Finite Group Databasebeta

← C107×#24456 #41050420

Subgroups — C107×#24456 #41050420

Order 27392.

1410 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C107C211yesmaximal, characteristic, complemented
2C2×#472×C107C211yesmaximal, characteristic, complemented
3C107×#3045C211yesmaximal, characteristic, complemented
4C2×#453×C107C211yesmaximal, characteristic, complemented
5C107×#3008C211yesmaximal, characteristic, complemented
6C107×#2897C211yesmaximal, characteristic, complemented
7C107×#2051C211yesmaximal, characteristic, complemented
8C107×#2045C211yesmaximal, characteristic, complemented
9C107×#2011C211yesmaximal, characteristic, complemented
10C107×#2002C211yesmaximal, characteristic, complemented
11C107×#1907C211yesmaximal, characteristic, complemented
12C107×#1883C211yesmaximal, characteristic, complemented
13C107×#1876C211yesmaximal, characteristic, complemented
14C107×#1866C211yesmaximal, characteristic, complemented
15C107×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18#576×C107—24no—
19#576×C107—24no—
20C2×AGL(1,ℤ/8)×C107—21no—
21C2×AGL(1,ℤ/8)×C107—21no—
22C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
26C2×#135×C107—21no—
27C2×#135×C107C2211yescharacteristic
28C22×D8×C107—21no—
29C22×D8×C107C2211yescharacteristic
30C22×D8×C107C2211yescharacteristic, complemented
31C2×#131×C107C2211yescharacteristic
32C2×#131×C107C2211yescharacteristic, complemented
33#535×C107C2211yescharacteristic, complemented
34C2×#127×C107C2211yescharacteristic, complemented
35#520×C107C2211yescharacteristic, complemented
36#472×C107—24no—
37#464×C107—21no—
38#463×C107—21no—
39#460×C107—21no—
40#459×C107—21no—
41#453×C107—24no—
42#449×C107—21no—
43#449×C107—21no—
44#447×C107—21no—
45#447×C107—21no—
46C2×#108×C107C2211yescharacteristic, complemented
47#424×C107C2211yescharacteristic, complemented
48C2×#104×C107C2211yescharacteristic
49C2×#104×C107C2211yescharacteristic, complemented
50C2×#104×C107C2211yescharacteristic, complemented
51#418×C107—21no—
52#418×C107C2211yescharacteristic, complemented
53#418×C107C2211yescharacteristic, complemented
54#417×C107—21no—
55#417×C107C2211yescharacteristic
56#417×C107C2211yescharacteristic, complemented
57#416×C107—21no—
58#416×C107C2211yescharacteristic
59C2×#102×C107—21no—
60C2×#102×C107C2211yescharacteristic, complemented
61C2×#102×C107C2211yescharacteristic, complemented
62C2×#100×C107C2211yescharacteristic, complemented
63C2×#100×C107C2211yescharacteristic, complemented
64C2×#100×C107C2211yescharacteristic, complemented
65#408×C107C2211yescharacteristic, complemented
66#390×C107C2211yescharacteristic, complemented
67#343×C107C2211yescharacteristic, complemented
68#341×C107C2211yescharacteristic, complemented
69#339×C107C2211yescharacteristic, complemented
70#336×C107C2211yescharacteristic, complemented
71H(5,𝔽2)×C107—22no—
72H(5,𝔽2)×C107—22no—
73H(5,𝔽2)×C107—22no—
74H(5,𝔽2)×C107—22no—
75H(5,𝔽2)×C107—22no—
76H(5,𝔽2)×C107—41no—
77H(5,𝔽2)×C107—41no—
78H(5,𝔽2)×C107D414yescomplemented
79C2×#41×C107—21no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—21no—
83C2×#41×C107C2311yescharacteristic
84C2×#41×C107C2311yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C22×D4×C107—21no—
87C22×D4×C107—21no—
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—41no—
91C22×D4×C107—41no—
92C22×D4×C107—41no—
93C22×D4×C107C2311yescharacteristic
94C22×D4×C107C2311yescharacteristic
95C22×D4×C107C2311yescharacteristic
96AGL(1,ℤ/8)×C107—28no—
97AGL(1,ℤ/8)×C107—28no—
98AGL(1,ℤ/8)×C107—22no—
99AGL(1,ℤ/8)×C107—22no—
100AGL(1,ℤ/8)×C107—22no—
101AGL(1,ℤ/8)×C107—22no—
102AGL(1,ℤ/8)×C107—22no—
103AGL(1,ℤ/8)×C107—22no—
104AGL(1,ℤ/8)×C107—22no—
105AGL(1,ℤ/8)×C107D414yescomplemented
106#135×C107—28no—
107#135×C107—22no—
108#135×C107—22no—
109C2×Q16×C107D411yescharacteristic, complemented
110C2×SD16×C107—21no—
111C2×SD16×C107—21no—
112C2×SD16×C107—21no—
113C2×SD16×C107—21no—
114C2×SD16×C107D411yescharacteristic, complemented
115C2×SD16×C107D411yescharacteristic, complemented
116C2×D8×C107—28no—
117C2×D8×C107—21no—
118C2×D8×C107—21no—
119C2×D8×C107—22no—
120C2×D8×C107—22no—
121C2×D8×C107—21no—
122C2×D8×C107—21no—
123C2×D8×C107—22no—
124C2×D8×C107—21no—
125C2×D8×C107—21no—
126C2×D8×C107—21no—
127C2×D8×C107—21no—
128C2×D8×C107—41no—
129C2×D8×C107D411yescharacteristic, complemented
130#131×C107—22no—
131#131×C107—22no—
132#131×C107—22no—
133#131×C107—41no—
134C2×M16×C107—21no—
135C2×M16×C107—21no—
136C2×M16×C107C2311yescharacteristic
137C2×M16×C107C2311yescharacteristic
138C2×M16×C107C2311yescharacteristic
139C2×M16×C107C2311yescharacteristic
140C22×C8×C107—21no—
141C22×C8×C107—21no—
142C22×C8×C107C2311yescharacteristic
143C22×C8×C107C2311yescharacteristic
144#127×C107—22no—
145#127×C107—21no—
146#127×C107—41no—
147#124×C107—21no—
148#121×C107—21no—
149#121×C107—21no—
150#120×C107—41no—
151C4×Q8×C107—21no—
152C4×D4×C107—21no—
153C4×D4×C107—41no—
154#117×C107—21no—
155#117×C107C2311yescharacteristic
156C2×C4⋊C4×C107—21no—
157C2×C4⋊C4×C107C2311yescharacteristic
158C2×C22⋊C4×C107—41no—
159C2×C42×C107C2311yescharacteristic
160#108×C107—22no—
161C4⋊C8×C107—21no—
162C4⋊C8×C107—21no—
163#104×C107—22no—
164#104×C107—22no—
165#104×C107—41no—
166#103×C107—21no—
167#103×C107—21no—
168#103×C107D411yescharacteristic, complemented
169#103×C107D411yescharacteristic, complemented
170#102×C107—21no—
171#102×C107—21no—
172#102×C107—21no—
173#102×C107—21no—
174#102×C107—21no—
175#102×C107—21no—
176#102×C107—21no—
177#102×C107—21no—
178#102×C107—21no—
179#102×C107—21no—
180#102×C107D411yescharacteristic, complemented
181#102×C107D411yescharacteristic, complemented
182#100×C107—22no—
183#100×C107—22no—
184#100×C107—22no—
185C22⋊C8×C107—21no—
186C22⋊C8×C107—21no—
187C24×C107—21no—
188C24×C107—21no—
189C24×C107—21no—
190C24×C107—41no—
191C24×C107—41no—
192#41×C107—21no—
193#41×C107—21no—
194#41×C107—21no—
195#41×C107—21no—
196#41×C107—24no—
197#41×C107—24no—
198#41×C107—24no—
199#41×C107—21no—
200#41×C107—21no—
201#41×C107—21no—
202#41×C107—21no—
203#41×C107—42no—
204#41×C107—42no—
205#41×C107—42no—
206#41×C107—42no—
207#41×C107—42no—
208#41×C107C2×D412yes—
209#41×C107C2×D412yes—
210#41×C107C2×D412yes—
211#41×C107#4112yes—
212C2×Q8×C107C2×D411yescharacteristic
213C2×Q8×C107C2×D411yescharacteristic
214C2×Q8×C107C2×D411yescharacteristic
215C2×D4×C107—21no—
216C2×D4×C107—21no—
217C2×D4×C107—24no—
218C2×D4×C107—24no—
219C2×D4×C107—24no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
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—42no—
239C2×D4×C107—42no—
240C2×D4×C107—41no—
241C2×D4×C107—41no—
242C2×D4×C107—41no—
243C2×D4×C107—41no—
244C2×D4×C107—41no—
245C2×D4×C107—41no—
246C2×D4×C107—44no—
247C2×D4×C107—42no—
248C2×D4×C107—44no—
249C2×D4×C107—44no—
250C2×D4×C107—44no—
251C2×D4×C107—42no—
252C2×D4×C107—44no—
253C2×D4×C107—82no—
254C2×D4×C107—82no—
255C2×D4×C107C2×D412yes—
256C2×D4×C107C2×D412yes—
257C2×D4×C107C2×D411yescharacteristic
258C2×D4×C107C2×D411yescharacteristic
259C2×D4×C107C2×D411yescharacteristic
260C22×C4×C107—21no—
261C22×C4×C107—21no—
262C22×C4×C107—21no—
263C22×C4×C107—21no—
264C22×C4×C107—21no—
265C22×C4×C107—41no—
266C22×C4×C107—41no—
267C22×C4×C107—41no—
268C22×C4×C107C2411yescharacteristic
269Q16×C107—22no—
270SD16×C107—24no—
271SD16×C107—24no—
272SD16×C107—22no—
273SD16×C107—22no—
274SD16×C107—42no—
275SD16×C107—42no—
276D8×C107—24no—
277D8×C107—24no—
278D8×C107—24no—
279D8×C107—22no—
280D8×C107—24no—
281D8×C107—42no—
282D8×C107—42no—
283D8×C107—42no—
284D8×C107—42no—
285M16×C107—24no—
286M16×C107—21no—
287M16×C107—21no—
288M16×C107—21no—
289M16×C107—21no—
290M16×C107—21no—
291M16×C107—21no—
292M16×C107—21no—
293M16×C107—42no—
294M16×C107C2×D412yes—
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—21no—
302C2×C8×C107—21no—
303C2×C8×C107—21no—
304C2×C8×C107—42no—
305C2×C8×C107C2×D411yescharacteristic
306C2×C8×C107C2×D411yescharacteristic
307C2×C8×C107C2×D411yescharacteristic
308C2×C8×C107C2×D411yescharacteristic
309C4⋊C4×C107—21no—
310C4⋊C4×C107—21no—
311C4⋊C4×C107—41no—
312C4⋊C4×C107C2×D411yescharacteristic
313C4⋊C4×C107C2×D411yescharacteristic
314C22⋊C4×C107—21no—
315C22⋊C4×C107—41no—
316C22⋊C4×C107—41no—
317C22⋊C4×C107—41no—
318C22⋊C4×C107—82no—
319C42×C107—21no—
320C42×C107—21no—
321C42×C107—21no—
322C42×C107—41no—
323C23×C107—21no—
324C23×C107—21no—
325C23×C107—21no—
326C23×C107—22no—
327C23×C107—22no—
328C23×C107—44no—
329C23×C107—44no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—41no—
333C23×C107—41no—
334C23×C107—41no—
335C23×C107—41no—
336C23×C107—41no—
337C23×C107—81no—
338C23×C107—81no—
339C23×C107—81no—
340C23×C107—81no—
341C23×C107—81no—
342C23×C107—81no—
343C23×C107—161no—
344C23×C107—161no—
345C23×C107—161no—
346C23×C107—161no—
347C23×C107H(5,𝔽2)11yescharacteristic
348Q8×C107—21no—
349Q8×C107—21no—
350Q8×C107—21no—
351Q8×C107—21no—
352Q8×C107#12012yes—
353Q8×C107#12112yes—
354D4×C107—22no—
355D4×C107—22no—
356D4×C107—22no—
357D4×C107—22no—
358D4×C107—22no—
359D4×C107—22no—
360D4×C107—21no—
361D4×C107—22no—
362D4×C107—21no—
363D4×C107—22no—
364D4×C107—21no—
365D4×C107—21no—
366D4×C107—44no—
367D4×C107—44no—
368D4×C107—44no—
369D4×C107—44no—
370D4×C107—41no—
371D4×C107—41no—
372D4×C107—41no—
373D4×C107—41no—
374D4×C107—41no—
375D4×C107—41no—
376D4×C107—41no—
377D4×C107—41no—
378D4×C107—41no—
379D4×C107—41no—
380D4×C107—88no—
381D4×C107—161no—
382D4×C107—161no—
383D4×C107#12012yes—
384D4×C107#12112yes—
385C2×C4×C107—21no—
386C2×C4×C107—21no—
387C2×C4×C107—22no—
388C2×C4×C107—22no—
389C2×C4×C107—22no—
390C2×C4×C107—22no—
391C2×C4×C107—22no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—21no—
395C2×C4×C107—44no—
396C2×C4×C107—44no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—81no—
403C2×C4×C107—161no—
404C2×C4×C107C22×D411yescharacteristic
405C2×C4×C107C22×D411yescharacteristic
406C2×C4×C107C22×D411yescharacteristic
407C2×C4×C107C22×D411yescharacteristic
408C2×C4×C107C2×#4111yescharacteristic
409C2×C4×C107H(5,𝔽2)11yescharacteristic
410C8×C107—21no—
411C8×C107—22no—
412C8×C107—21no—
413C8×C107—21no—
414C8×C107—21no—
415C8×C107—41no—
416C8×C107—41no—
417C8×C107—41no—
418C22×C107—21no—
419C22×C107—21no—
420C22×C107—22no—
421C22×C107—22no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—41no—
425C22×C107—41no—
426C22×C107—41no—
427C22×C107—42no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—82no—
432C22×C107—82no—
433C22×C107—82no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—161no—
442C22×C107—161no—
443C22×C107—161no—
444C22×C107—164no—
445C22×C107—164no—
446C22×C107#53411yescharacteristic
447C22×C107D4211yescharacteristic
448C22×C107#54611yescharacteristic
449C4×C107—22no—
450C4×C107—22no—
451C4×C107—42no—
452C4×C107—41no—
453C4×C107—41no—
454C4×C107—41no—
455C4×C107—81no—
456C4×C107C2×#12011yescharacteristic
457C4×C107C2×#12111yescharacteristic
458C4×C107D4211yescharacteristic
459C4×C107#54611yescharacteristic
460#24456C10711yesmaximal, characteristic, direct product factor, Sylow
461C2×C107—21no—
462C2×C107—21no—
463C2×C107—42no—
464C2×C107—42no—
465C2×C107—81no—
466C2×C107—82no—
467C2×C107—82no—
468C2×C107—161no—
469C2×C107#241011yescharacteristic
470C2×C107#328811yescharacteristic
471C2×C107#329211yescharacteristic
472C2×#576C2×C10711yescharacteristic, complemented
473C2×#472C2×C10711yescharacteristic, complemented
474#3045C2×C10711yescharacteristic, complemented
475C2×#453C2×C10711yescharacteristic, complemented
476#3008C2×C10711yescharacteristic, complemented
477#2897C2×C10711yescharacteristic, complemented
478#2051C2×C10711yescharacteristic, complemented
479#2045C2×C10711yescharacteristic, complemented
480#2011C2×C10711yescharacteristic, complemented
481#2002C2×C10711yescharacteristic, complemented
482#1907C2×C10711yescharacteristic, complemented
483#1883C2×C10711yescharacteristic, complemented
484#1876C2×C10711yescharacteristic, complemented
485#1866C2×C10711yescharacteristic, complemented
486#1792C2×C10711yescharacteristic, complemented
487C107#2445611yescharacteristic, direct product factor, Sylow
488C2×H(5,𝔽2)C22×C10711yescharacteristic
489C2×H(5,𝔽2)C22×C10711yescharacteristic
490#576—24no—
491#576—24no—
492C2×AGL(1,ℤ/8)—21no—
493C2×AGL(1,ℤ/8)—21no—
494C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
495C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
496C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
497C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
498C2×#135—21no—
499C2×#135C22×C10711yescharacteristic
500C22×D8—21no—
501C22×D8C22×C10711yescharacteristic
502C22×D8C22×C10711yescharacteristic, complemented
503C2×#131C22×C10711yescharacteristic
504C2×#131C22×C10711yescharacteristic, complemented
505#535C22×C10711yescharacteristic, complemented
506C2×#127C22×C10711yescharacteristic, complemented
507#520C22×C10711yescharacteristic, complemented
508#472—24no—
509#464—21no—
510#463—21no—
511#460—21no—
512#459—21no—
513#453—24no—
514#449—21no—
515#449—21no—
516#447—21no—
517#447—21no—
518C2×#108C22×C10711yescharacteristic, complemented
519#424C22×C10711yescharacteristic, complemented
520C2×#104C22×C10711yescharacteristic
521C2×#104C22×C10711yescharacteristic, complemented
522C2×#104C22×C10711yescharacteristic, complemented
523#418—21no—
524#418C22×C10711yescharacteristic, complemented
525#418C22×C10711yescharacteristic, complemented
526#417—21no—
527#417C22×C10711yescharacteristic
528#417C22×C10711yescharacteristic, complemented
529#416—21no—
530#416C22×C10711yescharacteristic
531C2×#102—21no—
532C2×#102C22×C10711yescharacteristic, complemented
533C2×#102C22×C10711yescharacteristic, complemented
534C2×#100C22×C10711yescharacteristic, complemented
535C2×#100C22×C10711yescharacteristic, complemented
536C2×#100C22×C10711yescharacteristic, complemented
537#408C22×C10711yescharacteristic, complemented
538#390C22×C10711yescharacteristic, complemented
539#343C22×C10711yescharacteristic, complemented
540#341C22×C10711yescharacteristic, complemented
541#339C22×C10711yescharacteristic, complemented
542#336C22×C10711yescharacteristic, complemented
543H(5,𝔽2)—22no—
544H(5,𝔽2)—22no—
545H(5,𝔽2)—22no—
546H(5,𝔽2)—22no—
547H(5,𝔽2)—22no—
548H(5,𝔽2)—41no—
549H(5,𝔽2)—41no—
550H(5,𝔽2)D4×C10714yescomplemented
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41C23×C10711yescharacteristic
556C2×#41C23×C10711yescharacteristic
557C2×#41C23×C10711yescharacteristic
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4—41no—
565C22×D4C23×C10711yescharacteristic
566C22×D4C23×C10711yescharacteristic
567C22×D4C23×C10711yescharacteristic
568AGL(1,ℤ/8)—28no—
569AGL(1,ℤ/8)—28no—
570AGL(1,ℤ/8)—22no—
571AGL(1,ℤ/8)—22no—
572AGL(1,ℤ/8)—22no—
573AGL(1,ℤ/8)—22no—
574AGL(1,ℤ/8)—22no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)—22no—
577AGL(1,ℤ/8)D4×C10714yescomplemented
578#135—28no—
579#135—22no—
580#135—22no—
581C2×Q16D4×C10711yescharacteristic, complemented
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—21no—
585C2×SD16—21no—
586C2×SD16D4×C10711yescharacteristic, complemented
587C2×SD16D4×C10711yescharacteristic, complemented
588C2×D8—28no—
589C2×D8—21no—
590C2×D8—21no—
591C2×D8—22no—
592C2×D8—22no—
593C2×D8—22no—
594C2×D8—21no—
595C2×D8—21no—
596C2×D8—21no—
597C2×D8—21no—
598C2×D8—21no—
599C2×D8—21no—
600C2×D8—41no—
601C2×D8D4×C10711yescharacteristic, complemented
602#131—22no—
603#131—22no—
604#131—22no—
605#131—41no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16C23×C10711yescharacteristic
609C2×M16C23×C10711yescharacteristic
610C2×M16C23×C10711yescharacteristic
611C2×M16C23×C10711yescharacteristic
612C22×C8—21no—
613C22×C8—21no—
614C22×C8C23×C10711yescharacteristic
615C22×C8C23×C10711yescharacteristic
616#127—22no—
617#127—21no—
618#127—41no—
619#124—21no—
620#121—21no—
621#121—21no—
622#120—41no—
623C4×Q8—21no—
624C4×D4—21no—
625C4×D4—41no—
626#117—21no—
627#117C23×C10711yescharacteristic
628C2×C4⋊C4—21no—
629C2×C4⋊C4C23×C10711yescharacteristic
630C2×C22⋊C4—41no—
631C2×C42C23×C10711yescharacteristic
632#108—22no—
633C4⋊C8—21no—
634C4⋊C8—21no—
635#104—22no—
636#104—22no—
637#104—41no—
638#103—21no—
639#103—21no—
640#103D4×C10711yescharacteristic, complemented
641#103D4×C10711yescharacteristic, complemented
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649#102—21no—
650#102—21no—
651#102—21no—
652#102D4×C10711yescharacteristic, complemented
653#102D4×C10711yescharacteristic, complemented
654#100—22no—
655#100—22no—
656#100—22no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—41no—
663C24—41no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—24no—
669#41—24no—
670#41—24no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—21no—
675#41—42no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—42no—
680#41C2×D4×C10712yes—
681#41C2×D4×C10712yes—
682#41C2×D4×C10712yes—
683#41#41×C10712yes—
684C2×Q8C2×D4×C10711yescharacteristic
685C2×Q8C2×D4×C10711yescharacteristic
686C2×Q8C2×D4×C10711yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—44no—
725C2×D4—82no—
726C2×D4—82no—
727C2×D4C2×D4×C10712yes—
728C2×D4C2×D4×C10712yes—
729C2×D4C2×D4×C10711yescharacteristic
730C2×D4C2×D4×C10711yescharacteristic
731C2×D4C2×D4×C10711yescharacteristic
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4C24×C10711yescharacteristic
741Q16—22no—
742SD16—24no—
743SD16—24no—
744SD16—22no—
745SD16—22no—
746SD16—42no—
747SD16—42no—
748D8—24no—
749D8—24no—
750D8—24no—
751D8—22no—
752D8—24no—
753D8—42no—
754D8—42no—
755D8—42no—
756D8—42no—
757M16—24no—
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—21no—
765M16—42no—
766M16C2×D4×C10712yes—
767C2×C8—24no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—42no—
777C2×C8C2×D4×C10711yescharacteristic
778C2×C8C2×D4×C10711yescharacteristic
779C2×C8C2×D4×C10711yescharacteristic
780C2×C8C2×D4×C10711yescharacteristic
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—41no—
784C4⋊C4C2×D4×C10711yescharacteristic
785C4⋊C4C2×D4×C10711yescharacteristic
786C22⋊C4—21no—
787C22⋊C4—41no—
788C22⋊C4—41no—
789C22⋊C4—41no—
790C22⋊C4—82no—
791C42—21no—
792C42—21no—
793C42—21no—
794C42—41no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—22no—
799C23—22no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—81no—
810C23—81no—
811C23—81no—
812C23—81no—
813C23—81no—
814C23—81no—
815C23—161no—
816C23—161no—
817C23—161no—
818C23—161no—
819C23H(5,𝔽2)×C10711yescharacteristic
820Q8—21no—
821Q8—21no—
822Q8—21no—
823Q8—21no—
824Q8#120×C10712yes—
825Q8#121×C10712yes—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—21no—
833D4—22no—
834D4—21no—
835D4—22no—
836D4—21no—
837D4—21no—
838D4—44no—
839D4—44no—
840D4—44no—
841D4—44no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—88no—
853D4—161no—
854D4—161no—
855D4#120×C10712yes—
856D4#121×C10712yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—81no—
875C2×C4—161no—
876C2×C4C22×D4×C10711yescharacteristic
877C2×C4C22×D4×C10711yescharacteristic
878C2×C4C22×D4×C10711yescharacteristic
879C2×C4C22×D4×C10711yescharacteristic
880C2×C4C2×#41×C10711yescharacteristic
881C2×C4H(5,𝔽2)×C10711yescharacteristic
882C8—21no—
883C8—22no—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—22no—
893C22—22no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—82no—
904C22—82no—
905C22—82no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—161no—
914C22—161no—
915C22—161no—
916C22—164no—
917C22—164no—
918C22#534×C10711yescharacteristic
919C22D42×C10711yescharacteristic
920C22#546×C10711yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4C2×#120×C10711yescharacteristic
929C4C2×#121×C10711yescharacteristic
930C4D42×C10711yescharacteristic
931C4#546×C10711yescharacteristic
932C2—21no—
933C2—21no—
934C2—42no—
935C2—42no—
936C2—81no—
937C2—82no—
938C2—82no—
939C2—161no—
940C2C107×#241011yescharacteristic
941C2C107×#328811yescharacteristic
942C2C107×#329211yescharacteristic
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×#576×C107C2semidirect
2. C2×#472×C107C2semidirect
3. C107×#3045C2semidirect
4. C2×#453×C107C2semidirect
5. C107×#3008C2semidirect
6. C107×#2897C2semidirect
7. C107×#2051C2semidirect
8. C107×#2045C2semidirect
9. C107×#2011C2semidirect
10. C107×#2002C2semidirect
11. C107×#1907C2semidirect
12. C107×#1883C2semidirect
13. C107×#1876C2semidirect
14. C107×#1866C2semidirect
15. C107×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C107C22semidirect
30. C22×D8×C107C22semidirect
32. C2×#131×C107C22semidirect
33. #535×C107C22semidirect
34. C2×#127×C107C22semidirect
35. #520×C107C22semidirect
46. C2×#108×C107C22semidirect
47. #424×C107C22semidirect
49. C2×#104×C107C22semidirect
50. C2×#104×C107C22semidirect
52. #418×C107C22semidirect
53. #418×C107C22semidirect
56. #417×C107C22semidirect
60. C2×#102×C107C22semidirect
61. C2×#102×C107C22semidirect
62. C2×#100×C107C22semidirect
63. C2×#100×C107C22semidirect
64. C2×#100×C107C22semidirect
65. #408×C107C22semidirect
66. #390×C107C22semidirect
67. #343×C107C22semidirect
68. #341×C107C22semidirect
69. #339×C107C22semidirect
70. #336×C107C22semidirect
78. H(5,𝔽2)×C107D4semidirect
105. AGL(1,ℤ/8)×C107D4semidirect
109. C2×Q16×C107D4semidirect
114. C2×SD16×C107D4semidirect
115. C2×SD16×C107D4semidirect
129. C2×D8×C107D4semidirect
168. #103×C107D4semidirect
169. #103×C107D4semidirect
180. #102×C107D4semidirect
181. #102×C107D4semidirect
460. #24456C107direct (N × H)
472. C2×#576C2×C107semidirect
473. C2×#472C2×C107semidirect
474. #3045C2×C107semidirect
475. C2×#453C2×C107semidirect
476. #3008C2×C107semidirect
477. #2897C2×C107semidirect
478. #2051C2×C107semidirect
479. #2045C2×C107semidirect
480. #2011C2×C107semidirect
481. #2002C2×C107semidirect
482. #1907C2×C107semidirect
483. #1883C2×C107semidirect
484. #1876C2×C107semidirect
485. #1866C2×C107semidirect
486. #1792C2×C107semidirect
487. C107#24456direct (N × H)
497. C2×AGL(1,ℤ/8)C22×C107semidirect
502. C22×D8C22×C107semidirect
504. C2×#131C22×C107semidirect
505. #535C22×C107semidirect
506. C2×#127C22×C107semidirect
507. #520C22×C107semidirect
518. C2×#108C22×C107semidirect
519. #424C22×C107semidirect
521. C2×#104C22×C107semidirect
522. C2×#104C22×C107semidirect
524. #418C22×C107semidirect
525. #418C22×C107semidirect
528. #417C22×C107semidirect
532. C2×#102C22×C107semidirect
533. C2×#102C22×C107semidirect
534. C2×#100C22×C107semidirect
535. C2×#100C22×C107semidirect
536. C2×#100C22×C107semidirect
537. #408C22×C107semidirect
538. #390C22×C107semidirect
539. #343C22×C107semidirect
540. #341C22×C107semidirect
541. #339C22×C107semidirect
542. #336C22×C107semidirect
550. H(5,𝔽2)D4×C107semidirect
577. AGL(1,ℤ/8)D4×C107semidirect
581. C2×Q16D4×C107semidirect
586. C2×SD16D4×C107semidirect
587. C2×SD16D4×C107semidirect
601. C2×D8D4×C107semidirect
640. #103D4×C107semidirect
641. #103D4×C107semidirect
652. #102D4×C107semidirect
653. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1072
C2×#472×C1072
C107×#30452
C2×#453×C1072
C107×#30082
C107×#28972
C107×#20512
C107×#20452
C107×#20112
C107×#20022
C107×#19072
C107×#18832
C107×#18762
C107×#18662
C107×#17922
#24456107