Finite Group Databasebeta

← C107×#24474 #41050438

Subgroups — C107×#24474 #41050438

Order 27392.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3586C211yesmaximal, characteristic
2C107×#3069C211yesmaximal, characteristic, complemented
3C107×#3039C211yesmaximal, characteristic, complemented
4C107×#3022C211yesmaximal, characteristic, complemented
5C2×#456×C107C211yesmaximal, characteristic, complemented
6C107×#2901C211yesmaximal, characteristic, complemented
7C107×#2050C211yesmaximal, characteristic, complemented
8C107×#2049C211yesmaximal, characteristic, complemented
9C107×#2009C211yesmaximal, characteristic, complemented
10C107×#2005C211yesmaximal, characteristic, complemented
11C107×#1906C211yesmaximal, characteristic, complemented
12C107×#1902C211yesmaximal, characteristic, complemented
13C107×#1902C211yesmaximal, characteristic, complemented
14C107×#1861C211yesmaximal, characteristic, complemented
15C107×#1796C211yesmaximal, characteristic, complemented
16#585×C107C2211yescharacteristic
17C2×2−1+4×C107C2211yescharacteristic
18#578×C107—22no—
19#578×C107—22no—
20#577×C107—22no—
21#577×C107—22no—
22#575×C107—22no—
23#575×C107C2211yescharacteristic
24#575×C107C2211yescharacteristic
25C2×#137×C107—22no—
26C2×#137×C107C2211yescharacteristic
27C2×#137×C107C2211yescharacteristic
28C2×#137×C107C2211yescharacteristic
29C2×#137×C107C2211yescharacteristic
30C2×#137×C107C2211yescharacteristic, complemented
31#568×C107C2211yescharacteristic
32#568×C107C2211yescharacteristic
33#536×C107C2211yescharacteristic
34C2×C4⋊Q8×C107C2211yescharacteristic, complemented
35C4×#41×C107C2211yescharacteristic
36#473×C107—22no—
37#471×C107—22no—
38#462×C107—22no—
39#461×C107—22no—
40#456×C107—22no—
41#456×C107—22no—
42#456×C107—22no—
43#455×C107—22no—
44#430×C107C2211yescharacteristic, complemented
45#423×C107C2211yescharacteristic, complemented
46#421×C107—22no—
47#421×C107C2211yescharacteristic
48#421×C107C2211yescharacteristic
49#421×C107C2211yescharacteristic
50#421×C107C2211yescharacteristic
51C2×#104×C107—22no—
52C2×#104×C107C2211yescharacteristic
53C2×#104×C107C2211yescharacteristic
54C2×#104×C107C2211yescharacteristic, complemented
55#419×C107C2211yescharacteristic, complemented
56#419×C107C2211yescharacteristic, complemented
57#419×C107C2211yescharacteristic, complemented
58#413×C107C2211yescharacteristic
59#413×C107C2211yescharacteristic, complemented
60C2×#101×C107C2211yescharacteristic, complemented
61C2×#101×C107C2211yescharacteristic, complemented
62#410×C107C2211yescharacteristic, complemented
63#344×C107C2211yescharacteristic, complemented
64#344×C107C2211yescharacteristic, complemented
65#339×C107C2211yescharacteristic, complemented
66#338×C107C2211yescharacteristic, complemented
672−1+4×C107—22no—
682−1+4×C107—22no—
692−1+4×C107—21no—
702−1+4×C107—21no—
712−1+4×C107—22no—
722−1+4×C107—41no—
732−1+4×C107D412yes—
74H(5,𝔽2)×C107—21no—
75H(5,𝔽2)×C107—21no—
76H(5,𝔽2)×C107—41no—
77H(5,𝔽2)×C107D412yes—
78C2×#41×C107—22no—
79C2×#41×C107—22no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—41no—
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×Q8×C107C2311yescharacteristic
92#137×C107—24no—
93#137×C107—24no—
94#137×C107—24no—
95#137×C107—22no—
96#137×C107—22no—
97#137×C107—21no—
98#137×C107—22no—
99#137×C107—21no—
100#137×C107—21no—
101#137×C107—22no—
102#137×C107—22no—
103#137×C107—22no—
104#137×C107—22no—
105#137×C107—22no—
106#137×C107—22no—
107#137×C107—41no—
108#137×C107D412yes—
109AGL(1,ℤ/8)×C107—24no—
110AGL(1,ℤ/8)×C107—21no—
111AGL(1,ℤ/8)×C107—21no—
112AGL(1,ℤ/8)×C107—21no—
113AGL(1,ℤ/8)×C107D412yes—
114#135×C107—24no—
115#135×C107—24no—
116#135×C107—22no—
117#135×C107—22no—
118C2×Q16×C107—24no—
119C2×Q16×C107—21no—
120C2×Q16×C107—21no—
121C2×Q16×C107—21no—
122C2×Q16×C107—21no—
123C2×Q16×C107D412yes—
124C2×SD16×C107—24no—
125C2×SD16×C107—21no—
126C2×SD16×C107—21no—
127C2×SD16×C107—21no—
128C2×SD16×C107—21no—
129C2×SD16×C107D412yes—
130#131×C107—22no—
131#131×C107—22no—
132#131×C107—22no—
133#131×C107—41no—
134C2×M16×C107—22no—
135C2×M16×C107—22no—
136C2×M16×C107C2311yescharacteristic
137C2×M16×C107C2311yescharacteristic
138C2×M16×C107C2311yescharacteristic
139C2×M16×C107C2311yescharacteristic
140C2×M16×C107C2311yescharacteristic
141C2×M16×C107C2311yescharacteristic
142C4⋊Q8×C107—21no—
143C4⋊Q8×C107—22no—
144C4⋊Q8×C107—21no—
145C4⋊Q8×C107—21no—
146#124×C107—21no—
147#123×C107—41no—
148C22⋊Q8×C107—41no—
149C4×Q8×C107—21no—
150C4×D4×C107—21no—
151C4×D4×C107—41no—
152#117×C107—21no—
153#117×C107C2311yescharacteristic
154#117×C107C2311yescharacteristic
155C2×C4⋊C4×C107—41no—
156C2×C42×C107—21no—
157C2×C42×C107C2311yescharacteristic
158#108×C107—22no—
159C4⋊C8×C107—22no—
160#104×C107—22no—
161#104×C107—22no—
162#104×C107—22no—
163#104×C107—22no—
164#104×C107—21no—
165#104×C107—21no—
166#104×C107—21no—
167#104×C107—21no—
168#104×C107D412yes—
169#104×C107D412yes—
170#103×C107—22no—
171#103×C107—22no—
172#103×C107—41no—
173#101×C107—21no—
174#101×C107—21no—
175#101×C107—22no—
176#101×C107—22no—
177#100×C107—21no—
178#100×C107—21no—
179#99×C107—41no—
180#41×C107—21no—
181#41×C107—21no—
182#41×C107—21no—
183#41×C107—21no—
184#41×C107—24no—
185#41×C107—22no—
186#41×C107—22no—
187#41×C107—22no—
188#41×C107—22no—
189#41×C107—21no—
190#41×C107—21no—
191#41×C107—21no—
192#41×C107—21no—
193#41×C107—21no—
194#41×C107—21no—
195#41×C107—21no—
196#41×C107—21no—
197#41×C107—42no—
198#41×C107—42no—
199#41×C107—42no—
200#41×C107—42no—
201#41×C107—42no—
202#41×C107—44no—
203#41×C107—42no—
204#41×C107—41no—
205#41×C107—41no—
206#41×C107—44no—
207#41×C107—42no—
208#41×C107C2×D412yes—
209#41×C107C2×D412yes—
210#41×C107C2×D412yes—
211#41×C107C2×D412yes—
212C2×Q8×C107—21no—
213C2×Q8×C107—24no—
214C2×Q8×C107—22no—
215C2×Q8×C107—22no—
216C2×Q8×C107—21no—
217C2×Q8×C107—21no—
218C2×Q8×C107—21no—
219C2×Q8×C107—21no—
220C2×Q8×C107—21no—
221C2×Q8×C107—21no—
222C2×Q8×C107—21no—
223C2×Q8×C107—21no—
224C2×Q8×C107—21no—
225C2×Q8×C107—21no—
226C2×Q8×C107—41no—
227C2×Q8×C107—42no—
228C2×Q8×C107—42no—
229C2×Q8×C107—41no—
230C2×Q8×C107—42no—
231C2×Q8×C107C2×D411yescharacteristic
232C2×Q8×C107C2×D411yescharacteristic
233C2×Q8×C107C2×D412yes—
234C2×Q8×C107C2×D411yescharacteristic
235C2×Q8×C107#4111yescharacteristic
236C2×D4×C107—21no—
237C2×D4×C107—21no—
238C2×D4×C107—22no—
239C2×D4×C107—22no—
240C2×D4×C107—21no—
241C2×D4×C107—21no—
242C2×D4×C107—42no—
243C2×D4×C107—41no—
244C2×D4×C107—42no—
245C2×D4×C107—42no—
246C2×D4×C107—41no—
247C2×D4×C107C2×D411yescharacteristic
248C2×D4×C107C2×D411yescharacteristic
249C2×D4×C107C2×D411yescharacteristic
250C2×D4×C107#4111yescharacteristic
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—42no—
259C22×C4×C107—41no—
260C22×C4×C107—41no—
261C22×C4×C107—41no—
262C22×C4×C107C2411yescharacteristic
263Q16×C107—24no—
264Q16×C107—22no—
265Q16×C107—22no—
266Q16×C107—24no—
267Q16×C107—42no—
268Q16×C107—42no—
269Q16×C107—42no—
270SD16×C107—24no—
271SD16×C107—22no—
272SD16×C107—22no—
273SD16×C107—22no—
274SD16×C107—22no—
275SD16×C107—24no—
276SD16×C107—42no—
277SD16×C107—42no—
278SD16×C107—42no—
279D8×C107—22no—
280D8×C107—22no—
281M16×C107—24no—
282M16×C107—21no—
283M16×C107—21no—
284M16×C107—21no—
285M16×C107—21no—
286M16×C107—21no—
287M16×C107—21no—
288M16×C107—21no—
289M16×C107—21no—
290M16×C107—21no—
291M16×C107—21no—
292M16×C107—42no—
293M16×C107C2×D412yes—
294M16×C107C2×D412yes—
295C2×C8×C107—24no—
296C2×C8×C107—21no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107—21no—
300C2×C8×C107—21no—
301C2×C8×C107—42no—
302C2×C8×C107C2×D412yes—
303C4⋊C4×C107—21no—
304C4⋊C4×C107—21no—
305C4⋊C4×C107—42no—
306C4⋊C4×C107—42no—
307C4⋊C4×C107—41no—
308C4⋊C4×C107—42no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—41no—
312C22⋊C4×C107—42no—
313C42×C107—21no—
314C42×C107—21no—
315C42×C107—21no—
316C42×C107—41no—
317C42×C107C2×D411yescharacteristic
318C42×C107C2×D411yescharacteristic
319C23×C107—21no—
320C23×C107—21no—
321C23×C107—21no—
322C23×C107—21no—
323C23×C107—42no—
324C23×C107H(5,𝔽2)11yescharacteristic
325Q8×C107—21no—
326Q8×C107—21no—
327Q8×C107—21no—
328Q8×C107—22no—
329Q8×C107—21no—
330Q8×C107—21no—
331Q8×C107—21no—
332Q8×C107—22no—
333Q8×C107—42no—
334Q8×C107—44no—
335Q8×C107—41no—
336Q8×C107—41no—
337Q8×C107—41no—
338Q8×C107—41no—
339Q8×C107—41no—
340Q8×C107—41no—
341Q8×C107#12012yes—
342Q8×C107#12112yes—
343D4×C107—22no—
344D4×C107—22no—
345D4×C107—22no—
346D4×C107—22no—
347D4×C107—21no—
348D4×C107—21no—
349D4×C107—21no—
350D4×C107—21no—
351D4×C107—21no—
352D4×C107—21no—
353D4×C107—42no—
354D4×C107—42no—
355D4×C107—42no—
356D4×C107—44no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107#12012yes—
362D4×C107#12112yes—
363C2×C4×C107—21no—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—22no—
373C2×C4×C107—21no—
374C2×C4×C107—42no—
375C2×C4×C107—42no—
376C2×C4×C107—42no—
377C2×C4×C107—42no—
378C2×C4×C107—44no—
379C2×C4×C107—44no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—82no—
392C2×C4×C107C22×D411yescharacteristic
393C2×C4×C107C22×D411yescharacteristic
394C2×C4×C107C22×D411yescharacteristic
395C2×C4×C107C22×D411yescharacteristic
396C2×C4×C107C2×#4111yescharacteristic
397C2×C4×C107H(5,𝔽2)11yescharacteristic
398C8×C107—22no—
399C8×C107—22no—
400C8×C107—22no—
401C8×C107—41no—
402C8×C107—41no—
403C8×C107—41no—
404C22×C107—22no—
405C22×C107—22no—
406C22×C107—41no—
407C22×C107—41no—
408C22×C107—41no—
409C22×C107—81no—
410C22×C107—81no—
411C22×C107—81no—
412C22×C107—81no—
413C22×C107—162no—
414C22×C107#53411yescharacteristic
415C22×C107D4211yescharacteristic
416C22×C107#54611yescharacteristic
417C4×C107—22no—
418C4×C107—22no—
419C4×C107—22no—
420C4×C107—41no—
421C4×C107—41no—
422C4×C107—42no—
423C4×C107—41no—
424C4×C107—81no—
425C4×C107—81no—
426C4×C107—81no—
427C4×C107C2×#12011yescharacteristic
428C4×C107C2×#12111yescharacteristic
429C4×C107D4211yescharacteristic
430C4×C107#54611yescharacteristic
431#24474C10711yesmaximal, characteristic, direct product factor, Sylow
432C2×C107—21no—
433C2×C107—21no—
434C2×C107—21no—
435C2×C107—42no—
436C2×C107—42no—
437C2×C107—81no—
438C2×C107—81no—
439C2×C107#241011yescharacteristic
440#3586C2×C10711yescharacteristic
441#3069C2×C10711yescharacteristic, complemented
442#3039C2×C10711yescharacteristic, complemented
443#3022C2×C10711yescharacteristic, complemented
444C2×#456C2×C10711yescharacteristic, complemented
445#2901C2×C10711yescharacteristic, complemented
446#2050C2×C10711yescharacteristic, complemented
447#2049C2×C10711yescharacteristic, complemented
448#2009C2×C10711yescharacteristic, complemented
449#2005C2×C10711yescharacteristic, complemented
450#1906C2×C10711yescharacteristic, complemented
451#1902C2×C10711yescharacteristic, complemented
452#1902C2×C10711yescharacteristic, complemented
453#1861C2×C10711yescharacteristic, complemented
454#1796C2×C10711yescharacteristic, complemented
455C107#2447411yescharacteristic, direct product factor, Sylow
456#585C22×C10711yescharacteristic
457C2×2−1+4C22×C10711yescharacteristic
458#578—22no—
459#578—22no—
460#577—22no—
461#577—22no—
462#575—22no—
463#575C22×C10711yescharacteristic
464#575C22×C10711yescharacteristic
465C2×#137—22no—
466C2×#137C22×C10711yescharacteristic
467C2×#137C22×C10711yescharacteristic
468C2×#137C22×C10711yescharacteristic
469C2×#137C22×C10711yescharacteristic
470C2×#137C22×C10711yescharacteristic, complemented
471#568C22×C10711yescharacteristic
472#568C22×C10711yescharacteristic
473#536C22×C10711yescharacteristic
474C2×C4⋊Q8C22×C10711yescharacteristic, complemented
475C4×#41C22×C10711yescharacteristic
476#473—22no—
477#471—22no—
478#462—22no—
479#461—22no—
480#456—22no—
481#456—22no—
482#456—22no—
483#455—22no—
484#430C22×C10711yescharacteristic, complemented
485#423C22×C10711yescharacteristic, complemented
486#421—22no—
487#421C22×C10711yescharacteristic
488#421C22×C10711yescharacteristic
489#421C22×C10711yescharacteristic
490#421C22×C10711yescharacteristic
491C2×#104—22no—
492C2×#104C22×C10711yescharacteristic
493C2×#104C22×C10711yescharacteristic
494C2×#104C22×C10711yescharacteristic, complemented
495#419C22×C10711yescharacteristic, complemented
496#419C22×C10711yescharacteristic, complemented
497#419C22×C10711yescharacteristic, complemented
498#413C22×C10711yescharacteristic
499#413C22×C10711yescharacteristic, complemented
500C2×#101C22×C10711yescharacteristic, complemented
501C2×#101C22×C10711yescharacteristic, complemented
502#410C22×C10711yescharacteristic, complemented
503#344C22×C10711yescharacteristic, complemented
504#344C22×C10711yescharacteristic, complemented
505#339C22×C10711yescharacteristic, complemented
506#338C22×C10711yescharacteristic, complemented
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C10712yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C10712yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C10711yescharacteristic
525C2×#41C23×C10711yescharacteristic
526C2×#41C23×C10711yescharacteristic
527C2×#41C23×C10711yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C10711yescharacteristic
531C22×Q8C23×C10711yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C10712yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C10712yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C10712yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C10712yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C10711yescharacteristic
577C2×M16C23×C10711yescharacteristic
578C2×M16C23×C10711yescharacteristic
579C2×M16C23×C10711yescharacteristic
580C2×M16C23×C10711yescharacteristic
581C2×M16C23×C10711yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C10711yescharacteristic
594#117C23×C10711yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C10711yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C10712yes—
609#104D4×C10712yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C10712yes—
649#41C2×D4×C10712yes—
650#41C2×D4×C10712yes—
651#41C2×D4×C10712yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C10711yescharacteristic
672C2×Q8C2×D4×C10711yescharacteristic
673C2×Q8C2×D4×C10712yes—
674C2×Q8C2×D4×C10711yescharacteristic
675C2×Q8#41×C10711yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C10711yescharacteristic
688C2×D4C2×D4×C10711yescharacteristic
689C2×D4C2×D4×C10711yescharacteristic
690C2×D4#41×C10711yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C10711yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C10712yes—
734M16C2×D4×C10712yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C10712yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C10711yescharacteristic
758C42C2×D4×C10711yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C10711yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C10712yes—
782Q8#121×C10712yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C10712yes—
802D4#121×C10712yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C10711yescharacteristic
833C2×C4C22×D4×C10711yescharacteristic
834C2×C4C22×D4×C10711yescharacteristic
835C2×C4C22×D4×C10711yescharacteristic
836C2×C4C2×#41×C10711yescharacteristic
837C2×C4H(5,𝔽2)×C10711yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22#534×C10711yescharacteristic
855C22D42×C10711yescharacteristic
856C22#546×C10711yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C10711yescharacteristic
868C4C2×#121×C10711yescharacteristic
869C4D42×C10711yescharacteristic
870C4#546×C10711yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C107×#241011yescharacteristic
subgroupG/H
center, socleC2×C107#2410
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3586C2
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
2. C107×#3069C2semidirect
3. C107×#3039C2semidirect
4. C107×#3022C2semidirect
5. C2×#456×C107C2semidirect
6. C107×#2901C2semidirect
7. C107×#2050C2semidirect
8. C107×#2049C2semidirect
9. C107×#2009C2semidirect
10. C107×#2005C2semidirect
11. C107×#1906C2semidirect
12. C107×#1902C2semidirect
13. C107×#1902C2semidirect
14. C107×#1861C2semidirect
15. C107×#1796C2semidirect
30. C2×#137×C107C22semidirect
34. C2×C4⋊Q8×C107C22semidirect
44. #430×C107C22semidirect
45. #423×C107C22semidirect
54. C2×#104×C107C22semidirect
55. #419×C107C22semidirect
56. #419×C107C22semidirect
57. #419×C107C22semidirect
59. #413×C107C22semidirect
60. C2×#101×C107C22semidirect
61. C2×#101×C107C22semidirect
62. #410×C107C22semidirect
63. #344×C107C22semidirect
64. #344×C107C22semidirect
65. #339×C107C22semidirect
66. #338×C107C22semidirect
431. #24474C107direct (N × H)
441. #3069C2×C107semidirect
442. #3039C2×C107semidirect
443. #3022C2×C107semidirect
444. C2×#456C2×C107semidirect
445. #2901C2×C107semidirect
446. #2050C2×C107semidirect
447. #2049C2×C107semidirect
448. #2009C2×C107semidirect
449. #2005C2×C107semidirect
450. #1906C2×C107semidirect
451. #1902C2×C107semidirect
452. #1902C2×C107semidirect
453. #1861C2×C107semidirect
454. #1796C2×C107semidirect
455. C107#24474direct (N × H)
470. C2×#137C22×C107semidirect
474. C2×C4⋊Q8C22×C107semidirect
484. #430C22×C107semidirect
485. #423C22×C107semidirect
494. C2×#104C22×C107semidirect
495. #419C22×C107semidirect
496. #419C22×C107semidirect
497. #419C22×C107semidirect
499. #413C22×C107semidirect
500. C2×#101C22×C107semidirect
501. C2×#101C22×C107semidirect
502. #410C22×C107semidirect
503. #344C22×C107semidirect
504. #344C22×C107semidirect
505. #339C22×C107semidirect
506. #338C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35862
C107×#30692
C107×#30392
C107×#30222
C2×#456×C1072
C107×#29012
C107×#20502
C107×#20492
C107×#20092
C107×#20052
C107×#19062
C107×#19022
C107×#18612
C107×#17962
#24474107