Finite Group Databasebeta

← C107×#24405 #41050369

Subgroups — C107×#24405 #41050369

Order 27392.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3484C211yesmaximal, characteristic
2C2×#458×C107C211yesmaximal, characteristic, complemented
3C22×#99×C107C211yesmaximal, characteristic, complemented
4C107×#2412C212yesmaximal, complemented
5C107×#2405C211yesmaximal, characteristic, complemented
6C107×#2044C212yesmaximal, complemented
7C107×#2022C212yesmaximal, complemented
8C107×#1898C212yesmaximal, complemented
9C107×#1890C211yesmaximal, characteristic, complemented
10C107×#1867C211yesmaximal, characteristic, complemented
11C107×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C107C2211yescharacteristic
13C23×D4×C107C2211yescharacteristic
14#546×C107—22no—
15#546×C107—22no—
16D42×C107—22no—
17D42×C107—22no—
18#535×C107—21no—
19#534×C107—21no—
20#534×C107C2212yes—
21#525×C107—21no—
22C2×#123×C107C2211yescharacteristic
23C2×#123×C107C2212yescomplemented
24C2×#123×C107C2211yescharacteristic, complemented
25C2×#120×C107—21no—
26C2×#120×C107C2212yes—
27#518×C107C2211yescharacteristic
28C22×C22⋊C4×C107C2211yescharacteristic, complemented
29C22×C22⋊C4×C107C2212yescomplemented
30#458×C107—24no—
31C2×#99×C107—24no—
32C2×#99×C107C2211yescharacteristic
33C2×#99×C107C2211yescharacteristic
34C2×#99×C107C2212yescomplemented
35C2×#99×C107C2212yescomplemented
36C2×#99×C107C2212yescomplemented
37#397×C107—22no—
38#394×C107—21no—
39#394×C107—21no—
40#394×C107—22no—
41#386×C107—22no—
42#386×C107C2211yescharacteristic
43#386×C107C2211yescharacteristic, complemented
44#386×C107C2212yescomplemented
45#385×C107—21no—
46#385×C107C2212yescomplemented
47#381×C107C2212yescomplemented
48#380×C107—22no—
49#379×C107—21no—
50#379×C107C2211yescharacteristic, complemented
51#342×C107C2212yescomplemented
52#342×C107C2212yescomplemented
53C25×C107D411yescharacteristic
54C25×C107C2311yescharacteristic
55H(5,𝔽2)×C107—22no—
56H(5,𝔽2)×C107—22no—
57H(5,𝔽2)×C107—42no—
58C2×#41×C107—21no—
59C2×#41×C107—22no—
60C22×D4×C107—21no—
61C22×D4×C107—22no—
62C22×D4×C107—22no—
63C22×D4×C107—22no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—22no—
67C22×D4×C107—22no—
68C22×D4×C107—42no—
69C22×D4×C107D411yescharacteristic
70C22×D4×C107D411yescharacteristic
71C22×D4×C107D412yes—
72C22×D4×C107D412yes—
73C22×D4×C107C2312yes—
74C22×D4×C107C2311yescharacteristic
75C22×D4×C107C2311yescharacteristic
76C23×C4×C107—22no—
77C23×C4×C107D411yescharacteristic
78C23×C4×C107C2311yescharacteristic
79C23×C4×C107C2311yescharacteristic
80#127×C107—22no—
81#124×C107—22no—
82#123×C107—22no—
83#123×C107—22no—
84#123×C107—22no—
85#123×C107—22no—
86#123×C107—22no—
87#123×C107—24no—
88#123×C107—42no—
89#123×C107—42no—
90C22⋊Q8×C107—21no—
91C22⋊Q8×C107—21no—
92#121×C107—21no—
93#121×C107—21no—
94#121×C107—22no—
95#121×C107—22no—
96#121×C107—22no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107—22no—
100#120×C107—22no—
101#120×C107—22no—
102#120×C107—22no—
103#120×C107—22no—
104#120×C107—22no—
105#120×C107—22no—
106#120×C107—22no—
107#120×C107—22no—
108#120×C107—22no—
109C4×D4×C107—22no—
110C4×D4×C107—22no—
111C4×D4×C107—22no—
112C4×D4×C107—22no—
113#117×C107—21no—
114C2×C4⋊C4×C107—22no—
115C2×C4⋊C4×C107—21no—
116C2×C4⋊C4×C107—21no—
117C2×C4⋊C4×C107—22no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—24no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—22no—
127C2×C22⋊C4×C107—22no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—22no—
130C2×C22⋊C4×C107—22no—
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—22no—
135C2×C22⋊C4×C107—42no—
136C2×C22⋊C4×C107D412yes—
137C2×C22⋊C4×C107D412yes—
138C2×C22⋊C4×C107C2311yescharacteristic
139C2×C22⋊C4×C107C2311yescharacteristic
140C2×C22⋊C4×C107C2312yes—
141C2×C22⋊C4×C107C2312yes—
142C2×C22⋊C4×C107C2312yes—
143#99×C107—22no—
144#99×C107—24no—
145#99×C107—24no—
146#99×C107—42no—
147#99×C107D414yescomplemented
148#95×C107—22no—
149#95×C107—22no—
150#95×C107—22no—
151#95×C107—21no—
152#95×C107—21no—
153#95×C107—22no—
154C24×C107—21no—
155C24×C107—21no—
156C24×C107—22no—
157C24×C107—21no—
158C24×C107—21no—
159C24×C107—21no—
160C24×C107—22no—
161C24×C107—41no—
162C24×C107—42no—
163C24×C107—42no—
164C24×C107—81no—
165C24×C107—81no—
166C24×C107C2×D411yescharacteristic
167C24×C107C2×D412yes—
168C24×C107C2×D411yescharacteristic
169C24×C107C2×D412yes—
170C24×C107C2×D412yes—
171C24×C107C2×D411yescharacteristic
172C24×C107C2×D411yescharacteristic
173C24×C107C2411yescharacteristic
174#41×C107—44no—
175#41×C107—44no—
176#41×C107—42no—
177#41×C107—42no—
178C2×Q8×C107—21no—
179C2×D4×C107—22no—
180C2×D4×C107—22no—
181C2×D4×C107—22no—
182C2×D4×C107—21no—
183C2×D4×C107—22no—
184C2×D4×C107—22no—
185C2×D4×C107—22no—
186C2×D4×C107—22no—
187C2×D4×C107—22no—
188C2×D4×C107—21no—
189C2×D4×C107—22no—
190C2×D4×C107—22no—
191C2×D4×C107—22no—
192C2×D4×C107—22no—
193C2×D4×C107—21no—
194C2×D4×C107—22no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
197C2×D4×C107—22no—
198C2×D4×C107—22no—
199C2×D4×C107—22no—
200C2×D4×C107—22no—
201C2×D4×C107—22no—
202C2×D4×C107—22no—
203C2×D4×C107—41no—
204C2×D4×C107—41no—
205C2×D4×C107—44no—
206C2×D4×C107—44no—
207C2×D4×C107—44no—
208C2×D4×C107—44no—
209C2×D4×C107—44no—
210C2×D4×C107—44no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—44no—
214C2×D4×C107—82no—
215C2×D4×C107—82no—
216C2×D4×C107—82no—
217C2×D4×C107C2×D412yes—
218C2×D4×C107#4112yes—
219C22×C4×C107—21no—
220C22×C4×C107—22no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—22no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—22no—
227C22×C4×C107—22no—
228C22×C4×C107—21no—
229C22×C4×C107—22no—
230C22×C4×C107—22no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—22no—
237C22×C4×C107—41no—
238C22×C4×C107—44no—
239C22×C4×C107—44no—
240C22×C4×C107—81no—
241C22×C4×C107—82no—
242C22×C4×C107C2×D412yes—
243C22×C4×C107C2×D411yescharacteristic
244C22×C4×C107C2×D411yescharacteristic
245C22×C4×C107C2×D412yes—
246C22×C4×C107C2×D412yes—
247C4⋊C4×C107—21no—
248C4⋊C4×C107—21no—
249C4⋊C4×C107—22no—
250C4⋊C4×C107—22no—
251C4⋊C4×C107—44no—
252C4⋊C4×C107—42no—
253C4⋊C4×C107—42no—
254C4⋊C4×C107—82no—
255C22⋊C4×C107—22no—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—22no—
258C22⋊C4×C107—22no—
259C22⋊C4×C107—22no—
260C22⋊C4×C107—22no—
261C22⋊C4×C107—22no—
262C22⋊C4×C107—22no—
263C22⋊C4×C107—22no—
264C22⋊C4×C107—22no—
265C22⋊C4×C107—22no—
266C22⋊C4×C107—22no—
267C22⋊C4×C107—22no—
268C22⋊C4×C107—21no—
269C22⋊C4×C107—21no—
270C22⋊C4×C107—22no—
271C22⋊C4×C107—22no—
272C22⋊C4×C107—44no—
273C22⋊C4×C107—44no—
274C22⋊C4×C107—42no—
275C22⋊C4×C107—42no—
276C22⋊C4×C107—41no—
277C22⋊C4×C107—42no—
278C22⋊C4×C107—41no—
279C22⋊C4×C107—42no—
280C22⋊C4×C107—81no—
281C22⋊C4×C107—81no—
282C22⋊C4×C107—81no—
283C22⋊C4×C107—82no—
284C22⋊C4×C107C2×D414yescomplemented
285C42×C107—22no—
286C23×C107—21no—
287C23×C107—21no—
288C23×C107—21no—
289C23×C107—22no—
290C23×C107—22no—
291C23×C107—22no—
292C23×C107—24no—
293C23×C107—21no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—22no—
297C23×C107—22no—
298C23×C107—21no—
299C23×C107—22no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—22no—
303C23×C107—22no—
304C23×C107—42no—
305C23×C107—41no—
306C23×C107—41no—
307C23×C107—41no—
308C23×C107—41no—
309C23×C107—42no—
310C23×C107—42no—
311C23×C107—41no—
312C23×C107—42no—
313C23×C107—42no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—42no—
319C23×C107—42no—
320C23×C107—42no—
321C23×C107—42no—
322C23×C107—42no—
323C23×C107—81no—
324C23×C107—81no—
325C23×C107—82no—
326C23×C107—82no—
327C23×C107—84no—
328C23×C107—81no—
329C23×C107—81no—
330C23×C107—84no—
331C23×C107—84no—
332C23×C107#12011yescharacteristic
333C23×C107#12012yes—
334C23×C107#12011yescharacteristic
335C23×C107#12112yes—
336C23×C107C22×D411yescharacteristic
337C23×C107C22×D412yes—
338C23×C107C22×D411yescharacteristic
339C23×C107C2×#4111yescharacteristic
340C23×C107H(5,𝔽2)12yes—
341Q8×C107—42no—
342D4×C107—24no—
343D4×C107—24no—
344D4×C107—44no—
345D4×C107—42no—
346D4×C107—44no—
347D4×C107—44no—
348D4×C107—44no—
349D4×C107—42no—
350D4×C107—42no—
351D4×C107—42no—
352D4×C107—42no—
353D4×C107—42no—
354D4×C107—42no—
355D4×C107—44no—
356D4×C107—82no—
357D4×C107—82no—
358D4×C107—82no—
359D4×C107—82no—
360C2×C4×C107—21no—
361C2×C4×C107—21no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—22no—
365C2×C4×C107—21no—
366C2×C4×C107—21no—
367C2×C4×C107—21no—
368C2×C4×C107—24no—
369C2×C4×C107—22no—
370C2×C4×C107—22no—
371C2×C4×C107—42no—
372C2×C4×C107—42no—
373C2×C4×C107—44no—
374C2×C4×C107—42no—
375C2×C4×C107—42no—
376C2×C4×C107—42no—
377C2×C4×C107—42no—
378C2×C4×C107—42no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—42no—
384C2×C4×C107—42no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—42no—
388C2×C4×C107—42no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—42no—
396C2×C4×C107—42no—
397C2×C4×C107—42no—
398C2×C4×C107—81no—
399C2×C4×C107—81no—
400C2×C4×C107—88no—
401C2×C4×C107#12112yes—
402C22×C107—21no—
403C22×C107—22no—
404C22×C107—21no—
405C22×C107—22no—
406C22×C107—21no—
407C22×C107—21no—
408C22×C107—21no—
409C22×C107—22no—
410C22×C107—22no—
411C22×C107—22no—
412C22×C107—21no—
413C22×C107—21no—
414C22×C107—22no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—42no—
418C22×C107—44no—
419C22×C107—44no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—42no—
424C22×C107—41no—
425C22×C107—41no—
426C22×C107—42no—
427C22×C107—41no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—42no—
431C22×C107—41no—
432C22×C107—82no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—82no—
437C22×C107—84no—
438C22×C107—82no—
439C22×C107—82no—
440C22×C107—81no—
441C22×C107—84no—
442C22×C107—162no—
443C22×C107#45812yescomplemented
444C22×C107C2×#12011yescharacteristic
445C22×C107C2×#12111yescharacteristic
446C22×C107#53411yescharacteristic
447C22×C107D4212yes—
448C22×C107#54612yes—
449C4×C107—22no—
450C4×C107—44no—
451C4×C107—41no—
452C4×C107—42no—
453C4×C107—42no—
454C4×C107—42no—
455C4×C107—81no—
456C4×C107—81no—
457C4×C107—82no—
458C4×C107—81no—
459C4×C107—81no—
460#24405C10711yesmaximal, characteristic, direct product factor, Sylow
461C2×C107—22no—
462C2×C107—21no—
463C2×C107—21no—
464C2×C107—22no—
465C2×C107—22no—
466C2×C107—42no—
467C2×C107—41no—
468C2×C107—42no—
469C2×C107—81no—
470C2×C107—82no—
471C2×C107#241011yescharacteristic
472C2×C107C2×#45811yescharacteristic
473C2×C107#302611yescharacteristic
474#3484C2×C10711yescharacteristic
475C2×#458C2×C10711yescharacteristic, complemented
476C22×#99C2×C10711yescharacteristic, complemented
477#2412C2×C10712yescomplemented
478#2405C2×C10711yescharacteristic, complemented
479#2044C2×C10712yescomplemented
480#2022C2×C10712yescomplemented
481#1898C2×C10712yescomplemented
482#1890C2×C10711yescharacteristic, complemented
483#1867C2×C10711yescharacteristic, complemented
484#1790C2×C10711yescharacteristic, complemented
485C107#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C10711yescharacteristic
487C23×D4C22×C10711yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C10712yes—
495#525—21no—
496C2×#123C22×C10711yescharacteristic
497C2×#123C22×C10712yescomplemented
498C2×#123C22×C10711yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C10712yes—
501#518C22×C10711yescharacteristic
502C22×C22⋊C4C22×C10711yescharacteristic, complemented
503C22×C22⋊C4C22×C10712yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C10711yescharacteristic
507C2×#99C22×C10711yescharacteristic
508C2×#99C22×C10712yescomplemented
509C2×#99C22×C10712yescomplemented
510C2×#99C22×C10712yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C10711yescharacteristic
517#386C22×C10711yescharacteristic, complemented
518#386C22×C10712yescomplemented
519#385—21no—
520#385C22×C10712yescomplemented
521#381C22×C10712yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C10711yescharacteristic, complemented
525#342C22×C10712yescomplemented
526#342C22×C10712yescomplemented
527C25D4×C10711yescharacteristic
528C25C23×C10711yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C10711yescharacteristic
544C22×D4D4×C10711yescharacteristic
545C22×D4D4×C10712yes—
546C22×D4D4×C10712yes—
547C22×D4C23×C10712yes—
548C22×D4C23×C10711yescharacteristic
549C22×D4C23×C10711yescharacteristic
550C23×C4—22no—
551C23×C4D4×C10711yescharacteristic
552C23×C4C23×C10711yescharacteristic
553C23×C4C23×C10711yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C10712yes—
611C2×C22⋊C4D4×C10712yes—
612C2×C22⋊C4C23×C10712yes—
613C2×C22⋊C4C23×C10711yescharacteristic
614C2×C22⋊C4C23×C10711yescharacteristic
615C2×C22⋊C4C23×C10712yes—
616C2×C22⋊C4C23×C10712yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C10714yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C10711yescharacteristic
641C24C2×D4×C10712yes—
642C24C2×D4×C10711yescharacteristic
643C24C2×D4×C10712yes—
644C24C2×D4×C10712yes—
645C24C2×D4×C10711yescharacteristic
646C24C2×D4×C10711yescharacteristic
647C24C24×C10711yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C10712yes—
692C2×D4#41×C10712yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C10712yes—
717C22×C4C2×D4×C10711yescharacteristic
718C22×C4C2×D4×C10711yescharacteristic
719C22×C4C2×D4×C10712yes—
720C22×C4C2×D4×C10712yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C10714yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C10711yescharacteristic
807C23#120×C10712yes—
808C23#120×C10711yescharacteristic
809C23#121×C10712yes—
810C23C22×D4×C10711yescharacteristic
811C23C22×D4×C10712yes—
812C23C22×D4×C10711yescharacteristic
813C23C2×#41×C10711yescharacteristic
814C23H(5,𝔽2)×C10712yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C10712yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C10712yescomplemented
918C22C2×#120×C10711yescharacteristic
919C22C2×#121×C10711yescharacteristic
920C22#534×C10711yescharacteristic
921C22D42×C10712yes—
922C22#546×C10712yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C107×#241011yescharacteristic
945C2C2×#458×C10711yescharacteristic
946C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
prime radicalC107×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C107C2semidirect
3. C22×#99×C107C2semidirect
4. C107×#2412C2semidirect
5. C107×#2405C2semidirect
6. C107×#2044C2semidirect
7. C107×#2022C2semidirect
8. C107×#1898C2semidirect
9. C107×#1890C2semidirect
10. C107×#1867C2semidirect
11. C107×#1790C2semidirect
23. C2×#123×C107C22semidirect
24. C2×#123×C107C22semidirect
28. C22×C22⋊C4×C107C22semidirect
29. C22×C22⋊C4×C107C22semidirect
34. C2×#99×C107C22semidirect
35. C2×#99×C107C22semidirect
36. C2×#99×C107C22semidirect
43. #386×C107C22semidirect
44. #386×C107C22semidirect
46. #385×C107C22semidirect
47. #381×C107C22semidirect
50. #379×C107C22semidirect
51. #342×C107C22semidirect
52. #342×C107C22semidirect
147. #99×C107D4semidirect
284. C22⋊C4×C107C2×D4semidirect
443. C22×C107#458semidirect
460. #24405C107direct (N × H)
475. C2×#458C2×C107semidirect
476. C22×#99C2×C107semidirect
477. #2412C2×C107semidirect
478. #2405C2×C107semidirect
479. #2044C2×C107semidirect
480. #2022C2×C107semidirect
481. #1898C2×C107semidirect
482. #1890C2×C107semidirect
483. #1867C2×C107semidirect
484. #1790C2×C107semidirect
485. C107#24405direct (N × H)
497. C2×#123C22×C107semidirect
498. C2×#123C22×C107semidirect
502. C22×C22⋊C4C22×C107semidirect
503. C22×C22⋊C4C22×C107semidirect
508. C2×#99C22×C107semidirect
509. C2×#99C22×C107semidirect
510. C2×#99C22×C107semidirect
517. #386C22×C107semidirect
518. #386C22×C107semidirect
520. #385C22×C107semidirect
521. #381C22×C107semidirect
524. #379C22×C107semidirect
525. #342C22×C107semidirect
526. #342C22×C107semidirect
621. #99D4×C107semidirect
758. C22⋊C4C2×D4×C107semidirect
917. C22#458×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34842
C2×#458×C1072
C22×#99×C1072
C107×#24122
C107×#24052
C107×#20442
C107×#20222
C107×#18982
C107×#18902
C107×#18672
C107×#17902
#24405107