Finite Group Databasebeta

← C101×#25136 #38807287

Subgroups — C101×#25136 #38807287

Order 25856.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C101C211yesmaximal, characteristic, complemented
2C2×#450×C101C211yesmaximal, characteristic, complemented
3C2×#436×C101C211yesmaximal, characteristic, complemented
4C2×#418×C101C211yesmaximal, characteristic, complemented
5C101×#2415C211yesmaximal, characteristic, complemented
6C101×#2408C211yesmaximal, characteristic
7C101×#2067C211yesmaximal, characteristic, complemented
8C101×#2055C211yesmaximal, characteristic, complemented
9C101×#2034C211yesmaximal, characteristic, complemented
10C101×#2000C211yesmaximal, characteristic, complemented
11C101×#1968C211yesmaximal, characteristic, complemented
12C101×#1934C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1894C211yesmaximal, characteristic, complemented
15C101×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C22×M16×C101C2211yescharacteristic, complemented
21C2×C22⋊Q8×C101C2211yescharacteristic
22C2×C22⋊Q8×C101C2211yescharacteristic, complemented
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×#120×C101—21no—
26C2×C4×D4×C101C2211yescharacteristic
27C2×#117×C101C2211yescharacteristic
28#468×C101—24no—
29#450×C101—24no—
30#436×C101—24no—
31C2×#107×C101C2211yescharacteristic, complemented
32C2×#106×C101C2211yescharacteristic, complemented
33C2×C4⋊C8×C101C2211yescharacteristic, complemented
34#418×C101—24no—
35C2×#103×C101C2211yescharacteristic, complemented
36C2×#103×C101C2211yescharacteristic, complemented
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×C22⋊C8×C101C2211yescharacteristic, complemented
45C2×C4×C8×C101C2211yescharacteristic, complemented
46#397×C101—21no—
47#394×C101—21no—
48#394×C101—21no—
49#392×C101—21no—
50#391×C101C2211yescharacteristic, complemented
51#390×C101C2211yescharacteristic
52#390×C101C2211yescharacteristic
53#389×C101—21no—
54#389×C101C2211yescharacteristic, complemented
55#388×C101—21no—
56#380×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic, complemented
58#379×C101—21no—
59#340×C101C2211yescharacteristic, complemented
60#340×C101C2211yescharacteristic, complemented
61#340×C101C2211yescharacteristic, complemented
62#340×C101C2211yescharacteristic, complemented
63C25×C101—21no—
64C22×Q8×C101C2311yescharacteristic
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—22no—
70C22×D4×C101—21no—
71C22×D4×C101—22no—
72C22×D4×C101—41no—
73C22×D4×C101—41no—
74C22×D4×C101D411yescharacteristic
75C22×D4×C101C2311yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C23×C4×C101C2311yescharacteristic
79C2×SD16×C101—22no—
80C2×SD16×C101—22no—
81C2×SD16×C101—22no—
82C2×SD16×C101—22no—
83C2×SD16×C101—41no—
84C2×SD16×C101—41no—
85C2×M16×C101—22no—
86C2×M16×C101—22no—
87C2×M16×C101—22no—
88C2×M16×C101—22no—
89C2×M16×C101—41no—
90C2×M16×C101—41no—
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95C22⋊Q8×C101—22no—
96C22⋊Q8×C101—22no—
97C22⋊Q8×C101—22no—
98C22⋊Q8×C101—41no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—41no—
102#121×C101—41no—
103#120×C101—44no—
104C4×D4×C101—22no—
105C4×D4×C101—22no—
106#117×C101—22no—
107#117×C101—41no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101D411yescharacteristic
112C2×C4⋊C4×C101C2311yescharacteristic
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101D411yescharacteristic
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C42×C101—21no—
131C2×C42×C101C2311yescharacteristic
132#107×C101—22no—
133#106×C101—41no—
134C4⋊C8×C101—22no—
135#103×C101—22no—
136#103×C101—41no—
137#102×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101D414yescomplemented
143C22⋊C8×C101—22no—
144C22⋊C8×C101D414yescomplemented
145C4×C8×C101—22no—
146#95×C101—21no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101—21no—
150#95×C101—21no—
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—42no—
154C24×C101—42no—
155C24×C101—42no—
156C24×C101—42no—
157C24×C101—42no—
158C24×C101—81no—
159C24×C101—81no—
160C24×C101C2×D411yescharacteristic
161C24×C101C2×D411yescharacteristic
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101—21no—
165C2×Q8×C101—21no—
166C2×Q8×C101—21no—
167C2×Q8×C101—21no—
168C2×D4×C101—28no—
169C2×D4×C101—22no—
170C2×D4×C101—22no—
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—44no—
182C2×D4×C101—44no—
183C2×D4×C101—41no—
184C2×D4×C101—42no—
185C2×D4×C101—42no—
186C2×D4×C101—44no—
187C2×D4×C101—42no—
188C2×D4×C101—42no—
189C2×D4×C101—42no—
190C2×D4×C101—42no—
191C2×D4×C101—42no—
192C2×D4×C101—81no—
193C2×D4×C101—81no—
194C2×D4×C101C2×D412yes—
195C2×D4×C101#4112yes—
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—21no—
204C22×C4×C101—21no—
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×C101C2×D411yescharacteristic
213C22×C4×C101C2×D411yescharacteristic
214C22×C4×C101C2×D411yescharacteristic
215C22×C4×C101C2×D412yes—
216C22×C4×C101C2×D411yescharacteristic
217C22×C4×C101#4112yes—
218C22×C4×C101C2411yescharacteristic
219SD16×C101—44no—
220SD16×C101—44no—
221M16×C101—44no—
222M16×C101—44no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—21no—
232C2×C8×C101C2×D412yes—
233C2×C8×C101C2×D412yes—
234C2×C8×C101C2×D412yes—
235C4⋊C4×C101—22no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—21no—
238C4⋊C4×C101—21no—
239C4⋊C4×C101—21no—
240C4⋊C4×C101—21no—
241C4⋊C4×C101—21no—
242C4⋊C4×C101—21no—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—42no—
246C4⋊C4×C101—42no—
247C4⋊C4×C101—42no—
248C4⋊C4×C101C2×D412yes—
249C22⋊C4×C101—22no—
250C22⋊C4×C101—22no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—42no—
258C22⋊C4×C101—42no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—81no—
261C22⋊C4×C101—81no—
262C42×C101—21no—
263C42×C101—21no—
264C42×C101—42no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—22no—
274C23×C101—22no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—48no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—84no—
294C23×C101—84no—
295C23×C101—84no—
296C23×C101—84no—
297C23×C101—84no—
298C23×C101—84no—
299C23×C101#12112yes—
300C23×C101C22×D411yescharacteristic
301Q8×C101—41no—
302Q8×C101—41no—
303Q8×C101—41no—
304Q8×C101—41no—
305D4×C101—22no—
306D4×C101—22no—
307D4×C101—22no—
308D4×C101—22no—
309D4×C101—44no—
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—21no—
320C2×C4×C101—21no—
321C2×C4×C101—22no—
322C2×C4×C101—22no—
323C2×C4×C101—22no—
324C2×C4×C101—22no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—22no—
328C2×C4×C101—21no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—21no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
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#12112yes—
354C2×C4×C101AGL(1,ℤ/8)12yes—
355C2×C4×C101C22×D411yescharacteristic
356C2×C4×C101C22×D411yescharacteristic
357C2×C4×C101C2×#4111yescharacteristic
358C2×C4×C101C2×#4111yescharacteristic
359C2×C4×C101H(5,𝔽2)11yescharacteristic
360C2×C4×C101H(5,𝔽2)11yescharacteristic
361C8×C101—22no—
362C8×C101—22no—
363C8×C101—22no—
364C8×C101—41no—
365C22×C101—22no—
366C22×C101—22no—
367C22×C101—22no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—42no—
374C22×C101—42no—
375C22×C101—41no—
376C22×C101—42no—
377C22×C101—41no—
378C22×C101—42no—
379C22×C101—41no—
380C22×C101—41no—
381C22×C101—41no—
382C22×C101—42no—
383C22×C101—41no—
384C22×C101—42no—
385C22×C101—816no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101—81no—
393C22×C101—81no—
394C22×C101C2×#12111yescharacteristic
395C22×C101D4211yescharacteristic
396C22×C101#54611yescharacteristic
397C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C101#57511yescharacteristic
399C22×C101#57711yescharacteristic
400C22×C101#57711yescharacteristic
401C4×C101—22no—
402C4×C101—22no—
403C4×C101—41no—
404C4×C101—42no—
405C4×C101—41no—
406C4×C101—81no—
407C4×C101—81no—
408C4×C101—81no—
409C4×C101—81no—
410C4×C101—81no—
411C4×C101#52511yescharacteristic
412C4×C101#53811yescharacteristic
413C4×C101D4211yescharacteristic
414C4×C101#54611yescharacteristic
415#25136C10111yesmaximal, characteristic, direct product factor, Sylow
416C2×C101—42no—
417C2×C101—81no—
418C2×C101—82no—
419C2×C101—82no—
420C2×C101#242411yescharacteristic
421C2×C101#305511yescharacteristic
422C2×C101#305711yescharacteristic
423C2×C101#327211yescharacteristic
424C2×C101#327511yescharacteristic
425C2×C101#332311yescharacteristic
426C2×C101#332411yescharacteristic
427C2×#468C2×C10111yescharacteristic, complemented
428C2×#450C2×C10111yescharacteristic, complemented
429C2×#436C2×C10111yescharacteristic, complemented
430C2×#418C2×C10111yescharacteristic, complemented
431#2415C2×C10111yescharacteristic, complemented
432#2408C2×C10111yescharacteristic
433#2067C2×C10111yescharacteristic, complemented
434#2055C2×C10111yescharacteristic, complemented
435#2034C2×C10111yescharacteristic, complemented
436#2000C2×C10111yescharacteristic, complemented
437#1968C2×C10111yescharacteristic, complemented
438#1934C2×C10111yescharacteristic, complemented
439#1895C2×C10111yescharacteristic, complemented
440#1894C2×C10111yescharacteristic, complemented
441#1854C2×C10111yescharacteristic, complemented
442C101#2513611yescharacteristic, direct product factor, Sylow
443C23×D4C22×C10111yescharacteristic
444C22×SD16C22×C10111yescharacteristic
445C22×SD16C22×C10111yescharacteristic
446C22×M16C22×C10111yescharacteristic
447C22×M16C22×C10111yescharacteristic, complemented
448C2×C22⋊Q8C22×C10111yescharacteristic
449C2×C22⋊Q8C22×C10111yescharacteristic, complemented
450C2×#121C22×C10111yescharacteristic
451C2×#121C22×C10111yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C10111yescharacteristic
454C2×#117C22×C10111yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C10111yescharacteristic, complemented
459C2×#106C22×C10111yescharacteristic, complemented
460C2×C4⋊C8C22×C10111yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C10111yescharacteristic, complemented
463C2×#103C22×C10111yescharacteristic, complemented
464C2×#102C22×C10111yescharacteristic
465C2×#102C22×C10111yescharacteristic
466C2×#102C22×C10111yescharacteristic
467C2×#102C22×C10111yescharacteristic
468C2×#102C22×C10111yescharacteristic
469C2×#102C22×C10111yescharacteristic
470C2×C22⋊C8C22×C10111yescharacteristic
471C2×C22⋊C8C22×C10111yescharacteristic, complemented
472C2×C4×C8C22×C10111yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C10111yescharacteristic, complemented
478#390C22×C10111yescharacteristic
479#390C22×C10111yescharacteristic
480#389—21no—
481#389C22×C10111yescharacteristic, complemented
482#388—21no—
483#380C22×C10111yescharacteristic
484#380C22×C10111yescharacteristic, complemented
485#379—21no—
486#340C22×C10111yescharacteristic, complemented
487#340C22×C10111yescharacteristic, complemented
488#340C22×C10111yescharacteristic, complemented
489#340C22×C10111yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C10111yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C10111yescharacteristic
502C22×D4C23×C10111yescharacteristic
503C22×D4C23×C10111yescharacteristic
504C23×C4C23×C10111yescharacteristic
505C23×C4C23×C10111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C10111yescharacteristic
519C22×C8C23×C10111yescharacteristic
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C10111yescharacteristic
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C4⋊C4C23×C10111yescharacteristic
541C2×C4⋊C4C23×C10111yescharacteristic
542C2×C4⋊C4C23×C10111yescharacteristic
543C2×C4⋊C4C23×C10111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C10111yescharacteristic
556C2×C22⋊C4D4×C10111yescharacteristic
557C2×C42—21no—
558C2×C42C23×C10111yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C10114yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C10114yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C10111yescharacteristic
588C24C2×D4×C10111yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
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—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C10112yes—
622C2×D4#41×C10112yes—
623C22×C4—21no—
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—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C10111yescharacteristic
640C22×C4C2×D4×C10111yescharacteristic
641C22×C4C2×D4×C10111yescharacteristic
642C22×C4C2×D4×C10112yes—
643C22×C4C2×D4×C10111yescharacteristic
644C22×C4#41×C10112yes—
645C22×C4C24×C10111yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C10112yes—
660C2×C8C2×D4×C10112yes—
661C2×C8C2×D4×C10112yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C10112yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C10112yes—
727C23C22×D4×C10111yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
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—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
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#121×C10112yes—
781C2×C4AGL(1,ℤ/8)×C10112yes—
782C2×C4C22×D4×C10111yescharacteristic
783C2×C4C22×D4×C10111yescharacteristic
784C2×C4C2×#41×C10111yescharacteristic
785C2×C4C2×#41×C10111yescharacteristic
786C2×C4H(5,𝔽2)×C10111yescharacteristic
787C2×C4H(5,𝔽2)×C10111yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C10111yescharacteristic
822C22D42×C10111yescharacteristic
823C22#546×C10111yescharacteristic
824C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
825C22#575×C10111yescharacteristic
826C22#577×C10111yescharacteristic
827C22#577×C10111yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C10111yescharacteristic
839C4#538×C10111yescharacteristic
840C4D42×C10111yescharacteristic
841C4#546×C10111yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C101×#242411yescharacteristic
847C2C101×#305511yescharacteristic
848C2C101×#305711yescharacteristic
849C2C101×#327211yescharacteristic
850C2C101×#327511yescharacteristic
851C2C101×#332311yescharacteristic
852C2C101×#332411yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2408C2
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×#468×C101C2semidirect
2. C2×#450×C101C2semidirect
3. C2×#436×C101C2semidirect
4. C2×#418×C101C2semidirect
5. C101×#2415C2semidirect
7. C101×#2067C2semidirect
8. C101×#2055C2semidirect
9. C101×#2034C2semidirect
10. C101×#2000C2semidirect
11. C101×#1968C2semidirect
12. C101×#1934C2semidirect
13. C101×#1895C2semidirect
14. C101×#1894C2semidirect
15. C101×#1854C2semidirect
20. C22×M16×C101C22semidirect
22. C2×C22⋊Q8×C101C22semidirect
31. C2×#107×C101C22semidirect
32. C2×#106×C101C22semidirect
33. C2×C4⋊C8×C101C22semidirect
35. C2×#103×C101C22semidirect
36. C2×#103×C101C22semidirect
44. C2×C22⋊C8×C101C22semidirect
45. C2×C4×C8×C101C22semidirect
50. #391×C101C22semidirect
54. #389×C101C22semidirect
57. #380×C101C22semidirect
59. #340×C101C22semidirect
60. #340×C101C22semidirect
61. #340×C101C22semidirect
62. #340×C101C22semidirect
142. #102×C101D4semidirect
144. C22⋊C8×C101D4semidirect
415. #25136C101direct (N × H)
427. C2×#468C2×C101semidirect
428. C2×#450C2×C101semidirect
429. C2×#436C2×C101semidirect
430. C2×#418C2×C101semidirect
431. #2415C2×C101semidirect
433. #2067C2×C101semidirect
434. #2055C2×C101semidirect
435. #2034C2×C101semidirect
436. #2000C2×C101semidirect
437. #1968C2×C101semidirect
438. #1934C2×C101semidirect
439. #1895C2×C101semidirect
440. #1894C2×C101semidirect
441. #1854C2×C101semidirect
442. C101#25136direct (N × H)
447. C22×M16C22×C101semidirect
449. C2×C22⋊Q8C22×C101semidirect
458. C2×#107C22×C101semidirect
459. C2×#106C22×C101semidirect
460. C2×C4⋊C8C22×C101semidirect
462. C2×#103C22×C101semidirect
463. C2×#103C22×C101semidirect
471. C2×C22⋊C8C22×C101semidirect
472. C2×C4×C8C22×C101semidirect
477. #391C22×C101semidirect
481. #389C22×C101semidirect
484. #380C22×C101semidirect
486. #340C22×C101semidirect
487. #340C22×C101semidirect
488. #340C22×C101semidirect
489. #340C22×C101semidirect
569. #102D4×C101semidirect
571. C22⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1012
C2×#450×C1012
C2×#436×C1012
C2×#418×C1012
C101×#24152
C101×#24082
C101×#20672
C101×#20552
C101×#20342
C101×#20002
C101×#19682
C101×#19342
C101×#18952
C101×#18942
C101×#18542
#25136101