Finite Group Databasebeta

← C107×#24394 #41050358

Subgroups — C107×#24394 #41050358

Order 27392.

1578 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
2C2×#468×C107C211yesmaximal, characteristic, complemented
3C2×#465×C107C211yesmaximal, characteristic, complemented
4C2×#450×C107C211yesmaximal, characteristic, complemented
5C2×#408×C107C211yesmaximal, characteristic, complemented
6C107×#2616C211yesmaximal, characteristic, complemented
7C107×#2034C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1895C211yesmaximal, characteristic, complemented
12C107×#1893C211yesmaximal, characteristic, complemented
13C107×#1873C211yesmaximal, characteristic, complemented
14C107×#1854C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C23×D4×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×SD16×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic, complemented
21C23×C8×C107C2211yescharacteristic, complemented
22#535×C107—24no—
23#535×C107—24no—
24C2×#127×C107—21no—
25C2×#124×C107—21no—
26C2×C22⋊Q8×C107C2211yescharacteristic
27C2×C22⋊Q8×C107C2211yescharacteristic, complemented
28C2×C22⋊Q8×C107C2211yescharacteristic, complemented
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×#121×C107C2211yescharacteristic
32C2×#121×C107C2211yescharacteristic
33C2×#120×C107—21no—
34C2×#120×C107—21no—
35C2×#117×C107C2211yescharacteristic
36#468×C107—24no—
37#465×C107—24no—
38#450×C107—24no—
39C2×#107×C107C2211yescharacteristic, complemented
40C2×#106×C107C2211yescharacteristic, complemented
41C2×#103×C107C2211yescharacteristic, complemented
42C2×#103×C107C2211yescharacteristic, complemented
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46C2×#102×C107C2211yescharacteristic
47C2×#102×C107C2211yescharacteristic
48C2×#102×C107C2211yescharacteristic
49#408×C107—24no—
50C2×C22⋊C8×C107C2211yescharacteristic
51C2×C22⋊C8×C107C2211yescharacteristic
52C2×C22⋊C8×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic, complemented
54#395×C107—21no—
55#394×C107—21no—
56#394×C107—21no—
57#394×C107—21no—
58#380×C107C2211yescharacteristic
59#380×C107C2211yescharacteristic, complemented
60#380×C107C2211yescharacteristic, complemented
61#340×C107C2211yescharacteristic, complemented
62#340×C107C2211yescharacteristic, complemented
63#340×C107C2211yescharacteristic, complemented
64#340×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×C107D411yescharacteristic
73C22×Q8×C107C2311yescharacteristic
74C22×D4×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C22×D4×C107—22no—
79C22×D4×C107—22no—
80C22×D4×C107—21no—
81C22×D4×C107—22no—
82C22×D4×C107—22no—
83C22×D4×C107—41no—
84C22×D4×C107—41no—
85C22×D4×C107D411yescharacteristic
86C22×D4×C107D411yescharacteristic
87C22×D4×C107D411yescharacteristic
88C22×D4×C107C2311yescharacteristic
89C22×D4×C107C2311yescharacteristic
90C23×C4×C107C2311yescharacteristic
91C23×C4×C107C2311yescharacteristic
92C23×C4×C107C2311yescharacteristic
93C2×SD16×C107—22no—
94C2×SD16×C107—22no—
95C2×SD16×C107—22no—
96C2×SD16×C107—22no—
97C2×SD16×C107—41no—
98C2×SD16×C107—41no—
99C2×M16×C107—22no—
100C2×M16×C107—22no—
101C2×M16×C107—41no—
102C22×C8×C107—22no—
103C22×C8×C107—22no—
104C22×C8×C107—41no—
105C22×C8×C107C2311yescharacteristic
106C22×C8×C107C2311yescharacteristic
107C22×C8×C107C2311yescharacteristic
108C22×C8×C107C2311yescharacteristic
109#127×C107—28no—
110#124×C107—28no—
111C22⋊Q8×C107—22no—
112C22⋊Q8×C107—22no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—22no—
115C22⋊Q8×C107—41no—
116C22⋊Q8×C107—41no—
117#121×C107—22no—
118#121×C107—22no—
119#121×C107—22no—
120#121×C107—22no—
121#121×C107—22no—
122#121×C107—22no—
123#121×C107D414yes—
124#121×C107D414yes—
125#120×C107—28no—
126#120×C107—28no—
127#117×C107—22no—
128#117×C107—22no—
129C2×C4⋊C4×C107—21no—
130C2×C4⋊C4×C107—21no—
131C2×C4⋊C4×C107—21no—
132C2×C4⋊C4×C107C2311yescharacteristic
133C2×C4⋊C4×C107C2311yescharacteristic
134C2×C4⋊C4×C107C2311yescharacteristic
135C2×C4⋊C4×C107C2311yescharacteristic
136C2×C4⋊C4×C107C2311yescharacteristic
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×C107—21no—
143C2×C22⋊C4×C107—21no—
144C2×C22⋊C4×C107—21no—
145C2×C22⋊C4×C107—21no—
146C2×C22⋊C4×C107—21no—
147C2×C22⋊C4×C107—21no—
148C2×C42×C107—21no—
149#107×C107—22no—
150#106×C107—22no—
151#103×C107—22no—
152#103×C107—22no—
153#102×C107—22no—
154#102×C107—22no—
155#102×C107—22no—
156#102×C107—22no—
157#102×C107—41no—
158#102×C107—41no—
159C22⋊C8×C107—22no—
160C22⋊C8×C107—22no—
161C22⋊C8×C107—22no—
162C22⋊C8×C107D414yescomplemented
163#95×C107—21no—
164#95×C107—21no—
165#95×C107—21no—
166C24×C107—24no—
167C24×C107—21no—
168C24×C107—21no—
169C24×C107—42no—
170C24×C107—42no—
171C24×C107—81no—
172C24×C107—81no—
173C24×C107—81no—
174C24×C107—81no—
175C24×C107C2×D411yescharacteristic
176C24×C107C2×D411yescharacteristic
177C24×C107C2×D411yescharacteristic
178#41×C107—44no—
179#41×C107—44no—
180#41×C107—44no—
181#41×C107—44no—
182C2×Q8×C107—22no—
183C2×Q8×C107—22no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107—41no—
191C2×D4×C107—24no—
192C2×D4×C107—22no—
193C2×D4×C107—22no—
194C2×D4×C107—22no—
195C2×D4×C107—22no—
196C2×D4×C107—24no—
197C2×D4×C107—24no—
198C2×D4×C107—24no—
199C2×D4×C107—24no—
200C2×D4×C107—22no—
201C2×D4×C107—22no—
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—44no—
213C2×D4×C107—44no—
214C2×D4×C107—44no—
215C2×D4×C107—44no—
216C2×D4×C107—41no—
217C2×D4×C107—41no—
218C2×D4×C107—41no—
219C2×D4×C107—42no—
220C2×D4×C107—42no—
221C2×D4×C107—81no—
222C2×D4×C107—81no—
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×C107C2×D412yes—
230C2×D4×C107C2×D412yes—
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—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2×D411yescharacteristic
253C22×C4×C107C2×D412yes—
254C22×C4×C107C2×D412yes—
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2×D412yes—
257C22×C4×C107#4112yes—
258C22×C4×C107C2411yescharacteristic
259SD16×C107—44no—
260SD16×C107—44no—
261M16×C107—44no—
262C2×C8×C107—21no—
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—44no—
273C2×C8×C107C2×D412yes—
274C2×C8×C107C2×D412yes—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—42no—
284C4⋊C4×C107—42no—
285C4⋊C4×C107—42no—
286C4⋊C4×C107C2×D412yes—
287C4⋊C4×C107C2×D412yes—
288C22⋊C4×C107—24no—
289C22⋊C4×C107—24no—
290C22⋊C4×C107—24no—
291C22⋊C4×C107—24no—
292C22⋊C4×C107—24no—
293C22⋊C4×C107—42no—
294C22⋊C4×C107—42no—
295C22⋊C4×C107—42no—
296C22⋊C4×C107—81no—
297C22⋊C4×C107—81no—
298C22⋊C4×C107—81no—
299C42×C107—24no—
300C23×C107—21no—
301C23×C107—21no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—21no—
305C23×C107—21no—
306C23×C107—21no—
307C23×C107—21no—
308C23×C107—21no—
309C23×C107—21no—
310C23×C107—21no—
311C23×C107—21no—
312C23×C107—22no—
313C23×C107—22no—
314C23×C107—21no—
315C23×C107—21no—
316C23×C107—21no—
317C23×C107—21no—
318C23×C107—21no—
319C23×C107—21no—
320C23×C107—21no—
321C23×C107—48no—
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—84no—
335C23×C107—84no—
336C23×C107—84no—
337C23×C107—84no—
338C23×C107—84no—
339C23×C107—84no—
340C23×C107#12012yes—
341C23×C107#12112yes—
342C23×C107C22×D411yescharacteristic
343Q8×C107—44no—
344Q8×C107—41no—
345Q8×C107—41no—
346Q8×C107—41no—
347Q8×C107—41no—
348D4×C107—22no—
349D4×C107—22no—
350D4×C107—22no—
351D4×C107—22no—
352D4×C107—44no—
353D4×C107—44no—
354D4×C107—48no—
355D4×C107—44no—
356D4×C107—41no—
357D4×C107—41no—
358D4×C107—41no—
359D4×C107—41no—
360D4×C107—84no—
361D4×C107—84no—
362D4×C107—84no—
363D4×C107—84no—
364C2×C4×C107—21no—
365C2×C4×C107—21no—
366C2×C4×C107—21no—
367C2×C4×C107—21no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—22no—
371C2×C4×C107—22no—
372C2×C4×C107—22no—
373C2×C4×C107—22no—
374C2×C4×C107—22no—
375C2×C4×C107—22no—
376C2×C4×C107—22no—
377C2×C4×C107—22no—
378C2×C4×C107—21no—
379C2×C4×C107—21no—
380C2×C4×C107—21no—
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—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—41no—
400C2×C4×C107—41no—
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—22no—
410C8×C107—22no—
411C8×C107—41no—
412C8×C107—41no—
413C22×C107—22no—
414C22×C107—22no—
415C22×C107—22no—
416C22×C107—22no—
417C22×C107—22no—
418C22×C107—22no—
419C22×C107—41no—
420C22×C107—41no—
421C22×C107—41no—
422C22×C107—41no—
423C22×C107—41no—
424C22×C107—41no—
425C22×C107—41no—
426C22×C107—41no—
427C22×C107—41no—
428C22×C107—42no—
429C22×C107—42no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—42no—
434C22×C107—42no—
435C22×C107—41no—
436C22×C107—42no—
437C22×C107—42no—
438C22×C107—41no—
439C22×C107—41no—
440C22×C107—816no—
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#53411yescharacteristic
452C22×C107#57611yescharacteristic
453C22×C107#57711yescharacteristic
454C22×C107#57711yescharacteristic
455C22×C107#57711yescharacteristic
456C4×C107—22no—
457C4×C107—22no—
458C4×C107—41no—
459C4×C107—42no—
460C4×C107—42no—
461C4×C107—81no—
462C4×C107—81no—
463C4×C107—81no—
464C4×C107—81no—
465C4×C107D4211yescharacteristic
466C4×C107D4211yescharacteristic
467C4×C107#54611yescharacteristic
468C4×C107#54611yescharacteristic
469#24394C10711yesmaximal, characteristic, direct product factor, Sylow
470C2×C107—42no—
471C2×C107—42no—
472C2×C107—81no—
473C2×C107—82no—
474C2×C107—82no—
475C2×C107#241011yescharacteristic
476C2×C107#300911yescharacteristic
477C2×C107#301211yescharacteristic
478C2×C107#305711yescharacteristic
479C2×C107#306211yescharacteristic
480C2×C107#319811yescharacteristic
481C2×C107#320011yescharacteristic
482C2×#535C2×C10711yescharacteristic
483C2×#468C2×C10711yescharacteristic, complemented
484C2×#465C2×C10711yescharacteristic, complemented
485C2×#450C2×C10711yescharacteristic, complemented
486C2×#408C2×C10711yescharacteristic, complemented
487#2616C2×C10711yescharacteristic, complemented
488#2034C2×C10711yescharacteristic, complemented
489#2033C2×C10711yescharacteristic, complemented
490#2000C2×C10711yescharacteristic, complemented
491#2000C2×C10711yescharacteristic, complemented
492#1895C2×C10711yescharacteristic, complemented
493#1893C2×C10711yescharacteristic, complemented
494#1873C2×C10711yescharacteristic, complemented
495#1854C2×C10711yescharacteristic, complemented
496#1786C2×C10711yescharacteristic, complemented
497C107#2439411yescharacteristic, direct product factor, Sylow
498C22×#41C22×C10711yescharacteristic
499C23×D4C22×C10711yescharacteristic
500C22×SD16C22×C10711yescharacteristic
501C22×SD16C22×C10711yescharacteristic
502C22×M16C22×C10711yescharacteristic, complemented
503C23×C8C22×C10711yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127—21no—
507C2×#124—21no—
508C2×C22⋊Q8C22×C10711yescharacteristic
509C2×C22⋊Q8C22×C10711yescharacteristic, complemented
510C2×C22⋊Q8C22×C10711yescharacteristic, complemented
511C2×#121C22×C10711yescharacteristic
512C2×#121C22×C10711yescharacteristic
513C2×#121C22×C10711yescharacteristic
514C2×#121C22×C10711yescharacteristic
515C2×#120—21no—
516C2×#120—21no—
517C2×#117C22×C10711yescharacteristic
518#468—24no—
519#465—24no—
520#450—24no—
521C2×#107C22×C10711yescharacteristic, complemented
522C2×#106C22×C10711yescharacteristic, complemented
523C2×#103C22×C10711yescharacteristic, complemented
524C2×#103C22×C10711yescharacteristic, complemented
525C2×#102C22×C10711yescharacteristic
526C2×#102C22×C10711yescharacteristic
527C2×#102C22×C10711yescharacteristic
528C2×#102C22×C10711yescharacteristic
529C2×#102C22×C10711yescharacteristic
530C2×#102C22×C10711yescharacteristic
531#408—24no—
532C2×C22⋊C8C22×C10711yescharacteristic
533C2×C22⋊C8C22×C10711yescharacteristic
534C2×C22⋊C8C22×C10711yescharacteristic, complemented
535C2×C22⋊C8C22×C10711yescharacteristic, complemented
536#395—21no—
537#394—21no—
538#394—21no—
539#394—21no—
540#380C22×C10711yescharacteristic
541#380C22×C10711yescharacteristic, complemented
542#380C22×C10711yescharacteristic, complemented
543#340C22×C10711yescharacteristic, complemented
544#340C22×C10711yescharacteristic, complemented
545#340C22×C10711yescharacteristic, complemented
546#340C22×C10711yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C10711yescharacteristic
555C22×Q8C23×C10711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10711yescharacteristic
568C22×D4D4×C10711yescharacteristic
569C22×D4D4×C10711yescharacteristic
570C22×D4C23×C10711yescharacteristic
571C22×D4C23×C10711yescharacteristic
572C23×C4C23×C10711yescharacteristic
573C23×C4C23×C10711yescharacteristic
574C23×C4C23×C10711yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C10711yescharacteristic
588C22×C8C23×C10711yescharacteristic
589C22×C8C23×C10711yescharacteristic
590C22×C8C23×C10711yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C10714yes—
606#121D4×C10714yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C10711yescharacteristic
615C2×C4⋊C4C23×C10711yescharacteristic
616C2×C4⋊C4C23×C10711yescharacteristic
617C2×C4⋊C4C23×C10711yescharacteristic
618C2×C4⋊C4C23×C10711yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C10714yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C10711yescharacteristic
658C24C2×D4×C10711yescharacteristic
659C24C2×D4×C10711yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
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—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C10712yes—
712C2×D4C2×D4×C10712yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C10711yescharacteristic
734C22×C4C2×D4×C10711yescharacteristic
735C22×C4C2×D4×C10712yes—
736C22×C4C2×D4×C10712yes—
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C2×D4×C10712yes—
739C22×C4#41×C10712yes—
740C22×C4C24×C10711yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
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—44no—
755C2×C8C2×D4×C10712yes—
756C2×C8C2×D4×C10712yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C10712yes—
769C4⋊C4C2×D4×C10712yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
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—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C10712yes—
823C23#121×C10712yes—
824C23C22×D4×C10711yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
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—41no—
882C2×C4—41no—
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—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C10711yescharacteristic
932C22C2×#121×C10711yescharacteristic
933C22#534×C10711yescharacteristic
934C22#576×C10711yescharacteristic
935C22#577×C10711yescharacteristic
936C22#577×C10711yescharacteristic
937C22#577×C10711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C10711yescharacteristic
948C4D42×C10711yescharacteristic
949C4#546×C10711yescharacteristic
950C4#546×C10711yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C107×#241011yescharacteristic
957C2C107×#300911yescharacteristic
958C2C107×#301211yescharacteristic
959C2C107×#305711yescharacteristic
960C2C107×#306211yescharacteristic
961C2C107×#319811yescharacteristic
962C2C107×#320011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#535×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C22×#41×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C107C2semidirect
3. C2×#465×C107C2semidirect
4. C2×#450×C107C2semidirect
5. C2×#408×C107C2semidirect
6. C107×#2616C2semidirect
7. C107×#2034C2semidirect
8. C107×#2033C2semidirect
9. C107×#2000C2semidirect
10. C107×#2000C2semidirect
11. C107×#1895C2semidirect
12. C107×#1893C2semidirect
13. C107×#1873C2semidirect
14. C107×#1854C2semidirect
15. C107×#1786C2semidirect
20. C22×M16×C107C22semidirect
21. C23×C8×C107C22semidirect
27. C2×C22⋊Q8×C107C22semidirect
28. C2×C22⋊Q8×C107C22semidirect
39. C2×#107×C107C22semidirect
40. C2×#106×C107C22semidirect
41. C2×#103×C107C22semidirect
42. C2×#103×C107C22semidirect
52. C2×C22⋊C8×C107C22semidirect
53. C2×C22⋊C8×C107C22semidirect
59. #380×C107C22semidirect
60. #380×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
162. C22⋊C8×C107D4semidirect
469. #24394C107direct (N × H)
483. C2×#468C2×C107semidirect
484. C2×#465C2×C107semidirect
485. C2×#450C2×C107semidirect
486. C2×#408C2×C107semidirect
487. #2616C2×C107semidirect
488. #2034C2×C107semidirect
489. #2033C2×C107semidirect
490. #2000C2×C107semidirect
491. #2000C2×C107semidirect
492. #1895C2×C107semidirect
493. #1893C2×C107semidirect
494. #1873C2×C107semidirect
495. #1854C2×C107semidirect
496. #1786C2×C107semidirect
497. C107#24394direct (N × H)
502. C22×M16C22×C107semidirect
503. C23×C8C22×C107semidirect
509. C2×C22⋊Q8C22×C107semidirect
510. C2×C22⋊Q8C22×C107semidirect
521. C2×#107C22×C107semidirect
522. C2×#106C22×C107semidirect
523. C2×#103C22×C107semidirect
524. C2×#103C22×C107semidirect
534. C2×C22⋊C8C22×C107semidirect
535. C2×C22⋊C8C22×C107semidirect
541. #380C22×C107semidirect
542. #380C22×C107semidirect
543. #340C22×C107semidirect
544. #340C22×C107semidirect
545. #340C22×C107semidirect
546. #340C22×C107semidirect
644. C22⋊C8D4×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×#468×C1072
C2×#465×C1072
C2×#450×C1072
C2×#408×C1072
C107×#26162
C107×#20342
C107×#20332
C107×#20002
C107×#18952
C107×#18932
C107×#18732
C107×#18542
C107×#17862
#24394107