Finite Group Databasebeta

← C107×#24218 #41050182

Subgroups — C107×#24218 #41050182

Order 27392.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C107C211yesmaximal, characteristic, complemented
2C2×#463×C107C211yesmaximal, characteristic, complemented
3C2×#459×C107C211yesmaximal, characteristic, complemented
4C2×#449×C107C211yesmaximal, characteristic, complemented
5C2×#447×C107C211yesmaximal, characteristic, complemented
6C107×#2324C211yesmaximal, characteristic, complemented
7C107×#2042C211yesmaximal, characteristic, complemented
8C107×#2041C211yesmaximal, characteristic, complemented
9C107×#2012C211yesmaximal, characteristic, complemented
10C107×#2011C211yesmaximal, characteristic, complemented
11C107×#1983C211yesmaximal, characteristic, complemented
12C107×#1982C211yesmaximal, characteristic, complemented
13C107×#1798C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic, complemented
19C22×D8×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21C22×D8×C107C2211yescharacteristic, complemented
22#535×C107—24no—
23#535×C107—24no—
24C2×#127×C107C2211yescharacteristic
25C2×#127×C107C2211yescharacteristic
26C2×#124×C107C2211yescharacteristic
27C2×#124×C107C2211yescharacteristic
28C2×#121×C107—21no—
29C2×#121×C107—21no—
30C2×#121×C107C2211yescharacteristic
31C2×#120×C107—21no—
32C2×#120×C107—21no—
33C2×C4×D4×C107C2211yescharacteristic, complemented
34C2×#117×C107C2211yescharacteristic
35#463×C107—24no—
36#459×C107—24no—
37#449×C107—24no—
38#447×C107—24no—
39C2×C4⋊C8×C107C2211yescharacteristic, complemented
40C2×C4⋊C8×C107C2211yescharacteristic, complemented
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#103×C107C2211yescharacteristic, complemented
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic, complemented
51C2×#102×C107C2211yescharacteristic, complemented
52C2×#102×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55#390×C107—21no—
56#390×C107C2211yescharacteristic, complemented
57#389×C107C2211yescharacteristic, complemented
58#388×C107—21no—
59#386×C107—21no—
60#385×C107—21no—
61#380×C107C2211yescharacteristic
62C4×C4⋊C4×C107C2211yescharacteristic, complemented
63#336×C107C2211yescharacteristic, complemented
64#336×C107C2211yescharacteristic, complemented
65C25×C107—21no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—41no—
71C2×#41×C107—41no—
72C22×Q8×C107C2311yescharacteristic
73C22×D4×C107—21no—
74C22×D4×C107—21no—
75C22×D4×C107—22no—
76C22×D4×C107—22no—
77C22×D4×C107—21no—
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—22no—
83C22×D4×C107—22no—
84C22×D4×C107—41no—
85C22×D4×C107—41no—
86C22×D4×C107C2311yescharacteristic
87C22×D4×C107C2311yescharacteristic
88C22×D4×C107C2311yescharacteristic
89C22×D4×C107C2311yescharacteristic
90C23×C4×C107—21no—
91C23×C4×C107—21no—
92C23×C4×C107C2311yescharacteristic
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—41no—
96C2×D8×C107—22no—
97C2×D8×C107—22no—
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—22no—
101C2×D8×C107—22no—
102C2×D8×C107—41no—
103C2×D8×C107—41no—
104C2×D8×C107—41no—
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107C22×C8×C107C2311yescharacteristic
108C22×C8×C107C2311yescharacteristic
109#127×C107—22no—
110#127×C107—22no—
111#127×C107—22no—
112#127×C107D414yescomplemented
113#124×C107—22no—
114#124×C107—22no—
115#124×C107—22no—
116#124×C107D414yescomplemented
117#121×C107—28no—
118#121×C107—28no—
119#121×C107—22no—
120#121×C107D414yescomplemented
121#120×C107—28no—
122#120×C107—28no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125#117×C107—22no—
126#117×C107—22no—
127C2×C4⋊C4×C107—21no—
128C2×C4⋊C4×C107D411yescharacteristic
129C2×C4⋊C4×C107D411yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C22⋊C4×C107—21no—
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—21no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—21no—
138C2×C22⋊C4×C107—21no—
139C2×C22⋊C4×C107—21no—
140C2×C22⋊C4×C107—21no—
141C2×C22⋊C4×C107—21no—
142C2×C22⋊C4×C107D411yescharacteristic
143C2×C22⋊C4×C107D411yescharacteristic
144C2×C42×C107—21no—
145C2×C42×C107C2311yescharacteristic
146C2×C42×C107C2311yescharacteristic
147C4⋊C8×C107—22no—
148C4⋊C8×C107—22no—
149#103×C107—22no—
150#103×C107—22no—
151#103×C107—41no—
152#102×C107—22no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—22no—
158#102×C107—41no—
159#102×C107—41no—
160#102×C107—41no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107—22no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—24no—
167C24×C107—21no—
168C24×C107—21no—
169C24×C107—21no—
170C24×C107—21no—
171C24×C107—42no—
172C24×C107—42no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107—81no—
176C24×C107—81no—
177C24×C107C2×D411yescharacteristic
178#41×C107—44no—
179#41×C107—44no—
180#41×C107—44no—
181#41×C107—44no—
182C2×Q8×C107—21no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107C2×D412yes—
188C2×D4×C107—24no—
189C2×D4×C107—24no—
190C2×D4×C107—24no—
191C2×D4×C107—24no—
192C2×D4×C107—24no—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
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—21no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—21no—
213C2×D4×C107—21no—
214C2×D4×C107—21no—
215C2×D4×C107—44no—
216C2×D4×C107—44no—
217C2×D4×C107—44no—
218C2×D4×C107—44no—
219C2×D4×C107—42no—
220C2×D4×C107—42no—
221C2×D4×C107—42no—
222C2×D4×C107—42no—
223C2×D4×C107—81no—
224C2×D4×C107—81no—
225C2×D4×C107—81no—
226C2×D4×C107—81no—
227C2×D4×C107—81no—
228C2×D4×C107—81no—
229C2×D4×C107—81no—
230C2×D4×C107—81no—
231C2×D4×C107—81no—
232C2×D4×C107—81no—
233C2×D4×C107C2×D412yes—
234C2×D4×C107C2×D412yes—
235C2×D4×C107C2×D412yes—
236C2×D4×C107C2×D412yes—
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—24no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—42no—
247C22×C4×C107—42no—
248C22×C4×C107—42no—
249C22×C4×C107—81no—
250C22×C4×C107—81no—
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2×D411yescharacteristic
253C22×C4×C107C2×D411yescharacteristic
254C22×C4×C107C2×D411yescharacteristic
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2×D412yes—
257C22×C4×C107#4112yes—
258C22×C4×C107C2411yescharacteristic
259SD16×C107—44no—
260D8×C107—44no—
261D8×C107—44no—
262D8×C107—44no—
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—21no—
274C2×C8×C107—21no—
275C4⋊C4×C107—22no—
276C4⋊C4×C107—22no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—81no—
283C4⋊C4×C107C2×D412yes—
284C22⋊C4×C107—24no—
285C22⋊C4×C107—24no—
286C22⋊C4×C107—24no—
287C22⋊C4×C107—24no—
288C22⋊C4×C107—22no—
289C22⋊C4×C107—22no—
290C22⋊C4×C107—24no—
291C22⋊C4×C107—42no—
292C22⋊C4×C107—81no—
293C22⋊C4×C107—81no—
294C22⋊C4×C107—81no—
295C42×C107—21no—
296C42×C107—21no—
297C42×C107—81no—
298C42×C107C2×D412yes—
299C42×C107C2×D412yes—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—22no—
307C23×C107—22no—
308C23×C107—22no—
309C23×C107—22no—
310C23×C107—48no—
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—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107—41no—
327C23×C107—41no—
328C23×C107—41no—
329C23×C107—41no—
330C23×C107—41no—
331C23×C107—41no—
332C23×C107—41no—
333C23×C107—41no—
334C23×C107—41no—
335C23×C107—84no—
336C23×C107—84no—
337C23×C107—84no—
338C23×C107—84no—
339C23×C107—84no—
340C23×C107—84no—
341C23×C107#12112yes—
342C23×C107C22×D411yescharacteristic
343Q8×C107—22no—
344Q8×C107—22no—
345Q8×C107—41no—
346Q8×C107—41no—
347D4×C107—22no—
348D4×C107—22no—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—22no—
352D4×C107—22no—
353D4×C107—22no—
354D4×C107—22no—
355D4×C107—48no—
356D4×C107—48no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—84no—
366D4×C107—84no—
367D4×C107—84no—
368D4×C107—84no—
369D4×C107—84no—
370C2×C4×C107—21no—
371C2×C4×C107—21no—
372C2×C4×C107—21no—
373C2×C4×C107—21no—
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—21no—
381C2×C4×C107—21no—
382C2×C4×C107—22no—
383C2×C4×C107—22no—
384C2×C4×C107—21no—
385C2×C4×C107—21no—
386C2×C4×C107—21no—
387C2×C4×C107—21no—
388C2×C4×C107—48no—
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—41no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—84no—
400C2×C4×C107#12012yes—
401C2×C4×C107#12012yes—
402C2×C4×C107#12112yes—
403C2×C4×C107C22×D411yescharacteristic
404C2×C4×C107C22×D411yescharacteristic
405C2×C4×C107C22×D411yescharacteristic
406C2×C4×C107C2×#4111yescharacteristic
407C2×C4×C107H(5,𝔽2)11yescharacteristic
408C2×C4×C107H(5,𝔽2)11yescharacteristic
409C8×C107—41no—
410C8×C107—41no—
411C8×C107—41no—
412C8×C107—41no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—22no—
416C22×C107—41no—
417C22×C107—41no—
418C22×C107—41no—
419C22×C107—41no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—42no—
424C22×C107—42no—
425C22×C107—42no—
426C22×C107—42no—
427C22×C107—42no—
428C22×C107—42no—
429C22×C107—42no—
430C22×C107—42no—
431C22×C107—42no—
432C22×C107—816no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107—81no—
448C22×C107—81no—
449C22×C107C2×#12011yescharacteristic
450C22×C107C2×#12111yescharacteristic
451C22×C107#53511yescharacteristic
452C22×C107#57611yescharacteristic
453C22×C107#57611yescharacteristic
454C22×C107#57611yescharacteristic
455C22×C107#57711yescharacteristic
456C4×C107—22no—
457C4×C107—22no—
458C4×C107—22no—
459C4×C107—42no—
460C4×C107—41no—
461C4×C107—41no—
462C4×C107—42no—
463C4×C107—81no—
464C4×C107—81no—
465C4×C107D4211yescharacteristic
466C4×C107D4211yescharacteristic
467C4×C107#54611yescharacteristic
468C4×C107#54611yescharacteristic
469#24218C10711yesmaximal, characteristic, direct product factor, Sylow
470C2×C107—42no—
471C2×C107—82no—
472C2×C107—82no—
473C2×C107—82no—
474C2×C107—82no—
475C2×C107#240811yescharacteristic
476C2×C107#300811yescharacteristic
477C2×C107#301211yescharacteristic
478C2×C107#304111yescharacteristic
479C2×C107#304511yescharacteristic
480C2×C107#322011yescharacteristic
481C2×C107#322411yescharacteristic
482C2×#535C2×C10711yescharacteristic, complemented
483C2×#463C2×C10711yescharacteristic, complemented
484C2×#459C2×C10711yescharacteristic, complemented
485C2×#449C2×C10711yescharacteristic, complemented
486C2×#447C2×C10711yescharacteristic, complemented
487#2324C2×C10711yescharacteristic, complemented
488#2042C2×C10711yescharacteristic, complemented
489#2041C2×C10711yescharacteristic, complemented
490#2012C2×C10711yescharacteristic, complemented
491#2011C2×C10711yescharacteristic, complemented
492#1983C2×C10711yescharacteristic, complemented
493#1982C2×C10711yescharacteristic, complemented
494#1798C2×C10711yescharacteristic, complemented
495#1788C2×C10711yescharacteristic, complemented
496#1786C2×C10711yescharacteristic, complemented
497C107#2421811yescharacteristic, direct product factor, Sylow
498C22×#41C22×C10711yescharacteristic
499C23×D4C22×C10711yescharacteristic
500C22×SD16C22×C10711yescharacteristic, complemented
501C22×D8C22×C10711yescharacteristic
502C22×D8C22×C10711yescharacteristic
503C22×D8C22×C10711yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C10711yescharacteristic
507C2×#127C22×C10711yescharacteristic
508C2×#124C22×C10711yescharacteristic
509C2×#124C22×C10711yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C10711yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C10711yescharacteristic, complemented
516C2×#117C22×C10711yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C10711yescharacteristic, complemented
522C2×C4⋊C8C22×C10711yescharacteristic, complemented
523C2×#103C22×C10711yescharacteristic, complemented
524C2×#103C22×C10711yescharacteristic, complemented
525C2×#103C22×C10711yescharacteristic, complemented
526C2×#102C22×C10711yescharacteristic
527C2×#102C22×C10711yescharacteristic
528C2×#102C22×C10711yescharacteristic
529C2×#102C22×C10711yescharacteristic
530C2×#102C22×C10711yescharacteristic
531C2×#102C22×C10711yescharacteristic
532C2×#102C22×C10711yescharacteristic, complemented
533C2×#102C22×C10711yescharacteristic, complemented
534C2×#102C22×C10711yescharacteristic, complemented
535C2×C22⋊C8C22×C10711yescharacteristic
536C2×C22⋊C8C22×C10711yescharacteristic
537#390—21no—
538#390C22×C10711yescharacteristic, complemented
539#389C22×C10711yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C10711yescharacteristic
544C4×C4⋊C4C22×C10711yescharacteristic, complemented
545#336C22×C10711yescharacteristic, complemented
546#336C22×C10711yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C10711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C10711yescharacteristic
569C22×D4C23×C10711yescharacteristic
570C22×D4C23×C10711yescharacteristic
571C22×D4C23×C10711yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C10711yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C10711yescharacteristic
588C22×C8C23×C10711yescharacteristic
589C22×C8C23×C10711yescharacteristic
590C22×C8C23×C10711yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C10714yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C10714yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C10714yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C10711yescharacteristic
611C2×C4⋊C4D4×C10711yescharacteristic
612C2×C4⋊C4C23×C10711yescharacteristic
613C2×C4⋊C4C23×C10711yescharacteristic
614C2×C4⋊C4C23×C10711yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4D4×C10711yescharacteristic
625C2×C22⋊C4D4×C10711yescharacteristic
626C2×C42—21no—
627C2×C42C23×C10711yescharacteristic
628C2×C42C23×C10711yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C10711yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C10712yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
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—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C10712yes—
716C2×D4C2×D4×C10712yes—
717C2×D4C2×D4×C10712yes—
718C2×D4C2×D4×C10712yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C10711yescharacteristic
734C22×C4C2×D4×C10711yescharacteristic
735C22×C4C2×D4×C10711yescharacteristic
736C22×C4C2×D4×C10711yescharacteristic
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C2×D4×C10712yes—
739C22×C4#41×C10712yes—
740C22×C4C24×C10711yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C10712yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C10712yes—
781C42C2×D4×C10712yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C10712yes—
824C23C22×D4×C10711yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C10712yes—
883C2×C4#120×C10712yes—
884C2×C4#121×C10712yes—
885C2×C4C22×D4×C10711yescharacteristic
886C2×C4C22×D4×C10711yescharacteristic
887C2×C4C22×D4×C10711yescharacteristic
888C2×C4C2×#41×C10711yescharacteristic
889C2×C4H(5,𝔽2)×C10711yescharacteristic
890C2×C4H(5,𝔽2)×C10711yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C10711yescharacteristic
932C22C2×#121×C10711yescharacteristic
933C22#535×C10711yescharacteristic
934C22#576×C10711yescharacteristic
935C22#576×C10711yescharacteristic
936C22#576×C10711yescharacteristic
937C22#577×C10711yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—81no—
946C4—81no—
947C4D42×C10711yescharacteristic
948C4D42×C10711yescharacteristic
949C4#546×C10711yescharacteristic
950C4#546×C10711yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C107×#240811yescharacteristic
957C2C107×#300811yescharacteristic
958C2C107×#301211yescharacteristic
959C2C107×#304111yescharacteristic
960C2C107×#304511yescharacteristic
961C2C107×#322011yescharacteristic
962C2C107×#322411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C107C2semidirect
2. C2×#463×C107C2semidirect
3. C2×#459×C107C2semidirect
4. C2×#449×C107C2semidirect
5. C2×#447×C107C2semidirect
6. C107×#2324C2semidirect
7. C107×#2042C2semidirect
8. C107×#2041C2semidirect
9. C107×#2012C2semidirect
10. C107×#2011C2semidirect
11. C107×#1983C2semidirect
12. C107×#1982C2semidirect
13. C107×#1798C2semidirect
14. C107×#1788C2semidirect
15. C107×#1786C2semidirect
18. C22×SD16×C107C22semidirect
21. C22×D8×C107C22semidirect
33. C2×C4×D4×C107C22semidirect
39. C2×C4⋊C8×C107C22semidirect
40. C2×C4⋊C8×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
43. C2×#103×C107C22semidirect
50. C2×#102×C107C22semidirect
51. C2×#102×C107C22semidirect
52. C2×#102×C107C22semidirect
56. #390×C107C22semidirect
57. #389×C107C22semidirect
62. C4×C4⋊C4×C107C22semidirect
63. #336×C107C22semidirect
64. #336×C107C22semidirect
112. #127×C107D4semidirect
116. #124×C107D4semidirect
120. #121×C107D4semidirect
469. #24218C107direct (N × H)
482. C2×#535C2×C107semidirect
483. C2×#463C2×C107semidirect
484. C2×#459C2×C107semidirect
485. C2×#449C2×C107semidirect
486. C2×#447C2×C107semidirect
487. #2324C2×C107semidirect
488. #2042C2×C107semidirect
489. #2041C2×C107semidirect
490. #2012C2×C107semidirect
491. #2011C2×C107semidirect
492. #1983C2×C107semidirect
493. #1982C2×C107semidirect
494. #1798C2×C107semidirect
495. #1788C2×C107semidirect
496. #1786C2×C107semidirect
497. C107#24218direct (N × H)
500. C22×SD16C22×C107semidirect
503. C22×D8C22×C107semidirect
515. C2×C4×D4C22×C107semidirect
521. C2×C4⋊C8C22×C107semidirect
522. C2×C4⋊C8C22×C107semidirect
523. C2×#103C22×C107semidirect
524. C2×#103C22×C107semidirect
525. C2×#103C22×C107semidirect
532. C2×#102C22×C107semidirect
533. C2×#102C22×C107semidirect
534. C2×#102C22×C107semidirect
538. #390C22×C107semidirect
539. #389C22×C107semidirect
544. C4×C4⋊C4C22×C107semidirect
545. #336C22×C107semidirect
546. #336C22×C107semidirect
594. #127D4×C107semidirect
598. #124D4×C107semidirect
602. #121D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1072
C2×#463×C1072
C2×#459×C1072
C2×#449×C1072
C2×#447×C1072
C107×#23242
C107×#20422
C107×#20412
C107×#20122
C107×#20112
C107×#19832
C107×#19822
C107×#17982
C107×#17882
C107×#17862
#24218107