Finite Group Databasebeta

← C107×#24295 #41050259

Subgroups — C107×#24295 #41050259

Order 27392.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C107C211yesmaximal, characteristic, complemented
2C107×#3067C211yesmaximal, characteristic, complemented
3C107×#3057C211yesmaximal, characteristic, complemented
4C107×#3020C211yesmaximal, characteristic, complemented
5C107×#3019C211yesmaximal, characteristic, complemented
6C107×#2955C211yesmaximal, characteristic, complemented
7C107×#2049C211yesmaximal, characteristic, complemented
8C107×#2048C211yesmaximal, characteristic, complemented
9C107×#2009C211yesmaximal, characteristic, complemented
10C107×#2008C211yesmaximal, characteristic, complemented
11C107×#1977C211yesmaximal, characteristic, complemented
12C107×#1976C211yesmaximal, characteristic, complemented
13C107×#1814C211yesmaximal, characteristic, complemented
14C107×#1796C211yesmaximal, characteristic, complemented
15C107×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C107C2211yescharacteristic
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18#577×C107—22no—
19#577×C107—22no—
20#577×C107—22no—
21#577×C107—22no—
22#575×C107C2211yescharacteristic
23#575×C107C2211yescharacteristic
24#575×C107C2211yescharacteristic, complemented
25C2×#137×C107—21no—
26C2×#137×C107C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C107—21no—
28C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
29C2×#135×C107—21no—
30C2×#135×C107C2211yescharacteristic
31C22×SD16×C107—21no—
32C22×SD16×C107C2211yescharacteristic
33C2×#131×C107C2211yescharacteristic
34C2×#131×C107C2211yescharacteristic, complemented
35#536×C107C2211yescharacteristic, complemented
36#535×C107C2211yescharacteristic
37#473×C107—21no—
38#472×C107—21no—
39#471×C107—21no—
40#471×C107—21no—
41#468×C107—22no—
42#465×C107—22no—
43#456×C107—22no—
44#455×C107—22no—
45#454×C107—22no—
46#453×C107—22no—
47#444×C107—22no—
48#443×C107—22no—
49#430×C107C2211yescharacteristic, complemented
50C2×#108×C107C2211yescharacteristic, complemented
51#427×C107C2211yescharacteristic, complemented
52#421×C107C2211yescharacteristic
53#421×C107C2211yescharacteristic
54#421×C107C2211yescharacteristic
55#421×C107C2211yescharacteristic
56#421×C107C2211yescharacteristic, complemented
57#421×C107C2211yescharacteristic, complemented
58#419×C107C2211yescharacteristic, complemented
59#419×C107C2211yescharacteristic, complemented
60#418×C107C2211yescharacteristic
61#418×C107C2211yescharacteristic
62#413×C107C2211yescharacteristic
63#413×C107C2211yescharacteristic, complemented
64C2×#101×C107C2211yescharacteristic, complemented
65C2×#100×C107C2211yescharacteristic
66#410×C107C2211yescharacteristic
67#410×C107C2211yescharacteristic, complemented
68#405×C107C2211yescharacteristic, complemented
69#344×C107C2211yescharacteristic, complemented
70#344×C107C2211yescharacteristic, complemented
712−1+4×C107—22no—
722−1+4×C107—22no—
732−1+4×C107—22no—
742−1+4×C107—41no—
75H(5,𝔽2)×C107—22no—
76H(5,𝔽2)×C107—22no—
77H(5,𝔽2)×C107—22no—
78H(5,𝔽2)×C107—41no—
79C2×#41×C107—21no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—21no—
83C2×#41×C107—41no—
84C2×#41×C107C2311yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C2×#41×C107C2311yescharacteristic
87C2×#41×C107C2311yescharacteristic
88C22×Q8×C107—21no—
89C22×Q8×C107—21no—
90C22×Q8×C107C2311yescharacteristic
91C22×D4×C107—21no—
92C22×D4×C107—21no—
93C22×D4×C107—41no—
94C22×D4×C107C2311yescharacteristic
95#137×C107—24no—
96#137×C107—24no—
97#137×C107—22no—
98#137×C107—21no—
99#137×C107—21no—
100#137×C107—21no—
101#137×C107—21no—
102#137×C107—21no—
103#137×C107—22no—
104#137×C107D412yes—
105AGL(1,ℤ/8)×C107—24no—
106AGL(1,ℤ/8)×C107—24no—
107AGL(1,ℤ/8)×C107—22no—
108AGL(1,ℤ/8)×C107—21no—
109AGL(1,ℤ/8)×C107—21no—
110AGL(1,ℤ/8)×C107—21no—
111AGL(1,ℤ/8)×C107—21no—
112AGL(1,ℤ/8)×C107—21no—
113AGL(1,ℤ/8)×C107—22no—
114AGL(1,ℤ/8)×C107D412yes—
115#135×C107—24no—
116#135×C107—24no—
117#135×C107—22no—
118#135×C107—21no—
119#135×C107—21no—
120#135×C107—21no—
121#135×C107—21no—
122#135×C107—41no—
123#135×C107—41no—
124C2×Q16×C107—21no—
125C2×Q16×C107D411yescharacteristic, complemented
126C2×SD16×C107—24no—
127C2×SD16×C107—24no—
128C2×SD16×C107—21no—
129C2×SD16×C107—21no—
130C2×SD16×C107—21no—
131C2×SD16×C107—21no—
132C2×SD16×C107—21no—
133C2×SD16×C107—21no—
134C2×SD16×C107D412yes—
135C2×SD16×C107D412yes—
136C2×SD16×C107D411yescharacteristic, complemented
137C2×SD16×C107D411yescharacteristic, complemented
138C2×D8×C107—21no—
139C2×D8×C107D411yescharacteristic, complemented
140#131×C107—21no—
141#131×C107—21no—
142#131×C107—21no—
143#131×C107—21no—
144#131×C107—21no—
145#131×C107—21no—
146#131×C107D412yescomplemented
147#131×C107D412yescomplemented
148C2×M16×C107—21no—
149C2×M16×C107—21no—
150C2×M16×C107C2311yescharacteristic
151C2×M16×C107C2311yescharacteristic
152C2×M16×C107C2311yescharacteristic
153C2×M16×C107C2311yescharacteristic
154C2×M16×C107C2311yescharacteristic
155C22×C8×C107—21no—
156C22×C8×C107—21no—
157C22×C8×C107C2311yescharacteristic
158C4⋊Q8×C107—21no—
159#127×C107—21no—
160#124×C107—21no—
161#124×C107—21no—
162#123×C107—41no—
163C22⋊Q8×C107—22no—
164#121×C107—22no—
165#120×C107—41no—
166#117×C107C2311yescharacteristic
167#117×C107C2311yescharacteristic
168#117×C107C2311yescharacteristic
169#108×C107—22no—
170#108×C107—21no—
171#108×C107—21no—
172#107×C107—21no—
173#106×C107—21no—
174#104×C107—22no—
175#104×C107—22no—
176#104×C107—22no—
177#104×C107—22no—
178#104×C107—22no—
179#104×C107—22no—
180#103×C107—22no—
181#103×C107—41no—
182#102×C107—22no—
183#102×C107—41no—
184#101×C107—21no—
185#101×C107—21no—
186#101×C107—22no—
187#100×C107—21no—
188#100×C107—21no—
189#100×C107—22no—
190#99×C107—41no—
191#99×C107—41no—
192#97×C107—21no—
193C4×C8×C107—21no—
194C24×C107—21no—
195C24×C107—41no—
196#41×C107—21no—
197#41×C107—21no—
198#41×C107—24no—
199#41×C107—24no—
200#41×C107—21no—
201#41×C107—21no—
202#41×C107—21no—
203#41×C107—21no—
204#41×C107—21no—
205#41×C107—21no—
206#41×C107—21no—
207#41×C107—21no—
208#41×C107—21no—
209#41×C107—21no—
210#41×C107—21no—
211#41×C107—21no—
212#41×C107—42no—
213#41×C107—44no—
214#41×C107—42no—
215#41×C107—42no—
216#41×C107—42no—
217#41×C107—44no—
218#41×C107—42no—
219#41×C107—42no—
220#41×C107C2×D412yes—
221#41×C107C2×D412yes—
222C2×Q8×C107—21no—
223C2×Q8×C107—24no—
224C2×Q8×C107—21no—
225C2×Q8×C107—21no—
226C2×Q8×C107—21no—
227C2×Q8×C107—21no—
228C2×Q8×C107—41no—
229C2×Q8×C107—42no—
230C2×Q8×C107—42no—
231C2×Q8×C107—42no—
232C2×Q8×C107C2×D411yescharacteristic
233C2×Q8×C107C2×D411yescharacteristic
234C2×Q8×C107C2×D412yes—
235C2×Q8×C107C2×D411yescharacteristic
236C2×Q8×C107#4111yescharacteristic
237C2×D4×C107—21no—
238C2×D4×C107—24no—
239C2×D4×C107—21no—
240C2×D4×C107—21no—
241C2×D4×C107—21no—
242C2×D4×C107—21no—
243C2×D4×C107—21no—
244C2×D4×C107—21no—
245C2×D4×C107—21no—
246C2×D4×C107—21no—
247C2×D4×C107—42no—
248C2×D4×C107—41no—
249C2×D4×C107—41no—
250C2×D4×C107—42no—
251C2×D4×C107—44no—
252C2×D4×C107—44no—
253C2×D4×C107—41no—
254C2×D4×C107—42no—
255C2×D4×C107—42no—
256C2×D4×C107C2×D411yescharacteristic
257C2×D4×C107C2×D411yescharacteristic
258C2×D4×C107C2×D412yes—
259C2×D4×C107C2×D411yescharacteristic
260C2×D4×C107#4111yescharacteristic
261C22×C4×C107—21no—
262C22×C4×C107—21no—
263C22×C4×C107—21no—
264C22×C4×C107—21no—
265C22×C4×C107—21no—
266C22×C4×C107—41no—
267C22×C4×C107—41no—
268C22×C4×C107—41no—
269C22×C4×C107C2411yescharacteristic
270Q16×C107—24no—
271Q16×C107—22no—
272Q16×C107—21no—
273Q16×C107—21no—
274Q16×C107—41no—
275Q16×C107—41no—
276SD16×C107—24no—
277SD16×C107—24no—
278SD16×C107—22no—
279SD16×C107—22no—
280SD16×C107—22no—
281SD16×C107—22no—
282SD16×C107—21no—
283SD16×C107—21no—
284SD16×C107—22no—
285SD16×C107—22no—
286SD16×C107—21no—
287SD16×C107—21no—
288SD16×C107—41no—
289SD16×C107—41no—
290SD16×C107—41no—
291SD16×C107—41no—
292D8×C107—24no—
293D8×C107—22no—
294D8×C107—21no—
295D8×C107—21no—
296D8×C107—41no—
297D8×C107—41no—
298M16×C107—21no—
299M16×C107—21no—
300M16×C107—22no—
301M16×C107—22no—
302M16×C107—21no—
303M16×C107—21no—
304M16×C107—21no—
305M16×C107—21no—
306M16×C107—21no—
307M16×C107—21no—
308M16×C107—41no—
309M16×C107—41no—
310M16×C107C2×D412yes—
311M16×C107C2×D412yes—
312C2×C8×C107—21no—
313C2×C8×C107—21no—
314C2×C8×C107—22no—
315C2×C8×C107—22no—
316C2×C8×C107—21no—
317C2×C8×C107—21no—
318C2×C8×C107—21no—
319C2×C8×C107—41no—
320C2×C8×C107—41no—
321C2×C8×C107C2×D411yescharacteristic
322C2×C8×C107C2×D411yescharacteristic
323C2×C8×C107C2×D411yescharacteristic
324C2×C8×C107C2×D411yescharacteristic
325C2×C8×C107C2×D411yescharacteristic
326C2×C8×C107C2×D411yescharacteristic
327C4⋊C4×C107—21no—
328C4⋊C4×C107—21no—
329C4⋊C4×C107—21no—
330C4⋊C4×C107—42no—
331C22⋊C4×C107—21no—
332C22⋊C4×C107—21no—
333C22⋊C4×C107—21no—
334C22⋊C4×C107—42no—
335C22⋊C4×C107—42no—
336C42×C107—21no—
337C42×C107—21no—
338C42×C107—21no—
339C23×C107—21no—
340C23×C107—21no—
341C23×C107—22no—
342C23×C107—21no—
343C23×C107—21no—
344C23×C107—44no—
345C23×C107—41no—
346C23×C107—41no—
347C23×C107—161no—
348C23×C107—162no—
349C23×C107H(5,𝔽2)11yescharacteristic
350Q8×C107—21no—
351Q8×C107—21no—
352Q8×C107—22no—
353Q8×C107—21no—
354Q8×C107—21no—
355Q8×C107—21no—
356Q8×C107—21no—
357Q8×C107—21no—
358Q8×C107—22no—
359Q8×C107—44no—
360Q8×C107—41no—
361Q8×C107—41no—
362Q8×C107#12112yes—
363D4×C107—22no—
364D4×C107—22no—
365D4×C107—21no—
366D4×C107—22no—
367D4×C107—21no—
368D4×C107—21no—
369D4×C107—21no—
370D4×C107—21no—
371D4×C107—21no—
372D4×C107—21no—
373D4×C107—22no—
374D4×C107—44no—
375D4×C107—44no—
376D4×C107—44no—
377D4×C107—41no—
378D4×C107—41no—
379D4×C107—41no—
380D4×C107—41no—
381D4×C107—41no—
382D4×C107—41no—
383D4×C107—41no—
384D4×C107—41no—
385D4×C107—162no—
386D4×C107#12112yes—
387C2×C4×C107—21no—
388C2×C4×C107—22no—
389C2×C4×C107—22no—
390C2×C4×C107—21no—
391C2×C4×C107—22no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—44no—
395C2×C4×C107—44no—
396C2×C4×C107—44no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107C22×D411yescharacteristic
409C2×C4×C107C22×D411yescharacteristic
410C2×C4×C107C22×D411yescharacteristic
411C2×C4×C107C22×D411yescharacteristic
412C2×C4×C107C2×#4111yescharacteristic
413C2×C4×C107H(5,𝔽2)11yescharacteristic
414C8×C107—22no—
415C8×C107—22no—
416C8×C107—41no—
417C8×C107—41no—
418C8×C107—41no—
419C8×C107#12011yescharacteristic
420C8×C107#12011yescharacteristic
421C8×C107#12011yescharacteristic
422C8×C107#12011yescharacteristic
423C22×C107—22no—
424C22×C107—41no—
425C22×C107—42no—
426C22×C107—42no—
427C22×C107—41no—
428C22×C107—42no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—82no—
432C22×C107—81no—
433C22×C107—81no—
434C22×C107—82no—
435C22×C107—161no—
436C22×C107—164no—
437C22×C107#53511yescharacteristic
438C22×C107D4211yescharacteristic
439C22×C107#54611yescharacteristic
440C4×C107—22no—
441C4×C107—41no—
442C4×C107—42no—
443C4×C107—41no—
444C4×C107—41no—
445C4×C107—81no—
446C4×C107—81no—
447C4×C107—81no—
448C4×C107C2×#12011yescharacteristic
449C4×C107C2×#12111yescharacteristic
450C4×C107D4211yescharacteristic
451C4×C107#54611yescharacteristic
452#24295C10711yesmaximal, characteristic, direct product factor, Sylow
453C2×C107—21no—
454C2×C107—21no—
455C2×C107—21no—
456C2×C107—42no—
457C2×C107—81no—
458C2×C107—81no—
459C2×C107—82no—
460C2×C107—81no—
461C2×C107#240811yescharacteristic
462C2×#577C2×C10711yescharacteristic, complemented
463#3067C2×C10711yescharacteristic, complemented
464#3057C2×C10711yescharacteristic, complemented
465#3020C2×C10711yescharacteristic, complemented
466#3019C2×C10711yescharacteristic, complemented
467#2955C2×C10711yescharacteristic, complemented
468#2049C2×C10711yescharacteristic, complemented
469#2048C2×C10711yescharacteristic, complemented
470#2009C2×C10711yescharacteristic, complemented
471#2008C2×C10711yescharacteristic, complemented
472#1977C2×C10711yescharacteristic, complemented
473#1976C2×C10711yescharacteristic, complemented
474#1814C2×C10711yescharacteristic, complemented
475#1796C2×C10711yescharacteristic, complemented
476#1795C2×C10711yescharacteristic, complemented
477C107#2429511yescharacteristic, direct product factor, Sylow
478C2×2−1+4C22×C10711yescharacteristic
479C2×H(5,𝔽2)C22×C10711yescharacteristic
480#577—22no—
481#577—22no—
482#577—22no—
483#577—22no—
484#575C22×C10711yescharacteristic
485#575C22×C10711yescharacteristic
486#575C22×C10711yescharacteristic, complemented
487C2×#137—21no—
488C2×#137C22×C10711yescharacteristic
489C2×AGL(1,ℤ/8)—21no—
490C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
491C2×#135—21no—
492C2×#135C22×C10711yescharacteristic
493C22×SD16—21no—
494C22×SD16C22×C10711yescharacteristic
495C2×#131C22×C10711yescharacteristic
496C2×#131C22×C10711yescharacteristic, complemented
497#536C22×C10711yescharacteristic, complemented
498#535C22×C10711yescharacteristic
499#473—21no—
500#472—21no—
501#471—21no—
502#471—21no—
503#468—22no—
504#465—22no—
505#456—22no—
506#455—22no—
507#454—22no—
508#453—22no—
509#444—22no—
510#443—22no—
511#430C22×C10711yescharacteristic, complemented
512C2×#108C22×C10711yescharacteristic, complemented
513#427C22×C10711yescharacteristic, complemented
514#421C22×C10711yescharacteristic
515#421C22×C10711yescharacteristic
516#421C22×C10711yescharacteristic
517#421C22×C10711yescharacteristic
518#421C22×C10711yescharacteristic, complemented
519#421C22×C10711yescharacteristic, complemented
520#419C22×C10711yescharacteristic, complemented
521#419C22×C10711yescharacteristic, complemented
522#418C22×C10711yescharacteristic
523#418C22×C10711yescharacteristic
524#413C22×C10711yescharacteristic
525#413C22×C10711yescharacteristic, complemented
526C2×#101C22×C10711yescharacteristic, complemented
527C2×#100C22×C10711yescharacteristic
528#410C22×C10711yescharacteristic
529#410C22×C10711yescharacteristic, complemented
530#405C22×C10711yescharacteristic, complemented
531#344C22×C10711yescharacteristic, complemented
532#344C22×C10711yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C10711yescharacteristic
547C2×#41C23×C10711yescharacteristic
548C2×#41C23×C10711yescharacteristic
549C2×#41C23×C10711yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C10711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C10711yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C10712yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C10712yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C10711yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C10712yes—
597C2×SD16D4×C10712yes—
598C2×SD16D4×C10711yescharacteristic, complemented
599C2×SD16D4×C10711yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C10711yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C10712yescomplemented
609#131D4×C10712yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C10711yescharacteristic
613C2×M16C23×C10711yescharacteristic
614C2×M16C23×C10711yescharacteristic
615C2×M16C23×C10711yescharacteristic
616C2×M16C23×C10711yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C10711yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C10711yescharacteristic
629#117C23×C10711yescharacteristic
630#117C23×C10711yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C10712yes—
683#41C2×D4×C10712yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C10711yescharacteristic
695C2×Q8C2×D4×C10711yescharacteristic
696C2×Q8C2×D4×C10712yes—
697C2×Q8C2×D4×C10711yescharacteristic
698C2×Q8#41×C10711yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C10711yescharacteristic
719C2×D4C2×D4×C10711yescharacteristic
720C2×D4C2×D4×C10712yes—
721C2×D4C2×D4×C10711yescharacteristic
722C2×D4#41×C10711yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C10711yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C10712yes—
773M16C2×D4×C10712yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C10711yescharacteristic
784C2×C8C2×D4×C10711yescharacteristic
785C2×C8C2×D4×C10711yescharacteristic
786C2×C8C2×D4×C10711yescharacteristic
787C2×C8C2×D4×C10711yescharacteristic
788C2×C8C2×D4×C10711yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C10711yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C10712yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C10712yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C10711yescharacteristic
871C2×C4C22×D4×C10711yescharacteristic
872C2×C4C22×D4×C10711yescharacteristic
873C2×C4C22×D4×C10711yescharacteristic
874C2×C4C2×#41×C10711yescharacteristic
875C2×C4H(5,𝔽2)×C10711yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C10711yescharacteristic
882C8#120×C10711yescharacteristic
883C8#120×C10711yescharacteristic
884C8#120×C10711yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22#535×C10711yescharacteristic
900C22D42×C10711yescharacteristic
901C22#546×C10711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C10711yescharacteristic
911C4C2×#121×C10711yescharacteristic
912C4D42×C10711yescharacteristic
913C4#546×C10711yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C107×#240811yescharacteristic
subgroupG/H
center, socleC2×C107#2408
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C107C2semidirect
2. C107×#3067C2semidirect
3. C107×#3057C2semidirect
4. C107×#3020C2semidirect
5. C107×#3019C2semidirect
6. C107×#2955C2semidirect
7. C107×#2049C2semidirect
8. C107×#2048C2semidirect
9. C107×#2009C2semidirect
10. C107×#2008C2semidirect
11. C107×#1977C2semidirect
12. C107×#1976C2semidirect
13. C107×#1814C2semidirect
14. C107×#1796C2semidirect
15. C107×#1795C2semidirect
24. #575×C107C22semidirect
34. C2×#131×C107C22semidirect
35. #536×C107C22semidirect
49. #430×C107C22semidirect
50. C2×#108×C107C22semidirect
51. #427×C107C22semidirect
56. #421×C107C22semidirect
57. #421×C107C22semidirect
58. #419×C107C22semidirect
59. #419×C107C22semidirect
63. #413×C107C22semidirect
64. C2×#101×C107C22semidirect
67. #410×C107C22semidirect
68. #405×C107C22semidirect
69. #344×C107C22semidirect
70. #344×C107C22semidirect
125. C2×Q16×C107D4semidirect
136. C2×SD16×C107D4semidirect
137. C2×SD16×C107D4semidirect
139. C2×D8×C107D4semidirect
146. #131×C107D4semidirect
147. #131×C107D4semidirect
452. #24295C107direct (N × H)
462. C2×#577C2×C107semidirect
463. #3067C2×C107semidirect
464. #3057C2×C107semidirect
465. #3020C2×C107semidirect
466. #3019C2×C107semidirect
467. #2955C2×C107semidirect
468. #2049C2×C107semidirect
469. #2048C2×C107semidirect
470. #2009C2×C107semidirect
471. #2008C2×C107semidirect
472. #1977C2×C107semidirect
473. #1976C2×C107semidirect
474. #1814C2×C107semidirect
475. #1796C2×C107semidirect
476. #1795C2×C107semidirect
477. C107#24295direct (N × H)
486. #575C22×C107semidirect
496. C2×#131C22×C107semidirect
497. #536C22×C107semidirect
511. #430C22×C107semidirect
512. C2×#108C22×C107semidirect
513. #427C22×C107semidirect
518. #421C22×C107semidirect
519. #421C22×C107semidirect
520. #419C22×C107semidirect
521. #419C22×C107semidirect
525. #413C22×C107semidirect
526. C2×#101C22×C107semidirect
529. #410C22×C107semidirect
530. #405C22×C107semidirect
531. #344C22×C107semidirect
532. #344C22×C107semidirect
587. C2×Q16D4×C107semidirect
598. C2×SD16D4×C107semidirect
599. C2×SD16D4×C107semidirect
601. C2×D8D4×C107semidirect
608. #131D4×C107semidirect
609. #131D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1072
C107×#30672
C107×#30572
C107×#30202
C107×#30192
C107×#29552
C107×#20492
C107×#20482
C107×#20092
C107×#20082
C107×#19772
C107×#19762
C107×#18142
C107×#17962
C107×#17952
#24295107