Finite Group Databasebeta

← C107×#9113 #41035077

Subgroups — C107×#9113 #41035077

Order 27392.

1062 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
1C22×C22⋊C8×C107C211yesmaximal, characteristic, complemented
2C107×#2847C211yesmaximal, characteristic
3C2×#327×C107C212yesmaximal, complemented
4C107×C22⋊#95C211yesmaximal, characteristic, complemented
5C107×#1294C212yesmaximal, complemented
6C24×C4×C107C2211yescharacteristic
7C23×C8×C107—21no—
8C2×#121×C107C411yescharacteristic, complemented
9C2×#121×C107C411yescharacteristic, complemented
10C2×#121×C107C2211yescharacteristic
11C2×#120×C107—21no—
12C22×C22⋊C4×C107—21no—
13C2×C22⋊C8×C107—21no—
14C2×C22⋊C8×C107—24no—
15C2×C22⋊C8×C107C2212yes—
16#386×C107—21no—
17#386×C107—21no—
18#386×C107—21no—
19#380×C107C411yescharacteristic, complemented
20#380×C107C411yescharacteristic, complemented
21#380×C107C2211yescharacteristic
22C2×#95×C107—21no—
23C2×#95×C107C2212yes—
24#327×C107—24no—
25C25×C107D411yescharacteristic
26C22×D4×C107—21no—
27C22×D4×C107—21no—
28C22×D4×C107—21no—
29C22×D4×C107C2×C411yescharacteristic
30C23×C4×C107—22no—
31C23×C4×C107—22no—
32C23×C4×C107—22no—
33C23×C4×C107—42no—
34C23×C4×C107—42no—
35C23×C4×C107C2×C411yescharacteristic
36C23×C4×C107C2×C411yescharacteristic
37C23×C4×C107D411yescharacteristic
38C23×C4×C107D411yescharacteristic
39C23×C4×C107D411yescharacteristic
40C23×C4×C107C2311yescharacteristic
41C22×C8×C107—24no—
42C22×C8×C107—22no—
43C22×C8×C107—42no—
44C22×C8×C107—42no—
45#121×C107—22no—
46#121×C107—22no—
47#121×C107—42no—
48#121×C107—42no—
49#120×C107—42no—
50#120×C107—42no—
51C2×C4⋊C4×C107C2×C411yescharacteristic
52C2×C4⋊C4×C107C2×C411yescharacteristic
53C2×C4⋊C4×C107C2×C411yescharacteristic
54C2×C22⋊C4×C107—24no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—21no—
61C2×C22⋊C4×C107—42no—
62C2×C22⋊C4×C107—42no—
63C22⋊C8×C107—24no—
64C22⋊C8×C107—22no—
65C22⋊C8×C107D414yescomplemented
66#95×C107—21no—
67#95×C107—21no—
68#95×C107—21no—
69#95×C107—22no—
70#95×C107—22no—
71#95×C107—42no—
72C24×C107—22no—
73C24×C107—22no—
74C24×C107—22no—
75C24×C107—22no—
76C24×C107—21no—
77C24×C107—41no—
78C24×C107—41no—
79C24×C107C22⋊C411yescharacteristic
80C24×C107C22⋊C411yescharacteristic
81C24×C107D812yes—
82C24×C107SD1612yes—
83C24×C107C2×D411yescharacteristic
84C2×D4×C107—22no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C2×D4×C107—42no—
88C2×D4×C107—42no—
89C2×D4×C107—42no—
90C2×D4×C107—42no—
91C2×D4×C107—42no—
92C2×D4×C107—42no—
93C2×D4×C107—42no—
94C2×D4×C107—41no—
95C2×D4×C107—41no—
96C2×D4×C107—42no—
97C22×C4×C107—22no—
98C22×C4×C107—22no—
99C22×C4×C107—21no—
100C22×C4×C107—21no—
101C22×C4×C107—22no—
102C22×C4×C107—22no—
103C22×C4×C107—22no—
104C22×C4×C107—22no—
105C22×C4×C107—22no—
106C22×C4×C107—22no—
107C22×C4×C107—21no—
108C22×C4×C107—21no—
109C22×C4×C107—24no—
110C22×C4×C107—21no—
111C22×C4×C107—21no—
112C22×C4×C107—21no—
113C22×C4×C107—41no—
114C22×C4×C107—41no—
115C22×C4×C107—41no—
116C22×C4×C107—41no—
117C22×C4×C107—41no—
118C22×C4×C107—41no—
119C22×C4×C107—41no—
120C22×C4×C107—48no—
121C22×C4×C107—48no—
122C22×C4×C107—42no—
123C22×C4×C107—42no—
124C22×C4×C107—42no—
125C22×C4×C107—42no—
126C22×C4×C107—42no—
127C22×C4×C107—42no—
128C22×C4×C107C22⋊C411yescharacteristic
129C22×C4×C107C22⋊C411yescharacteristic
130C22×C4×C107C22×C411yescharacteristic
131C22×C4×C107C2×D411yescharacteristic
132C22×C4×C107C2×D412yes—
133C22×C4×C107#4112yes—
134C2×C8×C107—24no—
135C2×C8×C107—48no—
136C2×C8×C107—42no—
137C2×C8×C107—42no—
138C4⋊C4×C107—22no—
139C4⋊C4×C107—41no—
140C4⋊C4×C107—41no—
141C22⋊C4×C107—42no—
142C22⋊C4×C107—48no—
143C22⋊C4×C107—42no—
144C22⋊C4×C107—42no—
145C22⋊C4×C107—41no—
146C22⋊C4×C107—41no—
147C22⋊C4×C107—42no—
148C22⋊C4×C107—41no—
149C22⋊C4×C107—41no—
150C23×C107—21no—
151C23×C107—21no—
152C23×C107—21no—
153C23×C107—21no—
154C23×C107—21no—
155C23×C107—21no—
156C23×C107—21no—
157C23×C107—21no—
158C23×C107—24no—
159C23×C107—24no—
160C23×C107—21no—
161C23×C107—21no—
162C23×C107—21no—
163C23×C107—21no—
164C23×C107—21no—
165C23×C107—21no—
166C23×C107—24no—
167C23×C107—24no—
168C23×C107—42no—
169C23×C107—42no—
170C23×C107—44no—
171C23×C107—44no—
172C23×C107—44no—
173C23×C107—44no—
174C23×C107—41no—
175C23×C107—41no—
176C23×C107—41no—
177C23×C107—41no—
178C23×C107—41no—
179C23×C107—41no—
180C23×C107—41no—
181C23×C107#9912yes—
182C23×C107#10212yes—
183C23×C107#10212yes—
184C23×C107#10412yes—
185C23×C107C2×C22⋊C411yescharacteristic
186C23×C107#12112yes—
187C23×C107C2×D811yescharacteristic
188C23×C107C2×SD1611yescharacteristic
189C23×C107#13512yes—
190D4×C107—82no—
191D4×C107—84no—
192D4×C107—84no—
193D4×C107—82no—
194D4×C107—82no—
195C2×C4×C107—24no—
196C2×C4×C107—24no—
197C2×C4×C107—21no—
198C2×C4×C107—21no—
199C2×C4×C107—21no—
200C2×C4×C107—21no—
201C2×C4×C107—21no—
202C2×C4×C107—21no—
203C2×C4×C107—21no—
204C2×C4×C107—21no—
205C2×C4×C107—21no—
206C2×C4×C107—42no—
207C2×C4×C107—42no—
208C2×C4×C107—44no—
209C2×C4×C107—44no—
210C2×C4×C107—44no—
211C2×C4×C107—42no—
212C2×C4×C107—42no—
213C2×C4×C107—44no—
214C2×C4×C107—44no—
215C2×C4×C107—44no—
216C2×C4×C107—41no—
217C2×C4×C107—41no—
218C2×C4×C107—41no—
219C2×C4×C107—41no—
220C2×C4×C107—41no—
221C2×C4×C107—41no—
222C2×C4×C107—41no—
223C2×C4×C107—41no—
224C2×C4×C107—41no—
225C2×C4×C107—82no—
226C2×C4×C107—82no—
227C2×C4×C107—82no—
228C2×C4×C107—82no—
229C2×C4×C107#9912yes—
230C2×C4×C107C4×D412yes—
231C2×C4×C107#12011yescharacteristic
232C2×C4×C107#12311yescharacteristic
233C8×C107—44no—
234C22×C107—22no—
235C22×C107—22no—
236C22×C107—22no—
237C22×C107—22no—
238C22×C107—22no—
239C22×C107—21no—
240C22×C107—21no—
241C22×C107—22no—
242C22×C107—22no—
243C22×C107—22no—
244C22×C107—22no—
245C22×C107—21no—
246C22×C107—22no—
247C22×C107—21no—
248C22×C107—22no—
249C22×C107—22no—
250C22×C107—22no—
251C22×C107—48no—
252C22×C107—48no—
253C22×C107—41no—
254C22×C107—41no—
255C22×C107—41no—
256C22×C107—41no—
257C22×C107—81no—
258C22×C107—81no—
259C22×C107—81no—
260C22×C107—81no—
261C22×C107—81no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107#32714yescomplemented
265C22×C107#38611yescharacteristic
266C22×C107C2×#9911yescharacteristic
267C22×C107C2×#9911yescharacteristic
268C22×C107C2×#10211yescharacteristic
269C22×C107#41611yescharacteristic
270C22×C107C2×#10411yescharacteristic
271C22×C107#42111yescharacteristic
272C22×C107#46512yes—
273C22×C107#46612yes—
274C4×C107—21no—
275C4×C107—22no—
276C4×C107—21no—
277C4×C107—22no—
278C4×C107—41no—
279C4×C107—84no—
280C4×C107—81no—
281C4×C107—81no—
282C4×C107—81no—
283#9113C10711yesmaximal, characteristic, direct product factor, Sylow
284C2×C107—22no—
285C2×C107—24no—
286C2×C107—22no—
287C2×C107—42no—
288C2×C107—161no—
289C2×C107C2×#32711yescharacteristic
290C2×C107#150111yescharacteristic
291C2×C107#151611yescharacteristic
292C2×C107#151911yescharacteristic
293C2×C107#187111yescharacteristic
294C2×C107#189311yescharacteristic
295C2×C107#189811yescharacteristic
296C22×C22⋊C8C2×C10711yescharacteristic, complemented
297#2847C2×C10711yescharacteristic
298C2×#327C2×C10712yescomplemented
299C22⋊#95C2×C10711yescharacteristic, complemented
300#1294C2×C10712yescomplemented
301C107#911311yescharacteristic, direct product factor, Sylow
302C24×C4C22×C10711yescharacteristic
303C23×C8—21no—
304C2×#121C4×C10711yescharacteristic, complemented
305C2×#121C4×C10711yescharacteristic, complemented
306C2×#121C22×C10711yescharacteristic
307C2×#120—21no—
308C22×C22⋊C4—21no—
309C2×C22⋊C8—21no—
310C2×C22⋊C8—24no—
311C2×C22⋊C8C22×C10712yes—
312#386—21no—
313#386—21no—
314#386—21no—
315#380C4×C10711yescharacteristic, complemented
316#380C4×C10711yescharacteristic, complemented
317#380C22×C10711yescharacteristic
318C2×#95—21no—
319C2×#95C22×C10712yes—
320#327—24no—
321C25D4×C10711yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C10711yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C10711yescharacteristic
332C23×C4C2×C4×C10711yescharacteristic
333C23×C4D4×C10711yescharacteristic
334C23×C4D4×C10711yescharacteristic
335C23×C4D4×C10711yescharacteristic
336C23×C4C23×C10711yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C10711yescharacteristic
348C2×C4⋊C4C2×C4×C10711yescharacteristic
349C2×C4⋊C4C2×C4×C10711yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C10714yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C10711yescharacteristic
376C24C22⋊C4×C10711yescharacteristic
377C24D8×C10712yes—
378C24SD16×C10712yes—
379C24C2×D4×C10711yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C10711yescharacteristic
425C22×C4C22⋊C4×C10711yescharacteristic
426C22×C4C22×C4×C10711yescharacteristic
427C22×C4C2×D4×C10711yescharacteristic
428C22×C4C2×D4×C10712yes—
429C22×C4#41×C10712yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C10712yes—
478C23#102×C10712yes—
479C23#102×C10712yes—
480C23#104×C10712yes—
481C23C2×C22⋊C4×C10711yescharacteristic
482C23#121×C10712yes—
483C23C2×D8×C10711yescharacteristic
484C23C2×SD16×C10711yescharacteristic
485C23#135×C10712yes—
486D4—82no—
487D4—84no—
488D4—82no—
489D4—82no—
490D4—84no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C10712yes—
526C2×C4C4×D4×C10712yes—
527C2×C4#120×C10711yescharacteristic
528C2×C4#123×C10711yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#327×C10714yescomplemented
561C22#386×C10711yescharacteristic
562C22C2×#99×C10711yescharacteristic
563C22C2×#99×C10711yescharacteristic
564C22C2×#102×C10711yescharacteristic
565C22#416×C10711yescharacteristic
566C22C2×#104×C10711yescharacteristic
567C22#421×C10711yescharacteristic
568C22#465×C10712yes—
569C22#466×C10712yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—161no—
584C2C2×#327×C10711yescharacteristic
585C2C107×#150111yescharacteristic
586C2C107×#151611yescharacteristic
587C2C107×#151911yescharacteristic
588C2C107×#187111yescharacteristic
589C2C107×#189311yescharacteristic
590C2C107×#189811yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC107×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C107C2semidirect
3. C2×#327×C107C2semidirect
4. C107×C22⋊#95C2semidirect
5. C107×#1294C2semidirect
8. C2×#121×C107C4semidirect
9. C2×#121×C107C4semidirect
19. #380×C107C4semidirect
20. #380×C107C4semidirect
65. C22⋊C8×C107D4semidirect
264. C22×C107#327semidirect
283. #9113C107direct (N × H)
296. C22×C22⋊C8C2×C107semidirect
298. C2×#327C2×C107semidirect
299. C22⋊#95C2×C107semidirect
300. #1294C2×C107semidirect
301. C107#9113direct (N × H)
304. C2×#121C4×C107semidirect
305. C2×#121C4×C107semidirect
315. #380C4×C107semidirect
316. #380C4×C107semidirect
361. C22⋊C8D4×C107semidirect
560. C22#327×C107semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1072
C107×#28472
C2×#327×C1072
C107×C22⋊#952
C107×#12942
#9113107