Finite Group Databasebeta

← C101×#24455 #38806606

Subgroups — C101×#24455 #38806606

Order 25856.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C101C211yesmaximal, characteristic, complemented
2C2×#469×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×#448×C101C211yesmaximal, characteristic, complemented
5C2×#419×C101C211yesmaximal, characteristic, complemented
6C101×#2414C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2035C211yesmaximal, characteristic, complemented
9C101×#2012C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1880C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1870C211yesmaximal, characteristic, complemented
14C101×#1865C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C23×Q8×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×SD16×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C22×M16×C101C2211yescharacteristic
22#548×C101—24no—
23#548×C101—24no—
24C2×#124×C101—21no—
25C2×#124×C101C2211yescharacteristic
26C2×C22⋊Q8×C101—21no—
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×#121×C101—21no—
29C2×#121×C101C2211yescharacteristic
30C2×#121×C101C2211yescharacteristic
31C2×#121×C101C2211yescharacteristic
32C2×C4×Q8×C101C2211yescharacteristic
33C2×C4×D4×C101—21no—
34C2×C4×D4×C101C2211yescharacteristic
35C2×#117×C101C2211yescharacteristic
36#469×C101—24no—
37#449×C101—24no—
38#448×C101—24no—
39C2×#106×C101C2211yescharacteristic
40#419×C101—24no—
41C2×#103×C101C2211yescharacteristic
42C2×#103×C101C2211yescharacteristic
43C2×#103×C101C2211yescharacteristic
44C2×#103×C101C2211yescharacteristic
45C2×#103×C101C2211yescharacteristic
46C2×#103×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
54#394×C101—21no—
55#392×C101—21no—
56#390×C101—21no—
57#390×C101C2211yescharacteristic
58#389×C101C2211yescharacteristic
59#388×C101—21no—
60#380×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63#336×C101C2211yescharacteristic
64#336×C101C2211yescharacteristic
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—22no—
68C2×#41×C101—22no—
69C2×#41×C101—41no—
70C2×#41×C101—41no—
71C22×Q8×C101—21no—
72C22×Q8×C101—22no—
73C22×Q8×C101—22no—
74C22×Q8×C101—22no—
75C22×Q8×C101—41no—
76C22×Q8×C101—41no—
77C22×Q8×C101D414yescomplemented
78C22×Q8×C101C2311yescharacteristic
79C22×Q8×C101C2311yescharacteristic
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101—21no—
84C22×D4×C101D411yescharacteristic
85C22×D4×C101C2311yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C23×C4×C101—21no—
88C23×C4×C101—21no—
89C23×C4×C101C2311yescharacteristic
90C23×C4×C101C2311yescharacteristic
91C2×SD16×C101—22no—
92C2×SD16×C101—22no—
93C2×SD16×C101—22no—
94C2×SD16×C101—22no—
95C2×SD16×C101—41no—
96C2×SD16×C101—41no—
97C2×D8×C101—22no—
98C2×D8×C101—22no—
99C2×D8×C101—41no—
100C2×M16×C101—22no—
101C2×M16×C101—22no—
102C2×M16×C101—41no—
103C22×C8×C101C2311yescharacteristic
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107#124×C101—28no—
108#124×C101—22no—
109#124×C101—22no—
110C22⋊Q8×C101—28no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113#121×C101—28no—
114#121×C101—22no—
115#121×C101—22no—
116#121×C101—22no—
117#121×C101—22no—
118#121×C101—41no—
119#121×C101D414yescomplemented
120C4×Q8×C101—22no—
121C4×Q8×C101—22no—
122C4×D4×C101—28no—
123C4×D4×C101—22no—
124C4×D4×C101—22no—
125#117×C101—22no—
126#117×C101—41no—
127C2×C4⋊C4×C101—21no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101—21no—
130C2×C4⋊C4×C101D411yescharacteristic
131C2×C4⋊C4×C101C2311yescharacteristic
132C2×C4⋊C4×C101C2311yescharacteristic
133C2×C4⋊C4×C101C2311yescharacteristic
134C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
144C2×C22⋊C4×C101—21no—
145C2×C22⋊C4×C101D411yescharacteristic
146C2×C22⋊C4×C101D411yescharacteristic
147C2×C42×C101—21no—
148C2×C42×C101—21no—
149C2×C42×C101C2311yescharacteristic
150#106×C101—22no—
151#103×C101—22no—
152#103×C101—22no—
153#103×C101—22no—
154#103×C101—22no—
155#103×C101—22no—
156#103×C101D414yescomplemented
157#102×C101—22no—
158#102×C101—22no—
159#102×C101—22no—
160#102×C101—41no—
161C22⋊C8×C101—22no—
162C22⋊C8×C101—22no—
163C22⋊C8×C101—41no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—21no—
167C24×C101—21no—
168C24×C101C2×D411yescharacteristic
169C24×C101C2×D411yescharacteristic
170#41×C101—44no—
171#41×C101—44no—
172#41×C101—44no—
173#41×C101—44no—
174C2×Q8×C101—24no—
175C2×Q8×C101—21no—
176C2×Q8×C101—21no—
177C2×Q8×C101—21no—
178C2×Q8×C101—21no—
179C2×Q8×C101—28no—
180C2×Q8×C101—21no—
181C2×Q8×C101—21no—
182C2×Q8×C101—21no—
183C2×Q8×C101—21no—
184C2×Q8×C101—42no—
185C2×Q8×C101—42no—
186C2×Q8×C101—44no—
187C2×Q8×C101—44no—
188C2×Q8×C101—44no—
189C2×Q8×C101C2×D412yes—
190C2×Q8×C101C2×D412yes—
191C2×Q8×C101C2×D412yes—
192C2×Q8×C101#4112yes—
193C2×D4×C101—24no—
194C2×D4×C101—22no—
195C2×D4×C101—24no—
196C2×D4×C101—21no—
197C2×D4×C101—21no—
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—21no—
207C2×D4×C101—41no—
208C2×D4×C101—41no—
209C2×D4×C101—42no—
210C2×D4×C101—42no—
211C2×D4×C101—42no—
212C2×D4×C101—42no—
213C2×D4×C101—42no—
214C2×D4×C101—42no—
215C2×D4×C101—42no—
216C2×D4×C101—81no—
217C2×D4×C101—81no—
218C2×D4×C101—81no—
219C2×D4×C101C2×D412yes—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—24no—
226C22×C4×C101—24no—
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—21no—
238C22×C4×C101—42no—
239C22×C4×C101—42no—
240C22×C4×C101—42no—
241C22×C4×C101—42no—
242C22×C4×C101C2×D411yescharacteristic
243C22×C4×C101C2×D411yescharacteristic
244C22×C4×C101C2×D411yescharacteristic
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D412yes—
247C22×C4×C101C2×D412yes—
248C22×C4×C101C2411yescharacteristic
249SD16×C101—44no—
250SD16×C101—44no—
251D8×C101—44no—
252M16×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—24no—
267C4⋊C4×C101—22no—
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—81no—
275C4⋊C4×C101C2×D412yes—
276C4⋊C4×C101C2×D412yes—
277C22⋊C4×C101—24no—
278C22⋊C4×C101—24no—
279C22⋊C4×C101—24no—
280C22⋊C4×C101—22no—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—22no—
283C22⋊C4×C101—42no—
284C22⋊C4×C101—42no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—81no—
288C22⋊C4×C101—81no—
289C42×C101—24no—
290C42×C101—21no—
291C42×C101—21no—
292C42×C101—42no—
293C23×C101—21no—
294C23×C101—21no—
295C23×C101—21no—
296C23×C101—21no—
297C23×C101—21no—
298C23×C101—21no—
299C23×C101—21no—
300C23×C101—22no—
301C23×C101—21no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—41no—
308C23×C101—41no—
309C23×C101—41no—
310C23×C101—41no—
311C23×C101—41no—
312C23×C101—41no—
313C23×C101—41no—
314C23×C101—41no—
315C23×C101—41no—
316C23×C101—41no—
317C23×C101—41no—
318C23×C101—41no—
319C23×C101—41no—
320C23×C101#12012yes—
321C23×C101C22×D411yescharacteristic
322Q8×C101—22no—
323Q8×C101—22no—
324Q8×C101—22no—
325Q8×C101—22no—
326Q8×C101—22no—
327Q8×C101—48no—
328Q8×C101—41no—
329Q8×C101—41no—
330Q8×C101#12114yes—
331D4×C101—22no—
332D4×C101—22no—
333D4×C101—48no—
334D4×C101—44no—
335D4×C101—48no—
336D4×C101—41no—
337D4×C101—41no—
338D4×C101—41no—
339D4×C101—41no—
340D4×C101—41no—
341D4×C101—41no—
342D4×C101—84no—
343D4×C101—84no—
344C2×C4×C101—22no—
345C2×C4×C101—21no—
346C2×C4×C101—22no—
347C2×C4×C101—21no—
348C2×C4×C101—22no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—22no—
353C2×C4×C101—21no—
354C2×C4×C101—21no—
355C2×C4×C101—22no—
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—21no—
364C2×C4×C101—21no—
365C2×C4×C101—48no—
366C2×C4×C101—48no—
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#12012yes—
384C2×C4×C101C22×D411yescharacteristic
385C2×C4×C101C22×D411yescharacteristic
386C2×C4×C101C22×D411yescharacteristic
387C2×C4×C101C2×#4111yescharacteristic
388C2×C4×C101H(5,𝔽2)11yescharacteristic
389C2×C4×C101H(5,𝔽2)11yescharacteristic
390C8×C101—22no—
391C8×C101—41no—
392C8×C101—41no—
393C8×C101—41no—
394C22×C101—22no—
395C22×C101—22no—
396C22×C101—22no—
397C22×C101—41no—
398C22×C101—41no—
399C22×C101—41no—
400C22×C101—41no—
401C22×C101—42no—
402C22×C101—41no—
403C22×C101—41no—
404C22×C101—42no—
405C22×C101—41no—
406C22×C101—42no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101—41no—
411C22×C101—81no—
412C22×C101—81no—
413C22×C101—81no—
414C22×C101—81no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101C2×#12011yescharacteristic
423C22×C101D4211yescharacteristic
424C22×C101#54611yescharacteristic
425C22×C101#57511yescharacteristic
426C22×C101#57511yescharacteristic
427C22×C101#57711yescharacteristic
428C22×C101#57711yescharacteristic
429C4×C101—22no—
430C4×C101—24no—
431C4×C101—41no—
432C4×C101—42no—
433C4×C101—41no—
434C4×C101—42no—
435C4×C101—41no—
436C4×C101—42no—
437C4×C101—81no—
438C4×C101—81no—
439C4×C101C2×#12111yescharacteristic
440C4×C101#53411yescharacteristic
441C4×C101D4211yescharacteristic
442C4×C101#54611yescharacteristic
443#24455C10111yesmaximal, characteristic, direct product factor, Sylow
444C2×C101—42no—
445C2×C101—81no—
446C2×C101—82no—
447C2×C101—161no—
448C2×C101#241011yescharacteristic
449C2×C101#300511yescharacteristic
450C2×C101#301011yescharacteristic
451C2×C101#327111yescharacteristic
452C2×C101#327511yescharacteristic
453C2×C101#332111yescharacteristic
454C2×C101#332611yescharacteristic
455C2×#548C2×C10111yescharacteristic, complemented
456C2×#469C2×C10111yescharacteristic, complemented
457C2×#449C2×C10111yescharacteristic, complemented
458C2×#448C2×C10111yescharacteristic, complemented
459C2×#419C2×C10111yescharacteristic, complemented
460#2414C2×C10111yescharacteristic, complemented
461#2042C2×C10111yescharacteristic, complemented
462#2035C2×C10111yescharacteristic, complemented
463#2012C2×C10111yescharacteristic, complemented
464#2000C2×C10111yescharacteristic, complemented
465#1880C2×C10111yescharacteristic, complemented
466#1875C2×C10111yescharacteristic, complemented
467#1870C2×C10111yescharacteristic, complemented
468#1865C2×C10111yescharacteristic, complemented
469#1788C2×C10111yescharacteristic, complemented
470C101#2445511yescharacteristic, direct product factor, Sylow
471C22×#41C22×C10111yescharacteristic
472C23×Q8C22×C10111yescharacteristic
473C22×SD16C22×C10111yescharacteristic
474C22×SD16C22×C10111yescharacteristic
475C22×D8C22×C10111yescharacteristic
476C22×M16C22×C10111yescharacteristic
477#548—24no—
478#548—24no—
479C2×#124—21no—
480C2×#124C22×C10111yescharacteristic
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C10111yescharacteristic
483C2×#121—21no—
484C2×#121C22×C10111yescharacteristic
485C2×#121C22×C10111yescharacteristic
486C2×#121C22×C10111yescharacteristic
487C2×C4×Q8C22×C10111yescharacteristic
488C2×C4×D4—21no—
489C2×C4×D4C22×C10111yescharacteristic
490C2×#117C22×C10111yescharacteristic
491#469—24no—
492#449—24no—
493#448—24no—
494C2×#106C22×C10111yescharacteristic
495#419—24no—
496C2×#103C22×C10111yescharacteristic
497C2×#103C22×C10111yescharacteristic
498C2×#103C22×C10111yescharacteristic
499C2×#103C22×C10111yescharacteristic
500C2×#103C22×C10111yescharacteristic
501C2×#103C22×C10111yescharacteristic
502C2×#102C22×C10111yescharacteristic
503C2×#102C22×C10111yescharacteristic
504C2×#102C22×C10111yescharacteristic
505C2×#102C22×C10111yescharacteristic
506C2×C22⋊C8C22×C10111yescharacteristic
507C2×C22⋊C8C22×C10111yescharacteristic
508C2×C22⋊C8C22×C10111yescharacteristic
509#394—21no—
510#392—21no—
511#390—21no—
512#390C22×C10111yescharacteristic
513#389C22×C10111yescharacteristic
514#388—21no—
515#380C22×C10111yescharacteristic
516#340C22×C10111yescharacteristic
517#340C22×C10111yescharacteristic
518#336C22×C10111yescharacteristic
519#336C22×C10111yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—41no—
531C22×Q8—41no—
532C22×Q8D4×C10114yescomplemented
533C22×Q8C23×C10111yescharacteristic
534C22×Q8C23×C10111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C10111yescharacteristic
540C22×D4C23×C10111yescharacteristic
541C22×D4C23×C10111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C10111yescharacteristic
545C23×C4C23×C10111yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8C23×C10111yescharacteristic
559C22×C8C23×C10111yescharacteristic
560C22×C8C23×C10111yescharacteristic
561C22×C8C23×C10111yescharacteristic
562#124—28no—
563#124—22no—
564#124—22no—
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568#121—28no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—41no—
574#121D4×C10114yescomplemented
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580#117—22no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4D4×C10111yescharacteristic
586C2×C4⋊C4C23×C10111yescharacteristic
587C2×C4⋊C4C23×C10111yescharacteristic
588C2×C4⋊C4C23×C10111yescharacteristic
589C2×C4⋊C4C23×C10111yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C10111yescharacteristic
601C2×C22⋊C4D4×C10111yescharacteristic
602C2×C42—21no—
603C2×C42—21no—
604C2×C42C23×C10111yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C10114yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C10111yescharacteristic
624C24C2×D4×C10111yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—28no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C10112yes—
645C2×Q8C2×D4×C10112yes—
646C2×Q8C2×D4×C10112yes—
647C2×Q8#41×C10112yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4C2×D4×C10112yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
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—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C10111yescharacteristic
698C22×C4C2×D4×C10111yescharacteristic
699C22×C4C2×D4×C10111yescharacteristic
700C22×C4C2×D4×C10111yescharacteristic
701C22×C4C2×D4×C10112yes—
702C22×C4C2×D4×C10112yes—
703C22×C4C24×C10111yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707M16—44no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8C2×D4×C10112yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C10112yes—
731C4⋊C4C2×D4×C10112yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—22no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C10112yes—
776C23C22×D4×C10111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#121×C10114yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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#120×C10112yes—
839C2×C4C22×D4×C10111yescharacteristic
840C2×C4C22×D4×C10111yescharacteristic
841C2×C4C22×D4×C10111yescharacteristic
842C2×C4C2×#41×C10111yescharacteristic
843C2×C4H(5,𝔽2)×C10111yescharacteristic
844C2×C4H(5,𝔽2)×C10111yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C10111yescharacteristic
878C22D42×C10111yescharacteristic
879C22#546×C10111yescharacteristic
880C22#575×C10111yescharacteristic
881C22#575×C10111yescharacteristic
882C22#577×C10111yescharacteristic
883C22#577×C10111yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C10111yescharacteristic
895C4#534×C10111yescharacteristic
896C4D42×C10111yescharacteristic
897C4#546×C10111yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—161no—
902C2C101×#241011yescharacteristic
903C2C101×#300511yescharacteristic
904C2C101×#301011yescharacteristic
905C2C101×#327111yescharacteristic
906C2C101×#327511yescharacteristic
907C2C101×#332111yescharacteristic
908C2C101×#332611yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
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
1. C2×#548×C101C2semidirect
2. C2×#469×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×#448×C101C2semidirect
5. C2×#419×C101C2semidirect
6. C101×#2414C2semidirect
7. C101×#2042C2semidirect
8. C101×#2035C2semidirect
9. C101×#2012C2semidirect
10. C101×#2000C2semidirect
11. C101×#1880C2semidirect
12. C101×#1875C2semidirect
13. C101×#1870C2semidirect
14. C101×#1865C2semidirect
15. C101×#1788C2semidirect
77. C22×Q8×C101D4semidirect
119. #121×C101D4semidirect
156. #103×C101D4semidirect
443. #24455C101direct (N × H)
455. C2×#548C2×C101semidirect
456. C2×#469C2×C101semidirect
457. C2×#449C2×C101semidirect
458. C2×#448C2×C101semidirect
459. C2×#419C2×C101semidirect
460. #2414C2×C101semidirect
461. #2042C2×C101semidirect
462. #2035C2×C101semidirect
463. #2012C2×C101semidirect
464. #2000C2×C101semidirect
465. #1880C2×C101semidirect
466. #1875C2×C101semidirect
467. #1870C2×C101semidirect
468. #1865C2×C101semidirect
469. #1788C2×C101semidirect
470. C101#24455direct (N × H)
532. C22×Q8D4×C101semidirect
574. #121D4×C101semidirect
611. #103D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1012
C2×#469×C1012
C2×#449×C1012
C2×#448×C1012
C2×#419×C1012
C101×#24142
C101×#20422
C101×#20352
C101×#20122
C101×#20002
C101×#18802
C101×#18752
C101×#18702
C101×#18652
C101×#17882
#24455101