Finite Group Databasebeta

← C101×#24031 #38806182

Subgroups — C101×#24031 #38806182

Order 25856.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3488C211yesmaximal, characteristic
2C101×#3093C211yesmaximal, characteristic, complemented
3C101×#2896C211yesmaximal, characteristic, complemented
4C101×#2500C211yesmaximal, characteristic, complemented
5C101×#2040C211yesmaximal, characteristic, complemented
6C101×#2039C211yesmaximal, characteristic, complemented
7C101×#2037C211yesmaximal, characteristic, complemented
8C101×#2037C211yesmaximal, characteristic, complemented
9C101×#1900C211yesmaximal, characteristic, complemented
10C101×#1871C211yesmaximal, characteristic, complemented
11C101×#1860C211yesmaximal, characteristic, complemented
12C101×#1859C211yesmaximal, characteristic, complemented
13C101×#1792C211yesmaximal, characteristic, complemented
14C101×#1792C211yesmaximal, characteristic, complemented
15C101×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C101C2211yescharacteristic
17C22×#41×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic, complemented
19#550×C101—21no—
20#548×C101—21no—
21#546×C101—21no—
22#546×C101—22no—
23D42×C101—22no—
24D42×C101—21no—
25#537×C101—21no—
26#537×C101C2211yescharacteristic
27#535×C101—21no—
28#535×C101C2211yescharacteristic
29#525×C101—21no—
30#525×C101C2211yescharacteristic
31C2×#121×C101—21no—
32C2×#121×C101C2211yescharacteristic
33#520×C101C2211yescharacteristic
34C2×#117×C101C2211yescharacteristic, complemented
35#485×C101—21no—
36#485×C101—21no—
37#482×C101—21no—
38#482×C101—21no—
39#428×C101C2211yescharacteristic, complemented
40#428×C101C2211yescharacteristic, complemented
41C2×#104×C101C2211yescharacteristic
42C2×#104×C101C2211yescharacteristic
43C2×#104×C101C2211yescharacteristic, complemented
44C2×#104×C101C2211yescharacteristic, complemented
45C2×#104×C101C2211yescharacteristic, complemented
46C2×#104×C101C2211yescharacteristic, complemented
47#419×C101—21no—
48#418×C101—21no—
49#417×C101C2211yescharacteristic
50#417×C101C2211yescharacteristic
51#417×C101C2211yescharacteristic, complemented
52#417×C101C2211yescharacteristic, complemented
53#417×C101C2211yescharacteristic, complemented
54#417×C101C2211yescharacteristic, complemented
55#416×C101—21no—
56#416×C101—21no—
57C2×#100×C101C2211yescharacteristic, complemented
58C2×#100×C101C2211yescharacteristic, complemented
59#407×C101C2211yescharacteristic, complemented
60#394×C101—22no—
61#390×C101C2211yescharacteristic, complemented
62#390×C101C2211yescharacteristic, complemented
63#388×C101—22no—
64#384×C101C2211yescharacteristic, complemented
65#382×C101C2211yescharacteristic, complemented
66C4×C22⋊C4×C101C2211yescharacteristic, complemented
67#343×C101C2211yescharacteristic, complemented
68#343×C101C2211yescharacteristic, complemented
69#339×C101C2211yescharacteristic, complemented
70#339×C101C2211yescharacteristic, complemented
71H(5,𝔽2)×C101—22no—
72H(5,𝔽2)×C101—22no—
73H(5,𝔽2)×C101—41no—
74H(5,𝔽2)×C101—41no—
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—22no—
80C2×#41×C101—22no—
81C2×#41×C101—41no—
82C2×#41×C101—41no—
83C2×#41×C101D411yescharacteristic
84C2×#41×C101D411yescharacteristic
85C2×#41×C101C2311yescharacteristic
86C2×#41×C101C2311yescharacteristic
87C2×#41×C101C2311yescharacteristic
88C22×Q8×C101D411yescharacteristic
89C22×D4×C101—21no—
90C22×D4×C101—22no—
91C22×D4×C101—22no—
92C22×D4×C101—21no—
93C22×D4×C101—21no—
94C22×D4×C101D411yescharacteristic
95C22×D4×C101D412yes—
96C22×D4×C101C2311yescharacteristic
97C23×C4×C101—21no—
98C23×C4×C101C2311yescharacteristic
99C2×M16×C101—21no—
100C2×M16×C101—41no—
101C2×M16×C101—41no—
102C2×M16×C101C2311yescharacteristic
103C2×M16×C101C2311yescharacteristic
104C2×M16×C101C2311yescharacteristic
105C2×M16×C101C2311yescharacteristic
106C22×C8×C101—21no—
107#127×C101—22no—
108#127×C101—21no—
109#124×C101—22no—
110#124×C101—21no—
111#123×C101—22no—
112#123×C101—21no—
113C22⋊Q8×C101—22no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101—21no—
116C22⋊Q8×C101D411yescharacteristic
117C22⋊Q8×C101D411yescharacteristic
118#121×C101—22no—
119#121×C101—22no—
120#121×C101—22no—
121#121×C101—22no—
122#121×C101—22no—
123#121×C101—21no—
124#121×C101—21no—
125#121×C101—21no—
126#121×C101—21no—
127#121×C101—21no—
128#121×C101—21no—
129#121×C101—22no—
130#121×C101—21no—
131#121×C101—21no—
132#121×C101D411yescharacteristic
133#121×C101D411yescharacteristic
134#120×C101—22no—
135#120×C101—22no—
136#120×C101—22no—
137#120×C101—21no—
138#120×C101—22no—
139C4×Q8×C101—21no—
140C4×D4×C101—22no—
141C4×D4×C101—22no—
142C4×D4×C101—21no—
143C4×D4×C101—22no—
144C4×D4×C101—21no—
145C4×D4×C101—21no—
146#117×C101—21no—
147#117×C101—21no—
148#117×C101—21no—
149#117×C101—21no—
150#117×C101—21no—
151#117×C101C2311yescharacteristic
152C2×C4⋊C4×C101—21no—
153C2×C4⋊C4×C101—22no—
154C2×C4⋊C4×C101C2311yescharacteristic
155C2×C4⋊C4×C101C2311yescharacteristic
156C2×C4⋊C4×C101C2311yescharacteristic
157C2×C22⋊C4×C101—22no—
158C2×C22⋊C4×C101—21no—
159C2×C22⋊C4×C101—21no—
160C2×C22⋊C4×C101—22no—
161C2×C22⋊C4×C101—22no—
162C2×C22⋊C4×C101D412yes—
163C2×C42×C101—21no—
164C2×C42×C101C2311yescharacteristic
165C2×C42×C101C2311yescharacteristic
166#107×C101—21no—
167#107×C101—21no—
168#106×C101—21no—
169#106×C101—21no—
170#104×C101—22no—
171#104×C101—22no—
172#104×C101—41no—
173#104×C101—41no—
174#104×C101—41no—
175#104×C101—41no—
176#103×C101—21no—
177#103×C101—21no—
178#103×C101—21no—
179#103×C101—21no—
180#103×C101—21no—
181#103×C101—21no—
182#102×C101—21no—
183#102×C101—21no—
184#102×C101—21no—
185#102×C101—21no—
186#102×C101—21no—
187#102×C101—21no—
188#100×C101—41no—
189#100×C101—41no—
190C22⋊C8×C101—21no—
191C22⋊C8×C101—21no—
192#95×C101—21no—
193#95×C101—22no—
194C24×C101—22no—
195C24×C101—21no—
196C24×C101C2×D412yes—
197C24×C101C2×D411yescharacteristic
198#41×C101—21no—
199#41×C101—21no—
200#41×C101—22no—
201#41×C101—22no—
202#41×C101—21no—
203#41×C101—21no—
204#41×C101—21no—
205#41×C101—21no—
206#41×C101—21no—
207#41×C101—21no—
208#41×C101—21no—
209#41×C101—21no—
210#41×C101—42no—
211#41×C101—42no—
212#41×C101—41no—
213#41×C101—41no—
214#41×C101—42no—
215#41×C101—42no—
216#41×C101—42no—
217#41×C101—42no—
218#41×C101—42no—
219#41×C101—42no—
220#41×C101#4112yes—
221#41×C101#4112yes—
222C2×Q8×C101—21no—
223C2×Q8×C101—22no—
224C2×Q8×C101—41no—
225C2×Q8×C101C2×D411yescharacteristic
226C2×Q8×C101C2×D411yescharacteristic
227C2×Q8×C101C2×D411yescharacteristic
228C2×D4×C101—21no—
229C2×D4×C101—22no—
230C2×D4×C101—22no—
231C2×D4×C101—22no—
232C2×D4×C101—22no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—21no—
236C2×D4×C101—21no—
237C2×D4×C101—21no—
238C2×D4×C101—22no—
239C2×D4×C101—22no—
240C2×D4×C101—22no—
241C2×D4×C101—21no—
242C2×D4×C101—22no—
243C2×D4×C101—21no—
244C2×D4×C101—21no—
245C2×D4×C101—21no—
246C2×D4×C101—21no—
247C2×D4×C101—21no—
248C2×D4×C101—21no—
249C2×D4×C101—21no—
250C2×D4×C101—41no—
251C2×D4×C101—42no—
252C2×D4×C101—42no—
253C2×D4×C101—42no—
254C2×D4×C101—42no—
255C2×D4×C101—44no—
256C2×D4×C101—44no—
257C2×D4×C101—42no—
258C2×D4×C101—42no—
259C2×D4×C101—82no—
260C2×D4×C101—84no—
261C2×D4×C101C2×D411yescharacteristic
262C2×D4×C101C2×D411yescharacteristic
263C2×D4×C101C2×D411yescharacteristic
264C22×C4×C101—21no—
265C22×C4×C101—21no—
266C22×C4×C101—21no—
267C22×C4×C101—21no—
268C22×C4×C101—21no—
269C22×C4×C101—22no—
270C22×C4×C101—21no—
271C22×C4×C101—21no—
272C22×C4×C101—22no—
273C22×C4×C101—21no—
274C22×C4×C101—21no—
275C22×C4×C101—21no—
276C22×C4×C101—21no—
277C22×C4×C101—21no—
278C22×C4×C101—21no—
279C22×C4×C101—21no—
280C22×C4×C101—42no—
281C22×C4×C101—42no—
282C22×C4×C101C2×D411yescharacteristic
283C22×C4×C101C2×D411yescharacteristic
284C22×C4×C101C2×D411yescharacteristic
285C22×C4×C101C2×D411yescharacteristic
286C22×C4×C101C2×D411yescharacteristic
287C22×C4×C101C2×D412yes—
288C22×C4×C101C2411yescharacteristic
289M16×C101—21no—
290M16×C101—21no—
291M16×C101—21no—
292M16×C101—21no—
293M16×C101—21no—
294M16×C101—21no—
295M16×C101—21no—
296M16×C101—21no—
297M16×C101—42no—
298C2×C8×C101—21no—
299C2×C8×C101—21no—
300C2×C8×C101—21no—
301C2×C8×C101—21no—
302C2×C8×C101—42no—
303C4⋊C4×C101—22no—
304C4⋊C4×C101—22no—
305C4⋊C4×C101—21no—
306C4⋊C4×C101—21no—
307C4⋊C4×C101—21no—
308C4⋊C4×C101—21no—
309C4⋊C4×C101—21no—
310C4⋊C4×C101—21no—
311C4⋊C4×C101—21no—
312C4⋊C4×C101—21no—
313C4⋊C4×C101—82no—
314C4⋊C4×C101C2×D411yescharacteristic
315C4⋊C4×C101C2×D411yescharacteristic
316C22⋊C4×C101—22no—
317C22⋊C4×C101—22no—
318C22⋊C4×C101—22no—
319C22⋊C4×C101—22no—
320C22⋊C4×C101—22no—
321C22⋊C4×C101—21no—
322C22⋊C4×C101—21no—
323C22⋊C4×C101—21no—
324C22⋊C4×C101—21no—
325C22⋊C4×C101—22no—
326C22⋊C4×C101—22no—
327C22⋊C4×C101—21no—
328C22⋊C4×C101—42no—
329C22⋊C4×C101—44no—
330C22⋊C4×C101—41no—
331C22⋊C4×C101—41no—
332C22⋊C4×C101—82no—
333C42×C101—22no—
334C42×C101—21no—
335C42×C101—21no—
336C42×C101—21no—
337C42×C101—21no—
338C42×C101—21no—
339C42×C101—41no—
340C42×C101—41no—
341C23×C101—21no—
342C23×C101—21no—
343C23×C101—21no—
344C23×C101—22no—
345C23×C101—21no—
346C23×C101—21no—
347C23×C101—22no—
348C23×C101—22no—
349C23×C101—41no—
350C23×C101—41no—
351C23×C101—42no—
352C23×C101—42no—
353C23×C101—44no—
354C23×C101—42no—
355C23×C101—42no—
356C23×C101—81no—
357C23×C101—82no—
358C23×C101—82no—
359C23×C101#12011yescharacteristic
360C23×C101#12011yescharacteristic
361C23×C101C22×D411yescharacteristic
362Q8×C101—21no—
363Q8×C101—21no—
364Q8×C101—21no—
365Q8×C101—21no—
366Q8×C101—21no—
367Q8×C101—42no—
368Q8×C101#12312yes—
369D4×C101—22no—
370D4×C101—22no—
371D4×C101—21no—
372D4×C101—21no—
373D4×C101—21no—
374D4×C101—21no—
375D4×C101—21no—
376D4×C101—42no—
377D4×C101—42no—
378D4×C101—44no—
379D4×C101—42no—
380D4×C101—44no—
381D4×C101—44no—
382D4×C101—42no—
383D4×C101—41no—
384D4×C101—41no—
385D4×C101—41no—
386D4×C101—41no—
387D4×C101—41no—
388D4×C101—41no—
389D4×C101—41no—
390D4×C101—41no—
391D4×C101—81no—
392D4×C101—82no—
393D4×C101—82no—
394D4×C101—82no—
395D4×C101—82no—
396D4×C101#12312yes—
397C2×C4×C101—21no—
398C2×C4×C101—21no—
399C2×C4×C101—21no—
400C2×C4×C101—21no—
401C2×C4×C101—21no—
402C2×C4×C101—21no—
403C2×C4×C101—21no—
404C2×C4×C101—21no—
405C2×C4×C101—21no—
406C2×C4×C101—21no—
407C2×C4×C101—21no—
408C2×C4×C101—22no—
409C2×C4×C101—22no—
410C2×C4×C101—22no—
411C2×C4×C101—21no—
412C2×C4×C101—22no—
413C2×C4×C101—21no—
414C2×C4×C101—21no—
415C2×C4×C101—21no—
416C2×C4×C101—42no—
417C2×C4×C101—42no—
418C2×C4×C101—42no—
419C2×C4×C101—44no—
420C2×C4×C101—41no—
421C2×C4×C101—41no—
422C2×C4×C101—41no—
423C2×C4×C101—41no—
424C2×C4×C101—41no—
425C2×C4×C101—41no—
426C2×C4×C101—42no—
427C2×C4×C101—41no—
428C2×C4×C101—42no—
429C2×C4×C101—41no—
430C2×C4×C101—42no—
431C2×C4×C101—41no—
432C2×C4×C101—41no—
433C2×C4×C101—41no—
434C2×C4×C101—82no—
435C2×C4×C101#12011yescharacteristic
436C2×C4×C101#12011yescharacteristic
437C2×C4×C101C22×D411yescharacteristic
438C2×C4×C101C22×D411yescharacteristic
439C2×C4×C101C2×#4111yescharacteristic
440C2×C4×C101C2×#4111yescharacteristic
441C2×C4×C101H(5,𝔽2)11yescharacteristic
442C2×C4×C101H(5,𝔽2)11yescharacteristic
443C8×C101—41no—
444C8×C101—41no—
445C8×C101—41no—
446C8×C101—41no—
447C22×C101—21no—
448C22×C101—21no—
449C22×C101—21no—
450C22×C101—21no—
451C22×C101—22no—
452C22×C101—21no—
453C22×C101—21no—
454C22×C101—21no—
455C22×C101—21no—
456C22×C101—41no—
457C22×C101—41no—
458C22×C101—41no—
459C22×C101—41no—
460C22×C101—42no—
461C22×C101—41no—
462C22×C101—42no—
463C22×C101—41no—
464C22×C101—42no—
465C22×C101—41no—
466C22×C101—41no—
467C22×C101—81no—
468C22×C101—81no—
469C22×C101—82no—
470C22×C101—82no—
471C22×C101—84no—
472C22×C101—164no—
473C22×C101C2×#12011yescharacteristic
474C22×C101#54611yescharacteristic
475C22×C101#54611yescharacteristic
476C4×C101—21no—
477C4×C101—21no—
478C4×C101—22no—
479C4×C101—42no—
480C4×C101—41no—
481C4×C101—41no—
482C4×C101—41no—
483C4×C101—42no—
484C4×C101—41no—
485C4×C101—81no—
486C4×C101—81no—
487C4×C101—81no—
488C4×C101C2×#12311yescharacteristic
489C4×C101#53411yescharacteristic
490C4×C101#54611yescharacteristic
491C4×C101#54611yescharacteristic
492#24031C10111yesmaximal, characteristic, direct product factor, Sylow
493C2×C101—21no—
494C2×C101—21no—
495C2×C101—41no—
496C2×C101—41no—
497C2×C101—42no—
498C2×C101—81no—
499C2×C101—82no—
500C2×C101—81no—
501C2×C101#240511yescharacteristic
502C2×C101#301811yescharacteristic
503C2×C101#301911yescharacteristic
504#3488C2×C10111yescharacteristic
505#3093C2×C10111yescharacteristic, complemented
506#2896C2×C10111yescharacteristic, complemented
507#2500C2×C10111yescharacteristic, complemented
508#2040C2×C10111yescharacteristic, complemented
509#2039C2×C10111yescharacteristic, complemented
510#2037C2×C10111yescharacteristic, complemented
511#2037C2×C10111yescharacteristic, complemented
512#1900C2×C10111yescharacteristic, complemented
513#1871C2×C10111yescharacteristic, complemented
514#1860C2×C10111yescharacteristic, complemented
515#1859C2×C10111yescharacteristic, complemented
516#1792C2×C10111yescharacteristic, complemented
517#1792C2×C10111yescharacteristic, complemented
518#1789C2×C10111yescharacteristic, complemented
519C101#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C10111yescharacteristic
521C22×#41C22×C10111yescharacteristic
522C22×M16C22×C10111yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C10111yescharacteristic
531#535—21no—
532#535C22×C10111yescharacteristic
533#525—21no—
534#525C22×C10111yescharacteristic
535C2×#121—21no—
536C2×#121C22×C10111yescharacteristic
537#520C22×C10111yescharacteristic
538C2×#117C22×C10111yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C10111yescharacteristic, complemented
544#428C22×C10111yescharacteristic, complemented
545C2×#104C22×C10111yescharacteristic
546C2×#104C22×C10111yescharacteristic
547C2×#104C22×C10111yescharacteristic, complemented
548C2×#104C22×C10111yescharacteristic, complemented
549C2×#104C22×C10111yescharacteristic, complemented
550C2×#104C22×C10111yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C10111yescharacteristic
554#417C22×C10111yescharacteristic
555#417C22×C10111yescharacteristic, complemented
556#417C22×C10111yescharacteristic, complemented
557#417C22×C10111yescharacteristic, complemented
558#417C22×C10111yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C10111yescharacteristic, complemented
562C2×#100C22×C10111yescharacteristic, complemented
563#407C22×C10111yescharacteristic, complemented
564#394—22no—
565#390C22×C10111yescharacteristic, complemented
566#390C22×C10111yescharacteristic, complemented
567#388—22no—
568#384C22×C10111yescharacteristic, complemented
569#382C22×C10111yescharacteristic, complemented
570C4×C22⋊C4C22×C10111yescharacteristic, complemented
571#343C22×C10111yescharacteristic, complemented
572#343C22×C10111yescharacteristic, complemented
573#339C22×C10111yescharacteristic, complemented
574#339C22×C10111yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C10111yescharacteristic
588C2×#41D4×C10111yescharacteristic
589C2×#41C23×C10111yescharacteristic
590C2×#41C23×C10111yescharacteristic
591C2×#41C23×C10111yescharacteristic
592C22×Q8D4×C10111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C10111yescharacteristic
599C22×D4D4×C10112yes—
600C22×D4C23×C10111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C10111yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C10111yescharacteristic
607C2×M16C23×C10111yescharacteristic
608C2×M16C23×C10111yescharacteristic
609C2×M16C23×C10111yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C10111yescharacteristic
621C22⋊Q8D4×C10111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C10111yescharacteristic
637#121D4×C10111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C10111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C10111yescharacteristic
659C2×C4⋊C4C23×C10111yescharacteristic
660C2×C4⋊C4C23×C10111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C10112yes—
667C2×C42—21no—
668C2×C42C23×C10111yescharacteristic
669C2×C42C23×C10111yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C10112yes—
701C24C2×D4×C10111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C10112yes—
725#41#41×C10112yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C10111yescharacteristic
730C2×Q8C2×D4×C10111yescharacteristic
731C2×Q8C2×D4×C10111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C10111yescharacteristic
766C2×D4C2×D4×C10111yescharacteristic
767C2×D4C2×D4×C10111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C10111yescharacteristic
787C22×C4C2×D4×C10111yescharacteristic
788C22×C4C2×D4×C10111yescharacteristic
789C22×C4C2×D4×C10111yescharacteristic
790C22×C4C2×D4×C10111yescharacteristic
791C22×C4C2×D4×C10112yes—
792C22×C4C24×C10111yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C10111yescharacteristic
819C4⋊C4C2×D4×C10111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C10111yescharacteristic
864C23#120×C10111yescharacteristic
865C23C22×D4×C10111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C10112yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C10112yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C10111yescharacteristic
940C2×C4#120×C10111yescharacteristic
941C2×C4C22×D4×C10111yescharacteristic
942C2×C4C22×D4×C10111yescharacteristic
943C2×C4C2×#41×C10111yescharacteristic
944C2×C4C2×#41×C10111yescharacteristic
945C2×C4H(5,𝔽2)×C10111yescharacteristic
946C2×C4H(5,𝔽2)×C10111yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C10111yescharacteristic
978C22#546×C10111yescharacteristic
979C22#546×C10111yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C10111yescharacteristic
993C4#534×C10111yescharacteristic
994C4#546×C10111yescharacteristic
995C4#546×C10111yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C101×#240511yescharacteristic
1005C2C101×#301811yescharacteristic
1006C2C101×#301911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3093C2semidirect
3. C101×#2896C2semidirect
4. C101×#2500C2semidirect
5. C101×#2040C2semidirect
6. C101×#2039C2semidirect
7. C101×#2037C2semidirect
8. C101×#2037C2semidirect
9. C101×#1900C2semidirect
10. C101×#1871C2semidirect
11. C101×#1860C2semidirect
12. C101×#1859C2semidirect
13. C101×#1792C2semidirect
14. C101×#1792C2semidirect
15. C101×#1789C2semidirect
18. C22×M16×C101C22semidirect
34. C2×#117×C101C22semidirect
39. #428×C101C22semidirect
40. #428×C101C22semidirect
43. C2×#104×C101C22semidirect
44. C2×#104×C101C22semidirect
45. C2×#104×C101C22semidirect
46. C2×#104×C101C22semidirect
51. #417×C101C22semidirect
52. #417×C101C22semidirect
53. #417×C101C22semidirect
54. #417×C101C22semidirect
57. C2×#100×C101C22semidirect
58. C2×#100×C101C22semidirect
59. #407×C101C22semidirect
61. #390×C101C22semidirect
62. #390×C101C22semidirect
64. #384×C101C22semidirect
65. #382×C101C22semidirect
66. C4×C22⋊C4×C101C22semidirect
67. #343×C101C22semidirect
68. #343×C101C22semidirect
69. #339×C101C22semidirect
70. #339×C101C22semidirect
492. #24031C101direct (N × H)
505. #3093C2×C101semidirect
506. #2896C2×C101semidirect
507. #2500C2×C101semidirect
508. #2040C2×C101semidirect
509. #2039C2×C101semidirect
510. #2037C2×C101semidirect
511. #2037C2×C101semidirect
512. #1900C2×C101semidirect
513. #1871C2×C101semidirect
514. #1860C2×C101semidirect
515. #1859C2×C101semidirect
516. #1792C2×C101semidirect
517. #1792C2×C101semidirect
518. #1789C2×C101semidirect
519. C101#24031direct (N × H)
522. C22×M16C22×C101semidirect
538. C2×#117C22×C101semidirect
543. #428C22×C101semidirect
544. #428C22×C101semidirect
547. C2×#104C22×C101semidirect
548. C2×#104C22×C101semidirect
549. C2×#104C22×C101semidirect
550. C2×#104C22×C101semidirect
555. #417C22×C101semidirect
556. #417C22×C101semidirect
557. #417C22×C101semidirect
558. #417C22×C101semidirect
561. C2×#100C22×C101semidirect
562. C2×#100C22×C101semidirect
563. #407C22×C101semidirect
565. #390C22×C101semidirect
566. #390C22×C101semidirect
568. #384C22×C101semidirect
569. #382C22×C101semidirect
570. C4×C22⋊C4C22×C101semidirect
571. #343C22×C101semidirect
572. #343C22×C101semidirect
573. #339C22×C101semidirect
574. #339C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34882
C101×#30932
C101×#28962
C101×#25002
C101×#20402
C101×#20392
C101×#20372
C101×#19002
C101×#18712
C101×#18602
C101×#18592
C101×#17922
C101×#17892
#24031101