Finite Group Databasebeta

← C107×#24473 #41050437

Subgroups — C107×#24473 #41050437

Order 27392.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3586C211yesmaximal, characteristic, complemented
2C107×#3068C211yesmaximal, characteristic, complemented
3C107×#3040C211yesmaximal, characteristic, complemented
4C107×#3021C211yesmaximal, characteristic, complemented
5C2×#454×C107C211yesmaximal, characteristic, complemented
6C107×#2901C211yesmaximal, characteristic, complemented
7C107×#2050C211yesmaximal, characteristic, complemented
8C107×#2049C211yesmaximal, characteristic, complemented
9C107×#2008C211yesmaximal, characteristic, complemented
10C107×#2004C211yesmaximal, characteristic, complemented
11C107×#1906C211yesmaximal, characteristic, complemented
12C107×#1903C211yesmaximal, characteristic, complemented
13C107×#1902C211yesmaximal, characteristic, complemented
14C107×#1861C211yesmaximal, characteristic, complemented
15C107×#1796C211yesmaximal, characteristic, complemented
16#585×C107C2211yescharacteristic
17C2×2−1+4×C107C2211yescharacteristic
18#578×C107—22no—
19#578×C107—22no—
20#577×C107—22no—
21#577×C107—22no—
22#575×C107—22no—
23#575×C107C2211yescharacteristic
24#575×C107C2211yescharacteristic
25C2×#137×C107—22no—
26C2×#137×C107C2211yescharacteristic
27C2×#137×C107C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
31#568×C107C2211yescharacteristic
32#568×C107C2211yescharacteristic
33#535×C107C2211yescharacteristic
34C2×#124×C107C2211yescharacteristic, complemented
35C4×#41×C107C2211yescharacteristic
36#472×C107—22no—
37#471×C107—22no—
38#464×C107—22no—
39#463×C107—22no—
40#454×C107—22no—
41#454×C107—22no—
42#454×C107—22no—
43#453×C107—22no—
44#430×C107C2211yescharacteristic, complemented
45#423×C107C2211yescharacteristic, complemented
46#421×C107—22no—
47#421×C107C2211yescharacteristic
48#421×C107C2211yescharacteristic
49#421×C107C2211yescharacteristic
50#421×C107C2211yescharacteristic
51C2×#104×C107—22no—
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic
54C2×#104×C107C2211yescharacteristic, complemented
55#419×C107C2211yescharacteristic, complemented
56#419×C107C2211yescharacteristic, complemented
57#418×C107C2211yescharacteristic, complemented
58#413×C107C2211yescharacteristic
59#413×C107C2211yescharacteristic, complemented
60C2×#101×C107C2211yescharacteristic, complemented
61C2×#100×C107C2211yescharacteristic, complemented
62#410×C107C2211yescharacteristic, complemented
63#344×C107C2211yescharacteristic, complemented
64#344×C107C2211yescharacteristic, complemented
65#339×C107C2211yescharacteristic, complemented
66#338×C107C2211yescharacteristic, complemented
672−1+4×C107—22no—
682−1+4×C107—22no—
692−1+4×C107—21no—
702−1+4×C107—21no—
712−1+4×C107—22no—
722−1+4×C107—41no—
732−1+4×C107D412yes—
74H(5,𝔽2)×C107—21no—
75H(5,𝔽2)×C107—21no—
76H(5,𝔽2)×C107—41no—
77H(5,𝔽2)×C107D412yes—
78C2×#41×C107—22no—
79C2×#41×C107—22no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—41no—
83C2×#41×C107—41no—
84C2×#41×C107C2311yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C2×#41×C107C2311yescharacteristic
87C2×#41×C107C2311yescharacteristic
88C22×Q8×C107—21no—
89C22×Q8×C107—21no—
90C22×Q8×C107C2311yescharacteristic
91C22×D4×C107C2311yescharacteristic
92#137×C107—24no—
93#137×C107—24no—
94#137×C107—24no—
95#137×C107—22no—
96#137×C107—22no—
97#137×C107—21no—
98#137×C107—22no—
99#137×C107—21no—
100#137×C107—21no—
101#137×C107—22no—
102#137×C107D412yescomplemented
103AGL(1,ℤ/8)×C107—24no—
104AGL(1,ℤ/8)×C107—21no—
105AGL(1,ℤ/8)×C107—21no—
106AGL(1,ℤ/8)×C107—21no—
107AGL(1,ℤ/8)×C107—22no—
108AGL(1,ℤ/8)×C107—22no—
109AGL(1,ℤ/8)×C107—22no—
110AGL(1,ℤ/8)×C107—22no—
111AGL(1,ℤ/8)×C107—22no—
112AGL(1,ℤ/8)×C107—41no—
113AGL(1,ℤ/8)×C107D412yescomplemented
114#135×C107—24no—
115#135×C107—24no—
116#135×C107—22no—
117#135×C107—22no—
118C2×Q16×C107—24no—
119C2×Q16×C107—21no—
120C2×Q16×C107D412yescomplemented
121C2×SD16×C107—24no—
122C2×SD16×C107—21no—
123C2×SD16×C107—21no—
124C2×SD16×C107—21no—
125C2×SD16×C107—21no—
126C2×SD16×C107D412yescomplemented
127C2×D8×C107—21no—
128C2×D8×C107—21no—
129C2×D8×C107—21no—
130#131×C107—22no—
131#131×C107—22no—
132#131×C107—22no—
133#131×C107—41no—
134C2×M16×C107—22no—
135C2×M16×C107—22no—
136C2×M16×C107C2311yescharacteristic
137C2×M16×C107C2311yescharacteristic
138C2×M16×C107C2311yescharacteristic
139C2×M16×C107C2311yescharacteristic
140C2×M16×C107C2311yescharacteristic
141C2×M16×C107C2311yescharacteristic
142#127×C107—21no—
143#124×C107—21no—
144#124×C107—22no—
145#124×C107—21no—
146#124×C107—21no—
147#121×C107—41no—
148#120×C107—41no—
149C4×Q8×C107—21no—
150C4×D4×C107—21no—
151C4×D4×C107—41no—
152#117×C107—21no—
153#117×C107C2311yescharacteristic
154#117×C107C2311yescharacteristic
155C2×C22⋊C4×C107—41no—
156C2×C42×C107—21no—
157C2×C42×C107C2311yescharacteristic
158#108×C107—22no—
159C4⋊C8×C107—22no—
160#104×C107—22no—
161#104×C107—22no—
162#104×C107—22no—
163#104×C107—22no—
164#104×C107—21no—
165#104×C107—21no—
166#104×C107—21no—
167#104×C107—21no—
168#104×C107D412yescomplemented
169#104×C107D412yescomplemented
170#103×C107—22no—
171#103×C107—41no—
172#102×C107—22no—
173#101×C107—21no—
174#101×C107—21no—
175#101×C107—22no—
176#100×C107—21no—
177#100×C107—21no—
178#100×C107—22no—
179#99×C107—41no—
180C24×C107—21no—
181#41×C107—21no—
182#41×C107—21no—
183#41×C107—21no—
184#41×C107—21no—
185#41×C107—24no—
186#41×C107—22no—
187#41×C107—22no—
188#41×C107—22no—
189#41×C107—22no—
190#41×C107—21no—
191#41×C107—21no—
192#41×C107—21no—
193#41×C107—21no—
194#41×C107—21no—
195#41×C107—21no—
196#41×C107—21no—
197#41×C107—21no—
198#41×C107—42no—
199#41×C107—42no—
200#41×C107—42no—
201#41×C107—42no—
202#41×C107—42no—
203#41×C107—44no—
204#41×C107—42no—
205#41×C107—41no—
206#41×C107—41no—
207#41×C107—44no—
208#41×C107—42no—
209#41×C107C2×D412yes—
210#41×C107C2×D412yes—
211#41×C107C2×D412yes—
212#41×C107C2×D412yes—
213C2×Q8×C107—21no—
214C2×Q8×C107—24no—
215C2×Q8×C107—22no—
216C2×Q8×C107—22no—
217C2×Q8×C107—21no—
218C2×Q8×C107—21no—
219C2×Q8×C107—21no—
220C2×Q8×C107—21no—
221C2×Q8×C107—41no—
222C2×Q8×C107—42no—
223C2×Q8×C107—42no—
224C2×Q8×C107—41no—
225C2×Q8×C107—42no—
226C2×Q8×C107C2×D411yescharacteristic
227C2×Q8×C107C2×D411yescharacteristic
228C2×Q8×C107C2×D412yes—
229C2×Q8×C107C2×D411yescharacteristic
230C2×Q8×C107#4111yescharacteristic
231C2×D4×C107—21no—
232C2×D4×C107—21no—
233C2×D4×C107—22no—
234C2×D4×C107—22no—
235C2×D4×C107—21no—
236C2×D4×C107—21no—
237C2×D4×C107—21no—
238C2×D4×C107—21no—
239C2×D4×C107—21no—
240C2×D4×C107—21no—
241C2×D4×C107—21no—
242C2×D4×C107—21no—
243C2×D4×C107—42no—
244C2×D4×C107—41no—
245C2×D4×C107—42no—
246C2×D4×C107—42no—
247C2×D4×C107—41no—
248C2×D4×C107—42no—
249C2×D4×C107C2×D411yescharacteristic
250C2×D4×C107C2×D411yescharacteristic
251C2×D4×C107C2×D411yescharacteristic
252C2×D4×C107#4111yescharacteristic
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—21no—
259C22×C4×C107—42no—
260C22×C4×C107—41no—
261C22×C4×C107—41no—
262C22×C4×C107—41no—
263C22×C4×C107C2411yescharacteristic
264Q16×C107—24no—
265Q16×C107—22no—
266Q16×C107—22no—
267Q16×C107—24no—
268SD16×C107—24no—
269SD16×C107—22no—
270SD16×C107—22no—
271SD16×C107—22no—
272SD16×C107—22no—
273SD16×C107—24no—
274SD16×C107—42no—
275SD16×C107—42no—
276SD16×C107—42no—
277D8×C107—22no—
278D8×C107—22no—
279D8×C107—42no—
280D8×C107—42no—
281D8×C107—42no—
282M16×C107—24no—
283M16×C107—21no—
284M16×C107—21no—
285M16×C107—21no—
286M16×C107—21no—
287M16×C107—21no—
288M16×C107—21no—
289M16×C107—21no—
290M16×C107—21no—
291M16×C107—21no—
292M16×C107—21no—
293M16×C107—42no—
294M16×C107C2×D412yes—
295M16×C107C2×D412yes—
296C2×C8×C107—24no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107—21no—
300C2×C8×C107—21no—
301C2×C8×C107—21no—
302C2×C8×C107—42no—
303C2×C8×C107C2×D412yes—
304C4⋊C4×C107—21no—
305C4⋊C4×C107—21no—
306C4⋊C4×C107—41no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—42no—
310C22⋊C4×C107—42no—
311C22⋊C4×C107—41no—
312C22⋊C4×C107—42no—
313C42×C107—21no—
314C42×C107—21no—
315C42×C107—21no—
316C42×C107—41no—
317C42×C107C2×D411yescharacteristic
318C42×C107C2×D411yescharacteristic
319C23×C107—21no—
320C23×C107—21no—
321C23×C107—21no—
322C23×C107—21no—
323C23×C107—42no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—82no—
328C23×C107H(5,𝔽2)11yescharacteristic
329Q8×C107—21no—
330Q8×C107—21no—
331Q8×C107—21no—
332Q8×C107—22no—
333Q8×C107—21no—
334Q8×C107—21no—
335Q8×C107—21no—
336Q8×C107—22no—
337Q8×C107—42no—
338Q8×C107—44no—
339Q8×C107—41no—
340Q8×C107—41no—
341Q8×C107#12012yes—
342Q8×C107#12112yes—
343D4×C107—22no—
344D4×C107—22no—
345D4×C107—22no—
346D4×C107—22no—
347D4×C107—21no—
348D4×C107—21no—
349D4×C107—21no—
350D4×C107—21no—
351D4×C107—21no—
352D4×C107—21no—
353D4×C107—42no—
354D4×C107—42no—
355D4×C107—42no—
356D4×C107—44no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—162no—
366D4×C107#12012yes—
367D4×C107#12112yes—
368C2×C4×C107—21no—
369C2×C4×C107—21no—
370C2×C4×C107—22no—
371C2×C4×C107—22no—
372C2×C4×C107—22no—
373C2×C4×C107—22no—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—21no—
377C2×C4×C107—22no—
378C2×C4×C107—21no—
379C2×C4×C107—42no—
380C2×C4×C107—42no—
381C2×C4×C107—42no—
382C2×C4×C107—44no—
383C2×C4×C107—44no—
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—81no—
393C2×C4×C107—82no—
394C2×C4×C107C22×D411yescharacteristic
395C2×C4×C107C22×D411yescharacteristic
396C2×C4×C107C22×D411yescharacteristic
397C2×C4×C107C22×D411yescharacteristic
398C2×C4×C107C2×#4111yescharacteristic
399C2×C4×C107H(5,𝔽2)11yescharacteristic
400C8×C107—22no—
401C8×C107—22no—
402C8×C107—22no—
403C8×C107—41no—
404C8×C107—41no—
405C8×C107—41no—
406C22×C107—22no—
407C22×C107—22no—
408C22×C107—41no—
409C22×C107—41no—
410C22×C107—41no—
411C22×C107—81no—
412C22×C107—81no—
413C22×C107—81no—
414C22×C107—81no—
415C22×C107—82no—
416C22×C107—82no—
417C22×C107—81no—
418C22×C107—161no—
419C22×C107—162no—
420C22×C107#53411yescharacteristic
421C22×C107D4211yescharacteristic
422C22×C107#54611yescharacteristic
423C4×C107—22no—
424C4×C107—22no—
425C4×C107—41no—
426C4×C107—41no—
427C4×C107—41no—
428C4×C107—42no—
429C4×C107—41no—
430C4×C107—81no—
431C4×C107—81no—
432C4×C107C2×#12011yescharacteristic
433C4×C107C2×#12111yescharacteristic
434C4×C107D4211yescharacteristic
435C4×C107#54611yescharacteristic
436#24473C10711yesmaximal, characteristic, direct product factor, Sylow
437C2×C107—21no—
438C2×C107—21no—
439C2×C107—21no—
440C2×C107—42no—
441C2×C107—42no—
442C2×C107—81no—
443C2×C107—81no—
444C2×C107—161no—
445C2×C107#241011yescharacteristic
446#3586C2×C10711yescharacteristic, complemented
447#3068C2×C10711yescharacteristic, complemented
448#3040C2×C10711yescharacteristic, complemented
449#3021C2×C10711yescharacteristic, complemented
450C2×#454C2×C10711yescharacteristic, complemented
451#2901C2×C10711yescharacteristic, complemented
452#2050C2×C10711yescharacteristic, complemented
453#2049C2×C10711yescharacteristic, complemented
454#2008C2×C10711yescharacteristic, complemented
455#2004C2×C10711yescharacteristic, complemented
456#1906C2×C10711yescharacteristic, complemented
457#1903C2×C10711yescharacteristic, complemented
458#1902C2×C10711yescharacteristic, complemented
459#1861C2×C10711yescharacteristic, complemented
460#1796C2×C10711yescharacteristic, complemented
461C107#2447311yescharacteristic, direct product factor, Sylow
462#585C22×C10711yescharacteristic
463C2×2−1+4C22×C10711yescharacteristic
464#578—22no—
465#578—22no—
466#577—22no—
467#577—22no—
468#575—22no—
469#575C22×C10711yescharacteristic
470#575C22×C10711yescharacteristic
471C2×#137—22no—
472C2×#137C22×C10711yescharacteristic
473C2×#137C22×C10711yescharacteristic
474C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
475C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
476C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
477#568C22×C10711yescharacteristic
478#568C22×C10711yescharacteristic
479#535C22×C10711yescharacteristic
480C2×#124C22×C10711yescharacteristic, complemented
481C4×#41C22×C10711yescharacteristic
482#472—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#454—22no—
487#454—22no—
488#454—22no—
489#453—22no—
490#430C22×C10711yescharacteristic, complemented
491#423C22×C10711yescharacteristic, complemented
492#421—22no—
493#421C22×C10711yescharacteristic
494#421C22×C10711yescharacteristic
495#421C22×C10711yescharacteristic
496#421C22×C10711yescharacteristic
497C2×#104—22no—
498C2×#104C22×C10711yescharacteristic
499C2×#104C22×C10711yescharacteristic
500C2×#104C22×C10711yescharacteristic, complemented
501#419C22×C10711yescharacteristic, complemented
502#419C22×C10711yescharacteristic, complemented
503#418C22×C10711yescharacteristic, complemented
504#413C22×C10711yescharacteristic
505#413C22×C10711yescharacteristic, complemented
506C2×#101C22×C10711yescharacteristic, complemented
507C2×#100C22×C10711yescharacteristic, complemented
508#410C22×C10711yescharacteristic, complemented
509#344C22×C10711yescharacteristic, complemented
510#344C22×C10711yescharacteristic, complemented
511#339C22×C10711yescharacteristic, complemented
512#338C22×C10711yescharacteristic, complemented
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C10712yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C10712yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C10711yescharacteristic
531C2×#41C23×C10711yescharacteristic
532C2×#41C23×C10711yescharacteristic
533C2×#41C23×C10711yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C10711yescharacteristic
537C22×D4C23×C10711yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C10712yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C10712yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C10712yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C10712yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C10711yescharacteristic
583C2×M16C23×C10711yescharacteristic
584C2×M16C23×C10711yescharacteristic
585C2×M16C23×C10711yescharacteristic
586C2×M16C23×C10711yescharacteristic
587C2×M16C23×C10711yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C10711yescharacteristic
600#117C23×C10711yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C10711yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C10712yescomplemented
615#104D4×C10712yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C10712yes—
656#41C2×D4×C10712yes—
657#41C2×D4×C10712yes—
658#41C2×D4×C10712yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C10711yescharacteristic
673C2×Q8C2×D4×C10711yescharacteristic
674C2×Q8C2×D4×C10712yes—
675C2×Q8C2×D4×C10711yescharacteristic
676C2×Q8#41×C10711yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C10711yescharacteristic
696C2×D4C2×D4×C10711yescharacteristic
697C2×D4C2×D4×C10711yescharacteristic
698C2×D4#41×C10711yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C10711yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C10712yes—
741M16C2×D4×C10712yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C10712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C10711yescharacteristic
764C42C2×D4×C10711yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C10711yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C10712yes—
788Q8#121×C10712yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C10712yes—
813D4#121×C10712yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
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—81no—
839C2×C4—82no—
840C2×C4C22×D4×C10711yescharacteristic
841C2×C4C22×D4×C10711yescharacteristic
842C2×C4C22×D4×C10711yescharacteristic
843C2×C4C22×D4×C10711yescharacteristic
844C2×C4C2×#41×C10711yescharacteristic
845C2×C4H(5,𝔽2)×C10711yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22#534×C10711yescharacteristic
867C22D42×C10711yescharacteristic
868C22#546×C10711yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C10711yescharacteristic
879C4C2×#121×C10711yescharacteristic
880C4D42×C10711yescharacteristic
881C4#546×C10711yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2C107×#241011yescharacteristic
subgroupG/H
center, socleC2×C107#2410
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3586C2semidirect
2. C107×#3068C2semidirect
3. C107×#3040C2semidirect
4. C107×#3021C2semidirect
5. C2×#454×C107C2semidirect
6. C107×#2901C2semidirect
7. C107×#2050C2semidirect
8. C107×#2049C2semidirect
9. C107×#2008C2semidirect
10. C107×#2004C2semidirect
11. C107×#1906C2semidirect
12. C107×#1903C2semidirect
13. C107×#1902C2semidirect
14. C107×#1861C2semidirect
15. C107×#1796C2semidirect
30. C2×AGL(1,ℤ/8)×C107C22semidirect
34. C2×#124×C107C22semidirect
44. #430×C107C22semidirect
45. #423×C107C22semidirect
54. C2×#104×C107C22semidirect
55. #419×C107C22semidirect
56. #419×C107C22semidirect
57. #418×C107C22semidirect
59. #413×C107C22semidirect
60. C2×#101×C107C22semidirect
61. C2×#100×C107C22semidirect
62. #410×C107C22semidirect
63. #344×C107C22semidirect
64. #344×C107C22semidirect
65. #339×C107C22semidirect
66. #338×C107C22semidirect
102. #137×C107D4semidirect
113. AGL(1,ℤ/8)×C107D4semidirect
120. C2×Q16×C107D4semidirect
126. C2×SD16×C107D4semidirect
168. #104×C107D4semidirect
169. #104×C107D4semidirect
436. #24473C107direct (N × H)
446. #3586C2×C107semidirect
447. #3068C2×C107semidirect
448. #3040C2×C107semidirect
449. #3021C2×C107semidirect
450. C2×#454C2×C107semidirect
451. #2901C2×C107semidirect
452. #2050C2×C107semidirect
453. #2049C2×C107semidirect
454. #2008C2×C107semidirect
455. #2004C2×C107semidirect
456. #1906C2×C107semidirect
457. #1903C2×C107semidirect
458. #1902C2×C107semidirect
459. #1861C2×C107semidirect
460. #1796C2×C107semidirect
461. C107#24473direct (N × H)
476. C2×AGL(1,ℤ/8)C22×C107semidirect
480. C2×#124C22×C107semidirect
490. #430C22×C107semidirect
491. #423C22×C107semidirect
500. C2×#104C22×C107semidirect
501. #419C22×C107semidirect
502. #419C22×C107semidirect
503. #418C22×C107semidirect
505. #413C22×C107semidirect
506. C2×#101C22×C107semidirect
507. C2×#100C22×C107semidirect
508. #410C22×C107semidirect
509. #344C22×C107semidirect
510. #344C22×C107semidirect
511. #339C22×C107semidirect
512. #338C22×C107semidirect
548. #137D4×C107semidirect
559. AGL(1,ℤ/8)D4×C107semidirect
566. C2×Q16D4×C107semidirect
572. C2×SD16D4×C107semidirect
614. #104D4×C107semidirect
615. #104D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35862
C107×#30682
C107×#30402
C107×#30212
C2×#454×C1072
C107×#29012
C107×#20502
C107×#20492
C107×#20082
C107×#20042
C107×#19062
C107×#19032
C107×#19022
C107×#18612
C107×#17962
#24473107