Finite Group Databasebeta

← C107×#13080 #41039044

Subgroups — C107×#13080 #41039044

Order 27392.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C107C211yesmaximal, characteristic
2C107×#2405C211yesmaximal, characteristic
3C2×#352×C107C212yesmaximal, complemented
4C107×#1781C211yesmaximal, characteristic
5C107×#1390C212yesmaximal, complemented
6C23×D4×C107C2211yescharacteristic
7C22×M16×C107—21no—
8C2×#123×C107C411yescharacteristic, complemented
9C2×#123×C107C2211yescharacteristic
10C22×C22⋊C4×C107C411yescharacteristic, complemented
11C2×#100×C107—21no—
12C2×#100×C107—24no—
13C2×#100×C107C2212yes—
14C2×#99×C107—21no—
15C2×#99×C107C2212yes—
16#394×C107—21no—
17#394×C107—21no—
18#386×C107C411yescharacteristic, complemented
19#386×C107C2211yescharacteristic
20#385×C107—21no—
21#379×C107—21no—
22#379×C107—21no—
23#379×C107C411yescharacteristic, complemented
24#352×C107—24no—
25C25×C107C2×C411yescharacteristic
26C25×C107D411yescharacteristic
27C22×D4×C107—22no—
28C22×D4×C107—22no—
29C22×D4×C107—42no—
30C22×D4×C107—41no—
31C22×D4×C107—41no—
32C22×D4×C107C2×C411yescharacteristic
33C22×D4×C107D411yescharacteristic
34C22×D4×C107D411yescharacteristic
35C22×D4×C107C2311yescharacteristic
36C23×C4×C107C2×C411yescharacteristic
37C23×C4×C107C2×C411yescharacteristic
38C23×C4×C107D411yescharacteristic
39C2×M16×C107—24no—
40C2×M16×C107—22no—
41C2×M16×C107—41no—
42C2×M16×C107—42no—
43C22×C8×C107—41no—
44#123×C107—22no—
45#123×C107—22no—
46#123×C107—42no—
47C2×C4⋊C4×C107—21no—
48C2×C4⋊C4×C107—21no—
49C2×C22⋊C4×C107—21no—
50C2×C22⋊C4×C107—21no—
51C2×C22⋊C4×C107—21no—
52C2×C22⋊C4×C107—21no—
53C2×C22⋊C4×C107—21no—
54C2×C22⋊C4×C107—22no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—41no—
59C2×C22⋊C4×C107—41no—
60C2×C22⋊C4×C107—41no—
61C2×C22⋊C4×C107—41no—
62C2×C22⋊C4×C107C2×C411yescharacteristic
63C2×C22⋊C4×C107C2×C411yescharacteristic
64#100×C107—24no—
65#100×C107—22no—
66#100×C107D414yes—
67#99×C107—22no—
68#99×C107—22no—
69#99×C107—42no—
70#95×C107—21no—
71#95×C107—21no—
72C24×C107—21no—
73C24×C107—21no—
74C24×C107—21no—
75C24×C107—21no—
76C24×C107—22no—
77C24×C107—22no—
78C24×C107—41no—
79C24×C107—41no—
80C24×C107—42no—
81C24×C107—42no—
82C24×C107—81no—
83C24×C107—81no—
84C24×C107C22⋊C411yescharacteristic
85C24×C107C22⋊C411yescharacteristic
86C24×C107C22⋊C411yescharacteristic
87C24×C107C22×C411yescharacteristic
88C24×C107C2×D411yescharacteristic
89C2×D4×C107—22no—
90C2×D4×C107—22no—
91C2×D4×C107—22no—
92C2×D4×C107—22no—
93C2×D4×C107—21no—
94C2×D4×C107—21no—
95C2×D4×C107—41no—
96C2×D4×C107—41no—
97C2×D4×C107—41no—
98C2×D4×C107—41no—
99C2×D4×C107—41no—
100C2×D4×C107—41no—
101C2×D4×C107—44no—
102C2×D4×C107—44no—
103C2×D4×C107—44no—
104C2×D4×C107—44no—
105C2×D4×C107C2×D412yes—
106C2×D4×C107#4112yes—
107C22×C4×C107—21no—
108C22×C4×C107—21no—
109C22×C4×C107—22no—
110C22×C4×C107—21no—
111C22×C4×C107—21no—
112C22×C4×C107—21no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—22no—
117C22×C4×C107—41no—
118C22×C4×C107—41no—
119C22×C4×C107—41no—
120C22×C4×C107—42no—
121C22×C4×C107—81no—
122C22×C4×C107C22⋊C411yescharacteristic
123C22×C4×C107C2×D411yescharacteristic
124M16×C107—24no—
125M16×C107—44no—
126M16×C107—42no—
127C2×C8×C107—44no—
128C2×C8×C107—42no—
129C4⋊C4×C107—42no—
130C4⋊C4×C107—41no—
131C4⋊C4×C107—41no—
132C22⋊C4×C107—22no—
133C22⋊C4×C107—42no—
134C22⋊C4×C107—42no—
135C22⋊C4×C107—42no—
136C22⋊C4×C107—41no—
137C22⋊C4×C107—41no—
138C22⋊C4×C107—42no—
139C22⋊C4×C107—41no—
140C22⋊C4×C107—42no—
141C22⋊C4×C107—42no—
142C22⋊C4×C107—81no—
143C22⋊C4×C107—81no—
144C22⋊C4×C107—81no—
145C22⋊C4×C107—82no—
146C22⋊C4×C107—82no—
147C23×C107—22no—
148C23×C107—21no—
149C23×C107—21no—
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—21no—
159C23×C107—21no—
160C23×C107—41no—
161C23×C107—42no—
162C23×C107—42no—
163C23×C107—42no—
164C23×C107—42no—
165C23×C107—41no—
166C23×C107—41no—
167C23×C107—41no—
168C23×C107—41no—
169C23×C107—41no—
170C23×C107—41no—
171C23×C107—42no—
172C23×C107—42no—
173C23×C107—41no—
174C23×C107—41no—
175C23×C107—42no—
176C23×C107—42no—
177C23×C107—81no—
178C23×C107—81no—
179C23×C107—81no—
180C23×C107—81no—
181C23×C107—84no—
182C23×C107—84no—
183C23×C107—84no—
184C23×C107—84no—
185C23×C107#9911yescharacteristic
186C23×C107#9911yescharacteristic
187C23×C107C2×C22⋊C411yescharacteristic
188C23×C107C4×D412yes—
189C23×C107#12112yes—
190D4×C107—42no—
191D4×C107—42no—
192D4×C107—44no—
193D4×C107—44no—
194D4×C107—42no—
195D4×C107—42no—
196C2×C4×C107—22no—
197C2×C4×C107—22no—
198C2×C4×C107—22no—
199C2×C4×C107—22no—
200C2×C4×C107—21no—
201C2×C4×C107—21no—
202C2×C4×C107—21no—
203C2×C4×C107—21no—
204C2×C4×C107—41no—
205C2×C4×C107—41no—
206C2×C4×C107—41no—
207C2×C4×C107—41no—
208C2×C4×C107—41no—
209C2×C4×C107—41no—
210C2×C4×C107—41no—
211C2×C4×C107—41no—
212C2×C4×C107—41no—
213C2×C4×C107—41no—
214C2×C4×C107—41no—
215C2×C4×C107—41no—
216C2×C4×C107—82no—
217C2×C4×C107—82no—
218C2×C4×C107—82no—
219C2×C4×C107—82no—
220C2×C4×C107—82no—
221C2×C4×C107#9912yes—
222C2×C4×C107#12011yescharacteristic
223C2×C4×C107#12311yescharacteristic
224C8×C107—44no—
225C22×C107—21no—
226C22×C107—21no—
227C22×C107—21no—
228C22×C107—21no—
229C22×C107—21no—
230C22×C107—21no—
231C22×C107—21no—
232C22×C107—22no—
233C22×C107—22no—
234C22×C107—42no—
235C22×C107—42no—
236C22×C107—42no—
237C22×C107—42no—
238C22×C107—42no—
239C22×C107—42no—
240C22×C107—41no—
241C22×C107—41no—
242C22×C107—41no—
243C22×C107—41no—
244C22×C107—41no—
245C22×C107—41no—
246C22×C107—41no—
247C22×C107—41no—
248C22×C107—41no—
249C22×C107—41no—
250C22×C107—81no—
251C22×C107—84no—
252C22×C107—84no—
253C22×C107—81no—
254C22×C107—81no—
255C22×C107—81no—
256C22×C107—84no—
257C22×C107—84no—
258C22×C107#35212yescomplemented
259C22×C107#38611yescharacteristic
260C22×C107C2×#9911yescharacteristic
261C22×C107C2×#9911yescharacteristic
262C4×C107—21no—
263C4×C107—22no—
264C4×C107—21no—
265C4×C107—81no—
266C4×C107—81no—
267C4×C107—81no—
268C4×C107—81no—
269C4×C107—162no—
270#13080C10711yesmaximal, characteristic, direct product factor, Sylow
271C2×C107—21no—
272C2×C107—21no—
273C2×C107—22no—
274C2×C107—42no—
275C2×C107—41no—
276C2×C107—42no—
277C2×C107—81no—
278C2×C107—81no—
279C2×C107#189811yescharacteristic
280C2×C107C2×#35211yescharacteristic
281C2×C107#212111yescharacteristic
282C22×#100C2×C10711yescharacteristic
283#2405C2×C10711yescharacteristic
284C2×#352C2×C10712yescomplemented
285#1781C2×C10711yescharacteristic
286#1390C2×C10712yescomplemented
287C107#1308011yescharacteristic, direct product factor, Sylow
288C23×D4C22×C10711yescharacteristic
289C22×M16—21no—
290C2×#123C4×C10711yescharacteristic, complemented
291C2×#123C22×C10711yescharacteristic
292C22×C22⋊C4C4×C10711yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C10712yes—
296C2×#99—21no—
297C2×#99C22×C10712yes—
298#394—21no—
299#394—21no—
300#386C4×C10711yescharacteristic, complemented
301#386C22×C10711yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C10711yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C10711yescharacteristic
308C25D4×C10711yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C10711yescharacteristic
315C22×D4D4×C10711yescharacteristic
316C22×D4D4×C10711yescharacteristic
317C22×D4C23×C10711yescharacteristic
318C23×C4C2×C4×C10711yescharacteristic
319C23×C4C2×C4×C10711yescharacteristic
320C23×C4D4×C10711yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C10711yescharacteristic
345C2×C22⋊C4C2×C4×C10711yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C10714yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C10711yescharacteristic
367C24C22⋊C4×C10711yescharacteristic
368C24C22⋊C4×C10711yescharacteristic
369C24C22×C4×C10711yescharacteristic
370C24C2×D4×C10711yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C10712yes—
388C2×D4#41×C10712yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C10711yescharacteristic
405C22×C4C2×D4×C10711yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C10711yescharacteristic
468C23#99×C10711yescharacteristic
469C23C2×C22⋊C4×C10711yescharacteristic
470C23C4×D4×C10712yes—
471C23#121×C10712yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C10712yes—
504C2×C4#120×C10711yescharacteristic
505C2×C4#123×C10711yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C10712yescomplemented
541C22#386×C10711yescharacteristic
542C22C2×#99×C10711yescharacteristic
543C22C2×#99×C10711yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C107×#189811yescharacteristic
561C2C2×#352×C10711yescharacteristic
562C2C107×#212111yescharacteristic
subgroupG/H
center, socleC22×C107C2×#99
commutatorC24C22×C4×C107
Frattini, cosocleC22×D4C23×C107
prime radicalC23×D4×C107C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C24×C107 ◁ C23×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C107C2semidirect
5. C107×#1390C2semidirect
8. C2×#123×C107C4semidirect
10. C22×C22⋊C4×C107C4semidirect
18. #386×C107C4semidirect
23. #379×C107C4semidirect
258. C22×C107#352semidirect
270. #13080C107direct (N × H)
284. C2×#352C2×C107semidirect
286. #1390C2×C107semidirect
287. C107#13080direct (N × H)
290. C2×#123C4×C107semidirect
292. C22×C22⋊C4C4×C107semidirect
300. #386C4×C107semidirect
305. #379C4×C107semidirect
540. C22#352×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1072
C107×#24052
C2×#352×C1072
C107×#17812
C107×#13902
#13080107