Finite Group Databasebeta

← C101×#18406 #38800557

Subgroups — C101×#18406 #38800557

Order 25856.

998 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3506C211yesmaximal, characteristic
2C101×#3209C211yesmaximal, characteristic, complemented
3C101×#3206C211yesmaximal, characteristic, complemented
4C101×#2563C211yesmaximal, characteristic, complemented
5C101×#1606C218yesmaximal, complemented
6C101×#1503C211yesmaximal, characteristic, complemented
7C101×#1502C211yesmaximal, characteristic, complemented
8C101×#1460C211yesmaximal, characteristic, complemented
9#559×C101—22no—
10#556×C101—21no—
11#555×C101—21no—
12#553×C101—22no—
13#550×C101—21no—
14#547×C101—21no—
15#538×C101C2214yes—
16#535×C101—21no—
17#533×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19C2×C4⋊Q8×C101C2211yescharacteristic
20#525×C101—22no—
21#520×C101—21no—
22C2×C4×D4×C101C2211yescharacteristic
23#494×C101—21no—
24#492×C101—21no—
25#487×C101—21no—
26#487×C101—21no—
27#462×C101—22no—
28#461×C101—22no—
29#451×C101C2214yes—
30#448×C101C2214yes—
31#431×C101C2211yescharacteristic
32#431×C101C2211yescharacteristic
33#393×C101C2214yes—
34#390×C101—21no—
35#382×C101—21no—
36#380×C101—22no—
37C4×C4⋊C4×C101C2211yescharacteristic
38#328×C101C2214yes—
39#327×C101C2214yes—
40#323×C101C2214yes—
41C2×#41×C101—22no—
42C2×#41×C101—21no—
43C22×Q8×C101C2312yes—
44C22×D4×C101D411yescharacteristic
45C23×C4×C101D412yes—
46C2×Q16×C101—24no—
47C2×SD16×C101—24no—
48C4⋊Q8×C101—21no—
49C4⋊Q8×C101—21no—
50C4⋊Q8×C101—21no—
51C4⋊Q8×C101—21no—
52C4⋊Q8×C101D411yescharacteristic
53C4⋊Q8×C101D411yescharacteristic
54C4⋊Q8×C101D411yescharacteristic
55#127×C101—22no—
56#127×C101D411yescharacteristic
57#126×C101—24no—
58#125×C101—21no—
59#124×C101—22no—
60#124×C101—24no—
61#124×C101—21no—
62#123×C101—24no—
63#123×C101—24no—
64C22⋊Q8×C101—22no—
65C22⋊Q8×C101—21no—
66C22⋊Q8×C101C2312yes—
67#121×C101—22no—
68#121×C101—22no—
69#121×C101—22no—
70#121×C101—24no—
71#121×C101—21no—
72#121×C101C2312yes—
73#120×C101—24no—
74C4×Q8×C101—22no—
75C4×Q8×C101—21no—
76C4×Q8×C101D412yes—
77C4×D4×C101—22no—
78C4×D4×C101—24no—
79C4×D4×C101—24no—
80C4×D4×C101—21no—
81C4×D4×C101—21no—
82C4×D4×C101—21no—
83C4×D4×C101—21no—
84C4×D4×C101—21no—
85C4×D4×C101D412yes—
86#117×C101—22no—
87#117×C101—22no—
88#117×C101—21no—
89C2×C4⋊C4×C101—22no—
90C2×C4⋊C4×C101—21no—
91C2×C4⋊C4×C101—21no—
92C2×C4⋊C4×C101—21no—
93C2×C4⋊C4×C101D411yescharacteristic
94C2×C22⋊C4×C101—24no—
95C2×C22⋊C4×C101C2312yes—
96C2×C42×C101—21no—
97C2×C42×C101C2311yescharacteristic
98C4⋊C8×C101—21no—
99C4⋊C8×C101—21no—
100#103×C101—24no—
101#103×C101—24no—
102C22⋊C8×C101C2312yes—
103C22⋊C8×C101C2312yes—
104C4×C8×C101—21no—
105C4×C8×C101—21no—
106#95×C101—24no—
107#95×C101C2312yes—
108C24×C101C2×D412yes—
109#41×C101—42no—
110#41×C101—42no—
111#41×C101—84no—
112C2×Q8×C101—21no—
113C2×Q8×C101—21no—
114C2×Q8×C101—22no—
115C2×Q8×C101—22no—
116C2×Q8×C101—82no—
117C2×Q8×C101C2×D412yes—
118C2×D4×C101—22no—
119C2×D4×C101—24no—
120C2×D4×C101—24no—
121C2×D4×C101—21no—
122C2×D4×C101—21no—
123C2×D4×C101—21no—
124C2×D4×C101—21no—
125C2×D4×C101—22no—
126C2×D4×C101—22no—
127C2×D4×C101C2×D412yes—
128C22×C4×C101—24no—
129C22×C4×C101—22no—
130C22×C4×C101—22no—
131C22×C4×C101—22no—
132C22×C4×C101—22no—
133C22×C4×C101—22no—
134C22×C4×C101—44no—
135C22×C4×C101C2×D411yescharacteristic
136C22×C4×C101C2×D412yes—
137C22×C4×C101C2×D411yescharacteristic
138C22×C4×C101C2411yescharacteristic
139Q16×C101—84no—
140SD16×C101—84no—
141C2×C8×C101—22no—
142C2×C8×C101—22no—
143C4⋊C4×C101—24no—
144C4⋊C4×C101—21no—
145C4⋊C4×C101—21no—
146C4⋊C4×C101—21no—
147C4⋊C4×C101—21no—
148C4⋊C4×C101—21no—
149C4⋊C4×C101—21no—
150C4⋊C4×C101—22no—
151C4⋊C4×C101—22no—
152C4⋊C4×C101—42no—
153C4⋊C4×C101—41no—
154C4⋊C4×C101—41no—
155C4⋊C4×C101—41no—
156C4⋊C4×C101—41no—
157C4⋊C4×C101C2×D412yes—
158C4⋊C4×C101C2×D412yes—
159C22⋊C4×C101—24no—
160C22⋊C4×C101—24no—
161C22⋊C4×C101—24no—
162C22⋊C4×C101—22no—
163C22⋊C4×C101—22no—
164C22⋊C4×C101—22no—
165C22⋊C4×C101—22no—
166C22⋊C4×C101—22no—
167C22⋊C4×C101—84no—
168C42×C101—24no—
169C42×C101—22no—
170C42×C101—42no—
171C42×C101C2×D411yescharacteristic
172C42×C101C2×D411yescharacteristic
173C42×C101C2×D411yescharacteristic
174C42×C101C2×D411yescharacteristic
175C23×C101—22no—
176C23×C101—22no—
177C23×C101—22no—
178C23×C101—22no—
179C23×C101—42no—
180C23×C101—42no—
181C23×C101C22×D411yescharacteristic
182Q8×C101—42no—
183Q8×C101—44no—
184Q8×C101—44no—
185Q8×C101—42no—
186Q8×C101—42no—
187D4×C101—42no—
188D4×C101—42no—
189D4×C101—42no—
190D4×C101—42no—
191D4×C101—42no—
192D4×C101—42no—
193D4×C101—42no—
194D4×C101—84no—
195D4×C101—84no—
196C2×C4×C101—22no—
197C2×C4×C101—22no—
198C2×C4×C101—22no—
199C2×C4×C101—22no—
200C2×C4×C101—22no—
201C2×C4×C101—41no—
202C2×C4×C101—44no—
203C2×C4×C101—44no—
204C2×C4×C101—42no—
205C2×C4×C101—42no—
206C2×C4×C101—44no—
207C2×C4×C101—42no—
208C2×C4×C101—42no—
209C2×C4×C101—42no—
210C2×C4×C101—82no—
211C2×C4×C101—84no—
212C2×C4×C101#12011yescharacteristic
213C2×C4×C101#12011yescharacteristic
214C2×C4×C101#12011yescharacteristic
215C2×C4×C101#12011yescharacteristic
216C2×C4×C101#13512yes—
217C2×C4×C101#13712yes—
218C2×C4×C101C22×D411yescharacteristic
219C2×C4×C101C22×D411yescharacteristic
220C8×C101—42no—
221C8×C101—42no—
222C22×C101—21no—
223C22×C101—21no—
224C22×C101—44no—
225C22×C101—42no—
226C22×C101—42no—
227C22×C101—42no—
228C22×C101—42no—
229C22×C101—42no—
230C22×C101—42no—
231C22×C101—82no—
232C22×C101C2×#12011yescharacteristic
233C22×C101C2×#13511yescharacteristic
234C22×C101C2×#13711yescharacteristic
235C4×C101—21no—
236C4×C101—21no—
237C4×C101—21no—
238C4×C101—42no—
239C4×C101—42no—
240C4×C101—42no—
241C4×C101—42no—
242C4×C101—82no—
243C4×C101—82no—
244C4×C101#45212yes—
245C4×C101#45212yes—
246C4×C101#45512yes—
247#18406C10111yesmaximal, characteristic, direct product factor, Sylow
248C2×C101—21no—
249C2×C101—21no—
250C2×C101—82no—
251C2×C101—82no—
252C2×C101C2×#45211yescharacteristic
253C2×C101C2×#45511yescharacteristic
254C2×C101#302711yescharacteristic
255#3506C2×C10111yescharacteristic
256#3209C2×C10111yescharacteristic, complemented
257#3206C2×C10111yescharacteristic, complemented
258#2563C2×C10111yescharacteristic, complemented
259#1606C2×C10118yescomplemented
260#1503C2×C10111yescharacteristic, complemented
261#1502C2×C10111yescharacteristic, complemented
262#1460C2×C10111yescharacteristic, complemented
263C101#1840611yescharacteristic, direct product factor, Sylow
264#559—22no—
265#556—21no—
266#555—21no—
267#553—22no—
268#550—21no—
269#547—21no—
270#538C22×C10114yes—
271#535—21no—
272#533C22×C10111yescharacteristic
273#532C22×C10111yescharacteristic
274C2×C4⋊Q8C22×C10111yescharacteristic
275#525—22no—
276#520—21no—
277C2×C4×D4C22×C10111yescharacteristic
278#494—21no—
279#492—21no—
280#487—21no—
281#487—21no—
282#462—22no—
283#461—22no—
284#451C22×C10114yes—
285#448C22×C10114yes—
286#431C22×C10111yescharacteristic
287#431C22×C10111yescharacteristic
288#393C22×C10114yes—
289#390—21no—
290#382—21no—
291#380—22no—
292C4×C4⋊C4C22×C10111yescharacteristic
293#328C22×C10114yes—
294#327C22×C10114yes—
295#323C22×C10114yes—
296C2×#41—22no—
297C2×#41—21no—
298C22×Q8C23×C10112yes—
299C22×D4D4×C10111yescharacteristic
300C23×C4D4×C10112yes—
301C2×Q16—24no—
302C2×SD16—24no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8D4×C10111yescharacteristic
308C4⋊Q8D4×C10111yescharacteristic
309C4⋊Q8D4×C10111yescharacteristic
310#127—22no—
311#127D4×C10111yescharacteristic
312#126—24no—
313#125—21no—
314#124—22no—
315#124—24no—
316#124—21no—
317#123—24no—
318#123—24no—
319C22⋊Q8—22no—
320C22⋊Q8—21no—
321C22⋊Q8C23×C10112yes—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—24no—
326#121—21no—
327#121C23×C10112yes—
328#120—24no—
329C4×Q8—22no—
330C4×Q8—21no—
331C4×Q8D4×C10112yes—
332C4×D4—22no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4D4×C10112yes—
341#117—22no—
342#117—22no—
343#117—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4D4×C10111yescharacteristic
349C2×C22⋊C4—24no—
350C2×C22⋊C4C23×C10112yes—
351C2×C42—21no—
352C2×C42C23×C10111yescharacteristic
353C4⋊C8—21no—
354C4⋊C8—21no—
355#103—24no—
356#103—24no—
357C22⋊C8C23×C10112yes—
358C22⋊C8C23×C10112yes—
359C4×C8—21no—
360C4×C8—21no—
361#95—24no—
362#95C23×C10112yes—
363C24C2×D4×C10112yes—
364#41—42no—
365#41—42no—
366#41—84no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—82no—
372C2×Q8C2×D4×C10112yes—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4C2×D4×C10112yes—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—44no—
390C22×C4C2×D4×C10111yescharacteristic
391C22×C4C2×D4×C10112yes—
392C22×C4C2×D4×C10111yescharacteristic
393C22×C4C24×C10111yescharacteristic
394Q16—84no—
395SD16—84no—
396C2×C8—22no—
397C2×C8—22no—
398C4⋊C4—24no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C10112yes—
413C4⋊C4C2×D4×C10112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—84no—
423C42—24no—
424C42—22no—
425C42—42no—
426C42C2×D4×C10111yescharacteristic
427C42C2×D4×C10111yescharacteristic
428C42C2×D4×C10111yescharacteristic
429C42C2×D4×C10111yescharacteristic
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23C22×D4×C10111yescharacteristic
437Q8—42no—
438Q8—44no—
439Q8—44no—
440Q8—42no—
441Q8—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—84no—
450D4—84no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4—84no—
467C2×C4#120×C10111yescharacteristic
468C2×C4#120×C10111yescharacteristic
469C2×C4#120×C10111yescharacteristic
470C2×C4#120×C10111yescharacteristic
471C2×C4#135×C10112yes—
472C2×C4#137×C10112yes—
473C2×C4C22×D4×C10111yescharacteristic
474C2×C4C22×D4×C10111yescharacteristic
475C8—42no—
476C8—42no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—82no—
487C22C2×#120×C10111yescharacteristic
488C22C2×#135×C10111yescharacteristic
489C22C2×#137×C10111yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—82no—
499C4#452×C10112yes—
500C4#452×C10112yes—
501C4#455×C10112yes—
502C2—21no—
503C2—21no—
504C2—82no—
505C2—82no—
506C2C2×#452×C10111yescharacteristic
507C2C2×#455×C10111yescharacteristic
508C2C101×#302711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#3506C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3209C2semidirect
3. C101×#3206C2semidirect
4. C101×#2563C2semidirect
5. C101×#1606C2semidirect
6. C101×#1503C2semidirect
7. C101×#1502C2semidirect
8. C101×#1460C2semidirect
247. #18406C101direct (N × H)
256. #3209C2×C101semidirect
257. #3206C2×C101semidirect
258. #2563C2×C101semidirect
259. #1606C2×C101semidirect
260. #1503C2×C101semidirect
261. #1502C2×C101semidirect
262. #1460C2×C101semidirect
263. C101#18406direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35062
C101×#32092
C101×#32062
C101×#25632
C101×#16062
C101×#15032
C101×#15022
C101×#14602
#18406101