Finite Group Databasebeta

← C107×#33551 #41059515

Subgroups — C107×#33551 #41059515

Order 27392.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3532C211yesmaximal, characteristic, complemented
2C107×#3026C211yesmaximal, characteristic, complemented
3C2×B(4,𝔽2)×C107C211yesmaximal, characteristic, complemented
4C107×#3019C211yesmaximal, characteristic, complemented
5C107×#2200C212yesmaximal, complemented
6C107×#2199C212yesmaximal, complemented
7C107×#2197C212yesmaximal, complemented
8C107×#2196C212yesmaximal, complemented
9C107×#2127C211yesmaximal, characteristic, complemented
10C107×#2121C211yesmaximal, characteristic, complemented
11C2×AΣL(1,𝔽16)×C107C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C107C2211yescharacteristic, complemented
13#575×C107—21no—
14H(3,𝔽4)×C107C2211yescharacteristic, complemented
15#560×C107—21no—
16#560×C107C2211yescharacteristic, complemented
17#551×C107—21no—
18#551×C107C2211yescharacteristic, complemented
19#546×C107—21no—
20#546×C107—21no—
21#546×C107—21no—
22D42×C107—21no—
23D42×C107C2211yescharacteristic, complemented
24#538×C107—21no—
25#538×C107—21no—
26#538×C107—21no—
27#535×C107—21no—
28#535×C107C2211yescharacteristic
29#534×C107—21no—
30#534×C107—21no—
31#534×C107C2211yescharacteristic
32C2×#120×C107—21no—
33C2×#120×C107—21no—
34C2×#120×C107C2211yescharacteristic
35#458×C107—21no—
36#458×C107C2212yescomplemented
37B(4,𝔽2)×C107—21no—
38B(4,𝔽2)×C107—21no—
39B(4,𝔽2)×C107—21no—
40B(4,𝔽2)×C107C2212yes—
41B(4,𝔽2)×C107C2212yescomplemented
42B(4,𝔽2)×C107C2212yescomplemented
43#455×C107—21no—
44#455×C107C2212yescomplemented
45#453×C107—21no—
46#453×C107C2212yescomplemented
47#421×C107—21no—
48C2×#100×C107C2211yescharacteristic, complemented
49C2×#99×C107—21no—
50C2×#99×C107—21no—
51C2×#99×C107C2211yescharacteristic, complemented
52C2×#99×C107C2211yescharacteristic, complemented
53#354×C107C2212yescomplemented
54#353×C107C2212yescomplemented
55#352×C107C2212yescomplemented
56AΣL(1,𝔽16)×C107C2212yescomplemented
57AΣL(1,𝔽16)×C107C2212yescomplemented
58AΣL(1,𝔽16)×C107C2212yescomplemented
59C25×C107D411yescharacteristic, complemented
60H(5,𝔽2)×C107—21no—
61H(5,𝔽2)×C107—21no—
62H(5,𝔽2)×C107—21no—
63H(5,𝔽2)×C107—42no—
64H(5,𝔽2)×C107C2312yes—
65C2×#41×C107—21no—
66C2×#41×C107—21no—
67C2×#41×C107—41no—
68C2×#41×C107D411yescharacteristic, complemented
69C22×D4×C107—21no—
70C22×D4×C107—21no—
71C22×D4×C107—21no—
72C22×D4×C107—21no—
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—41no—
77C22×D4×C107—41no—
78C22×D4×C107D411yescharacteristic, complemented
79C22×D4×C107C2311yescharacteristic
80#137×C107—22no—
81#137×C107—41no—
82AGL(1,ℤ/8)×C107—22no—
83AGL(1,ℤ/8)×C107—41no—
84#135×C107—42no—
85C2×M16×C107—21no—
86#127×C107—21no—
87#127×C107D411yescharacteristic, complemented
88#127×C107C2311yescharacteristic
89#126×C107—21no—
90#126×C107—21no—
91#126×C107—21no—
92#126×C107—21no—
93#124×C107—21no—
94#124×C107—21no—
95#124×C107—21no—
96#124×C107—21no—
97#124×C107—21no—
98#124×C107D411yescharacteristic, complemented
99#124×C107C2311yescharacteristic
100#123×C107—21no—
101#123×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108#123×C107—22no—
109#123×C107—41no—
110#123×C107D411yescharacteristic, complemented
111#123×C107C2311yescharacteristic
112C22⋊Q8×C107—21no—
113C22⋊Q8×C107—21no—
114C22⋊Q8×C107—21no—
115#121×C107—21no—
116#121×C107—21no—
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—21no—
130#121×C107—42no—
131#120×C107—21no—
132#120×C107—21no—
133#120×C107—21no—
134#120×C107—21no—
135#120×C107—21no—
136#120×C107—21no—
137#120×C107—21no—
138#120×C107—21no—
139#120×C107—21no—
140#120×C107—21no—
141#120×C107—21no—
142#120×C107—21no—
143#120×C107—21no—
144#120×C107—21no—
145#120×C107—22no—
146#120×C107—22no—
147#120×C107—22no—
148#120×C107—42no—
149#120×C107—41no—
150#120×C107D411yescharacteristic, complemented
151#120×C107D411yescharacteristic, complemented
152#120×C107D411yescharacteristic, complemented
153#120×C107C2311yescharacteristic
154#120×C107C2311yescharacteristic
155#120×C107C2311yescharacteristic
156C4×D4×C107—21no—
157C4×D4×C107—21no—
158C4×D4×C107—21no—
159C4×D4×C107—21no—
160C4×D4×C107—21no—
161C4×D4×C107—21no—
162#117×C107—21no—
163#117×C107D411yescharacteristic, complemented
164C2×C22⋊C4×C107—21no—
165C2×C22⋊C4×C107—21no—
166C2×C22⋊C4×C107—21no—
167C2×C22⋊C4×C107—21no—
168C2×C22⋊C4×C107—21no—
169C2×C22⋊C4×C107—21no—
170C2×C22⋊C4×C107—21no—
171C2×C22⋊C4×C107—41no—
172C2×C22⋊C4×C107D411yescharacteristic, complemented
173C2×C22⋊C4×C107D411yescharacteristic, complemented
174#104×C107—22no—
175#104×C107—22no—
176#100×C107—21no—
177#100×C107C2312yes—
178#99×C107—21no—
179#99×C107—21no—
180#99×C107—22no—
181#99×C107—22no—
182#99×C107—22no—
183#99×C107—22no—
184#99×C107C2312yes—
185#99×C107C2312yes—
186C24×C107—21no—
187C24×C107—21no—
188C24×C107—21no—
189C24×C107—21no—
190C24×C107—21no—
191C24×C107—41no—
192C24×C107—41no—
193C24×C107—82no—
194C24×C107C2×D411yescharacteristic
195C24×C107C2×D411yescharacteristic
196C24×C107C2×D411yescharacteristic
197C24×C107C2×D411yescharacteristic
198C24×C107C2×D411yescharacteristic, complemented
199#41×C107—22no—
200#41×C107—22no—
201#41×C107—42no—
202#41×C107—41no—
203#41×C107—42no—
204#41×C107—42no—
205#41×C107—41no—
206#41×C107—41no—
207#41×C107—42no—
208#41×C107—41no—
209#41×C107—82no—
210C2×Q8×C107—21no—
211C2×Q8×C107—21no—
212C2×Q8×C107C2×D411yescharacteristic, complemented
213C2×D4×C107—21no—
214C2×D4×C107—21no—
215C2×D4×C107—21no—
216C2×D4×C107—22no—
217C2×D4×C107—22no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—22no—
222C2×D4×C107—22no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—21no—
232C2×D4×C107—21no—
233C2×D4×C107—21no—
234C2×D4×C107—21no—
235C2×D4×C107—21no—
236C2×D4×C107—21no—
237C2×D4×C107—21no—
238C2×D4×C107—41no—
239C2×D4×C107—41no—
240C2×D4×C107—42no—
241C2×D4×C107—42no—
242C2×D4×C107—41no—
243C2×D4×C107—41no—
244C2×D4×C107—41no—
245C2×D4×C107—41no—
246C2×D4×C107—42no—
247C2×D4×C107—42no—
248C2×D4×C107—41no—
249C2×D4×C107—41no—
250C2×D4×C107—41no—
251C2×D4×C107—41no—
252C2×D4×C107—41no—
253C2×D4×C107—42no—
254C2×D4×C107—42no—
255C2×D4×C107—42no—
256C2×D4×C107—82no—
257C2×D4×C107—82no—
258C2×D4×C107—82no—
259C2×D4×C107—82no—
260C2×D4×C107—81no—
261C2×D4×C107—81no—
262C2×D4×C107—84no—
263C2×D4×C107C2×D411yescharacteristic
264C2×D4×C107C2×D411yescharacteristic
265C2×D4×C107C2×D411yescharacteristic
266C2×D4×C107C2×D411yescharacteristic, complemented
267C2×D4×C107C2411yescharacteristic
268C22×C4×C107—21no—
269C22×C4×C107—21no—
270C22×C4×C107—21no—
271C22×C4×C107—21no—
272C22×C4×C107—21no—
273C22×C4×C107—21no—
274C22×C4×C107—21no—
275C22×C4×C107—21no—
276C22×C4×C107—21no—
277C22×C4×C107—21no—
278C22×C4×C107—41no—
279C22×C4×C107—41no—
280C22×C4×C107—41no—
281C22×C4×C107C2×D411yescharacteristic
282C22×C4×C107C2×D411yescharacteristic, complemented
283Q16×C107—42no—
284SD16×C107—42no—
285SD16×C107—42no—
286D8×C107—42no—
287M16×C107—22no—
288M16×C107—41no—
289C2×C8×C107—41no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—21no—
292C4⋊C4×C107—21no—
293C4⋊C4×C107—21no—
294C4⋊C4×C107—21no—
295C4⋊C4×C107—21no—
296C4⋊C4×C107—21no—
297C4⋊C4×C107—21no—
298C4⋊C4×C107—21no—
299C4⋊C4×C107—42no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—21no—
317C22⋊C4×C107—21no—
318C22⋊C4×C107—21no—
319C22⋊C4×C107—21no—
320C22⋊C4×C107—21no—
321C22⋊C4×C107—21no—
322C22⋊C4×C107—21no—
323C22⋊C4×C107—21no—
324C22⋊C4×C107—21no—
325C22⋊C4×C107—22no—
326C22⋊C4×C107—22no—
327C22⋊C4×C107—42no—
328C22⋊C4×C107—42no—
329C22⋊C4×C107—42no—
330C22⋊C4×C107—41no—
331C22⋊C4×C107—41no—
332C22⋊C4×C107—42no—
333C22⋊C4×C107C2×D411yescharacteristic
334C22⋊C4×C107C2×D411yescharacteristic
335C22⋊C4×C107C2×D411yescharacteristic, complemented
336C22⋊C4×C107C2×D411yescharacteristic, complemented
337C42×C107—21no—
338C42×C107—21no—
339C42×C107C2×D411yescharacteristic, complemented
340C42×C107C2×D411yescharacteristic, complemented
341C23×C107—21no—
342C23×C107—21no—
343C23×C107—21no—
344C23×C107—21no—
345C23×C107—21no—
346C23×C107—22no—
347C23×C107—22no—
348C23×C107—21no—
349C23×C107—21no—
350C23×C107—21no—
351C23×C107—41no—
352C23×C107—41no—
353C23×C107—42no—
354C23×C107—42no—
355C23×C107—42no—
356C23×C107—41no—
357C23×C107—41no—
358C23×C107—42no—
359C23×C107—41no—
360C23×C107—44no—
361C23×C107—41no—
362C23×C107—41no—
363C23×C107—41no—
364C23×C107—81no—
365C23×C107—81no—
366C23×C107—81no—
367C23×C107—81no—
368C23×C107—81no—
369C23×C107—81no—
370C23×C107—81no—
371C23×C107—81no—
372C23×C107—81no—
373C23×C107—82no—
374C23×C107—82no—
375C23×C107—82no—
376C23×C107—82no—
377C23×C107—161no—
378C23×C107#12011yescharacteristic
379C23×C107#12011yescharacteristic
380C23×C107#12011yescharacteristic
381C23×C107C22×D411yescharacteristic
382C23×C107C22×D411yescharacteristic
383Q8×C107—22no—
384Q8×C107—41no—
385Q8×C107—41no—
386Q8×C107—81no—
387D4×C107—22no—
388D4×C107—41no—
389D4×C107—41no—
390D4×C107—41no—
391D4×C107—41no—
392D4×C107—41no—
393D4×C107—41no—
394D4×C107—42no—
395D4×C107—42no—
396D4×C107—42no—
397D4×C107—42no—
398D4×C107—42no—
399D4×C107—42no—
400D4×C107—42no—
401D4×C107—42no—
402D4×C107—42no—
403D4×C107—42no—
404D4×C107—41no—
405D4×C107—41no—
406D4×C107—41no—
407D4×C107—41no—
408D4×C107—81no—
409D4×C107—81no—
410D4×C107—81no—
411D4×C107—81no—
412D4×C107—81no—
413D4×C107—81no—
414D4×C107—81no—
415D4×C107—81no—
416D4×C107—81no—
417D4×C107—81no—
418D4×C107—81no—
419D4×C107—81no—
420D4×C107—81no—
421D4×C107—81no—
422D4×C107—84no—
423D4×C107—84no—
424D4×C107—162no—
425C2×C4×C107—21no—
426C2×C4×C107—21no—
427C2×C4×C107—22no—
428C2×C4×C107—22no—
429C2×C4×C107—21no—
430C2×C4×C107—21no—
431C2×C4×C107—21no—
432C2×C4×C107—21no—
433C2×C4×C107—21no—
434C2×C4×C107—21no—
435C2×C4×C107—21no—
436C2×C4×C107—21no—
437C2×C4×C107—42no—
438C2×C4×C107—42no—
439C2×C4×C107—41no—
440C2×C4×C107—41no—
441C2×C4×C107—42no—
442C2×C4×C107—41no—
443C2×C4×C107—41no—
444C2×C4×C107—42no—
445C2×C4×C107—42no—
446C2×C4×C107—81no—
447C2×C4×C107—81no—
448C2×C4×C107—81no—
449C2×C4×C107—81no—
450C2×C4×C107—81no—
451C2×C4×C107—81no—
452C2×C4×C107—81no—
453C2×C4×C107—82no—
454C2×C4×C107—161no—
455C2×C4×C107#12011yescharacteristic
456C2×C4×C107C22×D411yescharacteristic
457C8×C107—42no—
458C22×C107—22no—
459C22×C107—21no—
460C22×C107—21no—
461C22×C107—21no—
462C22×C107—21no—
463C22×C107—41no—
464C22×C107—41no—
465C22×C107—41no—
466C22×C107—41no—
467C22×C107—41no—
468C22×C107—41no—
469C22×C107—42no—
470C22×C107—41no—
471C22×C107—41no—
472C22×C107—41no—
473C22×C107—41no—
474C22×C107—41no—
475C22×C107—41no—
476C22×C107—42no—
477C22×C107—41no—
478C22×C107—42no—
479C22×C107—42no—
480C22×C107—41no—
481C22×C107—41no—
482C22×C107—41no—
483C22×C107—81no—
484C22×C107—81no—
485C22×C107—81no—
486C22×C107—82no—
487C22×C107—82no—
488C22×C107—82no—
489C22×C107—81no—
490C22×C107—84no—
491C22×C107—82no—
492C22×C107—82no—
493C22×C107—82no—
494C22×C107—81no—
495C22×C107—162no—
496C22×C107—161no—
497C22×C107—161no—
498C22×C107B(4,𝔽2)11yescharacteristic
499C22×C107B(4,𝔽2)11yescharacteristic
500C22×C107C2×#12011yescharacteristic
501C4×C107—21no—
502C4×C107—21no—
503C4×C107—41no—
504C4×C107—41no—
505C4×C107—41no—
506C4×C107—41no—
507C4×C107—41no—
508C4×C107—41no—
509C4×C107—42no—
510C4×C107—41no—
511C4×C107—41no—
512C4×C107—82no—
513C4×C107—82no—
514#33551C10711yesmaximal, characteristic, direct product factor, Sylow
515C2×C107—21no—
516C2×C107—21no—
517C2×C107—21no—
518C2×C107—41no—
519C2×C107—41no—
520C2×C107—42no—
521C2×C107—41no—
522C2×C107—41no—
523C2×C107—81no—
524C2×C107—81no—
525C2×C107—81no—
526C2×C107—82no—
527C2×C107C2×B(4,𝔽2)11yescharacteristic
528#3532C2×C10711yescharacteristic, complemented
529#3026C2×C10711yescharacteristic, complemented
530C2×B(4,𝔽2)C2×C10711yescharacteristic, complemented
531#3019C2×C10711yescharacteristic, complemented
532#2200C2×C10712yescomplemented
533#2199C2×C10712yescomplemented
534#2197C2×C10712yescomplemented
535#2196C2×C10712yescomplemented
536#2127C2×C10711yescharacteristic, complemented
537#2121C2×C10711yescharacteristic, complemented
538C2×AΣL(1,𝔽16)C2×C10711yescharacteristic, complemented
539C107#3355111yescharacteristic, direct product factor, Sylow
540C2×H(5,𝔽2)C22×C10711yescharacteristic, complemented
541#575—21no—
542H(3,𝔽4)C22×C10711yescharacteristic, complemented
543#560—21no—
544#560C22×C10711yescharacteristic, complemented
545#551—21no—
546#551C22×C10711yescharacteristic, complemented
547#546—21no—
548#546—21no—
549#546—21no—
550D42—21no—
551D42C22×C10711yescharacteristic, complemented
552#538—21no—
553#538—21no—
554#538—21no—
555#535—21no—
556#535C22×C10711yescharacteristic
557#534—21no—
558#534—21no—
559#534C22×C10711yescharacteristic
560C2×#120—21no—
561C2×#120—21no—
562C2×#120C22×C10711yescharacteristic
563#458—21no—
564#458C22×C10712yescomplemented
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)—21no—
568B(4,𝔽2)C22×C10712yes—
569B(4,𝔽2)C22×C10712yescomplemented
570B(4,𝔽2)C22×C10712yescomplemented
571#455—21no—
572#455C22×C10712yescomplemented
573#453—21no—
574#453C22×C10712yescomplemented
575#421—21no—
576C2×#100C22×C10711yescharacteristic, complemented
577C2×#99—21no—
578C2×#99—21no—
579C2×#99C22×C10711yescharacteristic, complemented
580C2×#99C22×C10711yescharacteristic, complemented
581#354C22×C10712yescomplemented
582#353C22×C10712yescomplemented
583#352C22×C10712yescomplemented
584AΣL(1,𝔽16)C22×C10712yescomplemented
585AΣL(1,𝔽16)C22×C10712yescomplemented
586AΣL(1,𝔽16)C22×C10712yescomplemented
587C25D4×C10711yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C10712yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C10711yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C10711yescharacteristic, complemented
607C22×D4C23×C10711yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C10711yescharacteristic, complemented
616#127C23×C10711yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C10711yescharacteristic, complemented
627#124C23×C10711yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C10711yescharacteristic, complemented
639#123C23×C10711yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C10711yescharacteristic, complemented
679#120D4×C10711yescharacteristic, complemented
680#120D4×C10711yescharacteristic, complemented
681#120C23×C10711yescharacteristic
682#120C23×C10711yescharacteristic
683#120C23×C10711yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C10711yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C10711yescharacteristic, complemented
701C2×C22⋊C4D4×C10711yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C10712yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C10712yes—
713#99C23×C10712yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C10711yescharacteristic
723C24C2×D4×C10711yescharacteristic
724C24C2×D4×C10711yescharacteristic
725C24C2×D4×C10711yescharacteristic
726C24C2×D4×C10711yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C10711yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C10711yescharacteristic
792C2×D4C2×D4×C10711yescharacteristic
793C2×D4C2×D4×C10711yescharacteristic
794C2×D4C2×D4×C10711yescharacteristic, complemented
795C2×D4C24×C10711yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C10711yescharacteristic
810C22×C4C2×D4×C10711yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C10711yescharacteristic
862C22⋊C4C2×D4×C10711yescharacteristic
863C22⋊C4C2×D4×C10711yescharacteristic, complemented
864C22⋊C4C2×D4×C10711yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C10711yescharacteristic, complemented
868C42C2×D4×C10711yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C10711yescharacteristic
907C23#120×C10711yescharacteristic
908C23#120×C10711yescharacteristic
909C23C22×D4×C10711yescharacteristic
910C23C22×D4×C10711yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
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—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C10711yescharacteristic
984C2×C4C22×D4×C10711yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22B(4,𝔽2)×C10711yescharacteristic
1027C22B(4,𝔽2)×C10711yescharacteristic
1028C22C2×#120×C10711yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×B(4,𝔽2)×C10711yescharacteristic
subgroupG/H
center, socleC2×C107C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C107
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
1. C107×#3532C2semidirect
2. C107×#3026C2semidirect
3. C2×B(4,𝔽2)×C107C2semidirect
4. C107×#3019C2semidirect
5. C107×#2200C2semidirect
6. C107×#2199C2semidirect
7. C107×#2197C2semidirect
8. C107×#2196C2semidirect
9. C107×#2127C2semidirect
10. C107×#2121C2semidirect
11. C2×AΣL(1,𝔽16)×C107C2semidirect
12. C2×H(5,𝔽2)×C107C22semidirect
14. H(3,𝔽4)×C107C22semidirect
16. #560×C107C22semidirect
18. #551×C107C22semidirect
23. D42×C107C22semidirect
36. #458×C107C22semidirect
41. B(4,𝔽2)×C107C22semidirect
42. B(4,𝔽2)×C107C22semidirect
44. #455×C107C22semidirect
46. #453×C107C22semidirect
48. C2×#100×C107C22semidirect
51. C2×#99×C107C22semidirect
52. C2×#99×C107C22semidirect
53. #354×C107C22semidirect
54. #353×C107C22semidirect
55. #352×C107C22semidirect
56. AΣL(1,𝔽16)×C107C22semidirect
57. AΣL(1,𝔽16)×C107C22semidirect
58. AΣL(1,𝔽16)×C107C22semidirect
59. C25×C107D4semidirect
68. C2×#41×C107D4semidirect
78. C22×D4×C107D4semidirect
87. #127×C107D4semidirect
98. #124×C107D4semidirect
110. #123×C107D4semidirect
150. #120×C107D4semidirect
151. #120×C107D4semidirect
152. #120×C107D4semidirect
163. #117×C107D4semidirect
172. C2×C22⋊C4×C107D4semidirect
173. C2×C22⋊C4×C107D4semidirect
198. C24×C107C2×D4semidirect
212. C2×Q8×C107C2×D4semidirect
266. C2×D4×C107C2×D4semidirect
282. C22×C4×C107C2×D4semidirect
335. C22⋊C4×C107C2×D4semidirect
336. C22⋊C4×C107C2×D4semidirect
339. C42×C107C2×D4semidirect
340. C42×C107C2×D4semidirect
514. #33551C107direct (N × H)
528. #3532C2×C107semidirect
529. #3026C2×C107semidirect
530. C2×B(4,𝔽2)C2×C107semidirect
531. #3019C2×C107semidirect
532. #2200C2×C107semidirect
533. #2199C2×C107semidirect
534. #2197C2×C107semidirect
535. #2196C2×C107semidirect
536. #2127C2×C107semidirect
537. #2121C2×C107semidirect
538. C2×AΣL(1,𝔽16)C2×C107semidirect
539. C107#33551direct (N × H)
540. C2×H(5,𝔽2)C22×C107semidirect
542. H(3,𝔽4)C22×C107semidirect
544. #560C22×C107semidirect
546. #551C22×C107semidirect
551. D42C22×C107semidirect
564. #458C22×C107semidirect
569. B(4,𝔽2)C22×C107semidirect
570. B(4,𝔽2)C22×C107semidirect
572. #455C22×C107semidirect
574. #453C22×C107semidirect
576. C2×#100C22×C107semidirect
579. C2×#99C22×C107semidirect
580. C2×#99C22×C107semidirect
581. #354C22×C107semidirect
582. #353C22×C107semidirect
583. #352C22×C107semidirect
584. AΣL(1,𝔽16)C22×C107semidirect
585. AΣL(1,𝔽16)C22×C107semidirect
586. AΣL(1,𝔽16)C22×C107semidirect
587. C25D4×C107semidirect
596. C2×#41D4×C107semidirect
606. C22×D4D4×C107semidirect
615. #127D4×C107semidirect
626. #124D4×C107semidirect
638. #123D4×C107semidirect
678. #120D4×C107semidirect
679. #120D4×C107semidirect
680. #120D4×C107semidirect
691. #117D4×C107semidirect
700. C2×C22⋊C4D4×C107semidirect
701. C2×C22⋊C4D4×C107semidirect
726. C24C2×D4×C107semidirect
740. C2×Q8C2×D4×C107semidirect
794. C2×D4C2×D4×C107semidirect
810. C22×C4C2×D4×C107semidirect
863. C22⋊C4C2×D4×C107semidirect
864. C22⋊C4C2×D4×C107semidirect
867. C42C2×D4×C107semidirect
868. C42C2×D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35322
C107×#30262
C2×B(4,𝔽2)×C1072
C107×#30192
C107×#22002
C107×#21992
C107×#21972
C107×#21962
C107×#21272
C107×#21212
C2×AΣL(1,𝔽16)×C1072
#33551107