Finite Group Databasebeta

← C101×#25938 #38808089

Subgroups — C101×#25938 #38808089

Order 25856.

1104 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C101C211yesmaximal, characteristic, complemented
2C2×#488×C101C211yesmaximal, characteristic, complemented
3C2×#463×C101C211yesmaximal, characteristic
4C101×#2592C211yesmaximal, characteristic, complemented
5C101×#2026C211yesmaximal, characteristic, complemented
6C101×#2025C211yesmaximal, characteristic, complemented
7C101×#2024C211yesmaximal, characteristic, complemented
8C101×#2023C211yesmaximal, characteristic, complemented
9C101×#1989C211yesmaximal, characteristic, complemented
10C101×#1984C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic
12C101×#1879C211yesmaximal, characteristic
13C101×#1877C211yesmaximal, characteristic, complemented
14C101×#1877C211yesmaximal, characteristic, complemented
15C4×#102×C101C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18#554×C101—24no—
19#554×C101—24no—
20C2×C4⋊Q8×C101C2211yescharacteristic
21C2×#125×C101C2211yescharacteristic
22C2×#125×C101C2211yescharacteristic
23C2×#124×C101C2211yescharacteristic
24C2×C22⋊Q8×C101—21no—
25C2×C22⋊Q8×C101—21no—
26C2×C22⋊Q8×C101—21no—
27C2×C4×Q8×C101C2211yescharacteristic
28C2×C4×D4×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30C2×C4×D4×C101C2211yescharacteristic
31C22×C4⋊C4×C101—21no—
32#488×C101—24no—
33#463×C101—24no—
34C2×C4⋊C8×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#103×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×C4×C8×C101C2211yescharacteristic
44#397×C101—21no—
45#393×C101—21no—
46#391×C101C2211yescharacteristic
47#391×C101C2211yescharacteristic
48#390×C101C2211yescharacteristic
49#390×C101C2211yescharacteristic
50#388×C101—21no—
51#388×C101—21no—
52C4×C4⋊C4×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×Q8×C101—21no—
64C22×Q8×C101D411yescharacteristic
65C22×Q8×C101C2311yescharacteristic
66C22×D4×C101C2311yescharacteristic
67C22×D4×C101C2311yescharacteristic
68C23×C4×C101—21no—
69C23×C4×C101—21no—
70C23×C4×C101—21no—
71C2×SD16×C101—22no—
72C2×SD16×C101—22no—
73C2×SD16×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C22×C8×C101C2311yescharacteristic
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C4⋊Q8×C101—22no—
82C4⋊Q8×C101—22no—
83#125×C101—22no—
84#125×C101—22no—
85#125×C101—22no—
86#125×C101D414yes—
87#124×C101—22no—
88#124×C101—22no—
89C22⋊Q8×C101—28no—
90C22⋊Q8×C101—28no—
91C22⋊Q8×C101—28no—
92C4×Q8×C101—22no—
93C4×Q8×C101—22no—
94C4×D4×C101—22no—
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99C4×D4×C101D414yes—
100C2×C4⋊C4×C101—28no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—21no—
104C2×C4⋊C4×C101—21no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101D411yescharacteristic
107C2×C4⋊C4×C101D411yescharacteristic
108C2×C4⋊C4×C101D411yescharacteristic
109C2×C4⋊C4×C101C2311yescharacteristic
110C2×C4⋊C4×C101C2311yescharacteristic
111C2×C4⋊C4×C101C2311yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
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—21no—
122C2×C22⋊C4×C101—21no—
123C2×C42×C101—21no—
124C2×C42×C101C2311yescharacteristic
125C2×C42×C101C2311yescharacteristic
126C2×C42×C101C2311yescharacteristic
127C4⋊C8×C101—22no—
128#103×C101—22no—
129#103×C101—22no—
130#103×C101—22no—
131#102×C101—22no—
132#102×C101—22no—
133#102×C101—22no—
134#102×C101—22no—
135#102×C101—22no—
136C4×C8×C101—22no—
137#95×C101—21no—
138#95×C101—21no—
139#95×C101—21no—
140#95×C101—21no—
141#95×C101—21no—
142C24×C101—21no—
143C24×C101—21no—
144C2×Q8×C101—24no—
145C2×Q8×C101—22no—
146C2×Q8×C101—22no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—41no—
154C2×Q8×C101—81no—
155C2×Q8×C101—81no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
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×C101C2×D412yes—
166C2×D4×C101#4112yes—
167C2×D4×C101#4112yes—
168C22×C4×C101—24no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—24no—
173C22×C4×C101—24no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—42no—
178C22×C4×C101—42no—
179C22×C4×C101—81no—
180C22×C4×C101—81no—
181C22×C4×C101—81no—
182C22×C4×C101—81no—
183C22×C4×C101C2×D411yescharacteristic
184C22×C4×C101C2×D411yescharacteristic
185C22×C4×C101C2×D411yescharacteristic
186C22×C4×C101C2×D411yescharacteristic
187C22×C4×C101C2×D411yescharacteristic
188C22×C4×C101C2×D411yescharacteristic
189C22×C4×C101C2411yescharacteristic
190SD16×C101—44no—
191D8×C101—44no—
192C2×C8×C101—21no—
193C2×C8×C101—21no—
194C2×C8×C101—21no—
195C2×C8×C101—21no—
196C2×C8×C101—21no—
197C2×C8×C101—21no—
198C2×C8×C101—21no—
199C2×C8×C101—21no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C4⋊C4×C101—24no—
205C4⋊C4×C101—24no—
206C4⋊C4×C101—24no—
207C4⋊C4×C101—22no—
208C4⋊C4×C101—24no—
209C4⋊C4×C101—24no—
210C4⋊C4×C101—22no—
211C4⋊C4×C101—22no—
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101C2×D412yes—
220C4⋊C4×C101C2×D412yes—
221C4⋊C4×C101C2×D412yes—
222C22⋊C4×C101—24no—
223C22⋊C4×C101—24no—
224C22⋊C4×C101—24no—
225C22⋊C4×C101—42no—
226C22⋊C4×C101—42no—
227C22⋊C4×C101—42no—
228C22⋊C4×C101—42no—
229C22⋊C4×C101—81no—
230C22⋊C4×C101—81no—
231C42×C101—21no—
232C42×C101—21no—
233C42×C101—21no—
234C42×C101—21no—
235C42×C101—81no—
236C42×C101C2×D412yes—
237C42×C101C2×D412yes—
238C23×C101—22no—
239C23×C101—22no—
240C23×C101—22no—
241C23×C101—41no—
242C23×C101—41no—
243C23×C101—41no—
244C23×C101—41no—
245C23×C101—41no—
246C23×C101—41no—
247C23×C101—41no—
248C23×C101—41no—
249C23×C101—41no—
250C23×C101—41no—
251C23×C101—41no—
252C23×C101C22×D411yescharacteristic
253Q8×C101—44no—
254Q8×C101—41no—
255Q8×C101—41no—
256Q8×C101—41no—
257Q8×C101—41no—
258Q8×C101—84no—
259D4×C101—22no—
260D4×C101—22no—
261D4×C101—22no—
262D4×C101—41no—
263D4×C101—41no—
264D4×C101—41no—
265D4×C101—41no—
266D4×C101#12414yes—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—21no—
274C2×C4×C101—21no—
275C2×C4×C101—21no—
276C2×C4×C101—22no—
277C2×C4×C101—22no—
278C2×C4×C101—22no—
279C2×C4×C101—21no—
280C2×C4×C101—21no—
281C2×C4×C101—21no—
282C2×C4×C101—21no—
283C2×C4×C101—21no—
284C2×C4×C101—21no—
285C2×C4×C101—48no—
286C2×C4×C101—41no—
287C2×C4×C101—41no—
288C2×C4×C101—41no—
289C2×C4×C101—41no—
290C2×C4×C101—41no—
291C2×C4×C101—41no—
292C2×C4×C101—41no—
293C2×C4×C101—41no—
294C2×C4×C101—41no—
295C2×C4×C101—41no—
296C2×C4×C101—41no—
297C2×C4×C101—41no—
298C2×C4×C101—41no—
299C2×C4×C101—41no—
300C2×C4×C101—41no—
301C2×C4×C101—84no—
302C2×C4×C101—84no—
303C2×C4×C101#12012yes—
304C2×C4×C101#12012yes—
305C2×C4×C101#13512yes—
306C2×C4×C101C22×D411yescharacteristic
307C2×C4×C101C22×D411yescharacteristic
308C2×C4×C101C2×#4111yescharacteristic
309C2×C4×C101C2×#4111yescharacteristic
310C2×C4×C1012−1+411yescharacteristic
311C2×C4×C1012−1+411yescharacteristic
312C8×C101—41no—
313C8×C101—41no—
314C8×C101—41no—
315C8×C101—41no—
316C22×C101—24no—
317C22×C101—42no—
318C22×C101—42no—
319C22×C101—42no—
320C22×C101—42no—
321C22×C101—42no—
322C22×C101—42no—
323C22×C101—81no—
324C22×C101—81no—
325C22×C101—81no—
326C22×C101—81no—
327C22×C101—81no—
328C22×C101—81no—
329C22×C101—81no—
330C22×C101C2×#12011yescharacteristic
331C22×C101#54811yescharacteristic
332C22×C101#54811yescharacteristic
333C22×C101C2×#13511yescharacteristic
334C22×C101#57511yescharacteristic
335C22×C101#57611yescharacteristic
336C22×C101#57711yescharacteristic
337C4×C101—22no—
338C4×C101—22no—
339C4×C101—22no—
340C4×C101—41no—
341C4×C101—42no—
342C4×C101—41no—
343C4×C101—41no—
344C4×C101—42no—
345C4×C101—42no—
346C4×C101—81no—
347C4×C101—81no—
348C4×C101—81no—
349C4×C101C2×#12411yescharacteristic
350C4×C101#53611yescharacteristic
351C4×C101#54811yescharacteristic
352C4×C101#54811yescharacteristic
353#25938C10111yesmaximal, characteristic, direct product factor, Sylow
354C2×C101—44no—
355C2×C101—161no—
356C2×C101#243611yescharacteristic
357C2×C101#300211yescharacteristic
358C2×C101#301211yescharacteristic
359C2×C101#336011yescharacteristic
360C2×C101#336111yescharacteristic
361C2×C101#337011yescharacteristic
362C2×C101#337611yescharacteristic
363C2×#554C2×C10111yescharacteristic, complemented
364C2×#488C2×C10111yescharacteristic, complemented
365C2×#463C2×C10111yescharacteristic
366#2592C2×C10111yescharacteristic, complemented
367#2026C2×C10111yescharacteristic, complemented
368#2025C2×C10111yescharacteristic, complemented
369#2024C2×C10111yescharacteristic, complemented
370#2023C2×C10111yescharacteristic, complemented
371#1989C2×C10111yescharacteristic, complemented
372#1984C2×C10111yescharacteristic, complemented
373#1879C2×C10111yescharacteristic
374#1879C2×C10111yescharacteristic
375#1877C2×C10111yescharacteristic, complemented
376#1877C2×C10111yescharacteristic, complemented
377C4×#102C2×C10111yescharacteristic, complemented
378C101#2593811yescharacteristic, direct product factor, Sylow
379C22×SD16C22×C10111yescharacteristic
380C22×D8C22×C10111yescharacteristic
381#554—24no—
382#554—24no—
383C2×C4⋊Q8C22×C10111yescharacteristic
384C2×#125C22×C10111yescharacteristic
385C2×#125C22×C10111yescharacteristic
386C2×#124C22×C10111yescharacteristic
387C2×C22⋊Q8—21no—
388C2×C22⋊Q8—21no—
389C2×C22⋊Q8—21no—
390C2×C4×Q8C22×C10111yescharacteristic
391C2×C4×D4C22×C10111yescharacteristic
392C2×C4×D4C22×C10111yescharacteristic
393C2×C4×D4C22×C10111yescharacteristic
394C22×C4⋊C4—21no—
395#488—24no—
396#463—24no—
397C2×C4⋊C8C22×C10111yescharacteristic
398C2×#103C22×C10111yescharacteristic
399C2×#103C22×C10111yescharacteristic
400C2×#103C22×C10111yescharacteristic
401C2×#102C22×C10111yescharacteristic
402C2×#102C22×C10111yescharacteristic
403C2×#102C22×C10111yescharacteristic
404C2×#102C22×C10111yescharacteristic
405C2×#102C22×C10111yescharacteristic
406C2×C4×C8C22×C10111yescharacteristic
407#397—21no—
408#393—21no—
409#391C22×C10111yescharacteristic
410#391C22×C10111yescharacteristic
411#390C22×C10111yescharacteristic
412#390C22×C10111yescharacteristic
413#388—21no—
414#388—21no—
415C4×C4⋊C4C22×C10111yescharacteristic
416#340C22×C10111yescharacteristic
417#340C22×C10111yescharacteristic
418#340C22×C10111yescharacteristic
419#340C22×C10111yescharacteristic
420#340C22×C10111yescharacteristic
421#340C22×C10111yescharacteristic
422#336C22×C10111yescharacteristic
423#336C22×C10111yescharacteristic
424#336C22×C10111yescharacteristic
425#336C22×C10111yescharacteristic
426C22×Q8—21no—
427C22×Q8D4×C10111yescharacteristic
428C22×Q8C23×C10111yescharacteristic
429C22×D4C23×C10111yescharacteristic
430C22×D4C23×C10111yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×D8—22no—
438C2×D8—22no—
439C2×D8—22no—
440C22×C8C23×C10111yescharacteristic
441C22×C8C23×C10111yescharacteristic
442C22×C8C23×C10111yescharacteristic
443C22×C8C23×C10111yescharacteristic
444C4⋊Q8—22no—
445C4⋊Q8—22no—
446#125—22no—
447#125—22no—
448#125—22no—
449#125D4×C10114yes—
450#124—22no—
451#124—22no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C22⋊Q8—28no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4D4×C10114yes—
463C2×C4⋊C4—28no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4D4×C10111yescharacteristic
470C2×C4⋊C4D4×C10111yescharacteristic
471C2×C4⋊C4D4×C10111yescharacteristic
472C2×C4⋊C4C23×C10111yescharacteristic
473C2×C4⋊C4C23×C10111yescharacteristic
474C2×C4⋊C4C23×C10111yescharacteristic
475C2×C4⋊C4C23×C10111yescharacteristic
476C2×C4⋊C4C23×C10111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C42—21no—
487C2×C42C23×C10111yescharacteristic
488C2×C42C23×C10111yescharacteristic
489C2×C42C23×C10111yescharacteristic
490C4⋊C8—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499C4×C8—22no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505C24—21no—
506C24—21no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—41no—
517C2×Q8—81no—
518C2×Q8—81no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4C2×D4×C10112yes—
529C2×D4#41×C10112yes—
530C2×D4#41×C10112yes—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×D4×C10111yescharacteristic
547C22×C4C2×D4×C10111yescharacteristic
548C22×C4C2×D4×C10111yescharacteristic
549C22×C4C2×D4×C10111yescharacteristic
550C22×C4C2×D4×C10111yescharacteristic
551C22×C4C2×D4×C10111yescharacteristic
552C22×C4C24×C10111yescharacteristic
553SD16—44no—
554D8—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C2×D4×C10112yes—
583C4⋊C4C2×D4×C10112yes—
584C4⋊C4C2×D4×C10112yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—81no—
599C42C2×D4×C10112yes—
600C42C2×D4×C10112yes—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C22×D4×C10111yescharacteristic
616Q8—44no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621Q8—84no—
622D4—22no—
623D4—22no—
624D4—22no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4#124×C10114yes—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4#120×C10112yes—
667C2×C4#120×C10112yes—
668C2×C4#135×C10112yes—
669C2×C4C22×D4×C10111yescharacteristic
670C2×C4C22×D4×C10111yescharacteristic
671C2×C4C2×#41×C10111yescharacteristic
672C2×C4C2×#41×C10111yescharacteristic
673C2×C42−1+4×C10111yescharacteristic
674C2×C42−1+4×C10111yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C2×#120×C10111yescharacteristic
694C22#548×C10111yescharacteristic
695C22#548×C10111yescharacteristic
696C22C2×#135×C10111yescharacteristic
697C22#575×C10111yescharacteristic
698C22#576×C10111yescharacteristic
699C22#577×C10111yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—42no—
705C4—41no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4C2×#124×C10111yescharacteristic
713C4#536×C10111yescharacteristic
714C4#548×C10111yescharacteristic
715C4#548×C10111yescharacteristic
716C2—44no—
717C2—161no—
718C2C101×#243611yescharacteristic
719C2C101×#300211yescharacteristic
720C2C101×#301211yescharacteristic
721C2C101×#336011yescharacteristic
722C2C101×#336111yescharacteristic
723C2C101×#337011yescharacteristic
724C2C101×#337611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC22×D8×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×Q8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#554×C101C2semidirect
2. C2×#488×C101C2semidirect
4. C101×#2592C2semidirect
5. C101×#2026C2semidirect
6. C101×#2025C2semidirect
7. C101×#2024C2semidirect
8. C101×#2023C2semidirect
9. C101×#1989C2semidirect
10. C101×#1984C2semidirect
13. C101×#1877C2semidirect
14. C101×#1877C2semidirect
15. C4×#102×C101C2semidirect
353. #25938C101direct (N × H)
363. C2×#554C2×C101semidirect
364. C2×#488C2×C101semidirect
366. #2592C2×C101semidirect
367. #2026C2×C101semidirect
368. #2025C2×C101semidirect
369. #2024C2×C101semidirect
370. #2023C2×C101semidirect
371. #1989C2×C101semidirect
372. #1984C2×C101semidirect
375. #1877C2×C101semidirect
376. #1877C2×C101semidirect
377. C4×#102C2×C101semidirect
378. C101#25938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C1012
C2×#488×C1012
C2×#463×C1012
C101×#25922
C101×#20262
C101×#20252
C101×#20242
C101×#20232
C101×#19892
C101×#19842
C101×#18792
C101×#18772
C4×#102×C1012
#25938101