Finite Group Databasebeta

← C101×#10972 #38793123

Subgroups — C101×#10972 #38793123

Order 25856.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C101C211yesmaximal, characteristic
2C22×#99×C101C212yesmaximal, complemented
3C22×#99×C101C211yesmaximal, characteristic, complemented
4C101×#2308C211yesmaximal, characteristic, complemented
5C2×#342×C101C212yesmaximal, complemented
6C23×D4×C101C2211yescharacteristic
7C23×D4×C101C2211yescharacteristic
8#534×C101—24no—
9#534×C101—24no—
10C2×#123×C101—21no—
11C2×#123×C101C412yescomplemented
12C2×#121×C101—22no—
13C2×#120×C101—21no—
14C2×#120×C101C412yescomplemented
15C22×C22⋊C4×C101C2212yes—
16C22×C22⋊C4×C101C2212yes—
17C22×C22⋊C4×C101C2211yescharacteristic
18C2×#99×C101—22no—
19C2×#99×C101—24no—
20C2×#99×C101—24no—
21C2×#99×C101—24no—
22C2×#99×C101—24no—
23#386×C101—24no—
24#381×C101—21no—
25#379×C101—21no—
26#342×C101—24no—
27C25×C101C2×C411yescharacteristic
28C25×C101D411yescharacteristic
29C25×C101C2311yescharacteristic
30C22×D4×C101—22no—
31C22×D4×C101—22no—
32C22×D4×C101—22no—
33C22×D4×C101—21no—
34C22×D4×C101—21no—
35C22×D4×C101—22no—
36C22×D4×C101—22no—
37C22×D4×C101—22no—
38C22×D4×C101—22no—
39C22×D4×C101—22no—
40C22×D4×C101—22no—
41C22×D4×C101—22no—
42C22×D4×C101—22no—
43C22×D4×C101—22no—
44C22×D4×C101C2×C412yes—
45C22×D4×C101D412yes—
46C22×D4×C101D414yes—
47C23×C4×C101—21no—
48C23×C4×C101—22no—
49C23×C4×C101—22no—
50C23×C4×C101C2×C411yescharacteristic
51C23×C4×C101D411yescharacteristic
52#123×C101—28no—
53#123×C101—24no—
54#123×C101—24no—
55#121×C101—216no—
56#120×C101—28no—
57#120×C101—24no—
58#120×C101—24no—
59C2×C4⋊C4×C101—22no—
60C2×C22⋊C4×C101—22no—
61C2×C22⋊C4×C101—21no—
62C2×C22⋊C4×C101—22no—
63C2×C22⋊C4×C101—22no—
64C2×C22⋊C4×C101—22no—
65C2×C22⋊C4×C101—22no—
66C2×C22⋊C4×C101—22no—
67C2×C22⋊C4×C101—22no—
68C2×C22⋊C4×C101—22no—
69C2×C22⋊C4×C101—22no—
70C2×C22⋊C4×C101—22no—
71C2×C22⋊C4×C101—22no—
72C2×C22⋊C4×C101—22no—
73C2×C22⋊C4×C101—22no—
74C2×C22⋊C4×C101—24no—
75C2×C22⋊C4×C101C2×C412yes—
76C2×C22⋊C4×C101D414yes—
77C2×C22⋊C4×C101D414yescomplemented
78C2×C22⋊C4×C101D414yescomplemented
79#99×C101—28no—
80#99×C101—216no—
81#95×C101—24no—
82C24×C101—21no—
83C24×C101—21no—
84C24×C101—21no—
85C24×C101—22no—
86C24×C101—22no—
87C24×C101—22no—
88C24×C101—22no—
89C24×C101—21no—
90C24×C101—82no—
91C24×C101—82no—
92C24×C101—82no—
93C24×C101C22⋊C412yes—
94C24×C101C22⋊C412yescomplemented
95C24×C101C22×C411yescharacteristic
96C24×C101C2×D411yescharacteristic
97C24×C101C2×D411yescharacteristic
98C24×C101C2×D412yes—
99C24×C101C2×D412yes—
100C24×C101C2×D412yes—
101C24×C101C2×D412yes—
102C24×C101#4112yes—
103C24×C101#4112yes—
104C2×D4×C101—22no—
105C2×D4×C101—22no—
106C2×D4×C101—24no—
107C2×D4×C101—24no—
108C2×D4×C101—22no—
109C2×D4×C101—24no—
110C2×D4×C101—24no—
111C2×D4×C101—24no—
112C2×D4×C101—24no—
113C2×D4×C101—24no—
114C2×D4×C101—24no—
115C2×D4×C101—24no—
116C2×D4×C101—22no—
117C2×D4×C101—24no—
118C2×D4×C101—28no—
119C2×D4×C101—41no—
120C2×D4×C101—41no—
121C2×D4×C101—42no—
122C2×D4×C101—42no—
123C2×D4×C101—42no—
124C2×D4×C101—42no—
125C2×D4×C101—42no—
126C2×D4×C101—42no—
127C2×D4×C101—42no—
128C2×D4×C101—42no—
129C2×D4×C101—42no—
130C2×D4×C101—41no—
131C2×D4×C101—41no—
132C2×D4×C101—42no—
133C2×D4×C101—42no—
134C2×D4×C101—42no—
135C2×D4×C101—42no—
136C2×D4×C101—42no—
137C2×D4×C101—84no—
138C22×C4×C101—22no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—22no—
142C22×C4×C101—22no—
143C22×C4×C101—21no—
144C22×C4×C101—22no—
145C22×C4×C101—22no—
146C22×C4×C101—21no—
147C22×C4×C101—24no—
148C22×C4×C101—24no—
149C22×C4×C101—24no—
150C22×C4×C101—42no—
151C22×C4×C101—42no—
152C22×C4×C101—42no—
153C22×C4×C101—42no—
154C22×C4×C101—82no—
155C22×C4×C101—84no—
156C22×C4×C101—84no—
157C22×C4×C101C22⋊C412yes—
158C22×C4×C101C22⋊C412yescomplemented
159C4⋊C4×C101—28no—
160C22⋊C4×C101—28no—
161C22⋊C4×C101—28no—
162C22⋊C4×C101—22no—
163C22⋊C4×C101—24no—
164C22⋊C4×C101—24no—
165C22⋊C4×C101—24no—
166C22⋊C4×C101—24no—
167C22⋊C4×C101—24no—
168C22⋊C4×C101—42no—
169C22⋊C4×C101—42no—
170C22⋊C4×C101—42no—
171C22⋊C4×C101—42no—
172C22⋊C4×C101—84no—
173C22⋊C4×C101C22⋊C414yescomplemented
174C23×C101—22no—
175C23×C101—22no—
176C23×C101—22no—
177C23×C101—22no—
178C23×C101—24no—
179C23×C101—44no—
180C23×C101—42no—
181C23×C101—44no—
182C23×C101—42no—
183C23×C101—42no—
184C23×C101—44no—
185C23×C101—44no—
186C23×C101—44no—
187C23×C101—41no—
188C23×C101—41no—
189C23×C101—42no—
190C23×C101—42no—
191C23×C101—42no—
192C23×C101—82no—
193C23×C101—84no—
194C23×C101—82no—
195C23×C101—82no—
196C23×C101—82no—
197C23×C101—82no—
198C23×C101—82no—
199C23×C101—82no—
200C23×C101—84no—
201C23×C101—84no—
202C23×C101—84no—
203C23×C101C2×C22⋊C411yescharacteristic
204C23×C101C2×C22⋊C411yescharacteristic
205C23×C101C2×C22⋊C411yescharacteristic
206C23×C101C4×D412yes—
207C23×C101C4×D412yes—
208C23×C101#12011yescharacteristic
209C23×C101#12012yes—
210C23×C101#12012yes—
211C23×C101#12011yescharacteristic
212C23×C101#12012yes—
213C23×C101#12112yes—
214C23×C101#12112yes—
215C23×C101#12112yes—
216C23×C101#12112yes—
217C23×C101#12112yes—
218C23×C101#12112yes—
219C23×C101#12311yescharacteristic
220C23×C101#12311yescharacteristic
221C23×C101#12312yes—
222C23×C101#12412yes—
223C23×C101#12712yes—
224D4×C101—44no—
225D4×C101—44no—
226D4×C101—44no—
227D4×C101—44no—
228D4×C101—44no—
229D4×C101—44no—
230D4×C101—44no—
231D4×C101—44no—
232D4×C101—88no—
233C2×C4×C101—24no—
234C2×C4×C101—22no—
235C2×C4×C101—22no—
236C2×C4×C101—22no—
237C2×C4×C101—24no—
238C2×C4×C101—22no—
239C2×C4×C101—44no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—42no—
243C2×C4×C101—42no—
244C2×C4×C101—42no—
245C2×C4×C101—48no—
246C2×C4×C101—44no—
247C2×C4×C101—44no—
248C2×C4×C101—84no—
249C2×C4×C101—84no—
250C2×C4×C101—84no—
251C2×C4×C101—84no—
252C2×C4×C101—84no—
253C2×C4×C101—84no—
254C22×C101—22no—
255C22×C101—22no—
256C22×C101—24no—
257C22×C101—24no—
258C22×C101—22no—
259C22×C101—42no—
260C22×C101—42no—
261C22×C101—42no—
262C22×C101—42no—
263C22×C101—42no—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—42no—
267C22×C101—42no—
268C22×C101—42no—
269C22×C101—42no—
270C22×C101—41no—
271C22×C101—42no—
272C22×C101—41no—
273C22×C101—42no—
274C22×C101—42no—
275C22×C101—44no—
276C22×C101—44no—
277C22×C101—44no—
278C22×C101—42no—
279C22×C101—42no—
280C22×C101—82no—
281C22×C101—84no—
282C22×C101—84no—
283C22×C101—82no—
284C22×C101—84no—
285C22×C101—84no—
286C22×C101—82no—
287C22×C101#37911yescharacteristic
288C22×C101#38611yescharacteristic
289C22×C101#38612yes—
290C22×C101#38611yescharacteristic
291C22×C101#39012yes—
292C22×C101#39212yes—
293C22×C101#39212yes—
294C22×C101#39412yes—
295C22×C101#39412yes—
296C4×C101—44no—
297C4×C101—42no—
298C4×C101—42no—
299C4×C101—84no—
300C4×C101—84no—
301#10972C10111yesmaximal, characteristic, direct product factor, Sylow
302C2×C101—21no—
303C2×C101—22no—
304C2×C101—22no—
305C2×C101—21no—
306C2×C101—22no—
307C2×C101—22no—
308C2×C101—22no—
309C2×C101—22no—
310C2×C101—82no—
311C2×C101—82no—
312C2×C101#143811yescharacteristic
313C2×C101#191312yes—
314C2×#534C2×C10111yescharacteristic
315C22×#99C2×C10112yescomplemented
316C22×#99C2×C10111yescharacteristic, complemented
317#2308C2×C10111yescharacteristic, complemented
318C2×#342C2×C10112yescomplemented
319C101#1097211yescharacteristic, direct product factor, Sylow
320C23×D4C22×C10111yescharacteristic
321C23×D4C22×C10111yescharacteristic
322#534—24no—
323#534—24no—
324C2×#123—21no—
325C2×#123C4×C10112yescomplemented
326C2×#121—22no—
327C2×#120—21no—
328C2×#120C4×C10112yescomplemented
329C22×C22⋊C4C22×C10112yes—
330C22×C22⋊C4C22×C10112yes—
331C22×C22⋊C4C22×C10111yescharacteristic
332C2×#99—22no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336C2×#99—24no—
337#386—24no—
338#381—21no—
339#379—21no—
340#342—24no—
341C25C2×C4×C10111yescharacteristic
342C25D4×C10111yescharacteristic
343C25C23×C10111yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C10112yes—
359C22×D4D4×C10112yes—
360C22×D4D4×C10114yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C10111yescharacteristic
365C23×C4D4×C10111yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C10112yes—
390C2×C22⋊C4D4×C10114yes—
391C2×C22⋊C4D4×C10114yescomplemented
392C2×C22⋊C4D4×C10114yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C10112yes—
408C24C22⋊C4×C10112yescomplemented
409C24C22×C4×C10111yescharacteristic
410C24C2×D4×C10111yescharacteristic
411C24C2×D4×C10111yescharacteristic
412C24C2×D4×C10112yes—
413C24C2×D4×C10112yes—
414C24C2×D4×C10112yes—
415C24C2×D4×C10112yes—
416C24#41×C10112yes—
417C24#41×C10112yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C10112yes—
472C22×C4C22⋊C4×C10112yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C10114yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C10111yescharacteristic
518C23C2×C22⋊C4×C10111yescharacteristic
519C23C2×C22⋊C4×C10111yescharacteristic
520C23C4×D4×C10112yes—
521C23C4×D4×C10112yes—
522C23#120×C10111yescharacteristic
523C23#120×C10112yes—
524C23#120×C10112yes—
525C23#120×C10111yescharacteristic
526C23#120×C10112yes—
527C23#121×C10112yes—
528C23#121×C10112yes—
529C23#121×C10112yes—
530C23#121×C10112yes—
531C23#121×C10112yes—
532C23#121×C10112yes—
533C23#123×C10111yescharacteristic
534C23#123×C10111yescharacteristic
535C23#123×C10112yes—
536C23#124×C10112yes—
537C23#127×C10112yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22#379×C10111yescharacteristic
602C22#386×C10111yescharacteristic
603C22#386×C10112yes—
604C22#386×C10111yescharacteristic
605C22#390×C10112yes—
606C22#392×C10112yes—
607C22#392×C10112yes—
608C22#394×C10112yes—
609C22#394×C10112yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2C101×#143811yescharacteristic
626C2C101×#191312yes—
subgroupG/H
center, socleC22×C101#386
commutatorC24C22×C4×C101
Frattini, cosocleC25C23×C101
prime radicalC2×#534×C101C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C101C2semidirect
3. C22×#99×C101C2semidirect
4. C101×#2308C2semidirect
5. C2×#342×C101C2semidirect
11. C2×#123×C101C4semidirect
14. C2×#120×C101C4semidirect
77. C2×C22⋊C4×C101D4semidirect
78. C2×C22⋊C4×C101D4semidirect
94. C24×C101C22⋊C4semidirect
158. C22×C4×C101C22⋊C4semidirect
173. C22⋊C4×C101C22⋊C4semidirect
301. #10972C101direct (N × H)
315. C22×#99C2×C101semidirect
316. C22×#99C2×C101semidirect
317. #2308C2×C101semidirect
318. C2×#342C2×C101semidirect
319. C101#10972direct (N × H)
325. C2×#123C4×C101semidirect
328. C2×#120C4×C101semidirect
391. C2×C22⋊C4D4×C101semidirect
392. C2×C22⋊C4D4×C101semidirect
408. C24C22⋊C4×C101semidirect
472. C22×C4C22⋊C4×C101semidirect
487. C22⋊C4C22⋊C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1012
C22×#99×C1012
C101×#23082
C2×#342×C1012
#10972101