Finite Group Databasebeta

← C107×#24256 #41050220

Subgroups — C107×#24256 #41050220

Order 27392.

1510 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C107C211yesmaximal, characteristic, complemented
2C2×#463×C107C211yesmaximal, characteristic, complemented
3C2×#449×C107C211yesmaximal, characteristic, complemented
4C2×#448×C107C211yesmaximal, characteristic, complemented
5C2×#440×C107C211yesmaximal, characteristic, complemented
6C107×#2537C211yesmaximal, characteristic, complemented
7C107×#2036C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1959C211yesmaximal, characteristic, complemented
12C107×#1955C211yesmaximal, characteristic, complemented
13C107×#1803C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×Q8×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21#548×C107—24no—
22#548×C107—24no—
23C2×#124×C107—21no—
24C2×#124×C107C2211yescharacteristic
25C2×C22⋊Q8×C107—21no—
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×#121×C107—21no—
28C2×#121×C107—21no—
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×#121×C107C2211yescharacteristic
32C2×C4×Q8×C107C2211yescharacteristic
33C2×C4×D4×C107—21no—
34C2×C4×D4×C107C2211yescharacteristic
35C2×C4×D4×C107C2211yescharacteristic
36#463×C107—24no—
37#449×C107—24no—
38#448×C107—24no—
39#440×C107—24no—
40C2×#107×C107C2211yescharacteristic
41C2×C4⋊C8×C107C2211yescharacteristic
42C2×#103×C107C2211yescharacteristic
43C2×#103×C107C2211yescharacteristic
44C2×#103×C107C2211yescharacteristic
45C2×#103×C107C2211yescharacteristic
46C2×#103×C107C2211yescharacteristic
47C2×#103×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×#102×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55C2×C22⋊C8×C107C2211yescharacteristic
56C2×#97×C107C2211yescharacteristic
57#394×C107—21no—
58#394×C107—21no—
59#384×C107C2211yescharacteristic
60#380×C107—21no—
61#380×C107C2211yescharacteristic
62#380×C107C2211yescharacteristic
63#340×C107C2211yescharacteristic
64#340×C107C2211yescharacteristic
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—41no—
70C2×#41×C107—41no—
71C22×Q8×C107—22no—
72C22×Q8×C107—22no—
73C22×Q8×C107—21no—
74C22×Q8×C107—22no—
75C22×Q8×C107—22no—
76C22×Q8×C107—41no—
77C22×Q8×C107—41no—
78C22×Q8×C107C2311yescharacteristic
79C22×Q8×C107C2311yescharacteristic
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107D411yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C23×C4×C107—21no—
88C23×C4×C107—21no—
89C23×C4×C107—21no—
90C23×C4×C107C2311yescharacteristic
91C23×C4×C107C2311yescharacteristic
92C2×SD16×C107—22no—
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—41no—
97C2×SD16×C107D414yescomplemented
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—41no—
101C22×C8×C107C2311yescharacteristic
102C22×C8×C107C2311yescharacteristic
103C22×C8×C107C2311yescharacteristic
104C22×C8×C107C2311yescharacteristic
105#124×C107—28no—
106#124×C107—22no—
107#124×C107D414yescomplemented
108C22⋊Q8×C107—28no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—22no—
111#121×C107—28no—
112#121×C107—22no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—41no—
117#121×C107—41no—
118#121×C107—44no—
119C4×Q8×C107—22no—
120C4×Q8×C107D414yescomplemented
121C4×D4×C107—28no—
122C4×D4×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125C4×D4×C107—22no—
126C2×C4⋊C4×C107—21no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107—21no—
129C2×C4⋊C4×C107—21no—
130C2×C4⋊C4×C107D411yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C4⋊C4×C107C2311yescharacteristic
134C2×C4⋊C4×C107C2311yescharacteristic
135C2×C22⋊C4×C107—21no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—21no—
138C2×C22⋊C4×C107—21no—
139C2×C22⋊C4×C107—21no—
140C2×C22⋊C4×C107—21no—
141C2×C22⋊C4×C107—21no—
142C2×C22⋊C4×C107—21no—
143C2×C22⋊C4×C107—21no—
144C2×C22⋊C4×C107D411yescharacteristic
145C2×C22⋊C4×C107D411yescharacteristic
146C2×C42×C107—21no—
147C2×C42×C107C2311yescharacteristic
148#107×C107—22no—
149C4⋊C8×C107—22no—
150#103×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#103×C107—22no—
154#103×C107—22no—
155#103×C107—41no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—22no—
159#102×C107—41no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107—41no—
163C22⋊C8×C107—41no—
164#97×C107—22no—
165#95×C107—21no—
166#95×C107—21no—
167C24×C107—21no—
168C24×C107—21no—
169C24×C107C2×D411yescharacteristic
170C24×C107C2×D411yescharacteristic
171#41×C107—44no—
172#41×C107—44no—
173#41×C107—44no—
174#41×C107—44no—
175C2×Q8×C107—24no—
176C2×Q8×C107—21no—
177C2×Q8×C107—21no—
178C2×Q8×C107—21no—
179C2×Q8×C107—21no—
180C2×Q8×C107—21no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—42no—
185C2×Q8×C107—42no—
186C2×Q8×C107—44no—
187C2×Q8×C107—44no—
188C2×Q8×C107—44no—
189C2×Q8×C107—44no—
190C2×Q8×C107C2×D412yes—
191C2×Q8×C107C2×D412yes—
192C2×Q8×C107C2×D412yes—
193C2×Q8×C107#4112yes—
194C2×D4×C107—24no—
195C2×D4×C107—24no—
196C2×D4×C107—22no—
197C2×D4×C107—22no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—41no—
209C2×D4×C107—42no—
210C2×D4×C107—42no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—42no—
215C2×D4×C107—42no—
216C2×D4×C107—42no—
217C2×D4×C107—81no—
218C2×D4×C107—81no—
219C2×D4×C107C2×D412yes—
220C2×D4×C107C2×D412yes—
221C22×C4×C107—21no—
222C22×C4×C107—24no—
223C22×C4×C107—24no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—21no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—42no—
242C22×C4×C107—42no—
243C22×C4×C107—42no—
244C22×C4×C107—42no—
245C22×C4×C107—42no—
246C22×C4×C107—42no—
247C22×C4×C107—42no—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2411yescharacteristic
253SD16×C107—28no—
254SD16×C107—44no—
255D8×C107—44no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C2×C8×C107—21no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107C2×D412yes—
268C4⋊C4×C107—24no—
269C4⋊C4×C107—24no—
270C4⋊C4×C107—22no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—42no—
279C4⋊C4×C107—81no—
280C4⋊C4×C107C2×D412yes—
281C22⋊C4×C107—24no—
282C22⋊C4×C107—24no—
283C22⋊C4×C107—24no—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—22no—
286C22⋊C4×C107—22no—
287C22⋊C4×C107—42no—
288C22⋊C4×C107—42no—
289C22⋊C4×C107—42no—
290C22⋊C4×C107—42no—
291C22⋊C4×C107—42no—
292C42×C107—24no—
293C42×C107C2×D412yes—
294C42×C107C2×D412yes—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—22no—
303C23×C107—22no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—41no—
311C23×C107—41no—
312C23×C107—41no—
313C23×C107—41no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107AGL(1,ℤ/8)12yes—
323C23×C107C22×D411yescharacteristic
324Q8×C107—22no—
325Q8×C107—22no—
326Q8×C107—22no—
327Q8×C107—22no—
328Q8×C107—22no—
329Q8×C107—48no—
330Q8×C107—41no—
331Q8×C107—41no—
332Q8×C107#12114yescomplemented
333D4×C107—22no—
334D4×C107—22no—
335D4×C107—22no—
336D4×C107—22no—
337D4×C107—44no—
338D4×C107—48no—
339D4×C107—48no—
340D4×C107—41no—
341D4×C107—41no—
342D4×C107—41no—
343D4×C107—41no—
344D4×C107—84no—
345D4×C107—84no—
346C2×C4×C107—22no—
347C2×C4×C107—22no—
348C2×C4×C107—22no—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—21no—
352C2×C4×C107—21no—
353C2×C4×C107—22no—
354C2×C4×C107—22no—
355C2×C4×C107—21no—
356C2×C4×C107—21no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—48no—
362C2×C4×C107—48no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107—41no—
366C2×C4×C107—41no—
367C2×C4×C107—41no—
368C2×C4×C107—41no—
369C2×C4×C107—41no—
370C2×C4×C107—41no—
371C2×C4×C107—41no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—84no—
385C2×C4×C107#12012yes—
386C2×C4×C107#12012yes—
387C2×C4×C107C22×D411yescharacteristic
388C2×C4×C107C22×D411yescharacteristic
389C2×C4×C107C22×D411yescharacteristic
390C2×C4×C107C2×#4111yescharacteristic
391C2×C4×C107H(5,𝔽2)11yescharacteristic
392C2×C4×C107H(5,𝔽2)11yescharacteristic
393C8×C107—22no—
394C8×C107—41no—
395C8×C107—41no—
396C8×C107—41no—
397C22×C107—22no—
398C22×C107—22no—
399C22×C107—22no—
400C22×C107—41no—
401C22×C107—41no—
402C22×C107—41no—
403C22×C107—41no—
404C22×C107—42no—
405C22×C107—41no—
406C22×C107—42no—
407C22×C107—41no—
408C22×C107—42no—
409C22×C107—41no—
410C22×C107—42no—
411C22×C107—41no—
412C22×C107—42no—
413C22×C107—41no—
414C22×C107—42no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—81no—
418C22×C107—81no—
419C22×C107—81no—
420C22×C107—81no—
421C22×C107—81no—
422C22×C107—81no—
423C22×C107—81no—
424C22×C107—81no—
425C22×C107C2×#12011yescharacteristic
426C22×C107D4211yescharacteristic
427C22×C107#54611yescharacteristic
428C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C107#57511yescharacteristic
430C22×C107#57711yescharacteristic
431C22×C107#57811yescharacteristic
432C4×C107—24no—
433C4×C107—22no—
434C4×C107—22no—
435C4×C107—41no—
436C4×C107—41no—
437C4×C107—42no—
438C4×C107—42no—
439C4×C107—81no—
440C4×C107—81no—
441C4×C107—81no—
442C4×C107C2×#12111yescharacteristic
443C4×C107#53511yescharacteristic
444C4×C107D4211yescharacteristic
445C4×C107#54611yescharacteristic
446#24256C10711yesmaximal, characteristic, direct product factor, Sylow
447C2×C107—42no—
448C2×C107—81no—
449C2×C107—82no—
450C2×C107—82no—
451C2×C107#240811yescharacteristic
452C2×C107#300611yescharacteristic
453C2×C107#301311yescharacteristic
454C2×C107#326511yescharacteristic
455C2×C107#326911yescharacteristic
456C2×C107#330811yescharacteristic
457C2×C107#332111yescharacteristic
458C2×#548C2×C10711yescharacteristic, complemented
459C2×#463C2×C10711yescharacteristic, complemented
460C2×#449C2×C10711yescharacteristic, complemented
461C2×#448C2×C10711yescharacteristic, complemented
462C2×#440C2×C10711yescharacteristic, complemented
463#2537C2×C10711yescharacteristic, complemented
464#2036C2×C10711yescharacteristic, complemented
465#2033C2×C10711yescharacteristic, complemented
466#2000C2×C10711yescharacteristic, complemented
467#1999C2×C10711yescharacteristic, complemented
468#1959C2×C10711yescharacteristic, complemented
469#1955C2×C10711yescharacteristic, complemented
470#1803C2×C10711yescharacteristic, complemented
471#1788C2×C10711yescharacteristic, complemented
472#1787C2×C10711yescharacteristic, complemented
473C107#2425611yescharacteristic, direct product factor, Sylow
474C22×#41C22×C10711yescharacteristic
475C23×Q8C22×C10711yescharacteristic
476C22×SD16C22×C10711yescharacteristic
477C22×SD16C22×C10711yescharacteristic
478C22×D8C22×C10711yescharacteristic
479#548—24no—
480#548—24no—
481C2×#124—21no—
482C2×#124C22×C10711yescharacteristic
483C2×C22⋊Q8—21no—
484C2×C22⋊Q8C22×C10711yescharacteristic
485C2×#121—21no—
486C2×#121—21no—
487C2×#121C22×C10711yescharacteristic
488C2×#121C22×C10711yescharacteristic
489C2×#121C22×C10711yescharacteristic
490C2×C4×Q8C22×C10711yescharacteristic
491C2×C4×D4—21no—
492C2×C4×D4C22×C10711yescharacteristic
493C2×C4×D4C22×C10711yescharacteristic
494#463—24no—
495#449—24no—
496#448—24no—
497#440—24no—
498C2×#107C22×C10711yescharacteristic
499C2×C4⋊C8C22×C10711yescharacteristic
500C2×#103C22×C10711yescharacteristic
501C2×#103C22×C10711yescharacteristic
502C2×#103C22×C10711yescharacteristic
503C2×#103C22×C10711yescharacteristic
504C2×#103C22×C10711yescharacteristic
505C2×#103C22×C10711yescharacteristic
506C2×#102C22×C10711yescharacteristic
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×C22⋊C8C22×C10711yescharacteristic
511C2×C22⋊C8C22×C10711yescharacteristic
512C2×C22⋊C8C22×C10711yescharacteristic
513C2×C22⋊C8C22×C10711yescharacteristic
514C2×#97C22×C10711yescharacteristic
515#394—21no—
516#394—21no—
517#384C22×C10711yescharacteristic
518#380—21no—
519#380C22×C10711yescharacteristic
520#380C22×C10711yescharacteristic
521#340C22×C10711yescharacteristic
522#340C22×C10711yescharacteristic
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C23×C10711yescharacteristic
537C22×Q8C23×C10711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C10711yescharacteristic
543C22×D4C23×C10711yescharacteristic
544C22×D4C23×C10711yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C10711yescharacteristic
549C23×C4C23×C10711yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16D4×C10714yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C22×C8C23×C10711yescharacteristic
560C22×C8C23×C10711yescharacteristic
561C22×C8C23×C10711yescharacteristic
562C22×C8C23×C10711yescharacteristic
563#124—28no—
564#124—22no—
565#124D4×C10714yescomplemented
566C22⋊Q8—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569#121—28no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—44no—
577C4×Q8—22no—
578C4×Q8D4×C10714yescomplemented
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10711yescharacteristic
589C2×C4⋊C4C23×C10711yescharacteristic
590C2×C4⋊C4C23×C10711yescharacteristic
591C2×C4⋊C4C23×C10711yescharacteristic
592C2×C4⋊C4C23×C10711yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4D4×C10711yescharacteristic
603C2×C22⋊C4D4×C10711yescharacteristic
604C2×C42—21no—
605C2×C42C23×C10711yescharacteristic
606#107—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#97—22no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C10711yescharacteristic
628C24C2×D4×C10711yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8C2×D4×C10712yes—
649C2×Q8C2×D4×C10712yes—
650C2×Q8C2×D4×C10712yes—
651C2×Q8#41×C10712yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C10712yes—
678C2×D4C2×D4×C10712yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4C2×D4×C10711yescharacteristic
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C2×D4×C10711yescharacteristic
710C22×C4C24×C10711yescharacteristic
711SD16—28no—
712SD16—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C10712yes—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—81no—
738C4⋊C4C2×D4×C10712yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—24no—
751C42C2×D4×C10712yes—
752C42C2×D4×C10712yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23AGL(1,ℤ/8)×C10712yes—
781C23C22×D4×C10711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8#121×C10714yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4#120×C10712yes—
844C2×C4#120×C10712yes—
845C2×C4C22×D4×C10711yescharacteristic
846C2×C4C22×D4×C10711yescharacteristic
847C2×C4C22×D4×C10711yescharacteristic
848C2×C4C2×#41×C10711yescharacteristic
849C2×C4H(5,𝔽2)×C10711yescharacteristic
850C2×C4H(5,𝔽2)×C10711yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#120×C10711yescharacteristic
884C22D42×C10711yescharacteristic
885C22#546×C10711yescharacteristic
886C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
887C22#575×C10711yescharacteristic
888C22#577×C10711yescharacteristic
889C22#578×C10711yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#121×C10711yescharacteristic
901C4#535×C10711yescharacteristic
902C4D42×C10711yescharacteristic
903C4#546×C10711yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2C107×#240811yescharacteristic
909C2C107×#300611yescharacteristic
910C2C107×#301311yescharacteristic
911C2C107×#326511yescharacteristic
912C2C107×#326911yescharacteristic
913C2C107×#330811yescharacteristic
914C2C107×#332111yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#548×C107C2semidirect
2. C2×#463×C107C2semidirect
3. C2×#449×C107C2semidirect
4. C2×#448×C107C2semidirect
5. C2×#440×C107C2semidirect
6. C107×#2537C2semidirect
7. C107×#2036C2semidirect
8. C107×#2033C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1959C2semidirect
12. C107×#1955C2semidirect
13. C107×#1803C2semidirect
14. C107×#1788C2semidirect
15. C107×#1787C2semidirect
97. C2×SD16×C107D4semidirect
107. #124×C107D4semidirect
120. C4×Q8×C107D4semidirect
332. Q8×C107#121semidirect
446. #24256C107direct (N × H)
458. C2×#548C2×C107semidirect
459. C2×#463C2×C107semidirect
460. C2×#449C2×C107semidirect
461. C2×#448C2×C107semidirect
462. C2×#440C2×C107semidirect
463. #2537C2×C107semidirect
464. #2036C2×C107semidirect
465. #2033C2×C107semidirect
466. #2000C2×C107semidirect
467. #1999C2×C107semidirect
468. #1959C2×C107semidirect
469. #1955C2×C107semidirect
470. #1803C2×C107semidirect
471. #1788C2×C107semidirect
472. #1787C2×C107semidirect
473. C107#24256direct (N × H)
555. C2×SD16D4×C107semidirect
565. #124D4×C107semidirect
578. C4×Q8D4×C107semidirect
790. Q8#121×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1072
C2×#463×C1072
C2×#449×C1072
C2×#448×C1072
C2×#440×C1072
C107×#25372
C107×#20362
C107×#20332
C107×#20002
C107×#19992
C107×#19592
C107×#19552
C107×#18032
C107×#17882
C107×#17872
#24256107