Finite Group Databasebeta

← C107×#12753 #41038717

Subgroups — C107×#12753 #41038717

Order 27392.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3532C211yesmaximal, characteristic
2C107×#2127C211yesmaximal, characteristic, complemented
3C107×#2121C211yesmaximal, characteristic, complemented
4C2×AΣL(1,𝔽16)×C107C211yesmaximal, characteristic, complemented
5C107×#1913C211yesmaximal, characteristic, complemented
6C107×#1911C211yesmaximal, characteristic, complemented
7C107×#1889C211yesmaximal, characteristic, complemented
8H(3,𝔽4)×C107C411yescharacteristic, complemented
9#560×C107—21no—
10#560×C107C411yescharacteristic, complemented
11#551×C107—21no—
12#551×C107C411yescharacteristic, complemented
13#546×C107—21no—
14#546×C107—21no—
15#546×C107—21no—
16D42×C107—21no—
17D42×C107C411yescharacteristic, complemented
18#538×C107—21no—
19#538×C107—21no—
20#538×C107—21no—
21#535×C107—21no—
22#535×C107C2211yescharacteristic
23#534×C107—21no—
24#534×C107C2211yescharacteristic
25C2×#120×C107—21no—
26C2×#120×C107C2211yescharacteristic
27#518×C107C2211yescharacteristic, complemented
28#421×C107—21no—
29C2×#100×C107C2211yescharacteristic, complemented
30C2×#99×C107—21no—
31C2×#99×C107C2211yescharacteristic, complemented
32C2×#99×C107C2211yescharacteristic, complemented
33#379×C107—21no—
34#354×C107—21no—
35#353×C107—21no—
36#352×C107—21no—
37AΣL(1,𝔽16)×C107—21no—
38AΣL(1,𝔽16)×C107—21no—
39AΣL(1,𝔽16)×C107—21no—
40#342×C107—21no—
41#342×C107—21no—
42H(3,ℤ/4)×C107—21no—
43C25×C107D411yescharacteristic
44C2×#41×C107—21no—
45C2×#41×C107D411yescharacteristic
46C22×D4×C107—21no—
47C22×D4×C107—21no—
48C22×D4×C107—21no—
49C22×D4×C107—21no—
50C22×D4×C107—21no—
51C22×D4×C107D411yescharacteristic
52C22×D4×C107C2311yescharacteristic
53C2×M16×C107—21no—
54#127×C107—21no—
55#127×C107C2×C411yescharacteristic
56#127×C107D411yescharacteristic
57#126×C107—21no—
58#126×C107—21no—
59#126×C107—21no—
60#126×C107—21no—
61#124×C107—21no—
62#124×C107—21no—
63#124×C107—21no—
64#124×C107—21no—
65#124×C107—21no—
66#124×C107C2×C411yescharacteristic
67#124×C107D411yescharacteristic
68#123×C107—21no—
69#123×C107—21no—
70#123×C107—21no—
71#123×C107—21no—
72#123×C107—21no—
73#123×C107—21no—
74#123×C107—21no—
75#123×C107—21no—
76#123×C107C2×C411yescharacteristic
77#123×C107D411yescharacteristic
78C22⋊Q8×C107—21no—
79C22⋊Q8×C107—21no—
80C22⋊Q8×C107—21no—
81#121×C107—21no—
82#121×C107—21no—
83#121×C107—21no—
84#121×C107—21no—
85#121×C107—21no—
86#121×C107—21no—
87#121×C107—21no—
88#121×C107—21no—
89#121×C107—21no—
90#121×C107—21no—
91#121×C107—21no—
92#121×C107—21no—
93#121×C107—21no—
94#121×C107—21no—
95#121×C107—21no—
96#120×C107—21no—
97#120×C107—21no—
98#120×C107—21no—
99#120×C107—21no—
100#120×C107—21no—
101#120×C107—21no—
102#120×C107—21no—
103#120×C107—21no—
104#120×C107—21no—
105#120×C107—21no—
106#120×C107—21no—
107#120×C107—21no—
108#120×C107—21no—
109#120×C107—21no—
110#120×C107C2×C411yescharacteristic
111#120×C107C2×C411yescharacteristic
112#120×C107C2×C411yescharacteristic
113#120×C107D411yescharacteristic
114#120×C107D411yescharacteristic
115#120×C107D411yescharacteristic
116C4×D4×C107—21no—
117C4×D4×C107—21no—
118C4×D4×C107—21no—
119C4×D4×C107—21no—
120C4×D4×C107—21no—
121C4×D4×C107—21no—
122C4×D4×C107—42no—
123#117×C107—21no—
124#117×C107—21no—
125#117×C107D411yescharacteristic
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107—21no—
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—42no—
136C2×C22⋊C4×C107D411yescharacteristic
137C2×C22⋊C4×C107D411yescharacteristic
138#104×C107—42no—
139#100×C107—21no—
140#100×C107—21no—
141#99×C107—21no—
142#99×C107—21no—
143#99×C107—21no—
144#99×C107—21no—
145#99×C107—42no—
146C24×C107—21no—
147C24×C107—21no—
148C24×C107—21no—
149C24×C107—41no—
150C24×C107—41no—
151C24×C107—82no—
152C24×C107C22⋊C411yescharacteristic
153C24×C107C22⋊C411yescharacteristic
154C24×C107C22⋊C411yescharacteristic, complemented
155C24×C107C2×D411yescharacteristic
156C24×C107C2×D411yescharacteristic
157#41×C107—41no—
158#41×C107—41no—
159#41×C107—82no—
160C2×Q8×C107—21no—
161C2×Q8×C107C22⋊C411yescharacteristic, complemented
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—21no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—21no—
178C2×D4×C107—21no—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—41no—
183C2×D4×C107—41no—
184C2×D4×C107—41no—
185C2×D4×C107—41no—
186C2×D4×C107—82no—
187C2×D4×C107—82no—
188C2×D4×C107—82no—
189C2×D4×C107—82no—
190C2×D4×C107—81no—
191C2×D4×C107—81no—
192C2×D4×C107C22⋊C411yescharacteristic, complemented
193C2×D4×C107C22×C411yescharacteristic
194C2×D4×C107C2×D411yescharacteristic
195C2×D4×C107C2×D411yescharacteristic
196C2×D4×C107C2×D411yescharacteristic
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—22no—
206C22×C4×C107—41no—
207C22×C4×C107—41no—
208C22×C4×C107—41no—
209C22×C4×C107C22⋊C411yescharacteristic, complemented
210C22×C4×C107C2×D411yescharacteristic
211M16×C107—41no—
212M16×C107—41no—
213C2×C8×C107—41no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—41no—
224C22⋊C4×C107—21no—
225C22⋊C4×C107—21no—
226C22⋊C4×C107—21no—
227C22⋊C4×C107—21no—
228C22⋊C4×C107—21no—
229C22⋊C4×C107—21no—
230C22⋊C4×C107—21no—
231C22⋊C4×C107—21no—
232C22⋊C4×C107—21no—
233C22⋊C4×C107—21no—
234C22⋊C4×C107—21no—
235C22⋊C4×C107—21no—
236C22⋊C4×C107—21no—
237C22⋊C4×C107—21no—
238C22⋊C4×C107—21no—
239C22⋊C4×C107—21no—
240C22⋊C4×C107—21no—
241C22⋊C4×C107—21no—
242C22⋊C4×C107—21no—
243C22⋊C4×C107—21no—
244C22⋊C4×C107—21no—
245C22⋊C4×C107—21no—
246C22⋊C4×C107—21no—
247C22⋊C4×C107—21no—
248C22⋊C4×C107—21no—
249C22⋊C4×C107—22no—
250C22⋊C4×C107—41no—
251C22⋊C4×C107—41no—
252C22⋊C4×C107—41no—
253C22⋊C4×C107—41no—
254C22⋊C4×C107—41no—
255C22⋊C4×C107—41no—
256C22⋊C4×C107—84no—
257C22⋊C4×C107C22⋊C411yescharacteristic
258C22⋊C4×C107C22⋊C411yescharacteristic
259C22⋊C4×C107C22⋊C411yescharacteristic, complemented
260C22⋊C4×C107C22⋊C411yescharacteristic, complemented
261C42×C107—21no—
262C42×C107—21no—
263C42×C107—22no—
264C42×C107C22⋊C411yescharacteristic, complemented
265C42×C107C22⋊C411yescharacteristic, complemented
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—21no—
274C23×C107—42no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—42no—
278C23×C107—42no—
279C23×C107—42no—
280C23×C107—41no—
281C23×C107—44no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—81no—
285C23×C107—81no—
286C23×C107—81no—
287C23×C107—81no—
288C23×C107—81no—
289C23×C107—81no—
290C23×C107—81no—
291C23×C107—81no—
292C23×C107—81no—
293C23×C107—82no—
294C23×C107—82no—
295C23×C107—82no—
296C23×C107C2×C22⋊C411yescharacteristic
297C23×C107C2×C22⋊C411yescharacteristic
298C23×C107#12011yescharacteristic
299C23×C107#12011yescharacteristic
300C23×C107#12011yescharacteristic
301Q8×C107—41no—
302Q8×C107—81no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—41no—
308D4×C107—42no—
309D4×C107—42no—
310D4×C107—42no—
311D4×C107—42no—
312D4×C107—41no—
313D4×C107—41no—
314D4×C107—41no—
315D4×C107—41no—
316D4×C107—81no—
317D4×C107—81no—
318D4×C107—81no—
319D4×C107—81no—
320D4×C107—81no—
321D4×C107—81no—
322D4×C107—81no—
323D4×C107—81no—
324D4×C107—81no—
325D4×C107—81no—
326D4×C107—81no—
327D4×C107—81no—
328D4×C107—81no—
329D4×C107—81no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—21no—
336C2×C4×C107—21no—
337C2×C4×C107—21no—
338C2×C4×C107—21no—
339C2×C4×C107—21no—
340C2×C4×C107—42no—
341C2×C4×C107—41no—
342C2×C4×C107—42no—
343C2×C4×C107—81no—
344C2×C4×C107—81no—
345C2×C4×C107—81no—
346C2×C4×C107—81no—
347C2×C4×C107—81no—
348C2×C4×C107—81no—
349C2×C4×C107—81no—
350C2×C4×C107—82no—
351C2×C4×C107—81no—
352C2×C4×C107—81no—
353C2×C4×C107—82no—
354C2×C4×C107—161no—
355C2×C4×C107—161no—
356C2×C4×C107C2×C22⋊C411yescharacteristic
357C2×C4×C107#12011yescharacteristic
358C8×C107—81no—
359C22×C107—22no—
360C22×C107—21no—
361C22×C107—21no—
362C22×C107—21no—
363C22×C107—21no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—41no—
368C22×C107—41no—
369C22×C107—42no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—41no—
374C22×C107—41no—
375C22×C107—41no—
376C22×C107—41no—
377C22×C107—42no—
378C22×C107—41no—
379C22×C107—42no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107—81no—
386C22×C107—82no—
387C22×C107—82no—
388C22×C107—81no—
389C22×C107—84no—
390C22×C107—81no—
391C22×C107—161no—
392C22×C107—162no—
393C22×C107#37911yescharacteristic
394C22×C107B(4,𝔽2)11yescharacteristic
395C22×C107#45811yescharacteristic
396C4×C107—21no—
397C4×C107—21no—
398C4×C107—41no—
399C4×C107—41no—
400C4×C107—41no—
401C4×C107—41no—
402C4×C107—41no—
403C4×C107—41no—
404C4×C107—41no—
405C4×C107—41no—
406C4×C107—82no—
407C4×C107—161no—
408C4×C107—161no—
409#12753C10711yesmaximal, characteristic, direct product factor, Sylow
410C2×C107—21no—
411C2×C107—21no—
412C2×C107—21no—
413C2×C107—41no—
414C2×C107—41no—
415C2×C107—41no—
416C2×C107—42no—
417C2×C107—41no—
418C2×C107—81no—
419C2×C107—81no—
420C2×C107—81no—
421C2×C107#179011yescharacteristic
422#3532C2×C10711yescharacteristic
423#2127C2×C10711yescharacteristic, complemented
424#2121C2×C10711yescharacteristic, complemented
425C2×AΣL(1,𝔽16)C2×C10711yescharacteristic, complemented
426#1913C2×C10711yescharacteristic, complemented
427#1911C2×C10711yescharacteristic, complemented
428#1889C2×C10711yescharacteristic, complemented
429C107#1275311yescharacteristic, direct product factor, Sylow
430H(3,𝔽4)C4×C10711yescharacteristic, complemented
431#560—21no—
432#560C4×C10711yescharacteristic, complemented
433#551—21no—
434#551C4×C10711yescharacteristic, complemented
435#546—21no—
436#546—21no—
437#546—21no—
438D42—21no—
439D42C4×C10711yescharacteristic, complemented
440#538—21no—
441#538—21no—
442#538—21no—
443#535—21no—
444#535C22×C10711yescharacteristic
445#534—21no—
446#534C22×C10711yescharacteristic
447C2×#120—21no—
448C2×#120C22×C10711yescharacteristic
449#518C22×C10711yescharacteristic, complemented
450#421—21no—
451C2×#100C22×C10711yescharacteristic, complemented
452C2×#99—21no—
453C2×#99C22×C10711yescharacteristic, complemented
454C2×#99C22×C10711yescharacteristic, complemented
455#379—21no—
456#354—21no—
457#353—21no—
458#352—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461AΣL(1,𝔽16)—21no—
462#342—21no—
463#342—21no—
464H(3,ℤ/4)—21no—
465C25D4×C10711yescharacteristic
466C2×#41—21no—
467C2×#41D4×C10711yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C10711yescharacteristic
474C22×D4C23×C10711yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C10711yescharacteristic
478#127D4×C10711yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C10711yescharacteristic
489#124D4×C10711yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C10711yescharacteristic
499#123D4×C10711yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C10711yescharacteristic
533#120C2×C4×C10711yescharacteristic
534#120C2×C4×C10711yescharacteristic
535#120D4×C10711yescharacteristic
536#120D4×C10711yescharacteristic
537#120D4×C10711yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C10711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C10711yescharacteristic
559C2×C22⋊C4D4×C10711yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C10711yescharacteristic
575C24C22⋊C4×C10711yescharacteristic
576C24C22⋊C4×C10711yescharacteristic, complemented
577C24C2×D4×C10711yescharacteristic
578C24C2×D4×C10711yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C10711yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C10711yescharacteristic, complemented
615C2×D4C22×C4×C10711yescharacteristic
616C2×D4C2×D4×C10711yescharacteristic
617C2×D4C2×D4×C10711yescharacteristic
618C2×D4C2×D4×C10711yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C10711yescharacteristic, complemented
632C22×C4C2×D4×C10711yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C10711yescharacteristic
680C22⋊C4C22⋊C4×C10711yescharacteristic
681C22⋊C4C22⋊C4×C10711yescharacteristic, complemented
682C22⋊C4C22⋊C4×C10711yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C10711yescharacteristic, complemented
687C42C22⋊C4×C10711yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C10711yescharacteristic
719C23C2×C22⋊C4×C10711yescharacteristic
720C23#120×C10711yescharacteristic
721C23#120×C10711yescharacteristic
722C23#120×C10711yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C10711yescharacteristic
779C2×C4#120×C10711yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22#379×C10711yescharacteristic
816C22B(4,𝔽2)×C10711yescharacteristic
817C22#458×C10711yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C107×#179011yescharacteristic
subgroupG/H
center, socleC2×C107#1790
commutatorC2×D4C22×C4×C107
Frattini, cosocleC22×D4C23×C107
prime radicalC107×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C23×C107 ◁ C22×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2127C2semidirect
3. C107×#2121C2semidirect
4. C2×AΣL(1,𝔽16)×C107C2semidirect
5. C107×#1913C2semidirect
6. C107×#1911C2semidirect
7. C107×#1889C2semidirect
8. H(3,𝔽4)×C107C4semidirect
10. #560×C107C4semidirect
12. #551×C107C4semidirect
17. D42×C107C4semidirect
27. #518×C107C22semidirect
29. C2×#100×C107C22semidirect
31. C2×#99×C107C22semidirect
32. C2×#99×C107C22semidirect
154. C24×C107C22⋊C4semidirect
161. C2×Q8×C107C22⋊C4semidirect
192. C2×D4×C107C22⋊C4semidirect
209. C22×C4×C107C22⋊C4semidirect
259. C22⋊C4×C107C22⋊C4semidirect
260. C22⋊C4×C107C22⋊C4semidirect
264. C42×C107C22⋊C4semidirect
265. C42×C107C22⋊C4semidirect
409. #12753C107direct (N × H)
423. #2127C2×C107semidirect
424. #2121C2×C107semidirect
425. C2×AΣL(1,𝔽16)C2×C107semidirect
426. #1913C2×C107semidirect
427. #1911C2×C107semidirect
428. #1889C2×C107semidirect
429. C107#12753direct (N × H)
430. H(3,𝔽4)C4×C107semidirect
432. #560C4×C107semidirect
434. #551C4×C107semidirect
439. D42C4×C107semidirect
449. #518C22×C107semidirect
451. C2×#100C22×C107semidirect
453. C2×#99C22×C107semidirect
454. C2×#99C22×C107semidirect
576. C24C22⋊C4×C107semidirect
583. C2×Q8C22⋊C4×C107semidirect
614. C2×D4C22⋊C4×C107semidirect
631. C22×C4C22⋊C4×C107semidirect
681. C22⋊C4C22⋊C4×C107semidirect
682. C22⋊C4C22⋊C4×C107semidirect
686. C42C22⋊C4×C107semidirect
687. C42C22⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35322
C107×#21272
C107×#21212
C2×AΣL(1,𝔽16)×C1072
C107×#19132
C107×#19112
C107×#18892
#12753107