Finite Group Databasebeta

← C107×#9083 #41035047

Subgroups — C107×#9083 #41035047

Order 27392.

1100 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C107C211yesmaximal, characteristic, complemented
2C2×#386×C107C211yesmaximal, characteristic
3C107×#1779C211yesmaximal, characteristic, complemented
4C2×#323×C107C212yesmaximal, complemented
5C107×#1280C212yesmaximal, complemented
6C23×D4×C107C411yescharacteristic
7C24×C4×C107C2211yescharacteristic
8C22×M16×C107—21no—
9C22×C22⋊C4×C107C411yescharacteristic
10C22×C22⋊C4×C107C411yescharacteristic
11C22×C22⋊C4×C107C2211yescharacteristic
12#407×C107—24no—
13C2×C22⋊C8×C107—21no—
14C2×C22⋊C8×C107—21no—
15C2×C22⋊C8×C107—21no—
16C2×C22⋊C8×C107C2212yes—
17C2×C22⋊C8×C107C2212yes—
18#386×C107—21no—
19#386×C107—21no—
20#386×C107—21no—
21#386×C107—21no—
22C2×#95×C107C411yescharacteristic
23C2×#95×C107C2211yescharacteristic
24#323×C107—24no—
25C25×C107C2×C411yescharacteristic
26C25×C107C2×C411yescharacteristic
27C22×D4×C107—21no—
28C22×D4×C107—21no—
29C22×D4×C107—22no—
30C22×D4×C107—22no—
31C22×D4×C107—42no—
32C22×D4×C107—42no—
33C23×C4×C107—22no—
34C23×C4×C107—22no—
35C23×C4×C107—42no—
36C23×C4×C107—42no—
37C23×C4×C107C2×C411yescharacteristic
38C23×C4×C107C2×C411yescharacteristic
39C23×C4×C107C2×C411yescharacteristic
40C23×C4×C107C2×C411yescharacteristic
41C23×C4×C107D411yescharacteristic
42C23×C4×C107D411yescharacteristic
43C23×C4×C107D411yescharacteristic
44C23×C4×C107D411yescharacteristic
45C23×C4×C107C2311yescharacteristic
46C2×M16×C107—24no—
47C2×M16×C107—42no—
48C2×M16×C107—42no—
49C22×C8×C107—22no—
50C22×C8×C107—22no—
51C2×C22⋊C4×C107—21no—
52C2×C22⋊C4×C107—21no—
53C2×C22⋊C4×C107—21no—
54C2×C22⋊C4×C107—21no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—22no—
58C2×C22⋊C4×C107—22no—
59C2×C22⋊C4×C107—42no—
60C2×C22⋊C4×C107—42no—
61C22⋊C8×C107—24no—
62C22⋊C8×C107—22no—
63C22⋊C8×C107—22no—
64C22⋊C8×C107—22no—
65C22⋊C8×C107—42no—
66C22⋊C8×C107—42no—
67C22⋊C8×C107D414yescomplemented
68#95×C107—21no—
69#95×C107—21no—
70#95×C107—21no—
71#95×C107—21no—
72C24×C107—22no—
73C24×C107—22no—
74C24×C107—21no—
75C24×C107—21no—
76C24×C107—21no—
77C24×C107—22no—
78C24×C107—21no—
79C24×C107—22no—
80C24×C107—22no—
81C24×C107—22no—
82C24×C107—41no—
83C24×C107—41no—
84C24×C107—41no—
85C24×C107—41no—
86C24×C107—41no—
87C24×C107—41no—
88C24×C107C22⋊C411yescharacteristic
89C24×C107C22⋊C411yescharacteristic
90C24×C107M1612yescomplemented
91C24×C107C22×C411yescharacteristic
92C2×D4×C107—24no—
93C2×D4×C107—24no—
94C2×D4×C107—48no—
95C2×D4×C107—42no—
96C2×D4×C107—42no—
97C2×D4×C107—48no—
98C2×D4×C107—42no—
99C2×D4×C107—42no—
100C22×C4×C107—22no—
101C22×C4×C107—22no—
102C22×C4×C107—21no—
103C22×C4×C107—21no—
104C22×C4×C107—22no—
105C22×C4×C107—21no—
106C22×C4×C107—22no—
107C22×C4×C107—21no—
108C22×C4×C107—22no—
109C22×C4×C107—22no—
110C22×C4×C107—21no—
111C22×C4×C107—22no—
112C22×C4×C107—22no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—22no—
117C22×C4×C107—22no—
118C22×C4×C107—41no—
119C22×C4×C107—41no—
120C22×C4×C107—41no—
121C22×C4×C107—41no—
122C22×C4×C107—41no—
123C22×C4×C107—41no—
124C22×C4×C107—41no—
125C22×C4×C107—48no—
126C22×C4×C107—48no—
127C22×C4×C107—41no—
128C22×C4×C107—41no—
129C22×C4×C107—41no—
130C22×C4×C107—41no—
131C22×C4×C107—41no—
132C22×C4×C107—41no—
133C22×C4×C107C22⋊C411yescharacteristic
134C22×C4×C107C22⋊C411yescharacteristic
135C22×C4×C107M1612yescomplemented
136C22×C4×C107C2×D411yescharacteristic
137C22×C4×C107C2×D411yescharacteristic
138C22×C4×C107C2×D412yes—
139C22×C4×C107#4112yes—
140M16×C107—48no—
141C2×C8×C107—24no—
142C2×C8×C107—42no—
143C2×C8×C107—42no—
144C2×C8×C107—42no—
145C2×C8×C107—42no—
146C2×C8×C107—42no—
147C22⋊C4×C107—42no—
148C22⋊C4×C107—42no—
149C22⋊C4×C107—42no—
150C22⋊C4×C107—42no—
151C22⋊C4×C107—41no—
152C22⋊C4×C107—42no—
153C22⋊C4×C107—41no—
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—21no—
167C23×C107—21no—
168C23×C107—21no—
169C23×C107—21no—
170C23×C107—21no—
171C23×C107—21no—
172C23×C107—22no—
173C23×C107—24no—
174C23×C107—44no—
175C23×C107—44no—
176C23×C107—44no—
177C23×C107—44no—
178C23×C107—42no—
179C23×C107—42no—
180C23×C107—42no—
181C23×C107—42no—
182C23×C107—42no—
183C23×C107—42no—
184C23×C107—42no—
185C23×C107—42no—
186C23×C107—41no—
187C23×C107—41no—
188C23×C107—41no—
189C23×C107—41no—
190C23×C107—41no—
191C23×C107—41no—
192C23×C107—42no—
193C23×C107—82no—
194C23×C107—82no—
195C23×C107—82no—
196C23×C107—82no—
197C23×C107#9912yes—
198C23×C107#10012yes—
199C23×C107C2×C22⋊C411yescharacteristic
200C23×C107C4×D412yes—
201C23×C107C2×M1611yescharacteristic
202C23×C107C2×M1611yescharacteristic
203C23×C107#13112yes—
204D4×C107—48no—
205D4×C107—48no—
206C2×C4×C107—24no—
207C2×C4×C107—24no—
208C2×C4×C107—21no—
209C2×C4×C107—21no—
210C2×C4×C107—21no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—22no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—42no—
219C2×C4×C107—42no—
220C2×C4×C107—44no—
221C2×C4×C107—44no—
222C2×C4×C107—44no—
223C2×C4×C107—42no—
224C2×C4×C107—42no—
225C2×C4×C107—42no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—42no—
229C2×C4×C107—41no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—41no—
233C2×C4×C107—41no—
234C2×C4×C107—41no—
235C2×C4×C107—82no—
236C2×C4×C107—82no—
237C2×C4×C107#9912yes—
238C2×C4×C107#12011yescharacteristic
239C2×C4×C107#12112yes—
240C2×C4×C107#12311yescharacteristic
241C8×C107—44no—
242C8×C107—82no—
243C22×C107—22no—
244C22×C107—22no—
245C22×C107—21no—
246C22×C107—21no—
247C22×C107—21no—
248C22×C107—21no—
249C22×C107—22no—
250C22×C107—22no—
251C22×C107—22no—
252C22×C107—22no—
253C22×C107—22no—
254C22×C107—22no—
255C22×C107—22no—
256C22×C107—22no—
257C22×C107—48no—
258C22×C107—48no—
259C22×C107—41no—
260C22×C107—41no—
261C22×C107—41no—
262C22×C107—41no—
263C22×C107—41no—
264C22×C107—41no—
265C22×C107—41no—
266C22×C107—41no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—42no—
270C22×C107—84no—
271C22×C107—84no—
272C22×C107—81no—
273C22×C107—81no—
274C22×C107—81no—
275C22×C107—81no—
276C22×C107#38611yescharacteristic
277C22×C107#40711yescharacteristic
278C22×C107#40811yescharacteristic
279C22×C107C2×#9911yescharacteristic
280C22×C107C2×#9911yescharacteristic
281C22×C107C2×#10011yescharacteristic
282C22×C107#41311yescharacteristic
283C22×C107#43512yes—
284C22×C107#43612yes—
285C4×C107—21no—
286C4×C107—22no—
287C4×C107—22no—
288C4×C107—21no—
289C4×C107—41no—
290C4×C107—42no—
291C4×C107—81no—
292C4×C107—81no—
293#9083C10711yesmaximal, characteristic, direct product factor, Sylow
294C2×C107—22no—
295C2×C107—22no—
296C2×C107—42no—
297C2×C107—42no—
298C2×C107—82no—
299C2×C107#146211yescharacteristic
300C2×C107#146511yescharacteristic
301C2×C107#146811yescharacteristic
302C2×C107#147111yescharacteristic
303C2×C107#187011yescharacteristic
304C2×C107#189811yescharacteristic
305C2×C107#190011yescharacteristic
306C2×#407C2×C10711yescharacteristic, complemented
307C2×#386C2×C10711yescharacteristic
308#1779C2×C10711yescharacteristic, complemented
309C2×#323C2×C10712yescomplemented
310#1280C2×C10712yescomplemented
311C107#908311yescharacteristic, direct product factor, Sylow
312C23×D4C4×C10711yescharacteristic
313C24×C4C22×C10711yescharacteristic
314C22×M16—21no—
315C22×C22⋊C4C4×C10711yescharacteristic
316C22×C22⋊C4C4×C10711yescharacteristic
317C22×C22⋊C4C22×C10711yescharacteristic
318#407—24no—
319C2×C22⋊C8—21no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8—21no—
322C2×C22⋊C8C22×C10712yes—
323C2×C22⋊C8C22×C10712yes—
324#386—21no—
325#386—21no—
326#386—21no—
327#386—21no—
328C2×#95C4×C10711yescharacteristic
329C2×#95C22×C10711yescharacteristic
330#323—24no—
331C25C2×C4×C10711yescharacteristic
332C25C2×C4×C10711yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C10711yescharacteristic
344C23×C4C2×C4×C10711yescharacteristic
345C23×C4C2×C4×C10711yescharacteristic
346C23×C4C2×C4×C10711yescharacteristic
347C23×C4D4×C10711yescharacteristic
348C23×C4D4×C10711yescharacteristic
349C23×C4D4×C10711yescharacteristic
350C23×C4D4×C10711yescharacteristic
351C23×C4C23×C10711yescharacteristic
352C2×M16—24no—
353C2×M16—42no—
354C2×M16—42no—
355C22×C8—22no—
356C22×C8—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C10714yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24C22⋊C4×C10711yescharacteristic
395C24C22⋊C4×C10711yescharacteristic
396C24M16×C10712yescomplemented
397C24C22×C4×C10711yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—48no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C10711yescharacteristic
440C22×C4C22⋊C4×C10711yescharacteristic
441C22×C4M16×C10712yescomplemented
442C22×C4C2×D4×C10711yescharacteristic
443C22×C4C2×D4×C10711yescharacteristic
444C22×C4C2×D4×C10712yes—
445C22×C4#41×C10712yes—
446M16—48no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—24no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—42no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23#99×C10712yes—
504C23#100×C10712yes—
505C23C2×C22⋊C4×C10711yescharacteristic
506C23C4×D4×C10712yes—
507C23C2×M16×C10711yescharacteristic
508C23C2×M16×C10711yescharacteristic
509C23#131×C10712yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C10712yes—
544C2×C4#120×C10711yescharacteristic
545C2×C4#121×C10712yes—
546C2×C4#123×C10711yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—48no—
564C22—48no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—84no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22#386×C10711yescharacteristic
583C22#407×C10711yescharacteristic
584C22#408×C10711yescharacteristic
585C22C2×#99×C10711yescharacteristic
586C22C2×#99×C10711yescharacteristic
587C22C2×#100×C10711yescharacteristic
588C22#413×C10711yescharacteristic
589C22#435×C10712yes—
590C22#436×C10712yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—42no—
602C2—42no—
603C2—82no—
604C2C107×#146211yescharacteristic
605C2C107×#146511yescharacteristic
606C2C107×#146811yescharacteristic
607C2C107×#147111yescharacteristic
608C2C107×#187011yescharacteristic
609C2C107×#189811yescharacteristic
610C2C107×#190011yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC24C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC23×D4×C107C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#407×C107C2semidirect
3. C107×#1779C2semidirect
4. C2×#323×C107C2semidirect
5. C107×#1280C2semidirect
67. C22⋊C8×C107D4semidirect
90. C24×C107M16semidirect
135. C22×C4×C107M16semidirect
293. #9083C107direct (N × H)
306. C2×#407C2×C107semidirect
308. #1779C2×C107semidirect
309. C2×#323C2×C107semidirect
310. #1280C2×C107semidirect
311. C107#9083direct (N × H)
373. C22⋊C8D4×C107semidirect
396. C24M16×C107semidirect
441. C22×C4M16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C1072
C2×#386×C1072
C107×#17792
C2×#323×C1072
C107×#12802
#9083107