Finite Group Databasebeta

← C101×#24394 #38806545

Subgroups — C101×#24394 #38806545

Order 25856.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C101C211yesmaximal, characteristic
2C2×#468×C101C211yesmaximal, characteristic, complemented
3C2×#465×C101C211yesmaximal, characteristic, complemented
4C2×#450×C101C211yesmaximal, characteristic, complemented
5C2×#408×C101C211yesmaximal, characteristic, complemented
6C101×#2616C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1895C211yesmaximal, characteristic, complemented
12C101×#1893C211yesmaximal, characteristic, complemented
13C101×#1873C211yesmaximal, characteristic, complemented
14C101×#1854C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×D4×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×SD16×C101C2211yescharacteristic
20C22×M16×C101C2211yescharacteristic, complemented
21C23×C8×C101C2211yescharacteristic, complemented
22#535×C101—24no—
23#535×C101—24no—
24C2×#127×C101—21no—
25C2×#124×C101—21no—
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic, complemented
28C2×C22⋊Q8×C101C2211yescharacteristic, complemented
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×#121×C101C2211yescharacteristic
32C2×#121×C101C2211yescharacteristic
33C2×#120×C101—21no—
34C2×#120×C101—21no—
35C2×#117×C101C2211yescharacteristic
36#468×C101—24no—
37#465×C101—24no—
38#450×C101—24no—
39C2×#107×C101C2211yescharacteristic, complemented
40C2×#106×C101C2211yescharacteristic, complemented
41C2×#103×C101C2211yescharacteristic, complemented
42C2×#103×C101C2211yescharacteristic, complemented
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×#102×C101C2211yescharacteristic
46C2×#102×C101C2211yescharacteristic
47C2×#102×C101C2211yescharacteristic
48C2×#102×C101C2211yescharacteristic
49#408×C101—24no—
50C2×C22⋊C8×C101C2211yescharacteristic
51C2×C22⋊C8×C101C2211yescharacteristic
52C2×C22⋊C8×C101C2211yescharacteristic, complemented
53C2×C22⋊C8×C101C2211yescharacteristic, complemented
54#395×C101—21no—
55#394×C101—21no—
56#394×C101—21no—
57#394×C101—21no—
58#380×C101C2211yescharacteristic
59#380×C101C2211yescharacteristic, complemented
60#380×C101C2211yescharacteristic, complemented
61#340×C101C2211yescharacteristic, complemented
62#340×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×C101D411yescharacteristic
73C22×Q8×C101C2311yescharacteristic
74C22×D4×C101—21no—
75C22×D4×C101—21no—
76C22×D4×C101—21no—
77C22×D4×C101—21no—
78C22×D4×C101—22no—
79C22×D4×C101—22no—
80C22×D4×C101—21no—
81C22×D4×C101—22no—
82C22×D4×C101—22no—
83C22×D4×C101—41no—
84C22×D4×C101—41no—
85C22×D4×C101D411yescharacteristic
86C22×D4×C101D411yescharacteristic
87C22×D4×C101D411yescharacteristic
88C22×D4×C101C2311yescharacteristic
89C22×D4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C23×C4×C101C2311yescharacteristic
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—41no—
98C2×SD16×C101—41no—
99C2×M16×C101—22no—
100C2×M16×C101—22no—
101C2×M16×C101—41no—
102C22×C8×C101—22no—
103C22×C8×C101—22no—
104C22×C8×C101—41no—
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107C22×C8×C101C2311yescharacteristic
108C22×C8×C101C2311yescharacteristic
109#127×C101—28no—
110#124×C101—28no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—22no—
115C22⋊Q8×C101—41no—
116C22⋊Q8×C101—41no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—22no—
121#121×C101—22no—
122#121×C101—22no—
123#121×C101D414yes—
124#121×C101D414yes—
125#120×C101—28no—
126#120×C101—28no—
127#117×C101—22no—
128#117×C101—22no—
129C2×C4⋊C4×C101—21no—
130C2×C4⋊C4×C101—21no—
131C2×C4⋊C4×C101—21no—
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C4⋊C4×C101C2311yescharacteristic
135C2×C4⋊C4×C101C2311yescharacteristic
136C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
144C2×C22⋊C4×C101—21no—
145C2×C22⋊C4×C101—21no—
146C2×C22⋊C4×C101—21no—
147C2×C22⋊C4×C101—21no—
148C2×C42×C101—21no—
149#107×C101—22no—
150#106×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#102×C101—22no—
154#102×C101—22no—
155#102×C101—22no—
156#102×C101—22no—
157#102×C101—41no—
158#102×C101—41no—
159C22⋊C8×C101—22no—
160C22⋊C8×C101—22no—
161C22⋊C8×C101—22no—
162C22⋊C8×C101D414yescomplemented
163#95×C101—21no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—24no—
167C24×C101—21no—
168C24×C101—21no—
169C24×C101—42no—
170C24×C101—42no—
171C24×C101—81no—
172C24×C101—81no—
173C24×C101—81no—
174C24×C101—81no—
175C24×C101C2×D411yescharacteristic
176C24×C101C2×D411yescharacteristic
177C24×C101C2×D411yescharacteristic
178#41×C101—44no—
179#41×C101—44no—
180#41×C101—44no—
181#41×C101—44no—
182C2×Q8×C101—22no—
183C2×Q8×C101—22no—
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—41no—
191C2×D4×C101—24no—
192C2×D4×C101—22no—
193C2×D4×C101—22no—
194C2×D4×C101—22no—
195C2×D4×C101—22no—
196C2×D4×C101—24no—
197C2×D4×C101—24no—
198C2×D4×C101—24no—
199C2×D4×C101—24no—
200C2×D4×C101—22no—
201C2×D4×C101—22no—
202C2×D4×C101—21no—
203C2×D4×C101—21no—
204C2×D4×C101—21no—
205C2×D4×C101—21no—
206C2×D4×C101—21no—
207C2×D4×C101—21no—
208C2×D4×C101—21no—
209C2×D4×C101—21no—
210C2×D4×C101—21no—
211C2×D4×C101—21no—
212C2×D4×C101—44no—
213C2×D4×C101—44no—
214C2×D4×C101—44no—
215C2×D4×C101—44no—
216C2×D4×C101—41no—
217C2×D4×C101—41no—
218C2×D4×C101—41no—
219C2×D4×C101—42no—
220C2×D4×C101—42no—
221C2×D4×C101—81no—
222C2×D4×C101—81no—
223C2×D4×C101—81no—
224C2×D4×C101—81no—
225C2×D4×C101—81no—
226C2×D4×C101—81no—
227C2×D4×C101—81no—
228C2×D4×C101—81no—
229C2×D4×C101C2×D412yes—
230C2×D4×C101C2×D412yes—
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—21no—
238C22×C4×C101—21no—
239C22×C4×C101—21no—
240C22×C4×C101—21no—
241C22×C4×C101—21no—
242C22×C4×C101—21no—
243C22×C4×C101—21no—
244C22×C4×C101—21no—
245C22×C4×C101—21no—
246C22×C4×C101—21no—
247C22×C4×C101—21no—
248C22×C4×C101—21no—
249C22×C4×C101—21no—
250C22×C4×C101—21no—
251C22×C4×C101C2×D411yescharacteristic
252C22×C4×C101C2×D411yescharacteristic
253C22×C4×C101C2×D412yes—
254C22×C4×C101C2×D412yes—
255C22×C4×C101C2×D411yescharacteristic
256C22×C4×C101C2×D412yes—
257C22×C4×C101#4112yes—
258C22×C4×C101C2411yescharacteristic
259SD16×C101—44no—
260SD16×C101—44no—
261M16×C101—44no—
262C2×C8×C101—21no—
263C2×C8×C101—21no—
264C2×C8×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—21no—
267C2×C8×C101—21no—
268C2×C8×C101—21no—
269C2×C8×C101—21no—
270C2×C8×C101—21no—
271C2×C8×C101—21no—
272C2×C8×C101—44no—
273C2×C8×C101C2×D412yes—
274C2×C8×C101C2×D412yes—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—21no—
277C4⋊C4×C101—21no—
278C4⋊C4×C101—21no—
279C4⋊C4×C101—21no—
280C4⋊C4×C101—21no—
281C4⋊C4×C101—21no—
282C4⋊C4×C101—21no—
283C4⋊C4×C101—42no—
284C4⋊C4×C101—42no—
285C4⋊C4×C101—42no—
286C4⋊C4×C101C2×D412yes—
287C4⋊C4×C101C2×D412yes—
288C22⋊C4×C101—24no—
289C22⋊C4×C101—24no—
290C22⋊C4×C101—24no—
291C22⋊C4×C101—24no—
292C22⋊C4×C101—24no—
293C22⋊C4×C101—42no—
294C22⋊C4×C101—42no—
295C22⋊C4×C101—42no—
296C22⋊C4×C101—81no—
297C22⋊C4×C101—81no—
298C22⋊C4×C101—81no—
299C42×C101—24no—
300C23×C101—21no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
308C23×C101—21no—
309C23×C101—21no—
310C23×C101—21no—
311C23×C101—21no—
312C23×C101—22no—
313C23×C101—22no—
314C23×C101—21no—
315C23×C101—21no—
316C23×C101—21no—
317C23×C101—21no—
318C23×C101—21no—
319C23×C101—21no—
320C23×C101—21no—
321C23×C101—48no—
322C23×C101—41no—
323C23×C101—41no—
324C23×C101—41no—
325C23×C101—41no—
326C23×C101—41no—
327C23×C101—41no—
328C23×C101—41no—
329C23×C101—41no—
330C23×C101—41no—
331C23×C101—41no—
332C23×C101—41no—
333C23×C101—41no—
334C23×C101—84no—
335C23×C101—84no—
336C23×C101—84no—
337C23×C101—84no—
338C23×C101—84no—
339C23×C101—84no—
340C23×C101#12012yes—
341C23×C101#12112yes—
342C23×C101C22×D411yescharacteristic
343Q8×C101—44no—
344Q8×C101—41no—
345Q8×C101—41no—
346Q8×C101—41no—
347Q8×C101—41no—
348D4×C101—22no—
349D4×C101—22no—
350D4×C101—22no—
351D4×C101—22no—
352D4×C101—44no—
353D4×C101—44no—
354D4×C101—48no—
355D4×C101—44no—
356D4×C101—41no—
357D4×C101—41no—
358D4×C101—41no—
359D4×C101—41no—
360D4×C101—84no—
361D4×C101—84no—
362D4×C101—84no—
363D4×C101—84no—
364C2×C4×C101—21no—
365C2×C4×C101—21no—
366C2×C4×C101—21no—
367C2×C4×C101—21no—
368C2×C4×C101—22no—
369C2×C4×C101—22no—
370C2×C4×C101—22no—
371C2×C4×C101—22no—
372C2×C4×C101—22no—
373C2×C4×C101—22no—
374C2×C4×C101—22no—
375C2×C4×C101—22no—
376C2×C4×C101—22no—
377C2×C4×C101—22no—
378C2×C4×C101—21no—
379C2×C4×C101—21no—
380C2×C4×C101—21no—
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—41no—
388C2×C4×C101—41no—
389C2×C4×C101—41no—
390C2×C4×C101—41no—
391C2×C4×C101—41no—
392C2×C4×C101—41no—
393C2×C4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
399C2×C4×C101—41no—
400C2×C4×C101—41no—
401C2×C4×C101#12012yes—
402C2×C4×C101#12112yes—
403C2×C4×C101C22×D411yescharacteristic
404C2×C4×C101C22×D411yescharacteristic
405C2×C4×C101C22×D411yescharacteristic
406C2×C4×C101C2×#4111yescharacteristic
407C2×C4×C101H(5,𝔽2)11yescharacteristic
408C2×C4×C101H(5,𝔽2)11yescharacteristic
409C8×C101—22no—
410C8×C101—22no—
411C8×C101—41no—
412C8×C101—41no—
413C22×C101—22no—
414C22×C101—22no—
415C22×C101—22no—
416C22×C101—22no—
417C22×C101—22no—
418C22×C101—22no—
419C22×C101—41no—
420C22×C101—41no—
421C22×C101—41no—
422C22×C101—41no—
423C22×C101—41no—
424C22×C101—41no—
425C22×C101—41no—
426C22×C101—41no—
427C22×C101—41no—
428C22×C101—42no—
429C22×C101—42no—
430C22×C101—41no—
431C22×C101—41no—
432C22×C101—41no—
433C22×C101—42no—
434C22×C101—42no—
435C22×C101—41no—
436C22×C101—42no—
437C22×C101—42no—
438C22×C101—41no—
439C22×C101—41no—
440C22×C101—816no—
441C22×C101—81no—
442C22×C101—81no—
443C22×C101—81no—
444C22×C101—81no—
445C22×C101—81no—
446C22×C101—81no—
447C22×C101—81no—
448C22×C101—81no—
449C22×C101C2×#12011yescharacteristic
450C22×C101C2×#12111yescharacteristic
451C22×C101#53411yescharacteristic
452C22×C101#57611yescharacteristic
453C22×C101#57711yescharacteristic
454C22×C101#57711yescharacteristic
455C22×C101#57711yescharacteristic
456C4×C101—22no—
457C4×C101—22no—
458C4×C101—41no—
459C4×C101—42no—
460C4×C101—42no—
461C4×C101—81no—
462C4×C101—81no—
463C4×C101—81no—
464C4×C101—81no—
465C4×C101D4211yescharacteristic
466C4×C101D4211yescharacteristic
467C4×C101#54611yescharacteristic
468C4×C101#54611yescharacteristic
469#24394C10111yesmaximal, characteristic, direct product factor, Sylow
470C2×C101—42no—
471C2×C101—42no—
472C2×C101—81no—
473C2×C101—82no—
474C2×C101—82no—
475C2×C101#241011yescharacteristic
476C2×C101#300911yescharacteristic
477C2×C101#301211yescharacteristic
478C2×C101#305711yescharacteristic
479C2×C101#306211yescharacteristic
480C2×C101#319811yescharacteristic
481C2×C101#320011yescharacteristic
482C2×#535C2×C10111yescharacteristic
483C2×#468C2×C10111yescharacteristic, complemented
484C2×#465C2×C10111yescharacteristic, complemented
485C2×#450C2×C10111yescharacteristic, complemented
486C2×#408C2×C10111yescharacteristic, complemented
487#2616C2×C10111yescharacteristic, complemented
488#2034C2×C10111yescharacteristic, complemented
489#2033C2×C10111yescharacteristic, complemented
490#2000C2×C10111yescharacteristic, complemented
491#2000C2×C10111yescharacteristic, complemented
492#1895C2×C10111yescharacteristic, complemented
493#1893C2×C10111yescharacteristic, complemented
494#1873C2×C10111yescharacteristic, complemented
495#1854C2×C10111yescharacteristic, complemented
496#1786C2×C10111yescharacteristic, complemented
497C101#2439411yescharacteristic, direct product factor, Sylow
498C22×#41C22×C10111yescharacteristic
499C23×D4C22×C10111yescharacteristic
500C22×SD16C22×C10111yescharacteristic
501C22×SD16C22×C10111yescharacteristic
502C22×M16C22×C10111yescharacteristic, complemented
503C23×C8C22×C10111yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127—21no—
507C2×#124—21no—
508C2×C22⋊Q8C22×C10111yescharacteristic
509C2×C22⋊Q8C22×C10111yescharacteristic, complemented
510C2×C22⋊Q8C22×C10111yescharacteristic, complemented
511C2×#121C22×C10111yescharacteristic
512C2×#121C22×C10111yescharacteristic
513C2×#121C22×C10111yescharacteristic
514C2×#121C22×C10111yescharacteristic
515C2×#120—21no—
516C2×#120—21no—
517C2×#117C22×C10111yescharacteristic
518#468—24no—
519#465—24no—
520#450—24no—
521C2×#107C22×C10111yescharacteristic, complemented
522C2×#106C22×C10111yescharacteristic, complemented
523C2×#103C22×C10111yescharacteristic, complemented
524C2×#103C22×C10111yescharacteristic, complemented
525C2×#102C22×C10111yescharacteristic
526C2×#102C22×C10111yescharacteristic
527C2×#102C22×C10111yescharacteristic
528C2×#102C22×C10111yescharacteristic
529C2×#102C22×C10111yescharacteristic
530C2×#102C22×C10111yescharacteristic
531#408—24no—
532C2×C22⋊C8C22×C10111yescharacteristic
533C2×C22⋊C8C22×C10111yescharacteristic
534C2×C22⋊C8C22×C10111yescharacteristic, complemented
535C2×C22⋊C8C22×C10111yescharacteristic, complemented
536#395—21no—
537#394—21no—
538#394—21no—
539#394—21no—
540#380C22×C10111yescharacteristic
541#380C22×C10111yescharacteristic, complemented
542#380C22×C10111yescharacteristic, complemented
543#340C22×C10111yescharacteristic, complemented
544#340C22×C10111yescharacteristic, complemented
545#340C22×C10111yescharacteristic, complemented
546#340C22×C10111yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C10111yescharacteristic
555C22×Q8C23×C10111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10111yescharacteristic
568C22×D4D4×C10111yescharacteristic
569C22×D4D4×C10111yescharacteristic
570C22×D4C23×C10111yescharacteristic
571C22×D4C23×C10111yescharacteristic
572C23×C4C23×C10111yescharacteristic
573C23×C4C23×C10111yescharacteristic
574C23×C4C23×C10111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C10111yescharacteristic
588C22×C8C23×C10111yescharacteristic
589C22×C8C23×C10111yescharacteristic
590C22×C8C23×C10111yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C10114yes—
606#121D4×C10114yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C10111yescharacteristic
615C2×C4⋊C4C23×C10111yescharacteristic
616C2×C4⋊C4C23×C10111yescharacteristic
617C2×C4⋊C4C23×C10111yescharacteristic
618C2×C4⋊C4C23×C10111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C10114yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C10111yescharacteristic
658C24C2×D4×C10111yescharacteristic
659C24C2×D4×C10111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C10112yes—
712C2×D4C2×D4×C10112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C10111yescharacteristic
734C22×C4C2×D4×C10111yescharacteristic
735C22×C4C2×D4×C10112yes—
736C22×C4C2×D4×C10112yes—
737C22×C4C2×D4×C10111yescharacteristic
738C22×C4C2×D4×C10112yes—
739C22×C4#41×C10112yes—
740C22×C4C24×C10111yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C10112yes—
756C2×C8C2×D4×C10112yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C10112yes—
769C4⋊C4C2×D4×C10112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C10112yes—
823C23#121×C10112yes—
824C23C22×D4×C10111yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C10112yes—
884C2×C4#121×C10112yes—
885C2×C4C22×D4×C10111yescharacteristic
886C2×C4C22×D4×C10111yescharacteristic
887C2×C4C22×D4×C10111yescharacteristic
888C2×C4C2×#41×C10111yescharacteristic
889C2×C4H(5,𝔽2)×C10111yescharacteristic
890C2×C4H(5,𝔽2)×C10111yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C10111yescharacteristic
932C22C2×#121×C10111yescharacteristic
933C22#534×C10111yescharacteristic
934C22#576×C10111yescharacteristic
935C22#577×C10111yescharacteristic
936C22#577×C10111yescharacteristic
937C22#577×C10111yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C10111yescharacteristic
948C4D42×C10111yescharacteristic
949C4#546×C10111yescharacteristic
950C4#546×C10111yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C101×#241011yescharacteristic
957C2C101×#300911yescharacteristic
958C2C101×#301211yescharacteristic
959C2C101×#305711yescharacteristic
960C2C101×#306211yescharacteristic
961C2C101×#319811yescharacteristic
962C2C101×#320011yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#535×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C22×#41×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C101C2semidirect
3. C2×#465×C101C2semidirect
4. C2×#450×C101C2semidirect
5. C2×#408×C101C2semidirect
6. C101×#2616C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#2000C2semidirect
10. C101×#2000C2semidirect
11. C101×#1895C2semidirect
12. C101×#1893C2semidirect
13. C101×#1873C2semidirect
14. C101×#1854C2semidirect
15. C101×#1786C2semidirect
20. C22×M16×C101C22semidirect
21. C23×C8×C101C22semidirect
27. C2×C22⋊Q8×C101C22semidirect
28. C2×C22⋊Q8×C101C22semidirect
39. C2×#107×C101C22semidirect
40. C2×#106×C101C22semidirect
41. C2×#103×C101C22semidirect
42. C2×#103×C101C22semidirect
52. C2×C22⋊C8×C101C22semidirect
53. C2×C22⋊C8×C101C22semidirect
59. #380×C101C22semidirect
60. #380×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
63. #340×C101C22semidirect
64. #340×C101C22semidirect
162. C22⋊C8×C101D4semidirect
469. #24394C101direct (N × H)
483. C2×#468C2×C101semidirect
484. C2×#465C2×C101semidirect
485. C2×#450C2×C101semidirect
486. C2×#408C2×C101semidirect
487. #2616C2×C101semidirect
488. #2034C2×C101semidirect
489. #2033C2×C101semidirect
490. #2000C2×C101semidirect
491. #2000C2×C101semidirect
492. #1895C2×C101semidirect
493. #1893C2×C101semidirect
494. #1873C2×C101semidirect
495. #1854C2×C101semidirect
496. #1786C2×C101semidirect
497. C101#24394direct (N × H)
502. C22×M16C22×C101semidirect
503. C23×C8C22×C101semidirect
509. C2×C22⋊Q8C22×C101semidirect
510. C2×C22⋊Q8C22×C101semidirect
521. C2×#107C22×C101semidirect
522. C2×#106C22×C101semidirect
523. C2×#103C22×C101semidirect
524. C2×#103C22×C101semidirect
534. C2×C22⋊C8C22×C101semidirect
535. C2×C22⋊C8C22×C101semidirect
541. #380C22×C101semidirect
542. #380C22×C101semidirect
543. #340C22×C101semidirect
544. #340C22×C101semidirect
545. #340C22×C101semidirect
546. #340C22×C101semidirect
644. C22⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1012
C2×#468×C1012
C2×#465×C1012
C2×#450×C1012
C2×#408×C1012
C101×#26162
C101×#20342
C101×#20332
C101×#20002
C101×#18952
C101×#18932
C101×#18732
C101×#18542
C101×#17862
#24394101