Finite Group Databasebeta

← C107×#18149 #41044113

Subgroups — C107×#18149 #41044113

Order 27392.

1074 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#538×C107C211yesmaximal, characteristic
2C107×#3095C211yesmaximal, characteristic, complemented
3C107×#3094C211yesmaximal, characteristic, complemented
4C107×#2482C211yesmaximal, characteristic, complemented
5C107×#1618C214yesmaximal, complemented
6C107×#1612C214yesmaximal, complemented
7C107×#1511C211yesmaximal, characteristic, complemented
8C107×#1510C211yesmaximal, characteristic, complemented
9C107×#1462C211yesmaximal, characteristic, complemented
10#538×C107—22no—
11#538×C107—22no—
12#538×C107—22no—
13#538×C107C2214yes—
14C2×#126×C107—21no—
15C2×#124×C107—21no—
16C2×#123×C107—21no—
17C2×C22⋊Q8×C107C2211yescharacteristic
18C2×#121×C107—21no—
19C2×#121×C107C2211yescharacteristic
20C2×#120×C107—21no—
21C2×C4×D4×C107—21no—
22C2×#117×C107C2211yescharacteristic
23C22×C22⋊C4×C107C2211yescharacteristic
24#485×C107—22no—
25#484×C107C2212yescomplemented
26#483×C107C2212yescomplemented
27#482×C107—22no—
28#481×C107C2212yescomplemented
29#480×C107C2212yescomplemented
30#428×C107—21no—
31#428×C107—21no—
32#419×C107—21no—
33#418×C107—21no—
34#407×C107C2211yescharacteristic
35#407×C107C2211yescharacteristic
36#399×C107C2212yescomplemented
37#397×C107C2212yescomplemented
38#388×C107—22no—
39#385×C107—21no—
40#381×C107C2211yescharacteristic
41#379×C107—21no—
42#328×C107C2214yescomplemented
43#327×C107C2214yescomplemented
44#323×C107C2214yescomplemented
45C25×C107D411yescharacteristic
46C22×Q8×C107D411yescharacteristic
47C22×D4×C107—21no—
48C22×D4×C107—21no—
49C22×D4×C107—21no—
50C22×D4×C107D411yescharacteristic
51C23×C4×C107—21no—
52C23×C4×C107D411yescharacteristic
53C23×C4×C107C2311yescharacteristic
54C2×M16×C107—21no—
55C2×M16×C107—21no—
56#126×C107—24no—
57#126×C107—24no—
58#124×C107—24no—
59#124×C107—24no—
60#123×C107—24no—
61#123×C107—24no—
62C22⋊Q8×C107—21no—
63C22⋊Q8×C107—21no—
64C22⋊Q8×C107D412yes—
65C22⋊Q8×C107C2312yes—
66#121×C107—24no—
67#121×C107—24no—
68#121×C107—21no—
69#121×C107—21no—
70#121×C107D412yes—
71#121×C107C2312yes—
72#120×C107—24no—
73#120×C107—24no—
74C4×D4×C107—24no—
75C4×D4×C107—24no—
76#117×C107—21no—
77#117×C107—21no—
78#117×C107—21no—
79#117×C107—21no—
80C2×C4⋊C4×C107—21no—
81C2×C4⋊C4×C107—21no—
82C2×C4⋊C4×C107—22no—
83C2×C4⋊C4×C107D411yescharacteristic
84C2×C4⋊C4×C107D411yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C4⋊C4×C107C2311yescharacteristic
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C22⋊C4×C107—21no—
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C22⋊C4×C107—21no—
95C2×C22⋊C4×C107—21no—
96C2×C22⋊C4×C107—21no—
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—22no—
99C2×C22⋊C4×C107—22no—
100C2×C22⋊C4×C107D412yes—
101C2×C22⋊C4×C107C2312yes—
102C2×C42×C107—21no—
103C2×C42×C107—21no—
104#107×C107—22no—
105#107×C107—22no—
106#106×C107—22no—
107#106×C107—22no—
108#103×C107—22no—
109#103×C107—22no—
110#102×C107—22no—
111#102×C107—22no—
112C22⋊C8×C107—21no—
113C22⋊C8×C107—21no—
114C22⋊C8×C107C2312yes—
115C22⋊C8×C107C2312yes—
116#95×C107—21no—
117#95×C107—22no—
118#95×C107C2312yes—
119C24×C107—21no—
120C24×C107—21no—
121C24×C107—21no—
122C24×C107—42no—
123C24×C107—42no—
124C24×C107—81no—
125C24×C107C2×D411yescharacteristic
126C24×C107C2×D412yes—
127C2×Q8×C107—21no—
128C2×Q8×C107—42no—
129C2×Q8×C107C2×D412yes—
130C2×D4×C107—22no—
131C2×D4×C107—22no—
132C2×D4×C107—24no—
133C2×D4×C107—24no—
134C2×D4×C107—21no—
135C2×D4×C107—42no—
136C2×D4×C107—44no—
137C2×D4×C107—82no—
138C2×D4×C107—82no—
139C2×D4×C107C2×D412yes—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—21no—
144C22×C4×C107—24no—
145C22×C4×C107—21no—
146C22×C4×C107—22no—
147C22×C4×C107—21no—
148C22×C4×C107—21no—
149C22×C4×C107—42no—
150C22×C4×C107—81no—
151C22×C4×C107—82no—
152C22×C4×C107C2×D411yescharacteristic
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D412yes—
155C22×C4×C107C2×D411yescharacteristic
156C22×C4×C107C2×D411yescharacteristic
157C22×C4×C107C2×D411yescharacteristic
158C22×C4×C107C2411yescharacteristic
159M16×C107—42no—
160M16×C107—42no—
161C2×C8×C107—22no—
162C2×C8×C107—22no—
163C4⋊C4×C107—24no—
164C4⋊C4×C107—22no—
165C4⋊C4×C107—21no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—22no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—21no—
172C4⋊C4×C107—82no—
173C4⋊C4×C107C2×D412yes—
174C4⋊C4×C107C2×D412yes—
175C22⋊C4×C107—24no—
176C22⋊C4×C107—24no—
177C22⋊C4×C107—24no—
178C22⋊C4×C107—22no—
179C22⋊C4×C107—22no—
180C22⋊C4×C107—22no—
181C22⋊C4×C107—22no—
182C22⋊C4×C107—22no—
183C22⋊C4×C107—22no—
184C22⋊C4×C107—22no—
185C22⋊C4×C107—22no—
186C22⋊C4×C107—42no—
187C22⋊C4×C107—44no—
188C22⋊C4×C107—41no—
189C22⋊C4×C107—41no—
190C22⋊C4×C107—82no—
191C42×C107—24no—
192C42×C107—41no—
193C42×C107—41no—
194C23×C107—22no—
195C23×C107—22no—
196C23×C107—22no—
197C23×C107—22no—
198C23×C107—22no—
199C23×C107—22no—
200C23×C107—41no—
201C23×C107—42no—
202C23×C107—42no—
203C23×C107—42no—
204C23×C107—42no—
205C23×C107—42no—
206C23×C107—42no—
207C23×C107—42no—
208C23×C107—42no—
209C23×C107—42no—
210C23×C107—81no—
211C23×C107—81no—
212C23×C107—88no—
213C23×C107#12011yescharacteristic
214C23×C107#12011yescharacteristic
215C23×C107C22×D411yescharacteristic
216Q8×C107—42no—
217Q8×C107—81no—
218D4×C107—42no—
219D4×C107—44no—
220D4×C107—44no—
221D4×C107—81no—
222D4×C107—84no—
223D4×C107—84no—
224C2×C4×C107—22no—
225C2×C4×C107—22no—
226C2×C4×C107—22no—
227C2×C4×C107—22no—
228C2×C4×C107—22no—
229C2×C4×C107—22no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—41no—
233C2×C4×C107—41no—
234C2×C4×C107—42no—
235C2×C4×C107—42no—
236C2×C4×C107—42no—
237C2×C4×C107—42no—
238C2×C4×C107—42no—
239C2×C4×C107—42no—
240C2×C4×C107—42no—
241C2×C4×C107—42no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—42no—
245C2×C4×C107—42no—
246C2×C4×C107—81no—
247C2×C4×C107—84no—
248C2×C4×C107#12011yescharacteristic
249C2×C4×C107#12011yescharacteristic
250C2×C4×C107C22×D411yescharacteristic
251C2×C4×C107C22×D411yescharacteristic
252C8×C107—42no—
253C8×C107—42no—
254C22×C107—21no—
255C22×C107—21no—
256C22×C107—21no—
257C22×C107—21no—
258C22×C107—21no—
259C22×C107—21no—
260C22×C107—21no—
261C22×C107—44no—
262C22×C107—44no—
263C22×C107—42no—
264C22×C107—42no—
265C22×C107—42no—
266C22×C107—42no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—82no—
270C22×C107—84no—
271C22×C107—84no—
272C22×C107—84no—
273C22×C107#45812yes—
274C22×C107C2×#12011yescharacteristic
275C22×C107#57512yes—
276C4×C107—21no—
277C4×C107—21no—
278C4×C107—21no—
279C4×C107—21no—
280C4×C107—42no—
281C4×C107—42no—
282C4×C107—42no—
283C4×C107—42no—
284C4×C107—82no—
285C4×C107—81no—
286C4×C107—81no—
287#18149C10711yesmaximal, characteristic, direct product factor, Sylow
288C2×C107—22no—
289C2×C107—22no—
290C2×C107—41no—
291C2×C107—82no—
292C2×C107—82no—
293C2×C107#300511yescharacteristic
294C2×C107#301911yescharacteristic
295C2×C107C2×#45811yescharacteristic
296C2×#538C2×C10711yescharacteristic
297#3095C2×C10711yescharacteristic, complemented
298#3094C2×C10711yescharacteristic, complemented
299#2482C2×C10711yescharacteristic, complemented
300#1618C2×C10714yescomplemented
301#1612C2×C10714yescomplemented
302#1511C2×C10711yescharacteristic, complemented
303#1510C2×C10711yescharacteristic, complemented
304#1462C2×C10711yescharacteristic, complemented
305C107#1814911yescharacteristic, direct product factor, Sylow
306#538—22no—
307#538—22no—
308#538—22no—
309#538C22×C10714yes—
310C2×#126—21no—
311C2×#124—21no—
312C2×#123—21no—
313C2×C22⋊Q8C22×C10711yescharacteristic
314C2×#121—21no—
315C2×#121C22×C10711yescharacteristic
316C2×#120—21no—
317C2×C4×D4—21no—
318C2×#117C22×C10711yescharacteristic
319C22×C22⋊C4C22×C10711yescharacteristic
320#485—22no—
321#484C22×C10712yescomplemented
322#483C22×C10712yescomplemented
323#482—22no—
324#481C22×C10712yescomplemented
325#480C22×C10712yescomplemented
326#428—21no—
327#428—21no—
328#419—21no—
329#418—21no—
330#407C22×C10711yescharacteristic
331#407C22×C10711yescharacteristic
332#399C22×C10712yescomplemented
333#397C22×C10712yescomplemented
334#388—22no—
335#385—21no—
336#381C22×C10711yescharacteristic
337#379—21no—
338#328C22×C10714yescomplemented
339#327C22×C10714yescomplemented
340#323C22×C10714yescomplemented
341C25D4×C10711yescharacteristic
342C22×Q8D4×C10711yescharacteristic
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4D4×C10711yescharacteristic
347C23×C4—21no—
348C23×C4D4×C10711yescharacteristic
349C23×C4C23×C10711yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352#126—24no—
353#126—24no—
354#124—24no—
355#124—24no—
356#123—24no—
357#123—24no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8D4×C10712yes—
361C22⋊Q8C23×C10712yes—
362#121—24no—
363#121—24no—
364#121—21no—
365#121—21no—
366#121D4×C10712yes—
367#121C23×C10712yes—
368#120—24no—
369#120—24no—
370C4×D4—24no—
371C4×D4—24no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4D4×C10711yescharacteristic
380C2×C4⋊C4D4×C10711yescharacteristic
381C2×C4⋊C4C23×C10711yescharacteristic
382C2×C4⋊C4C23×C10711yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4D4×C10712yes—
397C2×C22⋊C4C23×C10712yes—
398C2×C42—21no—
399C2×C42—21no—
400#107—22no—
401#107—22no—
402#106—22no—
403#106—22no—
404#103—22no—
405#103—22no—
406#102—22no—
407#102—22no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8C23×C10712yes—
411C22⋊C8C23×C10712yes—
412#95—21no—
413#95—22no—
414#95C23×C10712yes—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—42no—
419C24—42no—
420C24—81no—
421C24C2×D4×C10711yescharacteristic
422C24C2×D4×C10712yes—
423C2×Q8—21no—
424C2×Q8—42no—
425C2×Q8C2×D4×C10712yes—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—21no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4C2×D4×C10712yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—82no—
448C22×C4C2×D4×C10711yescharacteristic
449C22×C4C2×D4×C10711yescharacteristic
450C22×C4C2×D4×C10712yes—
451C22×C4C2×D4×C10711yescharacteristic
452C22×C4C2×D4×C10711yescharacteristic
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C24×C10711yescharacteristic
455M16—42no—
456M16—42no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—82no—
469C4⋊C4C2×D4×C10712yes—
470C4⋊C4C2×D4×C10712yes—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—42no—
483C22⋊C4—44no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—82no—
487C42—24no—
488C42—41no—
489C42—41no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—81no—
507C23—81no—
508C23—88no—
509C23#120×C10711yescharacteristic
510C23#120×C10711yescharacteristic
511C23C22×D4×C10711yescharacteristic
512Q8—42no—
513Q8—81no—
514D4—42no—
515D4—44no—
516D4—44no—
517D4—81no—
518D4—84no—
519D4—84no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—81no—
543C2×C4—84no—
544C2×C4#120×C10711yescharacteristic
545C2×C4#120×C10711yescharacteristic
546C2×C4C22×D4×C10711yescharacteristic
547C2×C4C22×D4×C10711yescharacteristic
548C8—42no—
549C8—42no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—44no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—82no—
566C22—84no—
567C22—84no—
568C22—84no—
569C22#458×C10712yes—
570C22C2×#120×C10711yescharacteristic
571C22#575×C10712yes—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—42no—
580C4—82no—
581C4—81no—
582C4—81no—
583C2—22no—
584C2—22no—
585C2—41no—
586C2—82no—
587C2—82no—
588C2C107×#300511yescharacteristic
589C2C107×#301911yescharacteristic
590C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#538×C107C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3095C2semidirect
3. C107×#3094C2semidirect
4. C107×#2482C2semidirect
5. C107×#1618C2semidirect
6. C107×#1612C2semidirect
7. C107×#1511C2semidirect
8. C107×#1510C2semidirect
9. C107×#1462C2semidirect
25. #484×C107C22semidirect
26. #483×C107C22semidirect
28. #481×C107C22semidirect
29. #480×C107C22semidirect
36. #399×C107C22semidirect
37. #397×C107C22semidirect
42. #328×C107C22semidirect
43. #327×C107C22semidirect
44. #323×C107C22semidirect
287. #18149C107direct (N × H)
297. #3095C2×C107semidirect
298. #3094C2×C107semidirect
299. #2482C2×C107semidirect
300. #1618C2×C107semidirect
301. #1612C2×C107semidirect
302. #1511C2×C107semidirect
303. #1510C2×C107semidirect
304. #1462C2×C107semidirect
305. C107#18149direct (N × H)
321. #484C22×C107semidirect
322. #483C22×C107semidirect
324. #481C22×C107semidirect
325. #480C22×C107semidirect
332. #399C22×C107semidirect
333. #397C22×C107semidirect
338. #328C22×C107semidirect
339. #327C22×C107semidirect
340. #323C22×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#538×C1072
C107×#30952
C107×#30942
C107×#24822
C107×#16182
C107×#16122
C107×#15112
C107×#15102
C107×#14622
#18149107