Finite Group Databasebeta

← C101×#18647 #38800798

Subgroups — C101×#18647 #38800798

Order 25856.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3511C211yesmaximal, characteristic
2C101×#3227C211yesmaximal, characteristic, complemented
3C2×#487×C101C211yesmaximal, characteristic, complemented
4C101×#3079C211yesmaximal, characteristic, complemented
5C101×#1638C214yesmaximal, complemented
6C101×#1635C214yesmaximal, complemented
7C101×#1549C211yesmaximal, characteristic, complemented
8C101×#1492C211yesmaximal, characteristic, complemented
9C101×#1476C211yesmaximal, characteristic, complemented
10#556×C101C2212yes—
11#555×C101—21no—
12#554×C101—21no—
13#553×C101—22no—
14#548×C101—22no—
15#547×C101C2212yes—
16#542×C101—22no—
17#537×C101—21no—
18#533×C101—21no—
19#532×C101—21no—
20#532×C101C2211yescharacteristic
21C2×C4⋊Q8×C101C2211yescharacteristic
22C2×C4⋊Q8×C101C2211yescharacteristic
23#520×C101—21no—
24C4×#41×C101C2211yescharacteristic
25#498×C101—21no—
26#487×C101—22no—
27#487×C101C2214yes—
28#486×C101—21no—
29#481×C101—22no—
30#477×C101C2212yes—
31#476×C101C2212yes—
32#476×C101C2214yes—
33#475×C101—21no—
34#474×C101—21no—
35#431×C101C2211yescharacteristic
36#428×C101—21no—
37#423×C101C2211yescharacteristic
38#417×C101—21no—
39C2×#103×C101—22no—
40C2×C4×C8×C101C2211yescharacteristic
41#332×C101C2214yes—
42Q8⋊C8×C101C2212yes—
43D4⋊C8×C101C2212yes—
44D4⋊C8×C101C2214yes—
45C2×#41×C101—22no—
46C2×#41×C101—21no—
47C2×#41×C101D411yescharacteristic
48C22×Q8×C101—21no—
49C22×Q8×C101—21no—
50C2×M16×C101—21no—
51C22×C8×C101—21no—
52C4⋊Q8×C101—21no—
53C4⋊Q8×C101—21no—
54C4⋊Q8×C101—21no—
55C4⋊Q8×C101—21no—
56C4⋊Q8×C101—21no—
57C4⋊Q8×C101D412yes—
58C4⋊Q8×C101D411yescharacteristic
59C4⋊Q8×C101C2312yes—
60C4⋊Q8×C101C2312yes—
61#127×C101D411yescharacteristic
62#126×C101—24no—
63#125×C101—22no—
64#124×C101—24no—
65#124×C101—22no—
66#124×C101—21no—
67#123×C101—24no—
68C22⋊Q8×C101—22no—
69C22⋊Q8×C101—24no—
70C22⋊Q8×C101—22no—
71C22⋊Q8×C101—22no—
72#121×C101—22no—
73#121×C101—22no—
74#121×C101—24no—
75#121×C101—22no—
76#121×C101—21no—
77#121×C101D412yes—
78C4×Q8×C101—22no—
79C4×Q8×C101—22no—
80C4×Q8×C101D411yescharacteristic
81C4×Q8×C101C2311yescharacteristic
82C4×D4×C101—22no—
83C4×D4×C101—24no—
84C4×D4×C101—22no—
85C4×D4×C101—21no—
86C4×D4×C101—21no—
87C4×D4×C101—21no—
88C4×D4×C101D411yescharacteristic
89C4×D4×C101C2311yescharacteristic
90C4×D4×C101C2312yes—
91#117×C101—22no—
92#117×C101—22no—
93#117×C101—21no—
94#117×C101D411yescharacteristic
95C2×C4⋊C4×C101—21no—
96C2×C4⋊C4×C101—22no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101D412yes—
100C2×C42×C101—21no—
101C2×C42×C101C2311yescharacteristic
102#107×C101—22no—
103#106×C101—22no—
104#106×C101—24no—
105C4⋊C8×C101—21no—
106C4⋊C8×C101C2312yes—
107C4⋊C8×C101C2312yes—
108#103×C101—22no—
109#103×C101—28no—
110#102×C101—22no—
111#102×C101—24no—
112C22⋊C8×C101—21no—
113C4×C8×C101—21no—
114C4×C8×C101—21no—
115C4×C8×C101C2312yes—
116#41×C101—22no—
117#41×C101—22no—
118#41×C101—42no—
119#41×C101—42no—
120#41×C101—84no—
121C2×Q8×C101—21no—
122C2×Q8×C101—22no—
123C2×Q8×C101—22no—
124C2×Q8×C101—22no—
125C2×Q8×C101—44no—
126C2×Q8×C101—41no—
127C2×Q8×C101—82no—
128C2×Q8×C101C2×D411yescharacteristic
129C2×D4×C101—21no—
130C2×D4×C101—22no—
131C2×D4×C101—24no—
132C2×D4×C101—21no—
133C2×D4×C101—21no—
134C2×D4×C101C2×D411yescharacteristic
135C2×D4×C101C2×D412yes—
136C22×C4×C101—24no—
137C22×C4×C101—22no—
138C22×C4×C101—21no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—22no—
142C22×C4×C101—41no—
143C22×C4×C101C2×D411yescharacteristic
144C22×C4×C101C2×D411yescharacteristic
145C22×C4×C101C2×D411yescharacteristic
146M16×C101—42no—
147C2×C8×C101—22no—
148C2×C8×C101—22no—
149C2×C8×C101—22no—
150C2×C8×C101—42no—
151C4⋊C4×C101—24no—
152C4⋊C4×C101—24no—
153C4⋊C4×C101—22no—
154C4⋊C4×C101—22no—
155C4⋊C4×C101—21no—
156C4⋊C4×C101—21no—
157C4⋊C4×C101—22no—
158C4⋊C4×C101—21no—
159C4⋊C4×C101—22no—
160C4⋊C4×C101—22no—
161C4⋊C4×C101—41no—
162C4⋊C4×C101—41no—
163C4⋊C4×C101C2×D414yes—
164C4⋊C4×C101C2×D411yescharacteristic
165C4⋊C4×C101C2×D412yes—
166C4⋊C4×C101C2×D411yescharacteristic
167C22⋊C4×C101—24no—
168C22⋊C4×C101—24no—
169C22⋊C4×C101—24no—
170C22⋊C4×C101—21no—
171C22⋊C4×C101—21no—
172C22⋊C4×C101—22no—
173C22⋊C4×C101—21no—
174C22⋊C4×C101—22no—
175C42×C101—24no—
176C42×C101—21no—
177C42×C101—21no—
178C42×C101—21no—
179C42×C101C2×D411yescharacteristic
180C42×C101C2×D411yescharacteristic
181C42×C101C2×D411yescharacteristic
182C42×C101C2411yescharacteristic
183C23×C101—21no—
184C23×C101—22no—
185C23×C101#12011yescharacteristic
186Q8×C101—21no—
187Q8×C101—21no—
188Q8×C101—44no—
189Q8×C101—44no—
190Q8×C101—42no—
191Q8×C101—82no—
192Q8×C101—82no—
193D4×C101—21no—
194D4×C101—21no—
195D4×C101—24no—
196D4×C101—42no—
197D4×C101—44no—
198D4×C101—42no—
199D4×C101—42no—
200D4×C101—84no—
201C2×C4×C101—22no—
202C2×C4×C101—22no—
203C2×C4×C101—21no—
204C2×C4×C101—21no—
205C2×C4×C101—22no—
206C2×C4×C101—21no—
207C2×C4×C101—24no—
208C2×C4×C101—42no—
209C2×C4×C101—42no—
210C2×C4×C101—42no—
211C2×C4×C101—42no—
212C2×C4×C101—42no—
213C2×C4×C101—42no—
214C2×C4×C101—82no—
215C2×C4×C101—84no—
216C2×C4×C101—82no—
217C2×C4×C101#12011yescharacteristic
218C2×C4×C101#12011yescharacteristic
219C2×C4×C101#12011yescharacteristic
220C2×C4×C101#13512yes—
221C2×C4×C101#13712yes—
222C2×C4×C101C22×D411yescharacteristic
223C2×C4×C101C22×D411yescharacteristic
224C2×C4×C101C22×D411yescharacteristic
225C8×C101—42no—
226C8×C101—42no—
227C8×C101—42no—
228C22×C101—21no—
229C22×C101—21no—
230C22×C101—41no—
231C22×C101—42no—
232C22×C101—41no—
233C22×C101—42no—
234C22×C101—41no—
235C22×C101—42no—
236C22×C101#45212yes—
237C22×C101C2×#12011yescharacteristic
238C4×C101—21no—
239C4×C101—21no—
240C4×C101—41no—
241C4×C101—42no—
242C4×C101—41no—
243C4×C101—44no—
244C4×C101—41no—
245C4×C101—82no—
246C4×C101#45212yes—
247C4×C101#45412yes—
248C4×C101C2×#13511yescharacteristic
249C4×C101C2×#13711yescharacteristic
250C4×C101#57712yes—
251#18647C10111yesmaximal, characteristic, direct product factor, Sylow
252C2×C101—22no—
253C2×C101—81no—
254C2×C101—82no—
255C2×C101C2×#45211yescharacteristic
256C2×C101#300911yescharacteristic
257C2×C101C2×#45411yescharacteristic
258#3511C2×C10111yescharacteristic
259#3227C2×C10111yescharacteristic, complemented
260C2×#487C2×C10111yescharacteristic, complemented
261#3079C2×C10111yescharacteristic, complemented
262#1638C2×C10114yescomplemented
263#1635C2×C10114yescomplemented
264#1549C2×C10111yescharacteristic, complemented
265#1492C2×C10111yescharacteristic, complemented
266#1476C2×C10111yescharacteristic, complemented
267C101#1864711yescharacteristic, direct product factor, Sylow
268#556C22×C10112yes—
269#555—21no—
270#554—21no—
271#553—22no—
272#548—22no—
273#547C22×C10112yes—
274#542—22no—
275#537—21no—
276#533—21no—
277#532—21no—
278#532C22×C10111yescharacteristic
279C2×C4⋊Q8C22×C10111yescharacteristic
280C2×C4⋊Q8C22×C10111yescharacteristic
281#520—21no—
282C4×#41C22×C10111yescharacteristic
283#498—21no—
284#487—22no—
285#487C22×C10114yes—
286#486—21no—
287#481—22no—
288#477C22×C10112yes—
289#476C22×C10112yes—
290#476C22×C10114yes—
291#475—21no—
292#474—21no—
293#431C22×C10111yescharacteristic
294#428—21no—
295#423C22×C10111yescharacteristic
296#417—21no—
297C2×#103—22no—
298C2×C4×C8C22×C10111yescharacteristic
299#332C22×C10114yes—
300Q8⋊C8C22×C10112yes—
301D4⋊C8C22×C10112yes—
302D4⋊C8C22×C10114yes—
303C2×#41—22no—
304C2×#41—21no—
305C2×#41D4×C10111yescharacteristic
306C22×Q8—21no—
307C22×Q8—21no—
308C2×M16—21no—
309C22×C8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C10112yes—
316C4⋊Q8D4×C10111yescharacteristic
317C4⋊Q8C23×C10112yes—
318C4⋊Q8C23×C10112yes—
319#127D4×C10111yescharacteristic
320#126—24no—
321#125—22no—
322#124—24no—
323#124—22no—
324#124—21no—
325#123—24no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330#121—22no—
331#121—22no—
332#121—24no—
333#121—22no—
334#121—21no—
335#121D4×C10112yes—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8D4×C10111yescharacteristic
339C4×Q8C23×C10111yescharacteristic
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C10111yescharacteristic
347C4×D4C23×C10111yescharacteristic
348C4×D4C23×C10112yes—
349#117—22no—
350#117—22no—
351#117—21no—
352#117D4×C10111yescharacteristic
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C10112yes—
358C2×C42—21no—
359C2×C42C23×C10111yescharacteristic
360#107—22no—
361#106—22no—
362#106—24no—
363C4⋊C8—21no—
364C4⋊C8C23×C10112yes—
365C4⋊C8C23×C10112yes—
366#103—22no—
367#103—28no—
368#102—22no—
369#102—24no—
370C22⋊C8—21no—
371C4×C8—21no—
372C4×C8—21no—
373C4×C8C23×C10112yes—
374#41—22no—
375#41—22no—
376#41—42no—
377#41—42no—
378#41—84no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—41no—
385C2×Q8—82no—
386C2×Q8C2×D4×C10111yescharacteristic
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—24no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×D4×C10111yescharacteristic
393C2×D4C2×D4×C10112yes—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4C2×D4×C10111yescharacteristic
402C22×C4C2×D4×C10111yescharacteristic
403C22×C4C2×D4×C10111yescharacteristic
404M16—42no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—42no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C10114yes—
422C4⋊C4C2×D4×C10111yescharacteristic
423C4⋊C4C2×D4×C10112yes—
424C4⋊C4C2×D4×C10111yescharacteristic
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—22no—
431C22⋊C4—21no—
432C22⋊C4—22no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42C2×D4×C10111yescharacteristic
438C42C2×D4×C10111yescharacteristic
439C42C2×D4×C10111yescharacteristic
440C42C24×C10111yescharacteristic
441C23—21no—
442C23—22no—
443C23#120×C10111yescharacteristic
444Q8—21no—
445Q8—21no—
446Q8—44no—
447Q8—42no—
448Q8—44no—
449Q8—82no—
450Q8—82no—
451D4—21no—
452D4—21no—
453D4—24no—
454D4—42no—
455D4—44no—
456D4—42no—
457D4—42no—
458D4—84no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—82no—
473C2×C4—84no—
474C2×C4—82no—
475C2×C4#120×C10111yescharacteristic
476C2×C4#120×C10111yescharacteristic
477C2×C4#120×C10111yescharacteristic
478C2×C4#135×C10112yes—
479C2×C4#137×C10112yes—
480C2×C4C22×D4×C10111yescharacteristic
481C2×C4C22×D4×C10111yescharacteristic
482C2×C4C22×D4×C10111yescharacteristic
483C8—42no—
484C8—42no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—41no—
489C22—42no—
490C22—41no—
491C22—42no—
492C22—41no—
493C22—42no—
494C22#452×C10112yes—
495C22C2×#120×C10111yescharacteristic
496C4—21no—
497C4—21no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—44no—
502C4—41no—
503C4—82no—
504C4#452×C10112yes—
505C4#454×C10112yes—
506C4C2×#135×C10111yescharacteristic
507C4C2×#137×C10111yescharacteristic
508C4#577×C10112yes—
509C2—22no—
510C2—81no—
511C2—82no—
512C2C2×#452×C10111yescharacteristic
513C2C101×#300911yescharacteristic
514C2C2×#454×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3511C2
LCSG ▷ C42 ▷ 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×#3227C2semidirect
3. C2×#487×C101C2semidirect
4. C101×#3079C2semidirect
5. C101×#1638C2semidirect
6. C101×#1635C2semidirect
7. C101×#1549C2semidirect
8. C101×#1492C2semidirect
9. C101×#1476C2semidirect
251. #18647C101direct (N × H)
259. #3227C2×C101semidirect
260. C2×#487C2×C101semidirect
261. #3079C2×C101semidirect
262. #1638C2×C101semidirect
263. #1635C2×C101semidirect
264. #1549C2×C101semidirect
265. #1492C2×C101semidirect
266. #1476C2×C101semidirect
267. C101#18647direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35112
C101×#32272
C2×#487×C1012
C101×#30792
C101×#16382
C101×#16352
C101×#15492
C101×#14922
C101×#14762
#18647101