Finite Group Databasebeta

← C101×#24259 #38806410

Subgroups — C101×#24259 #38806410

Order 25856.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C101C211yesmaximal, characteristic
2C2×#464×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C2×#440×C101C211yesmaximal, characteristic, complemented
6C101×#2538C211yesmaximal, characteristic, complemented
7C101×#2036C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#2001C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1959C211yesmaximal, characteristic, complemented
12C101×#1955C211yesmaximal, characteristic, complemented
13C101×#1802C211yesmaximal, characteristic, complemented
14C101×#1788C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×Q16×C101C2211yescharacteristic, complemented
19C22×SD16×C101C2211yescharacteristic
20C22×SD16×C101C2211yescharacteristic
21#546×C101—24no—
22#546×C101—24no—
23C2×#124×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic, complemented
28C2×#121×C101—21no—
29C2×#121×C101C2211yescharacteristic
30C2×#120×C101—21no—
31C2×C4×Q8×C101C2211yescharacteristic, complemented
32C2×C4×D4×C101C2211yescharacteristic
33C2×C4×D4×C101C2211yescharacteristic
34C22×C22⋊C4×C101—21no—
35#464×C101—24no—
36#452×C101—24no—
37#450×C101—24no—
38#440×C101—24no—
39C2×#107×C101C2211yescharacteristic, complemented
40C2×C4⋊C8×C101C2211yescharacteristic, complemented
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#103×C101C2211yescharacteristic, complemented
44C2×#103×C101C2211yescharacteristic, complemented
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49C2×#102×C101C2211yescharacteristic
50C2×#102×C101C2211yescharacteristic
51C2×C22⋊C8×C101C2211yescharacteristic
52C2×C22⋊C8×C101C2211yescharacteristic
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55C2×#97×C101C2211yescharacteristic, complemented
56#396×C101—21no—
57#396×C101—21no—
58#390×C101—21no—
59#389×C101—21no—
60#384×C101C2211yescharacteristic, complemented
61#380×C101C2211yescharacteristic
62#380×C101C2211yescharacteristic, complemented
63#340×C101C2211yescharacteristic, complemented
64#340×C101C2211yescharacteristic, complemented
65C25×C101—21no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—22no—
70C2×#41×C101—41no—
71C2×#41×C101—41no—
72C22×Q8×C101C2311yescharacteristic
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—22no—
77C22×D4×C101—22no—
78C22×D4×C101—22no—
79C22×D4×C101—22no—
80C22×D4×C101—21no—
81C22×D4×C101—41no—
82C22×D4×C101—41no—
83C22×D4×C101D411yescharacteristic
84C22×D4×C101C2311yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C23×C4×C101—21no—
87C23×C4×C101—21no—
88C23×C4×C101C2311yescharacteristic
89C23×C4×C101C2311yescharacteristic
90C2×Q16×C101—22no—
91C2×Q16×C101—22no—
92C2×Q16×C101—41no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—41no—
98C2×SD16×C101D414yescomplemented
99C22×C8×C101C2311yescharacteristic
100C22×C8×C101C2311yescharacteristic
101C22×C8×C101C2311yescharacteristic
102C22×C8×C101C2311yescharacteristic
103#124×C101—22no—
104#124×C101D414yes—
105#123×C101—28no—
106C22⋊Q8×C101—22no—
107C22⋊Q8×C101—22no—
108C22⋊Q8×C101—22no—
109C22⋊Q8×C101—22no—
110C22⋊Q8×C101—41no—
111C22⋊Q8×C101—41no—
112#121×C101—28no—
113#121×C101—22no—
114#121×C101—22no—
115#120×C101—28no—
116C4×Q8×C101—22no—
117C4×Q8×C101—22no—
118C4×D4×C101—22no—
119C4×D4×C101—22no—
120C4×D4×C101—22no—
121C4×D4×C101D414yes—
122C2×C4⋊C4×C101—21no—
123C2×C4⋊C4×C101—21no—
124C2×C4⋊C4×C101—21no—
125C2×C4⋊C4×C101—21no—
126C2×C4⋊C4×C101—21no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101D411yescharacteristic
129C2×C4⋊C4×C101C2311yescharacteristic
130C2×C4⋊C4×C101C2311yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C22⋊C4×C101—28no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101—21no—
137C2×C22⋊C4×C101—21no—
138C2×C22⋊C4×C101—21no—
139C2×C22⋊C4×C101—21no—
140C2×C22⋊C4×C101—21no—
141C2×C22⋊C4×C101—21no—
142C2×C22⋊C4×C101—21no—
143C2×C22⋊C4×C101D411yescharacteristic
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C42×C101—21no—
146C2×C42×C101C2311yescharacteristic
147#107×C101—22no—
148C4⋊C8×C101—22no—
149#103×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101—41no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—22no—
158#102×C101—41no—
159C22⋊C8×C101—22no—
160C22⋊C8×C101—22no—
161C22⋊C8×C101—41no—
162C22⋊C8×C101—41no—
163#97×C101—22no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—21no—
167C24×C101—24no—
168C24×C101—21no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—42no—
172C24×C101—42no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101C2×D411yescharacteristic
176C24×C101C2×D411yescharacteristic
177#41×C101—44no—
178#41×C101—44no—
179#41×C101—44no—
180#41×C101—44no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—21no—
185C2×Q8×C101—21no—
186C2×Q8×C101—21no—
187C2×Q8×C101—21no—
188C2×Q8×C101—21no—
189C2×Q8×C101—21no—
190C2×Q8×C101—21no—
191C2×Q8×C101C2×D412yes—
192C2×Q8×C101C2×D412yes—
193C2×D4×C101—24no—
194C2×D4×C101—24no—
195C2×D4×C101—22no—
196C2×D4×C101—24no—
197C2×D4×C101—22no—
198C2×D4×C101—21no—
199C2×D4×C101—21no—
200C2×D4×C101—21no—
201C2×D4×C101—21no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—41no—
207C2×D4×C101—42no—
208C2×D4×C101—42no—
209C2×D4×C101—44no—
210C2×D4×C101—44no—
211C2×D4×C101—44no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—44no—
215C2×D4×C101—81no—
216C2×D4×C101—81no—
217C2×D4×C101C2×D412yes—
218C2×D4×C101C2×D412yes—
219C2×D4×C101C2×D412yes—
220C2×D4×C101#4112yes—
221C22×C4×C101—24no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—21no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—21no—
232C22×C4×C101—21no—
233C22×C4×C101—21no—
234C22×C4×C101—21no—
235C22×C4×C101—21no—
236C22×C4×C101—21no—
237C22×C4×C101—24no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—42no—
242C22×C4×C101—42no—
243C22×C4×C101—81no—
244C22×C4×C101—81no—
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D411yescharacteristic
249C22×C4×C101C2411yescharacteristic
250Q16×C101—44no—
251SD16×C101—28no—
252SD16×C101—44no—
253C2×C8×C101—21no—
254C2×C8×C101—21no—
255C2×C8×C101—21no—
256C2×C8×C101—21no—
257C2×C8×C101—21no—
258C2×C8×C101—21no—
259C2×C8×C101—21no—
260C2×C8×C101—21no—
261C2×C8×C101—21no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101C2×D412yes—
265C4⋊C4×C101—24no—
266C4⋊C4×C101—22no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—42no—
275C4⋊C4×C101—42no—
276C4⋊C4×C101—42no—
277C4⋊C4×C101—42no—
278C4⋊C4×C101—81no—
279C4⋊C4×C101C2×D412yes—
280C22⋊C4×C101—24no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—22no—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—24no—
285C22⋊C4×C101—24no—
286C22⋊C4×C101—22no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
289C22⋊C4×C101—81no—
290C22⋊C4×C101—81no—
291C42×C101—42no—
292C42×C101C2×D412yes—
293C42×C101C2×D412yes—
294C23×C101—21no—
295C23×C101—22no—
296C23×C101—21no—
297C23×C101—22no—
298C23×C101—21no—
299C23×C101—22no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—22no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—21no—
311C23×C101—48no—
312C23×C101—48no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101—41no—
321C23×C101—41no—
322C23×C101—41no—
323C23×C101—84no—
324C23×C101—84no—
325C23×C101—84no—
326C23×C101—84no—
327C23×C101—84no—
328C23×C101#13712yes—
329C23×C101C22×D411yescharacteristic
330Q8×C101—22no—
331Q8×C101—22no—
332Q8×C101—22no—
333Q8×C101—22no—
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—41no—
338D4×C101—22no—
339D4×C101—22no—
340D4×C101—22no—
341D4×C101—22no—
342D4×C101—22no—
343D4×C101—44no—
344D4×C101—48no—
345D4×C101—48no—
346D4×C101—41no—
347D4×C101—41no—
348D4×C101—84no—
349D4×C101#12114yes—
350C2×C4×C101—21no—
351C2×C4×C101—21no—
352C2×C4×C101—21no—
353C2×C4×C101—21no—
354C2×C4×C101—22no—
355C2×C4×C101—21no—
356C2×C4×C101—22no—
357C2×C4×C101—21no—
358C2×C4×C101—22no—
359C2×C4×C101—21no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—48no—
364C2×C4×C101—41no—
365C2×C4×C101—41no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—41no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—41no—
379C2×C4×C101—41no—
380C2×C4×C101—41no—
381C2×C4×C101—41no—
382C2×C4×C101—41no—
383C2×C4×C101—41no—
384C2×C4×C101—41no—
385C2×C4×C101—41no—
386C2×C4×C101—41no—
387C2×C4×C101—84no—
388C2×C4×C101#12012yes—
389C2×C4×C101#12012yes—
390C2×C4×C101C22×D411yescharacteristic
391C2×C4×C101C22×D411yescharacteristic
392C2×C4×C101C22×D411yescharacteristic
393C2×C4×C101C2×#4111yescharacteristic
394C2×C4×C101H(5,𝔽2)11yescharacteristic
395C2×C4×C101H(5,𝔽2)11yescharacteristic
396C8×C101—22no—
397C8×C101—41no—
398C8×C101—41no—
399C8×C101—41no—
400C22×C101—24no—
401C22×C101—22no—
402C22×C101—22no—
403C22×C101—22no—
404C22×C101—41no—
405C22×C101—42no—
406C22×C101—42no—
407C22×C101—42no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—42no—
411C22×C101—41no—
412C22×C101—42no—
413C22×C101—42no—
414C22×C101—41no—
415C22×C101—42no—
416C22×C101—41no—
417C22×C101—42no—
418C22×C101—41no—
419C22×C101—41no—
420C22×C101—42no—
421C22×C101—41no—
422C22×C101—41no—
423C22×C101—41no—
424C22×C101—816no—
425C22×C101—81no—
426C22×C101—81no—
427C22×C101—81no—
428C22×C101—81no—
429C22×C101C2×#12011yescharacteristic
430C22×C101D4211yescharacteristic
431C22×C101#54611yescharacteristic
432C22×C101C2×#13711yescharacteristic
433C22×C101#57511yescharacteristic
434C22×C101#57611yescharacteristic
435C22×C101#57711yescharacteristic
436C4×C101—22no—
437C4×C101—22no—
438C4×C101—41no—
439C4×C101—41no—
440C4×C101—42no—
441C4×C101—42no—
442C4×C101—42no—
443C4×C101—81no—
444C4×C101—81no—
445C4×C101—81no—
446C4×C101C2×#12111yescharacteristic
447C4×C101#53511yescharacteristic
448C4×C101D4211yescharacteristic
449C4×C101#54611yescharacteristic
450#24259C10111yesmaximal, characteristic, direct product factor, Sylow
451C2×C101—42no—
452C2×C101—44no—
453C2×C101—81no—
454C2×C101—82no—
455C2×C101#240811yescharacteristic
456C2×C101#300711yescharacteristic
457C2×C101#301211yescharacteristic
458C2×C101#326611yescharacteristic
459C2×C101#326811yescharacteristic
460C2×C101#331111yescharacteristic
461C2×C101#331411yescharacteristic
462C2×#546C2×C10111yescharacteristic
463C2×#464C2×C10111yescharacteristic, complemented
464C2×#452C2×C10111yescharacteristic, complemented
465C2×#450C2×C10111yescharacteristic, complemented
466C2×#440C2×C10111yescharacteristic, complemented
467#2538C2×C10111yescharacteristic, complemented
468#2036C2×C10111yescharacteristic, complemented
469#2033C2×C10111yescharacteristic, complemented
470#2001C2×C10111yescharacteristic, complemented
471#2000C2×C10111yescharacteristic, complemented
472#1959C2×C10111yescharacteristic, complemented
473#1955C2×C10111yescharacteristic, complemented
474#1802C2×C10111yescharacteristic, complemented
475#1788C2×C10111yescharacteristic, complemented
476#1786C2×C10111yescharacteristic, complemented
477C101#2425911yescharacteristic, direct product factor, Sylow
478C22×#41C22×C10111yescharacteristic
479C23×D4C22×C10111yescharacteristic
480C22×Q16C22×C10111yescharacteristic, complemented
481C22×SD16C22×C10111yescharacteristic
482C22×SD16C22×C10111yescharacteristic
483#546—24no—
484#546—24no—
485C2×#124C22×C10111yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C10111yescharacteristic
488C2×C22⋊Q8C22×C10111yescharacteristic
489C2×C22⋊Q8C22×C10111yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C10111yescharacteristic
492C2×#120—21no—
493C2×C4×Q8C22×C10111yescharacteristic, complemented
494C2×C4×D4C22×C10111yescharacteristic
495C2×C4×D4C22×C10111yescharacteristic
496C22×C22⋊C4—21no—
497#464—24no—
498#452—24no—
499#450—24no—
500#440—24no—
501C2×#107C22×C10111yescharacteristic, complemented
502C2×C4⋊C8C22×C10111yescharacteristic, complemented
503C2×#103C22×C10111yescharacteristic, complemented
504C2×#103C22×C10111yescharacteristic, complemented
505C2×#103C22×C10111yescharacteristic, complemented
506C2×#103C22×C10111yescharacteristic, complemented
507C2×#102C22×C10111yescharacteristic
508C2×#102C22×C10111yescharacteristic
509C2×#102C22×C10111yescharacteristic
510C2×#102C22×C10111yescharacteristic
511C2×#102C22×C10111yescharacteristic
512C2×#102C22×C10111yescharacteristic
513C2×C22⋊C8C22×C10111yescharacteristic
514C2×C22⋊C8C22×C10111yescharacteristic
515C2×C22⋊C8C22×C10111yescharacteristic, complemented
516C2×C22⋊C8C22×C10111yescharacteristic, complemented
517C2×#97C22×C10111yescharacteristic, complemented
518#396—21no—
519#396—21no—
520#390—21no—
521#389—21no—
522#384C22×C10111yescharacteristic, complemented
523#380C22×C10111yescharacteristic
524#380C22×C10111yescharacteristic, complemented
525#340C22×C10111yescharacteristic, complemented
526#340C22×C10111yescharacteristic, complemented
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8C23×C10111yescharacteristic
535C22×Q8C23×C10111yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4D4×C10111yescharacteristic
546C22×D4C23×C10111yescharacteristic
547C22×D4C23×C10111yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C10111yescharacteristic
551C23×C4C23×C10111yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C2×SD16D4×C10114yescomplemented
561C22×C8C23×C10111yescharacteristic
562C22×C8C23×C10111yescharacteristic
563C22×C8C23×C10111yescharacteristic
564C22×C8C23×C10111yescharacteristic
565#124—22no—
566#124D4×C10114yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574#121—28no—
575#121—22no—
576#121—22no—
577#120—28no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4D4×C10114yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C10111yescharacteristic
591C2×C4⋊C4C23×C10111yescharacteristic
592C2×C4⋊C4C23×C10111yescharacteristic
593C2×C4⋊C4C23×C10111yescharacteristic
594C2×C4⋊C4C23×C10111yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C10111yescharacteristic
606C2×C22⋊C4D4×C10111yescharacteristic
607C2×C42—21no—
608C2×C42C23×C10111yescharacteristic
609#107—22no—
610C4⋊C8—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—41no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—41no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624C22⋊C8—41no—
625#97—22no—
626#95—21no—
627#95—21no—
628C24—21no—
629C24—24no—
630C24—21no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24C2×D4×C10111yescharacteristic
638C24C2×D4×C10111yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C10112yes—
654C2×Q8C2×D4×C10112yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C2×D4×C10112yes—
680C2×D4C2×D4×C10112yes—
681C2×D4C2×D4×C10112yes—
682C2×D4#41×C10112yes—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—81no—
706C22×C4—81no—
707C22×C4C2×D4×C10111yescharacteristic
708C22×C4C2×D4×C10111yescharacteristic
709C22×C4C2×D4×C10111yescharacteristic
710C22×C4C2×D4×C10111yescharacteristic
711C22×C4C24×C10111yescharacteristic
712Q16—44no—
713SD16—28no—
714SD16—44no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8C2×D4×C10112yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C10112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C22⋊C4—81no—
753C42—42no—
754C42C2×D4×C10112yes—
755C42C2×D4×C10112yes—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23#137×C10112yes—
791C23C22×D4×C10111yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4#121×C10114yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—84no—
850C2×C4#120×C10112yes—
851C2×C4#120×C10112yes—
852C2×C4C22×D4×C10111yescharacteristic
853C2×C4C22×D4×C10111yescharacteristic
854C2×C4C22×D4×C10111yescharacteristic
855C2×C4C2×#41×C10111yescharacteristic
856C2×C4H(5,𝔽2)×C10111yescharacteristic
857C2×C4H(5,𝔽2)×C10111yescharacteristic
858C8—22no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—24no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×#120×C10111yescharacteristic
892C22D42×C10111yescharacteristic
893C22#546×C10111yescharacteristic
894C22C2×#137×C10111yescharacteristic
895C22#575×C10111yescharacteristic
896C22#576×C10111yescharacteristic
897C22#577×C10111yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4C2×#121×C10111yescharacteristic
909C4#535×C10111yescharacteristic
910C4D42×C10111yescharacteristic
911C4#546×C10111yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2C101×#240811yescharacteristic
917C2C101×#300711yescharacteristic
918C2C101×#301211yescharacteristic
919C2C101×#326611yescharacteristic
920C2C101×#326811yescharacteristic
921C2C101×#331111yescharacteristic
922C2C101×#331411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#546×C101C2
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
2. C2×#464×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C2×#440×C101C2semidirect
6. C101×#2538C2semidirect
7. C101×#2036C2semidirect
8. C101×#2033C2semidirect
9. C101×#2001C2semidirect
10. C101×#2000C2semidirect
11. C101×#1959C2semidirect
12. C101×#1955C2semidirect
13. C101×#1802C2semidirect
14. C101×#1788C2semidirect
15. C101×#1786C2semidirect
18. C22×Q16×C101C22semidirect
27. C2×C22⋊Q8×C101C22semidirect
31. C2×C4×Q8×C101C22semidirect
39. C2×#107×C101C22semidirect
40. C2×C4⋊C8×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
43. C2×#103×C101C22semidirect
44. C2×#103×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
55. C2×#97×C101C22semidirect
60. #384×C101C22semidirect
62. #380×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
98. C2×SD16×C101D4semidirect
450. #24259C101direct (N × H)
463. C2×#464C2×C101semidirect
464. C2×#452C2×C101semidirect
465. C2×#450C2×C101semidirect
466. C2×#440C2×C101semidirect
467. #2538C2×C101semidirect
468. #2036C2×C101semidirect
469. #2033C2×C101semidirect
470. #2001C2×C101semidirect
471. #2000C2×C101semidirect
472. #1959C2×C101semidirect
473. #1955C2×C101semidirect
474. #1802C2×C101semidirect
475. #1788C2×C101semidirect
476. #1786C2×C101semidirect
477. C101#24259direct (N × H)
480. C22×Q16C22×C101semidirect
489. C2×C22⋊Q8C22×C101semidirect
493. C2×C4×Q8C22×C101semidirect
501. C2×#107C22×C101semidirect
502. C2×C4⋊C8C22×C101semidirect
503. C2×#103C22×C101semidirect
504. C2×#103C22×C101semidirect
505. C2×#103C22×C101semidirect
506. C2×#103C22×C101semidirect
515. C2×C22⋊C8C22×C101semidirect
516. C2×C22⋊C8C22×C101semidirect
517. C2×#97C22×C101semidirect
522. #384C22×C101semidirect
524. #380C22×C101semidirect
525. #340C22×C101semidirect
526. #340C22×C101semidirect
560. C2×SD16D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1012
C2×#464×C1012
C2×#452×C1012
C2×#450×C1012
C2×#440×C1012
C101×#25382
C101×#20362
C101×#20332
C101×#20012
C101×#20002
C101×#19592
C101×#19552
C101×#18022
C101×#17882
C101×#17862
#24259101