Finite Group Databasebeta

← C101×#25132 #38807283

Subgroups — C101×#25132 #38807283

Order 25856.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C101C211yesmaximal, characteristic, complemented
2C2×#447×C101C211yesmaximal, characteristic, complemented
3C2×#436×C101C211yesmaximal, characteristic, complemented
4C2×#418×C101C211yesmaximal, characteristic, complemented
5C101×#2414C211yesmaximal, characteristic, complemented
6C101×#2408C211yesmaximal, characteristic, complemented
7C101×#2065C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2033C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1970C211yesmaximal, characteristic, complemented
12C101×#1934C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1895C211yesmaximal, characteristic, complemented
15C101×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C22×M16×C101C2211yescharacteristic, complemented
21C2×#121×C101C2211yescharacteristic
22C2×#121×C101C2211yescharacteristic
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic, complemented
25C2×#120×C101—21no—
26C2×C4×D4×C101C2211yescharacteristic
27C2×#117×C101C2211yescharacteristic
28#469×C101—24no—
29#447×C101—24no—
30#436×C101—24no—
31C2×#107×C101C2211yescharacteristic, complemented
32C2×#106×C101C2211yescharacteristic, complemented
33C2×C4⋊C8×C101C2211yescharacteristic, complemented
34#418×C101—24no—
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic, complemented
42C2×#102×C101C2211yescharacteristic, complemented
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×C22⋊C8×C101C2211yescharacteristic, complemented
45C2×C4×C8×C101C2211yescharacteristic, complemented
46#394×C101—21no—
47#394×C101—21no—
48#392×C101—21no—
49#392×C101—21no—
50#390×C101—21no—
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#390×C101C2211yescharacteristic, complemented
54#389×C101C2211yescharacteristic, complemented
55#388×C101—21no—
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic, complemented
58#379×C101—21no—
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63C25×C101—21no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101—22no—
71C22×D4×C101—21no—
72C22×D4×C101—22no—
73C22×D4×C101—41no—
74C22×D4×C101—41no—
75C22×D4×C101D411yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C22×D4×C101C2311yescharacteristic
78C22×D4×C101C2311yescharacteristic
79C23×C4×C101C2311yescharacteristic
80C23×C4×C101C2311yescharacteristic
81C2×D8×C101—22no—
82C2×D8×C101—22no—
83C2×D8×C101—22no—
84C2×D8×C101—22no—
85C2×D8×C101—41no—
86C2×D8×C101—41no—
87C2×M16×C101—22no—
88C2×M16×C101—22no—
89C2×M16×C101—22no—
90C2×M16×C101—22no—
91C2×M16×C101—41no—
92C2×M16×C101—41no—
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
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—
104#121×C101—41no—
105#120×C101—44no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108#117×C101—22no—
109#117×C101—41no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101D411yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C22⋊C4×C101D411yescharacteristic
132C2×C42×C101—21no—
133C2×C42×C101C2311yescharacteristic
134#107×C101—41no—
135#106×C101—22no—
136C4⋊C8×C101—22no—
137#102×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—41no—
144#102×C101D414yescomplemented
145C22⋊C8×C101—22no—
146C22⋊C8×C101D414yescomplemented
147C4×C8×C101—22no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101—21no—
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
162C24×C101C2×D411yescharacteristic
163C2×D4×C101—28no—
164C2×D4×C101—22no—
165C2×D4×C101—22no—
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—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—44no—
183C2×D4×C101—44no—
184C2×D4×C101—41no—
185C2×D4×C101—42no—
186C2×D4×C101—42no—
187C2×D4×C101—44no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—42no—
193C2×D4×C101—42no—
194C2×D4×C101—42no—
195C2×D4×C101—42no—
196C2×D4×C101—81no—
197C2×D4×C101—81no—
198C2×D4×C101—81no—
199C2×D4×C101—81no—
200C2×D4×C101—81no—
201C2×D4×C101C2×D412yes—
202C2×D4×C101#4112yes—
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—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—21no—
214C22×C4×C101—21no—
215C22×C4×C101—21no—
216C22×C4×C101—21no—
217C22×C4×C101—21no—
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D412yes—
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101#4112yes—
224C22×C4×C101C2411yescharacteristic
225D8×C101—44no—
226D8×C101—44no—
227M16×C101—44no—
228M16×C101—44no—
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×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101C2×D412yes—
239C2×C8×C101C2×D412yes—
240C2×C8×C101C2×D412yes—
241C4⋊C4×C101—22no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—81no—
252C4⋊C4×C101C2×D412yes—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—22no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—42no—
258C22⋊C4×C101—42no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—42no—
261C22⋊C4×C101—42no—
262C22⋊C4×C101—42no—
263C22⋊C4×C101—42no—
264C22⋊C4×C101—81no—
265C22⋊C4×C101—81no—
266C22⋊C4×C101—81no—
267C22⋊C4×C101—81no—
268C42×C101—21no—
269C42×C101—21no—
270C42×C101—42no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—22no—
279C23×C101—21no—
280C23×C101—22no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—48no—
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—84no—
307C23×C101—84no—
308C23×C101—84no—
309C23×C101—84no—
310C23×C101—84no—
311C23×C101—84no—
312C23×C101#12112yes—
313C23×C101C22×D411yescharacteristic
314D4×C101—22no—
315D4×C101—22no—
316D4×C101—22no—
317D4×C101—22no—
318D4×C101—44no—
319D4×C101—48no—
320D4×C101—41no—
321D4×C101—41no—
322D4×C101—41no—
323D4×C101—41no—
324D4×C101—41no—
325D4×C101—41no—
326D4×C101—41no—
327D4×C101—41no—
328D4×C101—84no—
329D4×C101—84no—
330D4×C101—84no—
331D4×C101—84no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—22no—
337C2×C4×C101—22no—
338C2×C4×C101—22no—
339C2×C4×C101—22no—
340C2×C4×C101—21no—
341C2×C4×C101—21no—
342C2×C4×C101—22no—
343C2×C4×C101—21no—
344C2×C4×C101—21no—
345C2×C4×C101—21no—
346C2×C4×C101—21no—
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—41no—
354C2×C4×C101—41no—
355C2×C4×C101—41no—
356C2×C4×C101—41no—
357C2×C4×C101—41no—
358C2×C4×C101—41no—
359C2×C4×C101—41no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101#12112yes—
366C2×C4×C101AGL(1,ℤ/8)12yes—
367C2×C4×C101C22×D411yescharacteristic
368C2×C4×C101C22×D411yescharacteristic
369C2×C4×C101C2×#4111yescharacteristic
370C2×C4×C101C2×#4111yescharacteristic
371C2×C4×C101H(5,𝔽2)11yescharacteristic
372C2×C4×C101H(5,𝔽2)11yescharacteristic
373C8×C101—22no—
374C8×C101—22no—
375C8×C101—22no—
376C8×C101—41no—
377C22×C101—22no—
378C22×C101—22no—
379C22×C101—22no—
380C22×C101—41no—
381C22×C101—41no—
382C22×C101—41no—
383C22×C101—41no—
384C22×C101—41no—
385C22×C101—42no—
386C22×C101—42no—
387C22×C101—41no—
388C22×C101—42no—
389C22×C101—41no—
390C22×C101—42no—
391C22×C101—41no—
392C22×C101—41no—
393C22×C101—41no—
394C22×C101—42no—
395C22×C101—41no—
396C22×C101—42no—
397C22×C101—816no—
398C22×C101—81no—
399C22×C101—81no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—81no—
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×C101C2×#12111yescharacteristic
414C22×C101D4211yescharacteristic
415C22×C101#54611yescharacteristic
416C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C101#57511yescharacteristic
418C22×C101#57611yescharacteristic
419C22×C101#57611yescharacteristic
420C4×C101—22no—
421C4×C101—22no—
422C4×C101—41no—
423C4×C101—42no—
424C4×C101—41no—
425C4×C101—81no—
426C4×C101—81no—
427C4×C101—81no—
428C4×C101—81no—
429C4×C101#52511yescharacteristic
430C4×C101#53811yescharacteristic
431C4×C101D4211yescharacteristic
432C4×C101#54611yescharacteristic
433#25132C10111yesmaximal, characteristic, direct product factor, Sylow
434C2×C101—42no—
435C2×C101—81no—
436C2×C101—82no—
437C2×C101—82no—
438C2×C101—161no—
439C2×C101#242411yescharacteristic
440C2×C101#305511yescharacteristic
441C2×C101#305811yescharacteristic
442C2×C101#327311yescharacteristic
443C2×C101#327411yescharacteristic
444C2×C101#332211yescharacteristic
445C2×C101#332511yescharacteristic
446C2×#469C2×C10111yescharacteristic, complemented
447C2×#447C2×C10111yescharacteristic, complemented
448C2×#436C2×C10111yescharacteristic, complemented
449C2×#418C2×C10111yescharacteristic, complemented
450#2414C2×C10111yescharacteristic, complemented
451#2408C2×C10111yescharacteristic, complemented
452#2065C2×C10111yescharacteristic, complemented
453#2054C2×C10111yescharacteristic, complemented
454#2033C2×C10111yescharacteristic, complemented
455#1999C2×C10111yescharacteristic, complemented
456#1970C2×C10111yescharacteristic, complemented
457#1934C2×C10111yescharacteristic, complemented
458#1895C2×C10111yescharacteristic, complemented
459#1895C2×C10111yescharacteristic, complemented
460#1854C2×C10111yescharacteristic, complemented
461C101#2513211yescharacteristic, direct product factor, Sylow
462C23×D4C22×C10111yescharacteristic
463C22×D8C22×C10111yescharacteristic
464C22×D8C22×C10111yescharacteristic
465C22×M16C22×C10111yescharacteristic
466C22×M16C22×C10111yescharacteristic, complemented
467C2×#121C22×C10111yescharacteristic
468C2×#121C22×C10111yescharacteristic
469C2×#121C22×C10111yescharacteristic
470C2×#121C22×C10111yescharacteristic, complemented
471C2×#120—21no—
472C2×C4×D4C22×C10111yescharacteristic
473C2×#117C22×C10111yescharacteristic
474#469—24no—
475#447—24no—
476#436—24no—
477C2×#107C22×C10111yescharacteristic, complemented
478C2×#106C22×C10111yescharacteristic, complemented
479C2×C4⋊C8C22×C10111yescharacteristic, complemented
480#418—24no—
481C2×#102C22×C10111yescharacteristic
482C2×#102C22×C10111yescharacteristic
483C2×#102C22×C10111yescharacteristic
484C2×#102C22×C10111yescharacteristic
485C2×#102C22×C10111yescharacteristic
486C2×#102C22×C10111yescharacteristic
487C2×#102C22×C10111yescharacteristic, complemented
488C2×#102C22×C10111yescharacteristic, complemented
489C2×C22⋊C8C22×C10111yescharacteristic
490C2×C22⋊C8C22×C10111yescharacteristic, complemented
491C2×C4×C8C22×C10111yescharacteristic, complemented
492#394—21no—
493#394—21no—
494#392—21no—
495#392—21no—
496#390—21no—
497#390C22×C10111yescharacteristic
498#390C22×C10111yescharacteristic
499#390C22×C10111yescharacteristic, complemented
500#389C22×C10111yescharacteristic, complemented
501#388—21no—
502#380C22×C10111yescharacteristic
503#380C22×C10111yescharacteristic, complemented
504#379—21no—
505#340C22×C10111yescharacteristic, complemented
506#340C22×C10111yescharacteristic, complemented
507#340C22×C10111yescharacteristic, complemented
508#340C22×C10111yescharacteristic, complemented
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C10111yescharacteristic
522C22×D4C23×C10111yescharacteristic
523C22×D4C23×C10111yescharacteristic
524C22×D4C23×C10111yescharacteristic
525C23×C4C23×C10111yescharacteristic
526C23×C4C23×C10111yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C10111yescharacteristic
540C22×C8C23×C10111yescharacteristic
541C22×C8C23×C10111yescharacteristic
542C22×C8C23×C10111yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C10111yescharacteristic
558C2×C4⋊C4C23×C10111yescharacteristic
559C2×C4⋊C4C23×C10111yescharacteristic
560C2×C4⋊C4C23×C10111yescharacteristic
561C2×C4⋊C4C23×C10111yescharacteristic
562C2×C4⋊C4C23×C10111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C10111yescharacteristic
577C2×C22⋊C4D4×C10111yescharacteristic
578C2×C42—21no—
579C2×C42C23×C10111yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C10114yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C10114yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C10111yescharacteristic
608C24C2×D4×C10111yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C10112yes—
648C2×D4#41×C10112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C10111yescharacteristic
665C22×C4C2×D4×C10111yescharacteristic
666C22×C4C2×D4×C10111yescharacteristic
667C22×C4C2×D4×C10112yes—
668C22×C4C2×D4×C10111yescharacteristic
669C22×C4#41×C10112yes—
670C22×C4C24×C10111yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C10112yes—
685C2×C8C2×D4×C10112yes—
686C2×C8C2×D4×C10112yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C10112yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C10112yes—
759C23C22×D4×C10111yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C10112yes—
812C2×C4AGL(1,ℤ/8)×C10112yes—
813C2×C4C22×D4×C10111yescharacteristic
814C2×C4C22×D4×C10111yescharacteristic
815C2×C4C2×#41×C10111yescharacteristic
816C2×C4C2×#41×C10111yescharacteristic
817C2×C4H(5,𝔽2)×C10111yescharacteristic
818C2×C4H(5,𝔽2)×C10111yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—41no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C10111yescharacteristic
860C22D42×C10111yescharacteristic
861C22#546×C10111yescharacteristic
862C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
863C22#575×C10111yescharacteristic
864C22#576×C10111yescharacteristic
865C22#576×C10111yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4#525×C10111yescharacteristic
876C4#538×C10111yescharacteristic
877C4D42×C10111yescharacteristic
878C4#546×C10111yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2C101×#242411yescharacteristic
885C2C101×#305511yescharacteristic
886C2C101×#305811yescharacteristic
887C2C101×#327311yescharacteristic
888C2C101×#327411yescharacteristic
889C2C101×#332211yescharacteristic
890C2C101×#332511yescharacteristic
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×#447×C101C2semidirect
3. C2×#436×C101C2semidirect
4. C2×#418×C101C2semidirect
5. C101×#2414C2semidirect
6. C101×#2408C2semidirect
7. C101×#2065C2semidirect
8. C101×#2054C2semidirect
9. C101×#2033C2semidirect
10. C101×#1999C2semidirect
11. C101×#1970C2semidirect
12. C101×#1934C2semidirect
13. C101×#1895C2semidirect
14. C101×#1895C2semidirect
15. C101×#1854C2semidirect
20. C22×M16×C101C22semidirect
24. C2×#121×C101C22semidirect
31. C2×#107×C101C22semidirect
32. C2×#106×C101C22semidirect
33. C2×C4⋊C8×C101C22semidirect
41. C2×#102×C101C22semidirect
42. C2×#102×C101C22semidirect
44. C2×C22⋊C8×C101C22semidirect
45. C2×C4×C8×C101C22semidirect
53. #390×C101C22semidirect
54. #389×C101C22semidirect
57. #380×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
144. #102×C101D4semidirect
146. C22⋊C8×C101D4semidirect
433. #25132C101direct (N × H)
446. C2×#469C2×C101semidirect
447. C2×#447C2×C101semidirect
448. C2×#436C2×C101semidirect
449. C2×#418C2×C101semidirect
450. #2414C2×C101semidirect
451. #2408C2×C101semidirect
452. #2065C2×C101semidirect
453. #2054C2×C101semidirect
454. #2033C2×C101semidirect
455. #1999C2×C101semidirect
456. #1970C2×C101semidirect
457. #1934C2×C101semidirect
458. #1895C2×C101semidirect
459. #1895C2×C101semidirect
460. #1854C2×C101semidirect
461. C101#25132direct (N × H)
466. C22×M16C22×C101semidirect
470. C2×#121C22×C101semidirect
477. C2×#107C22×C101semidirect
478. C2×#106C22×C101semidirect
479. C2×C4⋊C8C22×C101semidirect
487. C2×#102C22×C101semidirect
488. C2×#102C22×C101semidirect
490. C2×C22⋊C8C22×C101semidirect
491. C2×C4×C8C22×C101semidirect
499. #390C22×C101semidirect
500. #389C22×C101semidirect
503. #380C22×C101semidirect
505. #340C22×C101semidirect
506. #340C22×C101semidirect
507. #340C22×C101semidirect
508. #340C22×C101semidirect
590. #102D4×C101semidirect
592. C22⋊C8D4×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×#447×C1012
C2×#436×C1012
C2×#418×C1012
C101×#24142
C101×#24082
C101×#20652
C101×#20542
C101×#20332
C101×#19992
C101×#19702
C101×#19342
C101×#18952
C101×#18542
#25132101