Finite Group Databasebeta

← C107×#23850 #41049814

Subgroups — C107×#23850 #41049814

Order 27392.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C107C211yesmaximal, characteristic, complemented
2C2×#546×C107C211yesmaximal, characteristic, complemented
3C2×#449×C107C211yesmaximal, characteristic, complemented
4C2×#450×C107C211yesmaximal, characteristic, complemented
5C2×#447×C107C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2015C211yesmaximal, characteristic, complemented
8C107×#2012C211yesmaximal, characteristic, complemented
9C107×#2001C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1893C211yesmaximal, characteristic, complemented
12C107×#1879C211yesmaximal, characteristic, complemented
13C107×#1877C211yesmaximal, characteristic, complemented
14C107×#1869C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×#41×C107C2211yescharacteristic, complemented
18C23×D4×C107C2211yescharacteristic
19C2×#135×C107—24no—
20C2×#135×C107—24no—
21C2×#135×C107—24no—
22C22×Q16×C107C2211yescharacteristic, complemented
23C22×SD16×C107C2211yescharacteristic
24C22×SD16×C107C2211yescharacteristic
25C22×SD16×C107C2211yescharacteristic, complemented
26C22×D8×C107C2211yescharacteristic
27C22×D8×C107C2211yescharacteristic
28C23×C8×C107C2211yescharacteristic, complemented
29#546×C107—24no—
30#546×C107—24no—
31C2×#124×C107C2211yescharacteristic
32C2×#123×C107—21no—
33C2×C22⋊Q8×C107C2211yescharacteristic
34C2×C22⋊Q8×C107C2211yescharacteristic
35C2×#121×C107—21no—
36C2×#121×C107C2211yescharacteristic
37C2×#121×C107C2211yescharacteristic
38C2×#120×C107—21no—
39C2×C4×D4×C107C2211yescharacteristic
40C2×C4×D4×C107C2211yescharacteristic
41C22×C22⋊C4×C107—21no—
42#450×C107—24no—
43#449×C107—24no—
44#447×C107—24no—
45C2×#103×C107C2211yescharacteristic, complemented
46C2×#103×C107C2211yescharacteristic, complemented
47C2×#103×C107C2211yescharacteristic, complemented
48C2×#102×C107C2211yescharacteristic
49C2×#102×C107C2211yescharacteristic
50C2×#102×C107C2211yescharacteristic
51C2×#102×C107C2211yescharacteristic
52C2×#102×C107C2211yescharacteristic, complemented
53C2×C22⋊C8×C107C2211yescharacteristic
54C2×C22⋊C8×C107C2211yescharacteristic
55C2×C22⋊C8×C107C2211yescharacteristic, complemented
56#394×C107—21no—
57#392×C107—21no—
58#391×C107C2211yescharacteristic, complemented
59#390×C107C2211yescharacteristic, complemented
60#386×C107—21no—
61#385×C107—21no—
62#380×C107C2211yescharacteristic, complemented
63#340×C107C2211yescharacteristic, complemented
64#340×C107C2211yescharacteristic, complemented
65#336×C107C2211yescharacteristic, complemented
66#336×C107C2211yescharacteristic, complemented
67C25×C107—21no—
68C2×#41×C107—22no—
69C2×#41×C107—22no—
70C2×#41×C107—22no—
71C2×#41×C107—22no—
72C2×#41×C107—22no—
73C2×#41×C107—22no—
74C2×#41×C107—22no—
75C2×#41×C107—41no—
76C2×#41×C107—41no—
77C2×#41×C107—41no—
78C2×#41×C107—41no—
79C2×#41×C107D414yescomplemented
80C22×Q8×C107C2311yescharacteristic
81C22×Q8×C107C2311yescharacteristic
82C22×D4×C107—21no—
83C22×D4×C107—21no—
84C22×D4×C107—22no—
85C22×D4×C107—22no—
86C22×D4×C107—22no—
87C22×D4×C107—22no—
88C22×D4×C107—21no—
89C22×D4×C107—21no—
90C22×D4×C107—21no—
91C22×D4×C107—41no—
92C22×D4×C107—41no—
93C22×D4×C107D411yescharacteristic
94C22×D4×C107C2311yescharacteristic
95C22×D4×C107C2311yescharacteristic
96C22×D4×C107C2311yescharacteristic
97C23×C4×C107—21no—
98C23×C4×C107—21no—
99C23×C4×C107—21no—
100C23×C4×C107C2311yescharacteristic
101C23×C4×C107C2311yescharacteristic
102#135×C107—232no—
103C2×Q16×C107—22no—
104C2×Q16×C107—22no—
105C2×Q16×C107—22no—
106C2×SD16×C107—22no—
107C2×SD16×C107—22no—
108C2×SD16×C107—22no—
109C2×SD16×C107—22no—
110C2×SD16×C107—22no—
111C2×SD16×C107—22no—
112C2×SD16×C107—22no—
113C2×SD16×C107—41no—
114C2×SD16×C107D414yescomplemented
115C2×D8×C107—22no—
116C2×D8×C107—22no—
117C2×D8×C107—22no—
118C2×D8×C107—22no—
119C2×D8×C107—41no—
120C2×D8×C107D414yescomplemented
121C22×C8×C107—22no—
122C22×C8×C107—22no—
123C22×C8×C107—22no—
124C22×C8×C107C2311yescharacteristic
125C22×C8×C107C2311yescharacteristic
126C22×C8×C107C2311yescharacteristic
127C22×C8×C107C2311yescharacteristic
128#124×C107—22no—
129#124×C107—22no—
130#123×C107—28no—
131C22⋊Q8×C107—22no—
132C22⋊Q8×C107—22no—
133C22⋊Q8×C107—22no—
134C22⋊Q8×C107—41no—
135#121×C107—28no—
136#121×C107—22no—
137#121×C107—22no—
138#121×C107—41no—
139#121×C107D414yescomplemented
140#120×C107—28no—
141C4×D4×C107—22no—
142C4×D4×C107—22no—
143C4×D4×C107—22no—
144C4×D4×C107—22no—
145C2×C4⋊C4×C107—21no—
146C2×C4⋊C4×C107—21no—
147C2×C4⋊C4×C107D411yescharacteristic
148C2×C4⋊C4×C107C2311yescharacteristic
149C2×C4⋊C4×C107C2311yescharacteristic
150C2×C4⋊C4×C107C2311yescharacteristic
151C2×C22⋊C4×C107—28no—
152C2×C22⋊C4×C107—21no—
153C2×C22⋊C4×C107—21no—
154C2×C22⋊C4×C107—21no—
155C2×C22⋊C4×C107—21no—
156C2×C22⋊C4×C107—21no—
157C2×C22⋊C4×C107—21no—
158C2×C22⋊C4×C107—21no—
159C2×C22⋊C4×C107—21no—
160C2×C22⋊C4×C107—21no—
161C2×C22⋊C4×C107—21no—
162C2×C22⋊C4×C107D411yescharacteristic
163C2×C22⋊C4×C107D411yescharacteristic
164C2×C42×C107C2311yescharacteristic
165#103×C107—22no—
166#103×C107—41no—
167#103×C107—41no—
168#102×C107—22no—
169#102×C107—22no—
170#102×C107—22no—
171#102×C107—22no—
172#102×C107—22no—
173C22⋊C8×C107—22no—
174C22⋊C8×C107—22no—
175C22⋊C8×C107—22no—
176#95×C107—21no—
177#95×C107—21no—
178#95×C107—21no—
179C24×C107—21no—
180C24×C107—24no—
181C24×C107—21no—
182C24×C107—21no—
183C24×C107—42no—
184C24×C107—42no—
185C24×C107—42no—
186C24×C107—42no—
187C24×C107—81no—
188C24×C107—81no—
189C24×C107C2×D411yescharacteristic
190C24×C107C2×D411yescharacteristic
191#41×C107—28no—
192#41×C107—28no—
193#41×C107—44no—
194#41×C107—44no—
195#41×C107—44no—
196#41×C107—44no—
197#41×C107—44no—
198#41×C107—44no—
199C2×Q8×C107—21no—
200C2×Q8×C107—21no—
201C2×Q8×C107—21no—
202C2×Q8×C107—21no—
203C2×Q8×C107—21no—
204C2×Q8×C107—21no—
205C2×Q8×C107—21no—
206C2×Q8×C107—21no—
207C2×Q8×C107—21no—
208C2×Q8×C107—21no—
209C2×Q8×C107C2×D412yes—
210C2×Q8×C107C2×D412yes—
211C2×D4×C107—24no—
212C2×D4×C107—22no—
213C2×D4×C107—24no—
214C2×D4×C107—22no—
215C2×D4×C107—24no—
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—41no—
230C2×D4×C107—42no—
231C2×D4×C107—42no—
232C2×D4×C107—42no—
233C2×D4×C107—44no—
234C2×D4×C107—44no—
235C2×D4×C107—44no—
236C2×D4×C107—42no—
237C2×D4×C107—42no—
238C2×D4×C107—42no—
239C2×D4×C107—42no—
240C2×D4×C107—44no—
241C2×D4×C107—42no—
242C2×D4×C107—42no—
243C2×D4×C107—81no—
244C2×D4×C107—81no—
245C2×D4×C107—81no—
246C2×D4×C107C2×D412yes—
247C2×D4×C107C2×D412yes—
248C2×D4×C107C2×D412yes—
249C2×D4×C107C2×D412yes—
250C2×D4×C107C2×D412yes—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—21no—
258C22×C4×C107—24no—
259C22×C4×C107—24no—
260C22×C4×C107—21no—
261C22×C4×C107—21no—
262C22×C4×C107—21no—
263C22×C4×C107—21no—
264C22×C4×C107—21no—
265C22×C4×C107—21no—
266C22×C4×C107—21no—
267C22×C4×C107—21no—
268C22×C4×C107—42no—
269C22×C4×C107—42no—
270C22×C4×C107—42no—
271C22×C4×C107—42no—
272C22×C4×C107—42no—
273C22×C4×C107—81no—
274C22×C4×C107—81no—
275C22×C4×C107C2×D411yescharacteristic
276C22×C4×C107C2×D411yescharacteristic
277C22×C4×C107C2×D411yescharacteristic
278C22×C4×C107C2×D411yescharacteristic
279C22×C4×C107C2×D412yes—
280C22×C4×C107C2×D412yes—
281C22×C4×C107C2411yescharacteristic
282Q16×C107—28no—
283SD16×C107—28no—
284SD16×C107—28no—
285SD16×C107—44no—
286D8×C107—28no—
287D8×C107—44no—
288C2×C8×C107—28no—
289C2×C8×C107—21no—
290C2×C8×C107—21no—
291C2×C8×C107—21no—
292C2×C8×C107—21no—
293C2×C8×C107—21no—
294C2×C8×C107—21no—
295C2×C8×C107—21no—
296C2×C8×C107—21no—
297C2×C8×C107—21no—
298C2×C8×C107—21no—
299C2×C8×C107C2×D412yes—
300C2×C8×C107C2×D412yes—
301C4⋊C4×C107—24no—
302C4⋊C4×C107—22no—
303C4⋊C4×C107—21no—
304C4⋊C4×C107—21no—
305C4⋊C4×C107—21no—
306C4⋊C4×C107—21no—
307C4⋊C4×C107—21no—
308C4⋊C4×C107—42no—
309C4⋊C4×C107C2×D412yes—
310C22⋊C4×C107—24no—
311C22⋊C4×C107—24no—
312C22⋊C4×C107—24no—
313C22⋊C4×C107—24no—
314C22⋊C4×C107—22no—
315C22⋊C4×C107—22no—
316C22⋊C4×C107—24no—
317C22⋊C4×C107—42no—
318C22⋊C4×C107—42no—
319C22⋊C4×C107—42no—
320C22⋊C4×C107—81no—
321C22⋊C4×C107—81no—
322C42×C107—21no—
323C42×C107—21no—
324C23×C107—21no—
325C23×C107—22no—
326C23×C107—21no—
327C23×C107—21no—
328C23×C107—21no—
329C23×C107—21no—
330C23×C107—22no—
331C23×C107—22no—
332C23×C107—21no—
333C23×C107—21no—
334C23×C107—21no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—21no—
339C23×C107—22no—
340C23×C107—22no—
341C23×C107—48no—
342C23×C107—48no—
343C23×C107—41no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—41no—
347C23×C107—41no—
348C23×C107—41no—
349C23×C107—41no—
350C23×C107—41no—
351C23×C107—41no—
352C23×C107—41no—
353C23×C107—41no—
354C23×C107—41no—
355C23×C107—41no—
356C23×C107—41no—
357C23×C107—41no—
358C23×C107—41no—
359C23×C107—84no—
360C23×C107—84no—
361C23×C107—84no—
362C23×C107—84no—
363C23×C107—84no—
364C23×C107#12012yes—
365C23×C107#13512yescomplemented
366C23×C107C22×D411yescharacteristic
367Q8×C107—22no—
368Q8×C107—22no—
369Q8×C107—22no—
370Q8×C107—22no—
371Q8×C107—41no—
372Q8×C107—41no—
373Q8×C107—41no—
374Q8×C107—41no—
375D4×C107—22no—
376D4×C107—22no—
377D4×C107—22no—
378D4×C107—22no—
379D4×C107—22no—
380D4×C107—22no—
381D4×C107—22no—
382D4×C107—44no—
383D4×C107—48no—
384D4×C107—48no—
385D4×C107—48no—
386D4×C107—41no—
387D4×C107—41no—
388D4×C107—41no—
389D4×C107—41no—
390D4×C107—84no—
391D4×C107—84no—
392D4×C107#12014yes—
393C2×C4×C107—21no—
394C2×C4×C107—21no—
395C2×C4×C107—22no—
396C2×C4×C107—22no—
397C2×C4×C107—22no—
398C2×C4×C107—22no—
399C2×C4×C107—21no—
400C2×C4×C107—21no—
401C2×C4×C107—22no—
402C2×C4×C107—22no—
403C2×C4×C107—21no—
404C2×C4×C107—21no—
405C2×C4×C107—22no—
406C2×C4×C107—21no—
407C2×C4×C107—21no—
408C2×C4×C107—21no—
409C2×C4×C107—21no—
410C2×C4×C107—21no—
411C2×C4×C107—48no—
412C2×C4×C107—48no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—41no—
416C2×C4×C107—41no—
417C2×C4×C107—41no—
418C2×C4×C107—41no—
419C2×C4×C107—41no—
420C2×C4×C107—41no—
421C2×C4×C107—41no—
422C2×C4×C107—41no—
423C2×C4×C107—41no—
424C2×C4×C107—41no—
425C2×C4×C107—41no—
426C2×C4×C107—41no—
427C2×C4×C107—41no—
428C2×C4×C107—41no—
429C2×C4×C107—84no—
430C2×C4×C107#12012yes—
431C2×C4×C107C22×D411yescharacteristic
432C2×C4×C107C22×D411yescharacteristic
433C2×C4×C107C22×D411yescharacteristic
434C2×C4×C107C22×D411yescharacteristic
435C2×C4×C107H(5,𝔽2)11yescharacteristic
436C2×C4×C107H(5,𝔽2)11yescharacteristic
437C8×C107—22no—
438C8×C107—22no—
439C8×C107—41no—
440C8×C107—41no—
441C22×C107—22no—
442C22×C107—24no—
443C22×C107—22no—
444C22×C107—22no—
445C22×C107—22no—
446C22×C107—22no—
447C22×C107—22no—
448C22×C107—41no—
449C22×C107—42no—
450C22×C107—41no—
451C22×C107—41no—
452C22×C107—42no—
453C22×C107—42no—
454C22×C107—41no—
455C22×C107—41no—
456C22×C107—41no—
457C22×C107—42no—
458C22×C107—41no—
459C22×C107—42no—
460C22×C107—41no—
461C22×C107—42no—
462C22×C107—42no—
463C22×C107—42no—
464C22×C107—42no—
465C22×C107—42no—
466C22×C107—42no—
467C22×C107—42no—
468C22×C107—816no—
469C22×C107—81no—
470C22×C107—81no—
471C22×C107—81no—
472C22×C107—81no—
473C22×C107—81no—
474C22×C107—81no—
475C22×C107—81no—
476C22×C107—81no—
477C22×C107C2×#12011yescharacteristic
478C22×C107D4211yescharacteristic
479C22×C107D4211yescharacteristic
480C22×C107C2×#13511yescharacteristic
481C22×C107#57511yescharacteristic
482C22×C107#57611yescharacteristic
483C22×C107#57711yescharacteristic
484C4×C107—22no—
485C4×C107—41no—
486C4×C107—42no—
487C4×C107—42no—
488C4×C107—41no—
489C4×C107—41no—
490C4×C107—42no—
491C4×C107—81no—
492C4×C107—81no—
493C4×C107C2×#12011yescharacteristic
494C4×C107#53411yescharacteristic
495C4×C107D4211yescharacteristic
496C4×C107D4211yescharacteristic
497#23850C10711yesmaximal, characteristic, direct product factor, Sylow
498C2×C107—42no—
499C2×C107—42no—
500C2×C107—44no—
501C2×C107—82no—
502C2×C107—82no—
503C2×C107#240311yescharacteristic
504C2×C107#300211yescharacteristic
505C2×C107#301211yescharacteristic
506C2×C107#326711yescharacteristic
507C2×C107#326811yescharacteristic
508C2×C107#328011yescharacteristic
509C2×C107#328211yescharacteristic
510C22×#135C2×C10711yescharacteristic, complemented
511C2×#546C2×C10711yescharacteristic, complemented
512C2×#449C2×C10711yescharacteristic, complemented
513C2×#450C2×C10711yescharacteristic, complemented
514C2×#447C2×C10711yescharacteristic, complemented
515#2407C2×C10711yescharacteristic, complemented
516#2015C2×C10711yescharacteristic, complemented
517#2012C2×C10711yescharacteristic, complemented
518#2001C2×C10711yescharacteristic, complemented
519#2000C2×C10711yescharacteristic, complemented
520#1893C2×C10711yescharacteristic, complemented
521#1879C2×C10711yescharacteristic, complemented
522#1877C2×C10711yescharacteristic, complemented
523#1869C2×C10711yescharacteristic, complemented
524#1788C2×C10711yescharacteristic, complemented
525C107#2385011yescharacteristic, direct product factor, Sylow
526C22×#41C22×C10711yescharacteristic
527C22×#41C22×C10711yescharacteristic, complemented
528C23×D4C22×C10711yescharacteristic
529C2×#135—24no—
530C2×#135—24no—
531C2×#135—24no—
532C22×Q16C22×C10711yescharacteristic, complemented
533C22×SD16C22×C10711yescharacteristic
534C22×SD16C22×C10711yescharacteristic
535C22×SD16C22×C10711yescharacteristic, complemented
536C22×D8C22×C10711yescharacteristic
537C22×D8C22×C10711yescharacteristic
538C23×C8C22×C10711yescharacteristic, complemented
539#546—24no—
540#546—24no—
541C2×#124C22×C10711yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C10711yescharacteristic
544C2×C22⋊Q8C22×C10711yescharacteristic
545C2×#121—21no—
546C2×#121C22×C10711yescharacteristic
547C2×#121C22×C10711yescharacteristic
548C2×#120—21no—
549C2×C4×D4C22×C10711yescharacteristic
550C2×C4×D4C22×C10711yescharacteristic
551C22×C22⋊C4—21no—
552#450—24no—
553#449—24no—
554#447—24no—
555C2×#103C22×C10711yescharacteristic, complemented
556C2×#103C22×C10711yescharacteristic, complemented
557C2×#103C22×C10711yescharacteristic, complemented
558C2×#102C22×C10711yescharacteristic
559C2×#102C22×C10711yescharacteristic
560C2×#102C22×C10711yescharacteristic
561C2×#102C22×C10711yescharacteristic
562C2×#102C22×C10711yescharacteristic, complemented
563C2×C22⋊C8C22×C10711yescharacteristic
564C2×C22⋊C8C22×C10711yescharacteristic
565C2×C22⋊C8C22×C10711yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C10711yescharacteristic, complemented
569#390C22×C10711yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C10711yescharacteristic, complemented
573#340C22×C10711yescharacteristic, complemented
574#340C22×C10711yescharacteristic, complemented
575#336C22×C10711yescharacteristic, complemented
576#336C22×C10711yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C10714yescomplemented
590C22×Q8C23×C10711yescharacteristic
591C22×Q8C23×C10711yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C10711yescharacteristic
604C22×D4C23×C10711yescharacteristic
605C22×D4C23×C10711yescharacteristic
606C22×D4C23×C10711yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C10711yescharacteristic
611C23×C4C23×C10711yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C10714yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C10714yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C10711yescharacteristic
635C22×C8C23×C10711yescharacteristic
636C22×C8C23×C10711yescharacteristic
637C22×C8C23×C10711yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C10714yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C10711yescharacteristic
658C2×C4⋊C4C23×C10711yescharacteristic
659C2×C4⋊C4C23×C10711yescharacteristic
660C2×C4⋊C4C23×C10711yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C10711yescharacteristic
673C2×C22⋊C4D4×C10711yescharacteristic
674C2×C42C23×C10711yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10711yescharacteristic
700C24C2×D4×C10711yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C10712yes—
720C2×Q8C2×D4×C10712yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C10712yes—
757C2×D4C2×D4×C10712yes—
758C2×D4C2×D4×C10712yes—
759C2×D4C2×D4×C10712yes—
760C2×D4C2×D4×C10712yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C10711yescharacteristic
786C22×C4C2×D4×C10711yescharacteristic
787C22×C4C2×D4×C10711yescharacteristic
788C22×C4C2×D4×C10711yescharacteristic
789C22×C4C2×D4×C10712yes—
790C22×C4C2×D4×C10712yes—
791C22×C4C24×C10711yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C10712yes—
810C2×C8C2×D4×C10712yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C10712yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C10712yes—
875C23#135×C10712yescomplemented
876C23C22×D4×C10711yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C10714yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C10712yes—
941C2×C4C22×D4×C10711yescharacteristic
942C2×C4C22×D4×C10711yescharacteristic
943C2×C4C22×D4×C10711yescharacteristic
944C2×C4C22×D4×C10711yescharacteristic
945C2×C4H(5,𝔽2)×C10711yescharacteristic
946C2×C4H(5,𝔽2)×C10711yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C10711yescharacteristic
988C22D42×C10711yescharacteristic
989C22D42×C10711yescharacteristic
990C22C2×#135×C10711yescharacteristic
991C22#575×C10711yescharacteristic
992C22#576×C10711yescharacteristic
993C22#577×C10711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10711yescharacteristic
1004C4#534×C10711yescharacteristic
1005C4D42×C10711yescharacteristic
1006C4D42×C10711yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C107×#240311yescharacteristic
1013C2C107×#300211yescharacteristic
1014C2C107×#301211yescharacteristic
1015C2C107×#326711yescharacteristic
1016C2C107×#326811yescharacteristic
1017C2C107×#328011yescharacteristic
1018C2C107×#328211yescharacteristic
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. C22×#135×C107C2semidirect
2. C2×#546×C107C2semidirect
3. C2×#449×C107C2semidirect
4. C2×#450×C107C2semidirect
5. C2×#447×C107C2semidirect
6. C107×#2407C2semidirect
7. C107×#2015C2semidirect
8. C107×#2012C2semidirect
9. C107×#2001C2semidirect
10. C107×#2000C2semidirect
11. C107×#1893C2semidirect
12. C107×#1879C2semidirect
13. C107×#1877C2semidirect
14. C107×#1869C2semidirect
15. C107×#1788C2semidirect
17. C22×#41×C107C22semidirect
22. C22×Q16×C107C22semidirect
25. C22×SD16×C107C22semidirect
28. C23×C8×C107C22semidirect
45. C2×#103×C107C22semidirect
46. C2×#103×C107C22semidirect
47. C2×#103×C107C22semidirect
52. C2×#102×C107C22semidirect
55. C2×C22⋊C8×C107C22semidirect
58. #391×C107C22semidirect
59. #390×C107C22semidirect
62. #380×C107C22semidirect
63. #340×C107C22semidirect
64. #340×C107C22semidirect
65. #336×C107C22semidirect
66. #336×C107C22semidirect
79. C2×#41×C107D4semidirect
114. C2×SD16×C107D4semidirect
120. C2×D8×C107D4semidirect
139. #121×C107D4semidirect
365. C23×C107#135semidirect
497. #23850C107direct (N × H)
510. C22×#135C2×C107semidirect
511. C2×#546C2×C107semidirect
512. C2×#449C2×C107semidirect
513. C2×#450C2×C107semidirect
514. C2×#447C2×C107semidirect
515. #2407C2×C107semidirect
516. #2015C2×C107semidirect
517. #2012C2×C107semidirect
518. #2001C2×C107semidirect
519. #2000C2×C107semidirect
520. #1893C2×C107semidirect
521. #1879C2×C107semidirect
522. #1877C2×C107semidirect
523. #1869C2×C107semidirect
524. #1788C2×C107semidirect
525. C107#23850direct (N × H)
527. C22×#41C22×C107semidirect
532. C22×Q16C22×C107semidirect
535. C22×SD16C22×C107semidirect
538. C23×C8C22×C107semidirect
555. C2×#103C22×C107semidirect
556. C2×#103C22×C107semidirect
557. C2×#103C22×C107semidirect
562. C2×#102C22×C107semidirect
565. C2×C22⋊C8C22×C107semidirect
568. #391C22×C107semidirect
569. #390C22×C107semidirect
572. #380C22×C107semidirect
573. #340C22×C107semidirect
574. #340C22×C107semidirect
575. #336C22×C107semidirect
576. #336C22×C107semidirect
589. C2×#41D4×C107semidirect
624. C2×SD16D4×C107semidirect
630. C2×D8D4×C107semidirect
649. #121D4×C107semidirect
875. C23#135×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1072
C2×#546×C1072
C2×#449×C1072
C2×#450×C1072
C2×#447×C1072
C107×#24072
C107×#20152
C107×#20122
C107×#20012
C107×#20002
C107×#18932
C107×#18792
C107×#18772
C107×#18692
C107×#17882
#23850107