Finite Group Databasebeta

← C101×#23975 #38806126

Subgroups — C101×#23975 #38806126

Order 25856.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C101C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic, complemented
3C2×#417×C101C211yesmaximal, characteristic, complemented
4C101×#2407C211yesmaximal, characteristic, complemented
5C101×#2026C211yesmaximal, characteristic, complemented
6C101×#2025C211yesmaximal, characteristic, complemented
7C101×#2000C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1877C211yesmaximal, characteristic, complemented
12C101×#1875C211yesmaximal, characteristic, complemented
13C101×#1873C211yesmaximal, characteristic, complemented
14C101×#1870C211yesmaximal, characteristic, complemented
15C101×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20#553×C101—24no—
21#553×C101—24no—
22C2×#126×C101—21no—
23C2×#125×C101C2211yescharacteristic
24C2×#123×C101—21no—
25C2×C22⋊Q8×C101C2211yescharacteristic
26C2×#121×C101—21no—
27C2×#121×C101C2211yescharacteristic
28C2×#121×C101C2211yescharacteristic
29C2×#121×C101C2211yescharacteristic
30C2×C4×D4×C101—21no—
31C2×C4×D4×C101C2211yescharacteristic
32C2×C4×D4×C101C2211yescharacteristic
33C2×#117×C101C2211yescharacteristic
34C22×C4⋊C4×C101C2211yescharacteristic
35#449×C101—24no—
36#417×C101—24no—
37C2×#103×C101C2211yescharacteristic
38C2×#103×C101C2211yescharacteristic
39C2×#103×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×#102×C101C2211yescharacteristic
45C2×C22⋊C8×C101C2211yescharacteristic
46C2×C22⋊C8×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48#394×C101—21no—
49#392×C101—21no—
50#391×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#386×C101—21no—
53#385×C101—21no—
54#380×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—22no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C22×Q8×C101C2311yescharacteristic
70C22×D4×C101—21no—
71C22×D4×C101—21no—
72C22×D4×C101—21no—
73C22×D4×C101—21no—
74C22×D4×C101D411yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C23×C4×C101—21no—
78C23×C4×C101—21no—
79C23×C4×C101—21no—
80C23×C4×C101C2311yescharacteristic
81C23×C4×C101C2311yescharacteristic
82C2×SD16×C101—22no—
83C2×SD16×C101—22no—
84C2×SD16×C101—41no—
85C2×D8×C101—22no—
86C2×D8×C101—22no—
87C2×D8×C101—41no—
88C2×M16×C101—22no—
89C2×M16×C101—41no—
90C2×M16×C101—41no—
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95#126×C101—28no—
96#125×C101—22no—
97#125×C101—22no—
98#123×C101—28no—
99C22⋊Q8×C101—22no—
100C22⋊Q8×C101—41no—
101#121×C101—28no—
102#121×C101—22no—
103#121×C101—22no—
104#121×C101—22no—
105#121×C101—22no—
106#121×C101—41no—
107#121×C101D414yescomplemented
108C4×D4×C101—28no—
109C4×D4×C101—22no—
110C4×D4×C101—22no—
111C4×D4×C101—22no—
112C4×D4×C101—22no—
113#117×C101—22no—
114#117×C101—22no—
115C2×C4⋊C4×C101—21no—
116C2×C4⋊C4×C101—22no—
117C2×C4⋊C4×C101—21no—
118C2×C4⋊C4×C101—21no—
119C2×C4⋊C4×C101—21no—
120C2×C4⋊C4×C101D411yescharacteristic
121C2×C4⋊C4×C101D414yescomplemented
122C2×C4⋊C4×C101C2311yescharacteristic
123C2×C4⋊C4×C101C2311yescharacteristic
124C2×C4⋊C4×C101C2311yescharacteristic
125C2×C4⋊C4×C101C2311yescharacteristic
126C2×C4⋊C4×C101C2311yescharacteristic
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101—21no—
130C2×C22⋊C4×C101—21no—
131C2×C22⋊C4×C101—21no—
132C2×C22⋊C4×C101—21no—
133C2×C22⋊C4×C101—21no—
134C2×C22⋊C4×C101—21no—
135C2×C22⋊C4×C101—21no—
136C2×C22⋊C4×C101D411yescharacteristic
137C2×C22⋊C4×C101D411yescharacteristic
138C2×C42×C101—21no—
139C2×C42×C101C2311yescharacteristic
140#103×C101—22no—
141#103×C101—22no—
142#103×C101—22no—
143#102×C101—22no—
144#102×C101—22no—
145#102×C101—22no—
146#102×C101—41no—
147#102×C101—41no—
148C22⋊C8×C101—22no—
149C22⋊C8×C101—41no—
150C22⋊C8×C101—41no—
151#95×C101—21no—
152#95×C101—21no—
153#95×C101—21no—
154C24×C101—21no—
155C24×C101—21no—
156C24×C101C2×D411yescharacteristic
157C24×C101C2×D411yescharacteristic
158#41×C101—28no—
159#41×C101—44no—
160#41×C101—44no—
161#41×C101—44no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101#4112yes—
168C2×D4×C101—22no—
169C2×D4×C101—24no—
170C2×D4×C101—24no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—21no—
179C2×D4×C101—21no—
180C2×D4×C101—21no—
181C2×D4×C101—41no—
182C2×D4×C101—41no—
183C2×D4×C101—42no—
184C2×D4×C101—42no—
185C2×D4×C101—42no—
186C2×D4×C101—42no—
187C2×D4×C101—42no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—81no—
193C2×D4×C101C2×D412yes—
194C2×D4×C101#4112yes—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—24no—
204C22×C4×C101—24no—
205C22×C4×C101—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—21no—
211C22×C4×C101—21no—
212C22×C4×C101—21no—
213C22×C4×C101—42no—
214C22×C4×C101—42no—
215C22×C4×C101—42no—
216C22×C4×C101—81no—
217C22×C4×C101—81no—
218C22×C4×C101—81no—
219C22×C4×C101—81no—
220C22×C4×C101C2×D411yescharacteristic
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2×D412yes—
225C22×C4×C101C2×D412yes—
226C22×C4×C101C2411yescharacteristic
227SD16×C101—44no—
228D8×C101—44no—
229M16×C101—44no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101—21no—
242C4⋊C4×C101—24no—
243C4⋊C4×C101—24no—
244C4⋊C4×C101—24no—
245C4⋊C4×C101—22no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101—21no—
253C4⋊C4×C101—42no—
254C4⋊C4×C101C2×D412yes—
255C4⋊C4×C101C2×D412yes—
256C4⋊C4×C101C2×D412yes—
257C22⋊C4×C101—24no—
258C22⋊C4×C101—24no—
259C22⋊C4×C101—24no—
260C22⋊C4×C101—22no—
261C22⋊C4×C101—24no—
262C22⋊C4×C101—22no—
263C22⋊C4×C101—42no—
264C22⋊C4×C101—42no—
265C22⋊C4×C101—42no—
266C22⋊C4×C101—81no—
267C22⋊C4×C101—81no—
268C42×C101—24no—
269C42×C101—21no—
270C42×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—22no—
279C23×C101—21no—
280C23×C101—22no—
281C23×C101—21no—
282C23×C101—21no—
283C23×C101—21no—
284C23×C101—21no—
285C23×C101—21no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101—41no—
295C23×C101—41no—
296C23×C101—41no—
297C23×C101—41no—
298C23×C101#12012yes—
299C23×C101C22×D411yescharacteristic
300Q8×C101—22no—
301Q8×C101—22no—
302Q8×C101—41no—
303Q8×C101—41no—
304D4×C101—22no—
305D4×C101—22no—
306D4×C101—22no—
307D4×C101—22no—
308D4×C101—44no—
309D4×C101—48no—
310D4×C101—48no—
311D4×C101—41no—
312D4×C101—41no—
313D4×C101—41no—
314D4×C101—41no—
315D4×C101—84no—
316D4×C101—84no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—22no—
320C2×C4×C101—22no—
321C2×C4×C101—22no—
322C2×C4×C101—22no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—22no—
326C2×C4×C101—21no—
327C2×C4×C101—22no—
328C2×C4×C101—22no—
329C2×C4×C101—21no—
330C2×C4×C101—22no—
331C2×C4×C101—21no—
332C2×C4×C101—21no—
333C2×C4×C101—21no—
334C2×C4×C101—21no—
335C2×C4×C101—21no—
336C2×C4×C101—48no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—41no—
350C2×C4×C101—41no—
351C2×C4×C101—41no—
352C2×C4×C101—41no—
353C2×C4×C101—41no—
354C2×C4×C101—41no—
355C2×C4×C101—84no—
356C2×C4×C101—84no—
357C2×C4×C101#12012yes—
358C2×C4×C101C22×D411yescharacteristic
359C2×C4×C101C22×D411yescharacteristic
360C2×C4×C101C2×#4111yescharacteristic
361C2×C4×C101C2×#4111yescharacteristic
362C2×C4×C101H(5,𝔽2)11yescharacteristic
363C2×C4×C101H(5,𝔽2)11yescharacteristic
364C8×C101—41no—
365C8×C101—41no—
366C8×C101—41no—
367C8×C101—41no—
368C22×C101—22no—
369C22×C101—22no—
370C22×C101—22no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—42no—
376C22×C101—41no—
377C22×C101—42no—
378C22×C101—41no—
379C22×C101—42no—
380C22×C101—42no—
381C22×C101—41no—
382C22×C101—41no—
383C22×C101—42no—
384C22×C101—41no—
385C22×C101—41no—
386C22×C101—42no—
387C22×C101—41no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101—81no—
393C22×C101—81no—
394C22×C101—81no—
395C22×C101—81no—
396C22×C101C2×#12011yescharacteristic
397C22×C101#54611yescharacteristic
398C22×C101#54611yescharacteristic
399C22×C101#57511yescharacteristic
400C22×C101#57511yescharacteristic
401C22×C101#57611yescharacteristic
402C22×C101#57711yescharacteristic
403C4×C101—22no—
404C4×C101—41no—
405C4×C101—42no—
406C4×C101—41no—
407C4×C101—42no—
408C4×C101—41no—
409C4×C101—42no—
410C4×C101—42no—
411C4×C101—81no—
412C4×C101—81no—
413C4×C101#52511yescharacteristic
414C4×C101#53511yescharacteristic
415C4×C101#54611yescharacteristic
416C4×C101#54611yescharacteristic
417#23975C10111yesmaximal, characteristic, direct product factor, Sylow
418C2×C101—42no—
419C2×C101—81no—
420C2×C101—82no—
421C2×C101—82no—
422C2×C101#240411yescharacteristic
423C2×C101#300511yescharacteristic
424C2×C101#301211yescharacteristic
425C2×C101#330711yescharacteristic
426C2×C101#330911yescharacteristic
427C2×C101#332211yescharacteristic
428C2×C101#332611yescharacteristic
429C2×#553C2×C10111yescharacteristic, complemented
430C2×#449C2×C10111yescharacteristic, complemented
431C2×#417C2×C10111yescharacteristic, complemented
432#2407C2×C10111yescharacteristic, complemented
433#2026C2×C10111yescharacteristic, complemented
434#2025C2×C10111yescharacteristic, complemented
435#2000C2×C10111yescharacteristic, complemented
436#1999C2×C10111yescharacteristic, complemented
437#1895C2×C10111yescharacteristic, complemented
438#1879C2×C10111yescharacteristic, complemented
439#1877C2×C10111yescharacteristic, complemented
440#1875C2×C10111yescharacteristic, complemented
441#1873C2×C10111yescharacteristic, complemented
442#1870C2×C10111yescharacteristic, complemented
443#1823C2×C10111yescharacteristic, complemented
444C101#2397511yescharacteristic, direct product factor, Sylow
445C22×#41C22×C10111yescharacteristic
446C22×SD16C22×C10111yescharacteristic
447C22×D8C22×C10111yescharacteristic
448C22×M16C22×C10111yescharacteristic
449#553—24no—
450#553—24no—
451C2×#126—21no—
452C2×#125C22×C10111yescharacteristic
453C2×#123—21no—
454C2×C22⋊Q8C22×C10111yescharacteristic
455C2×#121—21no—
456C2×#121C22×C10111yescharacteristic
457C2×#121C22×C10111yescharacteristic
458C2×#121C22×C10111yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C10111yescharacteristic
461C2×C4×D4C22×C10111yescharacteristic
462C2×#117C22×C10111yescharacteristic
463C22×C4⋊C4C22×C10111yescharacteristic
464#449—24no—
465#417—24no—
466C2×#103C22×C10111yescharacteristic
467C2×#103C22×C10111yescharacteristic
468C2×#103C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×#102C22×C10111yescharacteristic
471C2×#102C22×C10111yescharacteristic
472C2×#102C22×C10111yescharacteristic
473C2×#102C22×C10111yescharacteristic
474C2×C22⋊C8C22×C10111yescharacteristic
475C2×C22⋊C8C22×C10111yescharacteristic
476C2×C22⋊C8C22×C10111yescharacteristic
477#394—21no—
478#392—21no—
479#391C22×C10111yescharacteristic
480#390C22×C10111yescharacteristic
481#386—21no—
482#385—21no—
483#380C22×C10111yescharacteristic
484#340C22×C10111yescharacteristic
485#340C22×C10111yescharacteristic
486#340C22×C10111yescharacteristic
487#340C22×C10111yescharacteristic
488#340C22×C10111yescharacteristic
489#340C22×C10111yescharacteristic
490#336C22×C10111yescharacteristic
491#336C22×C10111yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C10111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C10111yescharacteristic
504C22×D4C23×C10111yescharacteristic
505C22×D4C23×C10111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C10111yescharacteristic
510C23×C4C23×C10111yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522C22×C8C23×C10111yescharacteristic
523C22×C8C23×C10111yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C10114yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C10111yescharacteristic
550C2×C4⋊C4D4×C10114yescomplemented
551C2×C4⋊C4C23×C10111yescharacteristic
552C2×C4⋊C4C23×C10111yescharacteristic
553C2×C4⋊C4C23×C10111yescharacteristic
554C2×C4⋊C4C23×C10111yescharacteristic
555C2×C4⋊C4C23×C10111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C10111yescharacteristic
566C2×C22⋊C4D4×C10111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C10111yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C10111yescharacteristic
586C24C2×D4×C10111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C10112yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C10112yes—
623C2×D4#41×C10112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C10111yescharacteristic
650C22×C4C2×D4×C10111yescharacteristic
651C22×C4C2×D4×C10111yescharacteristic
652C22×C4C2×D4×C10111yescharacteristic
653C22×C4C2×D4×C10112yes—
654C22×C4C2×D4×C10112yes—
655C22×C4C24×C10111yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C10112yes—
684C4⋊C4C2×D4×C10112yes—
685C4⋊C4C2×D4×C10112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C10112yes—
728C23C22×D4×C10111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C10112yes—
787C2×C4C22×D4×C10111yescharacteristic
788C2×C4C22×D4×C10111yescharacteristic
789C2×C4C2×#41×C10111yescharacteristic
790C2×C4C2×#41×C10111yescharacteristic
791C2×C4H(5,𝔽2)×C10111yescharacteristic
792C2×C4H(5,𝔽2)×C10111yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C10111yescharacteristic
826C22#546×C10111yescharacteristic
827C22#546×C10111yescharacteristic
828C22#575×C10111yescharacteristic
829C22#575×C10111yescharacteristic
830C22#576×C10111yescharacteristic
831C22#577×C10111yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4#525×C10111yescharacteristic
843C4#535×C10111yescharacteristic
844C4#546×C10111yescharacteristic
845C4#546×C10111yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C101×#240411yescharacteristic
851C2C101×#300511yescharacteristic
852C2C101×#301211yescharacteristic
853C2C101×#330711yescharacteristic
854C2C101×#330911yescharacteristic
855C2C101×#332211yescharacteristic
856C2C101×#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×#553×C101C2semidirect
2. C2×#449×C101C2semidirect
3. C2×#417×C101C2semidirect
4. C101×#2407C2semidirect
5. C101×#2026C2semidirect
6. C101×#2025C2semidirect
7. C101×#2000C2semidirect
8. C101×#1999C2semidirect
9. C101×#1895C2semidirect
10. C101×#1879C2semidirect
11. C101×#1877C2semidirect
12. C101×#1875C2semidirect
13. C101×#1873C2semidirect
14. C101×#1870C2semidirect
15. C101×#1823C2semidirect
107. #121×C101D4semidirect
121. C2×C4⋊C4×C101D4semidirect
417. #23975C101direct (N × H)
429. C2×#553C2×C101semidirect
430. C2×#449C2×C101semidirect
431. C2×#417C2×C101semidirect
432. #2407C2×C101semidirect
433. #2026C2×C101semidirect
434. #2025C2×C101semidirect
435. #2000C2×C101semidirect
436. #1999C2×C101semidirect
437. #1895C2×C101semidirect
438. #1879C2×C101semidirect
439. #1877C2×C101semidirect
440. #1875C2×C101semidirect
441. #1873C2×C101semidirect
442. #1870C2×C101semidirect
443. #1823C2×C101semidirect
444. C101#23975direct (N × H)
536. #121D4×C101semidirect
550. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1012
C2×#449×C1012
C2×#417×C1012
C101×#24072
C101×#20262
C101×#20252
C101×#20002
C101×#19992
C101×#18952
C101×#18792
C101×#18772
C101×#18752
C101×#18732
C101×#18702
C101×#18232
#23975101