Finite Group Databasebeta

← C107×#22863 #41048827

Subgroups — C107×#22863 #41048827

Order 27392.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C107C211yesmaximal, characteristic
2C2×#440×C107C211yesmaximal, characteristic, complemented
3C2×#417×C107C211yesmaximal, characteristic, complemented
4C107×#2361C211yesmaximal, characteristic, complemented
5C107×#2341C211yesmaximal, characteristic, complemented
6C107×#1970C211yesmaximal, characteristic, complemented
7C107×#1936C211yesmaximal, characteristic, complemented
8C107×#1925C211yesmaximal, characteristic, complemented
9C107×#1895C211yesmaximal, characteristic, complemented
10C107×#1880C211yesmaximal, characteristic, complemented
11C107×#1879C211yesmaximal, characteristic, complemented
12C107×#1863C211yesmaximal, characteristic, complemented
13C107×#1852C211yesmaximal, characteristic, complemented
14C4×#103×C107C211yesmaximal, characteristic, complemented
15C107×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C2×#121×C107C2211yescharacteristic
21C2×C4×Q8×C107C2211yescharacteristic
22C2×C4×Q8×C107C2211yescharacteristic
23C2×C4×D4×C107—21no—
24C2×C4×D4×C107C2211yescharacteristic
25C22×C4⋊C4×C107C2211yescharacteristic
26#449×C107C418yescomplemented
27#440×C107—24no—
28C2×#107×C107C2211yescharacteristic
29C2×#107×C107C2211yescharacteristic
30#417×C107—24no—
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#103×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic
41C2×C4×C8×C107C2211yescharacteristic
42#390×C107—21no—
43#390×C107—21no—
44#390×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic
46#390×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#388×C107—21no—
49#386×C107—21no—
50#385×C107—21no—
51#380×C107—21no—
52#380×C107C2211yescharacteristic
53C4×C4⋊C4×C107C2211yescharacteristic
54C4×C22⋊C4×C107—21no—
55C4×C22⋊C4×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62C2×#41×C107—22no—
63C2×#41×C107—22no—
64C2×#41×C107—22no—
65C2×#41×C107—41no—
66C2×#41×C107—41no—
67C2×#41×C107C2×C414yescomplemented
68C22×Q8×C107C2311yescharacteristic
69C22×D4×C107—21no—
70C22×D4×C107—21no—
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×C107C2×C414yescomplemented
80C2×D8×C107—41no—
81C2×D8×C107—41no—
82C2×D8×C107C2×C414yescomplemented
83C2×M16×C107—22no—
84C2×M16×C107—22no—
85C2×M16×C107—41no—
86C22×C8×C107C2311yescharacteristic
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90#121×C107—22no—
91#121×C107C2×C414yes—
92C4×Q8×C107—22no—
93C4×Q8×C107—22no—
94C4×Q8×C107—41no—
95C4×Q8×C107—41no—
96C4×D4×C107—22no—
97C4×D4×C107—41no—
98C4×D4×C107—44no—
99C2×C4⋊C4×C107—22no—
100C2×C4⋊C4×C107—21no—
101C2×C4⋊C4×C107—21no—
102C2×C4⋊C4×C107—21no—
103C2×C4⋊C4×C107—21no—
104C2×C4⋊C4×C107—41no—
105C2×C4⋊C4×C107C2311yescharacteristic
106C2×C4⋊C4×C107C2311yescharacteristic
107C2×C4⋊C4×C107C2311yescharacteristic
108C2×C4⋊C4×C107C2311yescharacteristic
109C2×C4⋊C4×C107C2311yescharacteristic
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—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107D411yescharacteristic
120C2×C22⋊C4×C107D411yescharacteristic
121C2×C42×C107—21no—
122C2×C42×C107—21no—
123C2×C42×C107—21no—
124C2×C42×C107C2311yescharacteristic
125C2×C42×C107C2311yescharacteristic
126#107×C107—22no—
127#107×C107—41no—
128#103×C107—22no—
129#103×C107C2×C414yescomplemented
130#103×C107D414yescomplemented
131#102×C107—22no—
132#102×C107—22no—
133#102×C107—22no—
134#102×C107—41no—
135#102×C107C2×C414yescomplemented
136C22⋊C8×C107C2×C414yescomplemented
137#97×C107—22no—
138C4×C8×C107—41no—
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×C107C2×D411yescharacteristic
147#41×C107—28no—
148#41×C107—44no—
149#41×C107—44no—
150#41×C107—44no—
151C2×Q8×C107—21no—
152C2×Q8×C107—21no—
153C2×Q8×C107—21no—
154C2×Q8×C107C22×C412yes—
155C2×Q8×C107C2×D412yes—
156C2×Q8×C107#4112yes—
157C2×D4×C107—24no—
158C2×D4×C107—24no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
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—42no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—42no—
173C2×D4×C107C22×C412yes—
174C2×D4×C107C22×C412yes—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—24no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—42no—
187C22×C4×C107—42no—
188C22×C4×C107—42no—
189C22×C4×C107—42no—
190C22×C4×C107—42no—
191C22×C4×C107—42no—
192C22×C4×C107—81no—
193C22×C4×C107—81no—
194C22×C4×C107C22×C412yes—
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107#4112yes—
201C22×C4×C107C2411yescharacteristic
202SD16×C107—28no—
203D8×C107—44no—
204M16×C107—44no—
205C2×C8×C107—21no—
206C2×C8×C107—21no—
207C2×C8×C107—21no—
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×C107C22×C412yes—
215C2×C8×C107C22×C412yes—
216C2×C8×C107C2×D412yes—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—42no—
226C4⋊C4×C107—42no—
227C4⋊C4×C107—42no—
228C4⋊C4×C107—42no—
229C4⋊C4×C107C22×C412yes—
230C4⋊C4×C107C2×D412yes—
231C22⋊C4×C107—24no—
232C22⋊C4×C107—22no—
233C22⋊C4×C107—41no—
234C22⋊C4×C107—42no—
235C22⋊C4×C107—42no—
236C22⋊C4×C107—42no—
237C22⋊C4×C107—42no—
238C22⋊C4×C107—81no—
239C22⋊C4×C107—81no—
240C22⋊C4×C107—81no—
241C22⋊C4×C107—81no—
242C42×C107—21no—
243C42×C107—21no—
244C42×C107—21no—
245C42×C107—21no—
246C42×C107—42no—
247C42×C107—42no—
248C42×C107—42no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—22no—
256C23×C107—22no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
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×C107C4×D412yes—
270C23×C107C22×D411yescharacteristic
271Q8×C107—22no—
272Q8×C107—22no—
273Q8×C107—22no—
274Q8×C107C4×D414yescomplemented
275D4×C107—22no—
276D4×C107—22no—
277D4×C107—22no—
278D4×C107—22no—
279D4×C107—48no—
280D4×C107—48no—
281D4×C107—41no—
282D4×C107—41no—
283D4×C107—41no—
284D4×C107—41no—
285C2×C4×C107—22no—
286C2×C4×C107—22no—
287C2×C4×C107—21no—
288C2×C4×C107—21no—
289C2×C4×C107—22no—
290C2×C4×C107—21no—
291C2×C4×C107—21no—
292C2×C4×C107—22no—
293C2×C4×C107—22no—
294C2×C4×C107—22no—
295C2×C4×C107—22no—
296C2×C4×C107—22no—
297C2×C4×C107—21no—
298C2×C4×C107—21no—
299C2×C4×C107—22no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—48no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
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—84no—
322C2×C4×C107—84no—
323C2×C4×C107C4×D412yes—
324C2×C4×C107AGL(1,ℤ/8)12yes—
325C2×C4×C107C23×C411yescharacteristic
326C2×C4×C107C22×D411yescharacteristic
327C2×C4×C107C2×#4111yescharacteristic
328C2×C4×C107C2×#4111yescharacteristic
329C2×C4×C107H(5,𝔽2)11yescharacteristic
330C2×C4×C107H(5,𝔽2)11yescharacteristic
331C8×C107—22no—
332C8×C107—22no—
333C8×C107—22no—
334C8×C107—41no—
335C22×C107—22no—
336C22×C107—22no—
337C22×C107—22no—
338C22×C107—41no—
339C22×C107—41no—
340C22×C107—41no—
341C22×C107—41no—
342C22×C107—42no—
343C22×C107—42no—
344C22×C107—42no—
345C22×C107—42no—
346C22×C107—42no—
347C22×C107—42no—
348C22×C107—81no—
349C22×C107—81no—
350C22×C107—81no—
351C22×C107—81no—
352C22×C107—81no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107C2×C4×D411yescharacteristic
357C22×C107D4211yescharacteristic
358C22×C107#54611yescharacteristic
359C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C107#57511yescharacteristic
361C22×C107#57611yescharacteristic
362C22×C107#57811yescharacteristic
363C4×C107—22no—
364C4×C107—24no—
365C4×C107—22no—
366C4×C107—42no—
367C4×C107—41no—
368C4×C107—42no—
369C4×C107—41no—
370C4×C107—41no—
371C4×C107—81no—
372C4×C107—81no—
373C4×C107—81no—
374C4×C107C2×C4×D411yescharacteristic
375C4×C107#51811yescharacteristic
376C4×C107#54611yescharacteristic
377C4×C107#55111yescharacteristic
378#22863C10711yesmaximal, characteristic, direct product factor, Sylow
379C2×C107—42no—
380C2×C107—82no—
381C2×C107—82no—
382C2×C107#235811yescharacteristic
383C2×C107C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C107#295111yescharacteristic
385C2×C107#327411yescharacteristic
386C2×C107#327711yescharacteristic
387C2×C107#330811yescharacteristic
388C2×C107#330911yescharacteristic
389C2×#449C2×C10711yescharacteristic
390C2×#440C2×C10711yescharacteristic, complemented
391C2×#417C2×C10711yescharacteristic, complemented
392#2361C2×C10711yescharacteristic, complemented
393#2341C2×C10711yescharacteristic, complemented
394#1970C2×C10711yescharacteristic, complemented
395#1936C2×C10711yescharacteristic, complemented
396#1925C2×C10711yescharacteristic, complemented
397#1895C2×C10711yescharacteristic, complemented
398#1880C2×C10711yescharacteristic, complemented
399#1879C2×C10711yescharacteristic, complemented
400#1863C2×C10711yescharacteristic, complemented
401#1852C2×C10711yescharacteristic, complemented
402C4×#103C2×C10711yescharacteristic, complemented
403#1753C2×C10711yescharacteristic, complemented
404C107#2286311yescharacteristic, direct product factor, Sylow
405C22×#41C22×C10711yescharacteristic
406C22×SD16C22×C10711yescharacteristic
407C22×D8C22×C10711yescharacteristic
408C22×M16C22×C10711yescharacteristic
409C2×#121C22×C10711yescharacteristic
410C2×C4×Q8C22×C10711yescharacteristic
411C2×C4×Q8C22×C10711yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4C22×C10711yescharacteristic
414C22×C4⋊C4C22×C10711yescharacteristic
415#449C4×C10718yescomplemented
416#440—24no—
417C2×#107C22×C10711yescharacteristic
418C2×#107C22×C10711yescharacteristic
419#417—24no—
420C2×#103C22×C10711yescharacteristic
421C2×#103C22×C10711yescharacteristic
422C2×#103C22×C10711yescharacteristic
423C2×#102C22×C10711yescharacteristic
424C2×#102C22×C10711yescharacteristic
425C2×#102C22×C10711yescharacteristic
426C2×#102C22×C10711yescharacteristic
427C2×#102C22×C10711yescharacteristic
428C2×C22⋊C8C22×C10711yescharacteristic
429C2×#97C22×C10711yescharacteristic
430C2×C4×C8C22×C10711yescharacteristic
431#390—21no—
432#390—21no—
433#390C22×C10711yescharacteristic
434#390C22×C10711yescharacteristic
435#390C22×C10711yescharacteristic
436#389C22×C10711yescharacteristic
437#388—21no—
438#386—21no—
439#385—21no—
440#380—21no—
441#380C22×C10711yescharacteristic
442C4×C4⋊C4C22×C10711yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4C22×C10711yescharacteristic
445#340C22×C10711yescharacteristic
446#340C22×C10711yescharacteristic
447#340C22×C10711yescharacteristic
448#340C22×C10711yescharacteristic
449#336C22×C10711yescharacteristic
450#336C22×C10711yescharacteristic
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C2×C4×C10714yescomplemented
457C22×Q8C23×C10711yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C10711yescharacteristic
461C22×D4C23×C10711yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—21no—
465C23×C4C23×C10711yescharacteristic
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16C2×C4×C10714yescomplemented
469C2×D8—41no—
470C2×D8—41no—
471C2×D8C2×C4×C10714yescomplemented
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—41no—
475C22×C8C23×C10711yescharacteristic
476C22×C8C23×C10711yescharacteristic
477C22×C8C23×C10711yescharacteristic
478C22×C8C23×C10711yescharacteristic
479#121—22no—
480#121C2×C4×C10714yes—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—41no—
484C4×Q8—41no—
485C4×D4—22no—
486C4×D4—41no—
487C4×D4—44no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4C23×C10711yescharacteristic
495C2×C4⋊C4C23×C10711yescharacteristic
496C2×C4⋊C4C23×C10711yescharacteristic
497C2×C4⋊C4C23×C10711yescharacteristic
498C2×C4⋊C4C23×C10711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4D4×C10711yescharacteristic
509C2×C22⋊C4D4×C10711yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42C23×C10711yescharacteristic
514C2×C42C23×C10711yescharacteristic
515#107—22no—
516#107—41no—
517#103—22no—
518#103C2×C4×C10714yescomplemented
519#103D4×C10714yescomplemented
520#102—22no—
521#102—22no—
522#102—22no—
523#102—41no—
524#102C2×C4×C10714yescomplemented
525C22⋊C8C2×C4×C10714yescomplemented
526#97—22no—
527C4×C8—41no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C10711yescharacteristic
532#95D4×C10711yescharacteristic
533C24—21no—
534C24—21no—
535C24C2×D4×C10711yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C22×C4×C10712yes—
544C2×Q8C2×D4×C10712yes—
545C2×Q8#41×C10712yes—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C22×C4×C10712yes—
563C2×D4C22×C4×C10712yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4C22×C4×C10712yes—
584C22×C4C2×D4×C10711yescharacteristic
585C22×C4C2×D4×C10711yescharacteristic
586C22×C4C2×D4×C10711yescharacteristic
587C22×C4C2×D4×C10711yescharacteristic
588C22×C4C2×D4×C10711yescharacteristic
589C22×C4#41×C10712yes—
590C22×C4C24×C10711yescharacteristic
591SD16—28no—
592D8—44no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8C22×C4×C10712yes—
604C2×C8C22×C4×C10712yes—
605C2×C8C2×D4×C10712yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4C22×C4×C10712yes—
619C4⋊C4C2×D4×C10712yes—
620C22⋊C4—24no—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—42no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4×D4×C10712yes—
659C23C22×D4×C10711yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8C4×D4×C10714yescomplemented
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—48no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4C4×D4×C10712yes—
713C2×C4AGL(1,ℤ/8)×C10712yes—
714C2×C4C23×C4×C10711yescharacteristic
715C2×C4C22×D4×C10711yescharacteristic
716C2×C4C2×#41×C10711yescharacteristic
717C2×C4C2×#41×C10711yescharacteristic
718C2×C4H(5,𝔽2)×C10711yescharacteristic
719C2×C4H(5,𝔽2)×C10711yescharacteristic
720C8—22no—
721C8—22no—
722C8—22no—
723C8—41no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C2×C4×D4×C10711yescharacteristic
746C22D42×C10711yescharacteristic
747C22#546×C10711yescharacteristic
748C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
749C22#575×C10711yescharacteristic
750C22#576×C10711yescharacteristic
751C22#578×C10711yescharacteristic
752C4—22no—
753C4—22no—
754C4—24no—
755C4—42no—
756C4—41no—
757C4—42no—
758C4—41no—
759C4—41no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×C4×D4×C10711yescharacteristic
764C4#518×C10711yescharacteristic
765C4#546×C10711yescharacteristic
766C4#551×C10711yescharacteristic
767C2—42no—
768C2—82no—
769C2—82no—
770C2C107×#235811yescharacteristic
771C2C4×AGL(1,ℤ/8)×C10711yescharacteristic
772C2C107×#295111yescharacteristic
773C2C107×#327411yescharacteristic
774C2C107×#327711yescharacteristic
775C2C107×#330811yescharacteristic
776C2C107×#330911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC2×#449×C107C2
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×#440×C107C2semidirect
3. C2×#417×C107C2semidirect
4. C107×#2361C2semidirect
5. C107×#2341C2semidirect
6. C107×#1970C2semidirect
7. C107×#1936C2semidirect
8. C107×#1925C2semidirect
9. C107×#1895C2semidirect
10. C107×#1880C2semidirect
11. C107×#1879C2semidirect
12. C107×#1863C2semidirect
13. C107×#1852C2semidirect
14. C4×#103×C107C2semidirect
15. C107×#1753C2semidirect
26. #449×C107C4semidirect
67. C2×#41×C107C2×C4semidirect
79. C2×SD16×C107C2×C4semidirect
82. C2×D8×C107C2×C4semidirect
129. #103×C107C2×C4semidirect
130. #103×C107D4semidirect
135. #102×C107C2×C4semidirect
136. C22⋊C8×C107C2×C4semidirect
274. Q8×C107C4×D4semidirect
378. #22863C107direct (N × H)
390. C2×#440C2×C107semidirect
391. C2×#417C2×C107semidirect
392. #2361C2×C107semidirect
393. #2341C2×C107semidirect
394. #1970C2×C107semidirect
395. #1936C2×C107semidirect
396. #1925C2×C107semidirect
397. #1895C2×C107semidirect
398. #1880C2×C107semidirect
399. #1879C2×C107semidirect
400. #1863C2×C107semidirect
401. #1852C2×C107semidirect
402. C4×#103C2×C107semidirect
403. #1753C2×C107semidirect
404. C107#22863direct (N × H)
415. #449C4×C107semidirect
456. C2×#41C2×C4×C107semidirect
468. C2×SD16C2×C4×C107semidirect
471. C2×D8C2×C4×C107semidirect
518. #103C2×C4×C107semidirect
519. #103D4×C107semidirect
524. #102C2×C4×C107semidirect
525. C22⋊C8C2×C4×C107semidirect
663. Q8C4×D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1072
C2×#440×C1072
C2×#417×C1072
C107×#23612
C107×#23412
C107×#19702
C107×#19362
C107×#19252
C107×#18952
C107×#18802
C107×#18792
C107×#18632
C107×#18522
C4×#103×C1072
C107×#17532
#22863107