Finite Group Databasebeta

← C107×#24459 #41050423

Subgroups — C107×#24459 #41050423

Order 27392.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C107C211yesmaximal, characteristic
2C2×#471×C107C211yesmaximal, characteristic, complemented
3C107×#3046C211yesmaximal, characteristic, complemented
4C2×#455×C107C211yesmaximal, characteristic, complemented
5C107×#3009C211yesmaximal, characteristic, complemented
6C107×#2897C211yesmaximal, characteristic, complemented
7C107×#2051C211yesmaximal, characteristic, complemented
8C107×#2045C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2003C211yesmaximal, characteristic, complemented
11C107×#1908C211yesmaximal, characteristic, complemented
12C107×#1883C211yesmaximal, characteristic, complemented
13C107×#1876C211yesmaximal, characteristic, complemented
14C107×#1866C211yesmaximal, characteristic, complemented
15C107×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C107C2211yescharacteristic
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18#576×C107—24no—
19#576×C107—24no—
20C2×#137×C107C2211yescharacteristic
21C2×#137×C107C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C107—21no—
23C2×AGL(1,ℤ/8)×C107—21no—
24C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
26C2×#135×C107—21no—
27C2×#135×C107C2211yescharacteristic
28C22×SD16×C107C2211yescharacteristic, complemented
29C22×D8×C107—21no—
30C22×D8×C107C2211yescharacteristic
31C2×#131×C107C2211yescharacteristic
32C2×#131×C107C2211yescharacteristic, complemented
33#536×C107C2211yescharacteristic, complemented
34C2×#124×C107C2211yescharacteristic, complemented
35#520×C107C2211yescharacteristic, complemented
36#471×C107—24no—
37#464×C107—21no—
38#463×C107—21no—
39#462×C107—21no—
40#461×C107—21no—
41#455×C107—24no—
42#452×C107—21no—
43#452×C107—21no—
44#450×C107—21no—
45#450×C107—21no—
46C2×#108×C107C2211yescharacteristic, complemented
47#424×C107C2211yescharacteristic, complemented
48C2×#104×C107C2211yescharacteristic
49C2×#104×C107C2211yescharacteristic, complemented
50C2×#104×C107C2211yescharacteristic, complemented
51#418×C107—21no—
52#418×C107C2211yescharacteristic, complemented
53#418×C107C2211yescharacteristic, complemented
54#417×C107—21no—
55#417×C107C2211yescharacteristic
56#417×C107C2211yescharacteristic, complemented
57#416×C107—21no—
58#416×C107C2211yescharacteristic
59C2×#103×C107C2211yescharacteristic, complemented
60C2×#102×C107—21no—
61C2×#102×C107C2211yescharacteristic, complemented
62C2×#101×C107C2211yescharacteristic, complemented
63C2×#100×C107C2211yescharacteristic, complemented
64C2×#100×C107C2211yescharacteristic, complemented
65#408×C107C2211yescharacteristic, complemented
66#390×C107C2211yescharacteristic, complemented
67#343×C107C2211yescharacteristic, complemented
68#341×C107C2211yescharacteristic, complemented
69#339×C107C2211yescharacteristic, complemented
70#336×C107C2211yescharacteristic, complemented
71H(5,𝔽2)×C107—22no—
72H(5,𝔽2)×C107—22no—
73H(5,𝔽2)×C107—22no—
74H(5,𝔽2)×C107—22no—
75H(5,𝔽2)×C107—22no—
76H(5,𝔽2)×C107—41no—
77H(5,𝔽2)×C107—41no—
78H(5,𝔽2)×C107D414yes—
79C2×#41×C107—21no—
80C2×#41×C107—21no—
81C2×#41×C107—21no—
82C2×#41×C107—21no—
83C2×#41×C107C2311yescharacteristic
84C2×#41×C107C2311yescharacteristic
85C2×#41×C107C2311yescharacteristic
86C22×Q8×C107C2311yescharacteristic
87C22×D4×C107—21no—
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—21no—
91C22×D4×C107—41no—
92C22×D4×C107—41no—
93C22×D4×C107C2311yescharacteristic
94C22×D4×C107C2311yescharacteristic
95#137×C107—22no—
96#137×C107—22no—
97#137×C107—22no—
98#137×C107—22no—
99AGL(1,ℤ/8)×C107—28no—
100AGL(1,ℤ/8)×C107—28no—
101AGL(1,ℤ/8)×C107—22no—
102AGL(1,ℤ/8)×C107—22no—
103AGL(1,ℤ/8)×C107—22no—
104AGL(1,ℤ/8)×C107D414yes—
105#135×C107—28no—
106#135×C107—22no—
107#135×C107—22no—
108C2×Q16×C107—21no—
109C2×Q16×C107—21no—
110C2×Q16×C107D411yescharacteristic
111C2×SD16×C107—21no—
112C2×SD16×C107—21no—
113C2×SD16×C107—21no—
114C2×SD16×C107—21no—
115C2×SD16×C107—22no—
116C2×SD16×C107—21no—
117C2×SD16×C107—21no—
118C2×SD16×C107—41no—
119C2×SD16×C107D411yescharacteristic
120C2×SD16×C107D411yescharacteristic
121C2×D8×C107—28no—
122C2×D8×C107—21no—
123C2×D8×C107—21no—
124C2×D8×C107—22no—
125C2×D8×C107—22no—
126C2×D8×C107—21no—
127C2×D8×C107—21no—
128C2×D8×C107D411yescharacteristic
129#131×C107—22no—
130#131×C107—22no—
131#131×C107—22no—
132#131×C107—41no—
133C2×M16×C107—21no—
134C2×M16×C107—21no—
135C2×M16×C107C2311yescharacteristic
136C2×M16×C107C2311yescharacteristic
137C2×M16×C107C2311yescharacteristic
138C2×M16×C107C2311yescharacteristic
139C22×C8×C107—21no—
140C22×C8×C107—21no—
141C22×C8×C107C2311yescharacteristic
142C22×C8×C107C2311yescharacteristic
143C4⋊Q8×C107—21no—
144#124×C107—22no—
145#124×C107—21no—
146#124×C107—41no—
147#123×C107—41no—
148C22⋊Q8×C107—21no—
149C22⋊Q8×C107—21no—
150C4×Q8×C107—21no—
151C4×D4×C107—21no—
152C4×D4×C107—41no—
153#117×C107—21no—
154#117×C107C2311yescharacteristic
155C2×C4⋊C4×C107—21no—
156C2×C4⋊C4×C107C2311yescharacteristic
157C2×C22⋊C4×C107—41no—
158C2×C22⋊C4×C107—41no—
159C2×C42×C107C2311yescharacteristic
160#108×C107—22no—
161C4⋊C8×C107—21no—
162C4⋊C8×C107—21no—
163#104×C107—22no—
164#104×C107—22no—
165#104×C107—41no—
166#103×C107—21no—
167#103×C107—21no—
168#103×C107—21no—
169#103×C107—21no—
170#103×C107D411yescharacteristic
171#103×C107D411yescharacteristic
172#102×C107—21no—
173#102×C107—21no—
174#102×C107—21no—
175#102×C107—21no—
176#102×C107—21no—
177#102×C107—21no—
178#102×C107—21no—
179#102×C107—21no—
180#102×C107D411yescharacteristic
181#102×C107D411yescharacteristic
182#101×C107—22no—
183#100×C107—22no—
184#100×C107—22no—
185C22⋊C8×C107—21no—
186C22⋊C8×C107—21no—
187C24×C107—21no—
188C24×C107—21no—
189C24×C107—41no—
190C24×C107—41no—
191#41×C107—21no—
192#41×C107—21no—
193#41×C107—21no—
194#41×C107—21no—
195#41×C107—24no—
196#41×C107—24no—
197#41×C107—24no—
198#41×C107—21no—
199#41×C107—21no—
200#41×C107—21no—
201#41×C107—21no—
202#41×C107—42no—
203#41×C107—42no—
204#41×C107—42no—
205#41×C107—42no—
206#41×C107—42no—
207#41×C107C2×D412yes—
208#41×C107C2×D412yes—
209#41×C107C2×D412yes—
210#41×C107#4112yes—
211C2×Q8×C107—21no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107—21no—
215C2×Q8×C107—21no—
216C2×Q8×C107—21no—
217C2×Q8×C107C2×D411yescharacteristic
218C2×Q8×C107C2×D411yescharacteristic
219C2×Q8×C107C2×D411yescharacteristic
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—24no—
223C2×D4×C107—24no—
224C2×D4×C107—24no—
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—42no—
237C2×D4×C107—42no—
238C2×D4×C107—42no—
239C2×D4×C107—41no—
240C2×D4×C107—41no—
241C2×D4×C107—41no—
242C2×D4×C107—41no—
243C2×D4×C107—44no—
244C2×D4×C107—42no—
245C2×D4×C107—44no—
246C2×D4×C107—44no—
247C2×D4×C107—44no—
248C2×D4×C107—42no—
249C2×D4×C107C2×D412yes—
250C2×D4×C107C2×D412yes—
251C2×D4×C107C2×D411yescharacteristic
252C2×D4×C107C2×D411yescharacteristic
253C2×D4×C107C2×D411yescharacteristic
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—21no—
259C22×C4×C107—21no—
260C22×C4×C107—41no—
261C22×C4×C107—41no—
262C22×C4×C107—41no—
263C22×C4×C107C2411yescharacteristic
264Q16×C107—22no—
265Q16×C107—42no—
266Q16×C107—42no—
267SD16×C107—24no—
268SD16×C107—24no—
269SD16×C107—22no—
270SD16×C107—22no—
271SD16×C107—42no—
272SD16×C107—42no—
273SD16×C107—42no—
274SD16×C107—42no—
275D8×C107—24no—
276D8×C107—24no—
277D8×C107—24no—
278D8×C107—22no—
279D8×C107—24no—
280M16×C107—24no—
281M16×C107—21no—
282M16×C107—21no—
283M16×C107—21no—
284M16×C107—21no—
285M16×C107—21no—
286M16×C107—21no—
287M16×C107—21no—
288M16×C107—42no—
289M16×C107C2×D412yes—
290C2×C8×C107—24no—
291C2×C8×C107—21no—
292C2×C8×C107—21no—
293C2×C8×C107—21no—
294C2×C8×C107—21no—
295C2×C8×C107—21no—
296C2×C8×C107—21no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107—42no—
300C2×C8×C107C2×D411yescharacteristic
301C2×C8×C107C2×D411yescharacteristic
302C2×C8×C107C2×D411yescharacteristic
303C2×C8×C107C2×D411yescharacteristic
304C4⋊C4×C107—21no—
305C4⋊C4×C107—21no—
306C4⋊C4×C107—41no—
307C4⋊C4×C107—41no—
308C4⋊C4×C107—41no—
309C4⋊C4×C107C2×D411yescharacteristic
310C4⋊C4×C107C2×D411yescharacteristic
311C22⋊C4×C107—21no—
312C22⋊C4×C107—41no—
313C22⋊C4×C107—41no—
314C22⋊C4×C107—41no—
315C22⋊C4×C107—44no—
316C22⋊C4×C107—82no—
317C42×C107—21no—
318C42×C107—21no—
319C42×C107—21no—
320C42×C107—41no—
321C23×C107—21no—
322C23×C107—21no—
323C23×C107—21no—
324C23×C107—22no—
325C23×C107—22no—
326C23×C107—44no—
327C23×C107—44no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—81no—
333C23×C107—81no—
334C23×C107—81no—
335C23×C107—81no—
336C23×C107—161no—
337C23×C107—161no—
338C23×C107—161no—
339C23×C107—161no—
340C23×C107H(5,𝔽2)11yescharacteristic
341Q8×C107—21no—
342Q8×C107—21no—
343Q8×C107—21no—
344Q8×C107—21no—
345Q8×C107—41no—
346Q8×C107—41no—
347Q8×C107—41no—
348Q8×C107—41no—
349Q8×C107#12012yes—
350Q8×C107#12112yes—
351D4×C107—22no—
352D4×C107—22no—
353D4×C107—22no—
354D4×C107—22no—
355D4×C107—22no—
356D4×C107—22no—
357D4×C107—21no—
358D4×C107—22no—
359D4×C107—21no—
360D4×C107—22no—
361D4×C107—21no—
362D4×C107—21no—
363D4×C107—44no—
364D4×C107—44no—
365D4×C107—44no—
366D4×C107—44no—
367D4×C107—41no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—41no—
372D4×C107—41no—
373D4×C107#12012yes—
374D4×C107#12112yes—
375C2×C4×C107—21no—
376C2×C4×C107—21no—
377C2×C4×C107—22no—
378C2×C4×C107—22no—
379C2×C4×C107—22no—
380C2×C4×C107—22no—
381C2×C4×C107—21no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—44no—
385C2×C4×C107—44no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—81no—
396C2×C4×C107—161no—
397C2×C4×C107C22×D411yescharacteristic
398C2×C4×C107C22×D411yescharacteristic
399C2×C4×C107C22×D411yescharacteristic
400C2×C4×C107C22×D411yescharacteristic
401C2×C4×C107C2×#4111yescharacteristic
402C2×C4×C107H(5,𝔽2)11yescharacteristic
403C8×C107—21no—
404C8×C107—22no—
405C8×C107—21no—
406C8×C107—21no—
407C8×C107—21no—
408C8×C107—41no—
409C8×C107—41no—
410C8×C107—41no—
411C22×C107—21no—
412C22×C107—21no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—41no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—82no—
425C22×C107—82no—
426C22×C107—81no—
427C22×C107—81no—
428C22×C107—81no—
429C22×C107—81no—
430C22×C107—161no—
431C22×C107—161no—
432C22×C107—164no—
433C22×C107—164no—
434C22×C107#53411yescharacteristic
435C22×C107D4211yescharacteristic
436C22×C107#54611yescharacteristic
437C4×C107—22no—
438C4×C107—22no—
439C4×C107—41no—
440C4×C107—41no—
441C4×C107—41no—
442C4×C107—81no—
443C4×C107—81no—
444C4×C107—81no—
445C4×C107C2×#12011yescharacteristic
446C4×C107C2×#12111yescharacteristic
447C4×C107D4211yescharacteristic
448C4×C107#54611yescharacteristic
449#24459C10711yesmaximal, characteristic, direct product factor, Sylow
450C2×C107—21no—
451C2×C107—21no—
452C2×C107—42no—
453C2×C107—42no—
454C2×C107—81no—
455C2×C107—82no—
456C2×C107—82no—
457C2×C107#241011yescharacteristic
458C2×C107#328811yescharacteristic
459C2×C107#329011yescharacteristic
460C2×#576C2×C10711yescharacteristic
461C2×#471C2×C10711yescharacteristic, complemented
462#3046C2×C10711yescharacteristic, complemented
463C2×#455C2×C10711yescharacteristic, complemented
464#3009C2×C10711yescharacteristic, complemented
465#2897C2×C10711yescharacteristic, complemented
466#2051C2×C10711yescharacteristic, complemented
467#2045C2×C10711yescharacteristic, complemented
468#2012C2×C10711yescharacteristic, complemented
469#2003C2×C10711yescharacteristic, complemented
470#1908C2×C10711yescharacteristic, complemented
471#1883C2×C10711yescharacteristic, complemented
472#1876C2×C10711yescharacteristic, complemented
473#1866C2×C10711yescharacteristic, complemented
474#1792C2×C10711yescharacteristic, complemented
475C107#2445911yescharacteristic, direct product factor, Sylow
476C2×H(5,𝔽2)C22×C10711yescharacteristic
477C2×H(5,𝔽2)C22×C10711yescharacteristic
478#576—24no—
479#576—24no—
480C2×#137C22×C10711yescharacteristic
481C2×#137C22×C10711yescharacteristic, complemented
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
485C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
486C2×#135—21no—
487C2×#135C22×C10711yescharacteristic
488C22×SD16C22×C10711yescharacteristic, complemented
489C22×D8—21no—
490C22×D8C22×C10711yescharacteristic
491C2×#131C22×C10711yescharacteristic
492C2×#131C22×C10711yescharacteristic, complemented
493#536C22×C10711yescharacteristic, complemented
494C2×#124C22×C10711yescharacteristic, complemented
495#520C22×C10711yescharacteristic, complemented
496#471—24no—
497#464—21no—
498#463—21no—
499#462—21no—
500#461—21no—
501#455—24no—
502#452—21no—
503#452—21no—
504#450—21no—
505#450—21no—
506C2×#108C22×C10711yescharacteristic, complemented
507#424C22×C10711yescharacteristic, complemented
508C2×#104C22×C10711yescharacteristic
509C2×#104C22×C10711yescharacteristic, complemented
510C2×#104C22×C10711yescharacteristic, complemented
511#418—21no—
512#418C22×C10711yescharacteristic, complemented
513#418C22×C10711yescharacteristic, complemented
514#417—21no—
515#417C22×C10711yescharacteristic
516#417C22×C10711yescharacteristic, complemented
517#416—21no—
518#416C22×C10711yescharacteristic
519C2×#103C22×C10711yescharacteristic, complemented
520C2×#102—21no—
521C2×#102C22×C10711yescharacteristic, complemented
522C2×#101C22×C10711yescharacteristic, complemented
523C2×#100C22×C10711yescharacteristic, complemented
524C2×#100C22×C10711yescharacteristic, complemented
525#408C22×C10711yescharacteristic, complemented
526#390C22×C10711yescharacteristic, complemented
527#343C22×C10711yescharacteristic, complemented
528#341C22×C10711yescharacteristic, complemented
529#339C22×C10711yescharacteristic, complemented
530#336C22×C10711yescharacteristic, complemented
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C10714yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C10711yescharacteristic
544C2×#41C23×C10711yescharacteristic
545C2×#41C23×C10711yescharacteristic
546C22×Q8C23×C10711yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C10711yescharacteristic
554C22×D4C23×C10711yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C10714yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C10711yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C10711yescharacteristic
580C2×SD16D4×C10711yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C10711yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C10711yescharacteristic
596C2×M16C23×C10711yescharacteristic
597C2×M16C23×C10711yescharacteristic
598C2×M16C23×C10711yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C10711yescharacteristic
602C22×C8C23×C10711yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C10711yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C10711yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C42C23×C10711yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C10711yescharacteristic
631#103D4×C10711yescharacteristic
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C10711yescharacteristic
641#102D4×C10711yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41C2×D4×C10712yes—
668#41C2×D4×C10712yes—
669#41C2×D4×C10712yes—
670#41#41×C10712yes—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C10711yescharacteristic
678C2×Q8C2×D4×C10711yescharacteristic
679C2×Q8C2×D4×C10711yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C10712yes—
710C2×D4C2×D4×C10712yes—
711C2×D4C2×D4×C10711yescharacteristic
712C2×D4C2×D4×C10711yescharacteristic
713C2×D4C2×D4×C10711yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4C24×C10711yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C10712yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C10711yescharacteristic
761C2×C8C2×D4×C10711yescharacteristic
762C2×C8C2×D4×C10711yescharacteristic
763C2×C8C2×D4×C10711yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C10711yescharacteristic
770C4⋊C4C2×D4×C10711yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C10711yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C10712yes—
810Q8#121×C10712yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C10712yes—
834D4#121×C10712yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C10711yescharacteristic
858C2×C4C22×D4×C10711yescharacteristic
859C2×C4C22×D4×C10711yescharacteristic
860C2×C4C22×D4×C10711yescharacteristic
861C2×C4C2×#41×C10711yescharacteristic
862C2×C4H(5,𝔽2)×C10711yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22#534×C10711yescharacteristic
895C22D42×C10711yescharacteristic
896C22#546×C10711yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C10711yescharacteristic
906C4C2×#121×C10711yescharacteristic
907C4D42×C10711yescharacteristic
908C4#546×C10711yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2C107×#241011yescharacteristic
917C2C107×#328811yescharacteristic
918C2C107×#329011yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#576×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#471×C107C2semidirect
3. C107×#3046C2semidirect
4. C2×#455×C107C2semidirect
5. C107×#3009C2semidirect
6. C107×#2897C2semidirect
7. C107×#2051C2semidirect
8. C107×#2045C2semidirect
9. C107×#2012C2semidirect
10. C107×#2003C2semidirect
11. C107×#1908C2semidirect
12. C107×#1883C2semidirect
13. C107×#1876C2semidirect
14. C107×#1866C2semidirect
15. C107×#1792C2semidirect
21. C2×#137×C107C22semidirect
28. C22×SD16×C107C22semidirect
32. C2×#131×C107C22semidirect
33. #536×C107C22semidirect
34. C2×#124×C107C22semidirect
35. #520×C107C22semidirect
46. C2×#108×C107C22semidirect
47. #424×C107C22semidirect
49. C2×#104×C107C22semidirect
50. C2×#104×C107C22semidirect
52. #418×C107C22semidirect
53. #418×C107C22semidirect
56. #417×C107C22semidirect
59. C2×#103×C107C22semidirect
61. C2×#102×C107C22semidirect
62. C2×#101×C107C22semidirect
63. C2×#100×C107C22semidirect
64. C2×#100×C107C22semidirect
65. #408×C107C22semidirect
66. #390×C107C22semidirect
67. #343×C107C22semidirect
68. #341×C107C22semidirect
69. #339×C107C22semidirect
70. #336×C107C22semidirect
449. #24459C107direct (N × H)
461. C2×#471C2×C107semidirect
462. #3046C2×C107semidirect
463. C2×#455C2×C107semidirect
464. #3009C2×C107semidirect
465. #2897C2×C107semidirect
466. #2051C2×C107semidirect
467. #2045C2×C107semidirect
468. #2012C2×C107semidirect
469. #2003C2×C107semidirect
470. #1908C2×C107semidirect
471. #1883C2×C107semidirect
472. #1876C2×C107semidirect
473. #1866C2×C107semidirect
474. #1792C2×C107semidirect
475. C107#24459direct (N × H)
481. C2×#137C22×C107semidirect
488. C22×SD16C22×C107semidirect
492. C2×#131C22×C107semidirect
493. #536C22×C107semidirect
494. C2×#124C22×C107semidirect
495. #520C22×C107semidirect
506. C2×#108C22×C107semidirect
507. #424C22×C107semidirect
509. C2×#104C22×C107semidirect
510. C2×#104C22×C107semidirect
512. #418C22×C107semidirect
513. #418C22×C107semidirect
516. #417C22×C107semidirect
519. C2×#103C22×C107semidirect
521. C2×#102C22×C107semidirect
522. C2×#101C22×C107semidirect
523. C2×#100C22×C107semidirect
524. C2×#100C22×C107semidirect
525. #408C22×C107semidirect
526. #390C22×C107semidirect
527. #343C22×C107semidirect
528. #341C22×C107semidirect
529. #339C22×C107semidirect
530. #336C22×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1072
C2×#471×C1072
C107×#30462
C2×#455×C1072
C107×#30092
C107×#28972
C107×#20512
C107×#20452
C107×#20122
C107×#20032
C107×#19082
C107×#18832
C107×#18762
C107×#18662
C107×#17922
#24459107