Finite Group Databasebeta

← C101×#10395 #38792546

Subgroups — C101×#10395 #38792546

Order 25856.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2617C211yesmaximal, characteristic
2C101×#1874C211yesmaximal, characteristic, complemented
3C101×#1853C211yesmaximal, characteristic, complemented
4C2×#327×C101C211yesmaximal, characteristic, complemented
5C2×#323×C101C211yesmaximal, characteristic, complemented
6C101×#1439C211yesmaximal, characteristic, complemented
7C101×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C101C2211yescharacteristic
9C2×#120×C101—21no—
10C22×C4⋊C4×C101C2211yescharacteristic
11C22×C22⋊C4×C101—21no—
12C22×C22⋊C4×C101C2211yescharacteristic
13C2×#106×C101—21no—
14C2×#102×C101—21no—
15C2×C22⋊C8×C101C2211yescharacteristic
16C2×C22⋊C8×C101C2211yescharacteristic
17#397×C101—21no—
18#394×C101—21no—
19#394×C101—21no—
20#392×C101—21no—
21#386×C101—21no—
22#380×C101C2211yescharacteristic
23C2×#95×C101—21no—
24C2×#95×C101C2211yescharacteristic
25#340×C101—21no—
26#340×C101—21no—
27#327×C101—22no—
28#323×C101—22no—
29C25×C101D411yescharacteristic
30C22×D4×C101—21no—
31C22×D4×C101—21no—
32C22×D4×C101—21no—
33C22×D4×C101D411yescharacteristic
34C23×C4×C101—21no—
35C23×C4×C101—21no—
36C23×C4×C101D411yescharacteristic
37C23×C4×C101C2311yescharacteristic
38C22×C8×C101—21no—
39C22×C8×C101—21no—
40#121×C101—21no—
41#121×C101—21no—
42#121×C101—21no—
43#121×C101—21no—
44#120×C101—42no—
45#120×C101—42no—
46C2×C4⋊C4×C101—21no—
47C2×C4⋊C4×C101—21no—
48C2×C4⋊C4×C101—42no—
49C2×C4⋊C4×C101D411yescharacteristic
50C2×C4⋊C4×C101D411yescharacteristic
51C2×C4⋊C4×C101D411yescharacteristic
52C2×C22⋊C4×C101—21no—
53C2×C22⋊C4×C101—21no—
54C2×C22⋊C4×C101—21no—
55C2×C22⋊C4×C101—21no—
56C2×C22⋊C4×C101—21no—
57C2×C22⋊C4×C101—21no—
58C2×C22⋊C4×C101—21no—
59C2×C22⋊C4×C101—21no—
60C2×C22⋊C4×C101—21no—
61C2×C22⋊C4×C101—21no—
62C2×C22⋊C4×C101—21no—
63C2×C22⋊C4×C101—21no—
64C2×C22⋊C4×C101—42no—
65C2×C22⋊C4×C101—42no—
66C2×C22⋊C4×C101—42no—
67#106×C101—42no—
68#102×C101—42no—
69C22⋊C8×C101—21no—
70C22⋊C8×C101—21no—
71C22⋊C8×C101—21no—
72C22⋊C8×C101D412yescomplemented
73#95×C101—21no—
74#95×C101—21no—
75#95×C101—21no—
76#95×C101—21no—
77#95×C101—21no—
78#95×C101—42no—
79C24×C101—21no—
80C24×C101—21no—
81C24×C101—21no—
82C24×C101—21no—
83C24×C101—21no—
84C24×C101—21no—
85C24×C101—21no—
86C24×C101—41no—
87C24×C101—41no—
88C24×C101—41no—
89C24×C101—41no—
90C24×C101SD1612yes—
91C24×C101C2×D411yescharacteristic
92C2×D4×C101—21no—
93C2×D4×C101—21no—
94C2×D4×C101—41no—
95C2×D4×C101—41no—
96C2×D4×C101—42no—
97C2×D4×C101—42no—
98C2×D4×C101—41no—
99C2×D4×C101—41no—
100C2×D4×C101—41no—
101C2×D4×C101—41no—
102C2×D4×C101—41no—
103C2×D4×C101—41no—
104C2×D4×C101—81no—
105C2×D4×C101—81no—
106C2×D4×C101—81no—
107C2×D4×C101—81no—
108C22×C4×C101—22no—
109C22×C4×C101—22no—
110C22×C4×C101—21no—
111C22×C4×C101—21no—
112C22×C4×C101—21no—
113C22×C4×C101—21no—
114C22×C4×C101—21no—
115C22×C4×C101—21no—
116C22×C4×C101—41no—
117C22×C4×C101—41no—
118C22×C4×C101—41no—
119C22×C4×C101—41no—
120C22×C4×C101—41no—
121C22×C4×C101—41no—
122C22×C4×C101—41no—
123C22×C4×C101—41no—
124C22×C4×C101—41no—
125C22×C4×C101—41no—
126C22×C4×C101—41no—
127C22×C4×C101—41no—
128C22×C4×C101—41no—
129C22×C4×C101—41no—
130C22×C4×C101—41no—
131C22×C4×C101—41no—
132C22×C4×C101C2×D411yescharacteristic
133C22×C4×C101C2×D411yescharacteristic
134C22×C4×C101C2×D411yescharacteristic
135C22×C4×C101#4111yescharacteristic
136C22×C4×C101#4111yescharacteristic
137C22×C4×C101#4111yescharacteristic
138C2×C8×C101—22no—
139C2×C8×C101—41no—
140C2×C8×C101—41no—
141C2×C8×C101—41no—
142C2×C8×C101—41no—
143C2×C8×C101—41no—
144C4⋊C4×C101—22no—
145C4⋊C4×C101—22no—
146C4⋊C4×C101—21no—
147C4⋊C4×C101—21no—
148C4⋊C4×C101—41no—
149C4⋊C4×C101—41no—
150C4⋊C4×C101—41no—
151C4⋊C4×C101—41no—
152C22⋊C4×C101—42no—
153C22⋊C4×C101—42no—
154C22⋊C4×C101—48no—
155C22⋊C4×C101—41no—
156C22⋊C4×C101—41no—
157C22⋊C4×C101—41no—
158C22⋊C4×C101—41no—
159C22⋊C4×C101—41no—
160C22⋊C4×C101—41no—
161C22⋊C4×C101—41no—
162C22⋊C4×C101—41no—
163C22⋊C4×C101—81no—
164C22⋊C4×C101—81no—
165C23×C101—21no—
166C23×C101—21no—
167C23×C101—21no—
168C23×C101—21no—
169C23×C101—22no—
170C23×C101—22no—
171C23×C101—22no—
172C23×C101—42no—
173C23×C101—42no—
174C23×C101—42no—
175C23×C101—42no—
176C23×C101—42no—
177C23×C101—42no—
178C23×C101—41no—
179C23×C101—41no—
180C23×C101—41no—
181C23×C101—41no—
182C23×C101—41no—
183C23×C101—41no—
184C23×C101—41no—
185C23×C101—41no—
186C23×C101—41no—
187C23×C101—41no—
188C23×C101—41no—
189C23×C101—41no—
190C23×C101—41no—
191C23×C101—41no—
192C23×C101—41no—
193C23×C101—81no—
194C23×C101—81no—
195C23×C101—81no—
196C23×C101—81no—
197C23×C101—81no—
198C23×C101—81no—
199C23×C101#12011yescharacteristic
200C23×C101#12111yescharacteristic
201C23×C101#12311yescharacteristic
202C23×C101C2×SD1611yescharacteristic
203C23×C101#13511yescharacteristic
204C23×C101AGL(1,ℤ/8)11yescharacteristic
205C23×C101AGL(1,ℤ/8)11yescharacteristic
206D4×C101—42no—
207D4×C101—81no—
208D4×C101—84no—
209D4×C101—84no—
210D4×C101—81no—
211D4×C101—81no—
212D4×C101—81no—
213D4×C101—81no—
214C2×C4×C101—21no—
215C2×C4×C101—21no—
216C2×C4×C101—21no—
217C2×C4×C101—21no—
218C2×C4×C101—41no—
219C2×C4×C101—41no—
220C2×C4×C101—41no—
221C2×C4×C101—41no—
222C2×C4×C101—42no—
223C2×C4×C101—42no—
224C2×C4×C101—42no—
225C2×C4×C101—42no—
226C2×C4×C101—42no—
227C2×C4×C101—42no—
228C2×C4×C101—41no—
229C2×C4×C101—41no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—42no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—81no—
242C2×C4×C101—81no—
243C2×C4×C101—81no—
244C2×C4×C101—81no—
245C2×C4×C101—81no—
246C2×C4×C101—81no—
247C2×C4×C101—81no—
248C2×C4×C101—81no—
249C2×C4×C101—81no—
250C2×C4×C101#12111yescharacteristic
251C2×C4×C101#12111yescharacteristic
252C2×C4×C101#12311yescharacteristic
253C2×C4×C101#12411yescharacteristic
254C8×C101—42no—
255C8×C101—81no—
256C22×C101—21no—
257C22×C101—21no—
258C22×C101—21no—
259C22×C101—21no—
260C22×C101—21no—
261C22×C101—21no—
262C22×C101—21no—
263C22×C101—21no—
264C22×C101—21no—
265C22×C101—21no—
266C22×C101—21no—
267C22×C101—21no—
268C22×C101—44no—
269C22×C101—42no—
270C22×C101—42no—
271C22×C101—42no—
272C22×C101—82no—
273C22×C101—82no—
274C22×C101—82no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101#39411yescharacteristic
287C22×C101#44911yescharacteristic
288C22×C101#45011yescharacteristic
289C22×C101#45311yescharacteristic
290C22×C101#45511yescharacteristic
291C22×C101B(4,𝔽2)11yescharacteristic
292C22×C101#45811yescharacteristic
293C22×C101#46511yescharacteristic
294C22×C101#46911yescharacteristic
295C22×C101#48111yescharacteristic
296C22×C101#48211yescharacteristic
297C4×C101—21no—
298C4×C101—21no—
299C4×C101—21no—
300C4×C101—21no—
301C4×C101—82no—
302C4×C101—82no—
303C4×C101—81no—
304C4×C101—81no—
305C4×C101—81no—
306C4×C101—81no—
307#10395C10111yesmaximal, characteristic, direct product factor, Sylow
308C2×C101—21no—
309C2×C101—21no—
310C2×C101—21no—
311C2×C101—21no—
312C2×C101—82no—
313C2×C101—161no—
314C2×C101#160011yescharacteristic
315C2×C101#160111yescharacteristic
316C2×C101#161211yescharacteristic
317C2×C101#161311yescharacteristic
318C2×C101#203411yescharacteristic
319C2×C101#203711yescharacteristic
320C2×C101#204411yescharacteristic
321#2617C2×C10111yescharacteristic
322#1874C2×C10111yescharacteristic, complemented
323#1853C2×C10111yescharacteristic, complemented
324C2×#327C2×C10111yescharacteristic, complemented
325C2×#323C2×C10111yescharacteristic, complemented
326#1439C2×C10111yescharacteristic, complemented
327#1294C2×C10111yescharacteristic, complemented
328C101#1039511yescharacteristic, direct product factor, Sylow
329C2×#121C22×C10111yescharacteristic
330C2×#120—21no—
331C22×C4⋊C4C22×C10111yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4C22×C10111yescharacteristic
334C2×#106—21no—
335C2×#102—21no—
336C2×C22⋊C8C22×C10111yescharacteristic
337C2×C22⋊C8C22×C10111yescharacteristic
338#397—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#386—21no—
343#380C22×C10111yescharacteristic
344C2×#95—21no—
345C2×#95C22×C10111yescharacteristic
346#340—21no—
347#340—21no—
348#327—22no—
349#323—22no—
350C25D4×C10111yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C10111yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C10111yescharacteristic
358C23×C4C23×C10111yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C10111yescharacteristic
371C2×C4⋊C4D4×C10111yescharacteristic
372C2×C4⋊C4D4×C10111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#106—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C10112yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24SD16×C10112yes—
412C24C2×D4×C10111yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C10111yescharacteristic
454C22×C4C2×D4×C10111yescharacteristic
455C22×C4C2×D4×C10111yescharacteristic
456C22×C4#41×C10111yescharacteristic
457C22×C4#41×C10111yescharacteristic
458C22×C4#41×C10111yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C10111yescharacteristic
521C23#121×C10111yescharacteristic
522C23#123×C10111yescharacteristic
523C23C2×SD16×C10111yescharacteristic
524C23#135×C10111yescharacteristic
525C23AGL(1,ℤ/8)×C10111yescharacteristic
526C23AGL(1,ℤ/8)×C10111yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C10111yescharacteristic
572C2×C4#121×C10111yescharacteristic
573C2×C4#123×C10111yescharacteristic
574C2×C4#124×C10111yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#394×C10111yescharacteristic
608C22#449×C10111yescharacteristic
609C22#450×C10111yescharacteristic
610C22#453×C10111yescharacteristic
611C22#455×C10111yescharacteristic
612C22B(4,𝔽2)×C10111yescharacteristic
613C22#458×C10111yescharacteristic
614C22#465×C10111yescharacteristic
615C22#469×C10111yescharacteristic
616C22#481×C10111yescharacteristic
617C22#482×C10111yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2C101×#160011yescharacteristic
635C2C101×#160111yescharacteristic
636C2C101×#161211yescharacteristic
637C2C101×#161311yescharacteristic
638C2C101×#203411yescharacteristic
639C2C101×#203711yescharacteristic
640C2C101×#204411yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutator, Frattini, cosocleC23×C4C23×C101
prime radicalC101×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1874C2semidirect
3. C101×#1853C2semidirect
4. C2×#327×C101C2semidirect
5. C2×#323×C101C2semidirect
6. C101×#1439C2semidirect
7. C101×#1294C2semidirect
72. C22⋊C8×C101D4semidirect
307. #10395C101direct (N × H)
322. #1874C2×C101semidirect
323. #1853C2×C101semidirect
324. C2×#327C2×C101semidirect
325. C2×#323C2×C101semidirect
326. #1439C2×C101semidirect
327. #1294C2×C101semidirect
328. C101#10395direct (N × H)
393. C22⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#26172
C101×#18742
C101×#18532
C2×#327×C1012
C2×#323×C1012
C101×#14392
C101×#12942
#10395101