Finite Group Databasebeta

← C101×#25076 #38807227

Subgroups — C101×#25076 #38807227

Order 25856.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C101C211yesmaximal, characteristic, complemented
2C2×#459×C101C211yesmaximal, characteristic, complemented
3C2×#447×C101C211yesmaximal, characteristic, complemented
4C22×#102×C101C211yesmaximal, characteristic, complemented
5C101×#2433C211yesmaximal, characteristic, complemented
6C101×#2361C211yesmaximal, characteristic, complemented
7C101×#2067C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2041C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1982C211yesmaximal, characteristic, complemented
12C101×#1925C211yesmaximal, characteristic, complemented
13C101×#1879C211yesmaximal, characteristic, complemented
14C101×#1874C211yesmaximal, characteristic, complemented
15C101×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic, complemented
20C23×C8×C101C2211yescharacteristic
21C2×#127×C101C2211yescharacteristic
22C2×#127×C101C2211yescharacteristic
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#120×C101—21no—
26C2×#120×C101—21no—
27C2×C4×D4×C101—21no—
28C2×C4×D4×C101C2211yescharacteristic, complemented
29C22×C4⋊C4×C101C2211yescharacteristic
30#466×C101—24no—
31#459×C101—24no—
32#447×C101—24no—
33C2×#107×C101C2211yescharacteristic, complemented
34C2×C4⋊C8×C101C2211yescharacteristic, complemented
35C2×C4⋊C8×C101C2211yescharacteristic, complemented
36C2×#102×C101—24no—
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic, complemented
44C2×#102×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic, complemented
46C2×#102×C101C2211yescharacteristic, complemented
47C2×C22⋊C8×C101C2211yescharacteristic
48#392×C101—21no—
49#392×C101—21no—
50#390×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic, complemented
53#389×C101C2211yescharacteristic, complemented
54#388×C101—21no—
55#386×C101—21no—
56#385×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×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—22no—
69C22×D4×C101—21no—
70C22×D4×C101—21no—
71C22×D4×C101—21no—
72C22×D4×C101—21no—
73C22×D4×C101—21no—
74C22×D4×C101—22no—
75C22×D4×C101—41no—
76C22×D4×C101—41no—
77C22×D4×C101C2311yescharacteristic
78C22×D4×C101C2311yescharacteristic
79C22×D4×C101C2311yescharacteristic
80C22×D4×C101C2311yescharacteristic
81C23×C4×C101—21no—
82C23×C4×C101—21no—
83C23×C4×C101C2311yescharacteristic
84C2×D8×C101—22no—
85C2×D8×C101—22no—
86C2×D8×C101—22no—
87C2×D8×C101—22no—
88C2×D8×C101—22no—
89C2×D8×C101—22no—
90C2×D8×C101—41no—
91C2×D8×C101—41no—
92C2×D8×C101—41no—
93C22×C8×C101—22no—
94C22×C8×C101—22no—
95C22×C8×C101—41no—
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22×C8×C101C2311yescharacteristic
100#127×C101—22no—
101#127×C101—22no—
102#127×C101—41no—
103#127×C101—41no—
104#121×C101—22no—
105#121×C101—22no—
106#121×C101—22no—
107#121×C101D414yescomplemented
108#120×C101—44no—
109#120×C101—44no—
110C4×D4×C101—22no—
111C4×D4×C101—41no—
112C4×D4×C101—44no—
113C2×C4⋊C4×C101—22no—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—41no—
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
120C2×C4⋊C4×C101C2311yescharacteristic
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
134C2×C42×C101C2311yescharacteristic
135#107×C101—22no—
136C4⋊C8×C101—22no—
137C4⋊C8×C101—41no—
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×C101—22no—
145#102×C101—22no—
146#102×C101—41no—
147#102×C101D414yescomplemented
148C22⋊C8×C101—22no—
149#95×C101—21no—
150#95×C101—21no—
151#95×C101D411yescharacteristic
152#95×C101D411yescharacteristic
153C24×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101—21no—
157C24×C101—42no—
158C24×C101—42no—
159C24×C101—42no—
160C24×C101—42no—
161C24×C101—42no—
162C24×C101—81no—
163C24×C101—81no—
164C24×C101C2×D411yescharacteristic
165C2×D4×C101—28no—
166C2×D4×C101—24no—
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—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—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—44no—
189C2×D4×C101—44no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—44no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—42no—
196C2×D4×C101—42no—
197C2×D4×C101—42no—
198C2×D4×C101—42no—
199C2×D4×C101—42no—
200C2×D4×C101—42no—
201C2×D4×C101—42no—
202C2×D4×C101—42no—
203C2×D4×C101—42no—
204C2×D4×C101—42no—
205C2×D4×C101—42no—
206C2×D4×C101—42no—
207C2×D4×C101—81no—
208C2×D4×C101—81no—
209C2×D4×C101—81no—
210C2×D4×C101—81no—
211C2×D4×C101C2×D412yes—
212C2×D4×C101C2×D412yes—
213C2×D4×C101#4112yes—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—42no—
223C22×C4×C101—42no—
224C22×C4×C101—42no—
225C22×C4×C101—42no—
226C22×C4×C101—81no—
227C22×C4×C101—81no—
228C22×C4×C101C2×D411yescharacteristic
229C22×C4×C101C2×D411yescharacteristic
230C22×C4×C101C2×D411yescharacteristic
231C22×C4×C101C2×D412yes—
232C22×C4×C101C2×D411yescharacteristic
233C22×C4×C101C2×D411yescharacteristic
234C22×C4×C101#4112yes—
235C22×C4×C101C2411yescharacteristic
236D8×C101—44no—
237D8×C101—44no—
238D8×C101—44no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C2×C8×C101—21no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—21no—
248C2×C8×C101—21no—
249C2×C8×C101—21no—
250C2×C8×C101—44no—
251C2×C8×C101C2×D412yes—
252C4⋊C4×C101—21no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—21no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—42no—
259C4⋊C4×C101—42no—
260C4⋊C4×C101C2×D412yes—
261C4⋊C4×C101C2×D412yes—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—24no—
264C22⋊C4×C101—42no—
265C22⋊C4×C101—42no—
266C22⋊C4×C101—42no—
267C22⋊C4×C101—42no—
268C22⋊C4×C101—42no—
269C22⋊C4×C101—42no—
270C22⋊C4×C101—42no—
271C22⋊C4×C101—81no—
272C22⋊C4×C101D814yescomplemented
273C42×C101—21no—
274C42×C101—21no—
275C42×C101—21no—
276C42×C101—21no—
277C42×C101—42no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101—22no—
283C23×C101—22no—
284C23×C101—22no—
285C23×C101—48no—
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—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101—41no—
302C23×C101—41no—
303C23×C101—41no—
304C23×C101—41no—
305C23×C101—41no—
306C23×C101—41no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—84no—
312C23×C101—84no—
313C23×C101—84no—
314C23×C101—84no—
315C23×C101—84no—
316C23×C101—84no—
317C23×C101#12112yes—
318C23×C101C2×D812yes—
319C23×C101AGL(1,ℤ/8)12yes—
320C23×C101C22×D411yescharacteristic
321D4×C101—22no—
322D4×C101—22no—
323D4×C101—22no—
324D4×C101—22no—
325D4×C101—22no—
326D4×C101—22no—
327D4×C101—48no—
328D4×C101—48no—
329D4×C101—41no—
330D4×C101—41no—
331D4×C101—41no—
332D4×C101—41no—
333D4×C101—41no—
334D4×C101—41no—
335D4×C101—41no—
336D4×C101—41no—
337D4×C101—41no—
338D4×C101—41no—
339D4×C101—84no—
340D4×C101—84no—
341D4×C101—84no—
342D4×C101—84no—
343D4×C101—84no—
344C2×C4×C101—21no—
345C2×C4×C101—21no—
346C2×C4×C101—21no—
347C2×C4×C101—21no—
348C2×C4×C101—21no—
349C2×C4×C101—21no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—21no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101—41no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—84no—
373C2×C4×C101—84no—
374C2×C4×C101#12112yes—
375C2×C4×C101C2×D812yes—
376C2×C4×C101C2×D812yes—
377C2×C4×C101C22×D411yescharacteristic
378C2×C4×C101C22×D411yescharacteristic
379C2×C4×C101C2×#4111yescharacteristic
380C2×C4×C101C2×#4111yescharacteristic
381C2×C4×C101H(5,𝔽2)11yescharacteristic
382C2×C4×C101H(5,𝔽2)11yescharacteristic
383C8×C101—22no—
384C8×C101—41no—
385C8×C101—41no—
386C8×C101—41no—
387C22×C101—22no—
388C22×C101—22no—
389C22×C101—22no—
390C22×C101—22no—
391C22×C101—22no—
392C22×C101—22no—
393C22×C101—42no—
394C22×C101—42no—
395C22×C101—42no—
396C22×C101—42no—
397C22×C101—42no—
398C22×C101—42no—
399C22×C101—42no—
400C22×C101—42no—
401C22×C101—42no—
402C22×C101—816no—
403C22×C101—81no—
404C22×C101—81no—
405C22×C101—81no—
406C22×C101—81no—
407C22×C101—81no—
408C22×C101—81no—
409C22×C101—81no—
410C22×C101—81no—
411C22×C101—81no—
412C22×C101—81no—
413C22×C101—81no—
414C22×C101—81no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101#45914yescomplemented
423C22×C101C2×#12111yescharacteristic
424C22×C101D4211yescharacteristic
425C22×C101#54611yescharacteristic
426C22×C101C22×D811yescharacteristic
427C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C101#57611yescharacteristic
429C22×C101#57711yescharacteristic
430C4×C101—22no—
431C4×C101—22no—
432C4×C101—22no—
433C4×C101—41no—
434C4×C101—42no—
435C4×C101—42no—
436C4×C101—41no—
437C4×C101—81no—
438C4×C101—81no—
439C4×C101#52511yescharacteristic
440C4×C101#53811yescharacteristic
441C4×C101D4211yescharacteristic
442C4×C101#54611yescharacteristic
443#25076C10111yesmaximal, characteristic, direct product factor, Sylow
444C2×C101—24no—
445C2×C101—82no—
446C2×C101—82no—
447C2×C101—82no—
448C2×C101—161no—
449C2×C101#242411yescharacteristic
450C2×C101C2×#45911yescharacteristic
451C2×C101#304511yescharacteristic
452C2×C101#326511yescharacteristic
453C2×C101D4×D811yescharacteristic
454C2×C101#329411yescharacteristic
455C2×C101#331811yescharacteristic
456C2×#466C2×C10111yescharacteristic, complemented
457C2×#459C2×C10111yescharacteristic, complemented
458C2×#447C2×C10111yescharacteristic, complemented
459C22×#102C2×C10111yescharacteristic, complemented
460#2433C2×C10111yescharacteristic, complemented
461#2361C2×C10111yescharacteristic, complemented
462#2067C2×C10111yescharacteristic, complemented
463#2054C2×C10111yescharacteristic, complemented
464#2041C2×C10111yescharacteristic, complemented
465#2011C2×C10111yescharacteristic, complemented
466#1982C2×C10111yescharacteristic, complemented
467#1925C2×C10111yescharacteristic, complemented
468#1879C2×C10111yescharacteristic, complemented
469#1874C2×C10111yescharacteristic, complemented
470#1850C2×C10111yescharacteristic, complemented
471C101#2507611yescharacteristic, direct product factor, Sylow
472C23×D4C22×C10111yescharacteristic
473C22×D8C22×C10111yescharacteristic
474C22×D8C22×C10111yescharacteristic
475C22×D8C22×C10111yescharacteristic, complemented
476C23×C8C22×C10111yescharacteristic
477C2×#127C22×C10111yescharacteristic
478C2×#127C22×C10111yescharacteristic
479C2×#121C22×C10111yescharacteristic
480C2×#121C22×C10111yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C10111yescharacteristic, complemented
485C22×C4⋊C4C22×C10111yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C10111yescharacteristic, complemented
490C2×C4⋊C8C22×C10111yescharacteristic, complemented
491C2×C4⋊C8C22×C10111yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C10111yescharacteristic
494C2×#102C22×C10111yescharacteristic
495C2×#102C22×C10111yescharacteristic
496C2×#102C22×C10111yescharacteristic
497C2×#102C22×C10111yescharacteristic
498C2×#102C22×C10111yescharacteristic
499C2×#102C22×C10111yescharacteristic, complemented
500C2×#102C22×C10111yescharacteristic, complemented
501C2×#102C22×C10111yescharacteristic, complemented
502C2×#102C22×C10111yescharacteristic, complemented
503C2×C22⋊C8C22×C10111yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C10111yescharacteristic
507#390C22×C10111yescharacteristic
508#390C22×C10111yescharacteristic, complemented
509#389C22×C10111yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C10111yescharacteristic, complemented
514C4×C22⋊C4C22×C10111yescharacteristic
515#340C22×C10111yescharacteristic, complemented
516#340C22×C10111yescharacteristic, complemented
517#336C22×C10111yescharacteristic, complemented
518#336C22×C10111yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C10111yescharacteristic
534C22×D4C23×C10111yescharacteristic
535C22×D4C23×C10111yescharacteristic
536C22×D4C23×C10111yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C10111yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C10111yescharacteristic
553C22×C8C23×C10111yescharacteristic
554C22×C8C23×C10111yescharacteristic
555C22×C8C23×C10111yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C10114yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C10111yescharacteristic
574C2×C4⋊C4C23×C10111yescharacteristic
575C2×C4⋊C4C23×C10111yescharacteristic
576C2×C4⋊C4C23×C10111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C10111yescharacteristic
587C2×C22⋊C4D4×C10111yescharacteristic
588C2×C42—21no—
589C2×C42C23×C10111yescharacteristic
590C2×C42C23×C10111yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C10114yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C10111yescharacteristic
608#95D4×C10111yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C10111yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C10112yes—
668C2×D4C2×D4×C10112yes—
669C2×D4#41×C10112yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C10111yescharacteristic
685C22×C4C2×D4×C10111yescharacteristic
686C22×C4C2×D4×C10111yescharacteristic
687C22×C4C2×D4×C10112yes—
688C22×C4C2×D4×C10111yescharacteristic
689C22×C4C2×D4×C10111yescharacteristic
690C22×C4#41×C10112yes—
691C22×C4C24×C10111yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C10112yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C10112yes—
717C4⋊C4C2×D4×C10112yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C10114yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C10112yes—
774C23C2×D8×C10112yes—
775C23AGL(1,ℤ/8)×C10112yes—
776C23C22×D4×C10111yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C10112yes—
831C2×C4C2×D8×C10112yes—
832C2×C4C2×D8×C10112yes—
833C2×C4C22×D4×C10111yescharacteristic
834C2×C4C22×D4×C10111yescharacteristic
835C2×C4C2×#41×C10111yescharacteristic
836C2×C4C2×#41×C10111yescharacteristic
837C2×C4H(5,𝔽2)×C10111yescharacteristic
838C2×C4H(5,𝔽2)×C10111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C10114yescomplemented
879C22C2×#121×C10111yescharacteristic
880C22D42×C10111yescharacteristic
881C22#546×C10111yescharacteristic
882C22C22×D8×C10111yescharacteristic
883C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
884C22#576×C10111yescharacteristic
885C22#577×C10111yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4#525×C10111yescharacteristic
896C4#538×C10111yescharacteristic
897C4D42×C10111yescharacteristic
898C4#546×C10111yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C101×#242411yescharacteristic
905C2C2×#459×C10111yescharacteristic
906C2C101×#304511yescharacteristic
907C2C101×#326511yescharacteristic
908C2D4×D8×C10111yescharacteristic
909C2C101×#329411yescharacteristic
910C2C101×#331811yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
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×#466×C101C2semidirect
2. C2×#459×C101C2semidirect
3. C2×#447×C101C2semidirect
4. C22×#102×C101C2semidirect
5. C101×#2433C2semidirect
6. C101×#2361C2semidirect
7. C101×#2067C2semidirect
8. C101×#2054C2semidirect
9. C101×#2041C2semidirect
10. C101×#2011C2semidirect
11. C101×#1982C2semidirect
12. C101×#1925C2semidirect
13. C101×#1879C2semidirect
14. C101×#1874C2semidirect
15. C101×#1850C2semidirect
19. C22×D8×C101C22semidirect
28. C2×C4×D4×C101C22semidirect
33. C2×#107×C101C22semidirect
34. C2×C4⋊C8×C101C22semidirect
35. C2×C4⋊C8×C101C22semidirect
43. C2×#102×C101C22semidirect
44. C2×#102×C101C22semidirect
45. C2×#102×C101C22semidirect
46. C2×#102×C101C22semidirect
52. #390×C101C22semidirect
53. #389×C101C22semidirect
57. C4×C4⋊C4×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #336×C101C22semidirect
62. #336×C101C22semidirect
107. #121×C101D4semidirect
147. #102×C101D4semidirect
272. C22⋊C4×C101D8semidirect
422. C22×C101#459semidirect
443. #25076C101direct (N × H)
456. C2×#466C2×C101semidirect
457. C2×#459C2×C101semidirect
458. C2×#447C2×C101semidirect
459. C22×#102C2×C101semidirect
460. #2433C2×C101semidirect
461. #2361C2×C101semidirect
462. #2067C2×C101semidirect
463. #2054C2×C101semidirect
464. #2041C2×C101semidirect
465. #2011C2×C101semidirect
466. #1982C2×C101semidirect
467. #1925C2×C101semidirect
468. #1879C2×C101semidirect
469. #1874C2×C101semidirect
470. #1850C2×C101semidirect
471. C101#25076direct (N × H)
475. C22×D8C22×C101semidirect
484. C2×C4×D4C22×C101semidirect
489. C2×#107C22×C101semidirect
490. C2×C4⋊C8C22×C101semidirect
491. C2×C4⋊C8C22×C101semidirect
499. C2×#102C22×C101semidirect
500. C2×#102C22×C101semidirect
501. C2×#102C22×C101semidirect
502. C2×#102C22×C101semidirect
508. #390C22×C101semidirect
509. #389C22×C101semidirect
513. C4×C4⋊C4C22×C101semidirect
515. #340C22×C101semidirect
516. #340C22×C101semidirect
517. #336C22×C101semidirect
518. #336C22×C101semidirect
563. #121D4×C101semidirect
603. #102D4×C101semidirect
728. C22⋊C4D8×C101semidirect
878. C22#459×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1012
C2×#459×C1012
C2×#447×C1012
C22×#102×C1012
C101×#24332
C101×#23612
C101×#20672
C101×#20542
C101×#20412
C101×#20112
C101×#19822
C101×#19252
C101×#18792
C101×#18742
C101×#18502
#25076101