Finite Group Databasebeta

← C107×#25397 #41051361

Subgroups — C107×#25397 #41051361

Order 27392.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C107C211yesmaximal, characteristic, complemented
2C2×#466×C107C211yesmaximal, characteristic, complemented
3C2×#463×C107C211yesmaximal, characteristic, complemented
4C2×#435×C107C211yesmaximal, characteristic, complemented
5C107×#2540C211yesmaximal, characteristic, complemented
6C107×#2537C211yesmaximal, characteristic, complemented
7C107×#2036C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1959C211yesmaximal, characteristic, complemented
12C107×#1947C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1892C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×M16×C107C2211yescharacteristic
19C23×C8×C107C2211yescharacteristic
20C2×#124×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic
23C2×#121×C107—21no—
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×#121×C107C2211yescharacteristic
28C2×C4×D4×C107C2211yescharacteristic
29C2×C4×D4×C107C2211yescharacteristic
30#468×C107—24no—
31#466×C107—24no—
32#463×C107—24no—
33#435×C107—24no—
34C2×#107×C107C2211yescharacteristic
35C2×#107×C107C2211yescharacteristic
36C2×C4⋊C8×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#103×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C22⋊C8×C107C2211yescharacteristic
47C2×#97×C107C2211yescharacteristic
48#399×C107—21no—
49#394×C107—21no—
50#394×C107—21no—
51#392×C107—21no—
52#390×C107—21no—
53#390×C107—21no—
54#384×C107C2211yescharacteristic
55#380×C107—21no—
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic
58C4×C4⋊C4×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—21no—
68C22×D4×C107D411yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C23×C4×C107—21no—
72C23×C4×C107C2311yescharacteristic
73C23×C4×C107C2311yescharacteristic
74C2×SD16×C107—22no—
75C2×SD16×C107—22no—
76C2×SD16×C107—41no—
77C2×D8×C107—22no—
78C2×D8×C107—22no—
79C2×D8×C107—41no—
80C2×M16×C107—22no—
81C2×M16×C107—22no—
82C2×M16×C107—41no—
83C22×C8×C107—22no—
84C22×C8×C107—22no—
85C22×C8×C107—41no—
86C22×C8×C107C2311yescharacteristic
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90#124×C107—22no—
91#124×C107—22no—
92C22⋊Q8×C107—22no—
93C22⋊Q8×C107—22no—
94C22⋊Q8×C107—41no—
95C22⋊Q8×C107—41no—
96#121×C107—22no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—41no—
101#121×C107—41no—
102#121×C107—41no—
103#121×C107—41no—
104#121×C107—44no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108C4×D4×C107—22no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107—21no—
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×C107—21no—
130C2×C22⋊C4×C107D411yescharacteristic
131C2×C22⋊C4×C107D411yescharacteristic
132C2×C42×C107—21no—
133C2×C42×C107C2311yescharacteristic
134#107×C107—22no—
135#107×C107—22no—
136C4⋊C8×C107D414yescomplemented
137#103×C107—22no—
138#103×C107—22no—
139#103×C107—41no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—22no—
143#102×C107—41no—
144#102×C107D414yescomplemented
145C22⋊C8×C107—22no—
146C22⋊C8×C107—22no—
147#97×C107—22no—
148#95×C107—21no—
149#95×C107—21no—
150#95×C107—21no—
151C24×C107—21no—
152C24×C107—21no—
153C24×C107C2×D411yescharacteristic
154C24×C107C2×D411yescharacteristic
155C2×Q8×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×D4×C107—22no—
162C2×D4×C107—22no—
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—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—41no—
175C2×D4×C107—42no—
176C2×D4×C107—42no—
177C2×D4×C107—42no—
178C2×D4×C107—42no—
179C2×D4×C107—42no—
180C2×D4×C107—42no—
181C2×D4×C107—42no—
182C2×D4×C107—42no—
183C2×D4×C107—81no—
184C2×D4×C107—81no—
185C2×D4×C107—81no—
186C2×D4×C107—81no—
187C2×D4×C107C2×D412yes—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
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—42no—
207C22×C4×C107—42no—
208C22×C4×C107—42no—
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2411yescharacteristic
214SD16×C107—44no—
215D8×C107—44no—
216M16×C107—44no—
217C2×C8×C107—21no—
218C2×C8×C107—21no—
219C2×C8×C107—21no—
220C2×C8×C107—21no—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—44no—
227C2×C8×C107C2×D412yes—
228C2×C8×C107C2×D412yes—
229C2×C8×C107C2×D412yes—
230C4⋊C4×C107—22no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—42no—
240C4⋊C4×C107—42no—
241C4⋊C4×C107—42no—
242C4⋊C4×C107—81no—
243C4⋊C4×C107C2×D412yes—
244C4⋊C4×C107#4112yes—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—22no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—42no—
255C22⋊C4×C107—42no—
256C22⋊C4×C107—42no—
257C22⋊C4×C107—42no—
258C42×C107—81no—
259C42×C107C2×D412yes—
260C42×C107#4112yes—
261C23×C107—21no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—22no—
270C23×C107—21no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—21no—
274C23×C107—21no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107AGL(1,ℤ/8)12yes—
289C23×C107C22×D411yescharacteristic
290Q8×C107—41no—
291Q8×C107—41no—
292Q8×C107—41no—
293Q8×C107—41no—
294D4×C107—22no—
295D4×C107—22no—
296D4×C107—44no—
297D4×C107—41no—
298D4×C107—41no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—84no—
304D4×C107—84no—
305D4×C107—84no—
306D4×C107—84no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—22no—
315C2×C4×C107—21no—
316C2×C4×C107—22no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
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—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
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—84no—
344C2×C4×C107#12112yes—
345C2×C4×C107#12112yes—
346C2×C4×C107C22×D411yescharacteristic
347C2×C4×C107C22×D411yescharacteristic
348C2×C4×C107C2×#4111yescharacteristic
349C2×C4×C107C2×#4111yescharacteristic
350C2×C4×C107H(5,𝔽2)11yescharacteristic
351C2×C4×C107H(5,𝔽2)11yescharacteristic
352C8×C107—22no—
353C8×C107—22no—
354C8×C107—22no—
355C8×C107—41no—
356C22×C107—22no—
357C22×C107—22no—
358C22×C107—22no—
359C22×C107—41no—
360C22×C107—41no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—41no—
364C22×C107—42no—
365C22×C107—41no—
366C22×C107—42no—
367C22×C107—41no—
368C22×C107—42no—
369C22×C107—41no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107C2×#12111yescharacteristic
385C22×C107D4211yescharacteristic
386C22×C107#54611yescharacteristic
387C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C107#57511yescharacteristic
389C22×C107#57611yescharacteristic
390C22×C107#57811yescharacteristic
391C4×C107—22no—
392C4×C107—22no—
393C4×C107—41no—
394C4×C107—41no—
395C4×C107—42no—
396C4×C107—42no—
397C4×C107—81no—
398C4×C107—81no—
399C4×C107—81no—
400C4×C107—81no—
401C4×C107#53211yescharacteristic
402C4×C107#54011yescharacteristic
403C4×C107D4211yescharacteristic
404C4×C107#55011yescharacteristic
405#25397C10711yesmaximal, characteristic, direct product factor, Sylow
406C2×C107—42no—
407C2×C107—81no—
408C2×C107—82no—
409C2×C107—161no—
410C2×C107#242811yescharacteristic
411C2×C107#305511yescharacteristic
412C2×C107#306111yescharacteristic
413C2×C107#326411yescharacteristic
414C2×C107#326911yescharacteristic
415C2×C107#330811yescharacteristic
416C2×C107#331911yescharacteristic
417C2×#468C2×C10711yescharacteristic, complemented
418C2×#466C2×C10711yescharacteristic, complemented
419C2×#463C2×C10711yescharacteristic, complemented
420C2×#435C2×C10711yescharacteristic, complemented
421#2540C2×C10711yescharacteristic, complemented
422#2537C2×C10711yescharacteristic, complemented
423#2036C2×C10711yescharacteristic, complemented
424#2033C2×C10711yescharacteristic, complemented
425#2000C2×C10711yescharacteristic, complemented
426#1999C2×C10711yescharacteristic, complemented
427#1959C2×C10711yescharacteristic, complemented
428#1947C2×C10711yescharacteristic, complemented
429#1895C2×C10711yescharacteristic, complemented
430#1892C2×C10711yescharacteristic, complemented
431#1762C2×C10711yescharacteristic, complemented
432C107#2539711yescharacteristic, direct product factor, Sylow
433C22×SD16C22×C10711yescharacteristic
434C22×D8C22×C10711yescharacteristic
435C22×M16C22×C10711yescharacteristic
436C23×C8C22×C10711yescharacteristic
437C2×#124C22×C10711yescharacteristic
438C2×C22⋊Q8C22×C10711yescharacteristic
439C2×C22⋊Q8C22×C10711yescharacteristic
440C2×#121—21no—
441C2×#121C22×C10711yescharacteristic
442C2×#121C22×C10711yescharacteristic
443C2×#121C22×C10711yescharacteristic
444C2×#121C22×C10711yescharacteristic
445C2×C4×D4C22×C10711yescharacteristic
446C2×C4×D4C22×C10711yescharacteristic
447#468—24no—
448#466—24no—
449#463—24no—
450#435—24no—
451C2×#107C22×C10711yescharacteristic
452C2×#107C22×C10711yescharacteristic
453C2×C4⋊C8C22×C10711yescharacteristic
454C2×#103C22×C10711yescharacteristic
455C2×#103C22×C10711yescharacteristic
456C2×#103C22×C10711yescharacteristic
457C2×#102C22×C10711yescharacteristic
458C2×#102C22×C10711yescharacteristic
459C2×#102C22×C10711yescharacteristic
460C2×#102C22×C10711yescharacteristic
461C2×#102C22×C10711yescharacteristic
462C2×C22⋊C8C22×C10711yescharacteristic
463C2×C22⋊C8C22×C10711yescharacteristic
464C2×#97C22×C10711yescharacteristic
465#399—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#390—21no—
470#390—21no—
471#384C22×C10711yescharacteristic
472#380—21no—
473#380C22×C10711yescharacteristic
474#380C22×C10711yescharacteristic
475C4×C4⋊C4C22×C10711yescharacteristic
476#340C22×C10711yescharacteristic
477#340C22×C10711yescharacteristic
478#340C22×C10711yescharacteristic
479#340C22×C10711yescharacteristic
480C22×Q8C23×C10711yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C10711yescharacteristic
486C22×D4C23×C10711yescharacteristic
487C22×D4C23×C10711yescharacteristic
488C23×C4—21no—
489C23×C4C23×C10711yescharacteristic
490C23×C4C23×C10711yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C10711yescharacteristic
504C22×C8C23×C10711yescharacteristic
505C22×C8C23×C10711yescharacteristic
506C22×C8C23×C10711yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C10711yescharacteristic
531C2×C4⋊C4C23×C10711yescharacteristic
532C2×C4⋊C4C23×C10711yescharacteristic
533C2×C4⋊C4C23×C10711yescharacteristic
534C2×C4⋊C4C23×C10711yescharacteristic
535C2×C4⋊C4C23×C10711yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C10711yescharacteristic
548C2×C22⋊C4D4×C10711yescharacteristic
549C2×C42—21no—
550C2×C42C23×C10711yescharacteristic
551#107—22no—
552#107—22no—
553C4⋊C8D4×C10714yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C10714yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C10711yescharacteristic
571C24C2×D4×C10711yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C10712yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C10711yescharacteristic
627C22×C4C2×D4×C10711yescharacteristic
628C22×C4C2×D4×C10711yescharacteristic
629C22×C4C2×D4×C10711yescharacteristic
630C22×C4C24×C10711yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C10712yes—
645C2×C8C2×D4×C10712yes—
646C2×C8C2×D4×C10712yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C10712yes—
661C4⋊C4#41×C10712yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C10712yes—
677C42#41×C10712yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C10712yes—
706C23C22×D4×C10711yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4#121×C10712yes—
762C2×C4#121×C10712yes—
763C2×C4C22×D4×C10711yescharacteristic
764C2×C4C22×D4×C10711yescharacteristic
765C2×C4C2×#41×C10711yescharacteristic
766C2×C4C2×#41×C10711yescharacteristic
767C2×C4H(5,𝔽2)×C10711yescharacteristic
768C2×C4H(5,𝔽2)×C10711yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C10711yescharacteristic
802C22D42×C10711yescharacteristic
803C22#546×C10711yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
805C22#575×C10711yescharacteristic
806C22#576×C10711yescharacteristic
807C22#578×C10711yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#532×C10711yescharacteristic
819C4#540×C10711yescharacteristic
820C4D42×C10711yescharacteristic
821C4#550×C10711yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C107×#242811yescharacteristic
827C2C107×#305511yescharacteristic
828C2C107×#306111yescharacteristic
829C2C107×#326411yescharacteristic
830C2C107×#326911yescharacteristic
831C2C107×#330811yescharacteristic
832C2C107×#331911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C107C2semidirect
2. C2×#466×C107C2semidirect
3. C2×#463×C107C2semidirect
4. C2×#435×C107C2semidirect
5. C107×#2540C2semidirect
6. C107×#2537C2semidirect
7. C107×#2036C2semidirect
8. C107×#2033C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1959C2semidirect
12. C107×#1947C2semidirect
13. C107×#1895C2semidirect
14. C107×#1892C2semidirect
15. C107×#1762C2semidirect
136. C4⋊C8×C107D4semidirect
144. #102×C107D4semidirect
405. #25397C107direct (N × H)
417. C2×#468C2×C107semidirect
418. C2×#466C2×C107semidirect
419. C2×#463C2×C107semidirect
420. C2×#435C2×C107semidirect
421. #2540C2×C107semidirect
422. #2537C2×C107semidirect
423. #2036C2×C107semidirect
424. #2033C2×C107semidirect
425. #2000C2×C107semidirect
426. #1999C2×C107semidirect
427. #1959C2×C107semidirect
428. #1947C2×C107semidirect
429. #1895C2×C107semidirect
430. #1892C2×C107semidirect
431. #1762C2×C107semidirect
432. C107#25397direct (N × H)
553. C4⋊C8D4×C107semidirect
561. #102D4×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×#466×C1072
C2×#463×C1072
C2×#435×C1072
C107×#25402
C107×#25372
C107×#20362
C107×#20332
C107×#20002
C107×#19992
C107×#19592
C107×#19472
C107×#18952
C107×#18922
C107×#17622
#25397107