Finite Group Databasebeta

← C107×#24277 #41050241

Subgroups — C107×#24277 #41050241

Order 27392.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C107C211yesmaximal, characteristic, complemented
2C2×#469×C107C211yesmaximal, characteristic, complemented
3C2×#468×C107C211yesmaximal, characteristic, complemented
4C2×#436×C107C211yesmaximal, characteristic, complemented
5C107×#2408C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2055C211yesmaximal, characteristic, complemented
8C107×#2054C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1970C211yesmaximal, characteristic, complemented
12C107×#1968C211yesmaximal, characteristic, complemented
13C107×#1809C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107—24no—
19C2×AGL(1,ℤ/8)×C107—24no—
20C2×AGL(1,ℤ/8)×C107—24no—
21C22×SD16×C107C2211yescharacteristic
22C22×SD16×C107C2211yescharacteristic
23C22×D8×C107C2211yescharacteristic
24C22×D8×C107C2211yescharacteristic
25C22×M16×C107C2211yescharacteristic
26C22×M16×C107C2211yescharacteristic, complemented
27C2×C22⋊Q8×C107C2211yescharacteristic, complemented
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic, complemented
31C2×#120×C107—21no—
32C2×C4×D4×C107C2211yescharacteristic
33#469×C107—24no—
34#468×C107—24no—
35#436×C107—24no—
36C2×#107×C107C2211yescharacteristic, complemented
37C2×#106×C107C2211yescharacteristic, complemented
38C2×C4⋊C8×C107C2211yescharacteristic, complemented
39C2×#103×C107C2211yescharacteristic, complemented
40C2×#103×C107C2211yescharacteristic, complemented
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic, complemented
46C2×#102×C107C2211yescharacteristic, complemented
47C2×C22⋊C8×C107C2211yescharacteristic
48C2×C22⋊C8×C107C2211yescharacteristic, complemented
49C2×C4×C8×C107C2211yescharacteristic, complemented
50#394×C107—21no—
51#394×C107—21no—
52#392×C107—21no—
53#392×C107—21no—
54#391×C107C2211yescharacteristic, complemented
55#390×C107C2211yescharacteristic
56#390×C107C2211yescharacteristic
57#390×C107C2211yescharacteristic, complemented
58#386×C107—21no—
59#385×C107—21no—
60#380×C107C2211yescharacteristic
61#380×C107C2211yescharacteristic
62#379×C107—21no—
63#340×C107C2211yescharacteristic, complemented
64#340×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C22×Q8×C107C2311yescharacteristic
73C22×D4×C107—22no—
74C22×D4×C107—22no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—22no—
80C22×D4×C107—21no—
81C22×D4×C107—22no—
82C22×D4×C107—41no—
83C22×D4×C107—41no—
84C22×D4×C107D411yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C23×C4×C107—21no—
89C23×C4×C107C2311yescharacteristic
90C23×C4×C107C2311yescharacteristic
91AGL(1,ℤ/8)×C107—232no—
92C2×SD16×C107—22no—
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107D414yescomplemented
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—22no—
101C2×D8×C107—22no—
102C2×D8×C107—22no—
103C2×D8×C107D414yescomplemented
104C2×M16×C107—22no—
105C2×M16×C107—22no—
106C2×M16×C107—22no—
107C2×M16×C107—22no—
108C2×M16×C107—22no—
109C2×M16×C107D414yescomplemented
110C22×C8×C107C2311yescharacteristic
111C22×C8×C107C2311yescharacteristic
112C22×C8×C107C2311yescharacteristic
113C22×C8×C107C2311yescharacteristic
114C22⋊Q8×C107—22no—
115C22⋊Q8×C107—41no—
116#121×C107—22no—
117#121×C107—22no—
118#121×C107—22no—
119#121×C107—41no—
120#121×C107—41no—
121#121×C107—41no—
122#120×C107—44no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125C2×C4⋊C4×C107—21no—
126C2×C4⋊C4×C107D411yescharacteristic
127C2×C4⋊C4×C107C2311yescharacteristic
128C2×C4⋊C4×C107C2311yescharacteristic
129C2×C4⋊C4×C107C2311yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
144C2×C22⋊C4×C107D411yescharacteristic
145C2×C42×C107C2311yescharacteristic
146#107×C107—22no—
147#106×C107—22no—
148C4⋊C8×C107—22no—
149#103×C107—22no—
150#103×C107—41no—
151#102×C107—22no—
152#102×C107—22no—
153#102×C107—22no—
154#102×C107—41no—
155#102×C107—41no—
156#102×C107—41no—
157C22⋊C8×C107—22no—
158C22⋊C8×C107—22no—
159C4×C8×C107—22no—
160#95×C107—21no—
161#95×C107—21no—
162#95×C107—21no—
163#95×C107—21no—
164C24×C107—21no—
165C24×C107—21no—
166C24×C107—21no—
167C24×C107—42no—
168C24×C107—42no—
169C24×C107—42no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—81no—
173C24×C107—81no—
174C24×C107C2×D411yescharacteristic
175C24×C107C2×D411yescharacteristic
176#41×C107—28no—
177#41×C107—44no—
178#41×C107—44no—
179#41×C107—44no—
180C2×Q8×C107—21no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107C2×D412yes—
186C2×D4×C107—28no—
187C2×D4×C107—22no—
188C2×D4×C107—22no—
189C2×D4×C107—21no—
190C2×D4×C107—21no—
191C2×D4×C107—21no—
192C2×D4×C107—21no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
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—44no—
205C2×D4×C107—44no—
206C2×D4×C107—41no—
207C2×D4×C107—42no—
208C2×D4×C107—42no—
209C2×D4×C107—42no—
210C2×D4×C107—44no—
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—42no—
218C2×D4×C107—42no—
219C2×D4×C107—42no—
220C2×D4×C107—81no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
223C2×D4×C107C2×D412yes—
224C2×D4×C107C2×D412yes—
225C2×D4×C107C2×D412yes—
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×C107C2×D411yescharacteristic
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D412yes—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107#4112yes—
250C22×C4×C107C2411yescharacteristic
251SD16×C107—28no—
252SD16×C107—28no—
253D8×C107—28no—
254D8×C107—28no—
255M16×C107—28no—
256M16×C107—44no—
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×C107C2×D412yes—
266C2×C8×C107C2×D412yes—
267C2×C8×C107C2×D412yes—
268C2×C8×C107C2×D412yes—
269C4⋊C4×C107—22no—
270C4⋊C4×C107—21no—
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—
279C22⋊C4×C107—22no—
280C22⋊C4×C107—22no—
281C22⋊C4×C107—42no—
282C22⋊C4×C107—42no—
283C22⋊C4×C107—42no—
284C22⋊C4×C107—42no—
285C22⋊C4×C107—42no—
286C22⋊C4×C107—42no—
287C22⋊C4×C107—42no—
288C22⋊C4×C107—42no—
289C22⋊C4×C107—81no—
290C22⋊C4×C107—81no—
291C22⋊C4×C107—81no—
292C22⋊C4×C107—81no—
293C42×C107—21no—
294C42×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—22no—
304C23×C107—22no—
305C23×C107—22no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—48no—
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×C107—41no—
323C23×C107—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—84no—
331C23×C107—84no—
332C23×C107—84no—
333C23×C107—84no—
334C23×C107—84no—
335C23×C107—84no—
336C23×C107#12112yes—
337C23×C107C22×D411yescharacteristic
338Q8×C107—22no—
339Q8×C107—22no—
340Q8×C107—41no—
341Q8×C107—41no—
342D4×C107—22no—
343D4×C107—22no—
344D4×C107—22no—
345D4×C107—22no—
346D4×C107—22no—
347D4×C107—22no—
348D4×C107—44no—
349D4×C107—48no—
350D4×C107—48no—
351D4×C107—41no—
352D4×C107—41no—
353D4×C107—41no—
354D4×C107—41no—
355D4×C107—41no—
356D4×C107—41no—
357D4×C107—84no—
358D4×C107—84no—
359D4×C107—84no—
360C2×C4×C107—21no—
361C2×C4×C107—21no—
362C2×C4×C107—21no—
363C2×C4×C107—21no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—21no—
369C2×C4×C107—21no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—22no—
373C2×C4×C107—21no—
374C2×C4×C107—21no—
375C2×C4×C107—48no—
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—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107#12112yes—
395C2×C4×C107AGL(1,ℤ/8)12yescomplemented
396C2×C4×C107C22×D411yescharacteristic
397C2×C4×C107C22×D411yescharacteristic
398C2×C4×C107C22×D411yescharacteristic
399C2×C4×C107C2×#4111yescharacteristic
400C2×C4×C107H(5,𝔽2)11yescharacteristic
401C2×C4×C107H(5,𝔽2)11yescharacteristic
402C8×C107—22no—
403C8×C107—41no—
404C8×C107—41no—
405C8×C107#12014yescomplemented
406C22×C107—22no—
407C22×C107—22no—
408C22×C107—22no—
409C22×C107—41no—
410C22×C107—41no—
411C22×C107—41no—
412C22×C107—41no—
413C22×C107—42no—
414C22×C107—41no—
415C22×C107—42no—
416C22×C107—42no—
417C22×C107—41no—
418C22×C107—42no—
419C22×C107—42no—
420C22×C107—41no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—41no—
424C22×C107—42no—
425C22×C107—41no—
426C22×C107—42no—
427C22×C107—41no—
428C22×C107—41no—
429C22×C107—816no—
430C22×C107—81no—
431C22×C107—81no—
432C22×C107—81no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107C2×#12111yescharacteristic
443C22×C107D4211yescharacteristic
444C22×C107D4211yescharacteristic
445C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C107#57511yescharacteristic
447C22×C107#57611yescharacteristic
448C22×C107#57711yescharacteristic
449C4×C107—22no—
450C4×C107—22no—
451C4×C107—41no—
452C4×C107—42no—
453C4×C107—41no—
454C4×C107—81no—
455C4×C107—81no—
456C4×C107—81no—
457C4×C107—81no—
458C4×C107C2×#12011yescharacteristic
459C4×C107#53511yescharacteristic
460C4×C107#54611yescharacteristic
461C4×C107#54611yescharacteristic
462#24277C10711yesmaximal, characteristic, direct product factor, Sylow
463C2×C107—42no—
464C2×C107—81no—
465C2×C107—82no—
466C2×C107—82no—
467C2×C107—82no—
468C2×C107#240811yescharacteristic
469C2×C107#305511yescharacteristic
470C2×C107#306211yescharacteristic
471C2×C107#327211yescharacteristic
472C2×C107#327311yescharacteristic
473C2×C107#327411yescharacteristic
474C2×C107#327511yescharacteristic
475C22×AGL(1,ℤ/8)C2×C10711yescharacteristic, complemented
476C2×#469C2×C10711yescharacteristic, complemented
477C2×#468C2×C10711yescharacteristic, complemented
478C2×#436C2×C10711yescharacteristic, complemented
479#2408C2×C10711yescharacteristic, complemented
480#2407C2×C10711yescharacteristic, complemented
481#2055C2×C10711yescharacteristic, complemented
482#2054C2×C10711yescharacteristic, complemented
483#2000C2×C10711yescharacteristic, complemented
484#1999C2×C10711yescharacteristic, complemented
485#1970C2×C10711yescharacteristic, complemented
486#1968C2×C10711yescharacteristic, complemented
487#1809C2×C10711yescharacteristic, complemented
488#1788C2×C10711yescharacteristic, complemented
489#1786C2×C10711yescharacteristic, complemented
490C107#2427711yescharacteristic, direct product factor, Sylow
491C22×#41C22×C10711yescharacteristic
492C23×D4C22×C10711yescharacteristic
493C2×AGL(1,ℤ/8)—24no—
494C2×AGL(1,ℤ/8)—24no—
495C2×AGL(1,ℤ/8)—24no—
496C22×SD16C22×C10711yescharacteristic
497C22×SD16C22×C10711yescharacteristic
498C22×D8C22×C10711yescharacteristic
499C22×D8C22×C10711yescharacteristic
500C22×M16C22×C10711yescharacteristic
501C22×M16C22×C10711yescharacteristic, complemented
502C2×C22⋊Q8C22×C10711yescharacteristic, complemented
503C2×#121C22×C10711yescharacteristic
504C2×#121C22×C10711yescharacteristic
505C2×#121C22×C10711yescharacteristic, complemented
506C2×#120—21no—
507C2×C4×D4C22×C10711yescharacteristic
508#469—24no—
509#468—24no—
510#436—24no—
511C2×#107C22×C10711yescharacteristic, complemented
512C2×#106C22×C10711yescharacteristic, complemented
513C2×C4⋊C8C22×C10711yescharacteristic, complemented
514C2×#103C22×C10711yescharacteristic, complemented
515C2×#103C22×C10711yescharacteristic, complemented
516C2×#102C22×C10711yescharacteristic
517C2×#102C22×C10711yescharacteristic
518C2×#102C22×C10711yescharacteristic
519C2×#102C22×C10711yescharacteristic
520C2×#102C22×C10711yescharacteristic, complemented
521C2×#102C22×C10711yescharacteristic, complemented
522C2×C22⋊C8C22×C10711yescharacteristic
523C2×C22⋊C8C22×C10711yescharacteristic, complemented
524C2×C4×C8C22×C10711yescharacteristic, complemented
525#394—21no—
526#394—21no—
527#392—21no—
528#392—21no—
529#391C22×C10711yescharacteristic, complemented
530#390C22×C10711yescharacteristic
531#390C22×C10711yescharacteristic
532#390C22×C10711yescharacteristic, complemented
533#386—21no—
534#385—21no—
535#380C22×C10711yescharacteristic
536#380C22×C10711yescharacteristic
537#379—21no—
538#340C22×C10711yescharacteristic, complemented
539#340C22×C10711yescharacteristic, complemented
540C25—21no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—41no—
546C2×#41—41no—
547C22×Q8C23×C10711yescharacteristic
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—41no—
558C22×D4—41no—
559C22×D4D4×C10711yescharacteristic
560C22×D4C23×C10711yescharacteristic
561C22×D4C23×C10711yescharacteristic
562C22×D4C23×C10711yescharacteristic
563C23×C4—21no—
564C23×C4C23×C10711yescharacteristic
565C23×C4C23×C10711yescharacteristic
566AGL(1,ℤ/8)—232no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16D4×C10714yescomplemented
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8D4×C10714yescomplemented
579C2×M16—22no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—22no—
584C2×M16D4×C10714yescomplemented
585C22×C8C23×C10711yescharacteristic
586C22×C8C23×C10711yescharacteristic
587C22×C8C23×C10711yescharacteristic
588C22×C8C23×C10711yescharacteristic
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#120—44no—
598C4×D4—22no—
599C4×D4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4D4×C10711yescharacteristic
602C2×C4⋊C4C23×C10711yescharacteristic
603C2×C4⋊C4C23×C10711yescharacteristic
604C2×C4⋊C4C23×C10711yescharacteristic
605C2×C4⋊C4C23×C10711yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4D4×C10711yescharacteristic
619C2×C22⋊C4D4×C10711yescharacteristic
620C2×C42C23×C10711yescharacteristic
621#107—22no—
622#106—22no—
623C4⋊C8—22no—
624#103—22no—
625#103—41no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630#102—41no—
631#102—41no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634C4×C8—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C10711yescharacteristic
650C24C2×D4×C10711yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C10712yes—
661C2×D4—28no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C10712yes—
699C2×D4C2×D4×C10712yes—
700C2×D4C2×D4×C10712yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C10711yescharacteristic
720C22×C4C2×D4×C10711yescharacteristic
721C22×C4C2×D4×C10711yescharacteristic
722C22×C4C2×D4×C10712yes—
723C22×C4C2×D4×C10711yescharacteristic
724C22×C4#41×C10712yes—
725C22×C4C24×C10711yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731M16—44no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8C2×D4×C10712yes—
741C2×C8C2×D4×C10712yes—
742C2×C8C2×D4×C10712yes—
743C2×C8C2×D4×C10712yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—48no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23#121×C10712yes—
812C23C22×D4×C10711yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—44no—
824D4—48no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—48no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4#121×C10712yes—
870C2×C4AGL(1,ℤ/8)×C10712yescomplemented
871C2×C4C22×D4×C10711yescharacteristic
872C2×C4C22×D4×C10711yescharacteristic
873C2×C4C22×D4×C10711yescharacteristic
874C2×C4C2×#41×C10711yescharacteristic
875C2×C4H(5,𝔽2)×C10711yescharacteristic
876C2×C4H(5,𝔽2)×C10711yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8#120×C10714yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—41no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#121×C10711yescharacteristic
918C22D42×C10711yescharacteristic
919C22D42×C10711yescharacteristic
920C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
921C22#575×C10711yescharacteristic
922C22#576×C10711yescharacteristic
923C22#577×C10711yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—42no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×#120×C10711yescharacteristic
934C4#535×C10711yescharacteristic
935C4#546×C10711yescharacteristic
936C4#546×C10711yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C107×#240811yescharacteristic
943C2C107×#305511yescharacteristic
944C2C107×#306211yescharacteristic
945C2C107×#327211yescharacteristic
946C2C107×#327311yescharacteristic
947C2C107×#327411yescharacteristic
948C2C107×#327511yescharacteristic
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. C22×AGL(1,ℤ/8)×C107C2semidirect
2. C2×#469×C107C2semidirect
3. C2×#468×C107C2semidirect
4. C2×#436×C107C2semidirect
5. C107×#2408C2semidirect
6. C107×#2407C2semidirect
7. C107×#2055C2semidirect
8. C107×#2054C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1970C2semidirect
12. C107×#1968C2semidirect
13. C107×#1809C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
26. C22×M16×C107C22semidirect
27. C2×C22⋊Q8×C107C22semidirect
30. C2×#121×C107C22semidirect
36. C2×#107×C107C22semidirect
37. C2×#106×C107C22semidirect
38. C2×C4⋊C8×C107C22semidirect
39. C2×#103×C107C22semidirect
40. C2×#103×C107C22semidirect
45. C2×#102×C107C22semidirect
46. C2×#102×C107C22semidirect
48. C2×C22⋊C8×C107C22semidirect
49. C2×C4×C8×C107C22semidirect
54. #391×C107C22semidirect
57. #390×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
97. C2×SD16×C107D4semidirect
103. C2×D8×C107D4semidirect
109. C2×M16×C107D4semidirect
395. C2×C4×C107AGL(1,ℤ/8)semidirect
405. C8×C107#120semidirect
462. #24277C107direct (N × H)
475. C22×AGL(1,ℤ/8)C2×C107semidirect
476. C2×#469C2×C107semidirect
477. C2×#468C2×C107semidirect
478. C2×#436C2×C107semidirect
479. #2408C2×C107semidirect
480. #2407C2×C107semidirect
481. #2055C2×C107semidirect
482. #2054C2×C107semidirect
483. #2000C2×C107semidirect
484. #1999C2×C107semidirect
485. #1970C2×C107semidirect
486. #1968C2×C107semidirect
487. #1809C2×C107semidirect
488. #1788C2×C107semidirect
489. #1786C2×C107semidirect
490. C107#24277direct (N × H)
501. C22×M16C22×C107semidirect
502. C2×C22⋊Q8C22×C107semidirect
505. C2×#121C22×C107semidirect
511. C2×#107C22×C107semidirect
512. C2×#106C22×C107semidirect
513. C2×C4⋊C8C22×C107semidirect
514. C2×#103C22×C107semidirect
515. C2×#103C22×C107semidirect
520. C2×#102C22×C107semidirect
521. C2×#102C22×C107semidirect
523. C2×C22⋊C8C22×C107semidirect
524. C2×C4×C8C22×C107semidirect
529. #391C22×C107semidirect
532. #390C22×C107semidirect
538. #340C22×C107semidirect
539. #340C22×C107semidirect
572. C2×SD16D4×C107semidirect
578. C2×D8D4×C107semidirect
584. C2×M16D4×C107semidirect
870. C2×C4AGL(1,ℤ/8)×C107semidirect
880. C8#120×C107semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1072
C2×#469×C1072
C2×#468×C1072
C2×#436×C1072
C107×#24082
C107×#24072
C107×#20552
C107×#20542
C107×#20002
C107×#19992
C107×#19702
C107×#19682
C107×#18092
C107×#17882
C107×#17862
#24277107