Finite Group Databasebeta

← C101×#14041 #38796192

Subgroups — C101×#14041 #38796192

Order 25856.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C101C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C101C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C101C211yesmaximal, characteristic
4C101×#1445C212yesmaximal
5C101×#1442C212yesmaximal
6C101×#1436C212yesmaximal
7C101×#1436C212yesmaximal
8C101×C4⋊#95C211yesmaximal, characteristic
9C101×C4⋊#95C211yesmaximal, characteristic
10C101×C4⋊#95C211yesmaximal, characteristic
11C101×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C101C2211yescharacteristic
13C22×C4⋊C4×C101C2211yescharacteristic
14C22×C4⋊C4×C101C2211yescharacteristic
15C22×C4⋊C4×C101C2211yescharacteristic
16C22×C4⋊C4×C101C2211yescharacteristic
17C22×C4⋊C4×C101C2211yescharacteristic
18C22×C4⋊C4×C101C2212yes—
19C22×C42×C101C2211yescharacteristic
20C22×C42×C101C2211yescharacteristic
21C22×C42×C101C2211yescharacteristic
22C22×C42×C101C2212yes—
23#389×C101C418yescomplemented
24C4×C4⋊C4×C101—24no—
25C4×C4⋊C4×C101—24no—
26C2×#95×C101C2212yes—
27C2×#95×C101C2212yes—
28C2×#95×C101C2212yes—
29C2×#95×C101C2211yescharacteristic
30C2×#95×C101C2212yes—
31C2×#95×C101C2211yescharacteristic
32C2×#95×C101C2212yes—
33C2×#95×C101C2212yes—
34C2×#95×C101C2212yes—
35C2×#95×C101C2212yes—
36C2×#95×C101C2212yes—
37C2×#95×C101C2212yes—
38C23×C4×C101C2312yes—
39C23×C4×C101C2311yescharacteristic
40C23×C4×C101C2312yes—
41C23×C4×C101C2312yes—
42C23×C4×C101C2311yescharacteristic
43C23×C4×C101C2312yes—
44C23×C4×C101C2311yescharacteristic
45C23×C4×C101C2311yescharacteristic
46C23×C4×C101C2311yescharacteristic
47C23×C4×C101C2311yescharacteristic
48C23×C4×C101C2311yescharacteristic
49C2×C4⋊C4×C101—22no—
50C2×C4⋊C4×C101—22no—
51C2×C4⋊C4×C101—22no—
52C2×C4⋊C4×C101—22no—
53C2×C4⋊C4×C101—22no—
54C2×C4⋊C4×C101—22no—
55C2×C4⋊C4×C101—22no—
56C2×C4⋊C4×C101—22no—
57C2×C4⋊C4×C101—22no—
58C2×C4⋊C4×C101—22no—
59C2×C4⋊C4×C101—22no—
60C2×C4⋊C4×C101—22no—
61C2×C4⋊C4×C101—22no—
62C2×C4⋊C4×C101—22no—
63C2×C4⋊C4×C101—42no—
64C2×C4⋊C4×C101—42no—
65C2×C4⋊C4×C101C2×C414yes—
66C2×C4⋊C4×C101C2×C414yes—
67C2×C4⋊C4×C101C2×C418yes—
68C2×C4⋊C4×C101Q814yes—
69C2×C4⋊C4×C101Q814yes—
70C2×C42×C101—22no—
71C2×C42×C101—22no—
72C2×C42×C101—22no—
73C2×C42×C101—22no—
74C2×C42×C101—24no—
75C2×C42×C101—22no—
76C2×C42×C101—22no—
77C2×C42×C101—22no—
78C2×C42×C101—42no—
79C2×C42×C101—42no—
80C2×C42×C101C2×C414yes—
81C2×C42×C101D414yes—
82#95×C101—22no—
83#95×C101—22no—
84#95×C101—24no—
85#95×C101—24no—
86#95×C101—24no—
87#95×C101—24no—
88#95×C101—42no—
89#95×C101—42no—
90#95×C101—42no—
91#95×C101—42no—
92#95×C101—42no—
93#95×C101C2×C418yes—
94C24×C101C2411yescharacteristic
95C22×C4×C101—21no—
96C22×C4×C101—21no—
97C22×C4×C101—21no—
98C22×C4×C101—21no—
99C22×C4×C101—21no—
100C22×C4×C101—21no—
101C22×C4×C101—21no—
102C22×C4×C101—21no—
103C22×C4×C101—21no—
104C22×C4×C101—22no—
105C22×C4×C101—21no—
106C22×C4×C101—22no—
107C22×C4×C101—21no—
108C22×C4×C101—22no—
109C22×C4×C101—22no—
110C22×C4×C101—22no—
111C22×C4×C101—22no—
112C22×C4×C101—21no—
113C22×C4×C101—21no—
114C22×C4×C101—21no—
115C22×C4×C101—21no—
116C22×C4×C101—21no—
117C22×C4×C101—21no—
118C22×C4×C101—21no—
119C22×C4×C101—22no—
120C22×C4×C101—22no—
121C22×C4×C101—22no—
122C22×C4×C101—21no—
123C22×C4×C101—22no—
124C22×C4×C101—21no—
125C22×C4×C101—21no—
126C22×C4×C101—21no—
127C22×C4×C101—21no—
128C22×C4×C101—21no—
129C22×C4×C101—21no—
130C22×C4×C101—21no—
131C22×C4×C101—21no—
132C22×C4×C101—22no—
133C22×C4×C101—22no—
134C22×C4×C101—22no—
135C22×C4×C101—22no—
136C22×C4×C101—22no—
137C22×C4×C101—22no—
138C22×C4×C101—22no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—21no—
142C22×C4×C101—22no—
143C22×C4×C101—21no—
144C22×C4×C101—21no—
145C22×C4×C101—22no—
146C22×C4×C101—22no—
147C22×C4×C101—22no—
148C22×C4×C101—22no—
149C22×C4×C101—22no—
150C22×C4×C101—22no—
151C22×C4×C101—22no—
152C22×C4×C101C22×C414yes—
153C22×C4×C101C22×C414yes—
154C22×C4×C101C22×C412yes—
155C22×C4×C101C22×C412yes—
156C22×C4×C101C22×C412yes—
157C22×C4×C101C2×D412yes—
158C22×C4×C101C2×D412yes—
159C22×C4×C101C2×D412yes—
160C22×C4×C101C2×Q814yes—
161C22×C4×C101C2×Q812yes—
162C22×C4×C101C2×Q812yes—
163C22×C4×C101C2×Q812yes—
164C22×C4×C101C2×Q812yes—
165C22×C4×C101#4112yes—
166C22×C4×C101#4112yes—
167C22×C4×C101#4112yes—
168C22×C4×C101#4112yes—
169C22×C4×C101#4112yes—
170C22×C4×C101#4112yes—
171C22×C4×C101#4112yes—
172C4⋊C4×C101—28no—
173C4⋊C4×C101—28no—
174C4⋊C4×C101—28no—
175C4⋊C4×C101—28no—
176C4⋊C4×C101—28no—
177C4⋊C4×C101—48no—
178C4⋊C4×C101—44no—
179C42×C101—28no—
180C42×C101—28no—
181C42×C101—48no—
182C42×C101—44no—
183C23×C101C23×C411yescharacteristic
184C23×C101C22×D411yescharacteristic
185C23×C101C22×Q811yescharacteristic
186C23×C101C22×Q811yescharacteristic
187C23×C101C2×#4111yescharacteristic
188C23×C101C2×#4111yescharacteristic
189C23×C101C2×#4111yescharacteristic
190C23×C101C2×#4111yescharacteristic
191C23×C101C2×#4111yescharacteristic
192C23×C101C2×#4111yescharacteristic
193C23×C101C2×#4111yescharacteristic
194C23×C101H(5,𝔽2)11yescharacteristic
195C23×C101H(5,𝔽2)11yescharacteristic
196C23×C101H(5,𝔽2)11yescharacteristic
197C23×C1012−1+411yescharacteristic
198C2×C4×C101—22no—
199C2×C4×C101—22no—
200C2×C4×C101—22no—
201C2×C4×C101—22no—
202C2×C4×C101—22no—
203C2×C4×C101—22no—
204C2×C4×C101—22no—
205C2×C4×C101—22no—
206C2×C4×C101—22no—
207C2×C4×C101—22no—
208C2×C4×C101—22no—
209C2×C4×C101—22no—
210C2×C4×C101—24no—
211C2×C4×C101—22no—
212C2×C4×C101—24no—
213C2×C4×C101—24no—
214C2×C4×C101—22no—
215C2×C4×C101—24no—
216C2×C4×C101—24no—
217C2×C4×C101—22no—
218C2×C4×C101—24no—
219C2×C4×C101—24no—
220C2×C4×C101—22no—
221C2×C4×C101—22no—
222C2×C4×C101—22no—
223C2×C4×C101—22no—
224C2×C4×C101—22no—
225C2×C4×C101—22no—
226C2×C4×C101—22no—
227C2×C4×C101—24no—
228C2×C4×C101—24no—
229C2×C4×C101—22no—
230C2×C4×C101—22no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—42no—
234C2×C4×C101—42no—
235C2×C4×C101—42no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—42no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—42no—
243C2×C4×C101—41no—
244C2×C4×C101—42no—
245C2×C4×C101—41no—
246C2×C4×C101—42no—
247C2×C4×C101—42no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—42no—
256C2×C4×C101—42no—
257C2×C4×C101—42no—
258C2×C4×C101—42no—
259C2×C4×C101—42no—
260C2×C4×C101—42no—
261C2×C4×C101—42no—
262C2×C4×C101—42no—
263C2×C4×C101—42no—
264C2×C4×C101—42no—
265C2×C4×C101—42no—
266C2×C4×C101#11714yes—
267C2×C4×C101C4×D414yes—
268C2×C4×C101C4×Q814yes—
269C2×C4×C101C4×Q814yes—
270C2×C4×C101C22⋊Q814yes—
271C2×C4×C101C22⋊Q814yes—
272C2×C4×C101#12314yes—
273C2×C4×C101#12514yes—
274C2×C4×C101#12614yes—
275C22×C101C2×#11711yescharacteristic
276C22×C101C2×C4×D411yescharacteristic
277C22×C101C2×C4×Q811yescharacteristic
278C22×C101C2×C4×Q811yescharacteristic
279C22×C101C4×#4111yescharacteristic
280C22×C101#51811yescharacteristic
281C22×C101#52011yescharacteristic
282C22×C101C2×C22⋊Q811yescharacteristic
283C22×C101C2×C22⋊Q811yescharacteristic
284C22×C101C2×#12311yescharacteristic
285C22×C101#52511yescharacteristic
286C22×C101C2×#12511yescharacteristic
287C22×C101C2×#12611yescharacteristic
288C22×C101#52911yescharacteristic
289C22×C101#53311yescharacteristic
290C22×C101#53511yescharacteristic
291C22×C101#53711yescharacteristic
292C22×C101#54011yescharacteristic
293C22×C101#54211yescharacteristic
294C22×C101#55211yescharacteristic
295C22×C101#55311yescharacteristic
296C22×C101#55311yescharacteristic
297C22×C101#55311yescharacteristic
298C22×C101#55411yescharacteristic
299C22×C101#55411yescharacteristic
300C22×C101#55411yescharacteristic
301C22×C101#55411yescharacteristic
302C22×C101#55511yescharacteristic
303C22×C101#55611yescharacteristic
304C22×C101#55711yescharacteristic
305C22×C101#55711yescharacteristic
306C22×C101Q8211yescharacteristic
307C22×C101#55911yescharacteristic
308C22×C101#55911yescharacteristic
309C22×C101#55911yescharacteristic
310C4×C101—24no—
311C4×C101—24no—
312C4×C101—42no—
313C4×C101—44no—
314C4×C101—44no—
315C4×C101—44no—
316C4×C101—42no—
317C4×C101—42no—
318C4×C101—42no—
319C4×C101—82no—
320C4×C101#38718yes—
321#14041C10111yesmaximal, characteristic, direct product factor, Sylow
322C2×C101C2×#38711yescharacteristic
323C2×C101C4×C22⋊Q811yescharacteristic
324C2×C101#232411yescharacteristic
325C2×C101#235511yescharacteristic
326C2×C101#235711yescharacteristic
327C2×C101#236911yescharacteristic
328C2×C101#237011yescharacteristic
329C2×C101#248511yescharacteristic
330C2×C101#248711yescharacteristic
331C2×C101#250711yescharacteristic
332C2×C101#250911yescharacteristic
333C2×C101#251111yescharacteristic
334C2×C101#251311yescharacteristic
335C2×C101#258011yescharacteristic
336C2×C101#258211yescharacteristic
337C2×#389C2×C10111yescharacteristic
338C2×C4×C4⋊C4C2×C10111yescharacteristic
339C2×C4×C4⋊C4C2×C10111yescharacteristic
340#1445C2×C10112yes—
341#1442C2×C10112yes—
342#1436C2×C10112yes—
343#1436C2×C10112yes—
344C4⋊#95C2×C10111yescharacteristic
345C4⋊#95C2×C10111yescharacteristic
346C4⋊#95C2×C10111yescharacteristic
347C4⋊#95C2×C10111yescharacteristic
348C101#1404111yescharacteristic, direct product factor, Sylow
349C22×C4⋊C4C22×C10111yescharacteristic
350C22×C4⋊C4C22×C10111yescharacteristic
351C22×C4⋊C4C22×C10111yescharacteristic
352C22×C4⋊C4C22×C10111yescharacteristic
353C22×C4⋊C4C22×C10111yescharacteristic
354C22×C4⋊C4C22×C10111yescharacteristic
355C22×C4⋊C4C22×C10112yes—
356C22×C42C22×C10111yescharacteristic
357C22×C42C22×C10111yescharacteristic
358C22×C42C22×C10111yescharacteristic
359C22×C42C22×C10112yes—
360#389C4×C10118yescomplemented
361C4×C4⋊C4—24no—
362C4×C4⋊C4—24no—
363C2×#95C22×C10112yes—
364C2×#95C22×C10112yes—
365C2×#95C22×C10112yes—
366C2×#95C22×C10111yescharacteristic
367C2×#95C22×C10112yes—
368C2×#95C22×C10111yescharacteristic
369C2×#95C22×C10112yes—
370C2×#95C22×C10112yes—
371C2×#95C22×C10112yes—
372C2×#95C22×C10112yes—
373C2×#95C22×C10112yes—
374C2×#95C22×C10112yes—
375C23×C4C23×C10112yes—
376C23×C4C23×C10112yes—
377C23×C4C23×C10111yescharacteristic
378C23×C4C23×C10112yes—
379C23×C4C23×C10111yescharacteristic
380C23×C4C23×C10112yes—
381C23×C4C23×C10111yescharacteristic
382C23×C4C23×C10111yescharacteristic
383C23×C4C23×C10111yescharacteristic
384C23×C4C23×C10111yescharacteristic
385C23×C4C23×C10111yescharacteristic
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4C2×C4×C10114yes—
403C2×C4⋊C4C2×C4×C10114yes—
404C2×C4⋊C4C2×C4×C10118yes—
405C2×C4⋊C4Q8×C10114yes—
406C2×C4⋊C4Q8×C10114yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42C2×C4×C10114yes—
418C2×C42D4×C10114yes—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95C2×C4×C10118yes—
431C24C24×C10111yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4C22×C4×C10114yes—
490C22×C4C22×C4×C10114yes—
491C22×C4C22×C4×C10112yes—
492C22×C4C22×C4×C10112yes—
493C22×C4C22×C4×C10112yes—
494C22×C4C2×D4×C10112yes—
495C22×C4C2×D4×C10112yes—
496C22×C4C2×D4×C10112yes—
497C22×C4C2×Q8×C10114yes—
498C22×C4C2×Q8×C10112yes—
499C22×C4C2×Q8×C10112yes—
500C22×C4C2×Q8×C10112yes—
501C22×C4C2×Q8×C10112yes—
502C22×C4#41×C10112yes—
503C22×C4#41×C10112yes—
504C22×C4#41×C10112yes—
505C22×C4#41×C10112yes—
506C22×C4#41×C10112yes—
507C22×C4#41×C10112yes—
508C22×C4#41×C10112yes—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—28no—
514C4⋊C4—48no—
515C4⋊C4—44no—
516C42—28no—
517C42—28no—
518C42—48no—
519C42—44no—
520C23C23×C4×C10111yescharacteristic
521C23C22×D4×C10111yescharacteristic
522C23C22×Q8×C10111yescharacteristic
523C23C22×Q8×C10111yescharacteristic
524C23C2×#41×C10111yescharacteristic
525C23C2×#41×C10111yescharacteristic
526C23C2×#41×C10111yescharacteristic
527C23C2×#41×C10111yescharacteristic
528C23C2×#41×C10111yescharacteristic
529C23C2×#41×C10111yescharacteristic
530C23C2×#41×C10111yescharacteristic
531C23H(5,𝔽2)×C10111yescharacteristic
532C23H(5,𝔽2)×C10111yescharacteristic
533C23H(5,𝔽2)×C10111yescharacteristic
534C232−1+4×C10111yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4#117×C10114yes—
604C2×C4C4×D4×C10114yes—
605C2×C4C4×Q8×C10114yes—
606C2×C4C4×Q8×C10114yes—
607C2×C4C22⋊Q8×C10114yes—
608C2×C4C22⋊Q8×C10114yes—
609C2×C4#123×C10114yes—
610C2×C4#125×C10114yes—
611C2×C4#126×C10114yes—
612C22C2×#117×C10111yescharacteristic
613C22C2×C4×D4×C10111yescharacteristic
614C22C2×C4×Q8×C10111yescharacteristic
615C22C2×C4×Q8×C10111yescharacteristic
616C22C4×#41×C10111yescharacteristic
617C22#518×C10111yescharacteristic
618C22#520×C10111yescharacteristic
619C22C2×C22⋊Q8×C10111yescharacteristic
620C22C2×C22⋊Q8×C10111yescharacteristic
621C22C2×#123×C10111yescharacteristic
622C22#525×C10111yescharacteristic
623C22C2×#125×C10111yescharacteristic
624C22C2×#126×C10111yescharacteristic
625C22#529×C10111yescharacteristic
626C22#533×C10111yescharacteristic
627C22#535×C10111yescharacteristic
628C22#537×C10111yescharacteristic
629C22#540×C10111yescharacteristic
630C22#542×C10111yescharacteristic
631C22#552×C10111yescharacteristic
632C22#553×C10111yescharacteristic
633C22#553×C10111yescharacteristic
634C22#553×C10111yescharacteristic
635C22#554×C10111yescharacteristic
636C22#554×C10111yescharacteristic
637C22#554×C10111yescharacteristic
638C22#554×C10111yescharacteristic
639C22#555×C10111yescharacteristic
640C22#556×C10111yescharacteristic
641C22#557×C10111yescharacteristic
642C22#557×C10111yescharacteristic
643C22Q82×C10111yescharacteristic
644C22#559×C10111yescharacteristic
645C22#559×C10111yescharacteristic
646C22#559×C10111yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—44no—
654C4—44no—
655C4—44no—
656C4—82no—
657C4#387×C10118yes—
658C2C2×#387×C10111yescharacteristic
659C2C4×C22⋊Q8×C10111yescharacteristic
660C2C101×#232411yescharacteristic
661C2C101×#235511yescharacteristic
662C2C101×#235711yescharacteristic
663C2C101×#236911yescharacteristic
664C2C101×#237011yescharacteristic
665C2C101×#248511yescharacteristic
666C2C101×#248711yescharacteristic
667C2C101×#250711yescharacteristic
668C2C101×#250911yescharacteristic
669C2C101×#251111yescharacteristic
670C2C101×#251311yescharacteristic
671C2C101×#258011yescharacteristic
672C2C101×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
23. #389×C101C4semidirect
321. #14041C101direct (N × H)
348. C101#14041direct (N × H)
360. #389C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1012
C2×C4×C4⋊C4×C1012
C101×#14452
C101×#14422
C101×#14362
C101×C4⋊#952
#14041101