Finite Group Databasebeta

← C101×#21458 #38803609

Subgroups — C101×#21458 #38803609

Order 25856.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C101C211yesmaximal, characteristic, complemented
2C2×#447×C101C211yesmaximal, characteristic
3C2×#442×C101C211yesmaximal, characteristic, complemented
4C2×C4×D8×C101C211yesmaximal, characteristic, complemented
5C101×#2324C211yesmaximal, characteristic, complemented
6C101×#1879C211yesmaximal, characteristic, complemented
7C101×#1879C211yesmaximal, characteristic, complemented
8C101×#1875C211yesmaximal, characteristic, complemented
9C101×#1864C211yesmaximal, characteristic, complemented
10C101×#1862C211yesmaximal, characteristic, complemented
11C101×#1854C211yesmaximal, characteristic, complemented
12C101×#1786C211yesmaximal, characteristic, complemented
13C101×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C101C211yesmaximal, characteristic, complemented
15C101×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20#518×C101—24no—
21#518×C101—24no—
22C2×C4×D4×C101—21no—
23C2×C4×D4×C101—21no—
24C2×C4×D4×C101C2211yescharacteristic
25C2×C4×D4×C101C2211yescharacteristic
26C2×C4×D4×C101C2211yescharacteristic
27C2×C4×D4×C101C2211yescharacteristic
28C2×C4×D4×C101C2211yescharacteristic, complemented
29C2×#117×C101C2211yescharacteristic
30C2×#117×C101C2211yescharacteristic
31C22×C22⋊C4×C101—21no—
32C22×C22⋊C4×C101—21no—
33#447×C101C418yescomplemented
34#442×C101—24no—
35C4×D8×C101—24no—
36C2×#107×C101C2211yescharacteristic, complemented
37C2×#106×C101C2211yescharacteristic, complemented
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic, complemented
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48C2×#97×C101C2211yescharacteristic, complemented
49C2×C4×C8×C101C2211yescharacteristic, complemented
50#390×C101—21no—
51#390×C101C2211yescharacteristic, complemented
52#389×C101C2211yescharacteristic, complemented
53#388×C101—21no—
54#386×C101—21no—
55#385×C101—21no—
56#380×C101C2211yescharacteristic
57C4×C4⋊C4×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#340×C101C2211yescharacteristic, complemented
62#336×C101C2211yescharacteristic, complemented
63#336×C101C2211yescharacteristic, complemented
64C25×C101—21no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—22no—
68C22×D4×C101—22no—
69C22×D4×C101—21no—
70C22×D4×C101—21no—
71C22×D4×C101—22no—
72C22×D4×C101C2×C414yescomplemented
73C22×D4×C101C2311yescharacteristic
74C22×D4×C101C2311yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C23×C4×C101—21no—
77C23×C4×C101—21no—
78C23×C4×C101—21no—
79C23×C4×C101—21no—
80C23×C4×C101—21no—
81C23×C4×C101C2311yescharacteristic
82C2×D8×C101—22no—
83C2×D8×C101—22no—
84C2×D8×C101—22no—
85C2×D8×C101—22no—
86C2×D8×C101C2×C414yescomplemented
87C2×D8×C101C2×C414yescomplemented
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92#121×C101—22no—
93#121×C101C2×C414yescomplemented
94C4×D4×C101—28no—
95C4×D4×C101—28no—
96C4×D4×C101—22no—
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—22no—
102C4×D4×C101—22no—
103C4×D4×C101—22no—
104C4×D4×C101D414yescomplemented
105C4×D4×C101D414yescomplemented
106#117×C101—22no—
107#117×C101—22no—
108#117×C101—22no—
109#117×C101—22no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101D411yescharacteristic
112C2×C4⋊C4×C101D411yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C22⋊C4×C101—28no—
119C2×C22⋊C4×C101—28no—
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×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C42×C101—21no—
133C2×C42×C101—21no—
134C2×C42×C101C2311yescharacteristic
135C2×C42×C101C2311yescharacteristic
136#107×C101—22no—
137#106×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—22no—
144#102×C101C2×C414yescomplemented
145#102×C101C2×C414yescomplemented
146C22⋊C8×C101—22no—
147C22⋊C8×C101C2×C414yescomplemented
148#97×C101—22no—
149C4×C8×C101—22no—
150#95×C101—21no—
151#95×C101—21no—
152#95×C101—21no—
153C24×C101—24no—
154C24×C101—24no—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—24no—
158C24×C101—21no—
159C24×C101—81no—
160C24×C101—81no—
161C24×C101—81no—
162C24×C101—81no—
163C24×C101C2×D411yescharacteristic
164C2×D4×C101—24no—
165C2×D4×C101—24no—
166C2×D4×C101—28no—
167C2×D4×C101—28no—
168C2×D4×C101—28no—
169C2×D4×C101—28no—
170C2×D4×C101—24no—
171C2×D4×C101—24no—
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—81no—
184C2×D4×C101—81no—
185C2×D4×C101C22×C412yes—
186C2×D4×C101C22×C412yes—
187C2×D4×C101C22×C412yes—
188C2×D4×C101C2×D412yes—
189C2×D4×C101C2×D412yes—
190C2×D4×C101#4112yes—
191C2×D4×C101#4112yes—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—24no—
200C22×C4×C101—24no—
201C22×C4×C101—24no—
202C22×C4×C101—24no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—42no—
206C22×C4×C101—81no—
207C22×C4×C101—81no—
208C22×C4×C101—81no—
209C22×C4×C101—81no—
210C22×C4×C101—81no—
211C22×C4×C101—81no—
212C22×C4×C101—81no—
213C22×C4×C101—81no—
214C22×C4×C101—81no—
215C22×C4×C101—81no—
216C22×C4×C101C22×C412yes—
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101#4112yes—
223C22×C4×C101C2411yescharacteristic
224D8×C101—28no—
225D8×C101—28no—
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—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101C22×C412yes—
237C2×C8×C101C22×C412yes—
238C4⋊C4×C101—22no—
239C4⋊C4×C101—22no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—81no—
248C4⋊C4×C101C22×C412yes—
249C4⋊C4×C101C2×D412yes—
250C4⋊C4×C101C2×D412yes—
251C22⋊C4×C101—24no—
252C22⋊C4×C101—24no—
253C22⋊C4×C101—24no—
254C22⋊C4×C101—24no—
255C22⋊C4×C101—22no—
256C22⋊C4×C101—22no—
257C22⋊C4×C101—24no—
258C22⋊C4×C101—24no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—81no—
261C22⋊C4×C101—81no—
262C22⋊C4×C101—81no—
263C42×C101—24no—
264C42×C101—21no—
265C42×C101—21no—
266C42×C101—81no—
267C42×C101C2×D412yes—
268C42×C101C2×D412yes—
269C23×C101—216no—
270C23×C101—22no—
271C23×C101—22no—
272C23×C101—21no—
273C23×C101—22no—
274C23×C101—22no—
275C23×C101—21no—
276C23×C101—22no—
277C23×C101—22no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—22no—
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—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—84no—
298C23×C101—84no—
299C23×C101—84no—
300C23×C101—84no—
301C23×C101—84no—
302C23×C101—84no—
303C23×C101C4×D412yes—
304C23×C101C22×D411yescharacteristic
305D4×C101—216no—
306D4×C101—22no—
307D4×C101—22no—
308D4×C101—22no—
309D4×C101—22no—
310D4×C101—22no—
311D4×C101—22no—
312D4×C101—22no—
313D4×C101—22no—
314D4×C101—41no—
315D4×C101—41no—
316D4×C101—84no—
317D4×C101C4×D414yes—
318D4×C101C4×D414yes—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—22no—
326C2×C4×C101—22no—
327C2×C4×C101—22no—
328C2×C4×C101—22no—
329C2×C4×C101—22no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—22no—
333C2×C4×C101—22no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
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—41no—
349C2×C4×C101—41no—
350C2×C4×C101—84no—
351C2×C4×C101—84no—
352C2×C4×C101—84no—
353C2×C4×C101—84no—
354C2×C4×C101—84no—
355C2×C4×C101C4×D412yes—
356C2×C4×C101#12012yes—
357C2×C4×C101#12012yes—
358C2×C4×C101C23×C411yescharacteristic
359C2×C4×C101C22×D411yescharacteristic
360C2×C4×C101C22×D411yescharacteristic
361C2×C4×C101C2×#4111yescharacteristic
362C2×C4×C101C2×#4111yescharacteristic
363C2×C4×C101C2×#4111yescharacteristic
364C8×C101—22no—
365C8×C101—22no—
366C8×C101—41no—
367C8×C101—41no—
368C22×C101—22no—
369C22×C101—22no—
370C22×C101—22no—
371C22×C101—24no—
372C22×C101—24no—
373C22×C101—41no—
374C22×C101—42no—
375C22×C101—42no—
376C22×C101—41no—
377C22×C101—42no—
378C22×C101—42no—
379C22×C101—42no—
380C22×C101—42no—
381C22×C101—42no—
382C22×C101—42no—
383C22×C101—42no—
384C22×C101—42no—
385C22×C101—41no—
386C22×C101—42no—
387C22×C101—42no—
388C22×C101—41no—
389C22×C101—42no—
390C22×C101—42no—
391C22×C101—42no—
392C22×C101—816no—
393C22×C101—81no—
394C22×C101—81no—
395C22×C101—81no—
396C22×C101—81no—
397C22×C101C2×C4×D411yescharacteristic
398C22×C101C2×#12011yescharacteristic
399C22×C101#52511yescharacteristic
400C22×C101#57611yescharacteristic
401C22×C101#57611yescharacteristic
402C22×C101#57611yescharacteristic
403C22×C101#57711yescharacteristic
404C4×C101—22no—
405C4×C101—22no—
406C4×C101—22no—
407C4×C101—42no—
408C4×C101—41no—
409C4×C101—42no—
410C4×C101—41no—
411C4×C101—42no—
412C4×C101—81no—
413C4×C101—81no—
414C4×C101C2×C4×D411yescharacteristic
415C4×C101C2×C4×D411yescharacteristic
416C4×C101#52511yescharacteristic
417C4×C101#52511yescharacteristic
418#21458C10111yesmaximal, characteristic, direct product factor, Sylow
419C2×C101—42no—
420C2×C101—44no—
421C2×C101—44no—
422C2×C101—82no—
423C2×C101C4×#12011yescharacteristic
424C2×C101#294611yescharacteristic
425C2×C101#294811yescharacteristic
426C2×C101#300811yescharacteristic
427C2×C101#301211yescharacteristic
428C2×C101#311811yescharacteristic
429C2×C101#312211yescharacteristic
430C2×#518C2×C10111yescharacteristic, complemented
431C2×#447C2×C10111yescharacteristic
432C2×#442C2×C10111yescharacteristic, complemented
433C2×C4×D8C2×C10111yescharacteristic, complemented
434#2324C2×C10111yescharacteristic, complemented
435#1879C2×C10111yescharacteristic, complemented
436#1879C2×C10111yescharacteristic, complemented
437#1875C2×C10111yescharacteristic, complemented
438#1864C2×C10111yescharacteristic, complemented
439#1862C2×C10111yescharacteristic, complemented
440#1854C2×C10111yescharacteristic, complemented
441#1786C2×C10111yescharacteristic, complemented
442#1762C2×C10111yescharacteristic, complemented
443C4×#102C2×C10111yescharacteristic, complemented
444#1750C2×C10111yescharacteristic, complemented
445C101#2145811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C10111yescharacteristic
447C22×D8C22×C10111yescharacteristic
448C22×D8C22×C10111yescharacteristic
449C2×#121C22×C10111yescharacteristic
450#518—24no—
451#518—24no—
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4C22×C10111yescharacteristic
455C2×C4×D4C22×C10111yescharacteristic
456C2×C4×D4C22×C10111yescharacteristic
457C2×C4×D4C22×C10111yescharacteristic
458C2×C4×D4C22×C10111yescharacteristic, complemented
459C2×#117C22×C10111yescharacteristic
460C2×#117C22×C10111yescharacteristic
461C22×C22⋊C4—21no—
462C22×C22⋊C4—21no—
463#447C4×C10118yescomplemented
464#442—24no—
465C4×D8—24no—
466C2×#107C22×C10111yescharacteristic, complemented
467C2×#106C22×C10111yescharacteristic, complemented
468C2×#102C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×#102C22×C10111yescharacteristic
471C2×#102C22×C10111yescharacteristic
472C2×#102C22×C10111yescharacteristic
473C2×#102C22×C10111yescharacteristic
474C2×#102C22×C10111yescharacteristic, complemented
475C2×#102C22×C10111yescharacteristic, complemented
476C2×C22⋊C8C22×C10111yescharacteristic
477C2×C22⋊C8C22×C10111yescharacteristic
478C2×#97C22×C10111yescharacteristic, complemented
479C2×C4×C8C22×C10111yescharacteristic, complemented
480#390—21no—
481#390C22×C10111yescharacteristic, complemented
482#389C22×C10111yescharacteristic, complemented
483#388—21no—
484#386—21no—
485#385—21no—
486#380C22×C10111yescharacteristic
487C4×C4⋊C4C22×C10111yescharacteristic, complemented
488#340C22×C10111yescharacteristic, complemented
489#340C22×C10111yescharacteristic, complemented
490#340C22×C10111yescharacteristic, complemented
491#340C22×C10111yescharacteristic, complemented
492#336C22×C10111yescharacteristic, complemented
493#336C22×C10111yescharacteristic, complemented
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×C4×C10114yescomplemented
503C22×D4C23×C10111yescharacteristic
504C22×D4C23×C10111yescharacteristic
505C22×D4C23×C10111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C10111yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×C4×C10114yescomplemented
517C2×D8C2×C4×C10114yescomplemented
518C22×C8C23×C10111yescharacteristic
519C22×C8C23×C10111yescharacteristic
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522#121—22no—
523#121C2×C4×C10114yescomplemented
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4D4×C10114yescomplemented
535C4×D4D4×C10114yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C10111yescharacteristic
542C2×C4⋊C4D4×C10111yescharacteristic
543C2×C4⋊C4C23×C10111yescharacteristic
544C2×C4⋊C4C23×C10111yescharacteristic
545C2×C4⋊C4C23×C10111yescharacteristic
546C2×C4⋊C4C23×C10111yescharacteristic
547C2×C4⋊C4C23×C10111yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
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⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C10111yescharacteristic
561C2×C22⋊C4D4×C10111yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C10111yescharacteristic
565C2×C42C23×C10111yescharacteristic
566#107—22no—
567#106—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102C2×C4×C10114yescomplemented
575#102C2×C4×C10114yescomplemented
576C22⋊C8—22no—
577C22⋊C8C2×C4×C10114yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C10111yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
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—81no—
614C2×D4—81no—
615C2×D4C22×C4×C10112yes—
616C2×D4C22×C4×C10112yes—
617C2×D4C22×C4×C10112yes—
618C2×D4C2×D4×C10112yes—
619C2×D4C2×D4×C10112yes—
620C2×D4#41×C10112yes—
621C2×D4#41×C10112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C10112yes—
647C22×C4C2×D4×C10111yescharacteristic
648C22×C4C2×D4×C10111yescharacteristic
649C22×C4C2×D4×C10111yescharacteristic
650C22×C4C2×D4×C10111yescharacteristic
651C22×C4C2×D4×C10111yescharacteristic
652C22×C4#41×C10112yes—
653C22×C4C24×C10111yescharacteristic
654D8—28no—
655D8—28no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C22×C4×C10112yes—
667C2×C8C22×C4×C10112yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C10112yes—
679C4⋊C4C2×D4×C10112yes—
680C4⋊C4C2×D4×C10112yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C10112yes—
698C42C2×D4×C10112yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C10112yes—
734C23C22×D4×C10111yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C10114yes—
748D4C4×D4×C10114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
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—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C10112yes—
786C2×C4#120×C10112yes—
787C2×C4#120×C10112yes—
788C2×C4C23×C4×C10111yescharacteristic
789C2×C4C22×D4×C10111yescharacteristic
790C2×C4C22×D4×C10111yescharacteristic
791C2×C4C2×#41×C10111yescharacteristic
792C2×C4C2×#41×C10111yescharacteristic
793C2×C4C2×#41×C10111yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C10111yescharacteristic
828C22C2×#120×C10111yescharacteristic
829C22#525×C10111yescharacteristic
830C22#576×C10111yescharacteristic
831C22#576×C10111yescharacteristic
832C22#576×C10111yescharacteristic
833C22#577×C10111yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C10111yescharacteristic
845C4C2×C4×D4×C10111yescharacteristic
846C4#525×C10111yescharacteristic
847C4#525×C10111yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×#120×C10111yescharacteristic
853C2C101×#294611yescharacteristic
854C2C101×#294811yescharacteristic
855C2C101×#300811yescharacteristic
856C2C101×#301211yescharacteristic
857C2C101×#311811yescharacteristic
858C2C101×#312211yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#518×C101C2semidirect
3. C2×#442×C101C2semidirect
4. C2×C4×D8×C101C2semidirect
5. C101×#2324C2semidirect
6. C101×#1879C2semidirect
7. C101×#1879C2semidirect
8. C101×#1875C2semidirect
9. C101×#1864C2semidirect
10. C101×#1862C2semidirect
11. C101×#1854C2semidirect
12. C101×#1786C2semidirect
13. C101×#1762C2semidirect
14. C4×#102×C101C2semidirect
15. C101×#1750C2semidirect
28. C2×C4×D4×C101C22semidirect
33. #447×C101C4semidirect
36. C2×#107×C101C22semidirect
37. C2×#106×C101C22semidirect
44. C2×#102×C101C22semidirect
45. C2×#102×C101C22semidirect
48. C2×#97×C101C22semidirect
49. C2×C4×C8×C101C22semidirect
51. #390×C101C22semidirect
52. #389×C101C22semidirect
57. C4×C4⋊C4×C101C22semidirect
58. #340×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #340×C101C22semidirect
62. #336×C101C22semidirect
63. #336×C101C22semidirect
72. C22×D4×C101C2×C4semidirect
86. C2×D8×C101C2×C4semidirect
87. C2×D8×C101C2×C4semidirect
93. #121×C101C2×C4semidirect
104. C4×D4×C101D4semidirect
105. C4×D4×C101D4semidirect
144. #102×C101C2×C4semidirect
145. #102×C101C2×C4semidirect
147. C22⋊C8×C101C2×C4semidirect
418. #21458C101direct (N × H)
430. C2×#518C2×C101semidirect
432. C2×#442C2×C101semidirect
433. C2×C4×D8C2×C101semidirect
434. #2324C2×C101semidirect
435. #1879C2×C101semidirect
436. #1879C2×C101semidirect
437. #1875C2×C101semidirect
438. #1864C2×C101semidirect
439. #1862C2×C101semidirect
440. #1854C2×C101semidirect
441. #1786C2×C101semidirect
442. #1762C2×C101semidirect
443. C4×#102C2×C101semidirect
444. #1750C2×C101semidirect
445. C101#21458direct (N × H)
458. C2×C4×D4C22×C101semidirect
463. #447C4×C101semidirect
466. C2×#107C22×C101semidirect
467. C2×#106C22×C101semidirect
474. C2×#102C22×C101semidirect
475. C2×#102C22×C101semidirect
478. C2×#97C22×C101semidirect
479. C2×C4×C8C22×C101semidirect
481. #390C22×C101semidirect
482. #389C22×C101semidirect
487. C4×C4⋊C4C22×C101semidirect
488. #340C22×C101semidirect
489. #340C22×C101semidirect
490. #340C22×C101semidirect
491. #340C22×C101semidirect
492. #336C22×C101semidirect
493. #336C22×C101semidirect
502. C22×D4C2×C4×C101semidirect
516. C2×D8C2×C4×C101semidirect
517. C2×D8C2×C4×C101semidirect
523. #121C2×C4×C101semidirect
534. C4×D4D4×C101semidirect
535. C4×D4D4×C101semidirect
574. #102C2×C4×C101semidirect
575. #102C2×C4×C101semidirect
577. C22⋊C8C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1012
C2×#447×C1012
C2×#442×C1012
C2×C4×D8×C1012
C101×#23242
C101×#18792
C101×#18752
C101×#18642
C101×#18622
C101×#18542
C101×#17862
C101×#17622
C4×#102×C1012
C101×#17502
#21458101