Finite Group Databasebeta

← C107×#9259 #41035223

Subgroups — C107×#9259 #41035223

Order 27392.

966 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C107C211yesmaximal, characteristic
2D4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
3C107×#1964C211yesmaximal, characteristic, complemented
4C107×#1786C211yesmaximal, characteristic, complemented
5C107×#1519C211yesmaximal, characteristic, complemented
6C107×#1289C211yesmaximal, characteristic, complemented
7C107×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C107C2211yescharacteristic
9C22×D8×C107C412yescomplemented
10C2×#121×C107C2211yescharacteristic
11C2×C4×D4×C107—21no—
12C22×C22⋊C4×C107—21no—
13#447×C107—21no—
14#447×C107—22no—
15#447×C107—21no—
16C2×#102×C107—22no—
17C2×#102×C107C412yescomplemented
18C2×#99×C107—21no—
19C2×#99×C107—21no—
20C2×C22⋊C8×C107C2211yescharacteristic
21C2×C22⋊C8×C107C2211yescharacteristic
22#390×C107—21no—
23#386×C107—22no—
24#380×C107C2211yescharacteristic
25#380×C107C2211yescharacteristic
26#379×C107—21no—
27C4×C22⋊C4×C107C2211yescharacteristic
28#327×C107—22no—
29C25×C107—21no—
30C22×D4×C107—21no—
31C22×D4×C107—21no—
32C22×D4×C107—21no—
33C22×D4×C107—21no—
34C22×D4×C107—44no—
35C22×D4×C107C2×C412yes—
36C22×D4×C107C2×C411yescharacteristic, complemented
37C22×D4×C107D411yescharacteristic
38C22×D4×C107D412yes—
39C22×D4×C107D411yescharacteristic
40C23×C4×C107—22no—
41C23×C4×C107C2311yescharacteristic
42C2×D8×C107—22no—
43C2×D8×C107—22no—
44C2×D8×C107—44no—
45C22×C8×C107—21no—
46C22×C8×C107C2×C412yescomplemented
47#121×C107—21no—
48#121×C107—21no—
49#121×C107—21no—
50#121×C107—21no—
51C4×D4×C107—44no—
52C2×C4⋊C4×C107—21no—
53C2×C4⋊C4×C107—21no—
54C2×C4⋊C4×C107C2×C411yescharacteristic, complemented
55C2×C22⋊C4×C107—22no—
56C2×C22⋊C4×C107—22no—
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—22no—
61C2×C22⋊C4×C107—42no—
62C2×C22⋊C4×C107—42no—
63C2×C22⋊C4×C107D411yescharacteristic
64C2×C22⋊C4×C107D411yescharacteristic
65C2×C42×C107—21no—
66#102×C107—22no—
67#102×C107—22no—
68#102×C107—44no—
69#99×C107—42no—
70#99×C107—42no—
71C22⋊C8×C107—21no—
72C22⋊C8×C107—21no—
73C22⋊C8×C107—21no—
74C22⋊C8×C107—21no—
75#95×C107—21no—
76#95×C107—21no—
77#95×C107D412yes—
78C24×C107—21no—
79C24×C107—21no—
80C24×C107—22no—
81C24×C107—22no—
82C24×C107—21no—
83C24×C107—44no—
84C24×C107—41no—
85C24×C107—41no—
86C24×C107—41no—
87C24×C107—41no—
88C24×C107—82no—
89C24×C107C2×D411yescharacteristic
90C2×D4×C107—24no—
91C2×D4×C107—24no—
92C2×D4×C107—24no—
93C2×D4×C107—21no—
94C2×D4×C107—22no—
95C2×D4×C107—21no—
96C2×D4×C107—22no—
97C2×D4×C107—21no—
98C2×D4×C107—21no—
99C2×D4×C107—42no—
100C2×D4×C107—42no—
101C2×D4×C107—42no—
102C2×D4×C107—42no—
103C2×D4×C107—44no—
104C2×D4×C107—44no—
105C2×D4×C107—44no—
106C2×D4×C107—41no—
107C2×D4×C107—41no—
108C2×D4×C107—41no—
109C2×D4×C107—41no—
110C2×D4×C107—41no—
111C2×D4×C107—41no—
112C2×D4×C107C22⋊C412yes—
113C2×D4×C107C22⋊C412yes—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—21no—
117C22×C4×C107—22no—
118C22×C4×C107—42no—
119C22×C4×C107—44no—
120C22×C4×C107—44no—
121C22×C4×C107—41no—
122C22×C4×C107—82no—
123C22×C4×C107C22×C411yescharacteristic
124C22×C4×C107C2×D411yescharacteristic
125C22×C4×C107C2×D411yescharacteristic
126C22×C4×C107C2×D411yescharacteristic
127C22×C4×C107#4111yescharacteristic
128C22×C4×C107#4111yescharacteristic
129D8×C107—44no—
130D8×C107—44no—
131C2×C8×C107—22no—
132C2×C8×C107—42no—
133C2×C8×C107—42no—
134C2×C8×C107—41no—
135C4⋊C4×C107—21no—
136C4⋊C4×C107—21no—
137C4⋊C4×C107—42no—
138C4⋊C4×C107—42no—
139C22⋊C4×C107—21no—
140C22⋊C4×C107—21no—
141C22⋊C4×C107—21no—
142C22⋊C4×C107—44no—
143C22⋊C4×C107—44no—
144C22⋊C4×C107—41no—
145C22⋊C4×C107—41no—
146C22⋊C4×C107—41no—
147C22⋊C4×C107—41no—
148C22⋊C4×C107—41no—
149C22⋊C4×C107—41no—
150C22⋊C4×C107—82no—
151C22⋊C4×C107D812yescomplemented
152C42×C107—42no—
153C23×C107—24no—
154C23×C107—22no—
155C23×C107—22no—
156C23×C107—41no—
157C23×C107—41no—
158C23×C107—44no—
159C23×C107—44no—
160C23×C107—42no—
161C23×C107—42no—
162C23×C107—42no—
163C23×C107—41no—
164C23×C107—41no—
165C23×C107—42no—
166C23×C107—42no—
167C23×C107—41no—
168C23×C107—41no—
169C23×C107—42no—
170C23×C107—42no—
171C23×C107—41no—
172C23×C107—41no—
173C23×C107—41no—
174C23×C107—82no—
175C23×C107—82no—
176C23×C107—81no—
177C23×C107—81no—
178C23×C107—84no—
179C23×C107—84no—
180C23×C107—84no—
181C23×C107—84no—
182C23×C107C4×D411yescharacteristic
183C23×C107#12011yescharacteristic
184C23×C107#12111yescharacteristic
185C23×C107C2×D811yescharacteristic
186C23×C107#13511yescharacteristic
187C23×C107AGL(1,ℤ/8)11yescharacteristic
188C23×C107AGL(1,ℤ/8)11yescharacteristic
189D4×C107—24no—
190D4×C107—22no—
191D4×C107—22no—
192D4×C107—22no—
193D4×C107—44no—
194D4×C107—44no—
195D4×C107—42no—
196D4×C107—42no—
197D4×C107—81no—
198D4×C107—81no—
199D4×C107—81no—
200D4×C107—81no—
201D4×C107—81no—
202D4×C107#9914yescomplemented
203C2×C4×C107—22no—
204C2×C4×C107—22no—
205C2×C4×C107—22no—
206C2×C4×C107—22no—
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—42no—
214C2×C4×C107—41no—
215C2×C4×C107—42no—
216C2×C4×C107—41no—
217C2×C4×C107—41no—
218C2×C4×C107—41no—
219C2×C4×C107—42no—
220C2×C4×C107—41no—
221C2×C4×C107—88no—
222C2×C4×C107—81no—
223C2×C4×C107—81no—
224C2×C4×C107—81no—
225C2×C4×C107C2×C22⋊C411yescharacteristic
226C2×C4×C107C4×D411yescharacteristic
227C2×C4×C107#12111yescharacteristic
228C2×C4×C107#12311yescharacteristic
229C8×C107—42no—
230C8×C107—81no—
231C22×C107—21no—
232C22×C107—21no—
233C22×C107—21no—
234C22×C107—21no—
235C22×C107—21no—
236C22×C107—21no—
237C22×C107—24no—
238C22×C107—41no—
239C22×C107—41no—
240C22×C107—41no—
241C22×C107—41no—
242C22×C107—44no—
243C22×C107—44no—
244C22×C107—42no—
245C22×C107—42no—
246C22×C107—42no—
247C22×C107—42no—
248C22×C107—42no—
249C22×C107—84no—
250C22×C107—84no—
251C22×C107—84no—
252C22×C107—84no—
253C22×C107—82no—
254C22×C107—82no—
255C22×C107—81no—
256C22×C107—81no—
257C22×C107—81no—
258C22×C107—161no—
259C22×C107—161no—
260C22×C107#38611yescharacteristic
261C22×C107C4×D811yescharacteristic
262C22×C107#44211yescharacteristic
263C22×C107#44711yescharacteristic
264C22×C107#44911yescharacteristic
265C22×C107#45911yescharacteristic
266C22×C107#46311yescharacteristic
267C4×C107—21no—
268C4×C107—21no—
269C4×C107—21no—
270C4×C107—42no—
271C4×C107—81no—
272C4×C107—82no—
273C4×C107—81no—
274C4×C107—161no—
275C4×C107C2×#9912yes—
276#9259C10711yesmaximal, characteristic, direct product factor, Sylow
277C2×C107—21no—
278C2×C107—21no—
279C2×C107—21no—
280C2×C107—21no—
281C2×C107—21no—
282C2×C107—21no—
283C2×C107—44no—
284C2×C107—82no—
285C2×C107—161no—
286C2×C107#187911yescharacteristic
287C2×C107#189811yescharacteristic
288C2×C107#190411yescharacteristic
289C2×#447C2×C10711yescharacteristic
290D4×C22⋊C4C2×C10711yescharacteristic, complemented
291#1964C2×C10711yescharacteristic, complemented
292#1786C2×C10711yescharacteristic, complemented
293#1519C2×C10711yescharacteristic, complemented
294#1289C2×C10711yescharacteristic, complemented
295#1282C2×C10711yescharacteristic, complemented
296C107#925911yescharacteristic, direct product factor, Sylow
297C23×D4C22×C10711yescharacteristic
298C22×D8C4×C10712yescomplemented
299C2×#121C22×C10711yescharacteristic
300C2×C4×D4—21no—
301C22×C22⋊C4—21no—
302#447—21no—
303#447—22no—
304#447—21no—
305C2×#102—22no—
306C2×#102C4×C10712yescomplemented
307C2×#99—21no—
308C2×#99—21no—
309C2×C22⋊C8C22×C10711yescharacteristic
310C2×C22⋊C8C22×C10711yescharacteristic
311#390—21no—
312#386—22no—
313#380C22×C10711yescharacteristic
314#380C22×C10711yescharacteristic
315#379—21no—
316C4×C22⋊C4C22×C10711yescharacteristic
317#327—22no—
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—44no—
324C22×D4C2×C4×C10712yes—
325C22×D4C2×C4×C10711yescharacteristic, complemented
326C22×D4D4×C10711yescharacteristic
327C22×D4D4×C10712yes—
328C22×D4D4×C10711yescharacteristic
329C23×C4—22no—
330C23×C4C23×C10711yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—44no—
334C22×C8—21no—
335C22×C8C2×C4×C10712yescomplemented
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C2×C4×C10711yescharacteristic, complemented
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4D4×C10711yescharacteristic
353C2×C22⋊C4D4×C10711yescharacteristic
354C2×C42—21no—
355#102—22no—
356#102—22no—
357#102—44no—
358#99—42no—
359#99—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364#95—21no—
365#95—21no—
366#95D4×C10712yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—44no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—82no—
378C24C2×D4×C10711yescharacteristic
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C22⋊C4×C10712yes—
402C2×D4C22⋊C4×C10712yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—82no—
412C22×C4C22×C4×C10711yescharacteristic
413C22×C4C2×D4×C10711yescharacteristic
414C22×C4C2×D4×C10711yescharacteristic
415C22×C4C2×D4×C10711yescharacteristic
416C22×C4#41×C10711yescharacteristic
417C22×C4#41×C10711yescharacteristic
418D8—44no—
419D8—44no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—41no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—82no—
440C22⋊C4D8×C10712yescomplemented
441C42—42no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—82no—
464C23—82no—
465C23—81no—
466C23—81no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C4×D4×C10711yescharacteristic
472C23#120×C10711yescharacteristic
473C23#121×C10711yescharacteristic
474C23C2×D8×C10711yescharacteristic
475C23#135×C10711yescharacteristic
476C23AGL(1,ℤ/8)×C10711yescharacteristic
477C23AGL(1,ℤ/8)×C10711yescharacteristic
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—44no—
483D4—44no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—81no—
488D4—81no—
489D4—81no—
490D4—81no—
491D4#99×C10714yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—88no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4C2×C22⋊C4×C10711yescharacteristic
515C2×C4C4×D4×C10711yescharacteristic
516C2×C4#121×C10711yescharacteristic
517C2×C4#123×C10711yescharacteristic
518C8—42no—
519C8—81no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—161no—
548C22—161no—
549C22#386×C10711yescharacteristic
550C22C4×D8×C10711yescharacteristic
551C22#442×C10711yescharacteristic
552C22#447×C10711yescharacteristic
553C22#449×C10711yescharacteristic
554C22#459×C10711yescharacteristic
555C22#463×C10711yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—161no—
564C4C2×#99×C10712yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—44no—
572C2—82no—
573C2—161no—
574C2C107×#187911yescharacteristic
575C2C107×#189811yescharacteristic
576C2C107×#190411yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC2×#447×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. D4×C22⋊C4×C107C2semidirect
3. C107×#1964C2semidirect
4. C107×#1786C2semidirect
5. C107×#1519C2semidirect
6. C107×#1289C2semidirect
7. C107×#1282C2semidirect
9. C22×D8×C107C4semidirect
17. C2×#102×C107C4semidirect
36. C22×D4×C107C2×C4semidirect
46. C22×C8×C107C2×C4semidirect
54. C2×C4⋊C4×C107C2×C4semidirect
151. C22⋊C4×C107D8semidirect
202. D4×C107#99semidirect
276. #9259C107direct (N × H)
290. D4×C22⋊C4C2×C107semidirect
291. #1964C2×C107semidirect
292. #1786C2×C107semidirect
293. #1519C2×C107semidirect
294. #1289C2×C107semidirect
295. #1282C2×C107semidirect
296. C107#9259direct (N × H)
298. C22×D8C4×C107semidirect
306. C2×#102C4×C107semidirect
325. C22×D4C2×C4×C107semidirect
335. C22×C8C2×C4×C107semidirect
343. C2×C4⋊C4C2×C4×C107semidirect
440. C22⋊C4D8×C107semidirect
491. D4#99×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1072
D4×C22⋊C4×C1072
C107×#19642
C107×#17862
C107×#15192
C107×#12892
C107×#12822
#9259107