Finite Group Databasebeta

← C107×#25180 #41051144

Subgroups — C107×#25180 #41051144

Order 27392.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C107C211yesmaximal, characteristic, complemented
2C107×#3041C211yesmaximal, characteristic, complemented
3C2×#453×C107C211yesmaximal, characteristic, complemented
4C107×#3008C211yesmaximal, characteristic, complemented
5C107×#2946C211yesmaximal, characteristic, complemented
6C107×#2897C211yesmaximal, characteristic, complemented
7C107×#2063C211yesmaximal, characteristic, complemented
8C107×#2051C211yesmaximal, characteristic, complemented
9C107×#2037C211yesmaximal, characteristic, complemented
10C107×#2011C211yesmaximal, characteristic, complemented
11C107×#1978C211yesmaximal, characteristic, complemented
12C107×#1929C211yesmaximal, characteristic, complemented
13C107×#1887C211yesmaximal, characteristic, complemented
14C107×#1883C211yesmaximal, characteristic, complemented
15C107×#1866C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21C22×D8×C107C2211yescharacteristic, complemented
22C2×#131×C107C2211yescharacteristic
23#535×C107C2211yescharacteristic
24C2×#127×C107C2211yescharacteristic
25#520×C107C2211yescharacteristic
26#518×C107C2211yescharacteristic, complemented
27#472×C107—24no—
28#463×C107—21no—
29#463×C107—21no—
30#459×C107—21no—
31#459×C107—21no—
32#453×C107—24no—
33#449×C107—21no—
34#449×C107—21no—
35#447×C107—21no—
36#447×C107—21no—
37#442×C107—21no—
38#440×C107—21no—
39C4×SD16×C107—21no—
40C4×D8×C107—21no—
41C2×#108×C107C2211yescharacteristic, complemented
42C2×#108×C107C2211yescharacteristic, complemented
43#428×C107C2211yescharacteristic, complemented
44#424×C107C2211yescharacteristic, complemented
45C2×#104×C107C2211yescharacteristic
46C2×#104×C107C2211yescharacteristic
47#418×C107—21no—
48#418×C107C2211yescharacteristic
49#418×C107C2211yescharacteristic
50#418×C107C2211yescharacteristic, complemented
51#417×C107—21no—
52#417×C107C2211yescharacteristic
53#416×C107—21no—
54#416×C107C2211yescharacteristic
55#416×C107C2211yescharacteristic
56C2×#102×C107—21no—
57C2×#102×C107C2211yescharacteristic
58C2×#102×C107C2211yescharacteristic, complemented
59C2×#100×C107C2211yescharacteristic
60C2×#100×C107C2211yescharacteristic, complemented
61C2×#100×C107C2211yescharacteristic, complemented
62#408×C107C2211yescharacteristic
63#405×C107C2211yescharacteristic, complemented
64#390×C107C2211yescharacteristic, complemented
65#343×C107C2211yescharacteristic, complemented
66#339×C107C2211yescharacteristic, complemented
67#339×C107C2211yescharacteristic, complemented
68#336×C107C2211yescharacteristic, complemented
69H(5,𝔽2)×C107—22no—
70H(5,𝔽2)×C107—22no—
71H(5,𝔽2)×C107—22no—
72H(5,𝔽2)×C107—41no—
73C2×#41×C107—21no—
74C2×#41×C107—21no—
75C2×#41×C107C2311yescharacteristic
76C2×#41×C107C2311yescharacteristic
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—41no—
80C22×D4×C107—41no—
81C22×D4×C107C2311yescharacteristic
82C22×D4×C107C2311yescharacteristic
83C22×D4×C107C2311yescharacteristic
84AGL(1,ℤ/8)×C107—22no—
85AGL(1,ℤ/8)×C107—22no—
86AGL(1,ℤ/8)×C107—22no—
87AGL(1,ℤ/8)×C107—22no—
88AGL(1,ℤ/8)×C107—41no—
89AGL(1,ℤ/8)×C107D414yescomplemented
90C2×SD16×C107—21no—
91C2×SD16×C107—21no—
92C2×SD16×C107—21no—
93C2×D8×C107—21no—
94C2×D8×C107—21no—
95C2×D8×C107—21no—
96C2×D8×C107—22no—
97C2×D8×C107—22no—
98C2×D8×C107—21no—
99C2×D8×C107—21no—
100C2×D8×C107—21no—
101C2×D8×C107—21no—
102C2×D8×C107—41no—
103C2×D8×C107—41no—
104#131×C107—22no—
105#131×C107—41no—
106C2×M16×C107—21no—
107C2×M16×C107C2311yescharacteristic
108C2×M16×C107C2311yescharacteristic
109C2×M16×C107C2311yescharacteristic
110C2×M16×C107C2311yescharacteristic
111C22×C8×C107—21no—
112C22×C8×C107C2311yescharacteristic
113C22×C8×C107C2311yescharacteristic
114#127×C107—22no—
115#127×C107—21no—
116#127×C107—22no—
117#124×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#120×C107—41no—
121C4×Q8×C107—21no—
122C4×D4×C107—21no—
123C4×D4×C107—21no—
124C4×D4×C107—21no—
125C4×D4×C107—21no—
126C4×D4×C107—21no—
127C4×D4×C107—41no—
128#117×C107—21no—
129#117×C107C2311yescharacteristic
130#117×C107C2311yescharacteristic
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C22⋊C4×C107—41no—
134C2×C22⋊C4×C107—41no—
135C2×C42×C107C2311yescharacteristic
136#108×C107—22no—
137#108×C107—41no—
138#107×C107—21no—
139#106×C107—21no—
140C4⋊C8×C107—21no—
141C4⋊C8×C107—21no—
142#104×C107—22no—
143#104×C107—22no—
144#103×C107—21no—
145#103×C107D411yescharacteristic, complemented
146#103×C107D411yescharacteristic, complemented
147#103×C107D411yescharacteristic, complemented
148#103×C107D411yescharacteristic, complemented
149#102×C107—21no—
150#102×C107—21no—
151#102×C107—21no—
152#102×C107—21no—
153#102×C107—21no—
154#102×C107—21no—
155#102×C107—21no—
156#102×C107—21no—
157#102×C107—21no—
158#102×C107—21no—
159#102×C107—21no—
160#102×C107D411yescharacteristic, complemented
161#102×C107D411yescharacteristic, complemented
162#102×C107D411yescharacteristic, complemented
163#102×C107D411yescharacteristic, complemented
164#100×C107—22no—
165#100×C107—22no—
166#100×C107—22no—
167C22⋊C8×C107—21no—
168C22⋊C8×C107—21no—
169#97×C107—21no—
170C4×C8×C107—21no—
171C24×C107—21no—
172C24×C107—21no—
173C24×C107—21no—
174C24×C107—41no—
175#41×C107—21no—
176#41×C107—21no—
177#41×C107—24no—
178#41×C107—21no—
179#41×C107—21no—
180#41×C107—21no—
181#41×C107—21no—
182#41×C107—42no—
183#41×C107—42no—
184#41×C107—42no—
185#41×C107C2×D412yes—
186#41×C107#4112yes—
187C2×Q8×C107C2×D411yescharacteristic
188C2×Q8×C107C2×D411yescharacteristic
189C2×D4×C107—21no—
190C2×D4×C107—24no—
191C2×D4×C107—21no—
192C2×D4×C107—21no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—42no—
209C2×D4×C107—41no—
210C2×D4×C107—41no—
211C2×D4×C107—41no—
212C2×D4×C107—41no—
213C2×D4×C107—42no—
214C2×D4×C107—44no—
215C2×D4×C107—44no—
216C2×D4×C107—42no—
217C2×D4×C107—44no—
218C2×D4×C107—82no—
219C2×D4×C107—82no—
220C2×D4×C107C2×D412yes—
221C2×D4×C107C2×D411yescharacteristic
222C2×D4×C107C2×D411yescharacteristic
223C2×D4×C107#4112yes—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—41no—
229C22×C4×C107—41no—
230C22×C4×C107—41no—
231C22×C4×C107—41no—
232C22×C4×C107C2411yescharacteristic
233SD16×C107—24no—
234SD16×C107—42no—
235SD16×C107—42no—
236D8×C107—24no—
237D8×C107—42no—
238D8×C107—42no—
239D8×C107—42no—
240D8×C107—42no—
241D8×C107—42no—
242D8×C107—42no—
243M16×C107—21no—
244M16×C107—21no—
245M16×C107—21no—
246M16×C107—21no—
247M16×C107—21no—
248M16×C107—21no—
249M16×C107—21no—
250M16×C107—42no—
251M16×C107C2×D412yes—
252C2×C8×C107—21no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—42no—
261C2×C8×C107C2×D411yescharacteristic
262C2×C8×C107C2×D411yescharacteristic
263C2×C8×C107C2×D411yescharacteristic
264C2×C8×C107C2×D411yescharacteristic
265C4⋊C4×C107—21no—
266C4⋊C4×C107—21no—
267C4⋊C4×C107—41no—
268C4⋊C4×C107C2×D411yescharacteristic
269C4⋊C4×C107C2×D411yescharacteristic
270C4⋊C4×C107C2×D411yescharacteristic
271C4⋊C4×C107C2×D411yescharacteristic
272C22⋊C4×C107—21no—
273C22⋊C4×C107—21no—
274C22⋊C4×C107—41no—
275C22⋊C4×C107—41no—
276C22⋊C4×C107—41no—
277C22⋊C4×C107—41no—
278C22⋊C4×C107—41no—
279C22⋊C4×C107—82no—
280C42×C107—21no—
281C42×C107—21no—
282C42×C107—21no—
283C42×C107—21no—
284C42×C107—41no—
285C23×C107—21no—
286C23×C107—21no—
287C23×C107—22no—
288C23×C107—22no—
289C23×C107—44no—
290C23×C107—41no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—81no—
298C23×C107—81no—
299C23×C107—81no—
300C23×C107—81no—
301C23×C107—81no—
302C23×C107—81no—
303C23×C107—161no—
304C23×C107—161no—
305C23×C107H(5,𝔽2)11yescharacteristic
306Q8×C107—21no—
307Q8×C107—21no—
308Q8×C107—21no—
309Q8×C107#12112yes—
310D4×C107—22no—
311D4×C107—22no—
312D4×C107—22no—
313D4×C107—21no—
314D4×C107—22no—
315D4×C107—22no—
316D4×C107—21no—
317D4×C107—21no—
318D4×C107—22no—
319D4×C107—44no—
320D4×C107—44no—
321D4×C107—41no—
322D4×C107—41no—
323D4×C107—41no—
324D4×C107—41no—
325D4×C107—41no—
326D4×C107—41no—
327D4×C107—41no—
328D4×C107—41no—
329D4×C107—41no—
330D4×C107—41no—
331D4×C107—88no—
332D4×C107—161no—
333D4×C107—161no—
334D4×C107#12112yes—
335C2×C4×C107—21no—
336C2×C4×C107—22no—
337C2×C4×C107—22no—
338C2×C4×C107—22no—
339C2×C4×C107—21no—
340C2×C4×C107—21no—
341C2×C4×C107—21no—
342C2×C4×C107—21no—
343C2×C4×C107—21no—
344C2×C4×C107—44no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—81no—
351C2×C4×C107—161no—
352C2×C4×C107—161no—
353C2×C4×C107—161no—
354C2×C4×C107C22×D411yescharacteristic
355C2×C4×C107C22×D411yescharacteristic
356C2×C4×C107C22×D411yescharacteristic
357C2×C4×C107C2×#4111yescharacteristic
358C2×C4×C107C2×#4111yescharacteristic
359C2×C4×C107H(5,𝔽2)11yescharacteristic
360C8×C107—22no—
361C8×C107—21no—
362C8×C107—21no—
363C8×C107—21no—
364C8×C107—21no—
365C8×C107—41no—
366C8×C107—41no—
367C8×C107—41no—
368C22×C107—21no—
369C22×C107—21no—
370C22×C107—22no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—41no—
374C22×C107—42no—
375C22×C107—42no—
376C22×C107—41no—
377C22×C107—41no—
378C22×C107—82no—
379C22×C107—82no—
380C22×C107—82no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—81no—
387C22×C107—81no—
388C22×C107—161no—
389C22×C107—161no—
390C22×C107—161no—
391C22×C107—164no—
392C22×C107#53811yescharacteristic
393C22×C107D4211yescharacteristic
394C22×C107#54611yescharacteristic
395C4×C107—22no—
396C4×C107—42no—
397C4×C107—41no—
398C4×C107—41no—
399C4×C107—41no—
400C4×C107—41no—
401C4×C107—41no—
402C4×C107—81no—
403C4×C107C2×#12111yescharacteristic
404C4×C107#52511yescharacteristic
405C4×C107D4211yescharacteristic
406C4×C107#54611yescharacteristic
407#25180C10711yesmaximal, characteristic, direct product factor, Sylow
408C2×C107—21no—
409C2×C107—21no—
410C2×C107—42no—
411C2×C107—81no—
412C2×C107—82no—
413C2×C107—82no—
414C2×C107—161no—
415C2×C107#242411yescharacteristic
416C2×C107#328811yescharacteristic
417C2×C107#329211yescharacteristic
418C2×#472C2×C10711yescharacteristic, complemented
419#3041C2×C10711yescharacteristic, complemented
420C2×#453C2×C10711yescharacteristic, complemented
421#3008C2×C10711yescharacteristic, complemented
422#2946C2×C10711yescharacteristic, complemented
423#2897C2×C10711yescharacteristic, complemented
424#2063C2×C10711yescharacteristic, complemented
425#2051C2×C10711yescharacteristic, complemented
426#2037C2×C10711yescharacteristic, complemented
427#2011C2×C10711yescharacteristic, complemented
428#1978C2×C10711yescharacteristic, complemented
429#1929C2×C10711yescharacteristic, complemented
430#1887C2×C10711yescharacteristic, complemented
431#1883C2×C10711yescharacteristic, complemented
432#1866C2×C10711yescharacteristic, complemented
433C107#2518011yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C10711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
436C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
437C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
438C22×D8C22×C10711yescharacteristic
439C22×D8C22×C10711yescharacteristic, complemented
440C2×#131C22×C10711yescharacteristic
441#535C22×C10711yescharacteristic
442C2×#127C22×C10711yescharacteristic
443#520C22×C10711yescharacteristic
444#518C22×C10711yescharacteristic, complemented
445#472—24no—
446#463—21no—
447#463—21no—
448#459—21no—
449#459—21no—
450#453—24no—
451#449—21no—
452#449—21no—
453#447—21no—
454#447—21no—
455#442—21no—
456#440—21no—
457C4×SD16—21no—
458C4×D8—21no—
459C2×#108C22×C10711yescharacteristic, complemented
460C2×#108C22×C10711yescharacteristic, complemented
461#428C22×C10711yescharacteristic, complemented
462#424C22×C10711yescharacteristic, complemented
463C2×#104C22×C10711yescharacteristic
464C2×#104C22×C10711yescharacteristic
465#418—21no—
466#418C22×C10711yescharacteristic
467#418C22×C10711yescharacteristic
468#418C22×C10711yescharacteristic, complemented
469#417—21no—
470#417C22×C10711yescharacteristic
471#416—21no—
472#416C22×C10711yescharacteristic
473#416C22×C10711yescharacteristic
474C2×#102—21no—
475C2×#102C22×C10711yescharacteristic
476C2×#102C22×C10711yescharacteristic, complemented
477C2×#100C22×C10711yescharacteristic
478C2×#100C22×C10711yescharacteristic, complemented
479C2×#100C22×C10711yescharacteristic, complemented
480#408C22×C10711yescharacteristic
481#405C22×C10711yescharacteristic, complemented
482#390C22×C10711yescharacteristic, complemented
483#343C22×C10711yescharacteristic, complemented
484#339C22×C10711yescharacteristic, complemented
485#339C22×C10711yescharacteristic, complemented
486#336C22×C10711yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C10711yescharacteristic
494C2×#41C23×C10711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C10711yescharacteristic
500C22×D4C23×C10711yescharacteristic
501C22×D4C23×C10711yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C10714yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C10711yescharacteristic
526C2×M16C23×C10711yescharacteristic
527C2×M16C23×C10711yescharacteristic
528C2×M16C23×C10711yescharacteristic
529C22×C8—21no—
530C22×C8C23×C10711yescharacteristic
531C22×C8C23×C10711yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C10711yescharacteristic
548#117C23×C10711yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C10711yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C10711yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C10711yescharacteristic, complemented
564#103D4×C10711yescharacteristic, complemented
565#103D4×C10711yescharacteristic, complemented
566#103D4×C10711yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102D4×C10711yescharacteristic, complemented
579#102D4×C10711yescharacteristic, complemented
580#102D4×C10711yescharacteristic, complemented
581#102D4×C10711yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C10712yes—
604#41#41×C10712yes—
605C2×Q8C2×D4×C10711yescharacteristic
606C2×Q8C2×D4×C10711yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C10712yes—
639C2×D4C2×D4×C10711yescharacteristic
640C2×D4C2×D4×C10711yescharacteristic
641C2×D4#41×C10712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C10711yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C10712yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C10711yescharacteristic
680C2×C8C2×D4×C10711yescharacteristic
681C2×C8C2×D4×C10711yescharacteristic
682C2×C8C2×D4×C10711yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C10711yescharacteristic
687C4⋊C4C2×D4×C10711yescharacteristic
688C4⋊C4C2×D4×C10711yescharacteristic
689C4⋊C4C2×D4×C10711yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C10711yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C10712yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C10712yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
771C2×C4—161no—
772C2×C4C22×D4×C10711yescharacteristic
773C2×C4C22×D4×C10711yescharacteristic
774C2×C4C22×D4×C10711yescharacteristic
775C2×C4C2×#41×C10711yescharacteristic
776C2×C4C2×#41×C10711yescharacteristic
777C2×C4H(5,𝔽2)×C10711yescharacteristic
778C8—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—42no—
794C22—41no—
795C22—41no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C10711yescharacteristic
811C22D42×C10711yescharacteristic
812C22#546×C10711yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C10711yescharacteristic
822C4#525×C10711yescharacteristic
823C4D42×C10711yescharacteristic
824C4#546×C10711yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C107×#242411yescharacteristic
833C2C107×#328811yescharacteristic
834C2C107×#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×#472×C107C2semidirect
2. C107×#3041C2semidirect
3. C2×#453×C107C2semidirect
4. C107×#3008C2semidirect
5. C107×#2946C2semidirect
6. C107×#2897C2semidirect
7. C107×#2063C2semidirect
8. C107×#2051C2semidirect
9. C107×#2037C2semidirect
10. C107×#2011C2semidirect
11. C107×#1978C2semidirect
12. C107×#1929C2semidirect
13. C107×#1887C2semidirect
14. C107×#1883C2semidirect
15. C107×#1866C2semidirect
21. C22×D8×C107C22semidirect
26. #518×C107C22semidirect
41. C2×#108×C107C22semidirect
42. C2×#108×C107C22semidirect
43. #428×C107C22semidirect
44. #424×C107C22semidirect
50. #418×C107C22semidirect
58. C2×#102×C107C22semidirect
60. C2×#100×C107C22semidirect
61. C2×#100×C107C22semidirect
63. #405×C107C22semidirect
64. #390×C107C22semidirect
65. #343×C107C22semidirect
66. #339×C107C22semidirect
67. #339×C107C22semidirect
68. #336×C107C22semidirect
89. AGL(1,ℤ/8)×C107D4semidirect
145. #103×C107D4semidirect
146. #103×C107D4semidirect
147. #103×C107D4semidirect
148. #103×C107D4semidirect
160. #102×C107D4semidirect
161. #102×C107D4semidirect
162. #102×C107D4semidirect
163. #102×C107D4semidirect
407. #25180C107direct (N × H)
418. C2×#472C2×C107semidirect
419. #3041C2×C107semidirect
420. C2×#453C2×C107semidirect
421. #3008C2×C107semidirect
422. #2946C2×C107semidirect
423. #2897C2×C107semidirect
424. #2063C2×C107semidirect
425. #2051C2×C107semidirect
426. #2037C2×C107semidirect
427. #2011C2×C107semidirect
428. #1978C2×C107semidirect
429. #1929C2×C107semidirect
430. #1887C2×C107semidirect
431. #1883C2×C107semidirect
432. #1866C2×C107semidirect
433. C107#25180direct (N × H)
439. C22×D8C22×C107semidirect
444. #518C22×C107semidirect
459. C2×#108C22×C107semidirect
460. C2×#108C22×C107semidirect
461. #428C22×C107semidirect
462. #424C22×C107semidirect
468. #418C22×C107semidirect
476. C2×#102C22×C107semidirect
478. C2×#100C22×C107semidirect
479. C2×#100C22×C107semidirect
481. #405C22×C107semidirect
482. #390C22×C107semidirect
483. #343C22×C107semidirect
484. #339C22×C107semidirect
485. #339C22×C107semidirect
486. #336C22×C107semidirect
507. AGL(1,ℤ/8)D4×C107semidirect
563. #103D4×C107semidirect
564. #103D4×C107semidirect
565. #103D4×C107semidirect
566. #103D4×C107semidirect
578. #102D4×C107semidirect
579. #102D4×C107semidirect
580. #102D4×C107semidirect
581. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1072
C107×#30412
C2×#453×C1072
C107×#30082
C107×#29462
C107×#28972
C107×#20632
C107×#20512
C107×#20372
C107×#20112
C107×#19782
C107×#19292
C107×#18872
C107×#18832
C107×#18662
#25180107