Finite Group Databasebeta

← C107×#25128 #41051092

Subgroups — C107×#25128 #41051092

Order 27392.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C107C211yesmaximal, characteristic, complemented
2C2×#450×C107C211yesmaximal, characteristic, complemented
3C2×#435×C107C211yesmaximal, characteristic, complemented
4C22×#102×C107C211yesmaximal, characteristic, complemented
5C107×#2417C211yesmaximal, characteristic, complemented
6C107×#2408C211yesmaximal, characteristic
7C107×#2067C211yesmaximal, characteristic, complemented
8C107×#2055C211yesmaximal, characteristic, complemented
9C107×#2033C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1973C211yesmaximal, characteristic, complemented
12C107×#1936C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1892C211yesmaximal, characteristic, complemented
15C107×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic, complemented
20C23×C8×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic, complemented
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#120×C107—21no—
26C2×C4×D4×C107C2211yescharacteristic
27C22×C4⋊C4×C107C2211yescharacteristic
28#468×C107—24no—
29#450×C107—24no—
30#435×C107—24no—
31C2×#107×C107C2211yescharacteristic, complemented
32C2×#107×C107C2211yescharacteristic, complemented
33C2×C4⋊C8×C107C2211yescharacteristic, complemented
34C2×#103×C107C2211yescharacteristic, complemented
35C2×#103×C107C2211yescharacteristic, complemented
36C2×#102×C107—24no—
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×C22⋊C8×C107C2211yescharacteristic
44C2×C22⋊C8×C107C2211yescharacteristic, complemented
45C2×#97×C107C2211yescharacteristic, complemented
46#398×C107—21no—
47#396×C107—21no—
48#394×C107—21no—
49#392×C107—21no—
50#391×C107C2211yescharacteristic, complemented
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#389×C107C2211yescharacteristic, complemented
54#386×C107—21no—
55#380×C107—21no—
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic, complemented
58#379×C107—21no—
59#340×C107C2211yescharacteristic, complemented
60#340×C107C2211yescharacteristic, complemented
61#340×C107C2211yescharacteristic, complemented
62#340×C107C2211yescharacteristic, complemented
63C25×C107—21no—
64C22×Q8×C107C2311yescharacteristic
65C22×D4×C107—22no—
66C22×D4×C107—22no—
67C22×D4×C107—21no—
68C22×D4×C107—21no—
69C22×D4×C107—22no—
70C22×D4×C107—21no—
71C22×D4×C107—22no—
72C22×D4×C107—41no—
73C22×D4×C107—41no—
74C22×D4×C107D411yescharacteristic
75C22×D4×C107C2311yescharacteristic
76C22×D4×C107C2311yescharacteristic
77C23×C4×C107—21no—
78C23×C4×C107C2311yescharacteristic
79C23×C4×C107C2311yescharacteristic
80C2×SD16×C107—22no—
81C2×SD16×C107—22no—
82C2×SD16×C107—22no—
83C2×SD16×C107—22no—
84C2×SD16×C107—41no—
85C2×SD16×C107—41no—
86C2×M16×C107—22no—
87C2×M16×C107—22no—
88C2×M16×C107—41no—
89C22×C8×C107—22no—
90C22×C8×C107—22no—
91C22×C8×C107—41no—
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—22no—
98C22⋊Q8×C107—22no—
99C22⋊Q8×C107—41no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107—41no—
103#121×C107—41no—
104#120×C107—44no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C2×C4⋊C4×C107—22no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107—41no—
113C2×C4⋊C4×C107D411yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107D411yescharacteristic
130C2×C22⋊C4×C107D411yescharacteristic
131C2×C42×C107C2311yescharacteristic
132#107×C107—22no—
133#107×C107—41no—
134C4⋊C8×C107—22no—
135#103×C107—22no—
136#103×C107—41no—
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107D414yescomplemented
143C22⋊C8×C107—22no—
144C22⋊C8×C107D414yescomplemented
145#97×C107—22no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107—21no—
150#95×C107—21no—
151C24×C107—21no—
152C24×C107—21no—
153C24×C107—42no—
154C24×C107—42no—
155C24×C107—42no—
156C24×C107—42no—
157C24×C107—42no—
158C24×C107—81no—
159C24×C107—81no—
160C24×C107C2×D411yescharacteristic
161C24×C107C2×D411yescharacteristic
162C2×Q8×C107—21no—
163C2×Q8×C107—21no—
164C2×Q8×C107—21no—
165C2×Q8×C107—21no—
166C2×Q8×C107—21no—
167C2×Q8×C107—21no—
168C2×D4×C107—28no—
169C2×D4×C107—22no—
170C2×D4×C107—22no—
171C2×D4×C107—22no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—21no—
177C2×D4×C107—21no—
178C2×D4×C107—21no—
179C2×D4×C107—21no—
180C2×D4×C107—21no—
181C2×D4×C107—21no—
182C2×D4×C107—44no—
183C2×D4×C107—44no—
184C2×D4×C107—42no—
185C2×D4×C107—42no—
186C2×D4×C107—44no—
187C2×D4×C107—42no—
188C2×D4×C107—42no—
189C2×D4×C107—42no—
190C2×D4×C107—42no—
191C2×D4×C107—42no—
192C2×D4×C107—81no—
193C2×D4×C107—81no—
194C2×D4×C107C2×D412yes—
195C2×D4×C107#4112yes—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—42no—
213C22×C4×C107—42no—
214C22×C4×C107—81no—
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107C2×D412yes—
220C22×C4×C107#4112yes—
221C22×C4×C107C2411yescharacteristic
222SD16×C107—44no—
223SD16×C107—44no—
224M16×C107—44no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—21no—
231C2×C8×C107—21no—
232C2×C8×C107—21no—
233C2×C8×C107—21no—
234C2×C8×C107—44no—
235C2×C8×C107C2×D412yes—
236C2×C8×C107C2×D412yes—
237C2×C8×C107C2×D412yes—
238C4⋊C4×C107—22no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—21no—
243C4⋊C4×C107—21no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107—21no—
246C4⋊C4×C107—21no—
247C4⋊C4×C107—21no—
248C4⋊C4×C107—42no—
249C4⋊C4×C107—42no—
250C4⋊C4×C107—42no—
251C4⋊C4×C107—81no—
252C4⋊C4×C107C2×D412yes—
253C22⋊C4×C107—22no—
254C22⋊C4×C107—22no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—42no—
257C22⋊C4×C107—42no—
258C22⋊C4×C107—42no—
259C22⋊C4×C107—42no—
260C22⋊C4×C107—42no—
261C22⋊C4×C107—42no—
262C22⋊C4×C107—81no—
263C22⋊C4×C107—81no—
264C22⋊C4×C107—81no—
265C42×C107—21no—
266C42×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—21no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—22no—
274C23×C107—22no—
275C23×C107—21no—
276C23×C107—21no—
277C23×C107—21no—
278C23×C107—21no—
279C23×C107—21no—
280C23×C107—48no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—41no—
289C23×C107—41no—
290C23×C107—41no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—84no—
294C23×C107—84no—
295C23×C107—84no—
296C23×C107—84no—
297C23×C107—84no—
298C23×C107—84no—
299C23×C107#12112yes—
300C23×C107AGL(1,ℤ/8)12yes—
301C23×C107#13712yes—
302C23×C107C22×D411yescharacteristic
303Q8×C107—41no—
304Q8×C107—41no—
305Q8×C107—41no—
306Q8×C107—41no—
307D4×C107—22no—
308D4×C107—22no—
309D4×C107—22no—
310D4×C107—22no—
311D4×C107—48no—
312D4×C107—44no—
313D4×C107—41no—
314D4×C107—41no—
315D4×C107—41no—
316D4×C107—41no—
317D4×C107—84no—
318D4×C107—84no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—22no—
322C2×C4×C107—22no—
323C2×C4×C107—22no—
324C2×C4×C107—22no—
325C2×C4×C107—21no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—22no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—21no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107—41no—
347C2×C4×C107—41no—
348C2×C4×C107—41no—
349C2×C4×C107—41no—
350C2×C4×C107—41no—
351C2×C4×C107—41no—
352C2×C4×C107—41no—
353C2×C4×C107—41no—
354C2×C4×C107—41no—
355C2×C4×C107—41no—
356C2×C4×C107—84no—
357C2×C4×C107#12112yes—
358C2×C4×C107C22×D411yescharacteristic
359C2×C4×C107C22×D411yescharacteristic
360C2×C4×C107C2×#4111yescharacteristic
361C2×C4×C107C2×#4111yescharacteristic
362C2×C4×C107H(5,𝔽2)11yescharacteristic
363C2×C4×C107H(5,𝔽2)11yescharacteristic
364C8×C107—22no—
365C8×C107—22no—
366C8×C107—22no—
367C8×C107—41no—
368C22×C107—22no—
369C22×C107—22no—
370C22×C107—22no—
371C22×C107—22no—
372C22×C107—22no—
373C22×C107—22no—
374C22×C107—41no—
375C22×C107—42no—
376C22×C107—42no—
377C22×C107—41no—
378C22×C107—42no—
379C22×C107—41no—
380C22×C107—42no—
381C22×C107—41no—
382C22×C107—41no—
383C22×C107—42no—
384C22×C107—41no—
385C22×C107—42no—
386C22×C107—41no—
387C22×C107—816no—
388C22×C107—81no—
389C22×C107—81no—
390C22×C107—81no—
391C22×C107—81no—
392C22×C107—81no—
393C22×C107—81no—
394C22×C107—81no—
395C22×C107—81no—
396C22×C107#46814yescomplemented
397C22×C107C2×#12111yescharacteristic
398C22×C107D4211yescharacteristic
399C22×C107#54611yescharacteristic
400C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C107C2×#13711yescharacteristic
402C22×C107#57611yescharacteristic
403C22×C107#57711yescharacteristic
404C4×C107—22no—
405C4×C107—41no—
406C4×C107—42no—
407C4×C107—41no—
408C4×C107—41no—
409C4×C107—81no—
410C4×C107—81no—
411C4×C107—81no—
412C4×C107—81no—
413C4×C107—81no—
414C4×C107#52511yescharacteristic
415C4×C107#53811yescharacteristic
416C4×C107D4211yescharacteristic
417C4×C107#54611yescharacteristic
418#25128C10711yesmaximal, characteristic, direct product factor, Sylow
419C2×C107—24no—
420C2×C107—81no—
421C2×C107—82no—
422C2×C107—82no—
423C2×C107#242411yescharacteristic
424C2×C107C2×#46811yescharacteristic
425C2×C107#306211yescharacteristic
426C2×C107#326411yescharacteristic
427C2×C107#326611yescharacteristic
428C2×C107#331011yescharacteristic
429C2×C107#331411yescharacteristic
430C2×#468C2×C10711yescharacteristic, complemented
431C2×#450C2×C10711yescharacteristic, complemented
432C2×#435C2×C10711yescharacteristic, complemented
433C22×#102C2×C10711yescharacteristic, complemented
434#2417C2×C10711yescharacteristic, complemented
435#2408C2×C10711yescharacteristic
436#2067C2×C10711yescharacteristic, complemented
437#2055C2×C10711yescharacteristic, complemented
438#2033C2×C10711yescharacteristic, complemented
439#2000C2×C10711yescharacteristic, complemented
440#1973C2×C10711yescharacteristic, complemented
441#1936C2×C10711yescharacteristic, complemented
442#1895C2×C10711yescharacteristic, complemented
443#1892C2×C10711yescharacteristic, complemented
444#1852C2×C10711yescharacteristic, complemented
445C107#2512811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C10711yescharacteristic
447C22×SD16C22×C10711yescharacteristic
448C22×SD16C22×C10711yescharacteristic
449C22×M16C22×C10711yescharacteristic, complemented
450C23×C8C22×C10711yescharacteristic
451C2×C22⋊Q8C22×C10711yescharacteristic
452C2×C22⋊Q8C22×C10711yescharacteristic, complemented
453C2×#121C22×C10711yescharacteristic
454C2×#121C22×C10711yescharacteristic
455C2×#120—21no—
456C2×C4×D4C22×C10711yescharacteristic
457C22×C4⋊C4C22×C10711yescharacteristic
458#468—24no—
459#450—24no—
460#435—24no—
461C2×#107C22×C10711yescharacteristic, complemented
462C2×#107C22×C10711yescharacteristic, complemented
463C2×C4⋊C8C22×C10711yescharacteristic, complemented
464C2×#103C22×C10711yescharacteristic, complemented
465C2×#103C22×C10711yescharacteristic, complemented
466C2×#102—24no—
467C2×#102C22×C10711yescharacteristic
468C2×#102C22×C10711yescharacteristic
469C2×#102C22×C10711yescharacteristic
470C2×#102C22×C10711yescharacteristic
471C2×#102C22×C10711yescharacteristic
472C2×#102C22×C10711yescharacteristic
473C2×C22⋊C8C22×C10711yescharacteristic
474C2×C22⋊C8C22×C10711yescharacteristic, complemented
475C2×#97C22×C10711yescharacteristic, complemented
476#398—21no—
477#396—21no—
478#394—21no—
479#392—21no—
480#391C22×C10711yescharacteristic, complemented
481#390C22×C10711yescharacteristic
482#390C22×C10711yescharacteristic
483#389C22×C10711yescharacteristic, complemented
484#386—21no—
485#380—21no—
486#380C22×C10711yescharacteristic
487#380C22×C10711yescharacteristic, complemented
488#379—21no—
489#340C22×C10711yescharacteristic, complemented
490#340C22×C10711yescharacteristic, complemented
491#340C22×C10711yescharacteristic, complemented
492#340C22×C10711yescharacteristic, complemented
493C25—21no—
494C22×Q8C23×C10711yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C10711yescharacteristic
505C22×D4C23×C10711yescharacteristic
506C22×D4C23×C10711yescharacteristic
507C23×C4—21no—
508C23×C4C23×C10711yescharacteristic
509C23×C4C23×C10711yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C10711yescharacteristic
523C22×C8C23×C10711yescharacteristic
524C22×C8C23×C10711yescharacteristic
525C22×C8C23×C10711yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C10711yescharacteristic
544C2×C4⋊C4C23×C10711yescharacteristic
545C2×C4⋊C4C23×C10711yescharacteristic
546C2×C4⋊C4C23×C10711yescharacteristic
547C2×C4⋊C4C23×C10711yescharacteristic
548C2×C4⋊C4C23×C10711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C10711yescharacteristic
560C2×C22⋊C4D4×C10711yescharacteristic
561C2×C42C23×C10711yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C10714yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C10714yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C10711yescharacteristic
591C24C2×D4×C10711yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C10712yes—
625C2×D4#41×C10712yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C10711yescharacteristic
646C22×C4C2×D4×C10711yescharacteristic
647C22×C4C2×D4×C10711yescharacteristic
648C22×C4C2×D4×C10711yescharacteristic
649C22×C4C2×D4×C10712yes—
650C22×C4#41×C10712yes—
651C22×C4C24×C10711yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C10712yes—
666C2×C8C2×D4×C10712yes—
667C2×C8C2×D4×C10712yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C10712yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C10712yes—
730C23AGL(1,ℤ/8)×C10712yes—
731C23#137×C10712yes—
732C23C22×D4×C10711yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4#121×C10712yes—
788C2×C4C22×D4×C10711yescharacteristic
789C2×C4C22×D4×C10711yescharacteristic
790C2×C4C2×#41×C10711yescharacteristic
791C2×C4C2×#41×C10711yescharacteristic
792C2×C4H(5,𝔽2)×C10711yescharacteristic
793C2×C4H(5,𝔽2)×C10711yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#468×C10714yescomplemented
827C22C2×#121×C10711yescharacteristic
828C22D42×C10711yescharacteristic
829C22#546×C10711yescharacteristic
830C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
831C22C2×#137×C10711yescharacteristic
832C22#576×C10711yescharacteristic
833C22#577×C10711yescharacteristic
834C4—22no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4#525×C10711yescharacteristic
845C4#538×C10711yescharacteristic
846C4D42×C10711yescharacteristic
847C4#546×C10711yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C107×#242411yescharacteristic
853C2C2×#468×C10711yescharacteristic
854C2C107×#306211yescharacteristic
855C2C107×#326411yescharacteristic
856C2C107×#326611yescharacteristic
857C2C107×#331011yescharacteristic
858C2C107×#331411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#2408C2
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×#468×C107C2semidirect
2. C2×#450×C107C2semidirect
3. C2×#435×C107C2semidirect
4. C22×#102×C107C2semidirect
5. C107×#2417C2semidirect
7. C107×#2067C2semidirect
8. C107×#2055C2semidirect
9. C107×#2033C2semidirect
10. C107×#2000C2semidirect
11. C107×#1973C2semidirect
12. C107×#1936C2semidirect
13. C107×#1895C2semidirect
14. C107×#1892C2semidirect
15. C107×#1852C2semidirect
19. C22×M16×C107C22semidirect
22. C2×C22⋊Q8×C107C22semidirect
31. C2×#107×C107C22semidirect
32. C2×#107×C107C22semidirect
33. C2×C4⋊C8×C107C22semidirect
34. C2×#103×C107C22semidirect
35. C2×#103×C107C22semidirect
44. C2×C22⋊C8×C107C22semidirect
45. C2×#97×C107C22semidirect
50. #391×C107C22semidirect
53. #389×C107C22semidirect
57. #380×C107C22semidirect
59. #340×C107C22semidirect
60. #340×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
142. #102×C107D4semidirect
144. C22⋊C8×C107D4semidirect
396. C22×C107#468semidirect
418. #25128C107direct (N × H)
430. C2×#468C2×C107semidirect
431. C2×#450C2×C107semidirect
432. C2×#435C2×C107semidirect
433. C22×#102C2×C107semidirect
434. #2417C2×C107semidirect
436. #2067C2×C107semidirect
437. #2055C2×C107semidirect
438. #2033C2×C107semidirect
439. #2000C2×C107semidirect
440. #1973C2×C107semidirect
441. #1936C2×C107semidirect
442. #1895C2×C107semidirect
443. #1892C2×C107semidirect
444. #1852C2×C107semidirect
445. C107#25128direct (N × H)
449. C22×M16C22×C107semidirect
452. C2×C22⋊Q8C22×C107semidirect
461. C2×#107C22×C107semidirect
462. C2×#107C22×C107semidirect
463. C2×C4⋊C8C22×C107semidirect
464. C2×#103C22×C107semidirect
465. C2×#103C22×C107semidirect
474. C2×C22⋊C8C22×C107semidirect
475. C2×#97C22×C107semidirect
480. #391C22×C107semidirect
483. #389C22×C107semidirect
487. #380C22×C107semidirect
489. #340C22×C107semidirect
490. #340C22×C107semidirect
491. #340C22×C107semidirect
492. #340C22×C107semidirect
572. #102D4×C107semidirect
574. C22⋊C8D4×C107semidirect
826. C22#468×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1072
C2×#450×C1072
C2×#435×C1072
C22×#102×C1072
C107×#24172
C107×#24082
C107×#20672
C107×#20552
C107×#20332
C107×#20002
C107×#19732
C107×#19362
C107×#18952
C107×#18922
C107×#18522
#25128107