Finite Group Databasebeta

← C107×#23888 #41049852

Subgroups — C107×#23888 #41049852

Order 27392.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C107C211yesmaximal, characteristic, complemented
2C2×#576×C107C211yesmaximal, characteristic, complemented
3C2×#454×C107C211yesmaximal, characteristic, complemented
4C2×#455×C107C211yesmaximal, characteristic, complemented
5C107×#3013C211yesmaximal, characteristic, complemented
6C107×#3012C211yesmaximal, characteristic, complemented
7C107×#2019C211yesmaximal, characteristic, complemented
8C107×#2018C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2006C211yesmaximal, characteristic, complemented
11C107×#1908C211yesmaximal, characteristic, complemented
12C107×#1907C211yesmaximal, characteristic, complemented
13C107×#1876C211yesmaximal, characteristic, complemented
14C107×#1876C211yesmaximal, characteristic, complemented
15C107×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C107C2211yescharacteristic, complemented
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18C2×H(5,𝔽2)×C107C2211yescharacteristic
19#577×C107—24no—
20#577×C107—24no—
21#576×C107—24no—
22#576×C107—24no—
23C2×#137×C107—21no—
24C2×#137×C107C2211yescharacteristic
25C2×#137×C107C2211yescharacteristic, complemented
26C2×AGL(1,ℤ/8)×C107—21no—
27C2×AGL(1,ℤ/8)×C107—21no—
28C2×AGL(1,ℤ/8)×C107—21no—
29C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
31C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
32C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
33C2×#135×C107—21no—
34C2×#135×C107—21no—
35C2×#135×C107C2211yescharacteristic
36C2×#135×C107C2211yescharacteristic
37C22×SD16×C107—21no—
38C22×SD16×C107C2211yescharacteristic, complemented
39C22×D8×C107—21no—
40C22×D8×C107C2211yescharacteristic
41C2×#131×C107C2211yescharacteristic
42C2×#131×C107C2211yescharacteristic, complemented
43#537×C107C2211yescharacteristic, complemented
44C2×#124×C107C2211yescharacteristic, complemented
45#455×C107—24no—
46#454×C107—24no—
47#452×C107—21no—
48#452×C107—21no—
49#451×C107—21no—
50#450×C107—21no—
51#449×C107—21no—
52#449×C107—21no—
53#448×C107—21no—
54#447×C107—21no—
55C2×#104×C107C2211yescharacteristic
56C2×#104×C107C2211yescharacteristic, complemented
57C2×#104×C107C2211yescharacteristic, complemented
58C2×#104×C107C2211yescharacteristic, complemented
59#417×C107C2211yescharacteristic
60#417×C107C2211yescharacteristic, complemented
61C2×#103×C107C2211yescharacteristic, complemented
62C2×#102×C107C2211yescharacteristic, complemented
63C2×#101×C107C2211yescharacteristic, complemented
64C2×#100×C107C2211yescharacteristic, complemented
65C2×#100×C107C2211yescharacteristic, complemented
66#408×C107C2211yescharacteristic, complemented
67#408×C107C2211yescharacteristic, complemented
68#390×C107C2211yescharacteristic, complemented
69#343×C107C2211yescharacteristic, complemented
70#341×C107C2211yescharacteristic, complemented
71#341×C107C2211yescharacteristic, complemented
72#336×C107C2211yescharacteristic, complemented
732−1+4×C107—22no—
742−1+4×C107—22no—
752−1+4×C107—22no—
762−1+4×C107—41no—
77H(5,𝔽2)×C107—22no—
78H(5,𝔽2)×C107—22no—
79H(5,𝔽2)×C107—22no—
80H(5,𝔽2)×C107—22no—
81H(5,𝔽2)×C107—22no—
82H(5,𝔽2)×C107—41no—
83H(5,𝔽2)×C107—41no—
84H(5,𝔽2)×C107D414yescomplemented
85C2×#41×C107—21no—
86C2×#41×C107—21no—
87C2×#41×C107—21no—
88C2×#41×C107—21no—
89C2×#41×C107—21no—
90C2×#41×C107—21no—
91C2×#41×C107—41no—
92C2×#41×C107C2311yescharacteristic
93C2×#41×C107C2311yescharacteristic
94C2×#41×C107C2311yescharacteristic
95C2×#41×C107C2311yescharacteristic
96C22×Q8×C107—21no—
97C22×Q8×C107—21no—
98C22×Q8×C107C2311yescharacteristic
99C22×D4×C107—21no—
100C22×D4×C107—21no—
101C22×D4×C107—21no—
102C22×D4×C107—21no—
103C22×D4×C107—41no—
104C22×D4×C107—41no—
105C22×D4×C107C2311yescharacteristic
106C22×D4×C107C2311yescharacteristic
107#137×C107—28no—
108#137×C107—22no—
109#137×C107—22no—
110#137×C107—41no—
111#137×C107D414yescomplemented
112AGL(1,ℤ/8)×C107—28no—
113AGL(1,ℤ/8)×C107—28no—
114AGL(1,ℤ/8)×C107—28no—
115AGL(1,ℤ/8)×C107—22no—
116AGL(1,ℤ/8)×C107—22no—
117AGL(1,ℤ/8)×C107—22no—
118AGL(1,ℤ/8)×C107—22no—
119AGL(1,ℤ/8)×C107—22no—
120AGL(1,ℤ/8)×C107—22no—
121AGL(1,ℤ/8)×C107—41no—
122AGL(1,ℤ/8)×C107D414yescomplemented
123#135×C107—28no—
124#135×C107—28no—
125#135×C107—22no—
126#135×C107—22no—
127#135×C107—22no—
128#135×C107—22no—
129C2×Q16×C107—21no—
130C2×Q16×C107—21no—
131C2×Q16×C107D411yescharacteristic
132C2×Q16×C107D411yescharacteristic
133C2×SD16×C107—28no—
134C2×SD16×C107—21no—
135C2×SD16×C107—22no—
136C2×SD16×C107—21no—
137C2×SD16×C107—21no—
138C2×SD16×C107—21no—
139C2×SD16×C107—22no—
140C2×SD16×C107—21no—
141C2×SD16×C107—21no—
142C2×SD16×C107—21no—
143C2×SD16×C107—21no—
144C2×SD16×C107D411yescharacteristic
145C2×SD16×C107D411yescharacteristic
146C2×SD16×C107D411yescharacteristic
147C2×SD16×C107D411yescharacteristic
148C2×D8×C107—28no—
149C2×D8×C107—21no—
150C2×D8×C107—21no—
151C2×D8×C107—22no—
152C2×D8×C107—22no—
153C2×D8×C107—21no—
154C2×D8×C107—21no—
155C2×D8×C107—21no—
156C2×D8×C107—21no—
157C2×D8×C107D411yescharacteristic
158C2×D8×C107D411yescharacteristic
159#131×C107—22no—
160#131×C107—22no—
161#131×C107—22no—
162#131×C107—22no—
163C2×M16×C107—21no—
164C2×M16×C107—21no—
165C2×M16×C107C2311yescharacteristic
166C2×M16×C107C2311yescharacteristic
167C2×M16×C107C2311yescharacteristic
168C2×M16×C107C2311yescharacteristic
169C22×C8×C107—21no—
170C22×C8×C107—21no—
171C22×C8×C107C2311yescharacteristic
172C22×C8×C107C2311yescharacteristic
173#124×C107—22no—
174#124×C107—22no—
175C22⋊Q8×C107—21no—
176C22⋊Q8×C107—21no—
177#121×C107—21no—
178#121×C107—21no—
179#121×C107—41no—
180C2×C4⋊C4×C107C2311yescharacteristic
181C2×C22⋊C4×C107—41no—
182C2×C22⋊C4×C107—41no—
183C2×C42×C107C2311yescharacteristic
184#104×C107—22no—
185#104×C107—22no—
186#104×C107—22no—
187#104×C107—22no—
188#103×C107—21no—
189#103×C107—21no—
190#103×C107—21no—
191#103×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#102×C107—21no—
196#101×C107—22no—
197#100×C107—22no—
198#100×C107—41no—
199C22⋊C8×C107—21no—
200C22⋊C8×C107—21no—
201C22⋊C8×C107—21no—
202C22⋊C8×C107—21no—
203C24×C107—21no—
204C24×C107—21no—
205C24×C107—41no—
206C24×C107—41no—
207#41×C107—21no—
208#41×C107—21no—
209#41×C107—21no—
210#41×C107—21no—
211#41×C107—24no—
212#41×C107—24no—
213#41×C107—24no—
214#41×C107—24no—
215#41×C107—21no—
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—42no—
224#41×C107—44no—
225#41×C107—42no—
226#41×C107—42no—
227#41×C107—42no—
228#41×C107—42no—
229#41×C107—42no—
230#41×C107—44no—
231#41×C107—42no—
232#41×C107—42no—
233#41×C107C2×D412yes—
234#41×C107C2×D412yes—
235#41×C107C2×D412yes—
236#41×C107C2×D412yes—
237C2×Q8×C107—21no—
238C2×Q8×C107—24no—
239C2×Q8×C107—21no—
240C2×Q8×C107—21no—
241C2×Q8×C107—21no—
242C2×Q8×C107—21no—
243C2×Q8×C107—41no—
244C2×Q8×C107—42no—
245C2×Q8×C107—42no—
246C2×Q8×C107—42no—
247C2×Q8×C107C2×D411yescharacteristic
248C2×Q8×C107C2×D411yescharacteristic
249C2×Q8×C107C2×D412yes—
250C2×Q8×C107C2×D411yescharacteristic
251C2×Q8×C107C2×D411yescharacteristic
252C2×D4×C107—21no—
253C2×D4×C107—21no—
254C2×D4×C107—24no—
255C2×D4×C107—24no—
256C2×D4×C107—24no—
257C2×D4×C107—21no—
258C2×D4×C107—21no—
259C2×D4×C107—21no—
260C2×D4×C107—21no—
261C2×D4×C107—21no—
262C2×D4×C107—21no—
263C2×D4×C107—21no—
264C2×D4×C107—21no—
265C2×D4×C107—21no—
266C2×D4×C107—21no—
267C2×D4×C107—21no—
268C2×D4×C107—21no—
269C2×D4×C107—42no—
270C2×D4×C107—42no—
271C2×D4×C107—42no—
272C2×D4×C107—41no—
273C2×D4×C107—41no—
274C2×D4×C107—41no—
275C2×D4×C107—41no—
276C2×D4×C107—44no—
277C2×D4×C107—42no—
278C2×D4×C107—44no—
279C2×D4×C107—44no—
280C2×D4×C107—44no—
281C2×D4×C107—41no—
282C2×D4×C107—42no—
283C2×D4×C107—41no—
284C2×D4×C107C2×D411yescharacteristic
285C2×D4×C107C2×D411yescharacteristic
286C2×D4×C107C2×D412yes—
287C2×D4×C107C2×D412yes—
288C2×D4×C107C2×D411yescharacteristic
289C2×D4×C107C2×D411yescharacteristic
290C22×C4×C107—21no—
291C22×C4×C107—21no—
292C22×C4×C107—21no—
293C22×C4×C107—21no—
294C22×C4×C107—21no—
295C22×C4×C107—21no—
296C22×C4×C107—21no—
297C22×C4×C107—41no—
298C22×C4×C107—41no—
299C22×C4×C107—41no—
300C22×C4×C107—41no—
301C22×C4×C107C2411yescharacteristic
302Q16×C107—24no—
303Q16×C107—22no—
304Q16×C107—22no—
305Q16×C107—42no—
306SD16×C107—24no—
307SD16×C107—24no—
308SD16×C107—24no—
309SD16×C107—24no—
310SD16×C107—24no—
311SD16×C107—22no—
312SD16×C107—22no—
313SD16×C107—22no—
314SD16×C107—24no—
315SD16×C107—22no—
316SD16×C107—42no—
317SD16×C107—42no—
318D8×C107—24no—
319D8×C107—24no—
320D8×C107—24no—
321D8×C107—24no—
322D8×C107—22no—
323D8×C107—24no—
324D8×C107—22no—
325D8×C107—42no—
326M16×C107—24no—
327M16×C107—24no—
328M16×C107—21no—
329M16×C107—21no—
330M16×C107—21no—
331M16×C107—21no—
332M16×C107—21no—
333M16×C107—21no—
334M16×C107C2×D412yes—
335M16×C107C2×D412yes—
336C2×C8×C107—24no—
337C2×C8×C107—24no—
338C2×C8×C107—21no—
339C2×C8×C107—21no—
340C2×C8×C107—21no—
341C2×C8×C107—21no—
342C2×C8×C107—21no—
343C2×C8×C107—21no—
344C2×C8×C107—21no—
345C2×C8×C107—21no—
346C2×C8×C107C2×D411yescharacteristic
347C2×C8×C107C2×D411yescharacteristic
348C2×C8×C107C2×D411yescharacteristic
349C2×C8×C107C2×D411yescharacteristic
350C4⋊C4×C107—21no—
351C4⋊C4×C107—21no—
352C4⋊C4×C107—41no—
353C22⋊C4×C107—44no—
354C22⋊C4×C107—41no—
355C22⋊C4×C107—41no—
356C22⋊C4×C107—82no—
357C42×C107—21no—
358C42×C107—21no—
359C23×C107—21no—
360C23×C107—21no—
361C23×C107—21no—
362C23×C107—21no—
363C23×C107—22no—
364C23×C107—22no—
365C23×C107—44no—
366C23×C107—44no—
367C23×C107—41no—
368C23×C107—41no—
369C23×C107—41no—
370C23×C107—41no—
371C23×C107—81no—
372C23×C107—81no—
373C23×C107—81no—
374C23×C107—81no—
375C23×C107—161no—
376C23×C107—161no—
377C23×C107—161no—
378C23×C107—161no—
379C23×C107H(5,𝔽2)11yescharacteristic
380Q8×C107—21no—
381Q8×C107—21no—
382Q8×C107—22no—
383Q8×C107—21no—
384Q8×C107—21no—
385Q8×C107—21no—
386Q8×C107—22no—
387Q8×C107—21no—
388Q8×C107—44no—
389Q8×C107—41no—
390Q8×C107—41no—
391Q8×C107#12012yes—
392Q8×C107#12012yes—
393D4×C107—22no—
394D4×C107—22no—
395D4×C107—22no—
396D4×C107—22no—
397D4×C107—22no—
398D4×C107—22no—
399D4×C107—21no—
400D4×C107—21no—
401D4×C107—22no—
402D4×C107—21no—
403D4×C107—21no—
404D4×C107—21no—
405D4×C107—22no—
406D4×C107—21no—
407D4×C107—44no—
408D4×C107—44no—
409D4×C107—44no—
410D4×C107—44no—
411D4×C107—44no—
412D4×C107—41no—
413D4×C107—41no—
414D4×C107—41no—
415D4×C107—41no—
416D4×C107—41no—
417D4×C107—41no—
418D4×C107—41no—
419D4×C107—41no—
420D4×C107—161no—
421D4×C107#12012yes—
422D4×C107#12012yes—
423C2×C4×C107—21no—
424C2×C4×C107—21no—
425C2×C4×C107—22no—
426C2×C4×C107—22no—
427C2×C4×C107—22no—
428C2×C4×C107—22no—
429C2×C4×C107—22no—
430C2×C4×C107—21no—
431C2×C4×C107—21no—
432C2×C4×C107—44no—
433C2×C4×C107—44no—
434C2×C4×C107—44no—
435C2×C4×C107—44no—
436C2×C4×C107—41no—
437C2×C4×C107—41no—
438C2×C4×C107—41no—
439C2×C4×C107—41no—
440C2×C4×C107—41no—
441C2×C4×C107—41no—
442C2×C4×C107—41no—
443C2×C4×C107—41no—
444C2×C4×C107—41no—
445C2×C4×C107—41no—
446C2×C4×C107—81no—
447C2×C4×C107C22×D411yescharacteristic
448C2×C4×C107C22×D411yescharacteristic
449C2×C4×C107C22×D411yescharacteristic
450C2×C4×C107C22×D411yescharacteristic
451C2×C4×C107C22×D411yescharacteristic
452C2×C4×C107H(5,𝔽2)11yescharacteristic
453C8×C107—21no—
454C8×C107—21no—
455C8×C107—22no—
456C8×C107—22no—
457C8×C107—21no—
458C8×C107—21no—
459C8×C107—41no—
460C8×C107—41no—
461C22×C107—21no—
462C22×C107—21no—
463C22×C107—22no—
464C22×C107—22no—
465C22×C107—41no—
466C22×C107—41no—
467C22×C107—41no—
468C22×C107—41no—
469C22×C107—41no—
470C22×C107—41no—
471C22×C107—42no—
472C22×C107—42no—
473C22×C107—41no—
474C22×C107—41no—
475C22×C107—41no—
476C22×C107—41no—
477C22×C107—82no—
478C22×C107—82no—
479C22×C107—81no—
480C22×C107—81no—
481C22×C107—81no—
482C22×C107—81no—
483C22×C107—161no—
484C22×C107—161no—
485C22×C107—164no—
486C22×C107—164no—
487C22×C107#53411yescharacteristic
488C22×C107D4211yescharacteristic
489C22×C107D4211yescharacteristic
490C4×C107—22no—
491C4×C107—22no—
492C4×C107—41no—
493C4×C107—42no—
494C4×C107—41no—
495C4×C107—81no—
496C4×C107—81no—
497C4×C107C2×#12011yescharacteristic
498C4×C107C2×#12011yescharacteristic
499C4×C107D4211yescharacteristic
500C4×C107D4211yescharacteristic
501#23888C10711yesmaximal, characteristic, direct product factor, Sylow
502C2×C107—21no—
503C2×C107—21no—
504C2×C107—42no—
505C2×C107—42no—
506C2×C107—81no—
507C2×C107—81no—
508C2×C107—82no—
509C2×C107—82no—
510C2×C107#240311yescharacteristic
511C2×C107#328811yescharacteristic
512C2×C107#329011yescharacteristic
513C2×#577C2×C10711yescharacteristic, complemented
514C2×#576C2×C10711yescharacteristic, complemented
515C2×#454C2×C10711yescharacteristic, complemented
516C2×#455C2×C10711yescharacteristic, complemented
517#3013C2×C10711yescharacteristic, complemented
518#3012C2×C10711yescharacteristic, complemented
519#2019C2×C10711yescharacteristic, complemented
520#2018C2×C10711yescharacteristic, complemented
521#2012C2×C10711yescharacteristic, complemented
522#2006C2×C10711yescharacteristic, complemented
523#1908C2×C10711yescharacteristic, complemented
524#1907C2×C10711yescharacteristic, complemented
525#1876C2×C10711yescharacteristic, complemented
526#1876C2×C10711yescharacteristic, complemented
527#1792C2×C10711yescharacteristic, complemented
528C107#2388811yescharacteristic, direct product factor, Sylow
529C2×2−1+4C22×C10711yescharacteristic, complemented
530C2×H(5,𝔽2)C22×C10711yescharacteristic
531C2×H(5,𝔽2)C22×C10711yescharacteristic
532#577—24no—
533#577—24no—
534#576—24no—
535#576—24no—
536C2×#137—21no—
537C2×#137C22×C10711yescharacteristic
538C2×#137C22×C10711yescharacteristic, complemented
539C2×AGL(1,ℤ/8)—21no—
540C2×AGL(1,ℤ/8)—21no—
541C2×AGL(1,ℤ/8)—21no—
542C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
543C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
544C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
545C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
546C2×#135—21no—
547C2×#135—21no—
548C2×#135C22×C10711yescharacteristic
549C2×#135C22×C10711yescharacteristic
550C22×SD16—21no—
551C22×SD16C22×C10711yescharacteristic, complemented
552C22×D8—21no—
553C22×D8C22×C10711yescharacteristic
554C2×#131C22×C10711yescharacteristic
555C2×#131C22×C10711yescharacteristic, complemented
556#537C22×C10711yescharacteristic, complemented
557C2×#124C22×C10711yescharacteristic, complemented
558#455—24no—
559#454—24no—
560#452—21no—
561#452—21no—
562#451—21no—
563#450—21no—
564#449—21no—
565#449—21no—
566#448—21no—
567#447—21no—
568C2×#104C22×C10711yescharacteristic
569C2×#104C22×C10711yescharacteristic, complemented
570C2×#104C22×C10711yescharacteristic, complemented
571C2×#104C22×C10711yescharacteristic, complemented
572#417C22×C10711yescharacteristic
573#417C22×C10711yescharacteristic, complemented
574C2×#103C22×C10711yescharacteristic, complemented
575C2×#102C22×C10711yescharacteristic, complemented
576C2×#101C22×C10711yescharacteristic, complemented
577C2×#100C22×C10711yescharacteristic, complemented
578C2×#100C22×C10711yescharacteristic, complemented
579#408C22×C10711yescharacteristic, complemented
580#408C22×C10711yescharacteristic, complemented
581#390C22×C10711yescharacteristic, complemented
582#343C22×C10711yescharacteristic, complemented
583#341C22×C10711yescharacteristic, complemented
584#341C22×C10711yescharacteristic, complemented
585#336C22×C10711yescharacteristic, complemented
5862−1+4—22no—
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
590H(5,𝔽2)—22no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—22no—
593H(5,𝔽2)—22no—
594H(5,𝔽2)—22no—
595H(5,𝔽2)—41no—
596H(5,𝔽2)—41no—
597H(5,𝔽2)D4×C10714yescomplemented
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—41no—
605C2×#41C23×C10711yescharacteristic
606C2×#41C23×C10711yescharacteristic
607C2×#41C23×C10711yescharacteristic
608C2×#41C23×C10711yescharacteristic
609C22×Q8—21no—
610C22×Q8—21no—
611C22×Q8C23×C10711yescharacteristic
612C22×D4—21no—
613C22×D4—21no—
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4C23×C10711yescharacteristic
619C22×D4C23×C10711yescharacteristic
620#137—28no—
621#137—22no—
622#137—22no—
623#137—41no—
624#137D4×C10714yescomplemented
625AGL(1,ℤ/8)—28no—
626AGL(1,ℤ/8)—28no—
627AGL(1,ℤ/8)—28no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—22no—
631AGL(1,ℤ/8)—22no—
632AGL(1,ℤ/8)—22no—
633AGL(1,ℤ/8)—22no—
634AGL(1,ℤ/8)—41no—
635AGL(1,ℤ/8)D4×C10714yescomplemented
636#135—28no—
637#135—28no—
638#135—22no—
639#135—22no—
640#135—22no—
641#135—22no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16D4×C10711yescharacteristic
645C2×Q16D4×C10711yescharacteristic
646C2×SD16—28no—
647C2×SD16—21no—
648C2×SD16—22no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—22no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16D4×C10711yescharacteristic
658C2×SD16D4×C10711yescharacteristic
659C2×SD16D4×C10711yescharacteristic
660C2×SD16D4×C10711yescharacteristic
661C2×D8—28no—
662C2×D8—21no—
663C2×D8—21no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8—21no—
670C2×D8D4×C10711yescharacteristic
671C2×D8D4×C10711yescharacteristic
672#131—22no—
673#131—22no—
674#131—22no—
675#131—22no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16C23×C10711yescharacteristic
679C2×M16C23×C10711yescharacteristic
680C2×M16C23×C10711yescharacteristic
681C2×M16C23×C10711yescharacteristic
682C22×C8—21no—
683C22×C8—21no—
684C22×C8C23×C10711yescharacteristic
685C22×C8C23×C10711yescharacteristic
686#124—22no—
687#124—22no—
688C22⋊Q8—21no—
689C22⋊Q8—21no—
690#121—21no—
691#121—21no—
692#121—41no—
693C2×C4⋊C4C23×C10711yescharacteristic
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C42C23×C10711yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—21no—
704#103—21no—
705#102—21no—
706#102—21no—
707#102—21no—
708#102—21no—
709#101—22no—
710#100—22no—
711#100—41no—
712C22⋊C8—21no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—21no—
716C24—21no—
717C24—21no—
718C24—41no—
719C24—41no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—24no—
725#41—24no—
726#41—24no—
727#41—24no—
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—42no—
737#41—44no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41C2×D4×C10712yes—
747#41C2×D4×C10712yes—
748#41C2×D4×C10712yes—
749#41C2×D4×C10712yes—
750C2×Q8—21no—
751C2×Q8—24no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—41no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8C2×D4×C10711yescharacteristic
761C2×Q8C2×D4×C10711yescharacteristic
762C2×Q8C2×D4×C10712yes—
763C2×Q8C2×D4×C10711yescharacteristic
764C2×Q8C2×D4×C10711yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—44no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—41no—
797C2×D4C2×D4×C10711yescharacteristic
798C2×D4C2×D4×C10711yescharacteristic
799C2×D4C2×D4×C10712yes—
800C2×D4C2×D4×C10712yes—
801C2×D4C2×D4×C10711yescharacteristic
802C2×D4C2×D4×C10711yescharacteristic
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4C24×C10711yescharacteristic
815Q16—24no—
816Q16—22no—
817Q16—22no—
818Q16—42no—
819SD16—24no—
820SD16—24no—
821SD16—24no—
822SD16—24no—
823SD16—24no—
824SD16—22no—
825SD16—22no—
826SD16—22no—
827SD16—24no—
828SD16—22no—
829SD16—42no—
830SD16—42no—
831D8—24no—
832D8—24no—
833D8—24no—
834D8—24no—
835D8—22no—
836D8—24no—
837D8—22no—
838D8—42no—
839M16—24no—
840M16—24no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16C2×D4×C10712yes—
848M16C2×D4×C10712yes—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C10711yescharacteristic
860C2×C8C2×D4×C10711yescharacteristic
861C2×C8C2×D4×C10711yescharacteristic
862C2×C8C2×D4×C10711yescharacteristic
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—41no—
866C22⋊C4—44no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—82no—
870C42—21no—
871C42—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—44no—
879C23—44no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—81no—
885C23—81no—
886C23—81no—
887C23—81no—
888C23—161no—
889C23—161no—
890C23—161no—
891C23—161no—
892C23H(5,𝔽2)×C10711yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—22no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—22no—
900Q8—21no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C10712yes—
905Q8#120×C10712yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—22no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—22no—
919D4—21no—
920D4—44no—
921D4—44no—
922D4—44no—
923D4—44no—
924D4—44no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—161no—
934D4#120×C10712yes—
935D4#120×C10712yes—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—81no—
960C2×C4C22×D4×C10711yescharacteristic
961C2×C4C22×D4×C10711yescharacteristic
962C2×C4C22×D4×C10711yescharacteristic
963C2×C4C22×D4×C10711yescharacteristic
964C2×C4C22×D4×C10711yescharacteristic
965C2×C4H(5,𝔽2)×C10711yescharacteristic
966C8—21no—
967C8—21no—
968C8—22no—
969C8—22no—
970C8—21no—
971C8—21no—
972C8—41no—
973C8—41no—
974C22—21no—
975C22—21no—
976C22—22no—
977C22—22no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—82no—
991C22—82no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—161no—
997C22—161no—
998C22—164no—
999C22—164no—
1000C22#534×C10711yescharacteristic
1001C22D42×C10711yescharacteristic
1002C22D42×C10711yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#120×C10711yescharacteristic
1011C4C2×#120×C10711yescharacteristic
1012C4D42×C10711yescharacteristic
1013C4D42×C10711yescharacteristic
1014C2—21no—
1015C2—21no—
1016C2—42no—
1017C2—42no—
1018C2—81no—
1019C2—81no—
1020C2—82no—
1021C2—82no—
1022C2C107×#240311yescharacteristic
1023C2C107×#328811yescharacteristic
1024C2C107×#329011yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C107C2semidirect
2. C2×#576×C107C2semidirect
3. C2×#454×C107C2semidirect
4. C2×#455×C107C2semidirect
5. C107×#3013C2semidirect
6. C107×#3012C2semidirect
7. C107×#2019C2semidirect
8. C107×#2018C2semidirect
9. C107×#2012C2semidirect
10. C107×#2006C2semidirect
11. C107×#1908C2semidirect
12. C107×#1907C2semidirect
13. C107×#1876C2semidirect
14. C107×#1876C2semidirect
15. C107×#1792C2semidirect
16. C2×2−1+4×C107C22semidirect
25. C2×#137×C107C22semidirect
31. C2×AGL(1,ℤ/8)×C107C22semidirect
32. C2×AGL(1,ℤ/8)×C107C22semidirect
38. C22×SD16×C107C22semidirect
42. C2×#131×C107C22semidirect
43. #537×C107C22semidirect
44. C2×#124×C107C22semidirect
56. C2×#104×C107C22semidirect
57. C2×#104×C107C22semidirect
58. C2×#104×C107C22semidirect
60. #417×C107C22semidirect
61. C2×#103×C107C22semidirect
62. C2×#102×C107C22semidirect
63. C2×#101×C107C22semidirect
64. C2×#100×C107C22semidirect
65. C2×#100×C107C22semidirect
66. #408×C107C22semidirect
67. #408×C107C22semidirect
68. #390×C107C22semidirect
69. #343×C107C22semidirect
70. #341×C107C22semidirect
71. #341×C107C22semidirect
72. #336×C107C22semidirect
84. H(5,𝔽2)×C107D4semidirect
111. #137×C107D4semidirect
122. AGL(1,ℤ/8)×C107D4semidirect
501. #23888C107direct (N × H)
513. C2×#577C2×C107semidirect
514. C2×#576C2×C107semidirect
515. C2×#454C2×C107semidirect
516. C2×#455C2×C107semidirect
517. #3013C2×C107semidirect
518. #3012C2×C107semidirect
519. #2019C2×C107semidirect
520. #2018C2×C107semidirect
521. #2012C2×C107semidirect
522. #2006C2×C107semidirect
523. #1908C2×C107semidirect
524. #1907C2×C107semidirect
525. #1876C2×C107semidirect
526. #1876C2×C107semidirect
527. #1792C2×C107semidirect
528. C107#23888direct (N × H)
529. C2×2−1+4C22×C107semidirect
538. C2×#137C22×C107semidirect
544. C2×AGL(1,ℤ/8)C22×C107semidirect
545. C2×AGL(1,ℤ/8)C22×C107semidirect
551. C22×SD16C22×C107semidirect
555. C2×#131C22×C107semidirect
556. #537C22×C107semidirect
557. C2×#124C22×C107semidirect
569. C2×#104C22×C107semidirect
570. C2×#104C22×C107semidirect
571. C2×#104C22×C107semidirect
573. #417C22×C107semidirect
574. C2×#103C22×C107semidirect
575. C2×#102C22×C107semidirect
576. C2×#101C22×C107semidirect
577. C2×#100C22×C107semidirect
578. C2×#100C22×C107semidirect
579. #408C22×C107semidirect
580. #408C22×C107semidirect
581. #390C22×C107semidirect
582. #343C22×C107semidirect
583. #341C22×C107semidirect
584. #341C22×C107semidirect
585. #336C22×C107semidirect
597. H(5,𝔽2)D4×C107semidirect
624. #137D4×C107semidirect
635. AGL(1,ℤ/8)D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1072
C2×#576×C1072
C2×#454×C1072
C2×#455×C1072
C107×#30132
C107×#30122
C107×#20192
C107×#20182
C107×#20122
C107×#20062
C107×#19082
C107×#19072
C107×#18762
C107×#17922
#23888107