Finite Group Databasebeta

← C107×#23972 #41049936

Subgroups — C107×#23972 #41049936

Order 27392.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C107C211yesmaximal, characteristic, complemented
2C2×#449×C107C211yesmaximal, characteristic, complemented
3C2×#417×C107C211yesmaximal, characteristic, complemented
4C107×#2407C211yesmaximal, characteristic, complemented
5C107×#2024C211yesmaximal, characteristic, complemented
6C107×#2023C211yesmaximal, characteristic, complemented
7C107×#2000C211yesmaximal, characteristic, complemented
8C107×#1999C211yesmaximal, characteristic, complemented
9C107×#1895C211yesmaximal, characteristic, complemented
10C107×#1879C211yesmaximal, characteristic, complemented
11C107×#1877C211yesmaximal, characteristic, complemented
12C107×#1874C211yesmaximal, characteristic, complemented
13C107×#1872C211yesmaximal, characteristic, complemented
14C107×#1870C211yesmaximal, characteristic, complemented
15C107×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C107—21no—
17C22×#41×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×D8×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic
21#547×C107—24no—
22#547×C107—24no—
23C2×C4⋊Q8×C107C2211yescharacteristic
24C2×#123×C107—21no—
25C2×#123×C107—21no—
26C2×C22⋊Q8×C107—21no—
27C2×C22⋊Q8×C107C2211yescharacteristic
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×C4×D4×C107C2211yescharacteristic
32C2×C4×D4×C107C2211yescharacteristic
33C22×C4⋊C4×C107C2211yescharacteristic
34C22×C4⋊C4×C107C2211yescharacteristic
35#449×C107—24no—
36#417×C107—24no—
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#103×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C22⋊C8×C107C2211yescharacteristic
47C2×C22⋊C8×C107C2211yescharacteristic
48#394×C107—21no—
49#392×C107—21no—
50#391×C107C2211yescharacteristic
51#390×C107C2211yescharacteristic
52#386×C107—21no—
53#385×C107—21no—
54#380×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62#336×C107C2211yescharacteristic
63C2×#41×C107—28no—
64C2×#41×C107—22no—
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—41no—
69C2×#41×C107—41no—
70C2×#41×C107—44no—
71C2×#41×C107—44no—
72C22×Q8×C107—21no—
73C22×Q8×C107C2311yescharacteristic
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107D411yescharacteristic
79C22×D4×C107C2311yescharacteristic
80C22×D4×C107C2311yescharacteristic
81C23×C4×C107—21no—
82C23×C4×C107—21no—
83C23×C4×C107—21no—
84C23×C4×C107—21no—
85C23×C4×C107C2311yescharacteristic
86C23×C4×C107C2311yescharacteristic
87C2×SD16×C107—22no—
88C2×SD16×C107—22no—
89C2×SD16×C107—41no—
90C2×D8×C107—22no—
91C2×D8×C107—22no—
92C2×D8×C107—41no—
93C2×M16×C107—22no—
94C2×M16×C107—41no—
95C2×M16×C107—41no—
96C22×C8×C107C2311yescharacteristic
97C22×C8×C107C2311yescharacteristic
98C22×C8×C107C2311yescharacteristic
99C22×C8×C107C2311yescharacteristic
100C4⋊Q8×C107—22no—
101C4⋊Q8×C107—22no—
102#123×C107—28no—
103#123×C107—28no—
104C22⋊Q8×C107—28no—
105C22⋊Q8×C107—22no—
106C22⋊Q8×C107—41no—
107#121×C107—22no—
108#121×C107—22no—
109#121×C107—22no—
110#121×C107—22no—
111#121×C107—41no—
112#121×C107D414yescomplemented
113C4×D4×C107—22no—
114C4×D4×C107—22no—
115C4×D4×C107—22no—
116C4×D4×C107—22no—
117C2×C4⋊C4×C107—21no—
118C2×C4⋊C4×C107—21no—
119C2×C4⋊C4×C107—22no—
120C2×C4⋊C4×C107—21no—
121C2×C4⋊C4×C107—22no—
122C2×C4⋊C4×C107—22no—
123C2×C4⋊C4×C107—21no—
124C2×C4⋊C4×C107D411yescharacteristic
125C2×C4⋊C4×C107D414yescomplemented
126C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
140C2×C22⋊C4×C107D411yescharacteristic
141C2×C42×C107C2311yescharacteristic
142#103×C107—22no—
143#103×C107—22no—
144#103×C107—22no—
145#102×C107—22no—
146#102×C107—22no—
147#102×C107—22no—
148#102×C107—41no—
149#102×C107—41no—
150C22⋊C8×C107—22no—
151C22⋊C8×C107—41no—
152C22⋊C8×C107—41no—
153#95×C107—21no—
154#95×C107—21no—
155#95×C107—21no—
156C24×C107—21no—
157C24×C107—21no—
158C24×C107C2×D411yescharacteristic
159C24×C107C2×D411yescharacteristic
160#41×C107—28no—
161#41×C107—44no—
162#41×C107—44no—
163#41×C107—44no—
164#41×C107—432no—
165C2×Q8×C107—24no—
166C2×Q8×C107—21no—
167C2×Q8×C107—21no—
168C2×Q8×C107—21no—
169C2×Q8×C107—21no—
170C2×Q8×C107—21no—
171C2×Q8×C107—42no—
172C2×Q8×C107—42no—
173C2×Q8×C107#4112yescomplemented
174C2×D4×C107—22no—
175C2×D4×C107—22no—
176C2×D4×C107—24no—
177C2×D4×C107—24no—
178C2×D4×C107—22no—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—21no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—42no—
190C2×D4×C107—42no—
191C2×D4×C107—42no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—42no—
195C2×D4×C107—42no—
196C2×D4×C107—42no—
197C2×D4×C107—42no—
198C2×D4×C107—81no—
199C2×D4×C107C2×D412yes—
200C2×D4×C107#4112yescomplemented
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—24no—
206C22×C4×C107—24no—
207C22×C4×C107—24no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—42no—
221C22×C4×C107—42no—
222C22×C4×C107—42no—
223C22×C4×C107—42no—
224C22×C4×C107—42no—
225C22×C4×C107—42no—
226C22×C4×C107—42no—
227C22×C4×C107—42no—
228C22×C4×C107—42no—
229C22×C4×C107C2×D411yescharacteristic
230C22×C4×C107C2×D411yescharacteristic
231C22×C4×C107C2×D411yescharacteristic
232C22×C4×C107C2×D412yes—
233C22×C4×C107C2×D412yes—
234C22×C4×C107C2×D411yescharacteristic
235C22×C4×C107C2411yescharacteristic
236SD16×C107—44no—
237D8×C107—44no—
238M16×C107—44no—
239C2×C8×C107—21no—
240C2×C8×C107—21no—
241C2×C8×C107—21no—
242C2×C8×C107—21no—
243C2×C8×C107—21no—
244C2×C8×C107—21no—
245C2×C8×C107—21no—
246C2×C8×C107—21no—
247C2×C8×C107—21no—
248C2×C8×C107—21no—
249C2×C8×C107—21no—
250C2×C8×C107—21no—
251C4⋊C4×C107—24no—
252C4⋊C4×C107—24no—
253C4⋊C4×C107—24no—
254C4⋊C4×C107—22no—
255C4⋊C4×C107—21no—
256C4⋊C4×C107—21no—
257C4⋊C4×C107—21no—
258C4⋊C4×C107—21no—
259C4⋊C4×C107—21no—
260C4⋊C4×C107—21no—
261C4⋊C4×C107—21no—
262C4⋊C4×C107—42no—
263C4⋊C4×C107C2×D412yes—
264C4⋊C4×C107C2×D412yes—
265C4⋊C4×C107C2×D412yes—
266C22⋊C4×C107—24no—
267C22⋊C4×C107—24no—
268C22⋊C4×C107—22no—
269C22⋊C4×C107—24no—
270C22⋊C4×C107—22no—
271C22⋊C4×C107—42no—
272C22⋊C4×C107—42no—
273C22⋊C4×C107—42no—
274C22⋊C4×C107—81no—
275C22⋊C4×C107—81no—
276C42×C107—21no—
277C42×C107—21no—
278C23×C107—21no—
279C23×C107—21no—
280C23×C107—21no—
281C23×C107—21no—
282C23×C107—21no—
283C23×C107—21no—
284C23×C107—21no—
285C23×C107—21no—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—21no—
289C23×C107—21no—
290C23×C107—22no—
291C23×C107—22no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—41no—
298C23×C107—41no—
299C23×C107—41no—
300C23×C107—41no—
301C23×C107—41no—
302C23×C107—41no—
303C23×C107—41no—
304C23×C107#12012yes—
305C23×C107AGL(1,ℤ/8)12yes—
306C23×C107C22×D411yescharacteristic
307Q8×C107—22no—
308Q8×C107—22no—
309Q8×C107—48no—
310Q8×C107—41no—
311Q8×C107—41no—
312D4×C107—28no—
313D4×C107—22no—
314D4×C107—22no—
315D4×C107—22no—
316D4×C107—22no—
317D4×C107—48no—
318D4×C107—48no—
319D4×C107—48no—
320D4×C107—41no—
321D4×C107—41no—
322D4×C107—41no—
323D4×C107—41no—
324D4×C107—84no—
325C2×C4×C107—21no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—22no—
330C2×C4×C107—22no—
331C2×C4×C107—22no—
332C2×C4×C107—22no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—22no—
336C2×C4×C107—22no—
337C2×C4×C107—22no—
338C2×C4×C107—21no—
339C2×C4×C107—22no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—21no—
343C2×C4×C107—48no—
344C2×C4×C107—48no—
345C2×C4×C107—48no—
346C2×C4×C107—48no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—41no—
357C2×C4×C107—41no—
358C2×C4×C107—41no—
359C2×C4×C107—41no—
360C2×C4×C107—41no—
361C2×C4×C107—41no—
362C2×C4×C107—41no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107#12012yes—
366C2×C4×C107AGL(1,ℤ/8)12yes—
367C2×C4×C107C22×D411yescharacteristic
368C2×C4×C107C22×D411yescharacteristic
369C2×C4×C107C2×#4111yescharacteristic
370C2×C4×C107C2×#4111yescharacteristic
371C2×C4×C107H(5,𝔽2)11yescharacteristic
372C2×C4×C107H(5,𝔽2)11yescharacteristic
373C8×C107—41no—
374C8×C107—41no—
375C8×C107—41no—
376C8×C107—41no—
377C22×C107—22no—
378C22×C107—22no—
379C22×C107—22no—
380C22×C107—22no—
381C22×C107—22no—
382C22×C107—22no—
383C22×C107—41no—
384C22×C107—41no—
385C22×C107—41no—
386C22×C107—41no—
387C22×C107—41no—
388C22×C107—41no—
389C22×C107—41no—
390C22×C107—41no—
391C22×C107—42no—
392C22×C107—42no—
393C22×C107—42no—
394C22×C107—42no—
395C22×C107—42no—
396C22×C107—42no—
397C22×C107—81no—
398C22×C107—81no—
399C22×C107—81no—
400C22×C107—81no—
401C22×C107—81no—
402C22×C107—81no—
403C22×C107—81no—
404C22×C107—81no—
405C22×C107C2×#12011yescharacteristic
406C22×C107#54611yescharacteristic
407C22×C107#54611yescharacteristic
408C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C107#57711yescharacteristic
411C22×C107#57811yescharacteristic
412C4×C107—22no—
413C4×C107—22no—
414C4×C107—41no—
415C4×C107—42no—
416C4×C107—42no—
417C4×C107—42no—
418C4×C107—42no—
419C4×C107—41no—
420C4×C107—81no—
421C4×C107—81no—
422C4×C107#52511yescharacteristic
423C4×C107#53511yescharacteristic
424C4×C107#54611yescharacteristic
425C4×C107#54611yescharacteristic
426#23972C10711yesmaximal, characteristic, direct product factor, Sylow
427C2×C107—42no—
428C2×C107—42no—
429C2×C107—82no—
430C2×C107—82no—
431C2×C107#240411yescharacteristic
432C2×C107#300311yescharacteristic
433C2×C107#301311yescharacteristic
434C2×C107#330611yescharacteristic
435C2×C107#330811yescharacteristic
436C2×C107#333011yescharacteristic
437C2×C107#333211yescharacteristic
438C2×#547C2×C10711yescharacteristic, complemented
439C2×#449C2×C10711yescharacteristic, complemented
440C2×#417C2×C10711yescharacteristic, complemented
441#2407C2×C10711yescharacteristic, complemented
442#2024C2×C10711yescharacteristic, complemented
443#2023C2×C10711yescharacteristic, complemented
444#2000C2×C10711yescharacteristic, complemented
445#1999C2×C10711yescharacteristic, complemented
446#1895C2×C10711yescharacteristic, complemented
447#1879C2×C10711yescharacteristic, complemented
448#1877C2×C10711yescharacteristic, complemented
449#1874C2×C10711yescharacteristic, complemented
450#1872C2×C10711yescharacteristic, complemented
451#1870C2×C10711yescharacteristic, complemented
452#1824C2×C10711yescharacteristic, complemented
453C107#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C10711yescharacteristic
456C22×SD16C22×C10711yescharacteristic
457C22×D8C22×C10711yescharacteristic
458C22×M16C22×C10711yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C10711yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C10711yescharacteristic
466C2×#121C22×C10711yescharacteristic
467C2×#121C22×C10711yescharacteristic
468C2×#121C22×C10711yescharacteristic
469C2×C4×D4C22×C10711yescharacteristic
470C2×C4×D4C22×C10711yescharacteristic
471C22×C4⋊C4C22×C10711yescharacteristic
472C22×C4⋊C4C22×C10711yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C10711yescharacteristic
476C2×#103C22×C10711yescharacteristic
477C2×#103C22×C10711yescharacteristic
478C2×#102C22×C10711yescharacteristic
479C2×#102C22×C10711yescharacteristic
480C2×#102C22×C10711yescharacteristic
481C2×#102C22×C10711yescharacteristic
482C2×#102C22×C10711yescharacteristic
483C2×C22⋊C8C22×C10711yescharacteristic
484C2×C22⋊C8C22×C10711yescharacteristic
485C2×C22⋊C8C22×C10711yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C10711yescharacteristic
489#390C22×C10711yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C10711yescharacteristic
493#340C22×C10711yescharacteristic
494#340C22×C10711yescharacteristic
495#340C22×C10711yescharacteristic
496#340C22×C10711yescharacteristic
497#340C22×C10711yescharacteristic
498#340C22×C10711yescharacteristic
499#336C22×C10711yescharacteristic
500#336C22×C10711yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C10711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C10711yescharacteristic
517C22×D4C23×C10711yescharacteristic
518C22×D4C23×C10711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C10711yescharacteristic
524C23×C4C23×C10711yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C10711yescharacteristic
535C22×C8C23×C10711yescharacteristic
536C22×C8C23×C10711yescharacteristic
537C22×C8C23×C10711yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C10714yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C10711yescharacteristic
563C2×C4⋊C4D4×C10714yescomplemented
564C2×C4⋊C4C23×C10711yescharacteristic
565C2×C4⋊C4C23×C10711yescharacteristic
566C2×C4⋊C4C23×C10711yescharacteristic
567C2×C4⋊C4C23×C10711yescharacteristic
568C2×C4⋊C4C23×C10711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C10711yescharacteristic
578C2×C22⋊C4D4×C10711yescharacteristic
579C2×C42C23×C10711yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C10711yescharacteristic
597C24C2×D4×C10711yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C10712yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C10712yes—
638C2×D4#41×C10712yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C10711yescharacteristic
668C22×C4C2×D4×C10711yescharacteristic
669C22×C4C2×D4×C10711yescharacteristic
670C22×C4C2×D4×C10712yes—
671C22×C4C2×D4×C10712yes—
672C22×C4C2×D4×C10711yescharacteristic
673C22×C4C24×C10711yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C10712yes—
702C4⋊C4C2×D4×C10712yes—
703C4⋊C4C2×D4×C10712yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C10712yes—
743C23AGL(1,ℤ/8)×C10712yes—
744C23C22×D4×C10711yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C10712yes—
804C2×C4AGL(1,ℤ/8)×C10712yes—
805C2×C4C22×D4×C10711yescharacteristic
806C2×C4C22×D4×C10711yescharacteristic
807C2×C4C2×#41×C10711yescharacteristic
808C2×C4C2×#41×C10711yescharacteristic
809C2×C4H(5,𝔽2)×C10711yescharacteristic
810C2×C4H(5,𝔽2)×C10711yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C10711yescharacteristic
844C22#546×C10711yescharacteristic
845C22#546×C10711yescharacteristic
846C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
847C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
848C22#577×C10711yescharacteristic
849C22#578×C10711yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C10711yescharacteristic
861C4#535×C10711yescharacteristic
862C4#546×C10711yescharacteristic
863C4#546×C10711yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C107×#240411yescharacteristic
869C2C107×#300311yescharacteristic
870C2C107×#301311yescharacteristic
871C2C107×#330611yescharacteristic
872C2C107×#330811yescharacteristic
873C2C107×#333011yescharacteristic
874C2C107×#333211yescharacteristic
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×#547×C107C2semidirect
2. C2×#449×C107C2semidirect
3. C2×#417×C107C2semidirect
4. C107×#2407C2semidirect
5. C107×#2024C2semidirect
6. C107×#2023C2semidirect
7. C107×#2000C2semidirect
8. C107×#1999C2semidirect
9. C107×#1895C2semidirect
10. C107×#1879C2semidirect
11. C107×#1877C2semidirect
12. C107×#1874C2semidirect
13. C107×#1872C2semidirect
14. C107×#1870C2semidirect
15. C107×#1824C2semidirect
112. #121×C107D4semidirect
125. C2×C4⋊C4×C107D4semidirect
173. C2×Q8×C107#41semidirect
200. C2×D4×C107#41semidirect
426. #23972C107direct (N × H)
438. C2×#547C2×C107semidirect
439. C2×#449C2×C107semidirect
440. C2×#417C2×C107semidirect
441. #2407C2×C107semidirect
442. #2024C2×C107semidirect
443. #2023C2×C107semidirect
444. #2000C2×C107semidirect
445. #1999C2×C107semidirect
446. #1895C2×C107semidirect
447. #1879C2×C107semidirect
448. #1877C2×C107semidirect
449. #1874C2×C107semidirect
450. #1872C2×C107semidirect
451. #1870C2×C107semidirect
452. #1824C2×C107semidirect
453. C107#23972direct (N × H)
550. #121D4×C107semidirect
563. C2×C4⋊C4D4×C107semidirect
611. C2×Q8#41×C107semidirect
638. C2×D4#41×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1072
C2×#449×C1072
C2×#417×C1072
C107×#24072
C107×#20242
C107×#20232
C107×#20002
C107×#19992
C107×#18952
C107×#18792
C107×#18772
C107×#18742
C107×#18722
C107×#18702
C107×#18242
#23972107