Finite Group Databasebeta

← C107×#24247 #41050211

Subgroups — C107×#24247 #41050211

Order 27392.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C107C211yesmaximal, characteristic
2C2×#464×C107C211yesmaximal, characteristic, complemented
3C2×#452×C107C211yesmaximal, characteristic, complemented
4C2×#450×C107C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C107C211yesmaximal, characteristic, complemented
6C107×#2536C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#2001C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1958C211yesmaximal, characteristic, complemented
12C107×#1954C211yesmaximal, characteristic, complemented
13C107×#1804C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×Q16×C107C2211yescharacteristic, complemented
19C22×SD16×C107C2211yescharacteristic
20C22×SD16×C107C2211yescharacteristic
21#546×C107—24no—
22#546×C107—24no—
23C2×#124×C107C2211yescharacteristic
24C2×#123×C107—21no—
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×C22⋊Q8×C107C2211yescharacteristic, complemented
28C2×#121×C107—21no—
29C2×#121×C107C2211yescharacteristic
30C2×#120×C107—21no—
31C2×C4×Q8×C107C2211yescharacteristic, complemented
32C2×C4×D4×C107C2211yescharacteristic
33C2×C4×D4×C107C2211yescharacteristic
34C22×C22⋊C4×C107—21no—
35#464×C107—24no—
36#452×C107—24no—
37#450×C107—24no—
38C4×SD16×C107—24no—
39C2×#106×C107C2211yescharacteristic, complemented
40C2×C4⋊C8×C107C2211yescharacteristic, complemented
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#103×C107C2211yescharacteristic, complemented
44C2×#103×C107C2211yescharacteristic, complemented
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54C2×C22⋊C8×C107C2211yescharacteristic, complemented
55C2×C4×C8×C107C2211yescharacteristic, complemented
56#398×C107—21no—
57#394×C107—21no—
58#388×C107—21no—
59#388×C107—21no—
60#382×C107C2211yescharacteristic, complemented
61#380×C107C2211yescharacteristic
62#380×C107C2211yescharacteristic, complemented
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×Q8×C107C2311yescharacteristic
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—22no—
77C22×D4×C107—22no—
78C22×D4×C107—22no—
79C22×D4×C107—22no—
80C22×D4×C107—21no—
81C22×D4×C107—41no—
82C22×D4×C107—41no—
83C22×D4×C107D411yescharacteristic
84C22×D4×C107C2311yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C23×C4×C107—21no—
87C23×C4×C107—21no—
88C23×C4×C107C2311yescharacteristic
89C23×C4×C107C2311yescharacteristic
90C2×Q16×C107—22no—
91C2×Q16×C107—22no—
92C2×Q16×C107—41no—
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—41no—
98C2×SD16×C107D414yescomplemented
99C22×C8×C107C2311yescharacteristic
100C22×C8×C107C2311yescharacteristic
101C22×C8×C107C2311yescharacteristic
102C22×C8×C107C2311yescharacteristic
103#124×C107—22no—
104#124×C107D414yes—
105#123×C107—28no—
106C22⋊Q8×C107—22no—
107C22⋊Q8×C107—22no—
108C22⋊Q8×C107—22no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—41no—
111C22⋊Q8×C107—41no—
112#121×C107—28no—
113#121×C107—22no—
114#121×C107—22no—
115#120×C107—28no—
116C4×Q8×C107—22no—
117C4×Q8×C107—22no—
118C4×D4×C107—22no—
119C4×D4×C107—22no—
120C4×D4×C107—22no—
121C4×D4×C107D414yes—
122C2×C4⋊C4×C107—21no—
123C2×C4⋊C4×C107—21no—
124C2×C4⋊C4×C107—21no—
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—28no—
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×C107D411yescharacteristic
142C2×C22⋊C4×C107D411yescharacteristic
143C2×C42×C107—21no—
144C2×C42×C107C2311yescharacteristic
145#106×C107—22no—
146C4⋊C8×C107—22no—
147#103×C107—22no—
148#103×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—22no—
155#102×C107—22no—
156#102×C107—41no—
157C22⋊C8×C107—22no—
158C22⋊C8×C107—22no—
159C22⋊C8×C107—41no—
160C22⋊C8×C107—41no—
161C4×C8×C107—22no—
162#95×C107—21no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—24no—
168C24×C107—21no—
169C24×C107—42no—
170C24×C107—42no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107C2×D411yescharacteristic
176C24×C107C2×D411yescharacteristic
177#41×C107—44no—
178#41×C107—44no—
179#41×C107—44no—
180#41×C107—44no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107—21no—
191C2×Q8×C107C2×D412yes—
192C2×Q8×C107C2×D412yes—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—22no—
196C2×D4×C107—24no—
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—41no—
207C2×D4×C107—42no—
208C2×D4×C107—42no—
209C2×D4×C107—44no—
210C2×D4×C107—44no—
211C2×D4×C107—44no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—44no—
215C2×D4×C107—81no—
216C2×D4×C107—81no—
217C2×D4×C107C2×D412yes—
218C2×D4×C107C2×D412yes—
219C2×D4×C107C2×D412yes—
220C2×D4×C107#4112yes—
221C22×C4×C107—24no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
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—24no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—42no—
242C22×C4×C107—42no—
243C22×C4×C107—81no—
244C22×C4×C107—81no—
245C22×C4×C107C2×D411yescharacteristic
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2×D411yescharacteristic
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2411yescharacteristic
250Q16×C107—44no—
251SD16×C107—28no—
252SD16×C107—44no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
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×C107C2×D412yes—
265C4⋊C4×C107—24no—
266C4⋊C4×C107—22no—
267C4⋊C4×C107—21no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—42no—
275C4⋊C4×C107—42no—
276C4⋊C4×C107—42no—
277C4⋊C4×C107C2×D412yes—
278C22⋊C4×C107—24no—
279C22⋊C4×C107—24no—
280C22⋊C4×C107—22no—
281C22⋊C4×C107—24no—
282C22⋊C4×C107—24no—
283C22⋊C4×C107—24no—
284C22⋊C4×C107—22no—
285C22⋊C4×C107—42no—
286C22⋊C4×C107—42no—
287C22⋊C4×C107—42no—
288C22⋊C4×C107—42no—
289C42×C107—42no—
290C42×C107C2×D412yes—
291C42×C107C2×D412yes—
292C23×C107—21no—
293C23×C107—22no—
294C23×C107—21no—
295C23×C107—22no—
296C23×C107—21no—
297C23×C107—22no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—22no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—48no—
310C23×C107—48no—
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—84no—
322C23×C107—84no—
323C23×C107—84no—
324C23×C107—84no—
325C23×C107—84no—
326C23×C107#13512yes—
327C23×C107C22×D411yescharacteristic
328Q8×C107—22no—
329Q8×C107—22no—
330Q8×C107—22no—
331Q8×C107—22no—
332Q8×C107—41no—
333Q8×C107—41no—
334Q8×C107—41no—
335Q8×C107—41no—
336D4×C107—22no—
337D4×C107—22no—
338D4×C107—22no—
339D4×C107—22no—
340D4×C107—22no—
341D4×C107—44no—
342D4×C107—48no—
343D4×C107—48no—
344D4×C107—41no—
345D4×C107—41no—
346D4×C107—84no—
347D4×C107#12114yes—
348C2×C4×C107—21no—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—21no—
352C2×C4×C107—22no—
353C2×C4×C107—21no—
354C2×C4×C107—22no—
355C2×C4×C107—21no—
356C2×C4×C107—22no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—48no—
362C2×C4×C107—41no—
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—41no—
385C2×C4×C107—84no—
386C2×C4×C107#12012yes—
387C2×C4×C107#12012yes—
388C2×C4×C107C22×D411yescharacteristic
389C2×C4×C107C22×D411yescharacteristic
390C2×C4×C107C22×D411yescharacteristic
391C2×C4×C107C2×#4111yescharacteristic
392C2×C4×C107H(5,𝔽2)11yescharacteristic
393C2×C4×C107H(5,𝔽2)11yescharacteristic
394C8×C107—22no—
395C8×C107—41no—
396C8×C107—41no—
397C8×C107—41no—
398C22×C107—24no—
399C22×C107—22no—
400C22×C107—22no—
401C22×C107—22no—
402C22×C107—41no—
403C22×C107—42no—
404C22×C107—42no—
405C22×C107—41no—
406C22×C107—41no—
407C22×C107—42no—
408C22×C107—42no—
409C22×C107—42no—
410C22×C107—41no—
411C22×C107—42no—
412C22×C107—41no—
413C22×C107—42no—
414C22×C107—41no—
415C22×C107—42no—
416C22×C107—41no—
417C22×C107—42no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—41no—
421C22×C107—41no—
422C22×C107—816no—
423C22×C107—81no—
424C22×C107—81no—
425C22×C107—81no—
426C22×C107—81no—
427C22×C107C2×#12011yescharacteristic
428C22×C107D4211yescharacteristic
429C22×C107#54611yescharacteristic
430C22×C107C2×#13511yescharacteristic
431C22×C107#57511yescharacteristic
432C22×C107#57711yescharacteristic
433C22×C107#57711yescharacteristic
434C4×C107—22no—
435C4×C107—22no—
436C4×C107—41no—
437C4×C107—41no—
438C4×C107—42no—
439C4×C107—42no—
440C4×C107—42no—
441C4×C107—81no—
442C4×C107—81no—
443C4×C107—81no—
444C4×C107C2×#12111yescharacteristic
445C4×C107#53511yescharacteristic
446C4×C107D4211yescharacteristic
447C4×C107#54611yescharacteristic
448#24247C10711yesmaximal, characteristic, direct product factor, Sylow
449C2×C107—42no—
450C2×C107—44no—
451C2×C107—81no—
452C2×C107—82no—
453C2×C107#240811yescharacteristic
454C2×C107#300211yescharacteristic
455C2×C107#300911yescharacteristic
456C2×C107#327511yescharacteristic
457C2×C107#328211yescharacteristic
458C2×C107#329611yescharacteristic
459C2×C107#332311yescharacteristic
460C2×#546C2×C10711yescharacteristic
461C2×#464C2×C10711yescharacteristic, complemented
462C2×#452C2×C10711yescharacteristic, complemented
463C2×#450C2×C10711yescharacteristic, complemented
464C2×C4×SD16C2×C10711yescharacteristic, complemented
465#2536C2×C10711yescharacteristic, complemented
466#2035C2×C10711yescharacteristic, complemented
467#2034C2×C10711yescharacteristic, complemented
468#2001C2×C10711yescharacteristic, complemented
469#2000C2×C10711yescharacteristic, complemented
470#1958C2×C10711yescharacteristic, complemented
471#1954C2×C10711yescharacteristic, complemented
472#1804C2×C10711yescharacteristic, complemented
473#1788C2×C10711yescharacteristic, complemented
474#1786C2×C10711yescharacteristic, complemented
475C107#2424711yescharacteristic, direct product factor, Sylow
476C22×#41C22×C10711yescharacteristic
477C23×D4C22×C10711yescharacteristic
478C22×Q16C22×C10711yescharacteristic, complemented
479C22×SD16C22×C10711yescharacteristic
480C22×SD16C22×C10711yescharacteristic
481#546—24no—
482#546—24no—
483C2×#124C22×C10711yescharacteristic
484C2×#123—21no—
485C2×C22⋊Q8C22×C10711yescharacteristic
486C2×C22⋊Q8C22×C10711yescharacteristic
487C2×C22⋊Q8C22×C10711yescharacteristic, complemented
488C2×#121—21no—
489C2×#121C22×C10711yescharacteristic
490C2×#120—21no—
491C2×C4×Q8C22×C10711yescharacteristic, complemented
492C2×C4×D4C22×C10711yescharacteristic
493C2×C4×D4C22×C10711yescharacteristic
494C22×C22⋊C4—21no—
495#464—24no—
496#452—24no—
497#450—24no—
498C4×SD16—24no—
499C2×#106C22×C10711yescharacteristic, complemented
500C2×C4⋊C8C22×C10711yescharacteristic, complemented
501C2×#103C22×C10711yescharacteristic, complemented
502C2×#103C22×C10711yescharacteristic, complemented
503C2×#103C22×C10711yescharacteristic, complemented
504C2×#103C22×C10711yescharacteristic, complemented
505C2×#102C22×C10711yescharacteristic
506C2×#102C22×C10711yescharacteristic
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×#102C22×C10711yescharacteristic
511C2×C22⋊C8C22×C10711yescharacteristic
512C2×C22⋊C8C22×C10711yescharacteristic
513C2×C22⋊C8C22×C10711yescharacteristic, complemented
514C2×C22⋊C8C22×C10711yescharacteristic, complemented
515C2×C4×C8C22×C10711yescharacteristic, complemented
516#398—21no—
517#394—21no—
518#388—21no—
519#388—21no—
520#382C22×C10711yescharacteristic, complemented
521#380C22×C10711yescharacteristic
522#380C22×C10711yescharacteristic, complemented
523#340C22×C10711yescharacteristic, complemented
524#340C22×C10711yescharacteristic, complemented
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C10711yescharacteristic
533C22×Q8C23×C10711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C10711yescharacteristic
544C22×D4C23×C10711yescharacteristic
545C22×D4C23×C10711yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C10711yescharacteristic
549C23×C4C23×C10711yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C10714yescomplemented
559C22×C8C23×C10711yescharacteristic
560C22×C8C23×C10711yescharacteristic
561C22×C8C23×C10711yescharacteristic
562C22×C8C23×C10711yescharacteristic
563#124—22no—
564#124D4×C10714yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C10714yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C10711yescharacteristic
587C2×C4⋊C4C23×C10711yescharacteristic
588C2×C4⋊C4C23×C10711yescharacteristic
589C2×C4⋊C4C23×C10711yescharacteristic
590C2×C4⋊C4C23×C10711yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
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⋊C4D4×C10711yescharacteristic
602C2×C22⋊C4D4×C10711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10711yescharacteristic
605#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C10711yescharacteristic
636C24C2×D4×C10711yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8C2×D4×C10712yes—
652C2×Q8C2×D4×C10712yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
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—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C10712yes—
678C2×D4C2×D4×C10712yes—
679C2×D4C2×D4×C10712yes—
680C2×D4#41×C10712yes—
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—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C10711yescharacteristic
706C22×C4C2×D4×C10711yescharacteristic
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C24×C10711yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
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×C8C2×D4×C10712yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C10712yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C10712yes—
751C42C2×D4×C10712yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C10712yes—
787C23C22×D4×C10711yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C10714yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
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—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C10712yes—
847C2×C4#120×C10712yes—
848C2×C4C22×D4×C10711yescharacteristic
849C2×C4C22×D4×C10711yescharacteristic
850C2×C4C22×D4×C10711yescharacteristic
851C2×C4C2×#41×C10711yescharacteristic
852C2×C4H(5,𝔽2)×C10711yescharacteristic
853C2×C4H(5,𝔽2)×C10711yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C10711yescharacteristic
888C22D42×C10711yescharacteristic
889C22#546×C10711yescharacteristic
890C22C2×#135×C10711yescharacteristic
891C22#575×C10711yescharacteristic
892C22#577×C10711yescharacteristic
893C22#577×C10711yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C10711yescharacteristic
905C4#535×C10711yescharacteristic
906C4D42×C10711yescharacteristic
907C4#546×C10711yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2C107×#240811yescharacteristic
913C2C107×#300211yescharacteristic
914C2C107×#300911yescharacteristic
915C2C107×#327511yescharacteristic
916C2C107×#328211yescharacteristic
917C2C107×#329611yescharacteristic
918C2C107×#332311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#546×C107C2
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
2. C2×#464×C107C2semidirect
3. C2×#452×C107C2semidirect
4. C2×#450×C107C2semidirect
5. C2×C4×SD16×C107C2semidirect
6. C107×#2536C2semidirect
7. C107×#2035C2semidirect
8. C107×#2034C2semidirect
9. C107×#2001C2semidirect
10. C107×#2000C2semidirect
11. C107×#1958C2semidirect
12. C107×#1954C2semidirect
13. C107×#1804C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
18. C22×Q16×C107C22semidirect
27. C2×C22⋊Q8×C107C22semidirect
31. C2×C4×Q8×C107C22semidirect
39. C2×#106×C107C22semidirect
40. C2×C4⋊C8×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
44. C2×#103×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
54. C2×C22⋊C8×C107C22semidirect
55. C2×C4×C8×C107C22semidirect
60. #382×C107C22semidirect
62. #380×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
98. C2×SD16×C107D4semidirect
448. #24247C107direct (N × H)
461. C2×#464C2×C107semidirect
462. C2×#452C2×C107semidirect
463. C2×#450C2×C107semidirect
464. C2×C4×SD16C2×C107semidirect
465. #2536C2×C107semidirect
466. #2035C2×C107semidirect
467. #2034C2×C107semidirect
468. #2001C2×C107semidirect
469. #2000C2×C107semidirect
470. #1958C2×C107semidirect
471. #1954C2×C107semidirect
472. #1804C2×C107semidirect
473. #1788C2×C107semidirect
474. #1786C2×C107semidirect
475. C107#24247direct (N × H)
478. C22×Q16C22×C107semidirect
487. C2×C22⋊Q8C22×C107semidirect
491. C2×C4×Q8C22×C107semidirect
499. C2×#106C22×C107semidirect
500. C2×C4⋊C8C22×C107semidirect
501. C2×#103C22×C107semidirect
502. C2×#103C22×C107semidirect
503. C2×#103C22×C107semidirect
504. C2×#103C22×C107semidirect
513. C2×C22⋊C8C22×C107semidirect
514. C2×C22⋊C8C22×C107semidirect
515. C2×C4×C8C22×C107semidirect
520. #382C22×C107semidirect
522. #380C22×C107semidirect
523. #340C22×C107semidirect
524. #340C22×C107semidirect
558. C2×SD16D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1072
C2×#464×C1072
C2×#452×C1072
C2×#450×C1072
C2×C4×SD16×C1072
C107×#25362
C107×#20352
C107×#20342
C107×#20012
C107×#20002
C107×#19582
C107×#19542
C107×#18042
C107×#17882
C107×#17862
#24247107