Finite Group Databasebeta

← C107×#24475 #41050439

Subgroups — C107×#24475 #41050439

Order 27392.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3585C211yesmaximal, characteristic
2C107×#3069C211yesmaximal, characteristic, complemented
3C107×#3040C211yesmaximal, characteristic, complemented
4C107×#3022C211yesmaximal, characteristic, complemented
5C2×#455×C107C211yesmaximal, characteristic, complemented
6C107×#2901C211yesmaximal, characteristic, complemented
7C107×#2050C211yesmaximal, characteristic, complemented
8C107×#2048C211yesmaximal, characteristic, complemented
9C107×#2009C211yesmaximal, characteristic, complemented
10C107×#2003C211yesmaximal, characteristic, complemented
11C107×#1906C211yesmaximal, characteristic, complemented
12C107×#1903C211yesmaximal, characteristic, complemented
13C107×#1902C211yesmaximal, characteristic, complemented
14C107×#1861C211yesmaximal, characteristic, complemented
15C107×#1795C211yesmaximal, characteristic, complemented
16#585×C107C2211yescharacteristic
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18#577×C107—22no—
19#577×C107—22no—
20#576×C107—22no—
21#576×C107—22no—
22#575×C107—22no—
23#575×C107C2211yescharacteristic
24#575×C107C2211yescharacteristic
25C2×#137×C107C2211yescharacteristic
26C2×#137×C107C2211yescharacteristic, complemented
27C2×#137×C107C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C107—22no—
29C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
31#568×C107C2211yescharacteristic
32#568×C107C2211yescharacteristic, complemented
33#536×C107C2211yescharacteristic, complemented
34C2×#124×C107C2211yescharacteristic, complemented
35C4×#41×C107C2211yescharacteristic, complemented
36#473×C107—22no—
37#471×C107—22no—
38#464×C107—22no—
39#463×C107—22no—
40#456×C107—22no—
41#455×C107—22no—
42#455×C107—22no—
43#455×C107—22no—
44#430×C107C2211yescharacteristic, complemented
45#423×C107C2211yescharacteristic, complemented
46#421×C107—22no—
47#421×C107C2211yescharacteristic
48#421×C107C2211yescharacteristic
49#421×C107C2211yescharacteristic, complemented
50#421×C107C2211yescharacteristic, complemented
51C2×#104×C107—22no—
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic, complemented
54C2×#104×C107C2211yescharacteristic, complemented
55#419×C107C2211yescharacteristic, complemented
56#418×C107C2211yescharacteristic, complemented
57#418×C107C2211yescharacteristic, complemented
58#413×C107C2211yescharacteristic, complemented
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—21no—
682−1+4×C107—21no—
692−1+4×C107D412yes—
70H(5,𝔽2)×C107—22no—
71H(5,𝔽2)×C107—21no—
72H(5,𝔽2)×C107—22no—
73H(5,𝔽2)×C107—21no—
74H(5,𝔽2)×C107—22no—
75H(5,𝔽2)×C107—41no—
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×C107C2311yescharacteristic
84C2×#41×C107C2311yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C2×#41×C107C2311yescharacteristic
87C22×Q8×C107C2311yescharacteristic
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—41no—
91C22×D4×C107C2311yescharacteristic
92#137×C107—24no—
93#137×C107—21no—
94#137×C107—21no—
95#137×C107—21no—
96#137×C107—22no—
97#137×C107—22no—
98#137×C107—22no—
99#137×C107—22no—
100#137×C107—22no—
101#137×C107—41no—
102#137×C107D412yes—
103AGL(1,ℤ/8)×C107—24no—
104AGL(1,ℤ/8)×C107—24no—
105AGL(1,ℤ/8)×C107—24no—
106AGL(1,ℤ/8)×C107—22no—
107AGL(1,ℤ/8)×C107—22no—
108AGL(1,ℤ/8)×C107—21no—
109AGL(1,ℤ/8)×C107—22no—
110AGL(1,ℤ/8)×C107—21no—
111AGL(1,ℤ/8)×C107—21no—
112AGL(1,ℤ/8)×C107—22no—
113AGL(1,ℤ/8)×C107D412yes—
114#135×C107—24no—
115#135×C107—24no—
116#135×C107—22no—
117#135×C107—22no—
118C2×Q16×C107—21no—
119C2×Q16×C107—21no—
120C2×Q16×C107—21no—
121C2×SD16×C107—24no—
122C2×SD16×C107—21no—
123C2×SD16×C107—21no—
124C2×SD16×C107—21no—
125C2×SD16×C107—21no—
126C2×SD16×C107D412yes—
127C2×D8×C107—24no—
128C2×D8×C107—21no—
129C2×D8×C107D412yes—
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
142C4⋊Q8×C107—21no—
143#124×C107—21no—
144#124×C107—22no—
145#124×C107—21no—
146#124×C107—21no—
147#123×C107—41no—
148C22⋊Q8×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×C107D412yes—
169#104×C107D412yes—
170#103×C107—22no—
171#102×C107—22no—
172#102×C107—41no—
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—
181C24×C107—41no—
182#41×C107—21no—
183#41×C107—21no—
184#41×C107—21no—
185#41×C107—21no—
186#41×C107—24no—
187#41×C107—22no—
188#41×C107—22no—
189#41×C107—22no—
190#41×C107—22no—
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—21no—
199#41×C107—42no—
200#41×C107—42no—
201#41×C107—42no—
202#41×C107—42no—
203#41×C107—42no—
204#41×C107—42no—
205#41×C107—41no—
206#41×C107—41no—
207#41×C107—42no—
208#41×C107C2×D412yes—
209#41×C107C2×D412yes—
210#41×C107C2×D412yes—
211#41×C107C2×D412yes—
212C2×Q8×C107—22no—
213C2×Q8×C107—22no—
214C2×Q8×C107—21no—
215C2×Q8×C107—21no—
216C2×Q8×C107—21no—
217C2×Q8×C107—21no—
218C2×Q8×C107—21no—
219C2×Q8×C107—21no—
220C2×Q8×C107—41no—
221C2×Q8×C107C2×D411yescharacteristic
222C2×Q8×C107C2×D411yescharacteristic
223C2×Q8×C107C2×D411yescharacteristic
224C2×Q8×C107#4111yescharacteristic
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—24no—
228C2×D4×C107—22no—
229C2×D4×C107—22no—
230C2×D4×C107—21no—
231C2×D4×C107—21no—
232C2×D4×C107—21no—
233C2×D4×C107—21no—
234C2×D4×C107—21no—
235C2×D4×C107—21no—
236C2×D4×C107—21no—
237C2×D4×C107—42no—
238C2×D4×C107—41no—
239C2×D4×C107—41no—
240C2×D4×C107—42no—
241C2×D4×C107—42no—
242C2×D4×C107—41no—
243C2×D4×C107—44no—
244C2×D4×C107—42no—
245C2×D4×C107—42no—
246C2×D4×C107—44no—
247C2×D4×C107—42no—
248C2×D4×C107C2×D411yescharacteristic
249C2×D4×C107C2×D411yescharacteristic
250C2×D4×C107C2×D412yes—
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—41no—
260C22×C4×C107—42no—
261C22×C4×C107—41no—
262C22×C4×C107C2411yescharacteristic
263Q16×C107—22no—
264Q16×C107—22no—
265Q16×C107—42no—
266Q16×C107—42no—
267Q16×C107—42no—
268SD16×C107—24no—
269SD16×C107—22no—
270SD16×C107—22no—
271SD16×C107—22no—
272SD16×C107—24no—
273SD16×C107—22no—
274SD16×C107—42no—
275SD16×C107—42no—
276SD16×C107—42no—
277D8×C107—24no—
278D8×C107—22no—
279D8×C107—22no—
280D8×C107—24no—
281M16×C107—24no—
282M16×C107—21no—
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—42no—
293M16×C107C2×D412yes—
294M16×C107C2×D412yes—
295C2×C8×C107—24no—
296C2×C8×C107—21no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107—21no—
300C2×C8×C107—21no—
301C2×C8×C107—42no—
302C2×C8×C107C2×D412yes—
303C4⋊C4×C107—21no—
304C4⋊C4×C107—21no—
305C4⋊C4×C107—41no—
306C4⋊C4×C107—42no—
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—22no—
323C23×C107—21no—
324C23×C107—42no—
325C23×C107—44no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—82no—
329C23×C107—162no—
330C23×C107H(5,𝔽2)11yescharacteristic
331Q8×C107—21no—
332Q8×C107—21no—
333Q8×C107—21no—
334Q8×C107—21no—
335Q8×C107—21no—
336Q8×C107—21no—
337Q8×C107—42no—
338Q8×C107—41no—
339Q8×C107—41no—
340Q8×C107—41no—
341Q8×C107—41no—
342Q8×C107#12012yes—
343Q8×C107#12112yes—
344D4×C107—22no—
345D4×C107—22no—
346D4×C107—22no—
347D4×C107—22no—
348D4×C107—21no—
349D4×C107—21no—
350D4×C107—22no—
351D4×C107—21no—
352D4×C107—21no—
353D4×C107—21no—
354D4×C107—21no—
355D4×C107—22no—
356D4×C107—42no—
357D4×C107—42no—
358D4×C107—44no—
359D4×C107—42no—
360D4×C107—44no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—41no—
366D4×C107—41no—
367D4×C107#12012yes—
368D4×C107#12112yes—
369C2×C4×C107—21no—
370C2×C4×C107—21no—
371C2×C4×C107—22no—
372C2×C4×C107—22no—
373C2×C4×C107—22no—
374C2×C4×C107—22no—
375C2×C4×C107—21no—
376C2×C4×C107—21no—
377C2×C4×C107—21no—
378C2×C4×C107—21no—
379C2×C4×C107—42no—
380C2×C4×C107—42no—
381C2×C4×C107—42no—
382C2×C4×C107—44no—
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—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—42no—
411C22×C107—41no—
412C22×C107—81no—
413C22×C107—81no—
414C22×C107—81no—
415C22×C107—82no—
416C22×C107—81no—
417C22×C107—82no—
418C22×C107—161no—
419C22×C107—162no—
420C22×C107—164no—
421C22×C107#53411yescharacteristic
422C22×C107D4211yescharacteristic
423C22×C107#54611yescharacteristic
424C4×C107—22no—
425C4×C107—22no—
426C4×C107—41no—
427C4×C107—41no—
428C4×C107—41no—
429C4×C107—41no—
430C4×C107—81no—
431C4×C107—81no—
432C4×C107—81no—
433C4×C107C2×#12011yescharacteristic
434C4×C107C2×#12111yescharacteristic
435C4×C107D4211yescharacteristic
436C4×C107#54611yescharacteristic
437#24475C10711yesmaximal, characteristic, direct product factor, Sylow
438C2×C107—21no—
439C2×C107—21no—
440C2×C107—21no—
441C2×C107—42no—
442C2×C107—42no—
443C2×C107—82no—
444C2×C107—81no—
445C2×C107—81no—
446C2×C107#241011yescharacteristic
447#3585C2×C10711yescharacteristic
448#3069C2×C10711yescharacteristic, complemented
449#3040C2×C10711yescharacteristic, complemented
450#3022C2×C10711yescharacteristic, complemented
451C2×#455C2×C10711yescharacteristic, complemented
452#2901C2×C10711yescharacteristic, complemented
453#2050C2×C10711yescharacteristic, complemented
454#2048C2×C10711yescharacteristic, complemented
455#2009C2×C10711yescharacteristic, complemented
456#2003C2×C10711yescharacteristic, complemented
457#1906C2×C10711yescharacteristic, complemented
458#1903C2×C10711yescharacteristic, complemented
459#1902C2×C10711yescharacteristic, complemented
460#1861C2×C10711yescharacteristic, complemented
461#1795C2×C10711yescharacteristic, complemented
462C107#2447511yescharacteristic, direct product factor, Sylow
463#585C22×C10711yescharacteristic
464C2×H(5,𝔽2)C22×C10711yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C10711yescharacteristic
471#575C22×C10711yescharacteristic
472C2×#137C22×C10711yescharacteristic
473C2×#137C22×C10711yescharacteristic, complemented
474C2×#137C22×C10711yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
477C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
478#568C22×C10711yescharacteristic
479#568C22×C10711yescharacteristic, complemented
480#536C22×C10711yescharacteristic, complemented
481C2×#124C22×C10711yescharacteristic, complemented
482C4×#41C22×C10711yescharacteristic, complemented
483#473—22no—
484#471—22no—
485#464—22no—
486#463—22no—
487#456—22no—
488#455—22no—
489#455—22no—
490#455—22no—
491#430C22×C10711yescharacteristic, complemented
492#423C22×C10711yescharacteristic, complemented
493#421—22no—
494#421C22×C10711yescharacteristic
495#421C22×C10711yescharacteristic
496#421C22×C10711yescharacteristic, complemented
497#421C22×C10711yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C10711yescharacteristic
500C2×#104C22×C10711yescharacteristic, complemented
501C2×#104C22×C10711yescharacteristic, complemented
502#419C22×C10711yescharacteristic, complemented
503#418C22×C10711yescharacteristic, complemented
504#418C22×C10711yescharacteristic, complemented
505#413C22×C10711yescharacteristic, complemented
506#413C22×C10711yescharacteristic, complemented
507C2×#101C22×C10711yescharacteristic, complemented
508C2×#100C22×C10711yescharacteristic, complemented
509#410C22×C10711yescharacteristic, complemented
510#344C22×C10711yescharacteristic, complemented
511#344C22×C10711yescharacteristic, complemented
512#339C22×C10711yescharacteristic, complemented
513#338C22×C10711yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C10712yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C10712yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C10711yescharacteristic
531C2×#41C23×C10711yescharacteristic
532C2×#41C23×C10711yescharacteristic
533C2×#41C23×C10711yescharacteristic
534C22×Q8C23×C10711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C10711yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C10712yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C10712yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C10712yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C10712yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C10711yescharacteristic
584C2×M16C23×C10711yescharacteristic
585C2×M16C23×C10711yescharacteristic
586C2×M16C23×C10711yescharacteristic
587C2×M16C23×C10711yescharacteristic
588C2×M16C23×C10711yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C10711yescharacteristic
601#117C23×C10711yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C10711yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C10712yes—
616#104D4×C10712yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C10712yes—
656#41C2×D4×C10712yes—
657#41C2×D4×C10712yes—
658#41C2×D4×C10712yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C10711yescharacteristic
669C2×Q8C2×D4×C10711yescharacteristic
670C2×Q8C2×D4×C10711yescharacteristic
671C2×Q8#41×C10711yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C10711yescharacteristic
696C2×D4C2×D4×C10711yescharacteristic
697C2×D4C2×D4×C10712yes—
698C2×D4C2×D4×C10711yescharacteristic
699C2×D4#41×C10711yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C10711yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
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—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C10711yescharacteristic
765C42C2×D4×C10711yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C10711yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C10712yes—
790Q8#121×C10712yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C10712yes—
815D4#121×C10712yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
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—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C10711yescharacteristic
842C2×C4C22×D4×C10711yescharacteristic
843C2×C4C22×D4×C10711yescharacteristic
844C2×C4C22×D4×C10711yescharacteristic
845C2×C4C2×#41×C10711yescharacteristic
846C2×C4H(5,𝔽2)×C10711yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22#534×C10711yescharacteristic
869C22D42×C10711yescharacteristic
870C22#546×C10711yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C10711yescharacteristic
881C4C2×#121×C10711yescharacteristic
882C4D42×C10711yescharacteristic
883C4#546×C10711yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C107×#241011yescharacteristic
subgroupG/H
center, socleC2×C107#2410
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3585C2
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
2. C107×#3069C2semidirect
3. C107×#3040C2semidirect
4. C107×#3022C2semidirect
5. C2×#455×C107C2semidirect
6. C107×#2901C2semidirect
7. C107×#2050C2semidirect
8. C107×#2048C2semidirect
9. C107×#2009C2semidirect
10. C107×#2003C2semidirect
11. C107×#1906C2semidirect
12. C107×#1903C2semidirect
13. C107×#1902C2semidirect
14. C107×#1861C2semidirect
15. C107×#1795C2semidirect
26. C2×#137×C107C22semidirect
27. C2×#137×C107C22semidirect
32. #568×C107C22semidirect
33. #536×C107C22semidirect
34. C2×#124×C107C22semidirect
35. C4×#41×C107C22semidirect
44. #430×C107C22semidirect
45. #423×C107C22semidirect
49. #421×C107C22semidirect
50. #421×C107C22semidirect
53. C2×#104×C107C22semidirect
54. C2×#104×C107C22semidirect
55. #419×C107C22semidirect
56. #418×C107C22semidirect
57. #418×C107C22semidirect
58. #413×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
437. #24475C107direct (N × H)
448. #3069C2×C107semidirect
449. #3040C2×C107semidirect
450. #3022C2×C107semidirect
451. C2×#455C2×C107semidirect
452. #2901C2×C107semidirect
453. #2050C2×C107semidirect
454. #2048C2×C107semidirect
455. #2009C2×C107semidirect
456. #2003C2×C107semidirect
457. #1906C2×C107semidirect
458. #1903C2×C107semidirect
459. #1902C2×C107semidirect
460. #1861C2×C107semidirect
461. #1795C2×C107semidirect
462. C107#24475direct (N × H)
473. C2×#137C22×C107semidirect
474. C2×#137C22×C107semidirect
479. #568C22×C107semidirect
480. #536C22×C107semidirect
481. C2×#124C22×C107semidirect
482. C4×#41C22×C107semidirect
491. #430C22×C107semidirect
492. #423C22×C107semidirect
496. #421C22×C107semidirect
497. #421C22×C107semidirect
500. C2×#104C22×C107semidirect
501. C2×#104C22×C107semidirect
502. #419C22×C107semidirect
503. #418C22×C107semidirect
504. #418C22×C107semidirect
505. #413C22×C107semidirect
506. #413C22×C107semidirect
507. C2×#101C22×C107semidirect
508. C2×#100C22×C107semidirect
509. #410C22×C107semidirect
510. #344C22×C107semidirect
511. #344C22×C107semidirect
512. #339C22×C107semidirect
513. #338C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35852
C107×#30692
C107×#30402
C107×#30222
C2×#455×C1072
C107×#29012
C107×#20502
C107×#20482
C107×#20092
C107×#20032
C107×#19062
C107×#19032
C107×#19022
C107×#18612
C107×#17952
#24475107