Finite Group Databasebeta

← C107×#33553 #41059517

Subgroups — C107×#33553 #41059517

Order 27392.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3537C211yesmaximal, characteristic, complemented
2C107×#3027C211yesmaximal, characteristic, complemented
3C107×#3025C211yesmaximal, characteristic, complemented
4C107×#3021C211yesmaximal, characteristic, complemented
5C107×#2200C214yesmaximal, complemented
6C107×#2196C214yesmaximal, complemented
7C107×#2128C211yesmaximal, characteristic, complemented
8C107×#2122C211yesmaximal, characteristic, complemented
9C107×#2120C211yesmaximal, characteristic, complemented
10#585×C107C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C107—21no—
12#560×C107—21no—
13#560×C107C2212yescomplemented
14#553×C107—21no—
15#553×C107—21no—
16D42×C107—21no—
17D42×C107—21no—
18D42×C107—21no—
19D42×C107C2212yescomplemented
20#540×C107—21no—
21#538×C107—22no—
22#535×C107—21no—
23#535×C107C2211yescharacteristic
24#535×C107C2211yescharacteristic
25#534×C107—22no—
26#525×C107—21no—
27#525×C107C2211yescharacteristic
28C2×#121×C107—21no—
29#458×C107—21no—
30#458×C107C2212yescomplemented
31B(4,𝔽2)×C107—21no—
32B(4,𝔽2)×C107—22no—
33B(4,𝔽2)×C107C2212yescomplemented
34B(4,𝔽2)×C107C2214yescomplemented
35#454×C107—22no—
36#453×C107C2214yescomplemented
37#421×C107—21no—
38#413×C107C2211yescharacteristic, complemented
39#410×C107—21no—
40#410×C107—21no—
41#410×C107C2211yescharacteristic, complemented
42#410×C107C2211yescharacteristic, complemented
43#353×C107C2214yescomplemented
44#352×C107C2212yescomplemented
45AΣL(1,𝔽16)×C107C2212yescomplemented
46AΣL(1,𝔽16)×C107C2214yescomplemented
472−1+4×C107—21no—
482−1+4×C107—41no—
49H(5,𝔽2)×C107—21no—
50H(5,𝔽2)×C107—21no—
51H(5,𝔽2)×C107—41no—
52H(5,𝔽2)×C107C2312yes—
53C2×#41×C107—21no—
54C2×#41×C107—21no—
55C2×#41×C107—21no—
56C2×#41×C107—42no—
57C2×#41×C107C2311yescharacteristic
58C22×D4×C107—21no—
59C22×D4×C107—22no—
60C22×D4×C107—22no—
61C22×D4×C107—22no—
62C22×D4×C107D411yescharacteristic, complemented
63C22×D4×C107D411yescharacteristic, complemented
64C23×C4×C107D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C107—24no—
66AGL(1,ℤ/8)×C107—42no—
67C2×SD16×C107—41no—
68C2×D8×C107—41no—
69C2×M16×C107—21no—
70#127×C107—21no—
71#127×C107—21no—
72#127×C107—41no—
73#127×C107C2312yes—
74#126×C107—22no—
75#126×C107—22no—
76#125×C107—21no—
77#124×C107—21no—
78#124×C107—41no—
79#124×C107D412yescomplemented
80#123×C107—22no—
81#123×C107—22no—
82#123×C107—22no—
83#123×C107—22no—
84#123×C107—22no—
85#123×C107D411yescharacteristic, complemented
86#123×C107C2311yescharacteristic
87C22⋊Q8×C107—21no—
88C22⋊Q8×C107—41no—
89#121×C107—22no—
90#121×C107—21no—
91#121×C107—21no—
92#121×C107—22no—
93#121×C107—22no—
94#121×C107—21no—
95#121×C107—22no—
96#121×C107—21no—
97#121×C107—21no—
98#121×C107—22no—
99#121×C107—21no—
100#121×C107—21no—
101#121×C107—22no—
102#121×C107—22no—
103#121×C107—22no—
104#121×C107—42no—
105#121×C107—41no—
106#120×C107—22no—
107#120×C107—22no—
108#120×C107—22no—
109#120×C107—21no—
110#120×C107—21no—
111#120×C107—22no—
112#120×C107—22no—
113#120×C107—24no—
114#120×C107D411yescharacteristic, complemented
115#120×C107D412yescomplemented
116#120×C107C2311yescharacteristic
117#120×C107C2312yes—
118C4×D4×C107—22no—
119C4×D4×C107—21no—
120C4×D4×C107—21no—
121C4×D4×C107—21no—
122C4×D4×C107—21no—
123C4×D4×C107—22no—
124C4×D4×C107—42no—
125#117×C107—21no—
126#117×C107—21no—
127#117×C107D411yescharacteristic, complemented
128#117×C107D411yescharacteristic, complemented
129#117×C107D411yescharacteristic, complemented
130C2×C4⋊C4×C107—21no—
131C2×C22⋊C4×C107—22no—
132#104×C107—24no—
133#101×C107—21no—
134#100×C107C2312yes—
135#99×C107—21no—
136#99×C107—21no—
137#99×C107—24no—
138#99×C107—22no—
139#99×C107—22no—
140#99×C107C2312yes—
141#99×C107C2312yes—
142C24×C107—22no—
143C24×C107—21no—
144C24×C107C2×D411yescharacteristic
145C24×C107C2×D412yes—
146#41×C107—22no—
147#41×C107—22no—
148#41×C107—41no—
149#41×C107—41no—
150#41×C107—42no—
151#41×C107—41no—
152#41×C107—41no—
153#41×C107—41no—
154#41×C107—41no—
155#41×C107—41no—
156#41×C107—42no—
157#41×C107—42no—
158#41×C107—42no—
159#41×C107—41no—
160#41×C107—41no—
161#41×C107—41no—
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107—21no—
165C2×Q8×C107—42no—
166C2×Q8×C107C2×D411yescharacteristic
167C2×D4×C107—21no—
168C2×D4×C107—22no—
169C2×D4×C107—22no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—22no—
174C2×D4×C107—22no—
175C2×D4×C107—21no—
176C2×D4×C107—22no—
177C2×D4×C107—22no—
178C2×D4×C107—22no—
179C2×D4×C107—22no—
180C2×D4×C107—22no—
181C2×D4×C107—22no—
182C2×D4×C107—22no—
183C2×D4×C107—21no—
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—41no—
187C2×D4×C107—41no—
188C2×D4×C107—41no—
189C2×D4×C107—41no—
190C2×D4×C107—42no—
191C2×D4×C107—42no—
192C2×D4×C107—42no—
193C2×D4×C107—41no—
194C2×D4×C107—42no—
195C2×D4×C107—44no—
196C2×D4×C107—81no—
197C2×D4×C107—81no—
198C2×D4×C107—84no—
199C2×D4×C107—84no—
200C2×D4×C107—84no—
201C2×D4×C107C2×D411yescharacteristic
202C2×D4×C107C2×D411yescharacteristic
203C2×D4×C107C2×D412yes—
204C2×D4×C107C2411yescharacteristic
205C22×C4×C107—22no—
206C22×C4×C107—22no—
207C22×C4×C107—22no—
208C22×C4×C107—22no—
209C22×C4×C107—22no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—41no—
213C22×C4×C107—41no—
214C22×C4×C107—41no—
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219SD16×C107—44no—
220D8×C107—44no—
221M16×C107—22no—
222M16×C107—41no—
223C2×C8×C107—41no—
224C4⋊C4×C107—22no—
225C4⋊C4×C107—22no—
226C4⋊C4×C107—22no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—41no—
233C4⋊C4×C107—41no—
234C4⋊C4×C107—42no—
235C22⋊C4×C107—22no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—22no—
238C22⋊C4×C107—22no—
239C22⋊C4×C107—21no—
240C22⋊C4×C107—21no—
241C22⋊C4×C107—21no—
242C22⋊C4×C107—22no—
243C22⋊C4×C107—22no—
244C22⋊C4×C107—21no—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—21no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—22no—
249C22⋊C4×C107—22no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—44no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107C2×D412yes—
254C22⋊C4×C107C2×D411yescharacteristic
255C22⋊C4×C107C2×D411yescharacteristic
256C42×C107—21no—
257C42×C107—21no—
258C42×C107—41no—
259C42×C107—41no—
260C42×C107C2×D412yes—
261C23×C107—21no—
262C23×C107—22no—
263C23×C107—22no—
264C23×C107—22no—
265C23×C107—22no—
266C23×C107—41no—
267C23×C107—42no—
268C23×C107—41no—
269C23×C107—44no—
270C23×C107—42no—
271C23×C107—81no—
272C23×C107—82no—
273C23×C107—82no—
274C23×C107—82no—
275C23×C107—82no—
276C23×C107#12011yescharacteristic
277C23×C107C22×D411yescharacteristic
278C23×C107C22×D411yescharacteristic
279Q8×C107—22no—
280Q8×C107—41no—
281Q8×C107—41no—
282Q8×C107—41no—
283Q8×C107—41no—
284D4×C107—22no—
285D4×C107—41no—
286D4×C107—41no—
287D4×C107—41no—
288D4×C107—42no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—42no—
292D4×C107—42no—
293D4×C107—42no—
294D4×C107—42no—
295D4×C107—44no—
296D4×C107—44no—
297D4×C107—42no—
298D4×C107—42no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—41no—
304D4×C107—81no—
305D4×C107—82no—
306D4×C107—82no—
307D4×C107—82no—
308D4×C107—82no—
309D4×C107—82no—
310D4×C107—82no—
311D4×C107—82no—
312D4×C107—84no—
313D4×C107—164no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—21no—
320C2×C4×C107—22no—
321C2×C4×C107—22no—
322C2×C4×C107—22no—
323C2×C4×C107—21no—
324C2×C4×C107—21no—
325C2×C4×C107—22no—
326C2×C4×C107—21no—
327C2×C4×C107—42no—
328C2×C4×C107—42no—
329C2×C4×C107—42no—
330C2×C4×C107—41no—
331C2×C4×C107—42no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—42no—
336C2×C4×C107—42no—
337C2×C4×C107—81no—
338C2×C4×C107—82no—
339C2×C4×C107—82no—
340C2×C4×C107—82no—
341C2×C4×C107#12011yescharacteristic
342C2×C4×C107#12011yescharacteristic
343C2×C4×C107#12011yescharacteristic
344C2×C4×C107C22×D411yescharacteristic
345C8×C107—42no—
346C22×C107—22no—
347C22×C107—21no—
348C22×C107—21no—
349C22×C107—21no—
350C22×C107—41no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—42no—
355C22×C107—42no—
356C22×C107—42no—
357C22×C107—42no—
358C22×C107—42no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—42no—
363C22×C107—81no—
364C22×C107—82no—
365C22×C107—82no—
366C22×C107—84no—
367C22×C107—161no—
368C22×C107—164no—
369C22×C107—162no—
370C22×C107C2×#12011yescharacteristic
371C4×C107—21no—
372C4×C107—21no—
373C4×C107—21no—
374C4×C107—42no—
375C4×C107—41no—
376C4×C107—41no—
377C4×C107—42no—
378C4×C107—42no—
379C4×C107—41no—
380C4×C107—82no—
381C4×C107—82no—
382C4×C107B(4,𝔽2)11yescharacteristic
383C4×C107B(4,𝔽2)11yescharacteristic
384#33553C10711yesmaximal, characteristic, direct product factor, Sylow
385C2×C107—21no—
386C2×C107—41no—
387C2×C107—41no—
388C2×C107—42no—
389C2×C107—41no—
390C2×C107—82no—
391C2×C107—82no—
392C2×C107—82no—
393C2×C107C2×B(4,𝔽2)11yescharacteristic
394#3537C2×C10711yescharacteristic, complemented
395#3027C2×C10711yescharacteristic, complemented
396#3025C2×C10711yescharacteristic, complemented
397#3021C2×C10711yescharacteristic, complemented
398#2200C2×C10714yescomplemented
399#2196C2×C10714yescomplemented
400#2128C2×C10711yescharacteristic, complemented
401#2122C2×C10711yescharacteristic, complemented
402#2120C2×C10711yescharacteristic, complemented
403C107#3355311yescharacteristic, direct product factor, Sylow
404#585C22×C10711yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—21no—
406#560—21no—
407#560C22×C10712yescomplemented
408#553—21no—
409#553—21no—
410D42—21no—
411D42—21no—
412D42—21no—
413D42C22×C10712yescomplemented
414#540—21no—
415#538—22no—
416#535—21no—
417#535C22×C10711yescharacteristic
418#535C22×C10711yescharacteristic
419#534—22no—
420#525—21no—
421#525C22×C10711yescharacteristic
422C2×#121—21no—
423#458—21no—
424#458C22×C10712yescomplemented
425B(4,𝔽2)—21no—
426B(4,𝔽2)—22no—
427B(4,𝔽2)C22×C10712yescomplemented
428B(4,𝔽2)C22×C10714yescomplemented
429#454—22no—
430#453C22×C10714yescomplemented
431#421—21no—
432#413C22×C10711yescharacteristic, complemented
433#410—21no—
434#410—21no—
435#410C22×C10711yescharacteristic, complemented
436#410C22×C10711yescharacteristic, complemented
437#353C22×C10714yescomplemented
438#352C22×C10712yescomplemented
439AΣL(1,𝔽16)C22×C10712yescomplemented
440AΣL(1,𝔽16)C22×C10714yescomplemented
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C10712yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C10711yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C10711yescharacteristic, complemented
457C22×D4D4×C10711yescharacteristic, complemented
458C23×C4D4×C10711yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C10712yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C10712yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C10711yescharacteristic, complemented
480#123C23×C10711yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C10711yescharacteristic, complemented
509#120D4×C10712yescomplemented
510#120C23×C10711yescharacteristic
511#120C23×C10712yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C10711yescharacteristic, complemented
522#117D4×C10711yescharacteristic, complemented
523#117D4×C10711yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C10712yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C10712yes—
535#99C23×C10712yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C10711yescharacteristic
539C24C2×D4×C10712yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C10711yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C10711yescharacteristic
596C2×D4C2×D4×C10711yescharacteristic
597C2×D4C2×D4×C10712yes—
598C2×D4C24×C10711yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C10711yescharacteristic
610C22×C4C2×D4×C10711yescharacteristic
611C22×C4C2×D4×C10711yescharacteristic
612C22×C4C2×D4×C10711yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C10712yes—
648C22⋊C4C2×D4×C10711yescharacteristic
649C22⋊C4C2×D4×C10711yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C10712yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C10711yescharacteristic
671C23C22×D4×C10711yescharacteristic
672C23C22×D4×C10711yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C10711yescharacteristic
736C2×C4#120×C10711yescharacteristic
737C2×C4#120×C10711yescharacteristic
738C2×C4C22×D4×C10711yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C10711yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4B(4,𝔽2)×C10711yescharacteristic
777C4B(4,𝔽2)×C10711yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×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 ◁ C2×C4×C107 ◁ C2×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3537C2semidirect
2. C107×#3027C2semidirect
3. C107×#3025C2semidirect
4. C107×#3021C2semidirect
5. C107×#2200C2semidirect
6. C107×#2196C2semidirect
7. C107×#2128C2semidirect
8. C107×#2122C2semidirect
9. C107×#2120C2semidirect
10. #585×C107C22semidirect
13. #560×C107C22semidirect
19. D42×C107C22semidirect
30. #458×C107C22semidirect
33. B(4,𝔽2)×C107C22semidirect
34. B(4,𝔽2)×C107C22semidirect
36. #453×C107C22semidirect
38. #413×C107C22semidirect
41. #410×C107C22semidirect
42. #410×C107C22semidirect
43. #353×C107C22semidirect
44. #352×C107C22semidirect
45. AΣL(1,𝔽16)×C107C22semidirect
46. AΣL(1,𝔽16)×C107C22semidirect
62. C22×D4×C107D4semidirect
63. C22×D4×C107D4semidirect
64. C23×C4×C107D4semidirect
79. #124×C107D4semidirect
85. #123×C107D4semidirect
114. #120×C107D4semidirect
115. #120×C107D4semidirect
127. #117×C107D4semidirect
128. #117×C107D4semidirect
129. #117×C107D4semidirect
384. #33553C107direct (N × H)
394. #3537C2×C107semidirect
395. #3027C2×C107semidirect
396. #3025C2×C107semidirect
397. #3021C2×C107semidirect
398. #2200C2×C107semidirect
399. #2196C2×C107semidirect
400. #2128C2×C107semidirect
401. #2122C2×C107semidirect
402. #2120C2×C107semidirect
403. C107#33553direct (N × H)
404. #585C22×C107semidirect
407. #560C22×C107semidirect
413. D42C22×C107semidirect
424. #458C22×C107semidirect
427. B(4,𝔽2)C22×C107semidirect
428. B(4,𝔽2)C22×C107semidirect
430. #453C22×C107semidirect
432. #413C22×C107semidirect
435. #410C22×C107semidirect
436. #410C22×C107semidirect
437. #353C22×C107semidirect
438. #352C22×C107semidirect
439. AΣL(1,𝔽16)C22×C107semidirect
440. AΣL(1,𝔽16)C22×C107semidirect
456. C22×D4D4×C107semidirect
457. C22×D4D4×C107semidirect
458. C23×C4D4×C107semidirect
473. #124D4×C107semidirect
479. #123D4×C107semidirect
508. #120D4×C107semidirect
509. #120D4×C107semidirect
521. #117D4×C107semidirect
522. #117D4×C107semidirect
523. #117D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35372
C107×#30272
C107×#30252
C107×#30212
C107×#22002
C107×#21962
C107×#21282
C107×#21222
C107×#21202
#33553107