Finite Group Databasebeta

← C101×#8534 #38790685

Subgroups — C101×#8534 #38790685

Order 25856.

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic
2C101×#1898C214yesmaximal, complemented
3C101×#1781C211yesmaximal, characteristic, complemented
4C101×#1438C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C101C411yescharacteristic, complemented
6C23×D4×C101C2211yescharacteristic
7#546×C101—24no—
8D42×C101—24no—
9#535×C101—21no—
10#534×C101—21no—
11#534×C101C412yescomplemented
12#525×C101—21no—
13C2×#120×C101—21no—
14C2×#120×C101C2212yes—
15#518×C101C411yescharacteristic, complemented
16C22×C22⋊C4×C101—21no—
17C22×C22⋊C4×C101C2212yescomplemented
18C2×#99×C101—24no—
19C2×#99×C101—21no—
20C2×#99×C101—21no—
21#379×C101C2212yescomplemented
22C2×#95×C101—21no—
23#342×C101—24no—
24C25×C101D411yescharacteristic
25C25×C101C2311yescharacteristic
26H(5,𝔽2)×C101—42no—
27H(5,𝔽2)×C101—42no—
28C2×#41×C101—21no—
29C2×#41×C101—22no—
30C22×D4×C101—21no—
31C22×D4×C101—22no—
32C22×D4×C101—24no—
33C22×D4×C101—22no—
34C22×D4×C101—42no—
35C22×D4×C101—42no—
36C22×D4×C101C2×C411yescharacteristic
37C22×D4×C101C2×C411yescharacteristic
38C22×D4×C101C2×C412yes—
39C22×D4×C101D411yescharacteristic
40C22×D4×C101D411yescharacteristic
41C22×D4×C101D414yes—
42C23×C4×C101—22no—
43C23×C4×C101D411yescharacteristic
44#127×C101—22no—
45#124×C101—22no—
46#123×C101—22no—
47#123×C101—22no—
48#123×C101—22no—
49C22⋊Q8×C101—22no—
50#121×C101—22no—
51#121×C101—24no—
52#121×C101—24no—
53#121×C101—24no—
54#120×C101—24no—
55#120×C101—22no—
56#120×C101—22no—
57#120×C101—22no—
58#120×C101—22no—
59#120×C101—22no—
60#120×C101—24no—
61C4×D4×C101—24no—
62C4×D4×C101—24no—
63#117×C101—21no—
64C2×C22⋊C4×C101—22no—
65C2×C22⋊C4×C101—21no—
66C2×C22⋊C4×C101—24no—
67C2×C22⋊C4×C101—22no—
68C2×C22⋊C4×C101—24no—
69C2×C22⋊C4×C101—44no—
70C2×C22⋊C4×C101—44no—
71C2×C22⋊C4×C101—42no—
72C2×C22⋊C4×C101C2×C412yes—
73C2×C22⋊C4×C101D414yes—
74#99×C101—48no—
75#99×C101—42no—
76#99×C101—42no—
77#95×C101—42no—
78C24×C101—21no—
79C24×C101—22no—
80C24×C101—22no—
81C24×C101—42no—
82C24×C101—41no—
83C24×C101—41no—
84C24×C101—41no—
85C24×C101—42no—
86C24×C101—42no—
87C24×C101—42no—
88C24×C101C22⋊C411yescharacteristic
89C24×C101C22⋊C411yescharacteristic
90C24×C101C22⋊C412yescomplemented
91C24×C101C22×C411yescharacteristic
92C24×C101C2×D411yescharacteristic
93C24×C101C2×D414yes—
94C24×C101C2×D411yescharacteristic
95#41×C101—42no—
96#41×C101—48no—
97#41×C101—42no—
98C2×Q8×C101—21no—
99C2×D4×C101—22no—
100C2×D4×C101—22no—
101C2×D4×C101—22no—
102C2×D4×C101—21no—
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101—22no—
106C2×D4×C101—22no—
107C2×D4×C101—24no—
108C2×D4×C101—22no—
109C2×D4×C101—22no—
110C2×D4×C101—24no—
111C2×D4×C101—24no—
112C2×D4×C101—22no—
113C2×D4×C101—22no—
114C2×D4×C101—41no—
115C2×D4×C101—41no—
116C2×D4×C101—41no—
117C2×D4×C101—41no—
118C2×D4×C101—416no—
119C2×D4×C101—48no—
120C2×D4×C101—42no—
121C2×D4×C101—42no—
122C2×D4×C101—42no—
123C2×D4×C101—42no—
124C2×D4×C101—44no—
125C2×D4×C101—44no—
126C2×D4×C101—82no—
127C2×D4×C101—82no—
128C22×C4×C101—21no—
129C22×C4×C101—22no—
130C22×C4×C101—22no—
131C22×C4×C101—22no—
132C22×C4×C101—22no—
133C22×C4×C101—24no—
134C22×C4×C101—41no—
135C22×C4×C101—42no—
136C22×C4×C101—42no—
137C22×C4×C101—42no—
138C22×C4×C101—42no—
139C22×C4×C101—42no—
140C22×C4×C101—42no—
141C22×C4×C101—42no—
142C22×C4×C101C22⋊C411yescharacteristic
143C22×C4×C101C22⋊C411yescharacteristic
144C22×C4×C101C22⋊C414yescomplemented
145C22×C4×C101C22⋊C412yescomplemented
146C4⋊C4×C101—22no—
147C4⋊C4×C101—24no—
148C22⋊C4×C101—22no—
149C22⋊C4×C101—24no—
150C22⋊C4×C101—24no—
151C22⋊C4×C101—22no—
152C22⋊C4×C101—22no—
153C22⋊C4×C101—24no—
154C22⋊C4×C101—24no—
155C22⋊C4×C101—28no—
156C22⋊C4×C101—44no—
157C22⋊C4×C101—48no—
158C22⋊C4×C101—42no—
159C22⋊C4×C101—42no—
160C22⋊C4×C101—44no—
161C22⋊C4×C101—44no—
162C42×C101—22no—
163C23×C101—21no—
164C23×C101—21no—
165C23×C101—22no—
166C23×C101—22no—
167C23×C101—21no—
168C23×C101—21no—
169C23×C101—21no—
170C23×C101—21no—
171C23×C101—21no—
172C23×C101—21no—
173C23×C101—24no—
174C23×C101—24no—
175C23×C101—21no—
176C23×C101—22no—
177C23×C101—21no—
178C23×C101—21no—
179C23×C101—44no—
180C23×C101—42no—
181C23×C101—44no—
182C23×C101—42no—
183C23×C101—44no—
184C23×C101—42no—
185C23×C101—42no—
186C23×C101—42no—
187C23×C101—44no—
188C23×C101—42no—
189C23×C101—42no—
190C23×C101—42no—
191C23×C101—44no—
192C23×C101—42no—
193C23×C101—42no—
194C23×C101—82no—
195C23×C101—81no—
196C23×C101—82no—
197C23×C101—82no—
198C23×C101—81no—
199C23×C101—81no—
200C23×C101—82no—
201C23×C101—81no—
202C23×C101—81no—
203C23×C101—81no—
204C23×C101—82no—
205C23×C101#9912yescomplemented
206C23×C101C2×C22⋊C412yes—
207C23×C101C2×C22⋊C411yescharacteristic
208C23×C101#12012yes—
209C23×C101#12012yes—
210Q8×C101—42no—
211D4×C101—28no—
212D4×C101—44no—
213D4×C101—42no—
214D4×C101—44no—
215D4×C101—44no—
216D4×C101—44no—
217D4×C101—44no—
218D4×C101—42no—
219D4×C101—42no—
220D4×C101—44no—
221D4×C101—44no—
222D4×C101—84no—
223D4×C101—84no—
224C2×C4×C101—21no—
225C2×C4×C101—21no—
226C2×C4×C101—24no—
227C2×C4×C101—22no—
228C2×C4×C101—21no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—44no—
232C2×C4×C101—44no—
233C2×C4×C101—42no—
234C2×C4×C101—44no—
235C2×C4×C101—42no—
236C2×C4×C101—44no—
237C2×C4×C101—44no—
238C2×C4×C101—44no—
239C2×C4×C101—82no—
240C2×C4×C101—82no—
241C2×C4×C101—82no—
242C2×C4×C101—82no—
243C2×C4×C101—82no—
244C2×C4×C101—82no—
245C2×C4×C101—84no—
246C2×C4×C101#9912yescomplemented
247C22×C101—21no—
248C22×C101—22no—
249C22×C101—21no—
250C22×C101—22no—
251C22×C101—21no—
252C22×C101—21no—
253C22×C101—22no—
254C22×C101—22no—
255C22×C101—22no—
256C22×C101—22no—
257C22×C101—22no—
258C22×C101—22no—
259C22×C101—24no—
260C22×C101—24no—
261C22×C101—42no—
262C22×C101—42no—
263C22×C101—42no—
264C22×C101—42no—
265C22×C101—41no—
266C22×C101—44no—
267C22×C101—42no—
268C22×C101—84no—
269C22×C101—81no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101—81no—
274C22×C101—84no—
275C22×C101—84no—
276C22×C101—84no—
277C22×C101—81no—
278C22×C101—162no—
279C22×C101—162no—
280C22×C101#37911yescharacteristic
281C22×C101C2×#9911yescharacteristic
282C22×C101C2×#9911yescharacteristic
283C22×C101B(4,𝔽2)12yes—
284C22×C101#45812yes—
285C4×C101—22no—
286C4×C101—41no—
287C4×C101—42no—
288C4×C101—44no—
289C4×C101—84no—
290C4×C101—162no—
291#8534C10111yesmaximal, characteristic, direct product factor, Sylow
292C2×C101—22no—
293C2×C101—21no—
294C2×C101—21no—
295C2×C101—22no—
296C2×C101—42no—
297C2×C101—42no—
298C2×C101—42no—
299C2×C101—81no—
300C2×C101—82no—
301C2×C101#178111yescharacteristic
302C2×C101#179012yes—
303#3484C2×C10111yescharacteristic
304#1898C2×C10114yescomplemented
305#1781C2×C10111yescharacteristic, complemented
306#1438C2×C10111yescharacteristic, complemented
307C101#853411yescharacteristic, direct product factor, Sylow
308C2×H(5,𝔽2)C4×C10111yescharacteristic, complemented
309C23×D4C22×C10111yescharacteristic
310#546—24no—
311D42—24no—
312#535—21no—
313#534—21no—
314#534C4×C10112yescomplemented
315#525—21no—
316C2×#120—21no—
317C2×#120C22×C10112yes—
318#518C4×C10111yescharacteristic, complemented
319C22×C22⋊C4—21no—
320C22×C22⋊C4C22×C10112yescomplemented
321C2×#99—24no—
322C2×#99—21no—
323C2×#99—21no—
324#379C22×C10112yescomplemented
325C2×#95—21no—
326#342—24no—
327C25D4×C10111yescharacteristic
328C25C23×C10111yescharacteristic
329H(5,𝔽2)—42no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×C4×C10111yescharacteristic
340C22×D4C2×C4×C10111yescharacteristic
341C22×D4C2×C4×C10112yes—
342C22×D4D4×C10111yescharacteristic
343C22×D4D4×C10111yescharacteristic
344C22×D4D4×C10114yes—
345C23×C4—22no—
346C23×C4D4×C10111yescharacteristic
347#127—22no—
348#124—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352C22⋊Q8—22no—
353#121—22no—
354#121—24no—
355#121—24no—
356#121—24no—
357#120—24no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—22no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C2×C4×C10112yes—
376C2×C22⋊C4D4×C10114yes—
377#99—48no—
378#99—42no—
379#99—42no—
380#95—42no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊C4×C10111yescharacteristic
392C24C22⋊C4×C10111yescharacteristic
393C24C22⋊C4×C10112yescomplemented
394C24C22×C4×C10111yescharacteristic
395C24C2×D4×C10111yescharacteristic
396C24C2×D4×C10114yes—
397C24C2×D4×C10111yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C22⋊C4×C10111yescharacteristic
446C22×C4C22⋊C4×C10111yescharacteristic
447C22×C4C22⋊C4×C10114yescomplemented
448C22×C4C22⋊C4×C10112yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—28no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#99×C10112yescomplemented
509C23C2×C22⋊C4×C10112yes—
510C23C2×C22⋊C4×C10111yescharacteristic
511C23#120×C10112yes—
512C23#120×C10112yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—84no—
549C2×C4#99×C10112yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22#379×C10111yescharacteristic
584C22C2×#99×C10111yescharacteristic
585C22C2×#99×C10111yescharacteristic
586C22B(4,𝔽2)×C10112yes—
587C22#458×C10112yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—84no—
593C4—162no—
594C2—22no—
595C2—21no—
596C2—21no—
597C2—22no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2C101×#178111yescharacteristic
604C2C101×#179012yes—
subgroupG/H
center, socleC22×C101#379
commutatorC24C22×C4×C101
Frattini, cosocleC25C23×C101
prime radicalC101×#3484C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1898C2semidirect
3. C101×#1781C2semidirect
4. C101×#1438C2semidirect
5. C2×H(5,𝔽2)×C101C4semidirect
11. #534×C101C4semidirect
15. #518×C101C4semidirect
17. C22×C22⋊C4×C101C22semidirect
21. #379×C101C22semidirect
90. C24×C101C22⋊C4semidirect
144. C22×C4×C101C22⋊C4semidirect
145. C22×C4×C101C22⋊C4semidirect
205. C23×C101#99semidirect
246. C2×C4×C101#99semidirect
291. #8534C101direct (N × H)
304. #1898C2×C101semidirect
305. #1781C2×C101semidirect
306. #1438C2×C101semidirect
307. C101#8534direct (N × H)
308. C2×H(5,𝔽2)C4×C101semidirect
314. #534C4×C101semidirect
318. #518C4×C101semidirect
320. C22×C22⋊C4C22×C101semidirect
324. #379C22×C101semidirect
393. C24C22⋊C4×C101semidirect
447. C22×C4C22⋊C4×C101semidirect
448. C22×C4C22⋊C4×C101semidirect
508. C23#99×C101semidirect
549. C2×C4#99×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C101×#18982
C101×#17812
C101×#14382
#8534101