Finite Group Databasebeta

← C107×#23412 #41049376

Subgroups — C107×#23412 #41049376

Order 27392.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C107C211yesmaximal, characteristic, complemented
2C2×#575×C107C211yesmaximal, characteristic, complemented
3C107×#3449C211yesmaximal, characteristic, complemented
4C2×#421×C107C211yesmaximal, characteristic, complemented
5C107×#2896C211yesmaximal, characteristic, complemented
6C2×#410×C107C211yesmaximal, characteristic, complemented
7C107×#2009C214yesmaximal, complemented
8C107×#2008C214yesmaximal, complemented
9C2×#344×C107C211yesmaximal, characteristic, complemented
10C22×#41×C107C2211yescharacteristic
11C22×#41×C107C2211yescharacteristic
12C22×#41×C107C2211yescharacteristic
13#575×C107—22no—
14#575×C107—22no—
15#575×C107—22no—
16#575×C107—22no—
17#575×C107—22no—
18#575×C107—22no—
19#575×C107—22no—
20#575×C107C2214yes—
21C2×#137×C107—21no—
22C2×#137×C107—21no—
23C2×#137×C107—21no—
24C2×#137×C107C2212yescomplemented
25C2×AGL(1,ℤ/8)×C107—21no—
26C2×AGL(1,ℤ/8)×C107—21no—
27C2×AGL(1,ℤ/8)×C107—21no—
28C2×AGL(1,ℤ/8)×C107C2212yescomplemented
29C2×#135×C107—22no—
30C2×#135×C107—22no—
31C22×M16×C107C2211yescharacteristic
32C22×M16×C107C2211yescharacteristic
33#537×C107—22no—
34#536×C107—21no—
35#536×C107C2212yescomplemented
36#535×C107—21no—
37#535×C107C2212yescomplemented
38#534×C107—22no—
39#532×C107—22no—
40#525×C107—22no—
41#525×C107—22no—
42C2×#117×C107C2211yescharacteristic
43C2×#117×C107C2211yescharacteristic
44#421×C107—22no—
45#421×C107C2214yescomplemented
46C2×#104×C107—22no—
47#419×C107C2212yescomplemented
48#418×C107C2212yescomplemented
49#417×C107—22no—
50#416×C107—22no—
51#410×C107—22no—
52#410×C107C2214yescomplemented
53C2×#99×C107—22no—
54#344×C107C2214yescomplemented
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×C107—21no—
73C2×#41×C107—21no—
74C2×#41×C107—21no—
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C2×#41×C107—21no—
78C2×#41×C107—21no—
79C2×#41×C107—21no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—21no—
83C2×#41×C107—21no—
84C2×#41×C107—21no—
85C2×#41×C107D412yes—
86C2×#41×C107D412yes—
87C2×#41×C107D412yes—
88C2×#41×C107D412yescomplemented
89C2×#41×C107C2312yes—
90C2×#41×C107C2312yes—
91C22×Q8×C107D411yescharacteristic
92C22×Q8×C107D411yescharacteristic, complemented
93C22×Q8×C107C2311yescharacteristic
94C22×D4×C107—21no—
95C22×D4×C107—21no—
96C22×D4×C107—21no—
97C22×D4×C107D411yescharacteristic
98C22×D4×C107D411yescharacteristic, complemented
99C22×D4×C107C2311yescharacteristic
100C23×C4×C107—21no—
101C23×C4×C107—21no—
102C23×C4×C107—21no—
103C23×C4×C107C2311yescharacteristic
104#137×C107—24no—
105#137×C107—24no—
106#137×C107—24no—
107#137×C107—24no—
108#137×C107—24no—
109#137×C107—24no—
110#137×C107—24no—
111#137×C107—24no—
112AGL(1,ℤ/8)×C107—24no—
113AGL(1,ℤ/8)×C107—24no—
114AGL(1,ℤ/8)×C107—24no—
115AGL(1,ℤ/8)×C107—24no—
116AGL(1,ℤ/8)×C107—24no—
117AGL(1,ℤ/8)×C107—24no—
118AGL(1,ℤ/8)×C107—24no—
119AGL(1,ℤ/8)×C107—24no—
120#135×C107—28no—
121#135×C107—28no—
122#135×C107—28no—
123#135×C107—28no—
124C2×Q16×C107—22no—
125C2×Q16×C107—22no—
126C2×SD16×C107—22no—
127C2×SD16×C107—22no—
128C2×SD16×C107—22no—
129C2×SD16×C107—22no—
130C2×D8×C107—22no—
131C2×D8×C107—22no—
132C2×M16×C107—21no—
133C2×M16×C107—21no—
134C2×M16×C107—21no—
135C2×M16×C107—21no—
136C2×M16×C107—21no—
137C2×M16×C107—21no—
138C2×M16×C107—21no—
139C2×M16×C107D412yescomplemented
140C2×M16×C107D412yescomplemented
141C2×M16×C107D412yescomplemented
142C2×M16×C107C2312yes—
143C2×M16×C107C2312yes—
144C22×C8×C107—21no—
145C22×C8×C107D412yescomplemented
146C4⋊Q8×C107—22no—
147#127×C107—22no—
148#124×C107—22no—
149#124×C107—22no—
150#123×C107—24no—
151#123×C107—24no—
152C22⋊Q8×C107—24no—
153C22⋊Q8×C107—24no—
154#121×C107—24no—
155#121×C107—28no—
156#121×C107—24no—
157#120×C107—24no—
158#120×C107—24no—
159C4×D4×C107—28no—
160#117×C107—21no—
161#117×C107—21no—
162#117×C107—21no—
163#117×C107—21no—
164#117×C107—21no—
165#117×C107D412yes—
166#117×C107C2312yes—
167#117×C107C2312yes—
168C2×C4⋊C4×C107—21no—
169C2×C4⋊C4×C107—21no—
170C2×C22⋊C4×C107—21no—
171C2×C22⋊C4×C107D412yes—
172C2×C42×C107—21no—
173C2×C42×C107—21no—
174#104×C107—28no—
175#103×C107—24no—
176#102×C107—24no—
177#99×C107—28no—
178C24×C107—21no—
179C24×C107—21no—
180C24×C107—21no—
181C24×C107C2×D411yescharacteristic
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—22no—
192#41×C107—22no—
193#41×C107—22no—
194#41×C107—22no—
195#41×C107—22no—
196#41×C107—22no—
197#41×C107—22no—
198#41×C107—22no—
199#41×C107—22no—
200#41×C107—22no—
201#41×C107—22no—
202#41×C107—22no—
203#41×C107—22no—
204#41×C107—22no—
205#41×C107—22no—
206#41×C107—41no—
207#41×C107—41no—
208#41×C107—41no—
209#41×C107—41no—
210#41×C107—41no—
211#41×C107—41no—
212#41×C107—41no—
213#41×C107—41no—
214#41×C107—41no—
215#41×C107—41no—
216#41×C107—41no—
217#41×C107—41no—
218#41×C107—41no—
219#41×C107—41no—
220#41×C107—41no—
221#41×C107—41no—
222#41×C107—41no—
223#41×C107—41no—
224#41×C107—41no—
225#41×C107—41no—
226#41×C107—41no—
227#41×C107—41no—
228#41×C107—41no—
229#41×C107—41no—
230C2×Q8×C107—21no—
231C2×Q8×C107—21no—
232C2×Q8×C107—21no—
233C2×Q8×C107—21no—
234C2×Q8×C107—21no—
235C2×Q8×C107—21no—
236C2×Q8×C107—21no—
237C2×Q8×C107—21no—
238C2×Q8×C107—21no—
239C2×Q8×C107—21no—
240C2×Q8×C107—21no—
241C2×Q8×C107—21no—
242C2×Q8×C107—21no—
243C2×Q8×C107—21no—
244C2×Q8×C107—21no—
245C2×Q8×C107C2×D412yes—
246C2×Q8×C107C2×D412yes—
247C2×Q8×C107C2×D412yes—
248C2×D4×C107—22no—
249C2×D4×C107—22no—
250C2×D4×C107—22no—
251C2×D4×C107—22no—
252C2×D4×C107—22no—
253C2×D4×C107—22no—
254C2×D4×C107—28no—
255C2×D4×C107—21no—
256C2×D4×C107—21no—
257C2×D4×C107—21no—
258C2×D4×C107—21no—
259C2×D4×C107—21no—
260C2×D4×C107—21no—
261C2×D4×C107—21no—
262C2×D4×C107—21no—
263C2×D4×C107—21no—
264C2×D4×C107—21no—
265C2×D4×C107—21no—
266C2×D4×C107—21no—
267C2×D4×C107—21no—
268C2×D4×C107—21no—
269C2×D4×C107—21no—
270C2×D4×C107—41no—
271C2×D4×C107—41no—
272C2×D4×C107—41no—
273C2×D4×C107—41no—
274C2×D4×C107—41no—
275C2×D4×C107—41no—
276C2×D4×C107—41no—
277C2×D4×C107—41no—
278C2×D4×C107—41no—
279C2×D4×C107—41no—
280C2×D4×C107—41no—
281C2×D4×C107—41no—
282C2×D4×C107C2×D412yes—
283C2×D4×C107C2×D412yes—
284C2×D4×C107C2×D412yes—
285C22×C4×C107—21no—
286C22×C4×C107—21no—
287C22×C4×C107—21no—
288C22×C4×C107—22no—
289C22×C4×C107—22no—
290C22×C4×C107—22no—
291C22×C4×C107—22no—
292C22×C4×C107—22no—
293C22×C4×C107—22no—
294C22×C4×C107—22no—
295C22×C4×C107—41no—
296C22×C4×C107—41no—
297C22×C4×C107—41no—
298C22×C4×C107—41no—
299C22×C4×C107—41no—
300C22×C4×C107—41no—
301C22×C4×C107—41no—
302C22×C4×C107—41no—
303C22×C4×C107—41no—
304C22×C4×C107—41no—
305C22×C4×C107—41no—
306C22×C4×C107—41no—
307C22×C4×C107—41no—
308C22×C4×C107C2×D411yescharacteristic
309C22×C4×C107C2×D411yescharacteristic
310C22×C4×C107C2×D411yescharacteristic
311C22×C4×C107C2×D411yescharacteristic
312C22×C4×C107C2×D411yescharacteristic
313C22×C4×C107C2×D411yescharacteristic
314C22×C4×C107C2×D411yescharacteristic
315C22×C4×C107C2×D411yescharacteristic
316C22×C4×C107C2×D411yescharacteristic
317C22×C4×C107C2×D411yescharacteristic
318C22×C4×C107C2×D411yescharacteristic
319C22×C4×C107#4111yescharacteristic
320C22×C4×C107#4111yescharacteristic
321C22×C4×C107C2411yescharacteristic
322Q16×C107—28no—
323Q16×C107—28no—
324SD16×C107—28no—
325SD16×C107—28no—
326SD16×C107—28no—
327SD16×C107—28no—
328D8×C107—28no—
329D8×C107—28no—
330M16×C107—22no—
331M16×C107—22no—
332M16×C107—22no—
333M16×C107—22no—
334M16×C107—22no—
335M16×C107—22no—
336M16×C107—22no—
337M16×C107C2×D414yes—
338C2×C8×C107—22no—
339C2×C8×C107—22no—
340C2×C8×C107—22no—
341C2×C8×C107—22no—
342C2×C8×C107—22no—
343C2×C8×C107C2×D414yes—
344C4⋊C4×C107—28no—
345C4⋊C4×C107—22no—
346C4⋊C4×C107—22no—
347C4⋊C4×C107—22no—
348C4⋊C4×C107—41no—
349C22⋊C4×C107—28no—
350C22⋊C4×C107—28no—
351C22⋊C4×C107—22no—
352C22⋊C4×C107—22no—
353C22⋊C4×C107—41no—
354C22⋊C4×C107C2×D414yes—
355C42×C107—22no—
356C42×C107—22no—
357C42×C107—22no—
358C42×C107—41no—
359C23×C107—22no—
360C23×C107—22no—
361C23×C107—22no—
362C23×C107—41no—
363C23×C107—41no—
364C23×C107—41no—
365C23×C107—41no—
366C23×C107—41no—
367C23×C107—41no—
368C23×C107—81no—
369C23×C107—82no—
370C23×C107—82no—
371C23×C107—82no—
372C23×C107#12011yescharacteristic
373C23×C107#12011yescharacteristic
374C23×C107#12111yescharacteristic
375C23×C107#12111yescharacteristic
376C23×C107#12711yescharacteristic
377C23×C107#12711yescharacteristic
378C23×C107C22×D411yescharacteristic
379Q8×C107—22no—
380Q8×C107—22no—
381Q8×C107—22no—
382Q8×C107—22no—
383Q8×C107—22no—
384Q8×C107—22no—
385Q8×C107—41no—
386Q8×C107—41no—
387Q8×C107—41no—
388Q8×C107—41no—
389Q8×C107—41no—
390Q8×C107—41no—
391D4×C107—22no—
392D4×C107—22no—
393D4×C107—22no—
394D4×C107—22no—
395D4×C107—22no—
396D4×C107—22no—
397D4×C107—42no—
398D4×C107—42no—
399D4×C107—42no—
400D4×C107—42no—
401D4×C107—42no—
402D4×C107—42no—
403D4×C107—42no—
404D4×C107—42no—
405D4×C107—42no—
406D4×C107—42no—
407D4×C107—42no—
408D4×C107—42no—
409D4×C107—41no—
410D4×C107—41no—
411D4×C107—41no—
412D4×C107—41no—
413D4×C107—41no—
414D4×C107—41no—
415D4×C107—88no—
416C2×C4×C107—24no—
417C2×C4×C107—22no—
418C2×C4×C107—22no—
419C2×C4×C107—22no—
420C2×C4×C107—41no—
421C2×C4×C107—41no—
422C2×C4×C107—41no—
423C2×C4×C107—41no—
424C2×C4×C107—41no—
425C2×C4×C107—41no—
426C2×C4×C107—42no—
427C2×C4×C107—42no—
428C2×C4×C107—42no—
429C2×C4×C107—42no—
430C2×C4×C107—42no—
431C2×C4×C107—42no—
432C2×C4×C107—42no—
433C2×C4×C107—42no—
434C2×C4×C107—42no—
435C2×C4×C107—42no—
436C2×C4×C107—42no—
437C2×C4×C107—42no—
438C2×C4×C107—42no—
439C2×C4×C107—82no—
440C2×C4×C107—82no—
441C2×C4×C107#12011yescharacteristic
442C2×C4×C107#12011yescharacteristic
443C2×C4×C107#12011yescharacteristic
444C2×C4×C107#12011yescharacteristic
445C2×C4×C107#12011yescharacteristic
446C2×C4×C107#12011yescharacteristic
447C2×C4×C107#12011yescharacteristic
448C2×C4×C107#12011yescharacteristic
449C2×C4×C107#12011yescharacteristic
450C2×C4×C107#12011yescharacteristic
451C2×C4×C107#12111yescharacteristic
452C2×C4×C107#12111yescharacteristic
453C2×C4×C107#12111yescharacteristic
454C2×C4×C107#12111yescharacteristic
455C2×C4×C107#12111yescharacteristic
456C2×C4×C107#12111yescharacteristic
457C2×C4×C107#12111yescharacteristic
458C2×C4×C107#12111yescharacteristic
459C2×C4×C107#12111yescharacteristic
460C2×C4×C107#12111yescharacteristic
461C2×C4×C107#12711yescharacteristic
462C2×C4×C107#12711yescharacteristic
463C2×C4×C107C22×D411yescharacteristic
464C2×C4×C107C22×D411yescharacteristic
465C2×C4×C107C22×D411yescharacteristic
466C2×C4×C107C22×D411yescharacteristic
467C2×C4×C107C22×D411yescharacteristic
468C2×C4×C107C2×#4111yescharacteristic
469C8×C107—24no—
470C8×C107—24no—
471C22×C107—41no—
472C22×C107—41no—
473C22×C107—41no—
474C22×C107—41no—
475C22×C107—41no—
476C22×C107—41no—
477C22×C107—41no—
478C22×C107—44no—
479C22×C107—44no—
480C22×C107—42no—
481C22×C107—42no—
482C22×C107—42no—
483C22×C107—82no—
484C22×C107—82no—
485C22×C107—82no—
486C22×C107—82no—
487C22×C107—82no—
488C22×C107—82no—
489C22×C107—82no—
490C22×C107#39211yescharacteristic
491C22×C107#39211yescharacteristic
492C22×C107#39211yescharacteristic
493C22×C107#39211yescharacteristic
494C22×C107C2×#12011yescharacteristic
495C22×C107C2×#12111yescharacteristic
496C22×C107C2×#12711yescharacteristic
497C4×C107—44no—
498C4×C107—42no—
499C4×C107—42no—
500C4×C107—42no—
501C4×C107—82no—
502C4×C107#39211yescharacteristic
503C4×C107#39211yescharacteristic
504C4×C107#39211yescharacteristic
505C4×C107#39211yescharacteristic
506C4×C107C2×#12011yescharacteristic
507C4×C107C2×#12011yescharacteristic
508C4×C107C2×#12111yescharacteristic
509C4×C107C2×#12111yescharacteristic
510#23412C10711yesmaximal, characteristic, direct product factor, Sylow
511C2×C107—21no—
512C2×C107—21no—
513C2×C107—21no—
514C2×C107—21no—
515C2×C107—21no—
516C2×C107—21no—
517C2×C107—21no—
518C2×C107—82no—
519C2×C107—82no—
520C2×C107—82no—
521C2×C107C2×#39211yescharacteristic
522C2×#575C2×C10711yescharacteristic, complemented
523C2×#575C2×C10711yescharacteristic, complemented
524#3449C2×C10711yescharacteristic, complemented
525C2×#421C2×C10711yescharacteristic, complemented
526#2896C2×C10711yescharacteristic, complemented
527C2×#410C2×C10711yescharacteristic, complemented
528#2009C2×C10714yescomplemented
529#2008C2×C10714yescomplemented
530C2×#344C2×C10711yescharacteristic, complemented
531C107#2341211yescharacteristic, direct product factor, Sylow
532C22×#41C22×C10711yescharacteristic
533C22×#41C22×C10711yescharacteristic
534C22×#41C22×C10711yescharacteristic
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575—22no—
542#575C22×C10714yes—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137—21no—
546C2×#137C22×C10712yescomplemented
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)—21no—
550C2×AGL(1,ℤ/8)C22×C10712yescomplemented
551C2×#135—22no—
552C2×#135—22no—
553C22×M16C22×C10711yescharacteristic
554C22×M16C22×C10711yescharacteristic
555#537—22no—
556#536—21no—
557#536C22×C10712yescomplemented
558#535—21no—
559#535C22×C10712yescomplemented
560#534—22no—
561#532—22no—
562#525—22no—
563#525—22no—
564C2×#117C22×C10711yescharacteristic
565C2×#117C22×C10711yescharacteristic
566#421—22no—
567#421C22×C10714yescomplemented
568C2×#104—22no—
569#419C22×C10712yescomplemented
570#418C22×C10712yescomplemented
571#417—22no—
572#416—22no—
573#410—22no—
574#410C22×C10714yescomplemented
575C2×#99—22no—
576#344C22×C10714yescomplemented
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C10712yes—
608C2×#41D4×C10712yes—
609C2×#41D4×C10712yes—
610C2×#41D4×C10712yescomplemented
611C2×#41C23×C10712yes—
612C2×#41C23×C10712yes—
613C22×Q8D4×C10711yescharacteristic
614C22×Q8D4×C10711yescharacteristic, complemented
615C22×Q8C23×C10711yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C10711yescharacteristic
620C22×D4D4×C10711yescharacteristic, complemented
621C22×D4C23×C10711yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C10711yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C10712yescomplemented
662C2×M16D4×C10712yescomplemented
663C2×M16D4×C10712yescomplemented
664C2×M16C23×C10712yes—
665C2×M16C23×C10712yes—
666C22×C8—21no—
667C22×C8D4×C10712yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C10712yes—
688#117C23×C10712yes—
689#117C23×C10712yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C10712yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C10711yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C10712yes—
768C2×Q8C2×D4×C10712yes—
769C2×Q8C2×D4×C10712yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C10712yes—
805C2×D4C2×D4×C10712yes—
806C2×D4C2×D4×C10712yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C10711yescharacteristic
831C22×C4C2×D4×C10711yescharacteristic
832C22×C4C2×D4×C10711yescharacteristic
833C22×C4C2×D4×C10711yescharacteristic
834C22×C4C2×D4×C10711yescharacteristic
835C22×C4C2×D4×C10711yescharacteristic
836C22×C4C2×D4×C10711yescharacteristic
837C22×C4C2×D4×C10711yescharacteristic
838C22×C4C2×D4×C10711yescharacteristic
839C22×C4C2×D4×C10711yescharacteristic
840C22×C4C2×D4×C10711yescharacteristic
841C22×C4#41×C10711yescharacteristic
842C22×C4#41×C10711yescharacteristic
843C22×C4C24×C10711yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C10714yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C10714yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C10714yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C10711yescharacteristic
895C23#120×C10711yescharacteristic
896C23#121×C10711yescharacteristic
897C23#121×C10711yescharacteristic
898C23#127×C10711yescharacteristic
899C23#127×C10711yescharacteristic
900C23C22×D4×C10711yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C10711yescharacteristic
964C2×C4#120×C10711yescharacteristic
965C2×C4#120×C10711yescharacteristic
966C2×C4#120×C10711yescharacteristic
967C2×C4#120×C10711yescharacteristic
968C2×C4#120×C10711yescharacteristic
969C2×C4#120×C10711yescharacteristic
970C2×C4#120×C10711yescharacteristic
971C2×C4#120×C10711yescharacteristic
972C2×C4#120×C10711yescharacteristic
973C2×C4#121×C10711yescharacteristic
974C2×C4#121×C10711yescharacteristic
975C2×C4#121×C10711yescharacteristic
976C2×C4#121×C10711yescharacteristic
977C2×C4#121×C10711yescharacteristic
978C2×C4#121×C10711yescharacteristic
979C2×C4#121×C10711yescharacteristic
980C2×C4#121×C10711yescharacteristic
981C2×C4#121×C10711yescharacteristic
982C2×C4#121×C10711yescharacteristic
983C2×C4#127×C10711yescharacteristic
984C2×C4#127×C10711yescharacteristic
985C2×C4C22×D4×C10711yescharacteristic
986C2×C4C22×D4×C10711yescharacteristic
987C2×C4C22×D4×C10711yescharacteristic
988C2×C4C22×D4×C10711yescharacteristic
989C2×C4C22×D4×C10711yescharacteristic
990C2×C4C2×#41×C10711yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22#392×C10711yescharacteristic
1013C22#392×C10711yescharacteristic
1014C22#392×C10711yescharacteristic
1015C22#392×C10711yescharacteristic
1016C22C2×#120×C10711yescharacteristic
1017C22C2×#121×C10711yescharacteristic
1018C22C2×#127×C10711yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4#392×C10711yescharacteristic
1025C4#392×C10711yescharacteristic
1026C4#392×C10711yescharacteristic
1027C4#392×C10711yescharacteristic
1028C4C2×#120×C10711yescharacteristic
1029C4C2×#120×C10711yescharacteristic
1030C4C2×#121×C10711yescharacteristic
1031C4C2×#121×C10711yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×#392×C10711yescharacteristic
subgroupG/H
centerC4×C107#392
commutator, Frattini, cosocleC22×C4C24×C107
socleC2×C107C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C107C2semidirect
2. C2×#575×C107C2semidirect
3. C107×#3449C2semidirect
4. C2×#421×C107C2semidirect
5. C107×#2896C2semidirect
6. C2×#410×C107C2semidirect
7. C107×#2009C2semidirect
8. C107×#2008C2semidirect
9. C2×#344×C107C2semidirect
24. C2×#137×C107C22semidirect
28. C2×AGL(1,ℤ/8)×C107C22semidirect
35. #536×C107C22semidirect
37. #535×C107C22semidirect
45. #421×C107C22semidirect
47. #419×C107C22semidirect
48. #418×C107C22semidirect
52. #410×C107C22semidirect
54. #344×C107C22semidirect
88. C2×#41×C107D4semidirect
92. C22×Q8×C107D4semidirect
98. C22×D4×C107D4semidirect
139. C2×M16×C107D4semidirect
140. C2×M16×C107D4semidirect
141. C2×M16×C107D4semidirect
145. C22×C8×C107D4semidirect
510. #23412C107direct (N × H)
522. C2×#575C2×C107semidirect
523. C2×#575C2×C107semidirect
524. #3449C2×C107semidirect
525. C2×#421C2×C107semidirect
526. #2896C2×C107semidirect
527. C2×#410C2×C107semidirect
528. #2009C2×C107semidirect
529. #2008C2×C107semidirect
530. C2×#344C2×C107semidirect
531. C107#23412direct (N × H)
546. C2×#137C22×C107semidirect
550. C2×AGL(1,ℤ/8)C22×C107semidirect
557. #536C22×C107semidirect
559. #535C22×C107semidirect
567. #421C22×C107semidirect
569. #419C22×C107semidirect
570. #418C22×C107semidirect
574. #410C22×C107semidirect
576. #344C22×C107semidirect
610. C2×#41D4×C107semidirect
614. C22×Q8D4×C107semidirect
620. C22×D4D4×C107semidirect
661. C2×M16D4×C107semidirect
662. C2×M16D4×C107semidirect
663. C2×M16D4×C107semidirect
667. C22×C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1072
C107×#34492
C2×#421×C1072
C107×#28962
C2×#410×C1072
C107×#20092
C107×#20082
C2×#344×C1072
#23412107