Finite Group Databasebeta

← C101×#24901 #38807052

Subgroups — C101×#24901 #38807052

Order 25856.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C101C211yesmaximal, characteristic
2C2×C4×SD16×C101C211yesmaximal, characteristic, complemented
3C101×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C101C211yesmaximal, characteristic
5C101×#2094C211yesmaximal, characteristic, complemented
6C101×#2077C211yesmaximal, characteristic, complemented
7C101×#2055C211yesmaximal, characteristic, complemented
8C101×#2035C211yesmaximal, characteristic, complemented
9C101×#1934C211yesmaximal, characteristic, complemented
10C101×#1923C211yesmaximal, characteristic, complemented
11C101×#1880C211yesmaximal, characteristic, complemented
12C101×#1877C211yesmaximal, characteristic, complemented
13C101×#1864C211yesmaximal, characteristic, complemented
14C101×#1802C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic
16C23×D4×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C2×C22⋊Q8×C101C2211yescharacteristic
20C2×C4×Q8×C101C2211yescharacteristic, complemented
21C2×C4×D4×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C22×C22⋊C4×C101—21no—
24#450×C101—24no—
25C4×SD16×C101—24no—
26C2×#106×C101C2211yescharacteristic, complemented
27C2×#106×C101C2211yescharacteristic, complemented
28C2×C4⋊C8×C101C2211yescharacteristic, complemented
29C2×#103×C101C2211yescharacteristic, complemented
30C2×#103×C101C2211yescharacteristic, complemented
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×C22⋊C8×C101C2211yescharacteristic
38C2×C22⋊C8×C101C2211yescharacteristic
39C2×C4×C8×C101C2211yescharacteristic, complemented
40#399×C101—21no—
41#398×C101—21no—
42#391×C101C2211yescharacteristic, complemented
43#390×C101C2211yescharacteristic
44#390×C101C2211yescharacteristic
45#389×C101C2211yescharacteristic, complemented
46#388×C101—21no—
47#387×C101—21no—
48#386×C101—21no—
49#386×C101—21no—
50#384×C101C2211yescharacteristic, complemented
51#380×C101C2211yescharacteristic
52#380×C101C2211yescharacteristic
53#379×C101—21no—
54C4×C22⋊C4×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic, complemented
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#336×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61C25×C101—21no—
62C22×Q8×C101C2311yescharacteristic
63C22×D4×C101—22no—
64C22×D4×C101—22no—
65C22×D4×C101—22no—
66C22×D4×C101—22no—
67C22×D4×C101—21no—
68C22×D4×C101—41no—
69C22×D4×C101—41no—
70C22×D4×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C23×C4×C101—21no—
73C23×C4×C101—21no—
74C23×C4×C101C2311yescharacteristic
75C2×SD16×C101—22no—
76C2×SD16×C101—22no—
77C2×SD16×C101—22no—
78C2×SD16×C101—22no—
79C2×SD16×C101—41no—
80C2×SD16×C101D414yes—
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85C22⋊Q8×C101—22no—
86C22⋊Q8×C101—41no—
87C4×Q8×C101—22no—
88C4×Q8×C101—41no—
89C4×D4×C101—22no—
90C4×D4×C101—22no—
91C4×D4×C101—41no—
92C4×D4×C101—41no—
93C2×C4⋊C4×C101—21no—
94C2×C4⋊C4×C101—21no—
95C2×C4⋊C4×C101—21no—
96C2×C4⋊C4×C101—21no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101C2311yescharacteristic
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—21no—
105C2×C22⋊C4×C101—21no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—44no—
113C2×C22⋊C4×C101D411yescharacteristic
114C2×C22⋊C4×C101D411yescharacteristic
115C2×C42×C101—21no—
116C2×C42×C101C2311yescharacteristic
117C2×C42×C101C2311yescharacteristic
118#106×C101—22no—
119#106×C101—41no—
120C4⋊C8×C101—41no—
121#103×C101—22no—
122#103×C101—41no—
123#102×C101—22no—
124#102×C101—22no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—41no—
129C22⋊C8×C101—22no—
130C22⋊C8×C101—41no—
131C4×C8×C101—22no—
132#95×C101—21no—
133#95×C101—21no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101D411yescharacteristic
138#95×C101D411yescharacteristic
139C24×C101—21no—
140C24×C101—24no—
141C24×C101—21no—
142C24×C101—42no—
143C24×C101—42no—
144C24×C101—42no—
145C24×C101—42no—
146C24×C101—81no—
147C24×C101—81no—
148C24×C101C2×D411yescharacteristic
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—21no—
154C2×Q8×C101C2×D412yes—
155C2×D4×C101—24no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—21no—
164C2×D4×C101—42no—
165C2×D4×C101—42no—
166C2×D4×C101—44no—
167C2×D4×C101—44no—
168C2×D4×C101—44no—
169C2×D4×C101—44no—
170C2×D4×C101C2×D412yes—
171C2×D4×C101#4112yes—
172C2×D4×C101#4112yes—
173C2×D4×C101#4112yes—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—42no—
187C22×C4×C101—42no—
188C22×C4×C101—42no—
189C22×C4×C101—42no—
190C22×C4×C101—81no—
191C22×C4×C101—81no—
192C22×C4×C101C2×D411yescharacteristic
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2411yescharacteristic
198SD16×C101—28no—
199SD16×C101—44no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101—21no—
209C2×C8×C101—21no—
210C2×C8×C101—21no—
211C2×C8×C101C2×D412yes—
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—42no—
223C4⋊C4×C101—42no—
224C4⋊C4×C101—42no—
225C4⋊C4×C101—81no—
226C4⋊C4×C101—81no—
227C22⋊C4×C101—41no—
228C22⋊C4×C101—42no—
229C22⋊C4×C101—42no—
230C22⋊C4×C101—42no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—81no—
235C22⋊C4×C101—81no—
236C22⋊C4×C101—81no—
237C22⋊C4×C101SD1614yescomplemented
238C42×C101—21no—
239C42×C101—21no—
240C42×C101—21no—
241C42×C101—21no—
242C42×C101—42no—
243C23×C101—21no—
244C23×C101—22no—
245C23×C101—21no—
246C23×C101—22no—
247C23×C101—22no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—22no—
253C23×C101—48no—
254C23×C101—48no—
255C23×C101—41no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—41no—
261C23×C101—41no—
262C23×C101—41no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—84no—
266C23×C101—84no—
267C23×C101—84no—
268C23×C101—84no—
269C23×C101—84no—
270C23×C101C2×SD1612yes—
271C23×C101C22×D411yescharacteristic
272Q8×C101—22no—
273Q8×C101—22no—
274Q8×C101—41no—
275Q8×C101—41no—
276D4×C101—22no—
277D4×C101—22no—
278D4×C101—22no—
279D4×C101—22no—
280D4×C101—22no—
281D4×C101—48no—
282D4×C101—41no—
283D4×C101—41no—
284D4×C101#12314yes—
285C2×C4×C101—21no—
286C2×C4×C101—21no—
287C2×C4×C101—21no—
288C2×C4×C101—21no—
289C2×C4×C101—21no—
290C2×C4×C101—21no—
291C2×C4×C101—22no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—21no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—41no—
300C2×C4×C101—41no—
301C2×C4×C101—41no—
302C2×C4×C101—41no—
303C2×C4×C101—41no—
304C2×C4×C101—41no—
305C2×C4×C101—41no—
306C2×C4×C101—41no—
307C2×C4×C101—41no—
308C2×C4×C101—41no—
309C2×C4×C101—41no—
310C2×C4×C101—41no—
311C2×C4×C101—41no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—84no—
321C2×C4×C101—84no—
322C2×C4×C101C2×SD1612yes—
323C2×C4×C101C2×SD1612yes—
324C2×C4×C101C22×D411yescharacteristic
325C2×C4×C101C2×#4111yescharacteristic
326C2×C4×C101C2×#4111yescharacteristic
327C2×C4×C101C2×#4111yescharacteristic
328C2×C4×C101H(5,𝔽2)11yescharacteristic
329C2×C4×C101H(5,𝔽2)11yescharacteristic
330C8×C101—22no—
331C8×C101—41no—
332C8×C101—41no—
333C8×C101—41no—
334C22×C101—22no—
335C22×C101—24no—
336C22×C101—22no—
337C22×C101—22no—
338C22×C101—42no—
339C22×C101—41no—
340C22×C101—42no—
341C22×C101—41no—
342C22×C101—41no—
343C22×C101—42no—
344C22×C101—42no—
345C22×C101—42no—
346C22×C101—41no—
347C22×C101—42no—
348C22×C101—42no—
349C22×C101—42no—
350C22×C101—42no—
351C22×C101—816no—
352C22×C101—81no—
353C22×C101—81no—
354C22×C101—81no—
355C22×C101—81no—
356C22×C101#52511yescharacteristic
357C22×C101D4211yescharacteristic
358C22×C101#54611yescharacteristic
359C22×C101C22×SD1611yescharacteristic
360C22×C101#57511yescharacteristic
361C22×C101#57611yescharacteristic
362C22×C101#57711yescharacteristic
363C4×C101—22no—
364C4×C101—22no—
365C4×C101—41no—
366C4×C101—42no—
367C4×C101—41no—
368C4×C101—41no—
369C4×C101—81no—
370C4×C101—81no—
371C4×C101—81no—
372C4×C101—81no—
373C4×C101—81no—
374C4×C101C2×#12311yescharacteristic
375C4×C101#53811yescharacteristic
376C4×C101#54611yescharacteristic
377C4×C101#55111yescharacteristic
378#24901C10111yesmaximal, characteristic, direct product factor, Sylow
379C2×C101—42no—
380C2×C101—44no—
381C2×C101—82no—
382C2×C101#241811yescharacteristic
383C2×C101#310111yescharacteristic
384C2×C101#311811yescharacteristic
385C2×C101#326811yescharacteristic
386C2×C101D4×SD1611yescharacteristic
387C2×C101#329511yescharacteristic
388C2×C101#332311yescharacteristic
389C2×#450C2×C10111yescharacteristic
390C2×C4×SD16C2×C10111yescharacteristic, complemented
391#2423C2×C10111yescharacteristic, complemented
392D4×C22⋊C4C2×C10111yescharacteristic
393#2094C2×C10111yescharacteristic, complemented
394#2077C2×C10111yescharacteristic, complemented
395#2055C2×C10111yescharacteristic, complemented
396#2035C2×C10111yescharacteristic, complemented
397#1934C2×C10111yescharacteristic, complemented
398#1923C2×C10111yescharacteristic, complemented
399#1880C2×C10111yescharacteristic, complemented
400#1877C2×C10111yescharacteristic, complemented
401#1864C2×C10111yescharacteristic, complemented
402#1802C2×C10111yescharacteristic, complemented
403#1786C2×C10111yescharacteristic
404C101#2490111yescharacteristic, direct product factor, Sylow
405C23×D4C22×C10111yescharacteristic
406C22×SD16C22×C10111yescharacteristic
407C22×SD16C22×C10111yescharacteristic
408C2×C22⋊Q8C22×C10111yescharacteristic
409C2×C4×Q8C22×C10111yescharacteristic, complemented
410C2×C4×D4C22×C10111yescharacteristic
411C2×C4×D4C22×C10111yescharacteristic
412C22×C22⋊C4—21no—
413#450—24no—
414C4×SD16—24no—
415C2×#106C22×C10111yescharacteristic, complemented
416C2×#106C22×C10111yescharacteristic, complemented
417C2×C4⋊C8C22×C10111yescharacteristic, complemented
418C2×#103C22×C10111yescharacteristic, complemented
419C2×#103C22×C10111yescharacteristic, complemented
420C2×#102C22×C10111yescharacteristic
421C2×#102C22×C10111yescharacteristic
422C2×#102C22×C10111yescharacteristic
423C2×#102C22×C10111yescharacteristic
424C2×#102C22×C10111yescharacteristic
425C2×#102C22×C10111yescharacteristic
426C2×C22⋊C8C22×C10111yescharacteristic
427C2×C22⋊C8C22×C10111yescharacteristic
428C2×C4×C8C22×C10111yescharacteristic, complemented
429#399—21no—
430#398—21no—
431#391C22×C10111yescharacteristic, complemented
432#390C22×C10111yescharacteristic
433#390C22×C10111yescharacteristic
434#389C22×C10111yescharacteristic, complemented
435#388—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#384C22×C10111yescharacteristic, complemented
440#380C22×C10111yescharacteristic
441#380C22×C10111yescharacteristic
442#379—21no—
443C4×C22⋊C4C22×C10111yescharacteristic
444#340C22×C10111yescharacteristic, complemented
445#340C22×C10111yescharacteristic, complemented
446#340C22×C10111yescharacteristic, complemented
447#340C22×C10111yescharacteristic, complemented
448#336C22×C10111yescharacteristic, complemented
449#336C22×C10111yescharacteristic, complemented
450C25—21no—
451C22×Q8C23×C10111yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C10111yescharacteristic
460C22×D4C23×C10111yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C10111yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C10114yes—
470C22×C8C23×C10111yescharacteristic
471C22×C8C23×C10111yescharacteristic
472C22×C8C23×C10111yescharacteristic
473C22×C8C23×C10111yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C10111yescharacteristic
488C2×C4⋊C4C23×C10111yescharacteristic
489C2×C4⋊C4C23×C10111yescharacteristic
490C2×C4⋊C4C23×C10111yescharacteristic
491C2×C4⋊C4C23×C10111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C10111yescharacteristic
503C2×C22⋊C4D4×C10111yescharacteristic
504C2×C42—21no—
505C2×C42C23×C10111yescharacteristic
506C2×C42C23×C10111yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C10111yescharacteristic
527#95D4×C10111yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C10111yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C10112yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C10112yes—
560C2×D4#41×C10112yes—
561C2×D4#41×C10112yes—
562C2×D4#41×C10112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C10111yescharacteristic
582C22×C4C2×D4×C10111yescharacteristic
583C22×C4C2×D4×C10111yescharacteristic
584C22×C4C2×D4×C10111yescharacteristic
585C22×C4C2×D4×C10111yescharacteristic
586C22×C4C24×C10111yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C10112yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C10114yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C10112yes—
660C23C22×D4×C10111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C10114yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C10112yes—
712C2×C4C2×SD16×C10112yes—
713C2×C4C22×D4×C10111yescharacteristic
714C2×C4C2×#41×C10111yescharacteristic
715C2×C4C2×#41×C10111yescharacteristic
716C2×C4C2×#41×C10111yescharacteristic
717C2×C4H(5,𝔽2)×C10111yescharacteristic
718C2×C4H(5,𝔽2)×C10111yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—24no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#525×C10111yescharacteristic
746C22D42×C10111yescharacteristic
747C22#546×C10111yescharacteristic
748C22C22×SD16×C10111yescharacteristic
749C22#575×C10111yescharacteristic
750C22#576×C10111yescharacteristic
751C22#577×C10111yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C10111yescharacteristic
764C4#538×C10111yescharacteristic
765C4#546×C10111yescharacteristic
766C4#551×C10111yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C101×#241811yescharacteristic
771C2C101×#310111yescharacteristic
772C2C101×#311811yescharacteristic
773C2C101×#326811yescharacteristic
774C2D4×SD16×C10111yescharacteristic
775C2C101×#329511yescharacteristic
776C2C101×#332311yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC23×D4×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C101C2semidirect
3. C101×#2423C2semidirect
5. C101×#2094C2semidirect
6. C101×#2077C2semidirect
7. C101×#2055C2semidirect
8. C101×#2035C2semidirect
9. C101×#1934C2semidirect
10. C101×#1923C2semidirect
11. C101×#1880C2semidirect
12. C101×#1877C2semidirect
13. C101×#1864C2semidirect
14. C101×#1802C2semidirect
20. C2×C4×Q8×C101C22semidirect
26. C2×#106×C101C22semidirect
27. C2×#106×C101C22semidirect
28. C2×C4⋊C8×C101C22semidirect
29. C2×#103×C101C22semidirect
30. C2×#103×C101C22semidirect
39. C2×C4×C8×C101C22semidirect
42. #391×C101C22semidirect
45. #389×C101C22semidirect
50. #384×C101C22semidirect
55. #340×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #336×C101C22semidirect
60. #336×C101C22semidirect
237. C22⋊C4×C101SD16semidirect
378. #24901C101direct (N × H)
390. C2×C4×SD16C2×C101semidirect
391. #2423C2×C101semidirect
393. #2094C2×C101semidirect
394. #2077C2×C101semidirect
395. #2055C2×C101semidirect
396. #2035C2×C101semidirect
397. #1934C2×C101semidirect
398. #1923C2×C101semidirect
399. #1880C2×C101semidirect
400. #1877C2×C101semidirect
401. #1864C2×C101semidirect
402. #1802C2×C101semidirect
404. C101#24901direct (N × H)
409. C2×C4×Q8C22×C101semidirect
415. C2×#106C22×C101semidirect
416. C2×#106C22×C101semidirect
417. C2×C4⋊C8C22×C101semidirect
418. C2×#103C22×C101semidirect
419. C2×#103C22×C101semidirect
428. C2×C4×C8C22×C101semidirect
431. #391C22×C101semidirect
434. #389C22×C101semidirect
439. #384C22×C101semidirect
444. #340C22×C101semidirect
445. #340C22×C101semidirect
446. #340C22×C101semidirect
447. #340C22×C101semidirect
448. #336C22×C101semidirect
449. #336C22×C101semidirect
626. C22⋊C4SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1012
C2×C4×SD16×C1012
C101×#24232
D4×C22⋊C4×C1012
C101×#20942
C101×#20772
C101×#20552
C101×#20352
C101×#19342
C101×#19232
C101×#18802
C101×#18772
C101×#18642
C101×#18022
C101×#17862
#24901101