Finite Group Databasebeta

← C107×#24460 #41050424

Subgroups — C107×#24460 #41050424

Order 27392.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C107C211yesmaximal, characteristic, complemented
2C2×#472×C107C211yesmaximal, characteristic, complemented
3C107×#3045C211yesmaximal, characteristic, complemented
4C2×#454×C107C211yesmaximal, characteristic, complemented
5C107×#3008C211yesmaximal, characteristic, complemented
6C107×#2898C211yesmaximal, characteristic, complemented
7C107×#2052C211yesmaximal, characteristic, complemented
8C107×#2046C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2004C211yesmaximal, characteristic, complemented
11C107×#1907C211yesmaximal, characteristic, complemented
12C107×#1883C211yesmaximal, characteristic, complemented
13C107×#1876C211yesmaximal, characteristic, complemented
14C107×#1866C211yesmaximal, characteristic, complemented
15C107×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C107C2211yescharacteristic
17C2×H(5,𝔽2)×C107C2211yescharacteristic
18#577×C107—24no—
19#577×C107—24no—
20C2×#137×C107—21no—
21C2×#137×C107C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C107—21no—
23C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
26C2×#135×C107—21no—
27C2×#135×C107C2211yescharacteristic
28C22×SD16×C107—21no—
29C22×SD16×C107C2211yescharacteristic
30C22×D8×C107C2211yescharacteristic
31C2×#131×C107C2211yescharacteristic
32C2×#131×C107C2211yescharacteristic, complemented
33#535×C107C2211yescharacteristic
34C2×#124×C107C2211yescharacteristic, complemented
35#520×C107C2211yescharacteristic, complemented
36#472×C107—24no—
37#464×C107—21no—
38#463×C107—21no—
39#460×C107—21no—
40#459×C107—21no—
41#454×C107—24no—
42#449×C107—21no—
43#449×C107—21no—
44#447×C107—21no—
45#447×C107—21no—
46C2×#108×C107C2211yescharacteristic, complemented
47#424×C107C2211yescharacteristic, complemented
48C2×#104×C107C2211yescharacteristic
49C2×#104×C107C2211yescharacteristic
50C2×#104×C107C2211yescharacteristic, complemented
51#419×C107—21no—
52#419×C107C2211yescharacteristic, complemented
53#418×C107C2211yescharacteristic
54#417×C107—21no—
55#417×C107C2211yescharacteristic
56#417×C107C2211yescharacteristic
57#416×C107—21no—
58#416×C107C2211yescharacteristic
59C2×#103×C107—21no—
60C2×#103×C107C2211yescharacteristic, complemented
61C2×#102×C107C2211yescharacteristic, complemented
62C2×#101×C107C2211yescharacteristic, complemented
63C2×#100×C107C2211yescharacteristic
64C2×#100×C107C2211yescharacteristic, complemented
65#408×C107C2211yescharacteristic
66#390×C107C2211yescharacteristic
67#343×C107C2211yescharacteristic, complemented
68#341×C107C2211yescharacteristic, complemented
69#339×C107C2211yescharacteristic, complemented
70#336×C107C2211yescharacteristic, complemented
712−1+4×C107—22no—
722−1+4×C107—22no—
732−1+4×C107—41no—
742−1+4×C107D414yescomplemented
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
87C22×Q8×C107—21no—
88C22×Q8×C107—21no—
89C22×Q8×C107C2311yescharacteristic
90C22×D4×C107—21no—
91C22×D4×C107—21no—
92C22×D4×C107—41no—
93C22×D4×C107C2311yescharacteristic
94C22×D4×C107C2311yescharacteristic
95#137×C107—28no—
96#137×C107—22no—
97#137×C107—22no—
98AGL(1,ℤ/8)×C107—28no—
99AGL(1,ℤ/8)×C107—22no—
100AGL(1,ℤ/8)×C107—22no—
101AGL(1,ℤ/8)×C107—22no—
102AGL(1,ℤ/8)×C107—22no—
103AGL(1,ℤ/8)×C107—22no—
104AGL(1,ℤ/8)×C107D414yescomplemented
105#135×C107—28no—
106#135×C107—22no—
107#135×C107—22no—
108C2×Q16×C107—21no—
109C2×Q16×C107D411yescharacteristic
110C2×SD16×C107—28no—
111C2×SD16×C107—21no—
112C2×SD16×C107—22no—
113C2×SD16×C107—21no—
114C2×SD16×C107—22no—
115C2×SD16×C107—21no—
116C2×SD16×C107—21no—
117C2×SD16×C107—21no—
118C2×SD16×C107—21no—
119C2×SD16×C107D411yescharacteristic
120C2×SD16×C107D411yescharacteristic
121C2×D8×C107—21no—
122C2×D8×C107—21no—
123C2×D8×C107—21no—
124C2×D8×C107—22no—
125C2×D8×C107—21no—
126C2×D8×C107—21no—
127C2×D8×C107—41no—
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
143#127×C107—21no—
144#124×C107—22no—
145#124×C107—21no—
146#124×C107—41no—
147#121×C107—21no—
148#121×C107—21no—
149#120×C107—41no—
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×C107—21no—
171#103×C107—21no—
172#103×C107D411yescharacteristic
173#103×C107D411yescharacteristic
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—
190#41×C107—21no—
191#41×C107—21no—
192#41×C107—21no—
193#41×C107—21no—
194#41×C107—24no—
195#41×C107—24no—
196#41×C107—24no—
197#41×C107—21no—
198#41×C107—21no—
199#41×C107—21no—
200#41×C107—21no—
201#41×C107—44no—
202#41×C107—42no—
203#41×C107—42no—
204#41×C107—42no—
205#41×C107—44no—
206#41×C107—42no—
207#41×C107—42no—
208#41×C107C2×D412yes—
209#41×C107C2×D412yes—
210#41×C107C2×D412yes—
211#41×C107#4112yes—
212C2×Q8×C107—21no—
213C2×Q8×C107—24no—
214C2×Q8×C107—24no—
215C2×Q8×C107—21no—
216C2×Q8×C107—21no—
217C2×Q8×C107—21no—
218C2×Q8×C107—21no—
219C2×Q8×C107—41no—
220C2×Q8×C107—42no—
221C2×Q8×C107—42no—
222C2×Q8×C107C2×D412yes—
223C2×Q8×C107C2×D411yescharacteristic
224C2×Q8×C107C2×D411yescharacteristic
225C2×Q8×C107C2×D411yescharacteristic
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—24no—
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—21no—
239C2×D4×C107—21no—
240C2×D4×C107—21no—
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—44no—
248C2×D4×C107—44no—
249C2×D4×C107—41no—
250C2×D4×C107—42no—
251C2×D4×C107C2×D412yes—
252C2×D4×C107C2×D411yescharacteristic
253C2×D4×C107C2×D411yescharacteristic
254C2×D4×C107C2×D411yescharacteristic
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—21no—
259C22×C4×C107—21no—
260C22×C4×C107—21no—
261C22×C4×C107—41no—
262C22×C4×C107—41no—
263C22×C4×C107—41no—
264C22×C4×C107—41no—
265C22×C4×C107C2411yescharacteristic
266Q16×C107—24no—
267Q16×C107—22no—
268SD16×C107—24no—
269SD16×C107—24no—
270SD16×C107—24no—
271SD16×C107—22no—
272SD16×C107—24no—
273SD16×C107—22no—
274SD16×C107—42no—
275SD16×C107—42no—
276D8×C107—24no—
277D8×C107—22no—
278D8×C107—42no—
279D8×C107—42no—
280D8×C107—42no—
281D8×C107—42no—
282M16×C107—24no—
283M16×C107—21no—
284M16×C107—21no—
285M16×C107—21no—
286M16×C107—21no—
287M16×C107—21no—
288M16×C107—21no—
289M16×C107—21no—
290M16×C107—42no—
291M16×C107C2×D412yes—
292C2×C8×C107—24no—
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—21no—
300C2×C8×C107—21no—
301C2×C8×C107—42no—
302C2×C8×C107C2×D411yescharacteristic
303C2×C8×C107C2×D411yescharacteristic
304C2×C8×C107C2×D411yescharacteristic
305C2×C8×C107C2×D411yescharacteristic
306C4⋊C4×C107—21no—
307C4⋊C4×C107—21no—
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—44no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—81no—
332C23×C107—81no—
333C23×C107—81no—
334C23×C107—81no—
335C23×C107—161no—
336C23×C107—161no—
337C23×C107H(5,𝔽2)11yescharacteristic
338Q8×C107—21no—
339Q8×C107—21no—
340Q8×C107—22no—
341Q8×C107—21no—
342Q8×C107—22no—
343Q8×C107—21no—
344Q8×C107—44no—
345Q8×C107—41no—
346Q8×C107—41no—
347Q8×C107#12012yes—
348Q8×C107#12112yes—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—22no—
352D4×C107—22no—
353D4×C107—22no—
354D4×C107—21no—
355D4×C107—21no—
356D4×C107—22no—
357D4×C107—21no—
358D4×C107—21no—
359D4×C107—44no—
360D4×C107—44no—
361D4×C107—44no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—41no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—161no—
371D4×C107—161no—
372D4×C107#12012yes—
373D4×C107#12112yes—
374C2×C4×C107—21no—
375C2×C4×C107—21no—
376C2×C4×C107—22no—
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—44no—
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—41no—
422C22×C107—41no—
423C22×C107—82no—
424C22×C107—82no—
425C22×C107—81no—
426C22×C107—81no—
427C22×C107—81no—
428C22×C107—81no—
429C22×C107—81no—
430C22×C107—161no—
431C22×C107—161no—
432C22×C107—164no—
433C22×C107#53411yescharacteristic
434C22×C107D4211yescharacteristic
435C22×C107#54611yescharacteristic
436C4×C107—22no—
437C4×C107—22no—
438C4×C107—41no—
439C4×C107—42no—
440C4×C107—41no—
441C4×C107—41no—
442C4×C107—81no—
443C4×C107—81no—
444C4×C107C2×#12011yescharacteristic
445C4×C107C2×#12111yescharacteristic
446C4×C107D4211yescharacteristic
447C4×C107#54611yescharacteristic
448#24460C10711yesmaximal, characteristic, direct product factor, Sylow
449C2×C107—21no—
450C2×C107—21no—
451C2×C107—42no—
452C2×C107—42no—
453C2×C107—81no—
454C2×C107—82no—
455C2×C107—161no—
456C2×C107#241011yescharacteristic
457C2×C107#328811yescharacteristic
458C2×C107#329011yescharacteristic
459C2×#577C2×C10711yescharacteristic, complemented
460C2×#472C2×C10711yescharacteristic, complemented
461#3045C2×C10711yescharacteristic, complemented
462C2×#454C2×C10711yescharacteristic, complemented
463#3008C2×C10711yescharacteristic, complemented
464#2898C2×C10711yescharacteristic, complemented
465#2052C2×C10711yescharacteristic, complemented
466#2046C2×C10711yescharacteristic, complemented
467#2012C2×C10711yescharacteristic, complemented
468#2004C2×C10711yescharacteristic, complemented
469#1907C2×C10711yescharacteristic, complemented
470#1883C2×C10711yescharacteristic, complemented
471#1876C2×C10711yescharacteristic, complemented
472#1866C2×C10711yescharacteristic, complemented
473#1792C2×C10711yescharacteristic, complemented
474C107#2446011yescharacteristic, direct product factor, Sylow
475C2×2−1+4C22×C10711yescharacteristic
476C2×H(5,𝔽2)C22×C10711yescharacteristic
477#577—24no—
478#577—24no—
479C2×#137—21no—
480C2×#137C22×C10711yescharacteristic
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
483C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
484C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
485C2×#135—21no—
486C2×#135C22×C10711yescharacteristic
487C22×SD16—21no—
488C22×SD16C22×C10711yescharacteristic
489C22×D8C22×C10711yescharacteristic
490C2×#131C22×C10711yescharacteristic
491C2×#131C22×C10711yescharacteristic, complemented
492#535C22×C10711yescharacteristic
493C2×#124C22×C10711yescharacteristic, complemented
494#520C22×C10711yescharacteristic, complemented
495#472—24no—
496#464—21no—
497#463—21no—
498#460—21no—
499#459—21no—
500#454—24no—
501#449—21no—
502#449—21no—
503#447—21no—
504#447—21no—
505C2×#108C22×C10711yescharacteristic, complemented
506#424C22×C10711yescharacteristic, complemented
507C2×#104C22×C10711yescharacteristic
508C2×#104C22×C10711yescharacteristic
509C2×#104C22×C10711yescharacteristic, complemented
510#419—21no—
511#419C22×C10711yescharacteristic, complemented
512#418C22×C10711yescharacteristic
513#417—21no—
514#417C22×C10711yescharacteristic
515#417C22×C10711yescharacteristic
516#416—21no—
517#416C22×C10711yescharacteristic
518C2×#103—21no—
519C2×#103C22×C10711yescharacteristic, complemented
520C2×#102C22×C10711yescharacteristic, complemented
521C2×#101C22×C10711yescharacteristic, complemented
522C2×#100C22×C10711yescharacteristic
523C2×#100C22×C10711yescharacteristic, complemented
524#408C22×C10711yescharacteristic
525#390C22×C10711yescharacteristic
526#343C22×C10711yescharacteristic, complemented
527#341C22×C10711yescharacteristic, complemented
528#339C22×C10711yescharacteristic, complemented
529#336C22×C10711yescharacteristic, complemented
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C10714yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C10711yescharacteristic
544C2×#41C23×C10711yescharacteristic
545C2×#41C23×C10711yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C10711yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C10711yescharacteristic
553C22×D4C23×C10711yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C10714yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C10711yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C10711yescharacteristic
579C2×SD16D4×C10711yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C10711yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C10711yescharacteristic
595C2×M16C23×C10711yescharacteristic
596C2×M16C23×C10711yescharacteristic
597C2×M16C23×C10711yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C10711yescharacteristic
601C22×C8C23×C10711yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C10711yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C10711yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C10711yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C10711yescharacteristic
632#103D4×C10711yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C10711yescharacteristic
640#102D4×C10711yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
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—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C10712yes—
682C2×Q8C2×D4×C10711yescharacteristic
683C2×Q8C2×D4×C10711yescharacteristic
684C2×Q8C2×D4×C10711yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
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—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
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×C4—41no—
724C22×C4C24×C10711yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C10712yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C10711yescharacteristic
762C2×C8C2×D4×C10711yescharacteristic
763C2×C8C2×D4×C10711yescharacteristic
764C2×C8C2×D4×C10711yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C10711yescharacteristic
769C4⋊C4C2×D4×C10711yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C10711yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C10712yes—
807Q8#121×C10712yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C10712yes—
832D4#121×C10712yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
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—81no—
855C2×C4—161no—
856C2×C4C22×D4×C10711yescharacteristic
857C2×C4C22×D4×C10711yescharacteristic
858C2×C4C22×D4×C10711yescharacteristic
859C2×C4C22×D4×C10711yescharacteristic
860C2×C4C2×#41×C10711yescharacteristic
861C2×C4H(5,𝔽2)×C10711yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22#534×C10711yescharacteristic
893C22D42×C10711yescharacteristic
894C22#546×C10711yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4C2×#120×C10711yescharacteristic
904C4C2×#121×C10711yescharacteristic
905C4D42×C10711yescharacteristic
906C4#546×C10711yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C107×#241011yescharacteristic
915C2C107×#328811yescharacteristic
916C2C107×#329011yescharacteristic
subgroupG/H
center, socleC22×C107D42
commutator, Frattini, cosocleC22×C4C24×C107
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
1. C2×#577×C107C2semidirect
2. C2×#472×C107C2semidirect
3. C107×#3045C2semidirect
4. C2×#454×C107C2semidirect
5. C107×#3008C2semidirect
6. C107×#2898C2semidirect
7. C107×#2052C2semidirect
8. C107×#2046C2semidirect
9. C107×#2012C2semidirect
10. C107×#2004C2semidirect
11. C107×#1907C2semidirect
12. C107×#1883C2semidirect
13. C107×#1876C2semidirect
14. C107×#1866C2semidirect
15. C107×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C107C22semidirect
32. C2×#131×C107C22semidirect
34. C2×#124×C107C22semidirect
35. #520×C107C22semidirect
46. C2×#108×C107C22semidirect
47. #424×C107C22semidirect
50. C2×#104×C107C22semidirect
52. #419×C107C22semidirect
60. C2×#103×C107C22semidirect
61. C2×#102×C107C22semidirect
62. C2×#101×C107C22semidirect
64. C2×#100×C107C22semidirect
67. #343×C107C22semidirect
68. #341×C107C22semidirect
69. #339×C107C22semidirect
70. #336×C107C22semidirect
74. 2−1+4×C107D4semidirect
104. AGL(1,ℤ/8)×C107D4semidirect
448. #24460C107direct (N × H)
459. C2×#577C2×C107semidirect
460. C2×#472C2×C107semidirect
461. #3045C2×C107semidirect
462. C2×#454C2×C107semidirect
463. #3008C2×C107semidirect
464. #2898C2×C107semidirect
465. #2052C2×C107semidirect
466. #2046C2×C107semidirect
467. #2012C2×C107semidirect
468. #2004C2×C107semidirect
469. #1907C2×C107semidirect
470. #1883C2×C107semidirect
471. #1876C2×C107semidirect
472. #1866C2×C107semidirect
473. #1792C2×C107semidirect
474. C107#24460direct (N × H)
484. C2×AGL(1,ℤ/8)C22×C107semidirect
491. C2×#131C22×C107semidirect
493. C2×#124C22×C107semidirect
494. #520C22×C107semidirect
505. C2×#108C22×C107semidirect
506. #424C22×C107semidirect
509. C2×#104C22×C107semidirect
511. #419C22×C107semidirect
519. C2×#103C22×C107semidirect
520. C2×#102C22×C107semidirect
521. C2×#101C22×C107semidirect
523. C2×#100C22×C107semidirect
526. #343C22×C107semidirect
527. #341C22×C107semidirect
528. #339C22×C107semidirect
529. #336C22×C107semidirect
533. 2−1+4D4×C107semidirect
563. AGL(1,ℤ/8)D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1072
C2×#472×C1072
C107×#30452
C2×#454×C1072
C107×#30082
C107×#28982
C107×#20522
C107×#20462
C107×#20122
C107×#20042
C107×#19072
C107×#18832
C107×#18762
C107×#18662
C107×#17922
#24460107