Finite Group Databasebeta

← C101×#24427 #38806578

Subgroups — C101×#24427 #38806578

Order 25856.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C101C211yesmaximal, characteristic
2C2×#465×C101C211yesmaximal, characteristic, complemented
3C2×#452×C101C211yesmaximal, characteristic, complemented
4C2×#452×C101C211yesmaximal, characteristic, complemented
5C2×#416×C101C211yesmaximal, characteristic, complemented
6C101×#2415C211yesmaximal, characteristic, complemented
7C101×#2041C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2014C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1878C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1869C211yesmaximal, characteristic, complemented
14C101×#1865C211yesmaximal, characteristic, complemented
15C101×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×Q16×C101C2211yescharacteristic
19C22×SD16×C101C2211yescharacteristic
20C22×SD16×C101C2211yescharacteristic
21C23×C8×C101C2211yescharacteristic
22#550×C101—24no—
23#550×C101—24no—
24C2×#127×C101—21no—
25C2×#127×C101C2211yescharacteristic
26C2×C22⋊Q8×C101C2211yescharacteristic
27C2×C22⋊Q8×C101C2211yescharacteristic
28C2×#121×C101—21no—
29C2×#121×C101—21no—
30C2×#121×C101C2211yescharacteristic
31C2×#121×C101C2211yescharacteristic
32C2×C4×Q8×C101C2211yescharacteristic
33C2×C4×D4×C101—21no—
34C2×C4×D4×C101C2211yescharacteristic
35C2×#117×C101C2211yescharacteristic
36#465×C101—24no—
37#452×C101—24no—
38#452×C101—24no—
39C2×#106×C101C2211yescharacteristic
40#416×C101—24no—
41C2×#103×C101C2211yescharacteristic
42C2×#103×C101C2211yescharacteristic
43C2×#103×C101C2211yescharacteristic
44C2×#103×C101C2211yescharacteristic
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
54#397×C101—21no—
55#394×C101—21no—
56#391×C101C2211yescharacteristic
57#389×C101—21no—
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—22no—
70C2×#41×C101—22no—
71C2×#41×C101—22no—
72C2×#41×C101—41no—
73C2×#41×C101—41no—
74C2×#41×C101—41no—
75C2×#41×C101—41no—
76C2×#41×C101D414yes—
77C22×Q8×C101C2311yescharacteristic
78C22×Q8×C101C2311yescharacteristic
79C22×D4×C101—21no—
80C22×D4×C101—21no—
81C22×D4×C101—21no—
82C22×D4×C101—21no—
83C22×D4×C101—21no—
84C22×D4×C101—21no—
85C22×D4×C101D411yescharacteristic
86C22×D4×C101C2311yescharacteristic
87C22×D4×C101C2311yescharacteristic
88C23×C4×C101—21no—
89C23×C4×C101—21no—
90C23×C4×C101C2311yescharacteristic
91C23×C4×C101C2311yescharacteristic
92C2×Q16×C101—22no—
93C2×Q16×C101—22no—
94C2×Q16×C101—22no—
95C2×SD16×C101—22no—
96C2×SD16×C101—22no—
97C2×SD16×C101—22no—
98C2×SD16×C101—41no—
99C2×SD16×C101—41no—
100C2×SD16×C101—41no—
101C22×C8×C101—22no—
102C22×C8×C101—22no—
103C22×C8×C101—41no—
104C22×C8×C101C2311yescharacteristic
105C22×C8×C101C2311yescharacteristic
106C22×C8×C101C2311yescharacteristic
107C22×C8×C101C2311yescharacteristic
108#127×C101—28no—
109#127×C101—22no—
110#127×C101—22no—
111C22⋊Q8×C101—22no—
112C22⋊Q8×C101—22no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—41no—
115#121×C101—28no—
116#121×C101—28no—
117#121×C101—22no—
118#121×C101—22no—
119#121×C101—22no—
120#121×C101D414yes—
121C4×Q8×C101—22no—
122C4×Q8×C101—22no—
123C4×D4×C101—28no—
124C4×D4×C101—22no—
125C4×D4×C101—22no—
126#117×C101—22no—
127#117×C101—41no—
128C2×C4⋊C4×C101—21no—
129C2×C4⋊C4×C101—21no—
130C2×C4⋊C4×C101—21no—
131C2×C4⋊C4×C101—21no—
132C2×C4⋊C4×C101D411yescharacteristic
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×C101D411yescharacteristic
144C2×C22⋊C4×C101D411yescharacteristic
145C2×C42×C101—21no—
146C2×C42×C101—21no—
147C2×C42×C101C2311yescharacteristic
148#106×C101—22no—
149#103×C101—22no—
150#103×C101—22no—
151#103×C101—22no—
152#103×C101D414yescomplemented
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—
162#95×C101—21no—
163#95×C101—21no—
164#95×C101—21no—
165#95×C101—21no—
166C24×C101—21no—
167C24×C101—21no—
168C24×C101C2×D411yescharacteristic
169C24×C101C2×D411yescharacteristic
170#41×C101—28no—
171#41×C101—44no—
172#41×C101—44no—
173#41×C101—44no—
174#41×C101—44no—
175#41×C101—44no—
176#41×C101—44no—
177#41×C101—44no—
178C2×Q8×C101—21no—
179C2×Q8×C101—21no—
180C2×Q8×C101—21no—
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×C101C2×D412yes—
188C2×Q8×C101C2×D412yes—
189C2×Q8×C101#4112yes—
190C2×D4×C101—24no—
191C2×D4×C101—24no—
192C2×D4×C101—22no—
193C2×D4×C101—24no—
194C2×D4×C101—24no—
195C2×D4×C101—24no—
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—21no—
207C2×D4×C101—21no—
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—81no—
216C2×D4×C101—81no—
217C2×D4×C101—81no—
218C2×D4×C101—81no—
219C2×D4×C101—81no—
220C2×D4×C101—81no—
221C2×D4×C101C2×D412yes—
222C2×D4×C101C2×D412yes—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—24no—
229C22×C4×C101—21no—
230C22×C4×C101—21no—
231C22×C4×C101—24no—
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—42no—
242C22×C4×C101—42no—
243C22×C4×C101—42no—
244C22×C4×C101—42no—
245C22×C4×C101C2×D411yescharacteristic
246C22×C4×C101C2×D411yescharacteristic
247C22×C4×C101C2×D411yescharacteristic
248C22×C4×C101C2×D412yes—
249C22×C4×C101C2×D412yes—
250C22×C4×C101C2×D411yescharacteristic
251C22×C4×C101C2411yescharacteristic
252Q16×C101—44no—
253SD16×C101—44no—
254SD16×C101—44no—
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×C101—21no—
265C2×C8×C101—21no—
266C2×C8×C101—44no—
267C2×C8×C101C2×D412yes—
268C4⋊C4×C101—24no—
269C4⋊C4×C101—22no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—21no—
272C4⋊C4×C101—21no—
273C4⋊C4×C101—21no—
274C4⋊C4×C101—21no—
275C4⋊C4×C101—21no—
276C4⋊C4×C101—42no—
277C4⋊C4×C101—42no—
278C4⋊C4×C101—42no—
279C4⋊C4×C101C2×D412yes—
280C4⋊C4×C101C2×D412yes—
281C22⋊C4×C101—24no—
282C22⋊C4×C101—22no—
283C22⋊C4×C101—24no—
284C22⋊C4×C101—22no—
285C22⋊C4×C101—42no—
286C22⋊C4×C101—42no—
287C22⋊C4×C101—42no—
288C22⋊C4×C101—42no—
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—22no—
302C23×C101—21no—
303C23×C101—21no—
304C23×C101—21no—
305C23×C101—21no—
306C23×C101—21no—
307C23×C101—21no—
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—41no—
326Q8×C101—41no—
327Q8×C101—41no—
328Q8×C101—41no—
329Q8×C101#12114yes—
330D4×C101—22no—
331D4×C101—22no—
332D4×C101—22no—
333D4×C101—22no—
334D4×C101—44no—
335D4×C101—48no—
336D4×C101—48no—
337D4×C101—48no—
338D4×C101—41no—
339D4×C101—41no—
340D4×C101—41no—
341D4×C101—41no—
342D4×C101—84no—
343D4×C101—84no—
344D4×C101—84no—
345C2×C4×C101—21no—
346C2×C4×C101—22no—
347C2×C4×C101—21no—
348C2×C4×C101—22no—
349C2×C4×C101—21no—
350C2×C4×C101—22no—
351C2×C4×C101—21no—
352C2×C4×C101—22no—
353C2×C4×C101—22no—
354C2×C4×C101—22no—
355C2×C4×C101—22no—
356C2×C4×C101—21no—
357C2×C4×C101—22no—
358C2×C4×C101—21no—
359C2×C4×C101—22no—
360C2×C4×C101—21no—
361C2×C4×C101—21no—
362C2×C4×C101—21no—
363C2×C4×C101—21no—
364C2×C4×C101—48no—
365C2×C4×C101—48no—
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#12012yes—
384C2×C4×C101#13512yes—
385C2×C4×C101C22×D411yescharacteristic
386C2×C4×C101C22×D411yescharacteristic
387C2×C4×C101C22×D411yescharacteristic
388C2×C4×C101C2×#4111yescharacteristic
389C2×C4×C101H(5,𝔽2)11yescharacteristic
390C2×C4×C101H(5,𝔽2)11yescharacteristic
391C8×C101—22no—
392C8×C101—41no—
393C8×C101—41no—
394C8×C101—41no—
395C22×C101—22no—
396C22×C101—22no—
397C22×C101—22no—
398C22×C101—41no—
399C22×C101—41no—
400C22×C101—41no—
401C22×C101—41no—
402C22×C101—42no—
403C22×C101—42no—
404C22×C101—41no—
405C22×C101—41no—
406C22×C101—42no—
407C22×C101—42no—
408C22×C101—41no—
409C22×C101—42no—
410C22×C101—42no—
411C22×C101—41no—
412C22×C101—41no—
413C22×C101—41no—
414C22×C101—41no—
415C22×C101—81no—
416C22×C101—81no—
417C22×C101—81no—
418C22×C101—81no—
419C22×C101—81no—
420C22×C101—81no—
421C22×C101—81no—
422C22×C101—81no—
423C22×C101C2×#12011yescharacteristic
424C22×C101D4211yescharacteristic
425C22×C101#54611yescharacteristic
426C22×C101C2×#13511yescharacteristic
427C22×C101#57511yescharacteristic
428C22×C101#57711yescharacteristic
429C22×C101#57711yescharacteristic
430C4×C101—22no—
431C4×C101—24no—
432C4×C101—22no—
433C4×C101—41no—
434C4×C101—41no—
435C4×C101—42no—
436C4×C101—42no—
437C4×C101—81no—
438C4×C101—81no—
439C4×C101—81no—
440C4×C101C2×#12111yescharacteristic
441C4×C101#53411yescharacteristic
442C4×C101D4211yescharacteristic
443C4×C101#54611yescharacteristic
444#24427C10111yesmaximal, characteristic, direct product factor, Sylow
445C2×C101—42no—
446C2×C101—81no—
447C2×C101—82no—
448C2×C101—82no—
449C2×C101#241011yescharacteristic
450C2×C101#300211yescharacteristic
451C2×C101#300911yescharacteristic
452C2×C101#327111yescharacteristic
453C2×C101#328411yescharacteristic
454C2×C101#330411yescharacteristic
455C2×C101#331711yescharacteristic
456C2×#550C2×C10111yescharacteristic
457C2×#465C2×C10111yescharacteristic, complemented
458C2×#452C2×C10111yescharacteristic, complemented
459C2×#452C2×C10111yescharacteristic, complemented
460C2×#416C2×C10111yescharacteristic, complemented
461#2415C2×C10111yescharacteristic, complemented
462#2041C2×C10111yescharacteristic, complemented
463#2034C2×C10111yescharacteristic, complemented
464#2014C2×C10111yescharacteristic, complemented
465#2000C2×C10111yescharacteristic, complemented
466#1878C2×C10111yescharacteristic, complemented
467#1875C2×C10111yescharacteristic, complemented
468#1869C2×C10111yescharacteristic, complemented
469#1865C2×C10111yescharacteristic, complemented
470#1788C2×C10111yescharacteristic, complemented
471C101#2442711yescharacteristic, direct product factor, Sylow
472C22×#41C22×C10111yescharacteristic
473C22×#41C22×C10111yescharacteristic
474C22×Q16C22×C10111yescharacteristic
475C22×SD16C22×C10111yescharacteristic
476C22×SD16C22×C10111yescharacteristic
477C23×C8C22×C10111yescharacteristic
478#550—24no—
479#550—24no—
480C2×#127—21no—
481C2×#127C22×C10111yescharacteristic
482C2×C22⋊Q8C22×C10111yescharacteristic
483C2×C22⋊Q8C22×C10111yescharacteristic
484C2×#121—21no—
485C2×#121—21no—
486C2×#121C22×C10111yescharacteristic
487C2×#121C22×C10111yescharacteristic
488C2×C4×Q8C22×C10111yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4C22×C10111yescharacteristic
491C2×#117C22×C10111yescharacteristic
492#465—24no—
493#452—24no—
494#452—24no—
495C2×#106C22×C10111yescharacteristic
496#416—24no—
497C2×#103C22×C10111yescharacteristic
498C2×#103C22×C10111yescharacteristic
499C2×#103C22×C10111yescharacteristic
500C2×#103C22×C10111yescharacteristic
501C2×#102C22×C10111yescharacteristic
502C2×#102C22×C10111yescharacteristic
503C2×#102C22×C10111yescharacteristic
504C2×#102C22×C10111yescharacteristic
505C2×#102C22×C10111yescharacteristic
506C2×#102C22×C10111yescharacteristic
507C2×C22⋊C8C22×C10111yescharacteristic
508C2×C22⋊C8C22×C10111yescharacteristic
509C2×C22⋊C8C22×C10111yescharacteristic
510#397—21no—
511#394—21no—
512#391C22×C10111yescharacteristic
513#389—21no—
514#389C22×C10111yescharacteristic
515#388—21no—
516#380C22×C10111yescharacteristic
517#340C22×C10111yescharacteristic
518#340C22×C10111yescharacteristic
519#336C22×C10111yescharacteristic
520#336C22×C10111yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C10114yes—
533C22×Q8C23×C10111yescharacteristic
534C22×Q8C23×C10111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C10111yescharacteristic
542C22×D4C23×C10111yescharacteristic
543C22×D4C23×C10111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C10111yescharacteristic
547C23×C4C23×C10111yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C10111yescharacteristic
561C22×C8C23×C10111yescharacteristic
562C22×C8C23×C10111yescharacteristic
563C22×C8C23×C10111yescharacteristic
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C10114yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—22no—
583#117—41no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10111yescharacteristic
589C2×C4⋊C4C23×C10111yescharacteristic
590C2×C4⋊C4C23×C10111yescharacteristic
591C2×C4⋊C4C23×C10111yescharacteristic
592C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4D4×C10111yescharacteristic
600C2×C22⋊C4D4×C10111yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C10111yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103D4×C10114yescomplemented
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622C24—21no—
623C24—21no—
624C24C2×D4×C10111yescharacteristic
625C24C2×D4×C10111yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C10112yes—
644C2×Q8C2×D4×C10112yes—
645C2×Q8#41×C10112yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
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—21no—
663C2×D4—21no—
664C2×D4—41no—
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×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C10112yes—
678C2×D4C2×D4×C10112yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
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—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C10111yescharacteristic
702C22×C4C2×D4×C10111yescharacteristic
703C22×C4C2×D4×C10111yescharacteristic
704C22×C4C2×D4×C10112yes—
705C22×C4C2×D4×C10112yes—
706C22×C4C2×D4×C10111yescharacteristic
707C22×C4C24×C10111yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
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×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C10112yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C10112yes—
736C4⋊C4C2×D4×C10112yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#120×C10112yes—
777C23C22×D4×C10111yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8#121×C10114yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
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—41no—
839C2×C4#120×C10112yes—
840C2×C4#135×C10112yes—
841C2×C4C22×D4×C10111yescharacteristic
842C2×C4C22×D4×C10111yescharacteristic
843C2×C4C22×D4×C10111yescharacteristic
844C2×C4C2×#41×C10111yescharacteristic
845C2×C4H(5,𝔽2)×C10111yescharacteristic
846C2×C4H(5,𝔽2)×C10111yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C10111yescharacteristic
880C22D42×C10111yescharacteristic
881C22#546×C10111yescharacteristic
882C22C2×#135×C10111yescharacteristic
883C22#575×C10111yescharacteristic
884C22#577×C10111yescharacteristic
885C22#577×C10111yescharacteristic
886C4—22no—
887C4—24no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×#121×C10111yescharacteristic
897C4#534×C10111yescharacteristic
898C4D42×C10111yescharacteristic
899C4#546×C10111yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2C101×#241011yescharacteristic
905C2C101×#300211yescharacteristic
906C2C101×#300911yescharacteristic
907C2C101×#327111yescharacteristic
908C2C101×#328411yescharacteristic
909C2C101×#330411yescharacteristic
910C2C101×#331711yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#550×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×#465×C101C2semidirect
3. C2×#452×C101C2semidirect
4. C2×#452×C101C2semidirect
5. C2×#416×C101C2semidirect
6. C101×#2415C2semidirect
7. C101×#2041C2semidirect
8. C101×#2034C2semidirect
9. C101×#2014C2semidirect
10. C101×#2000C2semidirect
11. C101×#1878C2semidirect
12. C101×#1875C2semidirect
13. C101×#1869C2semidirect
14. C101×#1865C2semidirect
15. C101×#1788C2semidirect
152. #103×C101D4semidirect
444. #24427C101direct (N × H)
457. C2×#465C2×C101semidirect
458. C2×#452C2×C101semidirect
459. C2×#452C2×C101semidirect
460. C2×#416C2×C101semidirect
461. #2415C2×C101semidirect
462. #2041C2×C101semidirect
463. #2034C2×C101semidirect
464. #2014C2×C101semidirect
465. #2000C2×C101semidirect
466. #1878C2×C101semidirect
467. #1875C2×C101semidirect
468. #1869C2×C101semidirect
469. #1865C2×C101semidirect
470. #1788C2×C101semidirect
471. C101#24427direct (N × H)
608. #103D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1012
C2×#465×C1012
C2×#452×C1012
C2×#416×C1012
C101×#24152
C101×#20412
C101×#20342
C101×#20142
C101×#20002
C101×#18782
C101×#18752
C101×#18692
C101×#18652
C101×#17882
#24427101