Finite Group Databasebeta

← C107×#22874 #41048838

Subgroups — C107×#22874 #41048838

Order 27392.

1314 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C107C211yesmaximal, characteristic
2C2×C4×SD16×C107C211yesmaximal, characteristic, complemented
3C22×#102×C107C211yesmaximal, characteristic
4C107×#2360C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C107C211yesmaximal, characteristic
6C107×#1968C211yesmaximal, characteristic, complemented
7C107×#1934C211yesmaximal, characteristic, complemented
8C107×#1926C211yesmaximal, characteristic, complemented
9C107×#1892C211yesmaximal, characteristic, complemented
10C107×#1880C211yesmaximal, characteristic, complemented
11C107×#1877C211yesmaximal, characteristic, complemented
12C107×#1864C211yesmaximal, characteristic, complemented
13C107×#1853C211yesmaximal, characteristic, complemented
14C4×#102×C107C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C107C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C23×C8×C107C2211yescharacteristic
20C2×C22⋊Q8×C107C2211yescharacteristic
21C2×C4×Q8×C107C2211yescharacteristic, complemented
22C2×C4×D4×C107C2211yescharacteristic
23C2×C4×D4×C107C2211yescharacteristic
24C22×C4⋊C4×C107C2211yescharacteristic
25C22×C22⋊C4×C107—21no—
26#450×C107C418yescomplemented
27C4×SD16×C107—24no—
28C2×#106×C107C2211yescharacteristic, complemented
29C2×#106×C107C2211yescharacteristic, complemented
30C2×#103×C107C2211yescharacteristic, complemented
31C2×#103×C107C2211yescharacteristic, complemented
32C2×#102×C107—24no—
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×C4×C8×C107C2211yescharacteristic, complemented
41C2×C4×C8×C107C2211yescharacteristic, complemented
42#391×C107C2211yescharacteristic, complemented
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#389×C107—21no—
46#389×C107C2211yescharacteristic, complemented
47#387×C107—21no—
48#386×C107—21no—
49#386×C107—21no—
50#385×C107—21no—
51#380×C107C2211yescharacteristic
52#379×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic, complemented
54C4×C22⋊C4×C107—21no—
55C4×C22⋊C4×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic, complemented
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59#340×C107C2211yescharacteristic, complemented
60#336×C107C2211yescharacteristic, complemented
61#336×C107C2211yescharacteristic, complemented
62C25×C107—21no—
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107—22no—
65C22×D4×C107—22no—
66C22×D4×C107—21no—
67C22×D4×C107—22no—
68C22×D4×C107—41no—
69C22×D4×C107—41no—
70C22×D4×C107C2×C414yes—
71C22×D4×C107C2311yescharacteristic
72C22×D4×C107C2311yescharacteristic
73C23×C4×C107—21no—
74C23×C4×C107—21no—
75C23×C4×C107—21no—
76C23×C4×C107C2311yescharacteristic
77C2×SD16×C107—22no—
78C2×SD16×C107—22no—
79C2×SD16×C107—41no—
80C2×SD16×C107—41no—
81C2×SD16×C107C2×C414yescomplemented
82C2×SD16×C107C2×C414yescomplemented
83C22×C8×C107—22no—
84C22×C8×C107—22no—
85C22×C8×C107—41no—
86C22×C8×C107C2311yescharacteristic
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90C22⋊Q8×C107—22no—
91C22⋊Q8×C107C2×C414yescomplemented
92C4×Q8×C107—22no—
93C4×Q8×C107—41no—
94C4×D4×C107—22no—
95C4×D4×C107—22no—
96C4×D4×C107—41no—
97C4×D4×C107—41no—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—22no—
100C2×C4⋊C4×C107—21no—
101C2×C4⋊C4×C107—21no—
102C2×C4⋊C4×C107—21no—
103C2×C4⋊C4×C107—41no—
104C2×C4⋊C4×C107C2311yescharacteristic
105C2×C4⋊C4×C107C2311yescharacteristic
106C2×C4⋊C4×C107C2311yescharacteristic
107C2×C4⋊C4×C107C2311yescharacteristic
108C2×C4⋊C4×C107C2311yescharacteristic
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107—21no—
115C2×C22⋊C4×C107—21no—
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—44no—
118C2×C22⋊C4×C107D411yescharacteristic
119C2×C22⋊C4×C107D411yescharacteristic
120C2×C42×C107—21no—
121C2×C42×C107—21no—
122C2×C42×C107C2311yescharacteristic
123C2×C42×C107C2311yescharacteristic
124#106×C107—22no—
125#106×C107—41no—
126#103×C107—22no—
127#103×C107—41no—
128#102×C107—22no—
129#102×C107—22no—
130#102×C107—22no—
131#102×C107C2×C414yescomplemented
132#102×C107C2×C414yescomplemented
133#102×C107D414yes—
134C22⋊C8×C107C2×C414yescomplemented
135C4×C8×C107—22no—
136C4×C8×C107—41no—
137#95×C107—21no—
138#95×C107—21no—
139#95×C107—21no—
140#95×C107—21no—
141#95×C107—21no—
142#95×C107D411yescharacteristic
143#95×C107D411yescharacteristic
144C24×C107—21no—
145C24×C107—21no—
146C24×C107—24no—
147C24×C107—42no—
148C24×C107—42no—
149C24×C107—42no—
150C24×C107—42no—
151C24×C107—81no—
152C24×C107—81no—
153C24×C107C2×D411yescharacteristic
154C2×Q8×C107—21no—
155C2×Q8×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107C22×C412yes—
160C2×D4×C107—28no—
161C2×D4×C107—24no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—21no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—44no—
171C2×D4×C107—44no—
172C2×D4×C107—44no—
173C2×D4×C107—42no—
174C2×D4×C107—42no—
175C2×D4×C107C22×C412yes—
176C2×D4×C107C22×C412yes—
177C2×D4×C107C2×D412yes—
178C2×D4×C107#4112yes—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—42no—
190C22×C4×C107—42no—
191C22×C4×C107—42no—
192C22×C4×C107—42no—
193C22×C4×C107—42no—
194C22×C4×C107—42no—
195C22×C4×C107—81no—
196C22×C4×C107—81no—
197C22×C4×C107—81no—
198C22×C4×C107C22×C412yes—
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2×D411yescharacteristic
201C22×C4×C107C2×D411yescharacteristic
202C22×C4×C107C2×D411yescharacteristic
203C22×C4×C107C2×D411yescharacteristic
204C22×C4×C107#4112yes—
205C22×C4×C107C2411yescharacteristic
206SD16×C107—28no—
207SD16×C107—44no—
208C2×C8×C107—21no—
209C2×C8×C107—21no—
210C2×C8×C107—21no—
211C2×C8×C107—21no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107—21no—
217C2×C8×C107—44no—
218C2×C8×C107C22×C412yes—
219C2×C8×C107C22×C412yes—
220C2×C8×C107C2×D412yes—
221C4⋊C4×C107—24no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—42no—
231C4⋊C4×C107—42no—
232C4⋊C4×C107—81no—
233C4⋊C4×C107C22×C412yes—
234C4⋊C4×C107C2×D412yes—
235C22⋊C4×C107—24no—
236C22⋊C4×C107—22no—
237C22⋊C4×C107—42no—
238C22⋊C4×C107—42no—
239C22⋊C4×C107—42no—
240C22⋊C4×C107—42no—
241C22⋊C4×C107—42no—
242C22⋊C4×C107—81no—
243C22⋊C4×C107—81no—
244C22⋊C4×C107SD1614yescomplemented
245C42×C107—21no—
246C42×C107—21no—
247C42×C107—21no—
248C42×C107—21no—
249C42×C107—42no—
250C42×C107—81no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—22no—
256C23×C107—22no—
257C23×C107—22no—
258C23×C107—22no—
259C23×C107—48no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—41no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—48no—
271C23×C107—84no—
272C23×C107—84no—
273C23×C107—84no—
274C23×C107—84no—
275C23×C107—84no—
276C23×C107C4×D412yes—
277C23×C107C2×SD1612yes—
278C23×C107#13512yes—
279C23×C107C22×D411yescharacteristic
280Q8×C107—22no—
281Q8×C107—22no—
282Q8×C107—41no—
283Q8×C107—41no—
284D4×C107—22no—
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—22no—
288D4×C107—22no—
289D4×C107—48no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107C4×D414yes—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—22no—
300C2×C4×C107—22no—
301C2×C4×C107—22no—
302C2×C4×C107—22no—
303C2×C4×C107—22no—
304C2×C4×C107—22no—
305C2×C4×C107—21no—
306C2×C4×C107—22no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—84no—
328C2×C4×C107—84no—
329C2×C4×C107—84no—
330C2×C4×C107C4×D412yes—
331C2×C4×C107C2×SD1612yes—
332C2×C4×C107C2×SD1612yes—
333C2×C4×C107C23×C411yescharacteristic
334C2×C4×C107C22×D411yescharacteristic
335C2×C4×C107C2×#4111yescharacteristic
336C2×C4×C107C2×#4111yescharacteristic
337C2×C4×C107H(5,𝔽2)11yescharacteristic
338C2×C4×C107H(5,𝔽2)11yescharacteristic
339C8×C107—22no—
340C8×C107—22no—
341C8×C107—22no—
342C8×C107—41no—
343C22×C107—22no—
344C22×C107—22no—
345C22×C107—22no—
346C22×C107—22no—
347C22×C107—22no—
348C22×C107—22no—
349C22×C107—24no—
350C22×C107—42no—
351C22×C107—42no—
352C22×C107—42no—
353C22×C107—42no—
354C22×C107—42no—
355C22×C107—42no—
356C22×C107—42no—
357C22×C107—42no—
358C22×C107—42no—
359C22×C107—816no—
360C22×C107—81no—
361C22×C107—81no—
362C22×C107—81no—
363C22×C107—81no—
364C22×C107C4×SD1614yescomplemented
365C22×C107C2×C4×D411yescharacteristic
366C22×C107D4211yescharacteristic
367C22×C107#54611yescharacteristic
368C22×C107C22×SD1611yescharacteristic
369C22×C107C2×#13511yescharacteristic
370C22×C107#57611yescharacteristic
371C22×C107#57711yescharacteristic
372C4×C107—22no—
373C4×C107—22no—
374C4×C107—22no—
375C4×C107—42no—
376C4×C107—42no—
377C4×C107—41no—
378C4×C107—42no—
379C4×C107—41no—
380C4×C107—81no—
381C4×C107—81no—
382C4×C107—81no—
383C4×C107C2×C4×D411yescharacteristic
384C4×C107#51811yescharacteristic
385C4×C107#54611yescharacteristic
386C4×C107#55111yescharacteristic
387#22874C10711yesmaximal, characteristic, direct product factor, Sylow
388C2×C107—24no—
389C2×C107—44no—
390C2×C107—82no—
391C2×C107#235811yescharacteristic
392C2×C107C2×C4×SD1611yescharacteristic
393C2×C107#294611yescharacteristic
394C2×C107#328011yescharacteristic
395C2×C107D4×SD1611yescharacteristic
396C2×C107#329511yescharacteristic
397C2×C107#329611yescharacteristic
398C2×#450C2×C10711yescharacteristic
399C2×C4×SD16C2×C10711yescharacteristic, complemented
400C22×#102C2×C10711yescharacteristic
401#2360C2×C10711yescharacteristic, complemented
402D4×C22⋊C4C2×C10711yescharacteristic
403#1968C2×C10711yescharacteristic, complemented
404#1934C2×C10711yescharacteristic, complemented
405#1926C2×C10711yescharacteristic, complemented
406#1892C2×C10711yescharacteristic, complemented
407#1880C2×C10711yescharacteristic, complemented
408#1877C2×C10711yescharacteristic, complemented
409#1864C2×C10711yescharacteristic, complemented
410#1853C2×C10711yescharacteristic, complemented
411C4×#102C2×C10711yescharacteristic, complemented
412C8×C22⋊C4C2×C10711yescharacteristic, complemented
413C107#2287411yescharacteristic, direct product factor, Sylow
414C23×D4C22×C10711yescharacteristic
415C22×SD16C22×C10711yescharacteristic
416C22×SD16C22×C10711yescharacteristic
417C23×C8C22×C10711yescharacteristic
418C2×C22⋊Q8C22×C10711yescharacteristic
419C2×C4×Q8C22×C10711yescharacteristic, complemented
420C2×C4×D4C22×C10711yescharacteristic
421C2×C4×D4C22×C10711yescharacteristic
422C22×C4⋊C4C22×C10711yescharacteristic
423C22×C22⋊C4—21no—
424#450C4×C10718yescomplemented
425C4×SD16—24no—
426C2×#106C22×C10711yescharacteristic, complemented
427C2×#106C22×C10711yescharacteristic, complemented
428C2×#103C22×C10711yescharacteristic, complemented
429C2×#103C22×C10711yescharacteristic, complemented
430C2×#102—24no—
431C2×#102C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×#102C22×C10711yescharacteristic
434C2×#102C22×C10711yescharacteristic
435C2×#102C22×C10711yescharacteristic
436C2×#102C22×C10711yescharacteristic
437C2×C22⋊C8C22×C10711yescharacteristic
438C2×C4×C8C22×C10711yescharacteristic, complemented
439C2×C4×C8C22×C10711yescharacteristic, complemented
440#391C22×C10711yescharacteristic, complemented
441#390C22×C10711yescharacteristic
442#390C22×C10711yescharacteristic
443#389—21no—
444#389C22×C10711yescharacteristic, complemented
445#387—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#380C22×C10711yescharacteristic
450#379—21no—
451C4×C4⋊C4C22×C10711yescharacteristic, complemented
452C4×C22⋊C4—21no—
453C4×C22⋊C4C22×C10711yescharacteristic
454#340C22×C10711yescharacteristic, complemented
455#340C22×C10711yescharacteristic, complemented
456#340C22×C10711yescharacteristic, complemented
457#340C22×C10711yescharacteristic, complemented
458#336C22×C10711yescharacteristic, complemented
459#336C22×C10711yescharacteristic, complemented
460C25—21no—
461C22×Q8C23×C10711yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×C4×C10714yes—
469C22×D4C23×C10711yescharacteristic
470C22×D4C23×C10711yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4C23×C10711yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×C4×C10714yescomplemented
480C2×SD16C2×C4×C10714yescomplemented
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C23×C10711yescharacteristic
485C22×C8C23×C10711yescharacteristic
486C22×C8C23×C10711yescharacteristic
487C22×C8C23×C10711yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×C4×C10714yescomplemented
490C4×Q8—22no—
491C4×Q8—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C10711yescharacteristic
503C2×C4⋊C4C23×C10711yescharacteristic
504C2×C4⋊C4C23×C10711yescharacteristic
505C2×C4⋊C4C23×C10711yescharacteristic
506C2×C4⋊C4C23×C10711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4D4×C10711yescharacteristic
517C2×C22⋊C4D4×C10711yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C10711yescharacteristic
521C2×C42C23×C10711yescharacteristic
522#106—22no—
523#106—41no—
524#103—22no—
525#103—41no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102C2×C4×C10714yescomplemented
530#102C2×C4×C10714yescomplemented
531#102D4×C10714yes—
532C22⋊C8C2×C4×C10714yescomplemented
533C4×C8—22no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95D4×C10711yescharacteristic
541#95D4×C10711yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×D4×C10711yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×C4×C10712yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C22×C4×C10712yes—
574C2×D4C22×C4×C10712yes—
575C2×D4C2×D4×C10712yes—
576C2×D4#41×C10712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C10712yes—
597C22×C4C2×D4×C10711yescharacteristic
598C22×C4C2×D4×C10711yescharacteristic
599C22×C4C2×D4×C10711yescharacteristic
600C22×C4C2×D4×C10711yescharacteristic
601C22×C4C2×D4×C10711yescharacteristic
602C22×C4#41×C10712yes—
603C22×C4C24×C10711yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C22×C4×C10712yes—
617C2×C8C22×C4×C10712yes—
618C2×C8C2×D4×C10712yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C22×C4×C10712yes—
632C4⋊C4C2×D4×C10712yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4SD16×C10714yescomplemented
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×D4×C10712yes—
675C23C2×SD16×C10712yes—
676C23#135×C10712yes—
677C23C22×D4×C10711yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×D4×C10714yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4C4×D4×C10712yes—
729C2×C4C2×SD16×C10712yes—
730C2×C4C2×SD16×C10712yes—
731C2×C4C23×C4×C10711yescharacteristic
732C2×C4C22×D4×C10711yescharacteristic
733C2×C4C2×#41×C10711yescharacteristic
734C2×C4C2×#41×C10711yescharacteristic
735C2×C4H(5,𝔽2)×C10711yescharacteristic
736C2×C4H(5,𝔽2)×C10711yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C4×SD16×C10714yescomplemented
763C22C2×C4×D4×C10711yescharacteristic
764C22D42×C10711yescharacteristic
765C22#546×C10711yescharacteristic
766C22C22×SD16×C10711yescharacteristic
767C22C2×#135×C10711yescharacteristic
768C22#576×C10711yescharacteristic
769C22#577×C10711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C2×C4×D4×C10711yescharacteristic
782C4#518×C10711yescharacteristic
783C4#546×C10711yescharacteristic
784C4#551×C10711yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2C107×#235811yescharacteristic
789C2C2×C4×SD16×C10711yescharacteristic
790C2C107×#294611yescharacteristic
791C2C107×#328011yescharacteristic
792C2D4×SD16×C10711yescharacteristic
793C2C107×#329511yescharacteristic
794C2C107×#329611yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC23×D4×C107C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C107C2semidirect
4. C107×#2360C2semidirect
6. C107×#1968C2semidirect
7. C107×#1934C2semidirect
8. C107×#1926C2semidirect
9. C107×#1892C2semidirect
10. C107×#1880C2semidirect
11. C107×#1877C2semidirect
12. C107×#1864C2semidirect
13. C107×#1853C2semidirect
14. C4×#102×C107C2semidirect
15. C8×C22⋊C4×C107C2semidirect
21. C2×C4×Q8×C107C22semidirect
26. #450×C107C4semidirect
28. C2×#106×C107C22semidirect
29. C2×#106×C107C22semidirect
30. C2×#103×C107C22semidirect
31. C2×#103×C107C22semidirect
40. C2×C4×C8×C107C22semidirect
41. C2×C4×C8×C107C22semidirect
42. #391×C107C22semidirect
46. #389×C107C22semidirect
53. C4×C4⋊C4×C107C22semidirect
56. #340×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #340×C107C22semidirect
60. #336×C107C22semidirect
61. #336×C107C22semidirect
81. C2×SD16×C107C2×C4semidirect
82. C2×SD16×C107C2×C4semidirect
91. C22⋊Q8×C107C2×C4semidirect
131. #102×C107C2×C4semidirect
132. #102×C107C2×C4semidirect
134. C22⋊C8×C107C2×C4semidirect
244. C22⋊C4×C107SD16semidirect
364. C22×C107C4×SD16semidirect
387. #22874C107direct (N × H)
399. C2×C4×SD16C2×C107semidirect
401. #2360C2×C107semidirect
403. #1968C2×C107semidirect
404. #1934C2×C107semidirect
405. #1926C2×C107semidirect
406. #1892C2×C107semidirect
407. #1880C2×C107semidirect
408. #1877C2×C107semidirect
409. #1864C2×C107semidirect
410. #1853C2×C107semidirect
411. C4×#102C2×C107semidirect
412. C8×C22⋊C4C2×C107semidirect
413. C107#22874direct (N × H)
419. C2×C4×Q8C22×C107semidirect
424. #450C4×C107semidirect
426. C2×#106C22×C107semidirect
427. C2×#106C22×C107semidirect
428. C2×#103C22×C107semidirect
429. C2×#103C22×C107semidirect
438. C2×C4×C8C22×C107semidirect
439. C2×C4×C8C22×C107semidirect
440. #391C22×C107semidirect
444. #389C22×C107semidirect
451. C4×C4⋊C4C22×C107semidirect
454. #340C22×C107semidirect
455. #340C22×C107semidirect
456. #340C22×C107semidirect
457. #340C22×C107semidirect
458. #336C22×C107semidirect
459. #336C22×C107semidirect
479. C2×SD16C2×C4×C107semidirect
480. C2×SD16C2×C4×C107semidirect
489. C22⋊Q8C2×C4×C107semidirect
529. #102C2×C4×C107semidirect
530. #102C2×C4×C107semidirect
532. C22⋊C8C2×C4×C107semidirect
642. C22⋊C4SD16×C107semidirect
762. C22C4×SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1072
C2×C4×SD16×C1072
C22×#102×C1072
C107×#23602
D4×C22⋊C4×C1072
C107×#19682
C107×#19342
C107×#19262
C107×#18922
C107×#18802
C107×#18772
C107×#18642
C107×#18532
C4×#102×C1072
C8×C22⋊C4×C1072
#22874107