Finite Group Databasebeta

← C101×#25380 #38807531

Subgroups — C101×#25380 #38807531

Order 25856.

1184 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C101C211yesmaximal, characteristic, complemented
2C2×#460×C101C211yesmaximal, characteristic, complemented
3C2×#463×C101C211yesmaximal, characteristic, complemented
4C2×#459×C101C211yesmaximal, characteristic, complemented
5C101×#2541C211yesmaximal, characteristic, complemented
6C101×#2367C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#2014C211yesmaximal, characteristic, complemented
10C101×#2011C211yesmaximal, characteristic, complemented
11C101×#1982C211yesmaximal, characteristic, complemented
12C101×#1940C211yesmaximal, characteristic, complemented
13C101×#1880C211yesmaximal, characteristic, complemented
14C101×#1879C211yesmaximal, characteristic, complemented
15C101×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C22×D8×C101C2211yescharacteristic
22C2×#127×C101C2211yescharacteristic
23C2×#127×C101C2211yescharacteristic
24C2×#127×C101C2211yescharacteristic
25C2×#124×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101—21no—
28C2×C4×Q8×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31#496×C101—24no—
32#463×C101—24no—
33#460×C101—24no—
34#459×C101—24no—
35C2×C4⋊C8×C101C2211yescharacteristic
36C2×C4⋊C8×C101C2211yescharacteristic
37C2×C4⋊C8×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#97×C101C2211yescharacteristic
47#392×C101—21no—
48#392×C101—21no—
49#391×C101C2211yescharacteristic
50#390×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#388×C101—21no—
54#388×C101—21no—
55#385×C101—21no—
56C4×C4⋊C4×C101C2211yescharacteristic
57C4×C4⋊C4×C101C2211yescharacteristic
58C4×C22⋊C4×C101—21no—
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×Q8×C101C2311yescharacteristic
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101—21no—
75C23×C4×C101—21no—
76C2×SD16×C101—22no—
77C2×SD16×C101—22no—
78C2×SD16×C101—22no—
79C2×SD16×C101—22no—
80C2×SD16×C101—22no—
81C2×SD16×C101—22no—
82C2×SD16×C101—41no—
83C2×SD16×C101—41no—
84C2×SD16×C101—41no—
85C2×D8×C101—22no—
86C2×D8×C101—22no—
87C2×D8×C101—22no—
88C2×D8×C101—22no—
89C2×D8×C101—22no—
90C2×D8×C101—22no—
91C2×D8×C101—41no—
92C2×D8×C101—41no—
93C2×D8×C101—41no—
94C22×C8×C101C2311yescharacteristic
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98#127×C101—22no—
99#127×C101—22no—
100#127×C101—22no—
101#127×C101—22no—
102#127×C101—41no—
103#127×C101—41no—
104#124×C101—22no—
105#124×C101D414yescomplemented
106#121×C101—44no—
107#121×C101—44no—
108C4×Q8×C101—22no—
109C4×Q8×C101—41no—
110C4×D4×C101—22no—
111C4×D4×C101—22no—
112C4×D4×C101—22no—
113C4×D4×C101—41no—
114C2×C4⋊C4×C101—21no—
115C2×C4⋊C4×C101D411yescharacteristic
116C2×C4⋊C4×C101D411yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C4⋊C4×C101C2311yescharacteristic
119C2×C4⋊C4×C101C2311yescharacteristic
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×C42×C101—21no—
131C2×C42×C101—21no—
132C2×C42×C101C2311yescharacteristic
133C2×C42×C101C2311yescharacteristic
134C2×C42×C101C2311yescharacteristic
135C4⋊C8×C101—22no—
136C4⋊C8×C101—22no—
137C4⋊C8×C101—22no—
138#103×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—22no—
143#102×C101—41no—
144#102×C101—41no—
145#102×C101D414yescomplemented
146#97×C101—22no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101D411yescharacteristic
151#95×C101D411yescharacteristic
152C24×C101—21no—
153C24×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C2×Q8×C101—21no—
157C2×Q8×C101—21no—
158C2×Q8×C101—21no—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×Q8×C101C2×D412yes—
162C2×D4×C101—21no—
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—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—42no—
185C2×D4×C101—42no—
186C2×D4×C101—42no—
187C2×D4×C101—42no—
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×C101—81no—
202C2×D4×C101C2×D412yes—
203C2×D4×C101C2×D412yes—
204C22×C4×C101—21no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—42no—
209C22×C4×C101—42no—
210C22×C4×C101—42no—
211C22×C4×C101—42no—
212C22×C4×C101—42no—
213C22×C4×C101—81no—
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D411yescharacteristic
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101C2×D411yescharacteristic
218C22×C4×C101C2×D411yescharacteristic
219C22×C4×C101C2×D411yescharacteristic
220C22×C4×C101C2411yescharacteristic
221SD16×C101—44no—
222SD16×C101—44no—
223SD16×C101—44no—
224D8×C101—44no—
225D8×C101—44no—
226D8×C101—44no—
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×C101—21no—
237C2×C8×C101C2×D412yes—
238C2×C8×C101#4112yes—
239C4⋊C4×C101—22no—
240C4⋊C4×C101—22no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—42no—
247C4⋊C4×C101C2×D412yes—
248C22⋊C4×C101—24no—
249C22⋊C4×C101—24no—
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—81no—
258C42×C101—21no—
259C42×C101—21no—
260C42×C101—21no—
261C42×C101—21no—
262C42×C101—42no—
263C42×C101—81no—
264C42×C101C2×D412yes—
265C42×C101#4112yes—
266C23×C101—22no—
267C23×C101—22no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
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×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101C22×D411yescharacteristic
295Q8×C101—22no—
296Q8×C101—22no—
297Q8×C101—41no—
298Q8×C101—41no—
299D4×C101—22no—
300D4×C101—22no—
301D4×C101—22no—
302D4×C101—22no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—41no—
312D4×C101—41no—
313D4×C101—41no—
314D4×C101—41no—
315D4×C101—84no—
316D4×C101—84no—
317D4×C101—84no—
318D4×C101—84no—
319D4×C101—84no—
320D4×C101—84no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
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—21no—
336C2×C4×C101—21no—
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—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—84no—
348C2×C4×C101—84no—
349C2×C4×C101#12112yes—
350C2×C4×C101#12112yes—
351C2×C4×C101AGL(1,ℤ/8)12yes—
352C2×C4×C101AGL(1,ℤ/8)12yes—
353C2×C4×C101C22×D411yescharacteristic
354C2×C4×C101C22×D411yescharacteristic
355C2×C4×C101C2×#4111yescharacteristic
356C2×C4×C101C2×#4111yescharacteristic
357C2×C4×C101H(5,𝔽2)11yescharacteristic
358C2×C4×C101H(5,𝔽2)11yescharacteristic
359C8×C101—22no—
360C8×C101—22no—
361C8×C101—41no—
362C8×C101—41no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
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×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101C2×#12111yescharacteristic
392C22×C101D4211yescharacteristic
393C22×C101#55011yescharacteristic
394C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C101#57611yescharacteristic
397C22×C101#57711yescharacteristic
398C4×C101—22no—
399C4×C101—22no—
400C4×C101—22no—
401C4×C101—22no—
402C4×C101—42no—
403C4×C101—41no—
404C4×C101—42no—
405C4×C101—41no—
406C4×C101—81no—
407C4×C101—81no—
408C4×C101#53211yescharacteristic
409C4×C101#54011yescharacteristic
410C4×C101D4211yescharacteristic
411C4×C101#54611yescharacteristic
412#25380C10111yesmaximal, characteristic, direct product factor, Sylow
413C2×C101—82no—
414C2×C101—82no—
415C2×C101—161no—
416C2×C101—161no—
417C2×C101#242811yescharacteristic
418C2×C101#303811yescharacteristic
419C2×C101#304511yescharacteristic
420C2×C101#326411yescharacteristic
421C2×C101#326511yescharacteristic
422C2×C101#339711yescharacteristic
423C2×C101#339911yescharacteristic
424C2×#496C2×C10111yescharacteristic, complemented
425C2×#460C2×C10111yescharacteristic, complemented
426C2×#463C2×C10111yescharacteristic, complemented
427C2×#459C2×C10111yescharacteristic, complemented
428#2541C2×C10111yescharacteristic, complemented
429#2367C2×C10111yescharacteristic, complemented
430#2055C2×C10111yescharacteristic, complemented
431#2054C2×C10111yescharacteristic, complemented
432#2014C2×C10111yescharacteristic, complemented
433#2011C2×C10111yescharacteristic, complemented
434#1982C2×C10111yescharacteristic, complemented
435#1940C2×C10111yescharacteristic, complemented
436#1880C2×C10111yescharacteristic, complemented
437#1879C2×C10111yescharacteristic, complemented
438#1762C2×C10111yescharacteristic, complemented
439C101#2538011yescharacteristic, direct product factor, Sylow
440C22×SD16C22×C10111yescharacteristic
441C22×SD16C22×C10111yescharacteristic
442C22×SD16C22×C10111yescharacteristic
443C22×D8C22×C10111yescharacteristic
444C22×D8C22×C10111yescharacteristic
445C22×D8C22×C10111yescharacteristic
446C2×#127C22×C10111yescharacteristic
447C2×#127C22×C10111yescharacteristic
448C2×#127C22×C10111yescharacteristic
449C2×#124C22×C10111yescharacteristic
450C2×#121—21no—
451C2×#121—21no—
452C2×C4×Q8C22×C10111yescharacteristic
453C2×C4×D4C22×C10111yescharacteristic
454C2×C4×D4C22×C10111yescharacteristic
455#496—24no—
456#463—24no—
457#460—24no—
458#459—24no—
459C2×C4⋊C8C22×C10111yescharacteristic
460C2×C4⋊C8C22×C10111yescharacteristic
461C2×C4⋊C8C22×C10111yescharacteristic
462C2×#103C22×C10111yescharacteristic
463C2×#102C22×C10111yescharacteristic
464C2×#102C22×C10111yescharacteristic
465C2×#102C22×C10111yescharacteristic
466C2×#102C22×C10111yescharacteristic
467C2×#102C22×C10111yescharacteristic
468C2×#102C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×#97C22×C10111yescharacteristic
471#392—21no—
472#392—21no—
473#391C22×C10111yescharacteristic
474#390C22×C10111yescharacteristic
475#390C22×C10111yescharacteristic
476#390C22×C10111yescharacteristic
477#388—21no—
478#388—21no—
479#385—21no—
480C4×C4⋊C4C22×C10111yescharacteristic
481C4×C4⋊C4C22×C10111yescharacteristic
482C4×C22⋊C4—21no—
483#340C22×C10111yescharacteristic
484#340C22×C10111yescharacteristic
485#336C22×C10111yescharacteristic
486#336C22×C10111yescharacteristic
487C22×Q8C23×C10111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C23×C10111yescharacteristic
495C22×D4C23×C10111yescharacteristic
496C22×D4C23×C10111yescharacteristic
497C22×D4C23×C10111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C22×C8C23×C10111yescharacteristic
519C22×C8C23×C10111yescharacteristic
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522#127—22no—
523#127—22no—
524#127—22no—
525#127—22no—
526#127—41no—
527#127—41no—
528#124—22no—
529#124D4×C10114yescomplemented
530#121—44no—
531#121—44no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4D4×C10111yescharacteristic
540C2×C4⋊C4D4×C10111yescharacteristic
541C2×C4⋊C4C23×C10111yescharacteristic
542C2×C4⋊C4C23×C10111yescharacteristic
543C2×C4⋊C4C23×C10111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42C23×C10111yescharacteristic
557C2×C42C23×C10111yescharacteristic
558C2×C42C23×C10111yescharacteristic
559C4⋊C8—22no—
560C4⋊C8—22no—
561C4⋊C8—22no—
562#103—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568#102—41no—
569#102D4×C10114yescomplemented
570#97—22no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C10111yescharacteristic
575#95D4×C10111yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C10112yes—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4C2×D4×C10112yes—
627C2×D4C2×D4×C10112yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C10111yescharacteristic
639C22×C4C2×D4×C10111yescharacteristic
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4C2×D4×C10111yescharacteristic
642C22×C4C2×D4×C10111yescharacteristic
643C22×C4C2×D4×C10111yescharacteristic
644C22×C4C24×C10111yescharacteristic
645SD16—44no—
646SD16—44no—
647SD16—44no—
648D8—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C10112yes—
662C2×C8#41×C10112yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4C2×D4×C10112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—42no—
687C42—81no—
688C42C2×D4×C10112yes—
689C42#41×C10112yes—
690C23—22no—
691C23—22no—
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—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23C22×D4×C10111yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—84no—
742D4—84no—
743D4—84no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#121×C10112yes—
774C2×C4#121×C10112yes—
775C2×C4AGL(1,ℤ/8)×C10112yes—
776C2×C4AGL(1,ℤ/8)×C10112yes—
777C2×C4C22×D4×C10111yescharacteristic
778C2×C4C22×D4×C10111yescharacteristic
779C2×C4C2×#41×C10111yescharacteristic
780C2×C4C2×#41×C10111yescharacteristic
781C2×C4H(5,𝔽2)×C10111yescharacteristic
782C2×C4H(5,𝔽2)×C10111yescharacteristic
783C8—22no—
784C8—22no—
785C8—41no—
786C8—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C10111yescharacteristic
816C22D42×C10111yescharacteristic
817C22#550×C10111yescharacteristic
818C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
819C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
820C22#576×C10111yescharacteristic
821C22#577×C10111yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—42no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4#532×C10111yescharacteristic
833C4#540×C10111yescharacteristic
834C4D42×C10111yescharacteristic
835C4#546×C10111yescharacteristic
836C2—82no—
837C2—82no—
838C2—161no—
839C2—161no—
840C2C101×#242811yescharacteristic
841C2C101×#303811yescharacteristic
842C2C101×#304511yescharacteristic
843C2C101×#326411yescharacteristic
844C2C101×#326511yescharacteristic
845C2C101×#339711yescharacteristic
846C2C101×#339911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C4⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#496×C101C2semidirect
2. C2×#460×C101C2semidirect
3. C2×#463×C101C2semidirect
4. C2×#459×C101C2semidirect
5. C101×#2541C2semidirect
6. C101×#2367C2semidirect
7. C101×#2055C2semidirect
8. C101×#2054C2semidirect
9. C101×#2014C2semidirect
10. C101×#2011C2semidirect
11. C101×#1982C2semidirect
12. C101×#1940C2semidirect
13. C101×#1880C2semidirect
14. C101×#1879C2semidirect
15. C101×#1762C2semidirect
105. #124×C101D4semidirect
145. #102×C101D4semidirect
412. #25380C101direct (N × H)
424. C2×#496C2×C101semidirect
425. C2×#460C2×C101semidirect
426. C2×#463C2×C101semidirect
427. C2×#459C2×C101semidirect
428. #2541C2×C101semidirect
429. #2367C2×C101semidirect
430. #2055C2×C101semidirect
431. #2054C2×C101semidirect
432. #2014C2×C101semidirect
433. #2011C2×C101semidirect
434. #1982C2×C101semidirect
435. #1940C2×C101semidirect
436. #1880C2×C101semidirect
437. #1879C2×C101semidirect
438. #1762C2×C101semidirect
439. C101#25380direct (N × H)
529. #124D4×C101semidirect
569. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1012
C2×#460×C1012
C2×#463×C1012
C2×#459×C1012
C101×#25412
C101×#23672
C101×#20552
C101×#20542
C101×#20142
C101×#20112
C101×#19822
C101×#19402
C101×#18802
C101×#18792
C101×#17622
#25380101