—
479C4×C4⋊C4C22×C10111yescharacteristic
480#340C22×C10111yescharacteristic
481#340C22×C10111yescharacteristic
482#340C22×C10111yescharacteristic
483#340C22×C10111yescharacteristic
484#340C22×C10111yescharacteristic
485#340C22×C10111yescharacteristic
486C22×Q8C23×C10111yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C10111yescharacteristic
492C22×D4C23×C10111yescharacteristic
493C22×D4C23×C10111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C10111yescharacteristic
497C23×C4C23×C10111yescharacteristic
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C22×C8C23×C10111yescharacteristic
505C22×C8C23×C10111yescharacteristic
506C22×C8C23×C10111yescharacteristic
507C22×C8C23×C10111yescharacteristic
508#126—28no—
509#125—22no—
510#125D4×C10114yescomplemented
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4D4×C10114yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C10111yescharacteristic
542C2×C4⋊C4C23×C10111yescharacteristic
543C2×C4⋊C4C23×C10111yescharacteristic
544C2×C4⋊C4C23×C10111yescharacteristic
545C2×C4⋊C4C23×C10111yescharacteristic
546C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
557C2×C22⋊C4D4×C10111yescharacteristic
558C2×C22⋊C4D4×C10111yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C10111yescharacteristic
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C22⋊C8—41no—
575C4×C8—22no—
576#95—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C10111yescharacteristic
580C24C2×D4×C10111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C10112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
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—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C10111yescharacteristic
639C22×C4C2×D4×C10111yescharacteristic
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4C2×D4×C10111yescharacteristic
642C22×C4C24×C10111yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C10112yes—
669C4⋊C4C2×D4×C10112yes—
670C4⋊C4C2×D4×C10112yes—
671C4⋊C4#41×C10112yes—
672C4⋊C4#41×C10112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C10112yes—
688C42C2×D4×C10112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
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#135×C10112yes—
717C23C22×D4×C10111yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#120×C10112yes—
774C2×C4#120×C10112yes—
775C2×C4C22×D4×C10111yescharacteristic
776C2×C4C22×D4×C10111yescharacteristic
777C2×C4C2×#41×C10111yescharacteristic
778C2×C4C2×#41×C10111yescharacteristic
779C2×C4H(5,𝔽2)×C10111yescharacteristic
780C2×C4H(5,𝔽2)×C10111yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×#120×C10111yescharacteristic
814C22#546×C10111yescharacteristic
815C22#546×C10111yescharacteristic
816C22C2×#135×C10111yescharacteristic
817C22#575×C10111yescharacteristic
818C22#576×C10111yescharacteristic
819C22#577×C10111yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4#532×C10111yescharacteristic
831C4#535×C10111yescharacteristic
832C4#550×C10111yescharacteristic
833C4#550×C10111yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C101×#243111yescharacteristic
839C2C101×#300211yescharacteristic
840C2C101×#301211yescharacteristic
841C2C101×#329711yescharacteristic
842C2C101×#330111yescharacteristic
843C2C101×#332211yescharacteristic
844C2C101×#332611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C101C2semidirect
2. C2×#488×C101C2semidirect
3. C2×#463×C101C2semidirect
4. C101×#2540C2semidirect
5. C101×#2000C2semidirect
6. C101×#2000C2semidirect
7. C101×#1999C2semidirect
8. C101×#1999C2semidirect
9. C101×#1989C2semidirect
10. C101×#1954C2semidirect
11. C101×#1875C2semidirect
12. C101×#1874C2semidirect
13. C101×#1873C2semidirect
14. C101×#1872C2semidirect
15. C4×#102×C101C2semidirect
87. #125×C101D4semidirect
108. C4×D4×C101D4semidirect
411. #25575C101direct (N × H)
423. C2×#553C2×C101semidirect
424. C2×#488C2×C101semidirect
425. C2×#463C2×C101semidirect
426. #2540C2×C101semidirect
427. #2000C2×C101semidirect
428. #2000C2×C101semidirect
429. #1999C2×C101semidirect
430. #1999C2×C101semidirect
431. #1989C2×C101semidirect
432. #1954C2×C101semidirect
433. #1875C2×C101semidirect
434. #1874C2×C101semidirect
435. #1873C2×C101semidirect
436. #1872C2×C101semidirect
437. C4×#102C2×C101semidirect
438. C101#25575direct (N × H)
510. #125D4×C101semidirect
531. C4×D4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1012
C2×#488×C1012
C2×#463×C1012
C101×#25402
C101×#20002
C101×#19992
C101×#19892
C101×#19542
C101×#18752
C101×#18742
C101×#18732
C101×#18722
C4×#102×C1012
#25575101