Finite Group Databasebeta

← C107×#25136 #41051100

Subgroups — C107×#25136 #41051100

Order 27392.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 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×#436×C107C211yesmaximal, characteristic, complemented
4C2×#418×C107C211yesmaximal, characteristic, complemented
5C107×#2415C211yesmaximal, characteristic, complemented
6C107×#2408C211yesmaximal, characteristic
7C107×#2067C211yesmaximal, characteristic, complemented
8C107×#2055C211yesmaximal, characteristic, complemented
9C107×#2034C211yesmaximal, characteristic, complemented
10C107×#2000C211yesmaximal, characteristic, complemented
11C107×#1968C211yesmaximal, characteristic, complemented
12C107×#1934C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1894C211yesmaximal, characteristic, complemented
15C107×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×SD16×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C22×M16×C107C2211yescharacteristic, complemented
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic, complemented
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#120×C107—21no—
26C2×C4×D4×C107C2211yescharacteristic
27C2×#117×C107C2211yescharacteristic
28#468×C107—24no—
29#450×C107—24no—
30#436×C107—24no—
31C2×#107×C107C2211yescharacteristic, complemented
32C2×#106×C107C2211yescharacteristic, complemented
33C2×C4⋊C8×C107C2211yescharacteristic, complemented
34#418×C107—24no—
35C2×#103×C107C2211yescharacteristic, complemented
36C2×#103×C107C2211yescharacteristic, complemented
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×C4×C8×C107C2211yescharacteristic, complemented
46#397×C107—21no—
47#394×C107—21no—
48#394×C107—21no—
49#392×C107—21no—
50#391×C107C2211yescharacteristic, complemented
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#389×C107—21no—
54#389×C107C2211yescharacteristic, complemented
55#388×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×C107C2311yescharacteristic
78C23×C4×C107C2311yescharacteristic
79C2×SD16×C107—22no—
80C2×SD16×C107—22no—
81C2×SD16×C107—22no—
82C2×SD16×C107—22no—
83C2×SD16×C107—41no—
84C2×SD16×C107—41no—
85C2×M16×C107—22no—
86C2×M16×C107—22no—
87C2×M16×C107—22no—
88C2×M16×C107—22no—
89C2×M16×C107—41no—
90C2×M16×C107—41no—
91C22×C8×C107C2311yescharacteristic
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22⋊Q8×C107—22no—
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—22no—
98C22⋊Q8×C107—41no—
99#121×C107—22no—
100#121×C107—22no—
101#121×C107—41no—
102#121×C107—41no—
103#120×C107—44no—
104C4×D4×C107—22no—
105C4×D4×C107—22no—
106#117×C107—22no—
107#117×C107—41no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107D411yescharacteristic
112C2×C4⋊C4×C107C2311yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
129C2×C22⋊C4×C107D411yescharacteristic
130C2×C42×C107—21no—
131C2×C42×C107C2311yescharacteristic
132#107×C107—22no—
133#106×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
145C4×C8×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—21no—
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—44no—
182C2×D4×C107—44no—
183C2×D4×C107—41no—
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×C107C2×D411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D412yes—
216C22×C4×C107C2×D411yescharacteristic
217C22×C4×C107#4112yes—
218C22×C4×C107C2411yescharacteristic
219SD16×C107—44no—
220SD16×C107—44no—
221M16×C107—44no—
222M16×C107—44no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
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×C107C2×D412yes—
233C2×C8×C107C2×D412yes—
234C2×C8×C107C2×D412yes—
235C4⋊C4×C107—22no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
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—42no—
246C4⋊C4×C107—42no—
247C4⋊C4×C107—42no—
248C4⋊C4×C107C2×D412yes—
249C22⋊C4×C107—22no—
250C22⋊C4×C107—22no—
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—
258C22⋊C4×C107—42no—
259C22⋊C4×C107—42no—
260C22⋊C4×C107—81no—
261C22⋊C4×C107—81no—
262C42×C107—21no—
263C42×C107—21no—
264C42×C107—42no—
265C23×C107—21no—
266C23×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×C107C22×D411yescharacteristic
301Q8×C107—41no—
302Q8×C107—41no—
303Q8×C107—41no—
304Q8×C107—41no—
305D4×C107—22no—
306D4×C107—22no—
307D4×C107—22no—
308D4×C107—22no—
309D4×C107—44no—
310D4×C107—48no—
311D4×C107—41no—
312D4×C107—41no—
313D4×C107—41no—
314D4×C107—41no—
315D4×C107—84no—
316D4×C107—84no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
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—22no—
328C2×C4×C107—21no—
329C2×C4×C107—21no—
330C2×C4×C107—21no—
331C2×C4×C107—21no—
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—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#12112yes—
354C2×C4×C107AGL(1,ℤ/8)12yes—
355C2×C4×C107C22×D411yescharacteristic
356C2×C4×C107C22×D411yescharacteristic
357C2×C4×C107C2×#4111yescharacteristic
358C2×C4×C107C2×#4111yescharacteristic
359C2×C4×C107H(5,𝔽2)11yescharacteristic
360C2×C4×C107H(5,𝔽2)11yescharacteristic
361C8×C107—22no—
362C8×C107—22no—
363C8×C107—22no—
364C8×C107—41no—
365C22×C107—22no—
366C22×C107—22no—
367C22×C107—22no—
368C22×C107—41no—
369C22×C107—41no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—42no—
374C22×C107—42no—
375C22×C107—41no—
376C22×C107—42no—
377C22×C107—41no—
378C22×C107—42no—
379C22×C107—41no—
380C22×C107—41no—
381C22×C107—41no—
382C22×C107—42no—
383C22×C107—41no—
384C22×C107—42no—
385C22×C107—816no—
386C22×C107—81no—
387C22×C107—81no—
388C22×C107—81no—
389C22×C107—81no—
390C22×C107—81no—
391C22×C107—81no—
392C22×C107—81no—
393C22×C107—81no—
394C22×C107C2×#12111yescharacteristic
395C22×C107D4211yescharacteristic
396C22×C107#54611yescharacteristic
397C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C107#57511yescharacteristic
399C22×C107#57711yescharacteristic
400C22×C107#57711yescharacteristic
401C4×C107—22no—
402C4×C107—22no—
403C4×C107—41no—
404C4×C107—42no—
405C4×C107—41no—
406C4×C107—81no—
407C4×C107—81no—
408C4×C107—81no—
409C4×C107—81no—
410C4×C107—81no—
411C4×C107#52511yescharacteristic
412C4×C107#53811yescharacteristic
413C4×C107D4211yescharacteristic
414C4×C107#54611yescharacteristic
415#25136C10711yesmaximal, characteristic, direct product factor, Sylow
416C2×C107—42no—
417C2×C107—81no—
418C2×C107—82no—
419C2×C107—82no—
420C2×C107#242411yescharacteristic
421C2×C107#305511yescharacteristic
422C2×C107#305711yescharacteristic
423C2×C107#327211yescharacteristic
424C2×C107#327511yescharacteristic
425C2×C107#332311yescharacteristic
426C2×C107#332411yescharacteristic
427C2×#468C2×C10711yescharacteristic, complemented
428C2×#450C2×C10711yescharacteristic, complemented
429C2×#436C2×C10711yescharacteristic, complemented
430C2×#418C2×C10711yescharacteristic, complemented
431#2415C2×C10711yescharacteristic, complemented
432#2408C2×C10711yescharacteristic
433#2067C2×C10711yescharacteristic, complemented
434#2055C2×C10711yescharacteristic, complemented
435#2034C2×C10711yescharacteristic, complemented
436#2000C2×C10711yescharacteristic, complemented
437#1968C2×C10711yescharacteristic, complemented
438#1934C2×C10711yescharacteristic, complemented
439#1895C2×C10711yescharacteristic, complemented
440#1894C2×C10711yescharacteristic, complemented
441#1854C2×C10711yescharacteristic, complemented
442C107#2513611yescharacteristic, direct product factor, Sylow
443C23×D4C22×C10711yescharacteristic
444C22×SD16C22×C10711yescharacteristic
445C22×SD16C22×C10711yescharacteristic
446C22×M16C22×C10711yescharacteristic
447C22×M16C22×C10711yescharacteristic, complemented
448C2×C22⋊Q8C22×C10711yescharacteristic
449C2×C22⋊Q8C22×C10711yescharacteristic, complemented
450C2×#121C22×C10711yescharacteristic
451C2×#121C22×C10711yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C10711yescharacteristic
454C2×#117C22×C10711yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C10711yescharacteristic, complemented
459C2×#106C22×C10711yescharacteristic, complemented
460C2×C4⋊C8C22×C10711yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C10711yescharacteristic, complemented
463C2×#103C22×C10711yescharacteristic, complemented
464C2×#102C22×C10711yescharacteristic
465C2×#102C22×C10711yescharacteristic
466C2×#102C22×C10711yescharacteristic
467C2×#102C22×C10711yescharacteristic
468C2×#102C22×C10711yescharacteristic
469C2×#102C22×C10711yescharacteristic
470C2×C22⋊C8C22×C10711yescharacteristic
471C2×C22⋊C8C22×C10711yescharacteristic, complemented
472C2×C4×C8C22×C10711yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C10711yescharacteristic, complemented
478#390C22×C10711yescharacteristic
479#390C22×C10711yescharacteristic
480#389—21no—
481#389C22×C10711yescharacteristic, complemented
482#388—21no—
483#380C22×C10711yescharacteristic
484#380C22×C10711yescharacteristic, complemented
485#379—21no—
486#340C22×C10711yescharacteristic, complemented
487#340C22×C10711yescharacteristic, complemented
488#340C22×C10711yescharacteristic, complemented
489#340C22×C10711yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C10711yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C10711yescharacteristic
502C22×D4C23×C10711yescharacteristic
503C22×D4C23×C10711yescharacteristic
504C23×C4C23×C10711yescharacteristic
505C23×C4C23×C10711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C10711yescharacteristic
519C22×C8C23×C10711yescharacteristic
520C22×C8C23×C10711yescharacteristic
521C22×C8C23×C10711yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C10711yescharacteristic
539C2×C4⋊C4C23×C10711yescharacteristic
540C2×C4⋊C4C23×C10711yescharacteristic
541C2×C4⋊C4C23×C10711yescharacteristic
542C2×C4⋊C4C23×C10711yescharacteristic
543C2×C4⋊C4C23×C10711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
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⋊C4D4×C10711yescharacteristic
556C2×C22⋊C4D4×C10711yescharacteristic
557C2×C42—21no—
558C2×C42C23×C10711yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C10714yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C10714yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C10711yescharacteristic
588C24C2×D4×C10711yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C10712yes—
622C2×D4#41×C10712yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
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×C4C2×D4×C10711yescharacteristic
640C22×C4C2×D4×C10711yescharacteristic
641C22×C4C2×D4×C10711yescharacteristic
642C22×C4C2×D4×C10712yes—
643C22×C4C2×D4×C10711yescharacteristic
644C22×C4#41×C10712yes—
645C22×C4C24×C10711yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C10712yes—
660C2×C8C2×D4×C10712yes—
661C2×C8C2×D4×C10712yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C10712yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C10712yes—
727C23C22×D4×C10711yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
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#121×C10712yes—
781C2×C4AGL(1,ℤ/8)×C10712yes—
782C2×C4C22×D4×C10711yescharacteristic
783C2×C4C22×D4×C10711yescharacteristic
784C2×C4C2×#41×C10711yescharacteristic
785C2×C4C2×#41×C10711yescharacteristic
786C2×C4H(5,𝔽2)×C10711yescharacteristic
787C2×C4H(5,𝔽2)×C10711yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C10711yescharacteristic
822C22D42×C10711yescharacteristic
823C22#546×C10711yescharacteristic
824C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
825C22#575×C10711yescharacteristic
826C22#577×C10711yescharacteristic
827C22#577×C10711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C10711yescharacteristic
839C4#538×C10711yescharacteristic
840C4D42×C10711yescharacteristic
841C4#546×C10711yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C107×#242411yescharacteristic
847C2C107×#305511yescharacteristic
848C2C107×#305711yescharacteristic
849C2C107×#327211yescharacteristic
850C2C107×#327511yescharacteristic
851C2C107×#332311yescharacteristic
852C2C107×#332411yescharacteristic
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×#436×C107C2semidirect
4. C2×#418×C107C2semidirect
5. C107×#2415C2semidirect
7. C107×#2067C2semidirect
8. C107×#2055C2semidirect
9. C107×#2034C2semidirect
10. C107×#2000C2semidirect
11. C107×#1968C2semidirect
12. C107×#1934C2semidirect
13. C107×#1895C2semidirect
14. C107×#1894C2semidirect
15. C107×#1854C2semidirect
20. C22×M16×C107C22semidirect
22. C2×C22⋊Q8×C107C22semidirect
31. C2×#107×C107C22semidirect
32. C2×#106×C107C22semidirect
33. C2×C4⋊C8×C107C22semidirect
35. C2×#103×C107C22semidirect
36. C2×#103×C107C22semidirect
44. C2×C22⋊C8×C107C22semidirect
45. C2×C4×C8×C107C22semidirect
50. #391×C107C22semidirect
54. #389×C107C22semidirect
57. #380×C107C22semidirect
59. #340×C107C22semidirect
60. #340×C107C22semidirect
61. #340×C107C22semidirect
62. #340×C107C22semidirect
142. #102×C107D4semidirect
144. C22⋊C8×C107D4semidirect
415. #25136C107direct (N × H)
427. C2×#468C2×C107semidirect
428. C2×#450C2×C107semidirect
429. C2×#436C2×C107semidirect
430. C2×#418C2×C107semidirect
431. #2415C2×C107semidirect
433. #2067C2×C107semidirect
434. #2055C2×C107semidirect
435. #2034C2×C107semidirect
436. #2000C2×C107semidirect
437. #1968C2×C107semidirect
438. #1934C2×C107semidirect
439. #1895C2×C107semidirect
440. #1894C2×C107semidirect
441. #1854C2×C107semidirect
442. C107#25136direct (N × H)
447. C22×M16C22×C107semidirect
449. C2×C22⋊Q8C22×C107semidirect
458. C2×#107C22×C107semidirect
459. C2×#106C22×C107semidirect
460. C2×C4⋊C8C22×C107semidirect
462. C2×#103C22×C107semidirect
463. C2×#103C22×C107semidirect
471. C2×C22⋊C8C22×C107semidirect
472. C2×C4×C8C22×C107semidirect
477. #391C22×C107semidirect
481. #389C22×C107semidirect
484. #380C22×C107semidirect
486. #340C22×C107semidirect
487. #340C22×C107semidirect
488. #340C22×C107semidirect
489. #340C22×C107semidirect
569. #102D4×C107semidirect
571. C22⋊C8D4×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×#436×C1072
C2×#418×C1072
C107×#24152
C107×#24082
C107×#20672
C107×#20552
C107×#20342
C107×#20002
C107×#19682
C107×#19342
C107×#18952
C107×#18942
C107×#18542
#25136107