Finite Group Databasebeta

← C107×#25140 #41051104

Subgroups — C107×#25140 #41051104

Order 27392.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C107C211yesmaximal, characteristic, complemented
2C107×#3055C211yesmaximal, characteristic, complemented
3C107×#3003C211yesmaximal, characteristic, complemented
4C2×#447×C107C211yesmaximal, characteristic, complemented
5C107×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C107C211yesmaximal, characteristic, complemented
7C107×#2063C211yesmaximal, characteristic, complemented
8C107×#2051C211yesmaximal, characteristic, complemented
9C107×#2045C211yesmaximal, characteristic, complemented
10C107×#2018C211yesmaximal, characteristic, complemented
11C107×#1978C211yesmaximal, characteristic, complemented
12C107×#1931C211yesmaximal, characteristic, complemented
13C107×#1907C211yesmaximal, characteristic, complemented
14C107×#1900C211yesmaximal, characteristic, complemented
15C107×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C107C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C107C2211yescharacteristic, complemented
20C22×D8×C107C2211yescharacteristic
21C22×D8×C107C2211yescharacteristic
22C2×#131×C107C2211yescharacteristic, complemented
23C22×M16×C107C2211yescharacteristic
24C22×M16×C107C2211yescharacteristic
25#525×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27#472×C107—24no—
28#469×C107—21no—
29#468×C107—21no—
30#466×C107—21no—
31#465×C107—21no—
32#450×C107—21no—
33#450×C107—21no—
34#447×C107—21no—
35#447×C107—21no—
36#447×C107—21no—
37#447×C107—21no—
38#447×C107—21no—
39#447×C107—21no—
40#436×C107—21no—
41#435×C107—21no—
42#435×C107—21no—
43C8×D4×C107—21no—
44C2×#108×C107C2211yescharacteristic, complemented
45C2×#108×C107C2211yescharacteristic, complemented
46#428×C107C2211yescharacteristic, complemented
47#424×C107C2211yescharacteristic, complemented
48#418×C107C2211yescharacteristic
49#418×C107C2211yescharacteristic
50#418×C107C2211yescharacteristic, complemented
51#417×C107C2211yescharacteristic, complemented
52C2×#102×C107C2211yescharacteristic
53C2×#102×C107C2211yescharacteristic
54C2×#100×C107—24no—
55C2×#100×C107C2211yescharacteristic
56C2×#100×C107C2211yescharacteristic
57C2×#100×C107C2211yescharacteristic
58C2×#100×C107C2211yescharacteristic
59C2×#100×C107C2211yescharacteristic, complemented
60C2×#100×C107C2211yescharacteristic, complemented
61#408×C107C2211yescharacteristic, complemented
62#407×C107C2211yescharacteristic
63C2×C22⋊C8×C107C2211yescharacteristic
64#405×C107C2211yescharacteristic, complemented
65#343×C107C2211yescharacteristic, complemented
66#343×C107C2211yescharacteristic, complemented
67#341×C107C2211yescharacteristic, complemented
68#341×C107C2211yescharacteristic, complemented
69C25×C107—21no—
70C2×#41×C107C2311yescharacteristic
71C22×D4×C107—22no—
72C22×D4×C107—22no—
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—41no—
80C22×D4×C107—41no—
81C22×D4×C107C2311yescharacteristic
82C22×D4×C107C2311yescharacteristic
83C22×D4×C107C2311yescharacteristic
84C23×C4×C107C2311yescharacteristic
85AGL(1,ℤ/8)×C107—22no—
86AGL(1,ℤ/8)×C107—22no—
87AGL(1,ℤ/8)×C107—22no—
88AGL(1,ℤ/8)×C107—41no—
89AGL(1,ℤ/8)×C107—41no—
90AGL(1,ℤ/8)×C107—41no—
91C2×SD16×C107—21no—
92C2×SD16×C107—21no—
93C2×SD16×C107—21no—
94C2×D8×C107—21no—
95C2×D8×C107—21no—
96C2×D8×C107—21no—
97C2×D8×C107—22no—
98C2×D8×C107—22no—
99C2×D8×C107—21no—
100C2×D8×C107—21no—
101C2×D8×C107—21no—
102C2×D8×C107—21no—
103C2×D8×C107—41no—
104C2×D8×C107—41no—
105#131×C107—22no—
106#131×C107—41no—
107C2×M16×C107—21no—
108C2×M16×C107—21no—
109C2×M16×C107—21no—
110C2×M16×C107—22no—
111C2×M16×C107—22no—
112C2×M16×C107—41no—
113C2×M16×C107—41no—
114C2×M16×C107C2311yescharacteristic
115C2×M16×C107C2311yescharacteristic
116C2×M16×C107C2311yescharacteristic
117C2×M16×C107C2311yescharacteristic
118C2×M16×C107C2311yescharacteristic
119C2×M16×C107C2311yescharacteristic
120C22×C8×C107—21no—
121C22×C8×C107—21no—
122C22×C8×C107—21no—
123C22×C8×C107C2311yescharacteristic
124C22×C8×C107C2311yescharacteristic
125#123×C107—21no—
126C22⋊Q8×C107D411yescharacteristic
127C22⋊Q8×C107D411yescharacteristic
128#121×C107—21no—
129#121×C107—21no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107D411yescharacteristic
133#121×C107D411yescharacteristic
134#120×C107—21no—
135C4×D4×C107—21no—
136C4×D4×C107—21no—
137#117×C107C2311yescharacteristic
138C2×C4⋊C4×C107C2311yescharacteristic
139C2×C22⋊C4×C107—21no—
140#108×C107—22no—
141#108×C107—41no—
142#107×C107—21no—
143#106×C107—21no—
144C4⋊C8×C107—21no—
145C4⋊C8×C107—21no—
146#103×C107—21no—
147#102×C107—21no—
148#102×C107—21no—
149#102×C107—21no—
150#102×C107—21no—
151#102×C107—21no—
152#102×C107—21no—
153#102×C107—21no—
154#102×C107—21no—
155#102×C107—21no—
156#102×C107—21no—
157#102×C107—21no—
158#100×C107—22no—
159#100×C107—22no—
160#100×C107—22no—
161#100×C107—22no—
162#100×C107—41no—
163#100×C107D414yescomplemented
164C22⋊C8×C107—21no—
165C22⋊C8×C107—21no—
166C22⋊C8×C107—21no—
167C22⋊C8×C107—21no—
168C22⋊C8×C107D411yescharacteristic
169C22⋊C8×C107D411yescharacteristic
170C22⋊C8×C107D411yescharacteristic
171C22⋊C8×C107D411yescharacteristic
172#97×C107—21no—
173C4×C8×C107—21no—
174C24×C107—24no—
175C24×C107—21no—
176C24×C107—21no—
177C24×C107—21no—
178C24×C107—42no—
179C24×C107—41no—
180C24×C107—41no—
181C24×C107—82no—
182C24×C107—82no—
183C24×C107#4111yescharacteristic
184#41×C107—21no—
185#41×C107—21no—
186#41×C107—21no—
187#41×C107—21no—
188C2×Q8×C107C2×D411yescharacteristic
189C2×D4×C107—24no—
190C2×D4×C107—21no—
191C2×D4×C107—21no—
192C2×D4×C107—21no—
193C2×D4×C107—21no—
194C2×D4×C107—21no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—21no—
208C2×D4×C107—21no—
209C2×D4×C107—42no—
210C2×D4×C107—42no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—42no—
215C2×D4×C107—42no—
216C2×D4×C107—42no—
217C2×D4×C107—42no—
218C2×D4×C107—41no—
219C2×D4×C107—41no—
220C2×D4×C107—41no—
221C2×D4×C107—41no—
222C2×D4×C107—82no—
223C2×D4×C107C2×D412yes—
224C2×D4×C107C2×D411yescharacteristic
225C2×D4×C107#4112yes—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107C2×D411yescharacteristic
233C22×C4×C107C2×D411yescharacteristic
234C22×C4×C107C2×D411yescharacteristic
235C22×C4×C107C2×D411yescharacteristic
236C22×C4×C107#4111yescharacteristic
237C22×C4×C107C2411yescharacteristic
238SD16×C107—42no—
239SD16×C107—42no—
240SD16×C107—42no—
241D8×C107—42no—
242D8×C107—42no—
243D8×C107—42no—
244D8×C107—42no—
245D8×C107—42no—
246D8×C107—42no—
247D8×C107—42no—
248M16×C107—21no—
249M16×C107—21no—
250M16×C107—21no—
251M16×C107—21no—
252M16×C107—21no—
253M16×C107—21no—
254M16×C107—21no—
255M16×C107—21no—
256M16×C107—21no—
257M16×C107—21no—
258M16×C107—42no—
259M16×C107—42no—
260M16×C107—42no—
261M16×C107C2×D412yes—
262M16×C107C2×D412yes—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—21no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—21no—
270C2×C8×C107—21no—
271C2×C8×C107—21no—
272C2×C8×C107—21no—
273C2×C8×C107—42no—
274C2×C8×C107—42no—
275C2×C8×C107—42no—
276C2×C8×C107C2×D411yescharacteristic
277C2×C8×C107C2×D411yescharacteristic
278C2×C8×C107C2×D411yescharacteristic
279C2×C8×C107C2×D411yescharacteristic
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107C2×D411yescharacteristic
285C4⋊C4×C107C2×D411yescharacteristic
286C22⋊C4×C107—21no—
287C22⋊C4×C107—21no—
288C22⋊C4×C107—21no—
289C22⋊C4×C107—21no—
290C22⋊C4×C107—21no—
291C22⋊C4×C107—41no—
292C22⋊C4×C107—41no—
293C42×C107—21no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—22no—
297C23×C107—21no—
298C23×C107—22no—
299C23×C107—22no—
300C23×C107—41no—
301C23×C107—44no—
302C23×C107—44no—
303C23×C107—41no—
304C23×C107—41no—
305C23×C107—41no—
306C23×C107—41no—
307C23×C107—41no—
308C23×C107—41no—
309C23×C107—41no—
310C23×C107—81no—
311C23×C107—81no—
312C23×C107—81no—
313C23×C107—81no—
314C23×C107—82no—
315C23×C107—82no—
316C23×C107—82no—
317C23×C107—81no—
318C23×C107—81no—
319C23×C107—88no—
320C23×C107—88no—
321C23×C107—82no—
322C23×C107#12111yescharacteristic
323C23×C107#12111yescharacteristic
324C23×C107C2×#4111yescharacteristic
325Q8×C107—21no—
326Q8×C107—21no—
327D4×C107—21no—
328D4×C107—22no—
329D4×C107—22no—
330D4×C107—22no—
331D4×C107—21no—
332D4×C107—22no—
333D4×C107—44no—
334D4×C107—44no—
335D4×C107—41no—
336D4×C107—41no—
337D4×C107—42no—
338D4×C107—41no—
339D4×C107—41no—
340D4×C107—41no—
341D4×C107—41no—
342D4×C107—41no—
343D4×C107—41no—
344D4×C107—41no—
345D4×C107—41no—
346D4×C107—81no—
347D4×C107—82no—
348D4×C107—82no—
349C2×C4×C107—21no—
350C2×C4×C107—21no—
351C2×C4×C107—21no—
352C2×C4×C107—21no—
353C2×C4×C107—21no—
354C2×C4×C107—21no—
355C2×C4×C107—21no—
356C2×C4×C107—21no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—21no—
360C2×C4×C107—21no—
361C2×C4×C107—21no—
362C2×C4×C107—41no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107—81no—
366C2×C4×C107#12111yescharacteristic
367C2×C4×C107#12111yescharacteristic
368C2×C4×C107C22×D411yescharacteristic
369C2×C4×C107C22×D411yescharacteristic
370C2×C4×C107C22×D411yescharacteristic
371C2×C4×C107C2×#4111yescharacteristic
372C2×C4×C107H(5,𝔽2)11yescharacteristic
373C2×C4×C107H(5,𝔽2)11yescharacteristic
374C8×C107—21no—
375C8×C107—21no—
376C8×C107—22no—
377C8×C107—22no—
378C8×C107—21no—
379C8×C107—21no—
380C8×C107—41no—
381C8×C107—41no—
382C8×C107—41no—
383C8×C107—41no—
384C22×C107—21no—
385C22×C107—21no—
386C22×C107—21no—
387C22×C107—21no—
388C22×C107—21no—
389C22×C107—21no—
390C22×C107—21no—
391C22×C107—42no—
392C22×C107—42no—
393C22×C107—41no—
394C22×C107—42no—
395C22×C107—42no—
396C22×C107—41no—
397C22×C107—41no—
398C22×C107—82no—
399C22×C107—82no—
400C22×C107—88no—
401C22×C107—82no—
402C22×C107—82no—
403C22×C107—88no—
404C22×C107—81no—
405C22×C107—81no—
406C22×C107—81no—
407C22×C107—81no—
408C22×C107—81no—
409C22×C107—81no—
410C22×C107—81no—
411C22×C107—161no—
412C22×C107—161no—
413C22×C107#47212yescomplemented
414C22×C107C2×#12111yescharacteristic
415C22×C107#52511yescharacteristic
416C22×C107#53811yescharacteristic
417C4×C107—21no—
418C4×C107—21no—
419C4×C107—41no—
420C4×C107—41no—
421C4×C107—41no—
422C4×C107—81no—
423C4×C107D4211yescharacteristic
424C4×C107D4211yescharacteristic
425C4×C107#54611yescharacteristic
426C4×C107#54611yescharacteristic
427#25140C10711yesmaximal, characteristic, direct product factor, Sylow
428C2×C107—21no—
429C2×C107—21no—
430C2×C107—22no—
431C2×C107—41no—
432C2×C107—81no—
433C2×C107—82no—
434C2×C107—82no—
435C2×C107—161no—
436C2×C107#242411yescharacteristic
437C2×C107C2×#47211yescharacteristic
438C2×C107#306811yescharacteristic
439C2×#472C2×C10711yescharacteristic, complemented
440#3055C2×C10711yescharacteristic, complemented
441#3003C2×C10711yescharacteristic, complemented
442C2×#447C2×C10711yescharacteristic, complemented
443#2933C2×C10711yescharacteristic, complemented
444C22×#100C2×C10711yescharacteristic, complemented
445#2063C2×C10711yescharacteristic, complemented
446#2051C2×C10711yescharacteristic, complemented
447#2045C2×C10711yescharacteristic, complemented
448#2018C2×C10711yescharacteristic, complemented
449#1978C2×C10711yescharacteristic, complemented
450#1931C2×C10711yescharacteristic, complemented
451#1907C2×C10711yescharacteristic, complemented
452#1900C2×C10711yescharacteristic, complemented
453#1855C2×C10711yescharacteristic, complemented
454C107#2514011yescharacteristic, direct product factor, Sylow
455C23×D4C22×C10711yescharacteristic
456C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
457C2×AGL(1,ℤ/8)C22×C10711yescharacteristic
458C2×AGL(1,ℤ/8)C22×C10711yescharacteristic, complemented
459C22×D8C22×C10711yescharacteristic
460C22×D8C22×C10711yescharacteristic
461C2×#131C22×C10711yescharacteristic, complemented
462C22×M16C22×C10711yescharacteristic
463C22×M16C22×C10711yescharacteristic
464#525C22×C10711yescharacteristic
465C2×#121C22×C10711yescharacteristic
466#472—24no—
467#469—21no—
468#468—21no—
469#466—21no—
470#465—21no—
471#450—21no—
472#450—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#447—21no—
479#436—21no—
480#435—21no—
481#435—21no—
482C8×D4—21no—
483C2×#108C22×C10711yescharacteristic, complemented
484C2×#108C22×C10711yescharacteristic, complemented
485#428C22×C10711yescharacteristic, complemented
486#424C22×C10711yescharacteristic, complemented
487#418C22×C10711yescharacteristic
488#418C22×C10711yescharacteristic
489#418C22×C10711yescharacteristic, complemented
490#417C22×C10711yescharacteristic, complemented
491C2×#102C22×C10711yescharacteristic
492C2×#102C22×C10711yescharacteristic
493C2×#100—24no—
494C2×#100C22×C10711yescharacteristic
495C2×#100C22×C10711yescharacteristic
496C2×#100C22×C10711yescharacteristic
497C2×#100C22×C10711yescharacteristic
498C2×#100C22×C10711yescharacteristic, complemented
499C2×#100C22×C10711yescharacteristic, complemented
500#408C22×C10711yescharacteristic, complemented
501#407C22×C10711yescharacteristic
502C2×C22⋊C8C22×C10711yescharacteristic
503#405C22×C10711yescharacteristic, complemented
504#343C22×C10711yescharacteristic, complemented
505#343C22×C10711yescharacteristic, complemented
506#341C22×C10711yescharacteristic, complemented
507#341C22×C10711yescharacteristic, complemented
508C25—21no—
509C2×#41C23×C10711yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C10711yescharacteristic
521C22×D4C23×C10711yescharacteristic
522C22×D4C23×C10711yescharacteristic
523C23×C4C23×C10711yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C10711yescharacteristic
554C2×M16C23×C10711yescharacteristic
555C2×M16C23×C10711yescharacteristic
556C2×M16C23×C10711yescharacteristic
557C2×M16C23×C10711yescharacteristic
558C2×M16C23×C10711yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C10711yescharacteristic
563C22×C8C23×C10711yescharacteristic
564#123—21no—
565C22⋊Q8D4×C10711yescharacteristic
566C22⋊Q8D4×C10711yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C10711yescharacteristic
572#121D4×C10711yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C10711yescharacteristic
577C2×C4⋊C4C23×C10711yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C10714yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C10711yescharacteristic
608C22⋊C8D4×C10711yescharacteristic
609C22⋊C8D4×C10711yescharacteristic
610C22⋊C8D4×C10711yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C10711yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C10711yescharacteristic
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C10712yes—
663C2×D4C2×D4×C10711yescharacteristic
664C2×D4#41×C10712yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C10711yescharacteristic
672C22×C4C2×D4×C10711yescharacteristic
673C22×C4C2×D4×C10711yescharacteristic
674C22×C4C2×D4×C10711yescharacteristic
675C22×C4#41×C10711yescharacteristic
676C22×C4C24×C10711yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C10712yes—
701M16C2×D4×C10712yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C10711yescharacteristic
716C2×C8C2×D4×C10711yescharacteristic
717C2×C8C2×D4×C10711yescharacteristic
718C2×C8C2×D4×C10711yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C10711yescharacteristic
724C4⋊C4C2×D4×C10711yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C10711yescharacteristic
762C23#121×C10711yescharacteristic
763C23C2×#41×C10711yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—42no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C10711yescharacteristic
806C2×C4#121×C10711yescharacteristic
807C2×C4C22×D4×C10711yescharacteristic
808C2×C4C22×D4×C10711yescharacteristic
809C2×C4C22×D4×C10711yescharacteristic
810C2×C4C2×#41×C10711yescharacteristic
811C2×C4H(5,𝔽2)×C10711yescharacteristic
812C2×C4H(5,𝔽2)×C10711yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22#472×C10712yescomplemented
853C22C2×#121×C10711yescharacteristic
854C22#525×C10711yescharacteristic
855C22#538×C10711yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C10711yescharacteristic
863C4D42×C10711yescharacteristic
864C4#546×C10711yescharacteristic
865C4#546×C10711yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2C107×#242411yescharacteristic
875C2C2×#472×C10711yescharacteristic
876C2C107×#306811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#121
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#472×C107C2semidirect
2. C107×#3055C2semidirect
3. C107×#3003C2semidirect
4. C2×#447×C107C2semidirect
5. C107×#2933C2semidirect
6. C22×#100×C107C2semidirect
7. C107×#2063C2semidirect
8. C107×#2051C2semidirect
9. C107×#2045C2semidirect
10. C107×#2018C2semidirect
11. C107×#1978C2semidirect
12. C107×#1931C2semidirect
13. C107×#1907C2semidirect
14. C107×#1900C2semidirect
15. C107×#1855C2semidirect
19. C2×AGL(1,ℤ/8)×C107C22semidirect
22. C2×#131×C107C22semidirect
44. C2×#108×C107C22semidirect
45. C2×#108×C107C22semidirect
46. #428×C107C22semidirect
47. #424×C107C22semidirect
50. #418×C107C22semidirect
51. #417×C107C22semidirect
59. C2×#100×C107C22semidirect
60. C2×#100×C107C22semidirect
61. #408×C107C22semidirect
64. #405×C107C22semidirect
65. #343×C107C22semidirect
66. #343×C107C22semidirect
67. #341×C107C22semidirect
68. #341×C107C22semidirect
163. #100×C107D4semidirect
413. C22×C107#472semidirect
427. #25140C107direct (N × H)
439. C2×#472C2×C107semidirect
440. #3055C2×C107semidirect
441. #3003C2×C107semidirect
442. C2×#447C2×C107semidirect
443. #2933C2×C107semidirect
444. C22×#100C2×C107semidirect
445. #2063C2×C107semidirect
446. #2051C2×C107semidirect
447. #2045C2×C107semidirect
448. #2018C2×C107semidirect
449. #1978C2×C107semidirect
450. #1931C2×C107semidirect
451. #1907C2×C107semidirect
452. #1900C2×C107semidirect
453. #1855C2×C107semidirect
454. C107#25140direct (N × H)
458. C2×AGL(1,ℤ/8)C22×C107semidirect
461. C2×#131C22×C107semidirect
483. C2×#108C22×C107semidirect
484. C2×#108C22×C107semidirect
485. #428C22×C107semidirect
486. #424C22×C107semidirect
489. #418C22×C107semidirect
490. #417C22×C107semidirect
498. C2×#100C22×C107semidirect
499. C2×#100C22×C107semidirect
500. #408C22×C107semidirect
503. #405C22×C107semidirect
504. #343C22×C107semidirect
505. #343C22×C107semidirect
506. #341C22×C107semidirect
507. #341C22×C107semidirect
602. #100D4×C107semidirect
852. C22#472×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1072
C107×#30552
C107×#30032
C2×#447×C1072
C107×#29332
C22×#100×C1072
C107×#20632
C107×#20512
C107×#20452
C107×#20182
C107×#19782
C107×#19312
C107×#19072
C107×#19002
C107×#18552
#25140107