Finite Group Databasebeta

← C101×#25401 #38807552

Subgroups — C101×#25401 #38807552

Order 25856.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C101C211yesmaximal, characteristic, complemented
2C2×#465×C101C211yesmaximal, characteristic, complemented
3C2×#463×C101C211yesmaximal, characteristic, complemented
4C2×#435×C101C211yesmaximal, characteristic, complemented
5C101×#2540C211yesmaximal, characteristic, complemented
6C101×#2537C211yesmaximal, characteristic, complemented
7C101×#2035C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1959C211yesmaximal, characteristic, complemented
12C101×#1948C211yesmaximal, characteristic, complemented
13C101×#1894C211yesmaximal, characteristic, complemented
14C101×#1893C211yesmaximal, characteristic, complemented
15C101×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×#124×C101C2211yescharacteristic
21C2×C22⋊Q8×C101C2211yescharacteristic
22C2×C22⋊Q8×C101C2211yescharacteristic
23C2×#121×C101—21no—
24C2×#121×C101C2211yescharacteristic
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×D4×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30#469×C101—24no—
31#465×C101—24no—
32#463×C101—24no—
33#435×C101—24no—
34C2×#106×C101C2211yescharacteristic
35C2×#106×C101C2211yescharacteristic
36C2×C4⋊C8×C101C2211yescharacteristic
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×#97×C101C2211yescharacteristic
48#399×C101—21no—
49#394×C101—21no—
50#394×C101—21no—
51#392×C101—21no—
52#390×C101—21no—
53#390×C101—21no—
54#384×C101C2211yescharacteristic
55#380×C101—21no—
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58C4×C4⋊C4×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×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C2×SD16×C101—22no—
75C2×SD16×C101—22no—
76C2×SD16×C101—41no—
77C2×D8×C101—22no—
78C2×D8×C101—22no—
79C2×D8×C101—41no—
80C2×M16×C101—22no—
81C2×M16×C101—22no—
82C2×M16×C101—41no—
83C22×C8×C101—22no—
84C22×C8×C101—22no—
85C22×C8×C101—41no—
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90#124×C101—22no—
91#124×C101—22no—
92C22⋊Q8×C101—22no—
93C22⋊Q8×C101—22no—
94C22⋊Q8×C101—41no—
95C22⋊Q8×C101—41no—
96#121×C101—22no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—41no—
101#121×C101—41no—
102#121×C101—41no—
103#121×C101—41no—
104#121×C101—44no—
105C4×D4×C101—22no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108C4×D4×C101—22no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101D411yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C42×C101—21no—
133C2×C42×C101C2311yescharacteristic
134#106×C101—22no—
135#106×C101—22no—
136C4⋊C8×C101D414yescomplemented
137#103×C101—22no—
138#103×C101—22no—
139#103×C101—41no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—41no—
144#102×C101D414yescomplemented
145C22⋊C8×C101—22no—
146C22⋊C8×C101—22no—
147#97×C101—22no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101C2×D411yescharacteristic
154C24×C101C2×D411yescharacteristic
155C2×Q8×C101—21no—
156C2×Q8×C101—21no—
157C2×Q8×C101—21no—
158C2×Q8×C101—21no—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×D4×C101—22no—
162C2×D4×C101—22no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
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—41no—
175C2×D4×C101—42no—
176C2×D4×C101—42no—
177C2×D4×C101—42no—
178C2×D4×C101—42no—
179C2×D4×C101—42no—
180C2×D4×C101—42no—
181C2×D4×C101—42no—
182C2×D4×C101—42no—
183C2×D4×C101—81no—
184C2×D4×C101—81no—
185C2×D4×C101—81no—
186C2×D4×C101—81no—
187C2×D4×C101C2×D412yes—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
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—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—42no—
207C22×C4×C101—42no—
208C22×C4×C101—42no—
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D411yescharacteristic
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2411yescharacteristic
214SD16×C101—44no—
215D8×C101—44no—
216M16×C101—44no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—44no—
227C2×C8×C101C2×D412yes—
228C2×C8×C101C2×D412yes—
229C2×C8×C101C2×D412yes—
230C4⋊C4×C101—22no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—42no—
240C4⋊C4×C101—42no—
241C4⋊C4×C101—42no—
242C4⋊C4×C101—81no—
243C4⋊C4×C101C2×D412yes—
244C4⋊C4×C101#4112yes—
245C22⋊C4×C101—22no—
246C22⋊C4×C101—22no—
247C22⋊C4×C101—42no—
248C22⋊C4×C101—42no—
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—42no—
257C22⋊C4×C101—42no—
258C42×C101—81no—
259C42×C101C2×D412yes—
260C42×C101#4112yes—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—22no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
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×C101AGL(1,ℤ/8)12yes—
289C23×C101C22×D411yescharacteristic
290Q8×C101—41no—
291Q8×C101—41no—
292Q8×C101—41no—
293Q8×C101—41no—
294D4×C101—22no—
295D4×C101—22no—
296D4×C101—44no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—84no—
304D4×C101—84no—
305D4×C101—84no—
306D4×C101—84no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—22no—
315C2×C4×C101—21no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
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—84no—
344C2×C4×C101#12112yes—
345C2×C4×C101#12112yes—
346C2×C4×C101C22×D411yescharacteristic
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C2×#4111yescharacteristic
349C2×C4×C101C2×#4111yescharacteristic
350C2×C4×C101H(5,𝔽2)11yescharacteristic
351C2×C4×C101H(5,𝔽2)11yescharacteristic
352C8×C101—22no—
353C8×C101—22no—
354C8×C101—22no—
355C8×C101—41no—
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—42no—
365C22×C101—41no—
366C22×C101—42no—
367C22×C101—41no—
368C22×C101—42no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101C2×#12111yescharacteristic
385C22×C101D4211yescharacteristic
386C22×C101#54611yescharacteristic
387C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C101#57511yescharacteristic
389C22×C101#57711yescharacteristic
390C22×C101#57711yescharacteristic
391C4×C101—22no—
392C4×C101—22no—
393C4×C101—41no—
394C4×C101—41no—
395C4×C101—42no—
396C4×C101—42no—
397C4×C101—81no—
398C4×C101—81no—
399C4×C101—81no—
400C4×C101—81no—
401C4×C101#53211yescharacteristic
402C4×C101#54011yescharacteristic
403C4×C101D4211yescharacteristic
404C4×C101#55011yescharacteristic
405#25401C10111yesmaximal, characteristic, direct product factor, Sylow
406C2×C101—42no—
407C2×C101—81no—
408C2×C101—82no—
409C2×C101—161no—
410C2×C101#242811yescharacteristic
411C2×C101#305511yescharacteristic
412C2×C101#306011yescharacteristic
413C2×C101#326511yescharacteristic
414C2×C101#326711yescharacteristic
415C2×C101#330611yescharacteristic
416C2×C101#332111yescharacteristic
417C2×#469C2×C10111yescharacteristic, complemented
418C2×#465C2×C10111yescharacteristic, complemented
419C2×#463C2×C10111yescharacteristic, complemented
420C2×#435C2×C10111yescharacteristic, complemented
421#2540C2×C10111yescharacteristic, complemented
422#2537C2×C10111yescharacteristic, complemented
423#2035C2×C10111yescharacteristic, complemented
424#2034C2×C10111yescharacteristic, complemented
425#2000C2×C10111yescharacteristic, complemented
426#1999C2×C10111yescharacteristic, complemented
427#1959C2×C10111yescharacteristic, complemented
428#1948C2×C10111yescharacteristic, complemented
429#1894C2×C10111yescharacteristic, complemented
430#1893C2×C10111yescharacteristic, complemented
431#1762C2×C10111yescharacteristic, complemented
432C101#2540111yescharacteristic, direct product factor, Sylow
433C22×SD16C22×C10111yescharacteristic
434C22×D8C22×C10111yescharacteristic
435C22×M16C22×C10111yescharacteristic
436C23×C8C22×C10111yescharacteristic
437C2×#124C22×C10111yescharacteristic
438C2×C22⋊Q8C22×C10111yescharacteristic
439C2×C22⋊Q8C22×C10111yescharacteristic
440C2×#121—21no—
441C2×#121C22×C10111yescharacteristic
442C2×#121C22×C10111yescharacteristic
443C2×#121C22×C10111yescharacteristic
444C2×#121C22×C10111yescharacteristic
445C2×C4×D4C22×C10111yescharacteristic
446C2×C4×D4C22×C10111yescharacteristic
447#469—24no—
448#465—24no—
449#463—24no—
450#435—24no—
451C2×#106C22×C10111yescharacteristic
452C2×#106C22×C10111yescharacteristic
453C2×C4⋊C8C22×C10111yescharacteristic
454C2×#103C22×C10111yescharacteristic
455C2×#103C22×C10111yescharacteristic
456C2×#103C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×#102C22×C10111yescharacteristic
459C2×#102C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×#102C22×C10111yescharacteristic
462C2×C22⋊C8C22×C10111yescharacteristic
463C2×C22⋊C8C22×C10111yescharacteristic
464C2×#97C22×C10111yescharacteristic
465#399—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#390—21no—
470#390—21no—
471#384C22×C10111yescharacteristic
472#380—21no—
473#380C22×C10111yescharacteristic
474#380C22×C10111yescharacteristic
475C4×C4⋊C4C22×C10111yescharacteristic
476#340C22×C10111yescharacteristic
477#340C22×C10111yescharacteristic
478#340C22×C10111yescharacteristic
479#340C22×C10111yescharacteristic
480C22×Q8C23×C10111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C10111yescharacteristic
486C22×D4C23×C10111yescharacteristic
487C22×D4C23×C10111yescharacteristic
488C23×C4—21no—
489C23×C4C23×C10111yescharacteristic
490C23×C4C23×C10111yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C10111yescharacteristic
504C22×C8C23×C10111yescharacteristic
505C22×C8C23×C10111yescharacteristic
506C22×C8C23×C10111yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C10111yescharacteristic
531C2×C4⋊C4C23×C10111yescharacteristic
532C2×C4⋊C4C23×C10111yescharacteristic
533C2×C4⋊C4C23×C10111yescharacteristic
534C2×C4⋊C4C23×C10111yescharacteristic
535C2×C4⋊C4C23×C10111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C10111yescharacteristic
548C2×C22⋊C4D4×C10111yescharacteristic
549C2×C42—21no—
550C2×C42C23×C10111yescharacteristic
551#106—22no—
552#106—22no—
553C4⋊C8D4×C10114yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C10114yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C10111yescharacteristic
571C24C2×D4×C10111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C10112yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C10111yescharacteristic
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629C22×C4C2×D4×C10111yescharacteristic
630C22×C4C24×C10111yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C10112yes—
645C2×C8C2×D4×C10112yes—
646C2×C8C2×D4×C10112yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C10112yes—
661C4⋊C4#41×C10112yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C10112yes—
677C42#41×C10112yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C10112yes—
706C23C22×D4×C10111yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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—84no—
761C2×C4#121×C10112yes—
762C2×C4#121×C10112yes—
763C2×C4C22×D4×C10111yescharacteristic
764C2×C4C22×D4×C10111yescharacteristic
765C2×C4C2×#41×C10111yescharacteristic
766C2×C4C2×#41×C10111yescharacteristic
767C2×C4H(5,𝔽2)×C10111yescharacteristic
768C2×C4H(5,𝔽2)×C10111yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C10111yescharacteristic
802C22D42×C10111yescharacteristic
803C22#546×C10111yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
805C22#575×C10111yescharacteristic
806C22#577×C10111yescharacteristic
807C22#577×C10111yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#532×C10111yescharacteristic
819C4#540×C10111yescharacteristic
820C4D42×C10111yescharacteristic
821C4#550×C10111yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C101×#242811yescharacteristic
827C2C101×#305511yescharacteristic
828C2C101×#306011yescharacteristic
829C2C101×#326511yescharacteristic
830C2C101×#326711yescharacteristic
831C2C101×#330611yescharacteristic
832C2C101×#332111yescharacteristic
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×#469×C101C2semidirect
2. C2×#465×C101C2semidirect
3. C2×#463×C101C2semidirect
4. C2×#435×C101C2semidirect
5. C101×#2540C2semidirect
6. C101×#2537C2semidirect
7. C101×#2035C2semidirect
8. C101×#2034C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1959C2semidirect
12. C101×#1948C2semidirect
13. C101×#1894C2semidirect
14. C101×#1893C2semidirect
15. C101×#1762C2semidirect
136. C4⋊C8×C101D4semidirect
144. #102×C101D4semidirect
405. #25401C101direct (N × H)
417. C2×#469C2×C101semidirect
418. C2×#465C2×C101semidirect
419. C2×#463C2×C101semidirect
420. C2×#435C2×C101semidirect
421. #2540C2×C101semidirect
422. #2537C2×C101semidirect
423. #2035C2×C101semidirect
424. #2034C2×C101semidirect
425. #2000C2×C101semidirect
426. #1999C2×C101semidirect
427. #1959C2×C101semidirect
428. #1948C2×C101semidirect
429. #1894C2×C101semidirect
430. #1893C2×C101semidirect
431. #1762C2×C101semidirect
432. C101#25401direct (N × H)
553. C4⋊C8D4×C101semidirect
561. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1012
C2×#465×C1012
C2×#463×C1012
C2×#435×C1012
C101×#25402
C101×#25372
C101×#20352
C101×#20342
C101×#20002
C101×#19992
C101×#19592
C101×#19482
C101×#18942
C101×#18932
C101×#17622
#25401101