Finite Group Databasebeta

← C101×#22422 #38804573

Subgroups — C101×#22422 #38804573

Order 25856.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C101C211yesmaximal, characteristic
2C2×#435×C101C211yesmaximal, characteristic, complemented
3C2×#417×C101C211yesmaximal, characteristic, complemented
4C2×#416×C101C211yesmaximal, characteristic, complemented
5C101×#2352C211yesmaximal, characteristic, complemented
6C101×#1982C211yesmaximal, characteristic, complemented
7C101×#1961C211yesmaximal, characteristic, complemented
8C101×#1895C211yesmaximal, characteristic, complemented
9C101×#1893C211yesmaximal, characteristic, complemented
10C101×#1875C211yesmaximal, characteristic, complemented
11C101×#1874C211yesmaximal, characteristic, complemented
12C101×#1805C211yesmaximal, characteristic, complemented
13C101×#1788C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20#550×C101—24no—
21#550×C101C418yescomplemented
22C2×#127×C101—21no—
23C2×#127×C101C2211yescharacteristic
24C2×#121×C101—21no—
25C2×#121×C101—21no—
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×Q8×C101C2211yescharacteristic
29C2×C4×D4×C101—21no—
30C2×C4×D4×C101C2211yescharacteristic
31C2×#117×C101C2211yescharacteristic
32C22×C4⋊C4×C101C2211yescharacteristic
33#435×C101—24no—
34C2×C4⋊C8×C101C2211yescharacteristic
35#417×C101—24no—
36#416×C101—24no—
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#103×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×C22⋊C8×C101C2211yescharacteristic
50C2×C22⋊C8×C101C2211yescharacteristic
51C2×#97×C101C2211yescharacteristic
52#388×C101—21no—
53#387×C101—21no—
54#386×C101—21no—
55#382×C101C2211yescharacteristic
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58C4×C4⋊C4×C101C2211yescharacteristic
59C4×C22⋊C4×C101—21no—
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63#340×C101C2211yescharacteristic
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—41no—
71C2×#41×C101—41no—
72C2×#41×C101—41no—
73C2×#41×C101—41no—
74C2×#41×C101C2×C414yes—
75C2×#41×C101C2×C414yescomplemented
76C22×Q8×C101C2311yescharacteristic
77C22×D4×C101—21no—
78C22×D4×C101—21no—
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101D411yescharacteristic
84C22×D4×C101C2311yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C23×C4×C101—21no—
87C23×C4×C101—21no—
88C23×C4×C101—21no—
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C2×M16×C101—22no—
92C2×M16×C101—22no—
93C2×M16×C101—41no—
94C22×C8×C101—22no—
95C22×C8×C101—22no—
96C22×C8×C101—41no—
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99C22×C8×C101C2311yescharacteristic
100C22×C8×C101C2311yescharacteristic
101#127×C101—28no—
102#127×C101—22no—
103#127×C101C2×C414yescomplemented
104#121×C101—22no—
105#121×C101—22no—
106#121×C101—28no—
107#121×C101—28no—
108#121×C101C2×C414yes—
109#121×C101C2×C414yescomplemented
110C4×Q8×C101—22no—
111C4×Q8×C101C2×C414yescomplemented
112C4×D4×C101—28no—
113C4×D4×C101C2×C414yes—
114C4×D4×C101D414yes—
115#117×C101—22no—
116#117×C101—41no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101—22no—
119C2×C4⋊C4×C101—21no—
120C2×C4⋊C4×C101—41no—
121C2×C4⋊C4×C101D411yescharacteristic
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C4⋊C4×C101C2311yescharacteristic
124C2×C4⋊C4×C101C2311yescharacteristic
125C2×C4⋊C4×C101C2311yescharacteristic
126C2×C4⋊C4×C101C2311yescharacteristic
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×C101D411yescharacteristic
133C2×C22⋊C4×C101D411yescharacteristic
134C2×C42×C101—21no—
135C2×C42×C101—21no—
136C2×C42×C101—21no—
137C2×C42×C101C2311yescharacteristic
138C4⋊C8×C101—22no—
139#103×C101—22no—
140#103×C101—22no—
141#103×C101—22no—
142#103×C101D414yescomplemented
143#102×C101—22no—
144#102×C101—22no—
145#102×C101—22no—
146#102×C101—22no—
147#102×C101—41no—
148#102×C101—41no—
149#102×C101—41no—
150#102×C101—41no—
151C22⋊C8×C101—22no—
152C22⋊C8×C101—22no—
153#97×C101—22no—
154#95×C101—21no—
155#95×C101—21no—
156#95×C101—21no—
157#95×C101—21no—
158#95×C101—21no—
159C24×C101—21no—
160C24×C101—21no—
161C24×C101C2×D411yescharacteristic
162C24×C101C2×D411yescharacteristic
163#41×C101—28no—
164#41×C101—28no—
165#41×C101—44no—
166#41×C101—44no—
167#41×C101—44no—
168#41×C101—44no—
169#41×C101—44no—
170#41×C101—44no—
171C2×Q8×C101—21no—
172C2×Q8×C101—21no—
173C2×Q8×C101—21no—
174C2×Q8×C101C22×C412yes—
175C2×Q8×C101C2×D412yes—
176C2×Q8×C101#4112yes—
177C2×D4×C101—24no—
178C2×D4×C101—24no—
179C2×D4×C101—24no—
180C2×D4×C101—24no—
181C2×D4×C101—24no—
182C2×D4×C101—24no—
183C2×D4×C101—21no—
184C2×D4×C101—21no—
185C2×D4×C101—21no—
186C2×D4×C101—21no—
187C2×D4×C101—21no—
188C2×D4×C101—21no—
189C2×D4×C101—21no—
190C2×D4×C101—21no—
191C2×D4×C101—21no—
192C2×D4×C101—21no—
193C2×D4×C101—41no—
194C2×D4×C101—41no—
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—81no—
202C2×D4×C101—81no—
203C2×D4×C101—81no—
204C2×D4×C101—81no—
205C2×D4×C101—81no—
206C2×D4×C101—81no—
207C2×D4×C101C22⋊C414yes—
208C2×D4×C101C22×C412yes—
209C2×D4×C101C22×C412yes—
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×C101—21no—
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—24no—
222C22×C4×C101—24no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—42no—
227C22×C4×C101—42no—
228C22×C4×C101—42no—
229C22×C4×C101—42no—
230C22×C4×C101—42no—
231C22×C4×C101—42no—
232C22×C4×C101—81no—
233C22×C4×C101C22×C412yes—
234C22×C4×C101C22×C412yes—
235C22×C4×C101C2×D411yescharacteristic
236C22×C4×C101C2×D411yescharacteristic
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D412yes—
240C22×C4×C101C2×D412yes—
241C22×C4×C101C2411yescharacteristic
242M16×C101—44no—
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—21no—
251C2×C8×C101—21no—
252C2×C8×C101—21no—
253C2×C8×C101—21no—
254C2×C8×C101—44no—
255C2×C8×C101C2×D412yes—
256C4⋊C4×C101—24no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—42no—
266C4⋊C4×C101C22⋊C414yes—
267C4⋊C4×C101C22×C412yes—
268C4⋊C4×C101C2×D412yes—
269C22⋊C4×C101—24no—
270C22⋊C4×C101—24no—
271C22⋊C4×C101—42no—
272C22⋊C4×C101—42no—
273C22⋊C4×C101—81no—
274C22⋊C4×C101C22⋊C414yes—
275C22⋊C4×C101C22⋊C414yes—
276C42×C101—24no—
277C42×C101—42no—
278C42×C101—81no—
279C42×C101C22×C412yes—
280C42×C101C2×D412yes—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—21no—
287C23×C101—21no—
288C23×C101—21no—
289C23×C101—21no—
290C23×C101—21no—
291C23×C101—21no—
292C23×C101—21no—
293C23×C101—22no—
294C23×C101—22no—
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×C101C2×C22⋊C412yes—
308C23×C101C2×C22⋊C412yes—
309C23×C101C22×D411yescharacteristic
310Q8×C101—22no—
311Q8×C101—22no—
312Q8×C101—22no—
313Q8×C101C4×D414yes—
314D4×C101—22no—
315D4×C101—22no—
316D4×C101—22no—
317D4×C101—22no—
318D4×C101—44no—
319D4×C101—48no—
320D4×C101—48no—
321D4×C101—48no—
322D4×C101—41no—
323D4×C101—41no—
324D4×C101—41no—
325D4×C101—41no—
326D4×C101—84no—
327D4×C101—84no—
328D4×C101—84no—
329C2×C4×C101—22no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—22no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—22no—
336C2×C4×C101—21no—
337C2×C4×C101—21no—
338C2×C4×C101—21no—
339C2×C4×C101—21no—
340C2×C4×C101—22no—
341C2×C4×C101—22no—
342C2×C4×C101—22no—
343C2×C4×C101—22no—
344C2×C4×C101—22no—
345C2×C4×C101—22no—
346C2×C4×C101—22no—
347C2×C4×C101—22no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—48no—
351C2×C4×C101—48no—
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—84no—
366C2×C4×C101C2×C22⋊C412yes—
367C2×C4×C101C2×C22⋊C412yes—
368C2×C4×C101C2×C22⋊C412yes—
369C2×C4×C101C2×C22⋊C412yes—
370C2×C4×C101C23×C411yescharacteristic
371C2×C4×C101C22×D411yescharacteristic
372C2×C4×C101C22×D411yescharacteristic
373C2×C4×C101C2×#4111yescharacteristic
374C2×C4×C101H(5,𝔽2)11yescharacteristic
375C2×C4×C101H(5,𝔽2)11yescharacteristic
376C8×C101—22no—
377C8×C101—41no—
378C8×C101—41no—
379C8×C101—41no—
380C22×C101—22no—
381C22×C101—22no—
382C22×C101—22no—
383C22×C101—22no—
384C22×C101—22no—
385C22×C101—22no—
386C22×C101—41no—
387C22×C101—41no—
388C22×C101—41no—
389C22×C101—41no—
390C22×C101—41no—
391C22×C101—41no—
392C22×C101—41no—
393C22×C101—41no—
394C22×C101—42no—
395C22×C101—42no—
396C22×C101—42no—
397C22×C101—42no—
398C22×C101—42no—
399C22×C101—42no—
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×C101C22×C22⋊C411yescharacteristic
409C22×C101D4211yescharacteristic
410C22×C101#54611yescharacteristic
411C22×C101#57511yescharacteristic
412C22×C101#57511yescharacteristic
413C22×C101#57611yescharacteristic
414C22×C101#57711yescharacteristic
415C4×C101—22no—
416C4×C101—22no—
417C4×C101—24no—
418C4×C101—22no—
419C4×C101—22no—
420C4×C101—42no—
421C4×C101—42no—
422C4×C101—81no—
423C4×C101—81no—
424C4×C101—81no—
425C4×C101C2×C4×D411yescharacteristic
426C4×C101#51811yescharacteristic
427C4×C101D4211yescharacteristic
428C4×C101#54611yescharacteristic
429#22422C10111yesmaximal, characteristic, direct product factor, Sylow
430C2×C101—42no—
431C2×C101—42no—
432C2×C101—82no—
433C2×C101—82no—
434C2×C101D4×C22⋊C411yescharacteristic
435C2×C101#289611yescharacteristic
436C2×C101#289711yescharacteristic
437C2×C101#326811yescharacteristic
438C2×C101#327111yescharacteristic
439C2×C101#330911yescharacteristic
440C2×C101#331711yescharacteristic
441C2×#550C2×C10111yescharacteristic
442C2×#435C2×C10111yescharacteristic, complemented
443C2×#417C2×C10111yescharacteristic, complemented
444C2×#416C2×C10111yescharacteristic, complemented
445#2352C2×C10111yescharacteristic, complemented
446#1982C2×C10111yescharacteristic, complemented
447#1961C2×C10111yescharacteristic, complemented
448#1895C2×C10111yescharacteristic, complemented
449#1893C2×C10111yescharacteristic, complemented
450#1875C2×C10111yescharacteristic, complemented
451#1874C2×C10111yescharacteristic, complemented
452#1805C2×C10111yescharacteristic, complemented
453#1788C2×C10111yescharacteristic, complemented
454#1788C2×C10111yescharacteristic, complemented
455#1763C2×C10111yescharacteristic, complemented
456C101#2242211yescharacteristic, direct product factor, Sylow
457C22×#41C22×C10111yescharacteristic
458C22×#41C22×C10111yescharacteristic
459C22×M16C22×C10111yescharacteristic
460C23×C8C22×C10111yescharacteristic
461#550—24no—
462#550C4×C10118yescomplemented
463C2×#127—21no—
464C2×#127C22×C10111yescharacteristic
465C2×#121—21no—
466C2×#121—21no—
467C2×#121C22×C10111yescharacteristic
468C2×#121C22×C10111yescharacteristic
469C2×C4×Q8C22×C10111yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4C22×C10111yescharacteristic
472C2×#117C22×C10111yescharacteristic
473C22×C4⋊C4C22×C10111yescharacteristic
474#435—24no—
475C2×C4⋊C8C22×C10111yescharacteristic
476#417—24no—
477#416—24no—
478C2×#103C22×C10111yescharacteristic
479C2×#103C22×C10111yescharacteristic
480C2×#103C22×C10111yescharacteristic
481C2×#103C22×C10111yescharacteristic
482C2×#102C22×C10111yescharacteristic
483C2×#102C22×C10111yescharacteristic
484C2×#102C22×C10111yescharacteristic
485C2×#102C22×C10111yescharacteristic
486C2×#102C22×C10111yescharacteristic
487C2×#102C22×C10111yescharacteristic
488C2×#102C22×C10111yescharacteristic
489C2×#102C22×C10111yescharacteristic
490C2×C22⋊C8C22×C10111yescharacteristic
491C2×C22⋊C8C22×C10111yescharacteristic
492C2×#97C22×C10111yescharacteristic
493#388—21no—
494#387—21no—
495#386—21no—
496#382C22×C10111yescharacteristic
497#380C22×C10111yescharacteristic
498#380C22×C10111yescharacteristic
499C4×C4⋊C4C22×C10111yescharacteristic
500C4×C22⋊C4—21no—
501#340C22×C10111yescharacteristic
502#340C22×C10111yescharacteristic
503#340C22×C10111yescharacteristic
504#340C22×C10111yescharacteristic
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C10114yes—
516C2×#41C2×C4×C10114yescomplemented
517C22×Q8C23×C10111yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4D4×C10111yescharacteristic
525C22×D4C23×C10111yescharacteristic
526C22×D4C23×C10111yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C10111yescharacteristic
531C23×C4C23×C10111yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C23×C10111yescharacteristic
539C22×C8C23×C10111yescharacteristic
540C22×C8C23×C10111yescharacteristic
541C22×C8C23×C10111yescharacteristic
542#127—28no—
543#127—22no—
544#127C2×C4×C10114yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×C4×C10114yes—
550#121C2×C4×C10114yescomplemented
551C4×Q8—22no—
552C4×Q8C2×C4×C10114yescomplemented
553C4×D4—28no—
554C4×D4C2×C4×C10114yes—
555C4×D4D4×C10114yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4D4×C10111yescharacteristic
563C2×C4⋊C4C23×C10111yescharacteristic
564C2×C4⋊C4C23×C10111yescharacteristic
565C2×C4⋊C4C23×C10111yescharacteristic
566C2×C4⋊C4C23×C10111yescharacteristic
567C2×C4⋊C4C23×C10111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4D4×C10111yescharacteristic
574C2×C22⋊C4D4×C10111yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C23×C10111yescharacteristic
579C4⋊C8—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583#103D4×C10114yescomplemented
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593C22⋊C8—22no—
594#97—22no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—21no—
601C24—21no—
602C24C2×D4×C10111yescharacteristic
603C24C2×D4×C10111yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22×C4×C10112yes—
616C2×Q8C2×D4×C10112yes—
617C2×Q8#41×C10112yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
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—41no—
635C2×D4—41no—
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×D4—81no—
648C2×D4C22⋊C4×C10114yes—
649C2×D4C22×C4×C10112yes—
650C2×D4C22×C4×C10112yes—
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—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4C22×C4×C10112yes—
675C22×C4C22×C4×C10112yes—
676C22×C4C2×D4×C10111yescharacteristic
677C22×C4C2×D4×C10111yescharacteristic
678C22×C4C2×D4×C10111yescharacteristic
679C22×C4C2×D4×C10111yescharacteristic
680C22×C4C2×D4×C10112yes—
681C22×C4C2×D4×C10112yes—
682C22×C4C24×C10111yescharacteristic
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—44no—
696C2×C8C2×D4×C10112yes—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4C22⋊C4×C10114yes—
708C4⋊C4C22×C4×C10112yes—
709C4⋊C4C2×D4×C10112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4C22⋊C4×C10114yes—
716C22⋊C4C22⋊C4×C10114yes—
717C42—24no—
718C42—42no—
719C42—81no—
720C42C22×C4×C10112yes—
721C42C2×D4×C10112yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊C4×C10112yes—
749C23C2×C22⋊C4×C10112yes—
750C23C22×D4×C10111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×D4×C10114yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—48no—
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—84no—
807C2×C4C2×C22⋊C4×C10112yes—
808C2×C4C2×C22⋊C4×C10112yes—
809C2×C4C2×C22⋊C4×C10112yes—
810C2×C4C2×C22⋊C4×C10112yes—
811C2×C4C23×C4×C10111yescharacteristic
812C2×C4C22×D4×C10111yescharacteristic
813C2×C4C22×D4×C10111yescharacteristic
814C2×C4C2×#41×C10111yescharacteristic
815C2×C4H(5,𝔽2)×C10111yescharacteristic
816C2×C4H(5,𝔽2)×C10111yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊C4×C10111yescharacteristic
850C22D42×C10111yescharacteristic
851C22#546×C10111yescharacteristic
852C22#575×C10111yescharacteristic
853C22#575×C10111yescharacteristic
854C22#576×C10111yescharacteristic
855C22#577×C10111yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4C2×C4×D4×C10111yescharacteristic
867C4#518×C10111yescharacteristic
868C4D42×C10111yescharacteristic
869C4#546×C10111yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊C4×C10111yescharacteristic
875C2C101×#289611yescharacteristic
876C2C101×#289711yescharacteristic
877C2C101×#326811yescharacteristic
878C2C101×#327111yescharacteristic
879C2C101×#330911yescharacteristic
880C2C101×#331711yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#550×C101C2
LCSG ▷ C2×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
2. C2×#435×C101C2semidirect
3. C2×#417×C101C2semidirect
4. C2×#416×C101C2semidirect
5. C101×#2352C2semidirect
6. C101×#1982C2semidirect
7. C101×#1961C2semidirect
8. C101×#1895C2semidirect
9. C101×#1893C2semidirect
10. C101×#1875C2semidirect
11. C101×#1874C2semidirect
12. C101×#1805C2semidirect
13. C101×#1788C2semidirect
14. C101×#1788C2semidirect
15. C101×#1763C2semidirect
21. #550×C101C4semidirect
75. C2×#41×C101C2×C4semidirect
103. #127×C101C2×C4semidirect
109. #121×C101C2×C4semidirect
111. C4×Q8×C101C2×C4semidirect
142. #103×C101D4semidirect
429. #22422C101direct (N × H)
442. C2×#435C2×C101semidirect
443. C2×#417C2×C101semidirect
444. C2×#416C2×C101semidirect
445. #2352C2×C101semidirect
446. #1982C2×C101semidirect
447. #1961C2×C101semidirect
448. #1895C2×C101semidirect
449. #1893C2×C101semidirect
450. #1875C2×C101semidirect
451. #1874C2×C101semidirect
452. #1805C2×C101semidirect
453. #1788C2×C101semidirect
454. #1788C2×C101semidirect
455. #1763C2×C101semidirect
456. C101#22422direct (N × H)
462. #550C4×C101semidirect
516. C2×#41C2×C4×C101semidirect
544. #127C2×C4×C101semidirect
550. #121C2×C4×C101semidirect
552. C4×Q8C2×C4×C101semidirect
583. #103D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1012
C2×#435×C1012
C2×#417×C1012
C2×#416×C1012
C101×#23522
C101×#19822
C101×#19612
C101×#18952
C101×#18932
C101×#18752
C101×#18742
C101×#18052
C101×#17882
C101×#17632
#22422101