Finite Group Databasebeta

← C107×#23894 #41049858

Subgroups — C107×#23894 #41049858

Order 27392.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3586C211yesmaximal, characteristic, complemented
2C107×#3585C211yesmaximal, characteristic, complemented
3C107×#3020C211yesmaximal, characteristic, complemented
4C107×#3019C211yesmaximal, characteristic, complemented
5C107×#3010C211yesmaximal, characteristic, complemented
6C107×#3009C211yesmaximal, characteristic, complemented
7C107×#2019C211yesmaximal, characteristic, complemented
8C107×#2017C211yesmaximal, characteristic, complemented
9C107×#2009C211yesmaximal, characteristic, complemented
10C107×#2008C211yesmaximal, characteristic, complemented
11C107×#1903C211yesmaximal, characteristic, complemented
12C107×#1902C211yesmaximal, characteristic, complemented
13C107×#1881C211yesmaximal, characteristic, complemented
14C107×#1881C211yesmaximal, characteristic, complemented
15C107×#1794C211yesmaximal, characteristic, complemented
16#585×C107C2211yescharacteristic
17C2×2−1+4×C107C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C107C2211yescharacteristic
19#578×C107—22no—
20#578×C107—22no—
21#577×C107—22no—
22#577×C107—22no—
23#577×C107—22no—
24#577×C107—22no—
25#576×C107—22no—
26#576×C107—22no—
27#575×C107—22no—
28#575×C107—22no—
29#575×C107C2211yescharacteristic
30#575×C107C2211yescharacteristic
31#575×C107C2211yescharacteristic
32#575×C107C2211yescharacteristic, complemented
33#575×C107C2211yescharacteristic, complemented
34C2×#137×C107—22no—
35C2×#137×C107C2211yescharacteristic
36C2×#137×C107C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C107—22no—
38C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
40C22×SD16×C107C2211yescharacteristic, complemented
41#568×C107C2211yescharacteristic
42#568×C107C2211yescharacteristic, complemented
43#536×C107C2211yescharacteristic, complemented
44#535×C107C2211yescharacteristic, complemented
45#456×C107—22no—
46#455×C107—22no—
47#454×C107—22no—
48#453×C107—22no—
49#452×C107—22no—
50#450×C107—22no—
51#449×C107—22no—
52#448×C107—22no—
53#421×C107C2211yescharacteristic
54#421×C107C2211yescharacteristic, complemented
55#421×C107C2211yescharacteristic, complemented
56#421×C107C2211yescharacteristic, complemented
57#419×C107C2211yescharacteristic, complemented
58#418×C107C2211yescharacteristic, complemented
59#416×C107C2211yescharacteristic
60#416×C107C2211yescharacteristic, complemented
61C2×#101×C107C2211yescharacteristic, complemented
62C2×#100×C107C2211yescharacteristic, complemented
63#410×C107C2211yescharacteristic, complemented
64#408×C107C2211yescharacteristic, complemented
65#408×C107C2211yescharacteristic, complemented
66#408×C107C2211yescharacteristic, complemented
67#344×C107C2211yescharacteristic, complemented
68#344×C107C2211yescharacteristic, complemented
69#341×C107C2211yescharacteristic, complemented
70#338×C107C2211yescharacteristic, complemented
712−1+4×C107—22no—
722−1+4×C107—21no—
732−1+4×C107—22no—
742−1+4×C107—21no—
752−1+4×C107—22no—
762−1+4×C107—41no—
772−1+4×C107D412yescomplemented
78H(5,𝔽2)×C107—22no—
79H(5,𝔽2)×C107—21no—
80H(5,𝔽2)×C107—22no—
81H(5,𝔽2)×C107—21no—
82H(5,𝔽2)×C107—22no—
83H(5,𝔽2)×C107—41no—
84H(5,𝔽2)×C107—41no—
85H(5,𝔽2)×C107D412yescomplemented
86C2×#41×C107—22no—
87C2×#41×C107—22no—
88C2×#41×C107—21no—
89C2×#41×C107—21no—
90C2×#41×C107—21no—
91C2×#41×C107—21no—
92C2×#41×C107—41no—
93C2×#41×C107—41no—
94C2×#41×C107C2311yescharacteristic
95C2×#41×C107C2311yescharacteristic
96C2×#41×C107C2311yescharacteristic
97C2×#41×C107C2311yescharacteristic
98C2×#41×C107C2311yescharacteristic
99C22×Q8×C107—21no—
100C22×Q8×C107—21no—
101C22×Q8×C107C2311yescharacteristic
102C22×D4×C107—21no—
103C22×D4×C107—21no—
104C22×D4×C107—41no—
105C22×D4×C107C2311yescharacteristic
106#137×C107—24no—
107#137×C107—24no—
108#137×C107—24no—
109#137×C107—24no—
110#137×C107—22no—
111#137×C107—22no—
112#137×C107—21no—
113#137×C107—22no—
114#137×C107—21no—
115#137×C107—21no—
116#137×C107—21no—
117#137×C107—21no—
118#137×C107—21no—
119#137×C107—21no—
120#137×C107—21no—
121#137×C107—22no—
122#137×C107D412yes—
123#137×C107D412yescomplemented
124AGL(1,ℤ/8)×C107—24no—
125AGL(1,ℤ/8)×C107—24no—
126AGL(1,ℤ/8)×C107—24no—
127AGL(1,ℤ/8)×C107—24no—
128AGL(1,ℤ/8)×C107—22no—
129AGL(1,ℤ/8)×C107—22no—
130AGL(1,ℤ/8)×C107—21no—
131AGL(1,ℤ/8)×C107—22no—
132AGL(1,ℤ/8)×C107—21no—
133AGL(1,ℤ/8)×C107—21no—
134AGL(1,ℤ/8)×C107—21no—
135AGL(1,ℤ/8)×C107—21no—
136AGL(1,ℤ/8)×C107—21no—
137AGL(1,ℤ/8)×C107—21no—
138AGL(1,ℤ/8)×C107—21no—
139AGL(1,ℤ/8)×C107—22no—
140AGL(1,ℤ/8)×C107D412yes—
141AGL(1,ℤ/8)×C107D412yescomplemented
142#135×C107—24no—
143#135×C107—24no—
144#135×C107—24no—
145#135×C107—24no—
146#135×C107—22no—
147#135×C107—22no—
148#135×C107—22no—
149#135×C107—22no—
150#135×C107—41no—
151C2×Q16×C107—24no—
152C2×Q16×C107—21no—
153C2×Q16×C107D412yescomplemented
154C2×SD16×C107—24no—
155C2×SD16×C107—24no—
156C2×SD16×C107—21no—
157C2×SD16×C107—21no—
158C2×SD16×C107—22no—
159C2×SD16×C107—22no—
160C2×SD16×C107—41no—
161C2×SD16×C107D412yes—
162C2×SD16×C107D412yescomplemented
163C2×D8×C107—24no—
164C2×D8×C107—21no—
165C2×D8×C107D412yes—
166#131×C107—22no—
167#131×C107—22no—
168#131×C107—22no—
169#131×C107—22no—
170C2×M16×C107—22no—
171C2×M16×C107—22no—
172C2×M16×C107C2311yescharacteristic
173C2×M16×C107C2311yescharacteristic
174C2×M16×C107C2311yescharacteristic
175C2×M16×C107C2311yescharacteristic
176C2×M16×C107C2311yescharacteristic
177C22×C8×C107C2311yescharacteristic
178C4⋊Q8×C107—21no—
179#127×C107—21no—
180#124×C107—21no—
181#124×C107—21no—
182#123×C107—41no—
183C22⋊Q8×C107—22no—
184#121×C107—22no—
185#120×C107—41no—
186#117×C107C2311yescharacteristic
187#117×C107C2311yescharacteristic
188#104×C107—22no—
189#104×C107—22no—
190#104×C107—22no—
191#104×C107—22no—
192#103×C107—21no—
193#103×C107—21no—
194#103×C107—22no—
195#102×C107—21no—
196#102×C107—21no—
197#102×C107—22no—
198#101×C107—22no—
199#100×C107—22no—
200#99×C107—41no—
201C22⋊C8×C107—22no—
202C22⋊C8×C107—22no—
203C22⋊C8×C107—41no—
204C24×C107—21no—
205C24×C107—41no—
206#41×C107—21no—
207#41×C107—21no—
208#41×C107—21no—
209#41×C107—21no—
210#41×C107—24no—
211#41×C107—24no—
212#41×C107—22no—
213#41×C107—22no—
214#41×C107—22no—
215#41×C107—22no—
216#41×C107—21no—
217#41×C107—21no—
218#41×C107—21no—
219#41×C107—21no—
220#41×C107—21no—
221#41×C107—21no—
222#41×C107—21no—
223#41×C107—21no—
224#41×C107—21no—
225#41×C107—21no—
226#41×C107—21no—
227#41×C107—21no—
228#41×C107—42no—
229#41×C107—42no—
230#41×C107—42no—
231#41×C107—42no—
232#41×C107—42no—
233#41×C107—44no—
234#41×C107—42no—
235#41×C107—42no—
236#41×C107—42no—
237#41×C107—41no—
238#41×C107—41no—
239#41×C107—44no—
240#41×C107—42no—
241#41×C107—42no—
242#41×C107C2×D412yes—
243#41×C107C2×D412yes—
244#41×C107C2×D412yes—
245#41×C107C2×D412yes—
246C2×Q8×C107—21no—
247C2×Q8×C107—24no—
248C2×Q8×C107—22no—
249C2×Q8×C107—22no—
250C2×Q8×C107—21no—
251C2×Q8×C107—21no—
252C2×Q8×C107—21no—
253C2×Q8×C107—21no—
254C2×Q8×C107—41no—
255C2×Q8×C107—42no—
256C2×Q8×C107—42no—
257C2×Q8×C107—41no—
258C2×Q8×C107—42no—
259C2×Q8×C107C2×D412yes—
260C2×Q8×C107C2×D411yescharacteristic
261C2×Q8×C107C2×D411yescharacteristic
262C2×Q8×C107C2×D411yescharacteristic
263C2×Q8×C107C2×D411yescharacteristic
264C2×Q8×C107C2×D411yescharacteristic
265C2×D4×C107—21no—
266C2×D4×C107—21no—
267C2×D4×C107—24no—
268C2×D4×C107—22no—
269C2×D4×C107—22no—
270C2×D4×C107—21no—
271C2×D4×C107—21no—
272C2×D4×C107—21no—
273C2×D4×C107—21no—
274C2×D4×C107—21no—
275C2×D4×C107—21no—
276C2×D4×C107—21no—
277C2×D4×C107—21no—
278C2×D4×C107—42no—
279C2×D4×C107—41no—
280C2×D4×C107—41no—
281C2×D4×C107—42no—
282C2×D4×C107—42no—
283C2×D4×C107—41no—
284C2×D4×C107—44no—
285C2×D4×C107—42no—
286C2×D4×C107—42no—
287C2×D4×C107—44no—
288C2×D4×C107—41no—
289C2×D4×C107—42no—
290C2×D4×C107—42no—
291C2×D4×C107C2×D412yes—
292C2×D4×C107C2×D411yescharacteristic
293C2×D4×C107C2×D411yescharacteristic
294C2×D4×C107C2×D411yescharacteristic
295C2×D4×C107C2×D411yescharacteristic
296C2×D4×C107C2×D411yescharacteristic
297C22×C4×C107—21no—
298C22×C4×C107—21no—
299C22×C4×C107—21no—
300C22×C4×C107—21no—
301C22×C4×C107—21no—
302C22×C4×C107—21no—
303C22×C4×C107—41no—
304C22×C4×C107—42no—
305C22×C4×C107—41no—
306C22×C4×C107—41no—
307C22×C4×C107C2411yescharacteristic
308Q16×C107—24no—
309Q16×C107—22no—
310Q16×C107—22no—
311Q16×C107—22no—
312Q16×C107—24no—
313Q16×C107—22no—
314Q16×C107—41no—
315SD16×C107—24no—
316SD16×C107—22no—
317SD16×C107—24no—
318SD16×C107—22no—
319SD16×C107—22no—
320SD16×C107—22no—
321SD16×C107—22no—
322SD16×C107—24no—
323SD16×C107—22no—
324SD16×C107—22no—
325SD16×C107—24no—
326SD16×C107—22no—
327SD16×C107—44no—
328SD16×C107—41no—
329SD16×C107—41no—
330D8×C107—24no—
331D8×C107—22no—
332D8×C107—22no—
333D8×C107—22no—
334D8×C107—24no—
335D8×C107—22no—
336D8×C107—41no—
337M16×C107—24no—
338M16×C107—24no—
339M16×C107—21no—
340M16×C107—21no—
341M16×C107—21no—
342M16×C107—21no—
343M16×C107—21no—
344M16×C107—21no—
345M16×C107—21no—
346M16×C107—21no—
347M16×C107C2×D412yes—
348M16×C107C2×D412yes—
349C2×C8×C107—24no—
350C2×C8×C107—24no—
351C2×C8×C107—21no—
352C2×C8×C107—21no—
353C2×C8×C107—21no—
354C2×C8×C107—21no—
355C2×C8×C107—21no—
356C2×C8×C107—21no—
357C2×C8×C107C2×D412yes—
358C2×C8×C107C2×D412yes—
359C4⋊C4×C107—21no—
360C4⋊C4×C107—21no—
361C4⋊C4×C107—42no—
362C22⋊C4×C107—21no—
363C22⋊C4×C107—21no—
364C22⋊C4×C107—42no—
365C22⋊C4×C107—42no—
366C42×C107—21no—
367C42×C107—21no—
368C23×C107—21no—
369C23×C107—21no—
370C23×C107—21no—
371C23×C107—21no—
372C23×C107—21no—
373C23×C107—22no—
374C23×C107—42no—
375C23×C107—44no—
376C23×C107—41no—
377C23×C107—41no—
378C23×C107—161no—
379C23×C107—162no—
380C23×C107H(5,𝔽2)11yescharacteristic
381Q8×C107—21no—
382Q8×C107—21no—
383Q8×C107—21no—
384Q8×C107—21no—
385Q8×C107—22no—
386Q8×C107—21no—
387Q8×C107—21no—
388Q8×C107—22no—
389Q8×C107—21no—
390Q8×C107—21no—
391Q8×C107—42no—
392Q8×C107—44no—
393Q8×C107—41no—
394Q8×C107—41no—
395Q8×C107#12012yes—
396Q8×C107#12012yes—
397D4×C107—22no—
398D4×C107—22no—
399D4×C107—22no—
400D4×C107—22no—
401D4×C107—21no—
402D4×C107—21no—
403D4×C107—22no—
404D4×C107—21no—
405D4×C107—21no—
406D4×C107—21no—
407D4×C107—21no—
408D4×C107—21no—
409D4×C107—21no—
410D4×C107—22no—
411D4×C107—42no—
412D4×C107—42no—
413D4×C107—44no—
414D4×C107—42no—
415D4×C107—44no—
416D4×C107—44no—
417D4×C107—41no—
418D4×C107—41no—
419D4×C107—41no—
420D4×C107—41no—
421D4×C107—41no—
422D4×C107—41no—
423D4×C107—41no—
424D4×C107—41no—
425D4×C107—162no—
426D4×C107#12012yes—
427D4×C107#12012yes—
428C2×C4×C107—21no—
429C2×C4×C107—21no—
430C2×C4×C107—22no—
431C2×C4×C107—22no—
432C2×C4×C107—22no—
433C2×C4×C107—22no—
434C2×C4×C107—21no—
435C2×C4×C107—21no—
436C2×C4×C107—22no—
437C2×C4×C107—21no—
438C2×C4×C107—42no—
439C2×C4×C107—42no—
440C2×C4×C107—42no—
441C2×C4×C107—44no—
442C2×C4×C107—44no—
443C2×C4×C107—44no—
444C2×C4×C107—41no—
445C2×C4×C107—41no—
446C2×C4×C107—41no—
447C2×C4×C107—41no—
448C2×C4×C107—41no—
449C2×C4×C107—41no—
450C2×C4×C107—41no—
451C2×C4×C107—41no—
452C2×C4×C107—41no—
453C2×C4×C107—41no—
454C2×C4×C107C22×D411yescharacteristic
455C2×C4×C107C22×D411yescharacteristic
456C2×C4×C107C22×D411yescharacteristic
457C2×C4×C107C22×D411yescharacteristic
458C2×C4×C107C22×D411yescharacteristic
459C2×C4×C107H(5,𝔽2)11yescharacteristic
460C8×C107—22no—
461C8×C107—22no—
462C8×C107—22no—
463C8×C107—22no—
464C8×C107—41no—
465C8×C107—41no—
466C22×C107—22no—
467C22×C107—22no—
468C22×C107—41no—
469C22×C107—42no—
470C22×C107—42no—
471C22×C107—41no—
472C22×C107—41no—
473C22×C107—41no—
474C22×C107—42no—
475C22×C107—81no—
476C22×C107—81no—
477C22×C107—82no—
478C22×C107—81no—
479C22×C107—82no—
480C22×C107—161no—
481C22×C107—162no—
482C22×C107—164no—
483C22×C107#53411yescharacteristic
484C22×C107D4211yescharacteristic
485C22×C107D4211yescharacteristic
486C4×C107—22no—
487C4×C107—22no—
488C4×C107—41no—
489C4×C107—41no—
490C4×C107—41no—
491C4×C107—42no—
492C4×C107—81no—
493C4×C107—81no—
494C4×C107C2×#12011yescharacteristic
495C4×C107C2×#12011yescharacteristic
496C4×C107D4211yescharacteristic
497C4×C107D4211yescharacteristic
498#23894C10711yesmaximal, characteristic, direct product factor, Sylow
499C2×C107—21no—
500C2×C107—21no—
501C2×C107—21no—
502C2×C107—42no—
503C2×C107—42no—
504C2×C107—81no—
505C2×C107—81no—
506C2×C107—82no—
507C2×C107—81no—
508C2×C107#240311yescharacteristic
509#3586C2×C10711yescharacteristic, complemented
510#3585C2×C10711yescharacteristic, complemented
511#3020C2×C10711yescharacteristic, complemented
512#3019C2×C10711yescharacteristic, complemented
513#3010C2×C10711yescharacteristic, complemented
514#3009C2×C10711yescharacteristic, complemented
515#2019C2×C10711yescharacteristic, complemented
516#2017C2×C10711yescharacteristic, complemented
517#2009C2×C10711yescharacteristic, complemented
518#2008C2×C10711yescharacteristic, complemented
519#1903C2×C10711yescharacteristic, complemented
520#1902C2×C10711yescharacteristic, complemented
521#1881C2×C10711yescharacteristic, complemented
522#1881C2×C10711yescharacteristic, complemented
523#1794C2×C10711yescharacteristic, complemented
524C107#2389411yescharacteristic, direct product factor, Sylow
525#585C22×C10711yescharacteristic
526C2×2−1+4C22×C10711yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C10711yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C10711yescharacteristic
539#575C22×C10711yescharacteristic
540#575C22×C10711yescharacteristic
541#575C22×C10711yescharacteristic, complemented
542#575C22×C10711yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C10711yescharacteristic
545C2×#137C22×C10711yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
548C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
549C22×SD16C22×C10711yescharacteristic, complemented
550#568C22×C10711yescharacteristic
551#568C22×C10711yescharacteristic, complemented
552#536C22×C10711yescharacteristic, complemented
553#535C22×C10711yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C10711yescharacteristic
563#421C22×C10711yescharacteristic, complemented
564#421C22×C10711yescharacteristic, complemented
565#421C22×C10711yescharacteristic, complemented
566#419C22×C10711yescharacteristic, complemented
567#418C22×C10711yescharacteristic, complemented
568#416C22×C10711yescharacteristic
569#416C22×C10711yescharacteristic, complemented
570C2×#101C22×C10711yescharacteristic, complemented
571C2×#100C22×C10711yescharacteristic, complemented
572#410C22×C10711yescharacteristic, complemented
573#408C22×C10711yescharacteristic, complemented
574#408C22×C10711yescharacteristic, complemented
575#408C22×C10711yescharacteristic, complemented
576#344C22×C10711yescharacteristic, complemented
577#344C22×C10711yescharacteristic, complemented
578#341C22×C10711yescharacteristic, complemented
579#338C22×C10711yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C10712yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C10712yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C10711yescharacteristic
604C2×#41C23×C10711yescharacteristic
605C2×#41C23×C10711yescharacteristic
606C2×#41C23×C10711yescharacteristic
607C2×#41C23×C10711yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C10711yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C10711yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C10712yes—
632#137D4×C10712yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C10712yes—
650AGL(1,ℤ/8)D4×C10712yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C10712yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C10712yes—
671C2×SD16D4×C10712yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C10712yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C10711yescharacteristic
682C2×M16C23×C10711yescharacteristic
683C2×M16C23×C10711yescharacteristic
684C2×M16C23×C10711yescharacteristic
685C2×M16C23×C10711yescharacteristic
686C22×C8C23×C10711yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C10711yescharacteristic
696#117C23×C10711yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C10712yes—
752#41C2×D4×C10712yes—
753#41C2×D4×C10712yes—
754#41C2×D4×C10712yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C10712yes—
769C2×Q8C2×D4×C10711yescharacteristic
770C2×Q8C2×D4×C10711yescharacteristic
771C2×Q8C2×D4×C10711yescharacteristic
772C2×Q8C2×D4×C10711yescharacteristic
773C2×Q8C2×D4×C10711yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C10712yes—
801C2×D4C2×D4×C10711yescharacteristic
802C2×D4C2×D4×C10711yescharacteristic
803C2×D4C2×D4×C10711yescharacteristic
804C2×D4C2×D4×C10711yescharacteristic
805C2×D4C2×D4×C10711yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C10711yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C10712yes—
857M16C2×D4×C10712yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C10712yes—
867C2×C8C2×D4×C10712yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C10711yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C10712yes—
905Q8#120×C10712yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C10712yes—
936D4#120×C10712yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C10711yescharacteristic
964C2×C4C22×D4×C10711yescharacteristic
965C2×C4C22×D4×C10711yescharacteristic
966C2×C4C22×D4×C10711yescharacteristic
967C2×C4C22×D4×C10711yescharacteristic
968C2×C4H(5,𝔽2)×C10711yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C10711yescharacteristic
993C22D42×C10711yescharacteristic
994C22D42×C10711yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10711yescharacteristic
1004C4C2×#120×C10711yescharacteristic
1005C4D42×C10711yescharacteristic
1006C4D42×C10711yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C107×#240311yescharacteristic
subgroupG/H
center, socleC2×C107#2403
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×#3585C2semidirect
3. C107×#3020C2semidirect
4. C107×#3019C2semidirect
5. C107×#3010C2semidirect
6. C107×#3009C2semidirect
7. C107×#2019C2semidirect
8. C107×#2017C2semidirect
9. C107×#2009C2semidirect
10. C107×#2008C2semidirect
11. C107×#1903C2semidirect
12. C107×#1902C2semidirect
13. C107×#1881C2semidirect
14. C107×#1881C2semidirect
15. C107×#1794C2semidirect
17. C2×2−1+4×C107C22semidirect
32. #575×C107C22semidirect
33. #575×C107C22semidirect
36. C2×#137×C107C22semidirect
40. C22×SD16×C107C22semidirect
42. #568×C107C22semidirect
43. #536×C107C22semidirect
44. #535×C107C22semidirect
54. #421×C107C22semidirect
55. #421×C107C22semidirect
56. #421×C107C22semidirect
57. #419×C107C22semidirect
58. #418×C107C22semidirect
60. #416×C107C22semidirect
61. C2×#101×C107C22semidirect
62. C2×#100×C107C22semidirect
63. #410×C107C22semidirect
64. #408×C107C22semidirect
65. #408×C107C22semidirect
66. #408×C107C22semidirect
67. #344×C107C22semidirect
68. #344×C107C22semidirect
69. #341×C107C22semidirect
70. #338×C107C22semidirect
77. 2−1+4×C107D4semidirect
85. H(5,𝔽2)×C107D4semidirect
123. #137×C107D4semidirect
141. AGL(1,ℤ/8)×C107D4semidirect
153. C2×Q16×C107D4semidirect
162. C2×SD16×C107D4semidirect
498. #23894C107direct (N × H)
509. #3586C2×C107semidirect
510. #3585C2×C107semidirect
511. #3020C2×C107semidirect
512. #3019C2×C107semidirect
513. #3010C2×C107semidirect
514. #3009C2×C107semidirect
515. #2019C2×C107semidirect
516. #2017C2×C107semidirect
517. #2009C2×C107semidirect
518. #2008C2×C107semidirect
519. #1903C2×C107semidirect
520. #1902C2×C107semidirect
521. #1881C2×C107semidirect
522. #1881C2×C107semidirect
523. #1794C2×C107semidirect
524. C107#23894direct (N × H)
526. C2×2−1+4C22×C107semidirect
541. #575C22×C107semidirect
542. #575C22×C107semidirect
545. C2×#137C22×C107semidirect
549. C22×SD16C22×C107semidirect
551. #568C22×C107semidirect
552. #536C22×C107semidirect
553. #535C22×C107semidirect
563. #421C22×C107semidirect
564. #421C22×C107semidirect
565. #421C22×C107semidirect
566. #419C22×C107semidirect
567. #418C22×C107semidirect
569. #416C22×C107semidirect
570. C2×#101C22×C107semidirect
571. C2×#100C22×C107semidirect
572. #410C22×C107semidirect
573. #408C22×C107semidirect
574. #408C22×C107semidirect
575. #408C22×C107semidirect
576. #344C22×C107semidirect
577. #344C22×C107semidirect
578. #341C22×C107semidirect
579. #338C22×C107semidirect
586. 2−1+4D4×C107semidirect
594. H(5,𝔽2)D4×C107semidirect
632. #137D4×C107semidirect
650. AGL(1,ℤ/8)D4×C107semidirect
662. C2×Q16D4×C107semidirect
671. C2×SD16D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35862
C107×#35852
C107×#30202
C107×#30192
C107×#30102
C107×#30092
C107×#20192
C107×#20172
C107×#20092
C107×#20082
C107×#19032
C107×#19022
C107×#18812
C107×#17942
#23894107