Finite Group Databasebeta

← C101×#13045 #38795196

Subgroups — C101×#13045 #38795196

Order 25856.

654 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3025C211yesmaximal, characteristic
2C101×#2977C211yesmaximal, characteristic, complemented
3C101×#2120C211yesmaximal, characteristic, complemented
4C101×#1794C211yesmaximal, characteristic, complemented
5C101×#1791C211yesmaximal, characteristic, complemented
6C101×#1395C211yesmaximal, characteristic, complemented
7C101×#1391C211yesmaximal, characteristic, complemented
8#585×C101C2211yescharacteristic
9#525×C101—21no—
10#525×C101C2211yescharacteristic
11#458×C101—21no—
12#458×C101C412yescomplemented
13B(4,𝔽2)×C101—21no—
14B(4,𝔽2)×C101C412yescomplemented
15#435×C101—21no—
16#435×C101—21no—
17C8×D4×C101—21no—
18C8×D4×C101—21no—
19#433×C101—21no—
20#421×C101—21no—
21#416×C101—21no—
22#413×C101—21no—
23#413×C101C2211yescharacteristic
24#410×C101—21no—
25#410×C101C2211yescharacteristic
26#410×C101C2211yescharacteristic
27#408×C101—21no—
28#408×C101C2211yescharacteristic
29#408×C101C2211yescharacteristic
30C2×C22⋊C8×C101—21no—
31#352×C101—21no—
32AΣL(1,𝔽16)×C101—21no—
332−1+4×C101—21no—
342−1+4×C101—41no—
35H(5,𝔽2)×C101—21no—
36H(5,𝔽2)×C101—21no—
37H(5,𝔽2)×C101—41no—
38H(5,𝔽2)×C101C2×C412yes—
39C2×#41×C101—21no—
40C2×#41×C101—21no—
41C2×#41×C101—21no—
42C2×#41×C101—42no—
43C2×#41×C101C2311yescharacteristic
44C23×C4×C101D411yescharacteristic
45C2×M16×C101—21no—
46C2×M16×C101D411yescharacteristic, complemented
47C2×M16×C101D411yescharacteristic, complemented
48C22×C8×C101—21no—
49C22×C8×C101—21no—
50C22×C8×C101D411yescharacteristic, complemented
51C22×C8×C101D411yescharacteristic, complemented
52#123×C101—22no—
53#123×C101C2×C411yescharacteristic
54#123×C101D411yescharacteristic
55C22⋊Q8×C101—21no—
56C22⋊Q8×C101—41no—
57#121×C101—21no—
58#121×C101—41no—
59#120×C101—22no—
60#120×C101C2×C411yescharacteristic
61#120×C101D411yescharacteristic
62C4×D4×C101—21no—
63C4×D4×C101—21no—
64C4×D4×C101—42no—
65#117×C101—21no—
66#117×C101—21no—
67#117×C101D411yescharacteristic
68C4⋊C8×C101—21no—
69C4⋊C8×C101—21no—
70#104×C101—42no—
71#103×C101—41no—
72#102×C101—41no—
73#101×C101—21no—
74#101×C101—41no—
75#100×C101—21no—
76#100×C101—41no—
77#99×C101—21no—
78#99×C101—22no—
79#99×C101—22no—
80#99×C101—21no—
81#99×C101—21no—
82#99×C101C2×C412yes—
83C22⋊C8×C101—21no—
84C22⋊C8×C101—21no—
85C22⋊C8×C101—21no—
86C22⋊C8×C101—21no—
87C22⋊C8×C101—21no—
88C22⋊C8×C101—21no—
89C22⋊C8×C101—42no—
90#97×C101—21no—
91C4×C8×C101—21no—
92C24×C101C22⋊C411yescharacteristic
93#41×C101—22no—
94#41×C101—22no—
95#41×C101—41no—
96#41×C101—41no—
97#41×C101—42no—
98#41×C101—41no—
99#41×C101—41no—
100#41×C101—41no—
101#41×C101—41no—
102#41×C101—41no—
103#41×C101—42no—
104#41×C101—42no—
105#41×C101—42no—
106#41×C101—41no—
107#41×C101—41no—
108#41×C101—41no—
109C2×Q8×C101—21no—
110C2×Q8×C101—21no—
111C2×Q8×C101—21no—
112C2×Q8×C101—42no—
113C2×Q8×C101#4111yescharacteristic
114C2×D4×C101—21no—
115C2×D4×C101—21no—
116C2×D4×C101—21no—
117C2×D4×C101—22no—
118C2×D4×C101—21no—
119C2×D4×C101—22no—
120C2×D4×C101—21no—
121C2×D4×C101—42no—
122C2×D4×C101—42no—
123C2×D4×C101—42no—
124C2×D4×C101—41no—
125C2×D4×C101—42no—
126C2×D4×C101C22×C411yescharacteristic
127C2×D4×C101C2×D411yescharacteristic
128C2×D4×C101#4111yescharacteristic
129C22×C4×C101—22no—
130C22×C4×C101—22no—
131C22×C4×C101—21no—
132C22×C4×C101—21no—
133C22×C4×C101—41no—
134C22×C4×C101—41no—
135C22×C4×C101—41no—
136C22×C4×C101C22⋊C411yescharacteristic
137C22×C4×C101C2×D411yescharacteristic
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101C2×D411yescharacteristic
140M16×C101—41no—
141M16×C101—41no—
142M16×C101—41no—
143M16×C101—41no—
144C2×C8×C101—21no—
145C2×C8×C101—21no—
146C2×C8×C101—21no—
147C2×C8×C101—21no—
148C2×C8×C101—41no—
149C2×C8×C101—41no—
150C2×C8×C101—41no—
151C2×C8×C101—81no—
152C2×C8×C101—81no—
153C4⋊C4×C101—21no—
154C4⋊C4×C101—21no—
155C4⋊C4×C101—21no—
156C4⋊C4×C101—41no—
157C4⋊C4×C101—42no—
158C4⋊C4×C101—41no—
159C22⋊C4×C101—21no—
160C22⋊C4×C101—21no—
161C22⋊C4×C101—21no—
162C22⋊C4×C101—21no—
163C22⋊C4×C101—22no—
164C22⋊C4×C101—42no—
165C22⋊C4×C101—42no—
166C22⋊C4×C101—41no—
167C22⋊C4×C101C22⋊C411yescharacteristic
168C22⋊C4×C101C22⋊C411yescharacteristic
169C42×C101—21no—
170C42×C101—41no—
171C42×C101—41no—
172C23×C101—21no—
173C23×C101—22no—
174C23×C101—22no—
175C23×C101—41no—
176C23×C101—42no—
177C23×C101—41no—
178C23×C101C2×C22⋊C411yescharacteristic
179C23×C101C4×D411yescharacteristic
180C23×C101#12111yescharacteristic
181Q8×C101—22no—
182Q8×C101—41no—
183Q8×C101—41no—
184Q8×C101—41no—
185Q8×C101—41no—
186D4×C101—22no—
187D4×C101—41no—
188D4×C101—41no—
189D4×C101—41no—
190D4×C101—41no—
191D4×C101—41no—
192D4×C101—42no—
193D4×C101—42no—
194D4×C101—42no—
195D4×C101—42no—
196D4×C101—42no—
197D4×C101—42no—
198D4×C101—41no—
199D4×C101—84no—
200C2×C4×C101—21no—
201C2×C4×C101—21no—
202C2×C4×C101—21no—
203C2×C4×C101—21no—
204C2×C4×C101—21no—
205C2×C4×C101—21no—
206C2×C4×C101—22no—
207C2×C4×C101—22no—
208C2×C4×C101—21no—
209C2×C4×C101—21no—
210C2×C4×C101—21no—
211C2×C4×C101—42no—
212C2×C4×C101—42no—
213C2×C4×C101—42no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—41no—
217C2×C4×C101—42no—
218C2×C4×C101—41no—
219C2×C4×C101—42no—
220C2×C4×C101—81no—
221C2×C4×C101—81no—
222C2×C4×C101C4×D411yescharacteristic
223C2×C4×C101#12011yescharacteristic
224C2×C4×C101#12111yescharacteristic
225C2×C4×C101#12311yescharacteristic
226C8×C101—41no—
227C8×C101—41no—
228C8×C101—41no—
229C8×C101—41no—
230C8×C101—81no—
231C22×C101—22no—
232C22×C101—21no—
233C22×C101—21no—
234C22×C101—21no—
235C22×C101—41no—
236C22×C101—41no—
237C22×C101—41no—
238C22×C101—41no—
239C22×C101—42no—
240C22×C101—41no—
241C22×C101—42no—
242C22×C101—81no—
243C22×C101—82no—
244C22×C101—82no—
245C22×C101—161no—
246C22×C101#38611yescharacteristic
247C4×C101—21no—
248C4×C101—21no—
249C4×C101—21no—
250C4×C101—41no—
251C4×C101—41no—
252C4×C101—42no—
253C4×C101—41no—
254C4×C101—82no—
255C4×C101—161no—
256C4×C101B(4,𝔽2)11yescharacteristic
257C4×C101B(4,𝔽2)11yescharacteristic
258#13045C10111yesmaximal, characteristic, direct product factor, Sylow
259C2×C101—21no—
260C2×C101—41no—
261C2×C101—41no—
262C2×C101—42no—
263C2×C101—41no—
264C2×C101—82no—
265C2×C101#188911yescharacteristic
266#3025C2×C10111yescharacteristic
267#2977C2×C10111yescharacteristic, complemented
268#2120C2×C10111yescharacteristic, complemented
269#1794C2×C10111yescharacteristic, complemented
270#1791C2×C10111yescharacteristic, complemented
271#1395C2×C10111yescharacteristic, complemented
272#1391C2×C10111yescharacteristic, complemented
273C101#1304511yescharacteristic, direct product factor, Sylow
274#585C22×C10111yescharacteristic
275#525—21no—
276#525C22×C10111yescharacteristic
277#458—21no—
278#458C4×C10112yescomplemented
279B(4,𝔽2)—21no—
280B(4,𝔽2)C4×C10112yescomplemented
281#435—21no—
282#435—21no—
283C8×D4—21no—
284C8×D4—21no—
285#433—21no—
286#421—21no—
287#416—21no—
288#413—21no—
289#413C22×C10111yescharacteristic
290#410—21no—
291#410C22×C10111yescharacteristic
292#410C22×C10111yescharacteristic
293#408—21no—
294#408C22×C10111yescharacteristic
295#408C22×C10111yescharacteristic
296C2×C22⋊C8—21no—
297#352—21no—
298AΣL(1,𝔽16)—21no—
2992−1+4—21no—
3002−1+4—41no—
301H(5,𝔽2)—21no—
302H(5,𝔽2)—21no—
303H(5,𝔽2)—41no—
304H(5,𝔽2)C2×C4×C10112yes—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—21no—
308C2×#41—42no—
309C2×#41C23×C10111yescharacteristic
310C23×C4D4×C10111yescharacteristic
311C2×M16—21no—
312C2×M16D4×C10111yescharacteristic, complemented
313C2×M16D4×C10111yescharacteristic, complemented
314C22×C8—21no—
315C22×C8—21no—
316C22×C8D4×C10111yescharacteristic, complemented
317C22×C8D4×C10111yescharacteristic, complemented
318#123—22no—
319#123C2×C4×C10111yescharacteristic
320#123D4×C10111yescharacteristic
321C22⋊Q8—21no—
322C22⋊Q8—41no—
323#121—21no—
324#121—41no—
325#120—22no—
326#120C2×C4×C10111yescharacteristic
327#120D4×C10111yescharacteristic
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—42no—
331#117—21no—
332#117—21no—
333#117D4×C10111yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336#104—42no—
337#103—41no—
338#102—41no—
339#101—21no—
340#101—41no—
341#100—21no—
342#100—41no—
343#99—21no—
344#99—22no—
345#99—22no—
346#99—21no—
347#99—21no—
348#99C2×C4×C10112yes—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—42no—
356#97—21no—
357C4×C8—21no—
358C24C22⋊C4×C10111yescharacteristic
359#41—22no—
360#41—22no—
361#41—41no—
362#41—41no—
363#41—42no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—41no—
373#41—41no—
374#41—41no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8#41×C10111yescharacteristic
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4C22×C4×C10111yescharacteristic
393C2×D4C2×D4×C10111yescharacteristic
394C2×D4#41×C10111yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4C22⋊C4×C10111yescharacteristic
403C22×C4C2×D4×C10111yescharacteristic
404C22×C4C2×D4×C10111yescharacteristic
405C22×C4C2×D4×C10111yescharacteristic
406M16—41no—
407M16—41no—
408M16—41no—
409M16—41no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—81no—
418C2×C8—81no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—41no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—41no—
433C22⋊C4C22⋊C4×C10111yescharacteristic
434C22⋊C4C22⋊C4×C10111yescharacteristic
435C42—21no—
436C42—41no—
437C42—41no—
438C23—21no—
439C23—22no—
440C23—22no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23C2×C22⋊C4×C10111yescharacteristic
445C23C4×D4×C10111yescharacteristic
446C23#121×C10111yescharacteristic
447Q8—22no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—41no—
465D4—84no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C4×D4×C10111yescharacteristic
489C2×C4#120×C10111yescharacteristic
490C2×C4#121×C10111yescharacteristic
491C2×C4#123×C10111yescharacteristic
492C8—41no—
493C8—41no—
494C8—41no—
495C8—41no—
496C8—81no—
497C22—22no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—41no—
507C22—42no—
508C22—81no—
509C22—82no—
510C22—82no—
511C22—161no—
512C22#386×C10111yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4—161no—
522C4B(4,𝔽2)×C10111yescharacteristic
523C4B(4,𝔽2)×C10111yescharacteristic
524C2—21no—
525C2—41no—
526C2—41no—
527C2—42no—
528C2—41no—
529C2—82no—
530C2C101×#188911yescharacteristic
subgroupG/H
centerC4×C101B(4,𝔽2)
commutatorC2×D4C22×C4×C101
Frattini, cosocleC2×#41C23×C101
socleC2×C101#1889
prime radicalC101×#3025C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C101 ◁ C2×C4×C101 ◁ C2×#41×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2977C2semidirect
3. C101×#2120C2semidirect
4. C101×#1794C2semidirect
5. C101×#1791C2semidirect
6. C101×#1395C2semidirect
7. C101×#1391C2semidirect
12. #458×C101C4semidirect
14. B(4,𝔽2)×C101C4semidirect
46. C2×M16×C101D4semidirect
47. C2×M16×C101D4semidirect
50. C22×C8×C101D4semidirect
51. C22×C8×C101D4semidirect
258. #13045C101direct (N × H)
267. #2977C2×C101semidirect
268. #2120C2×C101semidirect
269. #1794C2×C101semidirect
270. #1791C2×C101semidirect
271. #1395C2×C101semidirect
272. #1391C2×C101semidirect
273. C101#13045direct (N × H)
278. #458C4×C101semidirect
280. B(4,𝔽2)C4×C101semidirect
312. C2×M16D4×C101semidirect
313. C2×M16D4×C101semidirect
316. C22×C8D4×C101semidirect
317. C22×C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30252
C101×#29772
C101×#21202
C101×#17942
C101×#17912
C101×#13952
C101×#13912
#13045101