Finite Group Databasebeta

← C107×#24044 #41050008

Subgroups — C107×#24044 #41050008

Order 27392.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C107C211yesmaximal, characteristic
2C2×#482×C107C211yesmaximal, characteristic, complemented
3C2×#418×C107C211yesmaximal, characteristic, complemented
4C107×#2485C211yesmaximal, characteristic, complemented
5C107×#2041C211yesmaximal, characteristic, complemented
6C107×#2041C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#1895C211yesmaximal, characteristic, complemented
10C107×#1870C211yesmaximal, characteristic, complemented
11C107×#1864C211yesmaximal, characteristic, complemented
12C107×#1862C211yesmaximal, characteristic, complemented
13C107×#1786C211yesmaximal, characteristic, complemented
14C107×#1786C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C107—21no—
17C23×D4×C107C2211yescharacteristic
18C23×D4×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic, complemented
20D42×C107—24no—
21D42×C107—24no—
22C2×#127×C107C2211yescharacteristic
23C2×#121×C107—21no—
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#120×C107—21no—
27C2×#120×C107—21no—
28C2×C4×D4×C107C2211yescharacteristic
29C2×C4×D4×C107C2211yescharacteristic
30C2×#117×C107C2211yescharacteristic, complemented
31#482×C107—24no—
32C2×#107×C107C2211yescharacteristic, complemented
33C2×#106×C107C2211yescharacteristic, complemented
34#418×C107—24no—
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic, complemented
40C2×#102×C107C2211yescharacteristic, complemented
41C2×#102×C107C2211yescharacteristic, complemented
42C2×#102×C107C2211yescharacteristic, complemented
43C2×#102×C107C2211yescharacteristic, complemented
44C2×#102×C107C2211yescharacteristic, complemented
45C2×#102×C107C2211yescharacteristic, complemented
46C2×#102×C107C2211yescharacteristic, complemented
47C2×C22⋊C8×C107C2211yescharacteristic, complemented
48C2×C22⋊C8×C107C2211yescharacteristic, complemented
49C2×C22⋊C8×C107C2211yescharacteristic, complemented
50#397×C107—21no—
51#394×C107—21no—
52#389×C107C2211yescharacteristic, complemented
53#389×C107C2211yescharacteristic, complemented
54#388×C107—21no—
55#387×C107—21no—
56#380×C107C2211yescharacteristic, complemented
57#380×C107C2211yescharacteristic, complemented
58#380×C107C2211yescharacteristic, complemented
59#340×C107C2211yescharacteristic, complemented
60#340×C107C2211yescharacteristic, complemented
61#336×C107C2211yescharacteristic, complemented
62#336×C107C2211yescharacteristic, complemented
63C25×C107—21no—
64C25×C107—21no—
65C22×D4×C107—22no—
66C22×D4×C107—22no—
67C22×D4×C107—28no—
68C22×D4×C107—21no—
69C22×D4×C107—21no—
70C22×D4×C107—22no—
71C22×D4×C107—22no—
72C22×D4×C107—22no—
73C22×D4×C107—22no—
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—22no—
78C22×D4×C107—21no—
79C22×D4×C107—41no—
80C22×D4×C107—41no—
81C22×D4×C107—41no—
82C22×D4×C107—41no—
83C22×D4×C107—44no—
84C22×D4×C107—44no—
85C22×D4×C107D411yescharacteristic
86C22×D4×C107D414yes—
87C22×D4×C107C2311yescharacteristic
88C22×D4×C107C2311yescharacteristic
89C22×D4×C107C2311yescharacteristic
90C23×C4×C107—21no—
91C23×C4×C107C2311yescharacteristic
92C23×C4×C107C2311yescharacteristic
93C2×M16×C107—22no—
94C2×M16×C107—41no—
95C2×M16×C107—41no—
96C22×C8×C107C2311yescharacteristic
97C22×C8×C107C2311yescharacteristic
98C22×C8×C107C2311yescharacteristic
99C22×C8×C107C2311yescharacteristic
100#127×C107—22no—
101#127×C107—22no—
102#121×C107—28no—
103#121×C107—22no—
104#121×C107—22no—
105#121×C107—22no—
106#121×C107D414yes—
107#120×C107—28no—
108#120×C107—28no—
109C4×D4×C107—22no—
110C4×D4×C107—22no—
111C4×D4×C107—22no—
112C4×D4×C107—22no—
113#117×C107—22no—
114#117×C107—22no—
115C2×C4⋊C4×C107—21no—
116C2×C4⋊C4×C107—21no—
117C2×C4⋊C4×C107D411yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C4⋊C4×C107C2311yescharacteristic
120C2×C4⋊C4×C107C2311yescharacteristic
121C2×C4⋊C4×C107C2311yescharacteristic
122C2×C4⋊C4×C107C2311yescharacteristic
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107D411yescharacteristic
131C2×C22⋊C4×C107D411yescharacteristic
132C2×C42×C107—21no—
133C2×C42×C107C2311yescharacteristic
134#107×C107—22no—
135#106×C107—22no—
136#102×C107—22no—
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—22no—
143#102×C107—22no—
144#102×C107—41no—
145#102×C107—41no—
146#102×C107—41no—
147#102×C107—41no—
148C22⋊C8×C107—22no—
149C22⋊C8×C107—41no—
150C22⋊C8×C107—41no—
151#95×C107—21no—
152#95×C107—21no—
153#95×C107—21no—
154#95×C107—21no—
155#95×C107—21no—
156C24×C107—21no—
157C24×C107—24no—
158C24×C107—21no—
159C24×C107—21no—
160C24×C107—24no—
161C24×C107—42no—
162C24×C107—42no—
163C24×C107—42no—
164C24×C107—42no—
165C24×C107—42no—
166C24×C107—42no—
167C24×C107—42no—
168C24×C107—42no—
169C24×C107—81no—
170C24×C107—81no—
171C24×C107—81no—
172C24×C107—81no—
173C24×C107C2×D411yescharacteristic
174C24×C107C2×D411yescharacteristic
175C2×D4×C107—22no—
176C2×D4×C107—22no—
177C2×D4×C107—28no—
178C2×D4×C107—24no—
179C2×D4×C107—24no—
180C2×D4×C107—24no—
181C2×D4×C107—24no—
182C2×D4×C107—24no—
183C2×D4×C107—24no—
184C2×D4×C107—22no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107—21no—
188C2×D4×C107—21no—
189C2×D4×C107—21no—
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—44no—
199C2×D4×C107—44no—
200C2×D4×C107—44no—
201C2×D4×C107—42no—
202C2×D4×C107—42no—
203C2×D4×C107—42no—
204C2×D4×C107—42no—
205C2×D4×C107—42no—
206C2×D4×C107—44no—
207C2×D4×C107—44no—
208C2×D4×C107—432no—
209C2×D4×C107—44no—
210C2×D4×C107—42no—
211C2×D4×C107—42no—
212C2×D4×C107—42no—
213C2×D4×C107—42no—
214C2×D4×C107—44no—
215C2×D4×C107—42no—
216C2×D4×C107—81no—
217C2×D4×C107—81no—
218C2×D4×C107C2×D412yes—
219C2×D4×C107C2×D412yes—
220C2×D4×C107C2×D412yes—
221C2×D4×C107#4112yes—
222C2×D4×C107#4112yes—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—24no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—21no—
236C22×C4×C107—21no—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—42no—
240C22×C4×C107—42no—
241C22×C4×C107C2×D411yescharacteristic
242C22×C4×C107C2×D411yescharacteristic
243C22×C4×C107C2×D411yescharacteristic
244C22×C4×C107C2×D412yes—
245C22×C4×C107C2×D412yes—
246C22×C4×C107C2×D411yescharacteristic
247C22×C4×C107C2411yescharacteristic
248M16×C107—44no—
249C2×C8×C107—21no—
250C2×C8×C107—21no—
251C2×C8×C107—21no—
252C2×C8×C107—21no—
253C2×C8×C107—21no—
254C2×C8×C107—21no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C4⋊C4×C107—22no—
262C4⋊C4×C107—21no—
263C4⋊C4×C107—21no—
264C4⋊C4×C107—21no—
265C4⋊C4×C107—21no—
266C4⋊C4×C107—21no—
267C4⋊C4×C107—21no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—42no—
272C4⋊C4×C107—81no—
273C4⋊C4×C107C2×D412yes—
274C22⋊C4×C107—24no—
275C22⋊C4×C107—24no—
276C22⋊C4×C107—22no—
277C22⋊C4×C107—24no—
278C22⋊C4×C107—22no—
279C22⋊C4×C107—42no—
280C22⋊C4×C107—42no—
281C22⋊C4×C107—81no—
282C22⋊C4×C107—81no—
283C42×C107—21no—
284C42×C107—21no—
285C42×C107—42no—
286C23×C107—21no—
287C23×C107—22no—
288C23×C107—21no—
289C23×C107—21no—
290C23×C107—21no—
291C23×C107—21no—
292C23×C107—22no—
293C23×C107—22no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—21no—
300C23×C107—21no—
301C23×C107—22no—
302C23×C107—22no—
303C23×C107—48no—
304C23×C107—48no—
305C23×C107—48no—
306C23×C107—48no—
307C23×C107—41no—
308C23×C107—41no—
309C23×C107—41no—
310C23×C107—41no—
311C23×C107—41no—
312C23×C107—41no—
313C23×C107—41no—
314C23×C107—41no—
315C23×C107—41no—
316C23×C107—41no—
317C23×C107—41no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—41no—
321C23×C107—41no—
322C23×C107—41no—
323C23×C107—84no—
324C23×C107—84no—
325C23×C107—84no—
326C23×C107—84no—
327C23×C107—84no—
328C23×C107—84no—
329C23×C107—84no—
330C23×C107—84no—
331C23×C107—84no—
332C23×C107—84no—
333C23×C107#12012yes—
334C23×C107AGL(1,ℤ/8)12yes—
335C23×C107C22×D411yescharacteristic
336D4×C107—28no—
337D4×C107—22no—
338D4×C107—22no—
339D4×C107—22no—
340D4×C107—22no—
341D4×C107—22no—
342D4×C107—22no—
343D4×C107—22no—
344D4×C107—48no—
345D4×C107—48no—
346D4×C107—48no—
347D4×C107—48no—
348D4×C107—48no—
349D4×C107—41no—
350D4×C107—41no—
351D4×C107—41no—
352D4×C107—41no—
353D4×C107—84no—
354D4×C107#12314yes—
355C2×C4×C107—21no—
356C2×C4×C107—21no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—22no—
360C2×C4×C107—22no—
361C2×C4×C107—22no—
362C2×C4×C107—22no—
363C2×C4×C107—21no—
364C2×C4×C107—21no—
365C2×C4×C107—22no—
366C2×C4×C107—21no—
367C2×C4×C107—21no—
368C2×C4×C107—21no—
369C2×C4×C107—21no—
370C2×C4×C107—48no—
371C2×C4×C107—41no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
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#12012yes—
390C2×C4×C107AGL(1,ℤ/8)12yes—
391C2×C4×C107C22×D411yescharacteristic
392C2×C4×C107C22×D411yescharacteristic
393C2×C4×C107C2×#4111yescharacteristic
394C2×C4×C107C2×#4111yescharacteristic
395C2×C4×C107H(5,𝔽2)11yescharacteristic
396C2×C4×C107H(5,𝔽2)11yescharacteristic
397C8×C107—41no—
398C8×C107—41no—
399C8×C107—41no—
400C8×C107—41no—
401C22×C107—22no—
402C22×C107—24no—
403C22×C107—22no—
404C22×C107—22no—
405C22×C107—22no—
406C22×C107—22no—
407C22×C107—22no—
408C22×C107—41no—
409C22×C107—42no—
410C22×C107—41no—
411C22×C107—42no—
412C22×C107—41no—
413C22×C107—42no—
414C22×C107—41no—
415C22×C107—42no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—42no—
419C22×C107—41no—
420C22×C107—41no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—42no—
424C22×C107—42no—
425C22×C107—42no—
426C22×C107—42no—
427C22×C107—42no—
428C22×C107—816no—
429C22×C107—816no—
430C22×C107—81no—
431C22×C107—81no—
432C22×C107—81no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107C2×#12011yescharacteristic
439C22×C107#54611yescharacteristic
440C22×C107#54611yescharacteristic
441C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C107#57611yescharacteristic
444C22×C107#57711yescharacteristic
445C4×C107—22no—
446C4×C107—22no—
447C4×C107—41no—
448C4×C107—42no—
449C4×C107—41no—
450C4×C107—81no—
451C4×C107—81no—
452C4×C107—81no—
453C4×C107—81no—
454C4×C107C2×#12311yescharacteristic
455C4×C107#53411yescharacteristic
456C4×C107#54611yescharacteristic
457C4×C107#54611yescharacteristic
458#24044C10711yesmaximal, characteristic, direct product factor, Sylow
459C2×C107—42no—
460C2×C107—42no—
461C2×C107—44no—
462C2×C107—82no—
463C2×C107—82no—
464C2×C107#240511yescharacteristic
465C2×C107#300311yescharacteristic
466C2×C107#301211yescharacteristic
467C2×C107#331011yescharacteristic
468C2×C107#331811yescharacteristic
469C2×C107#332411yescharacteristic
470C2×C107#332511yescharacteristic
471C2×D42C2×C10711yescharacteristic
472C2×#482C2×C10711yescharacteristic, complemented
473C2×#418C2×C10711yescharacteristic, complemented
474#2485C2×C10711yescharacteristic, complemented
475#2041C2×C10711yescharacteristic, complemented
476#2041C2×C10711yescharacteristic, complemented
477#2034C2×C10711yescharacteristic, complemented
478#2033C2×C10711yescharacteristic, complemented
479#1895C2×C10711yescharacteristic, complemented
480#1870C2×C10711yescharacteristic, complemented
481#1864C2×C10711yescharacteristic, complemented
482#1862C2×C10711yescharacteristic, complemented
483#1786C2×C10711yescharacteristic, complemented
484#1786C2×C10711yescharacteristic, complemented
485#1786C2×C10711yescharacteristic, complemented
486C107#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C10711yescharacteristic
489C23×D4C22×C10711yescharacteristic
490C22×M16C22×C10711yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C10711yescharacteristic
494C2×#121—21no—
495C2×#121C22×C10711yescharacteristic
496C2×#121C22×C10711yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C10711yescharacteristic
500C2×C4×D4C22×C10711yescharacteristic
501C2×#117C22×C10711yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C10711yescharacteristic, complemented
504C2×#106C22×C10711yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C10711yescharacteristic
507C2×#102C22×C10711yescharacteristic
508C2×#102C22×C10711yescharacteristic
509C2×#102C22×C10711yescharacteristic
510C2×#102C22×C10711yescharacteristic, complemented
511C2×#102C22×C10711yescharacteristic, complemented
512C2×#102C22×C10711yescharacteristic, complemented
513C2×#102C22×C10711yescharacteristic, complemented
514C2×#102C22×C10711yescharacteristic, complemented
515C2×#102C22×C10711yescharacteristic, complemented
516C2×#102C22×C10711yescharacteristic, complemented
517C2×#102C22×C10711yescharacteristic, complemented
518C2×C22⋊C8C22×C10711yescharacteristic, complemented
519C2×C22⋊C8C22×C10711yescharacteristic, complemented
520C2×C22⋊C8C22×C10711yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C10711yescharacteristic, complemented
524#389C22×C10711yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C10711yescharacteristic, complemented
528#380C22×C10711yescharacteristic, complemented
529#380C22×C10711yescharacteristic, complemented
530#340C22×C10711yescharacteristic, complemented
531#340C22×C10711yescharacteristic, complemented
532#336C22×C10711yescharacteristic, complemented
533#336C22×C10711yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C10711yescharacteristic
557C22×D4D4×C10714yes—
558C22×D4C23×C10711yescharacteristic
559C22×D4C23×C10711yescharacteristic
560C22×D4C23×C10711yescharacteristic
561C23×C4—21no—
562C23×C4C23×C10711yescharacteristic
563C23×C4C23×C10711yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C10711yescharacteristic
568C22×C8C23×C10711yescharacteristic
569C22×C8C23×C10711yescharacteristic
570C22×C8C23×C10711yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C10714yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10711yescharacteristic
589C2×C4⋊C4C23×C10711yescharacteristic
590C2×C4⋊C4C23×C10711yescharacteristic
591C2×C4⋊C4C23×C10711yescharacteristic
592C2×C4⋊C4C23×C10711yescharacteristic
593C2×C4⋊C4C23×C10711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C10711yescharacteristic
602C2×C22⋊C4D4×C10711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10711yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C10711yescharacteristic
645C24C2×D4×C10711yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C10712yes—
690C2×D4C2×D4×C10712yes—
691C2×D4C2×D4×C10712yes—
692C2×D4#41×C10712yes—
693C2×D4#41×C10712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C10711yescharacteristic
713C22×C4C2×D4×C10711yescharacteristic
714C22×C4C2×D4×C10711yescharacteristic
715C22×C4C2×D4×C10712yes—
716C22×C4C2×D4×C10712yes—
717C22×C4C2×D4×C10711yescharacteristic
718C22×C4C24×C10711yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C10712yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C10712yes—
805C23AGL(1,ℤ/8)×C10712yes—
806C23C22×D4×C10711yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C10714yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C10712yes—
861C2×C4AGL(1,ℤ/8)×C10712yes—
862C2×C4C22×D4×C10711yescharacteristic
863C2×C4C22×D4×C10711yescharacteristic
864C2×C4C2×#41×C10711yescharacteristic
865C2×C4C2×#41×C10711yescharacteristic
866C2×C4H(5,𝔽2)×C10711yescharacteristic
867C2×C4H(5,𝔽2)×C10711yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C10711yescharacteristic
910C22#546×C10711yescharacteristic
911C22#546×C10711yescharacteristic
912C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
913C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
914C22#576×C10711yescharacteristic
915C22#577×C10711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C10711yescharacteristic
926C4#534×C10711yescharacteristic
927C4#546×C10711yescharacteristic
928C4#546×C10711yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C107×#240511yescharacteristic
935C2C107×#300311yescharacteristic
936C2C107×#301211yescharacteristic
937C2C107×#331011yescharacteristic
938C2C107×#331811yescharacteristic
939C2C107×#332411yescharacteristic
940C2C107×#332511yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×D42×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C107C2semidirect
3. C2×#418×C107C2semidirect
4. C107×#2485C2semidirect
5. C107×#2041C2semidirect
6. C107×#2041C2semidirect
7. C107×#2034C2semidirect
8. C107×#2033C2semidirect
9. C107×#1895C2semidirect
10. C107×#1870C2semidirect
11. C107×#1864C2semidirect
12. C107×#1862C2semidirect
13. C107×#1786C2semidirect
14. C107×#1786C2semidirect
15. C107×#1786C2semidirect
19. C22×M16×C107C22semidirect
30. C2×#117×C107C22semidirect
32. C2×#107×C107C22semidirect
33. C2×#106×C107C22semidirect
39. C2×#102×C107C22semidirect
40. C2×#102×C107C22semidirect
41. C2×#102×C107C22semidirect
42. C2×#102×C107C22semidirect
43. C2×#102×C107C22semidirect
44. C2×#102×C107C22semidirect
45. C2×#102×C107C22semidirect
46. C2×#102×C107C22semidirect
47. C2×C22⋊C8×C107C22semidirect
48. C2×C22⋊C8×C107C22semidirect
49. C2×C22⋊C8×C107C22semidirect
52. #389×C107C22semidirect
53. #389×C107C22semidirect
56. #380×C107C22semidirect
57. #380×C107C22semidirect
58. #380×C107C22semidirect
59. #340×C107C22semidirect
60. #340×C107C22semidirect
61. #336×C107C22semidirect
62. #336×C107C22semidirect
458. #24044C107direct (N × H)
472. C2×#482C2×C107semidirect
473. C2×#418C2×C107semidirect
474. #2485C2×C107semidirect
475. #2041C2×C107semidirect
476. #2041C2×C107semidirect
477. #2034C2×C107semidirect
478. #2033C2×C107semidirect
479. #1895C2×C107semidirect
480. #1870C2×C107semidirect
481. #1864C2×C107semidirect
482. #1862C2×C107semidirect
483. #1786C2×C107semidirect
484. #1786C2×C107semidirect
485. #1786C2×C107semidirect
486. C107#24044direct (N × H)
490. C22×M16C22×C107semidirect
501. C2×#117C22×C107semidirect
503. C2×#107C22×C107semidirect
504. C2×#106C22×C107semidirect
510. C2×#102C22×C107semidirect
511. C2×#102C22×C107semidirect
512. C2×#102C22×C107semidirect
513. C2×#102C22×C107semidirect
514. C2×#102C22×C107semidirect
515. C2×#102C22×C107semidirect
516. C2×#102C22×C107semidirect
517. C2×#102C22×C107semidirect
518. C2×C22⋊C8C22×C107semidirect
519. C2×C22⋊C8C22×C107semidirect
520. C2×C22⋊C8C22×C107semidirect
523. #389C22×C107semidirect
524. #389C22×C107semidirect
527. #380C22×C107semidirect
528. #380C22×C107semidirect
529. #380C22×C107semidirect
530. #340C22×C107semidirect
531. #340C22×C107semidirect
532. #336C22×C107semidirect
533. #336C22×C107semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1072
C2×#482×C1072
C2×#418×C1072
C107×#24852
C107×#20412
C107×#20342
C107×#20332
C107×#18952
C107×#18702
C107×#18642
C107×#18622
C107×#17862
#24044107