Finite Group Databasebeta

← C107×#24244 #41050208

Subgroups — C107×#24244 #41050208

Order 27392.

1488 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C107C211yesmaximal, characteristic, complemented
2C2×#463×C107C211yesmaximal, characteristic, complemented
3C2×#449×C107C211yesmaximal, characteristic, complemented
4C2×#448×C107C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C107C211yesmaximal, characteristic, complemented
6C107×#2535C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2034C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1958C211yesmaximal, characteristic, complemented
12C107×#1954C211yesmaximal, characteristic, complemented
13C107×#1805C211yesmaximal, characteristic, complemented
14C107×#1788C211yesmaximal, characteristic, complemented
15C107×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×Q8×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×D8×C107C2211yescharacteristic
21#548×C107—24no—
22#548×C107—24no—
23C2×#124×C107—21no—
24C2×#124×C107C2211yescharacteristic
25C2×C22⋊Q8×C107—21no—
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×#121×C107—21no—
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×C4×Q8×C107C2211yescharacteristic
32C2×C4×D4×C107—21no—
33C2×C4×D4×C107C2211yescharacteristic
34C2×C4×D4×C107C2211yescharacteristic
35#463×C107—24no—
36#449×C107—24no—
37#448×C107—24no—
38C4×SD16×C107—24no—
39C2×#106×C107C2211yescharacteristic
40C2×C4⋊C8×C107C2211yescharacteristic
41C2×#103×C107C2211yescharacteristic
42C2×#103×C107C2211yescharacteristic
43C2×#103×C107C2211yescharacteristic
44C2×#103×C107C2211yescharacteristic
45C2×#103×C107C2211yescharacteristic
46C2×#103×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55C2×C4×C8×C107C2211yescharacteristic
56#397×C107—21no—
57#392×C107—21no—
58#386×C107—21no—
59#386×C107—21no—
60#382×C107C2211yescharacteristic
61#380×C107C2211yescharacteristic
62#380×C107C2211yescharacteristic
63#340×C107C2211yescharacteristic
64#340×C107C2211yescharacteristic
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—22no—
68C2×#41×C107—22no—
69C2×#41×C107—41no—
70C2×#41×C107—41no—
71C22×Q8×C107—22no—
72C22×Q8×C107—22no—
73C22×Q8×C107—21no—
74C22×Q8×C107—22no—
75C22×Q8×C107—22no—
76C22×Q8×C107—41no—
77C22×Q8×C107—41no—
78C22×Q8×C107C2311yescharacteristic
79C22×Q8×C107C2311yescharacteristic
80C22×D4×C107—21no—
81C22×D4×C107—21no—
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107D411yescharacteristic
85C22×D4×C107C2311yescharacteristic
86C22×D4×C107C2311yescharacteristic
87C23×C4×C107—21no—
88C23×C4×C107—21no—
89C23×C4×C107—21no—
90C23×C4×C107C2311yescharacteristic
91C23×C4×C107C2311yescharacteristic
92C2×SD16×C107—22no—
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—41no—
97C2×SD16×C107D414yescomplemented
98C2×D8×C107—22no—
99C2×D8×C107—22no—
100C2×D8×C107—41no—
101C22×C8×C107C2311yescharacteristic
102C22×C8×C107C2311yescharacteristic
103C22×C8×C107C2311yescharacteristic
104C22×C8×C107C2311yescharacteristic
105#124×C107—28no—
106#124×C107—22no—
107#124×C107D414yescomplemented
108C22⋊Q8×C107—28no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—22no—
111#121×C107—28no—
112#121×C107—22no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—41no—
117#121×C107—41no—
118C4×Q8×C107—22no—
119C4×Q8×C107D414yescomplemented
120C4×D4×C107—28no—
121C4×D4×C107—22no—
122C4×D4×C107—22no—
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125C2×C4⋊C4×C107—21no—
126C2×C4⋊C4×C107—21no—
127C2×C4⋊C4×C107D411yescharacteristic
128C2×C4⋊C4×C107C2311yescharacteristic
129C2×C4⋊C4×C107C2311yescharacteristic
130C2×C4⋊C4×C107C2311yescharacteristic
131C2×C4⋊C4×C107C2311yescharacteristic
132C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
142C2×C22⋊C4×C107D411yescharacteristic
143C2×C42×C107—21no—
144C2×C42×C107C2311yescharacteristic
145#106×C107—22no—
146C4⋊C8×C107—22no—
147#103×C107—22no—
148#103×C107—22no—
149#103×C107—22no—
150#103×C107—22no—
151#103×C107—22no—
152#103×C107—41no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—41no—
157C22⋊C8×C107—22no—
158C22⋊C8×C107—22no—
159C22⋊C8×C107—41no—
160C22⋊C8×C107—41no—
161C4×C8×C107—22no—
162#95×C107—21no—
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—21no—
167C24×C107—21no—
168C24×C107C2×D411yescharacteristic
169C24×C107C2×D411yescharacteristic
170#41×C107—44no—
171#41×C107—44no—
172#41×C107—44no—
173#41×C107—44no—
174C2×Q8×C107—24no—
175C2×Q8×C107—21no—
176C2×Q8×C107—21no—
177C2×Q8×C107—21no—
178C2×Q8×C107—21no—
179C2×Q8×C107—21no—
180C2×Q8×C107—21no—
181C2×Q8×C107—21no—
182C2×Q8×C107—21no—
183C2×Q8×C107—42no—
184C2×Q8×C107—42no—
185C2×Q8×C107—44no—
186C2×Q8×C107—44no—
187C2×Q8×C107—44no—
188C2×Q8×C107—44no—
189C2×Q8×C107C2×D412yes—
190C2×Q8×C107C2×D412yes—
191C2×Q8×C107C2×D412yes—
192C2×Q8×C107#4112yes—
193C2×D4×C107—24no—
194C2×D4×C107—24no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
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—41no—
208C2×D4×C107—42no—
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—81no—
217C2×D4×C107—81no—
218C2×D4×C107C2×D412yes—
219C2×D4×C107C2×D412yes—
220C22×C4×C107—21no—
221C22×C4×C107—24no—
222C22×C4×C107—24no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
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×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—21no—
240C22×C4×C107—42no—
241C22×C4×C107—42no—
242C22×C4×C107—42no—
243C22×C4×C107—42no—
244C22×C4×C107—42no—
245C22×C4×C107—81no—
246C22×C4×C107—81no—
247C22×C4×C107C2×D411yescharacteristic
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2411yescharacteristic
252SD16×C107—28no—
253SD16×C107—44no—
254D8×C107—44no—
255C2×C8×C107—21no—
256C2×C8×C107—21no—
257C2×C8×C107—21no—
258C2×C8×C107—21no—
259C2×C8×C107—21no—
260C2×C8×C107—21no—
261C2×C8×C107—21no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107C2×D412yes—
267C4⋊C4×C107—24no—
268C4⋊C4×C107—24no—
269C4⋊C4×C107—22no—
270C4⋊C4×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107C2×D412yes—
278C22⋊C4×C107—24no—
279C22⋊C4×C107—24no—
280C22⋊C4×C107—24no—
281C22⋊C4×C107—24no—
282C22⋊C4×C107—22no—
283C22⋊C4×C107—22no—
284C22⋊C4×C107—42no—
285C22⋊C4×C107—42no—
286C22⋊C4×C107—42no—
287C22⋊C4×C107—81no—
288C22⋊C4×C107—81no—
289C42×C107—24no—
290C42×C107C2×D412yes—
291C42×C107C2×D412yes—
292C23×C107—21no—
293C23×C107—21no—
294C23×C107—21no—
295C23×C107—21no—
296C23×C107—21no—
297C23×C107—21no—
298C23×C107—21no—
299C23×C107—22no—
300C23×C107—22no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
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#13512yes—
320C23×C107C22×D411yescharacteristic
321Q8×C107—22no—
322Q8×C107—22no—
323Q8×C107—22no—
324Q8×C107—22no—
325Q8×C107—22no—
326Q8×C107—48no—
327Q8×C107—41no—
328Q8×C107—41no—
329Q8×C107#12114yes—
330D4×C107—22no—
331D4×C107—22no—
332D4×C107—22no—
333D4×C107—22no—
334D4×C107—44no—
335D4×C107—48no—
336D4×C107—48no—
337D4×C107—41no—
338D4×C107—41no—
339D4×C107—41no—
340D4×C107—41no—
341D4×C107—84no—
342D4×C107—84no—
343C2×C4×C107—22no—
344C2×C4×C107—22no—
345C2×C4×C107—22no—
346C2×C4×C107—21no—
347C2×C4×C107—21no—
348C2×C4×C107—21no—
349C2×C4×C107—21no—
350C2×C4×C107—22no—
351C2×C4×C107—22no—
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—48no—
359C2×C4×C107—48no—
360C2×C4×C107—41no—
361C2×C4×C107—41no—
362C2×C4×C107—41no—
363C2×C4×C107—41no—
364C2×C4×C107—41no—
365C2×C4×C107—41no—
366C2×C4×C107—41no—
367C2×C4×C107—41no—
368C2×C4×C107—41no—
369C2×C4×C107—41no—
370C2×C4×C107—41no—
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—84no—
382C2×C4×C107#12012yes—
383C2×C4×C107#12012yes—
384C2×C4×C107C22×D411yescharacteristic
385C2×C4×C107C22×D411yescharacteristic
386C2×C4×C107C22×D411yescharacteristic
387C2×C4×C107C2×#4111yescharacteristic
388C2×C4×C107H(5,𝔽2)11yescharacteristic
389C2×C4×C107H(5,𝔽2)11yescharacteristic
390C8×C107—22no—
391C8×C107—41no—
392C8×C107—41no—
393C8×C107—41no—
394C22×C107—22no—
395C22×C107—22no—
396C22×C107—22no—
397C22×C107—41no—
398C22×C107—41no—
399C22×C107—41no—
400C22×C107—41no—
401C22×C107—42no—
402C22×C107—41no—
403C22×C107—42no—
404C22×C107—41no—
405C22×C107—42no—
406C22×C107—41no—
407C22×C107—42no—
408C22×C107—41no—
409C22×C107—42no—
410C22×C107—42no—
411C22×C107—41no—
412C22×C107—41no—
413C22×C107—41no—
414C22×C107—81no—
415C22×C107—81no—
416C22×C107—81no—
417C22×C107—81no—
418C22×C107—81no—
419C22×C107—81no—
420C22×C107—81no—
421C22×C107—81no—
422C22×C107C2×#12011yescharacteristic
423C22×C107D4211yescharacteristic
424C22×C107#54611yescharacteristic
425C22×C107C2×#13511yescharacteristic
426C22×C107#57511yescharacteristic
427C22×C107#57711yescharacteristic
428C22×C107#57711yescharacteristic
429C4×C107—24no—
430C4×C107—22no—
431C4×C107—22no—
432C4×C107—41no—
433C4×C107—41no—
434C4×C107—42no—
435C4×C107—42no—
436C4×C107—81no—
437C4×C107—81no—
438C4×C107—81no—
439C4×C107C2×#12111yescharacteristic
440C4×C107#53511yescharacteristic
441C4×C107D4211yescharacteristic
442C4×C107#54611yescharacteristic
443#24244C10711yesmaximal, characteristic, direct product factor, Sylow
444C2×C107—42no—
445C2×C107—81no—
446C2×C107—82no—
447C2×C107—82no—
448C2×C107#240811yescharacteristic
449C2×C107#300211yescharacteristic
450C2×C107#301011yescharacteristic
451C2×C107#327511yescharacteristic
452C2×C107#328211yescharacteristic
453C2×C107#330111yescharacteristic
454C2×C107#332611yescharacteristic
455C2×#548C2×C10711yescharacteristic, complemented
456C2×#463C2×C10711yescharacteristic, complemented
457C2×#449C2×C10711yescharacteristic, complemented
458C2×#448C2×C10711yescharacteristic, complemented
459C2×C4×SD16C2×C10711yescharacteristic, complemented
460#2535C2×C10711yescharacteristic, complemented
461#2035C2×C10711yescharacteristic, complemented
462#2034C2×C10711yescharacteristic, complemented
463#2000C2×C10711yescharacteristic, complemented
464#1999C2×C10711yescharacteristic, complemented
465#1958C2×C10711yescharacteristic, complemented
466#1954C2×C10711yescharacteristic, complemented
467#1805C2×C10711yescharacteristic, complemented
468#1788C2×C10711yescharacteristic, complemented
469#1787C2×C10711yescharacteristic, complemented
470C107#2424411yescharacteristic, direct product factor, Sylow
471C22×#41C22×C10711yescharacteristic
472C23×Q8C22×C10711yescharacteristic
473C22×SD16C22×C10711yescharacteristic
474C22×SD16C22×C10711yescharacteristic
475C22×D8C22×C10711yescharacteristic
476#548—24no—
477#548—24no—
478C2×#124—21no—
479C2×#124C22×C10711yescharacteristic
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C10711yescharacteristic
482C2×#121—21no—
483C2×#121C22×C10711yescharacteristic
484C2×#121C22×C10711yescharacteristic
485C2×#121C22×C10711yescharacteristic
486C2×C4×Q8C22×C10711yescharacteristic
487C2×C4×D4—21no—
488C2×C4×D4C22×C10711yescharacteristic
489C2×C4×D4C22×C10711yescharacteristic
490#463—24no—
491#449—24no—
492#448—24no—
493C4×SD16—24no—
494C2×#106C22×C10711yescharacteristic
495C2×C4⋊C8C22×C10711yescharacteristic
496C2×#103C22×C10711yescharacteristic
497C2×#103C22×C10711yescharacteristic
498C2×#103C22×C10711yescharacteristic
499C2×#103C22×C10711yescharacteristic
500C2×#103C22×C10711yescharacteristic
501C2×#103C22×C10711yescharacteristic
502C2×#102C22×C10711yescharacteristic
503C2×#102C22×C10711yescharacteristic
504C2×#102C22×C10711yescharacteristic
505C2×#102C22×C10711yescharacteristic
506C2×C22⋊C8C22×C10711yescharacteristic
507C2×C22⋊C8C22×C10711yescharacteristic
508C2×C22⋊C8C22×C10711yescharacteristic
509C2×C22⋊C8C22×C10711yescharacteristic
510C2×C4×C8C22×C10711yescharacteristic
511#397—21no—
512#392—21no—
513#386—21no—
514#386—21no—
515#382C22×C10711yescharacteristic
516#380C22×C10711yescharacteristic
517#380C22×C10711yescharacteristic
518#340C22×C10711yescharacteristic
519#340C22×C10711yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—41no—
525C2×#41—41no—
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8C23×C10711yescharacteristic
534C22×Q8C23×C10711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C10711yescharacteristic
540C22×D4C23×C10711yescharacteristic
541C22×D4C23×C10711yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C10711yescharacteristic
546C23×C4C23×C10711yescharacteristic
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16D4×C10714yescomplemented
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C22×C8C23×C10711yescharacteristic
557C22×C8C23×C10711yescharacteristic
558C22×C8C23×C10711yescharacteristic
559C22×C8C23×C10711yescharacteristic
560#124—28no—
561#124—22no—
562#124D4×C10714yescomplemented
563C22⋊Q8—28no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566#121—28no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—41no—
572#121—41no—
573C4×Q8—22no—
574C4×Q8D4×C10714yescomplemented
575C4×D4—28no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4D4×C10711yescharacteristic
583C2×C4⋊C4C23×C10711yescharacteristic
584C2×C4⋊C4C23×C10711yescharacteristic
585C2×C4⋊C4C23×C10711yescharacteristic
586C2×C4⋊C4C23×C10711yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4D4×C10711yescharacteristic
597C2×C22⋊C4D4×C10711yescharacteristic
598C2×C42—21no—
599C2×C42C23×C10711yescharacteristic
600#106—22no—
601C4⋊C8—22no—
602#103—22no—
603#103—22no—
604#103—22no—
605#103—22no—
606#103—22no—
607#103—41no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—41no—
612C22⋊C8—22no—
613C22⋊C8—22no—
614C22⋊C8—41no—
615C22⋊C8—41no—
616C4×C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C10711yescharacteristic
624C24C2×D4×C10711yescharacteristic
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C10712yes—
645C2×Q8C2×D4×C10712yes—
646C2×Q8C2×D4×C10712yes—
647C2×Q8#41×C10712yes—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—41no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C10712yes—
674C2×D4C2×D4×C10712yes—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—81no—
701C22×C4—81no—
702C22×C4C2×D4×C10711yescharacteristic
703C22×C4C2×D4×C10711yescharacteristic
704C22×C4C2×D4×C10711yescharacteristic
705C22×C4C2×D4×C10711yescharacteristic
706C22×C4C24×C10711yescharacteristic
707SD16—28no—
708SD16—44no—
709D8—44no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8C2×D4×C10712yes—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4C2×D4×C10712yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42C2×D4×C10712yes—
746C42C2×D4×C10712yes—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—22no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23#135×C10712yes—
775C23C22×D4×C10711yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—48no—
782Q8—41no—
783Q8—41no—
784Q8#121×C10714yes—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—44no—
790D4—48no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—84no—
797D4—84no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—48no—
814C2×C4—48no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—84no—
837C2×C4#120×C10712yes—
838C2×C4#120×C10712yes—
839C2×C4C22×D4×C10711yescharacteristic
840C2×C4C22×D4×C10711yescharacteristic
841C2×C4C22×D4×C10711yescharacteristic
842C2×C4C2×#41×C10711yescharacteristic
843C2×C4H(5,𝔽2)×C10711yescharacteristic
844C2×C4H(5,𝔽2)×C10711yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C10711yescharacteristic
878C22D42×C10711yescharacteristic
879C22#546×C10711yescharacteristic
880C22C2×#135×C10711yescharacteristic
881C22#575×C10711yescharacteristic
882C22#577×C10711yescharacteristic
883C22#577×C10711yescharacteristic
884C4—24no—
885C4—22no—
886C4—22no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—81no—
892C4—81no—
893C4—81no—
894C4C2×#121×C10711yescharacteristic
895C4#535×C10711yescharacteristic
896C4D42×C10711yescharacteristic
897C4#546×C10711yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—82no—
902C2C107×#240811yescharacteristic
903C2C107×#300211yescharacteristic
904C2C107×#301011yescharacteristic
905C2C107×#327511yescharacteristic
906C2C107×#328211yescharacteristic
907C2C107×#330111yescharacteristic
908C2C107×#332611yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
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
1. C2×#548×C107C2semidirect
2. C2×#463×C107C2semidirect
3. C2×#449×C107C2semidirect
4. C2×#448×C107C2semidirect
5. C2×C4×SD16×C107C2semidirect
6. C107×#2535C2semidirect
7. C107×#2035C2semidirect
8. C107×#2034C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1958C2semidirect
12. C107×#1954C2semidirect
13. C107×#1805C2semidirect
14. C107×#1788C2semidirect
15. C107×#1787C2semidirect
97. C2×SD16×C107D4semidirect
107. #124×C107D4semidirect
119. C4×Q8×C107D4semidirect
443. #24244C107direct (N × H)
455. C2×#548C2×C107semidirect
456. C2×#463C2×C107semidirect
457. C2×#449C2×C107semidirect
458. C2×#448C2×C107semidirect
459. C2×C4×SD16C2×C107semidirect
460. #2535C2×C107semidirect
461. #2035C2×C107semidirect
462. #2034C2×C107semidirect
463. #2000C2×C107semidirect
464. #1999C2×C107semidirect
465. #1958C2×C107semidirect
466. #1954C2×C107semidirect
467. #1805C2×C107semidirect
468. #1788C2×C107semidirect
469. #1787C2×C107semidirect
470. C107#24244direct (N × H)
552. C2×SD16D4×C107semidirect
562. #124D4×C107semidirect
574. C4×Q8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1072
C2×#463×C1072
C2×#449×C1072
C2×#448×C1072
C2×C4×SD16×C1072
C107×#25352
C107×#20352
C107×#20342
C107×#20002
C107×#19992
C107×#19582
C107×#19542
C107×#18052
C107×#17882
C107×#17872
#24244107