Finite Group Databasebeta

← C101×#22870 #38805021

Subgroups — C101×#22870 #38805021

Order 25856.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C101C211yesmaximal, characteristic
2C2×C4×D8×C101C211yesmaximal, characteristic, complemented
3C22×#102×C101C211yesmaximal, characteristic, complemented
4C101×#2361C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
6C101×#1970C211yesmaximal, characteristic, complemented
7C101×#1934C211yesmaximal, characteristic, complemented
8C101×#1925C211yesmaximal, characteristic, complemented
9C101×#1893C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1862C211yesmaximal, characteristic, complemented
13C101×#1852C211yesmaximal, characteristic, complemented
14C4×#102×C101C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C101C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×C4×D4×C101—21no—
22C2×C4×D4×C101C2211yescharacteristic
23C2×C4×D4×C101C2211yescharacteristic
24C2×C4×D4×C101C2211yescharacteristic, complemented
25C22×C4⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101—21no—
27#447×C101C418yescomplemented
28C4×D8×C101—24no—
29C2×#107×C101C2211yescharacteristic, complemented
30C2×#107×C101C2211yescharacteristic, complemented
31C2×#102×C101—24no—
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic, complemented
39C2×#102×C101C2211yescharacteristic, complemented
40C2×C22⋊C8×C101C2211yescharacteristic
41C2×C4×C8×C101C2211yescharacteristic, complemented
42C2×C4×C8×C101C2211yescharacteristic, complemented
43#390×C101C2211yescharacteristic
44#390×C101C2211yescharacteristic
45#390×C101C2211yescharacteristic, complemented
46#389×C101C2211yescharacteristic, complemented
47#388×C101—21no—
48#386×C101—21no—
49#386×C101—21no—
50#386×C101—21no—
51#385×C101—21no—
52#380×C101C2211yescharacteristic
53#379×C101—21no—
54C4×C4⋊C4×C101C2211yescharacteristic, complemented
55C4×C22⋊C4×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#340×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61#336×C101C2211yescharacteristic, complemented
62C25×C101—21no—
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—22no—
68C22×D4×C101—41no—
69C22×D4×C101—41no—
70C22×D4×C101C2×C414yescomplemented
71C22×D4×C101C2311yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101—21no—
75C23×C4×C101—21no—
76C23×C4×C101—21no—
77C23×C4×C101—21no—
78C23×C4×C101C2311yescharacteristic
79C2×D8×C101—22no—
80C2×D8×C101—22no—
81C2×D8×C101—41no—
82C2×D8×C101—41no—
83C2×D8×C101C2×C414yescomplemented
84C2×D8×C101C2×C414yescomplemented
85C22×C8×C101—22no—
86C22×C8×C101—22no—
87C22×C8×C101—41no—
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92#121×C101—22no—
93#121×C101C2×C414yescomplemented
94C4×D4×C101—22no—
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C4×D4×C101—41no—
98C4×D4×C101—41no—
99C4×D4×C101—41no—
100C4×D4×C101—44no—
101C2×C4⋊C4×C101—22no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—21no—
104C2×C4⋊C4×C101—41no—
105C2×C4⋊C4×C101C2311yescharacteristic
106C2×C4⋊C4×C101C2311yescharacteristic
107C2×C4⋊C4×C101C2311yescharacteristic
108C2×C4⋊C4×C101C2311yescharacteristic
109C2×C4⋊C4×C101C2311yescharacteristic
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101—21no—
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—44no—
122C2×C22⋊C4×C101D411yescharacteristic
123C2×C22⋊C4×C101D411yescharacteristic
124C2×C42×C101—21no—
125C2×C42×C101C2311yescharacteristic
126C2×C42×C101C2311yescharacteristic
127#107×C101—22no—
128#107×C101—41no—
129#102×C101—22no—
130#102×C101—22no—
131#102×C101—22no—
132#102×C101—22no—
133#102×C101—41no—
134#102×C101C2×C414yescomplemented
135#102×C101C2×C414yescomplemented
136#102×C101D414yescomplemented
137C22⋊C8×C101C2×C414yescomplemented
138C4×C8×C101—22no—
139C4×C8×C101—41no—
140#95×C101—21no—
141#95×C101—21no—
142#95×C101—21no—
143#95×C101D411yescharacteristic
144#95×C101D411yescharacteristic
145C24×C101—21no—
146C24×C101—21no—
147C24×C101—21no—
148C24×C101—24no—
149C24×C101—42no—
150C24×C101—42no—
151C24×C101—42no—
152C24×C101—42no—
153C24×C101—81no—
154C24×C101—81no—
155C24×C101C2×D411yescharacteristic
156C2×D4×C101—28no—
157C2×D4×C101—24no—
158C2×D4×C101—24no—
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—44no—
173C2×D4×C101—44no—
174C2×D4×C101—44no—
175C2×D4×C101—42no—
176C2×D4×C101—42no—
177C2×D4×C101—42no—
178C2×D4×C101—42no—
179C2×D4×C101C22×C412yes—
180C2×D4×C101C22×C412yes—
181C2×D4×C101C22×C412yes—
182C2×D4×C101C2×D412yes—
183C2×D4×C101#4112yes—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—42no—
194C22×C4×C101—42no—
195C22×C4×C101—42no—
196C22×C4×C101—42no—
197C22×C4×C101—42no—
198C22×C4×C101—42no—
199C22×C4×C101—42no—
200C22×C4×C101—42no—
201C22×C4×C101—81no—
202C22×C4×C101—81no—
203C22×C4×C101—81no—
204C22×C4×C101—81no—
205C22×C4×C101C22×C412yes—
206C22×C4×C101C2×D411yescharacteristic
207C22×C4×C101C2×D411yescharacteristic
208C22×C4×C101C2×D411yescharacteristic
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101#4112yes—
212C22×C4×C101C2411yescharacteristic
213D8×C101—28no—
214D8×C101—44no—
215C2×C8×C101—21no—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—44no—
225C2×C8×C101C22×C412yes—
226C2×C8×C101C22×C412yes—
227C2×C8×C101C2×D412yes—
228C4⋊C4×C101—21no—
229C4⋊C4×C101—21no—
230C4⋊C4×C101—21no—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—42no—
237C4⋊C4×C101—42no—
238C4⋊C4×C101C22×C412yes—
239C4⋊C4×C101C2×D412yes—
240C22⋊C4×C101—22no—
241C22⋊C4×C101—24no—
242C22⋊C4×C101—42no—
243C22⋊C4×C101—42no—
244C22⋊C4×C101—42no—
245C22⋊C4×C101—42no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—42no—
248C22⋊C4×C101—42no—
249C22⋊C4×C101—81no—
250C22⋊C4×C101—81no—
251C22⋊C4×C101—81no—
252C22⋊C4×C101D814yescomplemented
253C42×C101—21no—
254C42×C101—21no—
255C42×C101—21no—
256C42×C101—21no—
257C42×C101—42no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—22no—
263C23×C101—22no—
264C23×C101—22no—
265C23×C101—22no—
266C23×C101—22no—
267C23×C101—48no—
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—48no—
285C23×C101—84no—
286C23×C101—84no—
287C23×C101—84no—
288C23×C101—84no—
289C23×C101—84no—
290C23×C101C4×D412yes—
291C23×C101C2×D812yes—
292C23×C101#13512yes—
293C23×C101C22×D411yescharacteristic
294D4×C101—22no—
295D4×C101—22no—
296D4×C101—22no—
297D4×C101—22no—
298D4×C101—22no—
299D4×C101—22no—
300D4×C101—22no—
301D4×C101—48no—
302D4×C101—48no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101C4×D414yescomplemented
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—22no—
315C2×C4×C101—22no—
316C2×C4×C101—22no—
317C2×C4×C101—22no—
318C2×C4×C101—22no—
319C2×C4×C101—21no—
320C2×C4×C101—22no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—84no—
340C2×C4×C101—84no—
341C2×C4×C101—84no—
342C2×C4×C101—84no—
343C2×C4×C101C4×D412yes—
344C2×C4×C101C2×D812yes—
345C2×C4×C101C2×D812yes—
346C2×C4×C101C23×C411yescharacteristic
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C2×#4111yescharacteristic
349C2×C4×C101C2×#4111yescharacteristic
350C2×C4×C101H(5,𝔽2)11yescharacteristic
351C2×C4×C101H(5,𝔽2)11yescharacteristic
352C8×C101—22no—
353C8×C101—22no—
354C8×C101—22no—
355C8×C101—41no—
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—22no—
360C22×C101—22no—
361C22×C101—22no—
362C22×C101—24no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—42no—
370C22×C101—42no—
371C22×C101—42no—
372C22×C101—42no—
373C22×C101—42no—
374C22×C101—42no—
375C22×C101—816no—
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×C101C4×D814yescomplemented
385C22×C101C2×C4×D411yescharacteristic
386C22×C101D4211yescharacteristic
387C22×C101#54611yescharacteristic
388C22×C101C22×D811yescharacteristic
389C22×C101C2×#13511yescharacteristic
390C22×C101#57611yescharacteristic
391C22×C101#57711yescharacteristic
392C4×C101—22no—
393C4×C101—22no—
394C4×C101—22no—
395C4×C101—42no—
396C4×C101—42no—
397C4×C101—41no—
398C4×C101—41no—
399C4×C101—81no—
400C4×C101—81no—
401C4×C101—81no—
402C4×C101C2×C4×D411yescharacteristic
403C4×C101#51811yescharacteristic
404C4×C101#54611yescharacteristic
405C4×C101#55111yescharacteristic
406#22870C10111yesmaximal, characteristic, direct product factor, Sylow
407C2×C101—24no—
408C2×C101—44no—
409C2×C101—82no—
410C2×C101—82no—
411C2×C101#235811yescharacteristic
412C2×C101C2×C4×D811yescharacteristic
413C2×C101#294611yescharacteristic
414C2×C101D4×D811yescharacteristic
415C2×C101#328211yescharacteristic
416C2×C101#329411yescharacteristic
417C2×C101#329711yescharacteristic
418C2×#447C2×C10111yescharacteristic
419C2×C4×D8C2×C10111yescharacteristic, complemented
420C22×#102C2×C10111yescharacteristic, complemented
421#2361C2×C10111yescharacteristic, complemented
422D4×C22⋊C4C2×C10111yescharacteristic, complemented
423#1970C2×C10111yescharacteristic, complemented
424#1934C2×C10111yescharacteristic, complemented
425#1925C2×C10111yescharacteristic, complemented
426#1893C2×C10111yescharacteristic, complemented
427#1879C2×C10111yescharacteristic, complemented
428#1879C2×C10111yescharacteristic, complemented
429#1862C2×C10111yescharacteristic, complemented
430#1852C2×C10111yescharacteristic, complemented
431C4×#102C2×C10111yescharacteristic, complemented
432C8×C22⋊C4C2×C10111yescharacteristic, complemented
433C101#2287011yescharacteristic, direct product factor, Sylow
434C23×D4C22×C10111yescharacteristic
435C22×D8C22×C10111yescharacteristic
436C22×D8C22×C10111yescharacteristic
437C23×C8C22×C10111yescharacteristic
438C2×#121C22×C10111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C10111yescharacteristic
441C2×C4×D4C22×C10111yescharacteristic
442C2×C4×D4C22×C10111yescharacteristic, complemented
443C22×C4⋊C4C22×C10111yescharacteristic
444C22×C22⋊C4—21no—
445#447C4×C10118yescomplemented
446C4×D8—24no—
447C2×#107C22×C10111yescharacteristic, complemented
448C2×#107C22×C10111yescharacteristic, complemented
449C2×#102—24no—
450C2×#102C22×C10111yescharacteristic
451C2×#102C22×C10111yescharacteristic
452C2×#102C22×C10111yescharacteristic
453C2×#102C22×C10111yescharacteristic
454C2×#102C22×C10111yescharacteristic
455C2×#102C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic, complemented
457C2×#102C22×C10111yescharacteristic, complemented
458C2×C22⋊C8C22×C10111yescharacteristic
459C2×C4×C8C22×C10111yescharacteristic, complemented
460C2×C4×C8C22×C10111yescharacteristic, complemented
461#390C22×C10111yescharacteristic
462#390C22×C10111yescharacteristic
463#390C22×C10111yescharacteristic, complemented
464#389C22×C10111yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#380C22×C10111yescharacteristic
471#379—21no—
472C4×C4⋊C4C22×C10111yescharacteristic, complemented
473C4×C22⋊C4C22×C10111yescharacteristic
474#340C22×C10111yescharacteristic, complemented
475#340C22×C10111yescharacteristic, complemented
476#340C22×C10111yescharacteristic, complemented
477#340C22×C10111yescharacteristic, complemented
478#336C22×C10111yescharacteristic, complemented
479#336C22×C10111yescharacteristic, complemented
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—22no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×C4×C10114yescomplemented
489C22×D4C23×C10111yescharacteristic
490C22×D4C23×C10111yescharacteristic
491C22×D4C23×C10111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C10111yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×C4×C10114yescomplemented
502C2×D8C2×C4×C10114yescomplemented
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8C23×C10111yescharacteristic
507C22×C8C23×C10111yescharacteristic
508C22×C8C23×C10111yescharacteristic
509C22×C8C23×C10111yescharacteristic
510#121—22no—
511#121C2×C4×C10114yescomplemented
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—41no—
516C4×D4—41no—
517C4×D4—41no—
518C4×D4—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4C23×C10111yescharacteristic
524C2×C4⋊C4C23×C10111yescharacteristic
525C2×C4⋊C4C23×C10111yescharacteristic
526C2×C4⋊C4C23×C10111yescharacteristic
527C2×C4⋊C4C23×C10111yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4D4×C10111yescharacteristic
541C2×C22⋊C4D4×C10111yescharacteristic
542C2×C42—21no—
543C2×C42C23×C10111yescharacteristic
544C2×C42C23×C10111yescharacteristic
545#107—22no—
546#107—41no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102C2×C4×C10114yescomplemented
553#102C2×C4×C10114yescomplemented
554#102D4×C10114yescomplemented
555C22⋊C8C2×C4×C10114yescomplemented
556C4×C8—22no—
557C4×C8—41no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C10111yescharacteristic
562#95D4×C10111yescharacteristic
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24C2×D4×C10111yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C22×C4×C10112yes—
598C2×D4C22×C4×C10112yes—
599C2×D4C22×C4×C10112yes—
600C2×D4C2×D4×C10112yes—
601C2×D4#41×C10112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4C22×C4×C10112yes—
624C22×C4C2×D4×C10111yescharacteristic
625C22×C4C2×D4×C10111yescharacteristic
626C22×C4C2×D4×C10111yescharacteristic
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629C22×C4#41×C10112yes—
630C22×C4C24×C10111yescharacteristic
631D8—28no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C22×C4×C10112yes—
644C2×C8C22×C4×C10112yes—
645C2×C8C2×D4×C10112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4C22×C4×C10112yes—
657C4⋊C4C2×D4×C10112yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4D8×C10114yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—48no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23C4×D4×C10112yes—
709C23C2×D8×C10112yes—
710C23#135×C10112yes—
711C23C22×D4×C10111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4C4×D4×C10114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4C4×D4×C10112yes—
762C2×C4C2×D8×C10112yes—
763C2×C4C2×D8×C10112yes—
764C2×C4C23×C4×C10111yescharacteristic
765C2×C4C22×D4×C10111yescharacteristic
766C2×C4C2×#41×C10111yescharacteristic
767C2×C4C2×#41×C10111yescharacteristic
768C2×C4H(5,𝔽2)×C10111yescharacteristic
769C2×C4H(5,𝔽2)×C10111yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C4×D8×C10114yescomplemented
803C22C2×C4×D4×C10111yescharacteristic
804C22D42×C10111yescharacteristic
805C22#546×C10111yescharacteristic
806C22C22×D8×C10111yescharacteristic
807C22C2×#135×C10111yescharacteristic
808C22#576×C10111yescharacteristic
809C22#577×C10111yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×C4×D4×C10111yescharacteristic
821C4#518×C10111yescharacteristic
822C4#546×C10111yescharacteristic
823C4#551×C10111yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2C101×#235811yescharacteristic
829C2C2×C4×D8×C10111yescharacteristic
830C2C101×#294611yescharacteristic
831C2D4×D8×C10111yescharacteristic
832C2C101×#328211yescharacteristic
833C2C101×#329411yescharacteristic
834C2C101×#329711yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C2×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
2. C2×C4×D8×C101C2semidirect
3. C22×#102×C101C2semidirect
4. C101×#2361C2semidirect
5. D4×C22⋊C4×C101C2semidirect
6. C101×#1970C2semidirect
7. C101×#1934C2semidirect
8. C101×#1925C2semidirect
9. C101×#1893C2semidirect
10. C101×#1879C2semidirect
11. C101×#1879C2semidirect
12. C101×#1862C2semidirect
13. C101×#1852C2semidirect
14. C4×#102×C101C2semidirect
15. C8×C22⋊C4×C101C2semidirect
24. C2×C4×D4×C101C22semidirect
27. #447×C101C4semidirect
29. C2×#107×C101C22semidirect
30. C2×#107×C101C22semidirect
38. C2×#102×C101C22semidirect
39. C2×#102×C101C22semidirect
41. C2×C4×C8×C101C22semidirect
42. C2×C4×C8×C101C22semidirect
45. #390×C101C22semidirect
46. #389×C101C22semidirect
54. C4×C4⋊C4×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #340×C101C22semidirect
60. #336×C101C22semidirect
61. #336×C101C22semidirect
70. C22×D4×C101C2×C4semidirect
83. C2×D8×C101C2×C4semidirect
84. C2×D8×C101C2×C4semidirect
93. #121×C101C2×C4semidirect
134. #102×C101C2×C4semidirect
135. #102×C101C2×C4semidirect
136. #102×C101D4semidirect
137. C22⋊C8×C101C2×C4semidirect
252. C22⋊C4×C101D8semidirect
307. D4×C101C4×D4semidirect
384. C22×C101C4×D8semidirect
406. #22870C101direct (N × H)
419. C2×C4×D8C2×C101semidirect
420. C22×#102C2×C101semidirect
421. #2361C2×C101semidirect
422. D4×C22⋊C4C2×C101semidirect
423. #1970C2×C101semidirect
424. #1934C2×C101semidirect
425. #1925C2×C101semidirect
426. #1893C2×C101semidirect
427. #1879C2×C101semidirect
428. #1879C2×C101semidirect
429. #1862C2×C101semidirect
430. #1852C2×C101semidirect
431. C4×#102C2×C101semidirect
432. C8×C22⋊C4C2×C101semidirect
433. C101#22870direct (N × H)
442. C2×C4×D4C22×C101semidirect
445. #447C4×C101semidirect
447. C2×#107C22×C101semidirect
448. C2×#107C22×C101semidirect
456. C2×#102C22×C101semidirect
457. C2×#102C22×C101semidirect
459. C2×C4×C8C22×C101semidirect
460. C2×C4×C8C22×C101semidirect
463. #390C22×C101semidirect
464. #389C22×C101semidirect
472. C4×C4⋊C4C22×C101semidirect
474. #340C22×C101semidirect
475. #340C22×C101semidirect
476. #340C22×C101semidirect
477. #340C22×C101semidirect
478. #336C22×C101semidirect
479. #336C22×C101semidirect
488. C22×D4C2×C4×C101semidirect
501. C2×D8C2×C4×C101semidirect
502. C2×D8C2×C4×C101semidirect
511. #121C2×C4×C101semidirect
552. #102C2×C4×C101semidirect
553. #102C2×C4×C101semidirect
554. #102D4×C101semidirect
555. C22⋊C8C2×C4×C101semidirect
670. C22⋊C4D8×C101semidirect
725. D4C4×D4×C101semidirect
802. C22C4×D8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1012
C2×C4×D8×C1012
C22×#102×C1012
C101×#23612
D4×C22⋊C4×C1012
C101×#19702
C101×#19342
C101×#19252
C101×#18932
C101×#18792
C101×#18622
C101×#18522
C4×#102×C1012
C8×C22⋊C4×C1012
#22870101