Finite Group Databasebeta

← C101×#25396 #38807547

Subgroups — C101×#25396 #38807547

Order 25856.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C101C211yesmaximal, characteristic, complemented
2C2×#466×C101C211yesmaximal, characteristic, complemented
3C2×#459×C101C211yesmaximal, characteristic, complemented
4C2×#435×C101C211yesmaximal, characteristic, complemented
5C101×#2541C211yesmaximal, characteristic, complemented
6C101×#2535C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1999C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1961C211yesmaximal, characteristic, complemented
12C101×#1949C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1893C211yesmaximal, characteristic, complemented
15C101×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×#127×C101—21no—
21C2×#127×C101C2211yescharacteristic
22C2×#121×C101C2211yescharacteristic
23C2×#121×C101C2211yescharacteristic
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#466×C101—24no—
32#459×C101—24no—
33#435×C101—24no—
34C2×#107×C101C2211yescharacteristic
35C2×#106×C101C2211yescharacteristic
36C2×C4⋊C8×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×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#397×C101—21no—
49#392×C101—21no—
50#392×C101—21no—
51#392×C101—21no—
52#390×C101—21no—
53#386×C101—21no—
54#386×C101—21no—
55#382×C101C2211yescharacteristic
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58C4×C4⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63C22×D4×C101—21no—
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×C101—21no—
71C22×D4×C101D411yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C22×D4×C101C2311yescharacteristic
75C23×C4×C101—21no—
76C23×C4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C2×D8×C101—22no—
79C2×D8×C101—22no—
80C2×D8×C101—22no—
81C2×D8×C101—22no—
82C2×D8×C101—41no—
83C2×D8×C101—41no—
84C2×M16×C101—22no—
85C2×M16×C101—22no—
86C2×M16×C101—41no—
87C22×C8×C101—22no—
88C22×C8×C101—22no—
89C22×C8×C101—41no—
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94#127×C101—22no—
95#127×C101—22no—
96#127×C101—44no—
97#121×C101—22no—
98#121×C101—22no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—22no—
103#121×C101—41no—
104#121×C101—41no—
105#121×C101—41no—
106#121×C101—41no—
107#121×C101—41no—
108#121×C101—41no—
109C4×D4×C101—22no—
110C4×D4×C101—22no—
111C4×D4×C101—22no—
112C4×D4×C101—22no—
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×C101D411yescharacteristic
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132#107×C101—22no—
133#106×C101—22no—
134C4⋊C8×C101D414yescomplemented
135#102×C101—22no—
136#102×C101—22no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—41no—
141#102×C101—41no—
142#102×C101D414yescomplemented
143C22⋊C8×C101—22no—
144C22⋊C8×C101—22no—
145#97×C101—22no—
146#95×C101—21no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101C2×D411yescharacteristic
155C24×C101C2×D411yescharacteristic
156C2×D4×C101—22no—
157C2×D4×C101—22no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
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—41no—
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—42no—
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—81no—
193C2×D4×C101—81no—
194C2×D4×C101—81no—
195C2×D4×C101—81no—
196C2×D4×C101—81no—
197C2×D4×C101—81no—
198C2×D4×C101—81no—
199C2×D4×C101—81no—
200C2×D4×C101C2×D412yes—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
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×C101—42no—
219C22×C4×C101—81no—
220C22×C4×C101—81no—
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2×D411yescharacteristic
225C22×C4×C101C2411yescharacteristic
226D8×C101—44no—
227D8×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×C101—44no—
239C2×C8×C101C2×D412yes—
240C2×C8×C101C2×D412yes—
241C2×C8×C101C2×D412yes—
242C4⋊C4×C101—22no—
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×C101C2×D412yes—
252C4⋊C4×C101#4112yes—
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—81no—
263C22⋊C4×C101—81no—
264C42×C101—42no—
265C42×C101C2×D412yes—
266C42×C101#4112yes—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—22no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
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×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101—41no—
299C23×C101—41no—
300C23×C101—41no—
301C23×C101AGL(1,ℤ/8)12yes—
302C23×C101C22×D411yescharacteristic
303D4×C101—22no—
304D4×C101—22no—
305D4×C101—44no—
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—41no—
316D4×C101—84no—
317D4×C101—84no—
318D4×C101—84no—
319D4×C101—84no—
320D4×C101—84no—
321D4×C101—84no—
322D4×C101—84no—
323D4×C101—84no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—22no—
333C2×C4×C101—22no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
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—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
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—84no—
358C2×C4×C101#12112yes—
359C2×C4×C101#12112yes—
360C2×C4×C101C22×D411yescharacteristic
361C2×C4×C101C22×D411yescharacteristic
362C2×C4×C101C2×#4111yescharacteristic
363C2×C4×C101C2×#4111yescharacteristic
364C2×C4×C101H(5,𝔽2)11yescharacteristic
365C2×C4×C101H(5,𝔽2)11yescharacteristic
366C8×C101—22no—
367C8×C101—22no—
368C8×C101—22no—
369C8×C101—41no—
370C22×C101—22no—
371C22×C101—22no—
372C22×C101—22no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—42no—
379C22×C101—41no—
380C22×C101—42no—
381C22×C101—41no—
382C22×C101—42no—
383C22×C101—41no—
384C22×C101—41no—
385C22×C101—41no—
386C22×C101—41no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101—81no—
393C22×C101—81no—
394C22×C101—81no—
395C22×C101—81no—
396C22×C101—81no—
397C22×C101—81no—
398C22×C101—81no—
399C22×C101—81no—
400C22×C101—81no—
401C22×C101—81no—
402C22×C101—81no—
403C22×C101—81no—
404C22×C101—81no—
405C22×C101C2×#12111yescharacteristic
406C22×C101D4211yescharacteristic
407C22×C101#54611yescharacteristic
408C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C101#57511yescharacteristic
410C22×C101#57611yescharacteristic
411C22×C101#57611yescharacteristic
412C4×C101—22no—
413C4×C101—22no—
414C4×C101—41no—
415C4×C101—41no—
416C4×C101—42no—
417C4×C101—42no—
418C4×C101—81no—
419C4×C101—81no—
420C4×C101—81no—
421C4×C101#53211yescharacteristic
422C4×C101#54011yescharacteristic
423C4×C101D4211yescharacteristic
424C4×C101#55011yescharacteristic
425#25396C10111yesmaximal, characteristic, direct product factor, Sylow
426C2×C101—42no—
427C2×C101—81no—
428C2×C101—82no—
429C2×C101—161no—
430C2×C101—161no—
431C2×C101#242811yescharacteristic
432C2×C101#305511yescharacteristic
433C2×C101#305811yescharacteristic
434C2×C101#326411yescharacteristic
435C2×C101#326811yescharacteristic
436C2×C101#330911yescharacteristic
437C2×C101#331811yescharacteristic
438C2×#469C2×C10111yescharacteristic, complemented
439C2×#466C2×C10111yescharacteristic, complemented
440C2×#459C2×C10111yescharacteristic, complemented
441C2×#435C2×C10111yescharacteristic, complemented
442#2541C2×C10111yescharacteristic, complemented
443#2535C2×C10111yescharacteristic, complemented
444#2034C2×C10111yescharacteristic, complemented
445#2033C2×C10111yescharacteristic, complemented
446#1999C2×C10111yescharacteristic, complemented
447#1999C2×C10111yescharacteristic, complemented
448#1961C2×C10111yescharacteristic, complemented
449#1949C2×C10111yescharacteristic, complemented
450#1895C2×C10111yescharacteristic, complemented
451#1893C2×C10111yescharacteristic, complemented
452#1762C2×C10111yescharacteristic, complemented
453C101#2539611yescharacteristic, direct product factor, Sylow
454C22×D8C22×C10111yescharacteristic
455C22×D8C22×C10111yescharacteristic
456C22×M16C22×C10111yescharacteristic
457C23×C8C22×C10111yescharacteristic
458C2×#127—21no—
459C2×#127C22×C10111yescharacteristic
460C2×#121C22×C10111yescharacteristic
461C2×#121C22×C10111yescharacteristic
462C2×#121C22×C10111yescharacteristic
463C2×#121C22×C10111yescharacteristic
464C2×#121C22×C10111yescharacteristic
465C2×#121C22×C10111yescharacteristic
466C2×C4×D4C22×C10111yescharacteristic
467C2×C4×D4C22×C10111yescharacteristic
468#469—24no—
469#466—24no—
470#459—24no—
471#435—24no—
472C2×#107C22×C10111yescharacteristic
473C2×#106C22×C10111yescharacteristic
474C2×C4⋊C8C22×C10111yescharacteristic
475C2×#102C22×C10111yescharacteristic
476C2×#102C22×C10111yescharacteristic
477C2×#102C22×C10111yescharacteristic
478C2×#102C22×C10111yescharacteristic
479C2×#102C22×C10111yescharacteristic
480C2×#102C22×C10111yescharacteristic
481C2×#102C22×C10111yescharacteristic
482C2×#102C22×C10111yescharacteristic
483C2×C22⋊C8C22×C10111yescharacteristic
484C2×C22⋊C8C22×C10111yescharacteristic
485C2×#97C22×C10111yescharacteristic
486#397—21no—
487#392—21no—
488#392—21no—
489#392—21no—
490#390—21no—
491#386—21no—
492#386—21no—
493#382C22×C10111yescharacteristic
494#380C22×C10111yescharacteristic
495#380C22×C10111yescharacteristic
496C4×C4⋊C4C22×C10111yescharacteristic
497#340C22×C10111yescharacteristic
498#340C22×C10111yescharacteristic
499#340C22×C10111yescharacteristic
500#340C22×C10111yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C10111yescharacteristic
510C22×D4C23×C10111yescharacteristic
511C22×D4C23×C10111yescharacteristic
512C22×D4C23×C10111yescharacteristic
513C23×C4—21no—
514C23×C4C23×C10111yescharacteristic
515C23×C4C23×C10111yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C10111yescharacteristic
529C22×C8C23×C10111yescharacteristic
530C22×C8C23×C10111yescharacteristic
531C22×C8C23×C10111yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C10111yescharacteristic
552C2×C4⋊C4C23×C10111yescharacteristic
553C2×C4⋊C4C23×C10111yescharacteristic
554C2×C4⋊C4C23×C10111yescharacteristic
555C2×C4⋊C4C23×C10111yescharacteristic
556C2×C4⋊C4C23×C10111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C10111yescharacteristic
567C2×C22⋊C4D4×C10111yescharacteristic
568C2×C42—21no—
569C2×C42C23×C10111yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C10114yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C10114yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C10111yescharacteristic
593C24C2×D4×C10111yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
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—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C10112yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C10111yescharacteristic
660C22×C4C2×D4×C10111yescharacteristic
661C22×C4C2×D4×C10111yescharacteristic
662C22×C4C2×D4×C10111yescharacteristic
663C22×C4C24×C10111yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C10112yes—
678C2×C8C2×D4×C10112yes—
679C2×C8C2×D4×C10112yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C10112yes—
690C4⋊C4#41×C10112yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C10112yes—
704C42#41×C10112yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C10112yes—
740C23C22×D4×C10111yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C10112yes—
797C2×C4#121×C10112yes—
798C2×C4C22×D4×C10111yescharacteristic
799C2×C4C22×D4×C10111yescharacteristic
800C2×C4C2×#41×C10111yescharacteristic
801C2×C4C2×#41×C10111yescharacteristic
802C2×C4H(5,𝔽2)×C10111yescharacteristic
803C2×C4H(5,𝔽2)×C10111yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C10111yescharacteristic
844C22D42×C10111yescharacteristic
845C22#546×C10111yescharacteristic
846C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
847C22#575×C10111yescharacteristic
848C22#576×C10111yescharacteristic
849C22#576×C10111yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—41no—
854C4—42no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4#532×C10111yescharacteristic
860C4#540×C10111yescharacteristic
861C4D42×C10111yescharacteristic
862C4#550×C10111yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2C101×#242811yescharacteristic
869C2C101×#305511yescharacteristic
870C2C101×#305811yescharacteristic
871C2C101×#326411yescharacteristic
872C2C101×#326811yescharacteristic
873C2C101×#330911yescharacteristic
874C2C101×#331811yescharacteristic
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×#466×C101C2semidirect
3. C2×#459×C101C2semidirect
4. C2×#435×C101C2semidirect
5. C101×#2541C2semidirect
6. C101×#2535C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#1999C2semidirect
10. C101×#1999C2semidirect
11. C101×#1961C2semidirect
12. C101×#1949C2semidirect
13. C101×#1895C2semidirect
14. C101×#1893C2semidirect
15. C101×#1762C2semidirect
134. C4⋊C8×C101D4semidirect
142. #102×C101D4semidirect
425. #25396C101direct (N × H)
438. C2×#469C2×C101semidirect
439. C2×#466C2×C101semidirect
440. C2×#459C2×C101semidirect
441. C2×#435C2×C101semidirect
442. #2541C2×C101semidirect
443. #2535C2×C101semidirect
444. #2034C2×C101semidirect
445. #2033C2×C101semidirect
446. #1999C2×C101semidirect
447. #1999C2×C101semidirect
448. #1961C2×C101semidirect
449. #1949C2×C101semidirect
450. #1895C2×C101semidirect
451. #1893C2×C101semidirect
452. #1762C2×C101semidirect
453. C101#25396direct (N × H)
572. C4⋊C8D4×C101semidirect
580. #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×#466×C1012
C2×#459×C1012
C2×#435×C1012
C101×#25412
C101×#25352
C101×#20342
C101×#20332
C101×#19992
C101×#19612
C101×#19492
C101×#18952
C101×#18932
C101×#17622
#25396101