Finite Group Databasebeta

← C107×#23889 #41049853

Subgroups — C107×#23889 #41049853

Order 27392.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C107C211yesmaximal, characteristic, complemented
2C2×#577×C107C211yesmaximal, characteristic, complemented
3C2×#454×C107C211yesmaximal, characteristic, complemented
4C2×#455×C107C211yesmaximal, characteristic, complemented
5C107×#3013C211yesmaximal, characteristic, complemented
6C107×#3012C211yesmaximal, characteristic, complemented
7C107×#2020C211yesmaximal, characteristic, complemented
8C107×#2019C211yesmaximal, characteristic, complemented
9C107×#2015C211yesmaximal, characteristic, complemented
10C107×#2007C211yesmaximal, characteristic, complemented
11C107×#1908C211yesmaximal, characteristic, complemented
12C107×#1907C211yesmaximal, characteristic, complemented
13C107×#1876C211yesmaximal, characteristic, complemented
14C107×#1876C211yesmaximal, characteristic, complemented
15C107×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C107C2211yescharacteristic
17C2×2−1+4×C107C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C107C2211yescharacteristic
19#578×C107—24no—
20#578×C107—24no—
21#577×C107—24no—
22#577×C107—24no—
23C2×#137×C107—21no—
24C2×#137×C107—21no—
25C2×#137×C107—21no—
26C2×#137×C107C2211yescharacteristic
27C2×#137×C107C2211yescharacteristic
28C2×#137×C107C2211yescharacteristic
29C2×#137×C107C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C107—21no—
31C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
33C2×#135×C107—21no—
34C2×#135×C107—21no—
35C2×#135×C107C2211yescharacteristic
36C2×#135×C107C2211yescharacteristic
37C22×Q16×C107—21no—
38C22×Q16×C107C2211yescharacteristic, complemented
39C22×SD16×C107—21no—
40C22×SD16×C107C2211yescharacteristic
41C2×#131×C107C2211yescharacteristic
42C2×#131×C107C2211yescharacteristic, complemented
43#537×C107C2211yescharacteristic
44C2×#124×C107C2211yescharacteristic
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
57C2×#104×C107C2211yescharacteristic, complemented
58C2×#104×C107C2211yescharacteristic, complemented
59#417×C107C2211yescharacteristic
60#417×C107C2211yescharacteristic, complemented
61C2×#103×C107C2211yescharacteristic, complemented
62C2×#102×C107C2211yescharacteristic
63C2×#101×C107C2211yescharacteristic, complemented
64C2×#101×C107C2211yescharacteristic, complemented
65C2×#100×C107C2211yescharacteristic
66#408×C107C2211yescharacteristic
67#408×C107C2211yescharacteristic, complemented
68#391×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—22no—
772−1+4×C107—22no—
782−1+4×C107—41no—
792−1+4×C107—41no—
802−1+4×C107D414yescomplemented
81H(5,𝔽2)×C107—22no—
82H(5,𝔽2)×C107—22no—
83H(5,𝔽2)×C107—22no—
84H(5,𝔽2)×C107—41no—
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×C107—41no—
93C2×#41×C107C2311yescharacteristic
94C2×#41×C107C2311yescharacteristic
95C2×#41×C107C2311yescharacteristic
96C2×#41×C107C2311yescharacteristic
97C22×Q8×C107—21no—
98C22×Q8×C107—21no—
99C22×Q8×C107—21no—
100C22×Q8×C107—21no—
101C22×Q8×C107C2311yescharacteristic
102C22×Q8×C107C2311yescharacteristic
103C22×D4×C107—21no—
104C22×D4×C107—21no—
105C22×D4×C107—41no—
106C22×D4×C107C2311yescharacteristic
107#137×C107—28no—
108#137×C107—28no—
109#137×C107—28no—
110#137×C107—22no—
111#137×C107—22no—
112#137×C107—22no—
113#137×C107—22no—
114#137×C107—22no—
115#137×C107—22no—
116#137×C107—41no—
117#137×C107D414yescomplemented
118AGL(1,ℤ/8)×C107—28no—
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—28no—
130C2×Q16×C107—21no—
131C2×Q16×C107—21no—
132C2×Q16×C107—22no—
133C2×Q16×C107—22no—
134C2×Q16×C107—21no—
135C2×Q16×C107—21no—
136C2×Q16×C107—21no—
137C2×Q16×C107—21no—
138C2×Q16×C107D411yescharacteristic
139C2×Q16×C107D411yescharacteristic
140C2×SD16×C107—28no—
141C2×SD16×C107—21no—
142C2×SD16×C107—22no—
143C2×SD16×C107—21no—
144C2×SD16×C107—22no—
145C2×SD16×C107—21no—
146C2×SD16×C107—21no—
147C2×SD16×C107—21no—
148C2×SD16×C107—21no—
149C2×SD16×C107—21no—
150C2×SD16×C107—21no—
151C2×SD16×C107D411yescharacteristic
152C2×SD16×C107D411yescharacteristic
153C2×SD16×C107D411yescharacteristic
154C2×SD16×C107D411yescharacteristic
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×C42×C107C2311yescharacteristic
183#104×C107—22no—
184#104×C107—22no—
185#104×C107—22no—
186#104×C107—22no—
187#103×C107—21no—
188#103×C107—21no—
189#103×C107—21no—
190#103×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#101×C107—22no—
196#101×C107—41no—
197#100×C107—22no—
198C22⋊C8×C107—21no—
199C22⋊C8×C107—21no—
200C22⋊C8×C107—21no—
201C22⋊C8×C107—21no—
202#95×C107—41no—
203C24×C107—21no—
204C24×C107—41no—
205#41×C107—21no—
206#41×C107—21no—
207#41×C107—21no—
208#41×C107—21no—
209#41×C107—24no—
210#41×C107—24no—
211#41×C107—24no—
212#41×C107—24no—
213#41×C107—21no—
214#41×C107—21no—
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—44no—
222#41×C107—42no—
223#41×C107—42no—
224#41×C107—42no—
225#41×C107—44no—
226#41×C107—42no—
227#41×C107—44no—
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—21no—
239C2×Q8×C107—24no—
240C2×Q8×C107—24no—
241C2×Q8×C107—24no—
242C2×Q8×C107—21no—
243C2×Q8×C107—21no—
244C2×Q8×C107—21no—
245C2×Q8×C107—21no—
246C2×Q8×C107—21no—
247C2×Q8×C107—21no—
248C2×Q8×C107—21no—
249C2×Q8×C107—21no—
250C2×Q8×C107—41no—
251C2×Q8×C107—41no—
252C2×Q8×C107—42no—
253C2×Q8×C107—42no—
254C2×Q8×C107—42no—
255C2×Q8×C107—42no—
256C2×Q8×C107—42no—
257C2×Q8×C107C2×D411yescharacteristic
258C2×Q8×C107C2×D411yescharacteristic
259C2×Q8×C107C2×D412yes—
260C2×Q8×C107C2×D412yes—
261C2×Q8×C107C2×D411yescharacteristic
262C2×Q8×C107C2×D411yescharacteristic
263C2×D4×C107—21no—
264C2×D4×C107—21no—
265C2×D4×C107—24no—
266C2×D4×C107—21no—
267C2×D4×C107—21no—
268C2×D4×C107—21no—
269C2×D4×C107—21no—
270C2×D4×C107—21no—
271C2×D4×C107—21no—
272C2×D4×C107—21no—
273C2×D4×C107—42no—
274C2×D4×C107—41no—
275C2×D4×C107—41no—
276C2×D4×C107—42no—
277C2×D4×C107—44no—
278C2×D4×C107—44no—
279C2×D4×C107—41no—
280C2×D4×C107—41no—
281C2×D4×C107—42no—
282C2×D4×C107—41no—
283C2×D4×C107C2×D411yescharacteristic
284C2×D4×C107C2×D411yescharacteristic
285C2×D4×C107C2×D412yes—
286C2×D4×C107C2×D411yescharacteristic
287C2×D4×C107C2×D411yescharacteristic
288C22×C4×C107—21no—
289C22×C4×C107—21no—
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—41no—
297C22×C4×C107—41no—
298C22×C4×C107—41no—
299C22×C4×C107—41no—
300C22×C4×C107—41no—
301C22×C4×C107C2411yescharacteristic
302Q16×C107—24no—
303Q16×C107—24no—
304Q16×C107—24no—
305Q16×C107—24no—
306Q16×C107—22no—
307Q16×C107—24no—
308Q16×C107—22no—
309Q16×C107—42no—
310SD16×C107—24no—
311SD16×C107—24no—
312SD16×C107—24no—
313SD16×C107—24no—
314SD16×C107—22no—
315SD16×C107—24no—
316SD16×C107—22no—
317SD16×C107—24no—
318SD16×C107—22no—
319SD16×C107—22no—
320SD16×C107—42no—
321SD16×C107—42no—
322D8×C107—24no—
323D8×C107—22no—
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—
356C42×C107—21no—
357C42×C107—21no—
358C23×C107—21no—
359C23×C107—21no—
360C23×C107—21no—
361C23×C107—21no—
362C23×C107—22no—
363C23×C107—44no—
364C23×C107—41no—
365C23×C107—41no—
366C23×C107—81no—
367C23×C107—81no—
368C23×C107—161no—
369C23×C107—161no—
370C23×C107H(5,𝔽2)11yescharacteristic
371Q8×C107—21no—
372Q8×C107—21no—
373Q8×C107—22no—
374Q8×C107—22no—
375Q8×C107—22no—
376Q8×C107—21no—
377Q8×C107—21no—
378Q8×C107—21no—
379Q8×C107—22no—
380Q8×C107—21no—
381Q8×C107—44no—
382Q8×C107—44no—
383Q8×C107—41no—
384Q8×C107—41no—
385Q8×C107—41no—
386Q8×C107—41no—
387Q8×C107#12012yes—
388Q8×C107#12012yes—
389D4×C107—22no—
390D4×C107—22no—
391D4×C107—22no—
392D4×C107—22no—
393D4×C107—22no—
394D4×C107—21no—
395D4×C107—21no—
396D4×C107—21no—
397D4×C107—21no—
398D4×C107—21no—
399D4×C107—22no—
400D4×C107—21no—
401D4×C107—44no—
402D4×C107—44no—
403D4×C107—44no—
404D4×C107—44no—
405D4×C107—41no—
406D4×C107—41no—
407D4×C107—41no—
408D4×C107—41no—
409D4×C107—41no—
410D4×C107—41no—
411D4×C107—161no—
412D4×C107#12012yes—
413D4×C107#12012yes—
414C2×C4×C107—21no—
415C2×C4×C107—21no—
416C2×C4×C107—22no—
417C2×C4×C107—22no—
418C2×C4×C107—22no—
419C2×C4×C107—22no—
420C2×C4×C107—22no—
421C2×C4×C107—22no—
422C2×C4×C107—21no—
423C2×C4×C107—21no—
424C2×C4×C107—44no—
425C2×C4×C107—44no—
426C2×C4×C107—44no—
427C2×C4×C107—44no—
428C2×C4×C107—44no—
429C2×C4×C107—41no—
430C2×C4×C107—41no—
431C2×C4×C107—41no—
432C2×C4×C107—41no—
433C2×C4×C107—41no—
434C2×C4×C107—41no—
435C2×C4×C107—41no—
436C2×C4×C107—41no—
437C2×C4×C107—41no—
438C2×C4×C107—41no—
439C2×C4×C107—41no—
440C2×C4×C107—41no—
441C2×C4×C107—81no—
442C2×C4×C107C22×D411yescharacteristic
443C2×C4×C107C22×D411yescharacteristic
444C2×C4×C107C22×D411yescharacteristic
445C2×C4×C107C22×D411yescharacteristic
446C2×C4×C107C22×D411yescharacteristic
447C2×C4×C107H(5,𝔽2)11yescharacteristic
448C8×C107—21no—
449C8×C107—21no—
450C8×C107—22no—
451C8×C107—22no—
452C8×C107—21no—
453C8×C107—21no—
454C8×C107—41no—
455C8×C107—41no—
456C22×C107—21no—
457C22×C107—21no—
458C22×C107—22no—
459C22×C107—22no—
460C22×C107—41no—
461C22×C107—41no—
462C22×C107—41no—
463C22×C107—41no—
464C22×C107—41no—
465C22×C107—41no—
466C22×C107—42no—
467C22×C107—41no—
468C22×C107—41no—
469C22×C107—41no—
470C22×C107—41no—
471C22×C107—82no—
472C22×C107—81no—
473C22×C107—81no—
474C22×C107—161no—
475C22×C107—164no—
476C22×C107#53411yescharacteristic
477C22×C107D4211yescharacteristic
478C22×C107D4211yescharacteristic
479C4×C107—22no—
480C4×C107—22no—
481C4×C107—41no—
482C4×C107—42no—
483C4×C107—42no—
484C4×C107—41no—
485C4×C107—81no—
486C4×C107—81no—
487C4×C107C2×#12011yescharacteristic
488C4×C107C2×#12011yescharacteristic
489C4×C107D4211yescharacteristic
490C4×C107D4211yescharacteristic
491#23889C10711yesmaximal, characteristic, direct product factor, Sylow
492C2×C107—21no—
493C2×C107—21no—
494C2×C107—42no—
495C2×C107—42no—
496C2×C107—81no—
497C2×C107—81no—
498C2×C107—82no—
499C2×C107#240311yescharacteristic
500C2×C107#328911yescharacteristic
501C2×C107#329011yescharacteristic
502C2×#578C2×C10711yescharacteristic, complemented
503C2×#577C2×C10711yescharacteristic, complemented
504C2×#454C2×C10711yescharacteristic, complemented
505C2×#455C2×C10711yescharacteristic, complemented
506#3013C2×C10711yescharacteristic, complemented
507#3012C2×C10711yescharacteristic, complemented
508#2020C2×C10711yescharacteristic, complemented
509#2019C2×C10711yescharacteristic, complemented
510#2015C2×C10711yescharacteristic, complemented
511#2007C2×C10711yescharacteristic, complemented
512#1908C2×C10711yescharacteristic, complemented
513#1907C2×C10711yescharacteristic, complemented
514#1876C2×C10711yescharacteristic, complemented
515#1876C2×C10711yescharacteristic, complemented
516#1793C2×C10711yescharacteristic, complemented
517C107#2388911yescharacteristic, direct product factor, Sylow
518C2×2−1+4C22×C10711yescharacteristic
519C2×2−1+4C22×C10711yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C10711yescharacteristic
521#578—24no—
522#578—24no—
523#577—24no—
524#577—24no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137—21no—
528C2×#137C22×C10711yescharacteristic
529C2×#137C22×C10711yescharacteristic
530C2×#137C22×C10711yescharacteristic
531C2×#137C22×C10711yescharacteristic, complemented
532C2×AGL(1,ℤ/8)—21no—
533C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
534C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
535C2×#135—21no—
536C2×#135—21no—
537C2×#135C22×C10711yescharacteristic
538C2×#135C22×C10711yescharacteristic
539C22×Q16—21no—
540C22×Q16C22×C10711yescharacteristic, complemented
541C22×SD16—21no—
542C22×SD16C22×C10711yescharacteristic
543C2×#131C22×C10711yescharacteristic
544C2×#131C22×C10711yescharacteristic, complemented
545#537C22×C10711yescharacteristic
546C2×#124C22×C10711yescharacteristic
547#455—24no—
548#454—24no—
549#452—21no—
550#452—21no—
551#451—21no—
552#450—21no—
553#449—21no—
554#449—21no—
555#448—21no—
556#447—21no—
557C2×#104C22×C10711yescharacteristic
558C2×#104C22×C10711yescharacteristic
559C2×#104C22×C10711yescharacteristic, complemented
560C2×#104C22×C10711yescharacteristic, complemented
561#417C22×C10711yescharacteristic
562#417C22×C10711yescharacteristic, complemented
563C2×#103C22×C10711yescharacteristic, complemented
564C2×#102C22×C10711yescharacteristic
565C2×#101C22×C10711yescharacteristic, complemented
566C2×#101C22×C10711yescharacteristic, complemented
567C2×#100C22×C10711yescharacteristic
568#408C22×C10711yescharacteristic
569#408C22×C10711yescharacteristic, complemented
570#391C22×C10711yescharacteristic, complemented
571#343C22×C10711yescharacteristic, complemented
572#341C22×C10711yescharacteristic, complemented
573#341C22×C10711yescharacteristic, complemented
574#336C22×C10711yescharacteristic, complemented
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C10714yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C10711yescharacteristic
596C2×#41C23×C10711yescharacteristic
597C2×#41C23×C10711yescharacteristic
598C2×#41C23×C10711yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C10711yescharacteristic
604C22×Q8C23×C10711yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C10711yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C10714yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C10714yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C10711yescharacteristic
641C2×Q16D4×C10711yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C10711yescharacteristic
654C2×SD16D4×C10711yescharacteristic
655C2×SD16D4×C10711yescharacteristic
656C2×SD16D4×C10711yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C10711yescharacteristic
660C2×D8D4×C10711yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C10711yescharacteristic
668C2×M16C23×C10711yescharacteristic
669C2×M16C23×C10711yescharacteristic
670C2×M16C23×C10711yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C10711yescharacteristic
674C22×C8C23×C10711yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C10711yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C10711yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C10712yes—
736#41C2×D4×C10712yes—
737#41C2×D4×C10712yes—
738#41C2×D4×C10712yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C10711yescharacteristic
760C2×Q8C2×D4×C10711yescharacteristic
761C2×Q8C2×D4×C10712yes—
762C2×Q8C2×D4×C10712yes—
763C2×Q8C2×D4×C10711yescharacteristic
764C2×Q8C2×D4×C10711yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C10711yescharacteristic
786C2×D4C2×D4×C10711yescharacteristic
787C2×D4C2×D4×C10712yes—
788C2×D4C2×D4×C10711yescharacteristic
789C2×D4C2×D4×C10711yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C10711yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C10712yes—
837M16C2×D4×C10712yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C10711yescharacteristic
849C2×C8C2×D4×C10711yescharacteristic
850C2×C8C2×D4×C10711yescharacteristic
851C2×C8C2×D4×C10711yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C10711yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C10712yes—
890Q8#120×C10712yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C10712yes—
915D4#120×C10712yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C10711yescharacteristic
945C2×C4C22×D4×C10711yescharacteristic
946C2×C4C22×D4×C10711yescharacteristic
947C2×C4C22×D4×C10711yescharacteristic
948C2×C4C22×D4×C10711yescharacteristic
949C2×C4H(5,𝔽2)×C10711yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22#534×C10711yescharacteristic
979C22D42×C10711yescharacteristic
980C22D42×C10711yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C10711yescharacteristic
990C4C2×#120×C10711yescharacteristic
991C4D42×C10711yescharacteristic
992C4D42×C10711yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C107×#240311yescharacteristic
1001C2C107×#328911yescharacteristic
1002C2C107×#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×#578×C107C2semidirect
2. C2×#577×C107C2semidirect
3. C2×#454×C107C2semidirect
4. C2×#455×C107C2semidirect
5. C107×#3013C2semidirect
6. C107×#3012C2semidirect
7. C107×#2020C2semidirect
8. C107×#2019C2semidirect
9. C107×#2015C2semidirect
10. C107×#2007C2semidirect
11. C107×#1908C2semidirect
12. C107×#1907C2semidirect
13. C107×#1876C2semidirect
14. C107×#1876C2semidirect
15. C107×#1793C2semidirect
17. C2×2−1+4×C107C22semidirect
29. C2×#137×C107C22semidirect
38. C22×Q16×C107C22semidirect
42. C2×#131×C107C22semidirect
57. C2×#104×C107C22semidirect
58. C2×#104×C107C22semidirect
60. #417×C107C22semidirect
61. C2×#103×C107C22semidirect
63. C2×#101×C107C22semidirect
64. C2×#101×C107C22semidirect
67. #408×C107C22semidirect
68. #391×C107C22semidirect
69. #343×C107C22semidirect
70. #341×C107C22semidirect
71. #341×C107C22semidirect
72. #336×C107C22semidirect
80. 2−1+4×C107D4semidirect
117. #137×C107D4semidirect
122. AGL(1,ℤ/8)×C107D4semidirect
491. #23889C107direct (N × H)
502. C2×#578C2×C107semidirect
503. C2×#577C2×C107semidirect
504. C2×#454C2×C107semidirect
505. C2×#455C2×C107semidirect
506. #3013C2×C107semidirect
507. #3012C2×C107semidirect
508. #2020C2×C107semidirect
509. #2019C2×C107semidirect
510. #2015C2×C107semidirect
511. #2007C2×C107semidirect
512. #1908C2×C107semidirect
513. #1907C2×C107semidirect
514. #1876C2×C107semidirect
515. #1876C2×C107semidirect
516. #1793C2×C107semidirect
517. C107#23889direct (N × H)
519. C2×2−1+4C22×C107semidirect
531. C2×#137C22×C107semidirect
540. C22×Q16C22×C107semidirect
544. C2×#131C22×C107semidirect
559. C2×#104C22×C107semidirect
560. C2×#104C22×C107semidirect
562. #417C22×C107semidirect
563. C2×#103C22×C107semidirect
565. C2×#101C22×C107semidirect
566. C2×#101C22×C107semidirect
569. #408C22×C107semidirect
570. #391C22×C107semidirect
571. #343C22×C107semidirect
572. #341C22×C107semidirect
573. #341C22×C107semidirect
574. #336C22×C107semidirect
582. 2−1+4D4×C107semidirect
619. #137D4×C107semidirect
624. 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×#578×C1072
C2×#577×C1072
C2×#454×C1072
C2×#455×C1072
C107×#30132
C107×#30122
C107×#20202
C107×#20192
C107×#20152
C107×#20072
C107×#19082
C107×#19072
C107×#18762
C107×#17932
#23889107