Finite Group Databasebeta

← C2×C107×#2008 #41049374

Subgroups — C2×C107×#2008 #41049374

Order 27392.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C107C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C107C211yesmaximal, characteristic, complemented
3C2×#535×C107C211yesmaximal, characteristic, complemented
4C2×#421×C107C211yesmaximal, characteristic, complemented
5C2×#418×C107C211yesmaximal, characteristic, complemented
6C2×#410×C107C211yesmaximal, characteristic, complemented
7C107×#2008C218yesmaximal, direct product factor
8C2×#344×C107C211yesmaximal, characteristic, complemented
9C22×#41×C107C2211yescharacteristic
10C22×#41×C107C2211yescharacteristic
11C23×D4×C107C2211yescharacteristic
12#575×C107—22no—
13#575×C107—22no—
14#575×C107—22no—
15#575×C107C2214yescomplemented
16C2×#137×C107—21no—
17C2×#137×C107—21no—
18C2×AGL(1,ℤ/8)×C107—22no—
19C2×AGL(1,ℤ/8)×C107—22no—
20C2×AGL(1,ℤ/8)×C107—22no—
21C2×AGL(1,ℤ/8)×C107—21no—
22C2×AGL(1,ℤ/8)×C107—21no—
23C2×AGL(1,ℤ/8)×C107—22no—
24C2×AGL(1,ℤ/8)×C107—22no—
25C2×AGL(1,ℤ/8)×C107C2214yescomplemented
26C2×#135×C107—22no—
27C22×SD16×C107—21no—
28C22×D8×C107—21no—
29C22×M16×C107C2211yescharacteristic
30C22×M16×C107C2211yescharacteristic
31#535×C107—22no—
32#535×C107—22no—
33#535×C107—22no—
34#535×C107C2214yescomplemented
35C2×#127×C107—21no—
36C2×#124×C107—21no—
37C2×#121×C107—22no—
38C2×#120×C107—22no—
39C2×#117×C107C2211yescharacteristic
40C2×#117×C107C2211yescharacteristic
41#421×C107—22no—
42#421×C107C2214yescomplemented
43C2×#104×C107—22no—
44#418×C107—22no—
45#418×C107C2214yescomplemented
46C2×#102×C107—22no—
47#410×C107—22no—
48#410×C107C2214yescomplemented
49C2×#99×C107—22no—
50#344×C107C2214yescomplemented
51C25×C107—21no—
52C2×#41×C107—21no—
53C2×#41×C107—21no—
54C2×#41×C107—21no—
55C2×#41×C107—21no—
56C2×#41×C107—21no—
57C2×#41×C107—21no—
58C2×#41×C107—21no—
59C2×#41×C107—21no—
60C2×#41×C107—21no—
61C2×#41×C107—21no—
62C2×#41×C107—21no—
63C2×#41×C107—21no—
64C2×#41×C107—21no—
65C2×#41×C107—21no—
66C2×#41×C107—21no—
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69C2×#41×C107—21no—
70C2×#41×C107—21no—
71C2×#41×C107—21no—
72C2×#41×C107D412yes—
73C2×#41×C107D412yescomplemented
74C2×#41×C107C2312yes—
75C2×#41×C107C2312yes—
76C22×Q8×C107D411yescharacteristic
77C22×Q8×C107D411yescharacteristic, complemented
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—24no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107—21no—
85C22×D4×C107—21no—
86C22×D4×C107—21no—
87C22×D4×C107—21no—
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—21no—
91C22×D4×C107—21no—
92C22×D4×C107D412yes—
93C22×D4×C107D411yescharacteristic
94C22×D4×C107D412yes—
95C22×D4×C107D411yescharacteristic, complemented
96C22×D4×C107C2312yes—
97C23×C4×C107—21no—
98C23×C4×C107—21no—
99C23×C4×C107C2311yescharacteristic
100#137×C107—24no—
101#137×C107—24no—
102#137×C107—24no—
103#137×C107—24no—
104AGL(1,ℤ/8)×C107—28no—
105AGL(1,ℤ/8)×C107—28no—
106AGL(1,ℤ/8)×C107—24no—
107AGL(1,ℤ/8)×C107—24no—
108AGL(1,ℤ/8)×C107—28no—
109AGL(1,ℤ/8)×C107—24no—
110AGL(1,ℤ/8)×C107—24no—
111AGL(1,ℤ/8)×C107—28no—
112#135×C107—28no—
113#135×C107—28no—
114C2×Q16×C107—22no—
115C2×SD16×C107—24no—
116C2×SD16×C107—24no—
117C2×SD16×C107—22no—
118C2×SD16×C107—22no—
119C2×SD16×C107—24no—
120C2×D8×C107—24no—
121C2×D8×C107—24no—
122C2×D8×C107—22no—
123C2×D8×C107—24no—
124C2×M16×C107—21no—
125C2×M16×C107—21no—
126C2×M16×C107—21no—
127C2×M16×C107—21no—
128C2×M16×C107—21no—
129C2×M16×C107—21no—
130C2×M16×C107—21no—
131C2×M16×C107D412yescomplemented
132C2×M16×C107D412yescomplemented
133C2×M16×C107D412yescomplemented
134C2×M16×C107C2312yes—
135C2×M16×C107C2312yes—
136C22×C8×C107—21no—
137C22×C8×C107D412yescomplemented
138#127×C107—24no—
139#127×C107—24no—
140#124×C107—24no—
141#124×C107—24no—
142#121×C107—28no—
143#121×C107—28no—
144#120×C107—28no—
145#120×C107—28no—
146#117×C107—21no—
147#117×C107—21no—
148#117×C107—21no—
149#117×C107—21no—
150#117×C107—21no—
151#117×C107D412yes—
152#117×C107C2312yes—
153#117×C107C2312yes—
154C2×C4⋊C4×C107—21no—
155C2×C4⋊C4×C107—21no—
156C2×C22⋊C4×C107—24no—
157C2×C22⋊C4×C107—21no—
158C2×C22⋊C4×C107D412yes—
159C2×C42×C107—21no—
160C2×C42×C107—21no—
161#104×C107—28no—
162#102×C107—28no—
163#99×C107—28no—
164C24×C107—22no—
165C24×C107—21no—
166C24×C107—22no—
167C24×C107—21no—
168C24×C107—22no—
169C24×C107—41no—
170C24×C107—41no—
171C24×C107—41no—
172C24×C107—41no—
173C24×C107—84no—
174C24×C107C2×D411yescharacteristic
175#41×C107—22no—
176#41×C107—22no—
177#41×C107—22no—
178#41×C107—22no—
179#41×C107—22no—
180#41×C107—22no—
181#41×C107—22no—
182#41×C107—22no—
183#41×C107—22no—
184#41×C107—22no—
185#41×C107—22no—
186#41×C107—22no—
187#41×C107—22no—
188#41×C107—22no—
189#41×C107—22no—
190#41×C107—22no—
191#41×C107—41no—
192#41×C107—41no—
193#41×C107—41no—
194#41×C107—41no—
195#41×C107—41no—
196#41×C107—41no—
197#41×C107—41no—
198#41×C107—41no—
199#41×C107—41no—
200#41×C107—41no—
201#41×C107—41no—
202#41×C107—41no—
203#41×C107—41no—
204#41×C107—41no—
205#41×C107—41no—
206#41×C107—41no—
207C2×Q8×C107—21no—
208C2×Q8×C107—21no—
209C2×Q8×C107—21no—
210C2×Q8×C107—21no—
211C2×Q8×C107—21no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107—21no—
215C2×Q8×C107—21no—
216C2×Q8×C107—21no—
217C2×Q8×C107C2×D412yes—
218C2×Q8×C107C2×D412yescomplemented
219C2×D4×C107—22no—
220C2×D4×C107—22no—
221C2×D4×C107—22no—
222C2×D4×C107—22no—
223C2×D4×C107—216no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—22no—
227C2×D4×C107—22no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—22no—
231C2×D4×C107—22no—
232C2×D4×C107—21no—
233C2×D4×C107—21no—
234C2×D4×C107—22no—
235C2×D4×C107—22no—
236C2×D4×C107—21no—
237C2×D4×C107—22no—
238C2×D4×C107—22no—
239C2×D4×C107—22no—
240C2×D4×C107—22no—
241C2×D4×C107—21no—
242C2×D4×C107—21no—
243C2×D4×C107—21no—
244C2×D4×C107—22no—
245C2×D4×C107—22no—
246C2×D4×C107—22no—
247C2×D4×C107—22no—
248C2×D4×C107—22no—
249C2×D4×C107—41no—
250C2×D4×C107—41no—
251C2×D4×C107—41no—
252C2×D4×C107—41no—
253C2×D4×C107—41no—
254C2×D4×C107—41no—
255C2×D4×C107—41no—
256C2×D4×C107—41no—
257C2×D4×C107—41no—
258C2×D4×C107—41no—
259C2×D4×C107—41no—
260C2×D4×C107—41no—
261C2×D4×C107—41no—
262C2×D4×C107—41no—
263C2×D4×C107—41no—
264C2×D4×C107—41no—
265C2×D4×C107—41no—
266C2×D4×C107—41no—
267C2×D4×C107—41no—
268C2×D4×C107—41no—
269C2×D4×C107—88no—
270C2×D4×C107C2×D414yes—
271C2×D4×C107C2×D412yes—
272C2×D4×C107C2×D412yescomplemented
273C22×C4×C107—22no—
274C22×C4×C107—21no—
275C22×C4×C107—21no—
276C22×C4×C107—22no—
277C22×C4×C107—22no—
278C22×C4×C107—22no—
279C22×C4×C107—22no—
280C22×C4×C107—41no—
281C22×C4×C107—41no—
282C22×C4×C107—41no—
283C22×C4×C107—41no—
284C22×C4×C107—41no—
285C22×C4×C107—41no—
286C22×C4×C107—41no—
287C22×C4×C107—41no—
288C22×C4×C107—41no—
289C22×C4×C107C2×D411yescharacteristic
290C22×C4×C107C2×D411yescharacteristic
291C22×C4×C107C2×D411yescharacteristic
292C22×C4×C107C2×D411yescharacteristic
293C22×C4×C107C2×D411yescharacteristic
294C22×C4×C107C2×D411yescharacteristic
295C22×C4×C107C2×D411yescharacteristic
296C22×C4×C107C2×D411yescharacteristic
297C22×C4×C107C2×D411yescharacteristic
298C22×C4×C107C2×D411yescharacteristic
299C22×C4×C107C2×D411yescharacteristic
300C22×C4×C107#4111yescharacteristic
301C22×C4×C107#4111yescharacteristic
302C22×C4×C107C2411yescharacteristic
303Q16×C107—28no—
304SD16×C107—216no—
305SD16×C107—28no—
306SD16×C107—28no—
307D8×C107—216no—
308D8×C107—28no—
309M16×C107—22no—
310M16×C107—22no—
311M16×C107—22no—
312M16×C107—22no—
313M16×C107—22no—
314M16×C107—22no—
315M16×C107—22no—
316M16×C107C2×D414yescomplemented
317C2×C8×C107—22no—
318C2×C8×C107—22no—
319C2×C8×C107—22no—
320C2×C8×C107—22no—
321C2×C8×C107—22no—
322C2×C8×C107C2×D414yescomplemented
323C4⋊C4×C107—22no—
324C4⋊C4×C107—22no—
325C4⋊C4×C107—22no—
326C4⋊C4×C107—41no—
327C22⋊C4×C107—216no—
328C22⋊C4×C107—22no—
329C22⋊C4×C107—22no—
330C22⋊C4×C107—41no—
331C22⋊C4×C107C2×D414yes—
332C42×C107—22no—
333C42×C107—22no—
334C42×C107—22no—
335C42×C107—41no—
336C23×C107—24no—
337C23×C107—22no—
338C23×C107—22no—
339C23×C107—42no—
340C23×C107—44no—
341C23×C107—48no—
342C23×C107—42no—
343C23×C107—42no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—42no—
347C23×C107—42no—
348C23×C107—42no—
349C23×C107—41no—
350C23×C107—41no—
351C23×C107—42no—
352C23×C107—82no—
353C23×C107—84no—
354C23×C107—84no—
355C23×C107—84no—
356C23×C107—84no—
357C23×C107—84no—
358C23×C107—84no—
359C23×C107#12011yescharacteristic
360C23×C107#12011yescharacteristic
361C23×C107#12111yescharacteristic
362C23×C107#12111yescharacteristic
363C23×C107#12711yescharacteristic
364C23×C107#12711yescharacteristic
365C23×C107C22×D411yescharacteristic
366Q8×C107—22no—
367Q8×C107—22no—
368Q8×C107—22no—
369Q8×C107—22no—
370Q8×C107—41no—
371Q8×C107—41no—
372Q8×C107—41no—
373Q8×C107—41no—
374D4×C107—22no—
375D4×C107—24no—
376D4×C107—22no—
377D4×C107—22no—
378D4×C107—24no—
379D4×C107—22no—
380D4×C107—42no—
381D4×C107—42no—
382D4×C107—42no—
383D4×C107—42no—
384D4×C107—42no—
385D4×C107—42no—
386D4×C107—42no—
387D4×C107—42no—
388D4×C107—42no—
389D4×C107—42no—
390D4×C107—42no—
391D4×C107—42no—
392D4×C107—42no—
393D4×C107—42no—
394D4×C107—41no—
395D4×C107—41no—
396D4×C107—41no—
397D4×C107—41no—
398D4×C107—816no—
399C2×C4×C107—24no—
400C2×C4×C107—22no—
401C2×C4×C107—22no—
402C2×C4×C107—44no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—42no—
408C2×C4×C107—42no—
409C2×C4×C107—42no—
410C2×C4×C107—42no—
411C2×C4×C107—42no—
412C2×C4×C107—42no—
413C2×C4×C107—42no—
414C2×C4×C107—42no—
415C2×C4×C107—42no—
416C2×C4×C107—82no—
417C2×C4×C107#12011yescharacteristic
418C2×C4×C107#12011yescharacteristic
419C2×C4×C107#12011yescharacteristic
420C2×C4×C107#12011yescharacteristic
421C2×C4×C107#12011yescharacteristic
422C2×C4×C107#12011yescharacteristic
423C2×C4×C107#12011yescharacteristic
424C2×C4×C107#12011yescharacteristic
425C2×C4×C107#12011yescharacteristic
426C2×C4×C107#12011yescharacteristic
427C2×C4×C107#12111yescharacteristic
428C2×C4×C107#12111yescharacteristic
429C2×C4×C107#12111yescharacteristic
430C2×C4×C107#12111yescharacteristic
431C2×C4×C107#12111yescharacteristic
432C2×C4×C107#12111yescharacteristic
433C2×C4×C107#12111yescharacteristic
434C2×C4×C107#12111yescharacteristic
435C2×C4×C107#12111yescharacteristic
436C2×C4×C107#12111yescharacteristic
437C2×C4×C107#12711yescharacteristic
438C2×C4×C107#12711yescharacteristic
439C2×C4×C107C22×D411yescharacteristic
440C2×C4×C107C22×D411yescharacteristic
441C2×C4×C107C22×D411yescharacteristic
442C2×C4×C107C22×D411yescharacteristic
443C2×C4×C107C22×D411yescharacteristic
444C2×C4×C107C2×#4111yescharacteristic
445C8×C107—24no—
446C8×C107—24no—
447C22×C107—22no—
448C22×C107—22no—
449C22×C107—22no—
450C22×C107—41no—
451C22×C107—41no—
452C22×C107—41no—
453C22×C107—41no—
454C22×C107—44no—
455C22×C107—48no—
456C22×C107—42no—
457C22×C107—42no—
458C22×C107—44no—
459C22×C107—82no—
460C22×C107—82no—
461C22×C107—84no—
462C22×C107—82no—
463C22×C107—84no—
464C22×C107—84no—
465C22×C107—84no—
466C22×C107—84no—
467C22×C107—82no—
468C22×C107—84no—
469C22×C107—82no—
470C22×C107#39211yescharacteristic
471C22×C107#39211yescharacteristic
472C22×C107#39211yescharacteristic
473C22×C107#39211yescharacteristic
474C22×C107C2×#12011yescharacteristic
475C22×C107C2×#12111yescharacteristic
476C22×C107C2×#12711yescharacteristic
477C4×C107—44no—
478C4×C107—42no—
479C4×C107—42no—
480C4×C107—82no—
481C4×C107#39211yescharacteristic
482C4×C107#39211yescharacteristic
483C4×C107#39211yescharacteristic
484C4×C107#39211yescharacteristic
485C4×C107C2×#12011yescharacteristic
486C4×C107C2×#12011yescharacteristic
487C4×C107C2×#12111yescharacteristic
488C4×C107C2×#12111yescharacteristic
489C2×#2008C10711yesmaximal, characteristic, direct product factor, Sylow
490C2×C107—21no—
491C2×C107—21no—
492C2×C107—21no—
493C2×C107—21no—
494C2×C107—21no—
495C2×C107—21no—
496C2×C107—82no—
497C2×C107—84no—
498C2×C107—82no—
499C2×C107#200812yesdirect product factor
500C2×C107C2×#39211yescharacteristic
501C2×#575C2×C10711yescharacteristic, complemented
502C22×AGL(1,ℤ/8)C2×C10711yescharacteristic, complemented
503C2×#535C2×C10711yescharacteristic, complemented
504C2×#421C2×C10711yescharacteristic, complemented
505C2×#418C2×C10711yescharacteristic, complemented
506C2×#410C2×C10711yescharacteristic, complemented
507#2008C2×C10718yesdirect product factor
508C2×#344C2×C10711yescharacteristic, complemented
509C107C2×#200811yescharacteristic, direct product factor, Sylow
510C22×#41C22×C10711yescharacteristic
511C22×#41C22×C10711yescharacteristic
512C23×D4C22×C10711yescharacteristic
513#575—22no—
514#575—22no—
515#575—22no—
516#575C22×C10714yescomplemented
517C2×#137—21no—
518C2×#137—21no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—22no—
522C2×AGL(1,ℤ/8)—21no—
523C2×AGL(1,ℤ/8)—21no—
524C2×AGL(1,ℤ/8)—22no—
525C2×AGL(1,ℤ/8)—22no—
526C2×AGL(1,ℤ/8)C22×C10714yescomplemented
527C2×#135—22no—
528C22×SD16—21no—
529C22×D8—21no—
530C22×M16C22×C10711yescharacteristic
531C22×M16C22×C10711yescharacteristic
532#535—22no—
533#535—22no—
534#535—22no—
535#535C22×C10714yescomplemented
536C2×#127—21no—
537C2×#124—21no—
538C2×#121—22no—
539C2×#120—22no—
540C2×#117C22×C10711yescharacteristic
541C2×#117C22×C10711yescharacteristic
542#421—22no—
543#421C22×C10714yescomplemented
544C2×#104—22no—
545#418—22no—
546#418C22×C10714yescomplemented
547C2×#102—22no—
548#410—22no—
549#410C22×C10714yescomplemented
550C2×#99—22no—
551#344C22×C10714yescomplemented
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41D4×C10712yes—
574C2×#41D4×C10712yescomplemented
575C2×#41C23×C10712yes—
576C2×#41C23×C10712yes—
577C22×Q8D4×C10711yescharacteristic
578C22×Q8D4×C10711yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—24no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4D4×C10712yes—
594C22×D4D4×C10711yescharacteristic
595C22×D4D4×C10712yes—
596C22×D4D4×C10711yescharacteristic, complemented
597C22×D4C23×C10712yes—
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C23×C10711yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—28no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—24no—
612AGL(1,ℤ/8)—28no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—24no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—22no—
624C2×D8—24no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16D4×C10712yescomplemented
633C2×M16D4×C10712yescomplemented
634C2×M16D4×C10712yescomplemented
635C2×M16C23×C10712yes—
636C2×M16C23×C10712yes—
637C22×C8—21no—
638C22×C8D4×C10712yescomplemented
639#127—24no—
640#127—24no—
641#124—24no—
642#124—24no—
643#121—28no—
644#121—28no—
645#120—28no—
646#120—28no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117D4×C10712yes—
653#117C23×C10712yes—
654#117C23×C10712yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4D4×C10712yes—
660C2×C42—21no—
661C2×C42—21no—
662#104—28no—
663#102—28no—
664#99—28no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C10711yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C10712yes—
719C2×Q8C2×D4×C10712yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C10714yes—
772C2×D4C2×D4×C10712yes—
773C2×D4C2×D4×C10712yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C10711yescharacteristic
791C22×C4C2×D4×C10711yescharacteristic
792C22×C4C2×D4×C10711yescharacteristic
793C22×C4C2×D4×C10711yescharacteristic
794C22×C4C2×D4×C10711yescharacteristic
795C22×C4C2×D4×C10711yescharacteristic
796C22×C4C2×D4×C10711yescharacteristic
797C22×C4C2×D4×C10711yescharacteristic
798C22×C4C2×D4×C10711yescharacteristic
799C22×C4C2×D4×C10711yescharacteristic
800C22×C4C2×D4×C10711yescharacteristic
801C22×C4#41×C10711yescharacteristic
802C22×C4#41×C10711yescharacteristic
803C22×C4C24×C10711yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C10714yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C10714yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C10714yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23#120×C10711yescharacteristic
861C23#120×C10711yescharacteristic
862C23#121×C10711yescharacteristic
863C23#121×C10711yescharacteristic
864C23#127×C10711yescharacteristic
865C23#127×C10711yescharacteristic
866C23C22×D4×C10711yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—41no—
897D4—42no—
898D4—42no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4#120×C10711yescharacteristic
919C2×C4#120×C10711yescharacteristic
920C2×C4#120×C10711yescharacteristic
921C2×C4#120×C10711yescharacteristic
922C2×C4#120×C10711yescharacteristic
923C2×C4#120×C10711yescharacteristic
924C2×C4#120×C10711yescharacteristic
925C2×C4#120×C10711yescharacteristic
926C2×C4#120×C10711yescharacteristic
927C2×C4#120×C10711yescharacteristic
928C2×C4#121×C10711yescharacteristic
929C2×C4#121×C10711yescharacteristic
930C2×C4#121×C10711yescharacteristic
931C2×C4#121×C10711yescharacteristic
932C2×C4#121×C10711yescharacteristic
933C2×C4#121×C10711yescharacteristic
934C2×C4#121×C10711yescharacteristic
935C2×C4#121×C10711yescharacteristic
936C2×C4#121×C10711yescharacteristic
937C2×C4#121×C10711yescharacteristic
938C2×C4#127×C10711yescharacteristic
939C2×C4#127×C10711yescharacteristic
940C2×C4C22×D4×C10711yescharacteristic
941C2×C4C22×D4×C10711yescharacteristic
942C2×C4C22×D4×C10711yescharacteristic
943C2×C4C22×D4×C10711yescharacteristic
944C2×C4C22×D4×C10711yescharacteristic
945C2×C4C2×#41×C10711yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22#392×C10711yescharacteristic
972C22#392×C10711yescharacteristic
973C22#392×C10711yescharacteristic
974C22#392×C10711yescharacteristic
975C22C2×#120×C10711yescharacteristic
976C22C2×#121×C10711yescharacteristic
977C22C2×#127×C10711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4#392×C10711yescharacteristic
983C4#392×C10711yescharacteristic
984C4#392×C10711yescharacteristic
985C4#392×C10711yescharacteristic
986C4C2×#120×C10711yescharacteristic
987C4C2×#120×C10711yescharacteristic
988C4C2×#121×C10711yescharacteristic
989C4C2×#121×C10711yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C107×#200812yesdirect product factor
1000C2C2×#392×C10711yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C107C2semidirect
2. C22×AGL(1,ℤ/8)×C107C2semidirect
3. C2×#535×C107C2semidirect
4. C2×#421×C107C2semidirect
5. C2×#418×C107C2semidirect
6. C2×#410×C107C2semidirect
7. C107×#2008C2direct (N × H)
8. C2×#344×C107C2semidirect
15. #575×C107C22semidirect
25. C2×AGL(1,ℤ/8)×C107C22semidirect
34. #535×C107C22semidirect
42. #421×C107C22semidirect
45. #418×C107C22semidirect
48. #410×C107C22semidirect
50. #344×C107C22semidirect
73. C2×#41×C107D4semidirect
77. C22×Q8×C107D4semidirect
95. C22×D4×C107D4semidirect
131. C2×M16×C107D4semidirect
132. C2×M16×C107D4semidirect
133. C2×M16×C107D4semidirect
137. C22×C8×C107D4semidirect
218. C2×Q8×C107C2×D4semidirect
272. C2×D4×C107C2×D4semidirect
316. M16×C107C2×D4semidirect
322. C2×C8×C107C2×D4semidirect
489. C2×#2008C107direct (N × H)
499. C2×C107#2008direct (N × H)
501. C2×#575C2×C107semidirect
502. C22×AGL(1,ℤ/8)C2×C107semidirect
503. C2×#535C2×C107semidirect
504. C2×#421C2×C107semidirect
505. C2×#418C2×C107semidirect
506. C2×#410C2×C107semidirect
507. #2008C2×C107direct (N × H)
508. C2×#344C2×C107semidirect
509. C107C2×#2008direct (N × H)
516. #575C22×C107semidirect
526. C2×AGL(1,ℤ/8)C22×C107semidirect
535. #535C22×C107semidirect
543. #421C22×C107semidirect
546. #418C22×C107semidirect
549. #410C22×C107semidirect
551. #344C22×C107semidirect
574. C2×#41D4×C107semidirect
578. C22×Q8D4×C107semidirect
596. C22×D4D4×C107semidirect
632. C2×M16D4×C107semidirect
633. C2×M16D4×C107semidirect
634. C2×M16D4×C107semidirect
638. C22×C8D4×C107semidirect
719. C2×Q8C2×D4×C107semidirect
773. C2×D4C2×D4×C107semidirect
817. M16C2×D4×C107semidirect
823. C2×C8C2×D4×C107semidirect
999. C2C107×#2008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#575×C1072
C22×AGL(1,ℤ/8)×C1072
C2×#535×C1072
C2×#421×C1072
C2×#418×C1072
C2×#410×C1072
C107×#20082
C2×#344×C1072
C2×#2008107