Finite Group Databasebeta

← C107×#23482 #41049446

Subgroups — C107×#23482 #41049446

Order 27392.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C107C211yesmaximal, characteristic
2C2×#428×C107C211yesmaximal, characteristic, complemented
3C2×#417×C107C211yesmaximal, characteristic, complemented
4C2×#417×C107C211yesmaximal, characteristic, complemented
5C2×#407×C107C211yesmaximal, characteristic, complemented
6C2×#380×C107C211yesmaximal, characteristic, complemented
7C107×#2036C212yesmaximal, complemented
8C107×#2035C212yesmaximal, complemented
9C107×#2034C212yesmaximal, complemented
10C107×#2033C212yesmaximal, complemented
11C107×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C107C2211yescharacteristic
13C24×C4×C107C2211yescharacteristic
14C22×M16×C107C2211yescharacteristic
15C22×M16×C107C2211yescharacteristic
16#525×C107—24no—
17#525×C107—24no—
18C2×#123×C107—21no—
19C2×C22⋊Q8×C107C2211yescharacteristic
20C2×C22⋊Q8×C107C2211yescharacteristic
21C2×#121×C107C2211yescharacteristic
22C2×#121×C107C2211yescharacteristic
23C2×#120×C107—21no—
24C2×C4×D4×C107—21no—
25C2×C4×D4×C107—21no—
26C2×#117×C107C2211yescharacteristic
27C22×C4⋊C4×C107C2211yescharacteristic
28C22×C4⋊C4×C107C2211yescharacteristic
29C22×C22⋊C4×C107—21no—
30#428×C107—24no—
31C2×#107×C107C2212yescomplemented
32C2×#106×C107C2212yescomplemented
33#417×C107—24no—
34#417×C107—24no—
35C2×#103×C107C2212yescomplemented
36C2×#103×C107C2212yescomplemented
37C2×#102×C107C2212yescomplemented
38C2×#102×C107C2212yescomplemented
39#407×C107—24no—
40C2×C22⋊C8×C107C2212yes—
41C2×C22⋊C8×C107C2212yes—
42#380×C107—21no—
43#380×C107—21no—
44#380×C107C2212yes—
45#380×C107C2212yes—
46C2×#95×C107—21no—
47#340×C107C2212yescomplemented
48#340×C107C2212yescomplemented
49C25×C107D411yescharacteristic
50C2×#41×C107—22no—
51C2×#41×C107—22no—
52C2×#41×C107—22no—
53C2×#41×C107—22no—
54C2×#41×C107—22no—
55C2×#41×C107D414yes—
56C22×Q8×C107C2311yescharacteristic
57C22×D4×C107—21no—
58C22×D4×C107—21no—
59C22×D4×C107—21no—
60C22×D4×C107C2311yescharacteristic
61C23×C4×C107—22no—
62C23×C4×C107—21no—
63C23×C4×C107—22no—
64C23×C4×C107—22no—
65C23×C4×C107—22no—
66C23×C4×C107—22no—
67C23×C4×C107—22no—
68C23×C4×C107—21no—
69C23×C4×C107—21no—
70C23×C4×C107D411yescharacteristic
71C23×C4×C107D411yescharacteristic
72C23×C4×C107D411yescharacteristic
73C23×C4×C107C2311yescharacteristic
74C23×C4×C107C2311yescharacteristic
75C23×C4×C107C2311yescharacteristic
76C2×M16×C107—22no—
77C2×M16×C107—22no—
78C2×M16×C107—22no—
79C2×M16×C107—22no—
80C2×M16×C107—22no—
81C2×M16×C107D414yescomplemented
82C22×C8×C107C2312yes—
83C22×C8×C107C2312yes—
84#123×C107—28no—
85C22⋊Q8×C107—22no—
86C22⋊Q8×C107—22no—
87C22⋊Q8×C107—22no—
88C22⋊Q8×C107—22no—
89#121×C107—22no—
90#121×C107—22no—
91#121×C107—22no—
92#121×C107—22no—
93#120×C107—28no—
94C4×D4×C107—28no—
95C4×D4×C107—28no—
96#117×C107—22no—
97#117×C107D414yes—
98C2×C4⋊C4×C107—21no—
99C2×C4⋊C4×C107—21no—
100C2×C4⋊C4×C107—22no—
101C2×C4⋊C4×C107—22no—
102C2×C4⋊C4×C107—22no—
103C2×C4⋊C4×C107—22no—
104C2×C4⋊C4×C107—21no—
105C2×C4⋊C4×C107—21no—
106C2×C4⋊C4×C107C2312yes—
107C2×C4⋊C4×C107C2312yes—
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—22no—
116C2×C22⋊C4×C107—22no—
117C2×C22⋊C4×C107—44no—
118C2×C42×C107—21no—
119#107×C107—24no—
120#106×C107—24no—
121#103×C107—24no—
122#103×C107—24no—
123#102×C107—24no—
124#102×C107—24no—
125C22⋊C8×C107—24no—
126C22⋊C8×C107—24no—
127#95×C107—22no—
128#95×C107—22no—
129C24×C107—22no—
130C24×C107—22no—
131C24×C107—22no—
132C24×C107—22no—
133C24×C107—22no—
134C24×C107—21no—
135C24×C107—41no—
136C24×C107—41no—
137C24×C107C2×D411yescharacteristic
138C24×C107C2×D411yescharacteristic
139C24×C107C2×D411yescharacteristic
140#41×C107—28no—
141#41×C107—28no—
142#41×C107—44no—
143#41×C107—44no—
144C2×Q8×C107—21no—
145C2×Q8×C107—21no—
146C2×Q8×C107—21no—
147C2×Q8×C107—21no—
148C2×Q8×C107—21no—
149C2×Q8×C107C2×D412yes—
150C2×D4×C107—24no—
151C2×D4×C107—24no—
152C2×D4×C107—24no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—42no—
159C2×D4×C107—42no—
160C2×D4×C107—42no—
161C2×D4×C107—42no—
162C2×D4×C107—42no—
163C2×D4×C107—42no—
164C2×D4×C107C2×D412yes—
165C22×C4×C107—22no—
166C22×C4×C107—22no—
167C22×C4×C107—22no—
168C22×C4×C107—21no—
169C22×C4×C107—21no—
170C22×C4×C107—21no—
171C22×C4×C107—22no—
172C22×C4×C107—22no—
173C22×C4×C107—24no—
174C22×C4×C107—22no—
175C22×C4×C107—22no—
176C22×C4×C107—22no—
177C22×C4×C107—22no—
178C22×C4×C107—21no—
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—21no—
190C22×C4×C107—22no—
191C22×C4×C107—22no—
192C22×C4×C107—44no—
193C22×C4×C107—44no—
194C22×C4×C107—42no—
195C22×C4×C107—44no—
196C22×C4×C107—42no—
197C22×C4×C107—44no—
198C22×C4×C107—42no—
199C22×C4×C107—42no—
200C22×C4×C107—42no—
201C22×C4×C107—42no—
202C22×C4×C107—42no—
203C22×C4×C107—42no—
204C22×C4×C107C2×D411yescharacteristic
205C22×C4×C107C2×D411yescharacteristic
206C22×C4×C107C2×D411yescharacteristic
207C22×C4×C107C2×D412yes—
208C22×C4×C107C2×D412yes—
209C22×C4×C107C2×D412yes—
210C22×C4×C107#4112yes—
211C22×C4×C107#4112yes—
212C22×C4×C107#4112yes—
213C22×C4×C107C2411yescharacteristic
214M16×C107—28no—
215M16×C107—44no—
216C2×C8×C107—22no—
217C2×C8×C107—22no—
218C2×C8×C107—22no—
219C2×C8×C107—22no—
220C2×C8×C107—22no—
221C2×C8×C107C2×D414yes—
222C4⋊C4×C107—24no—
223C4⋊C4×C107—24no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—22no—
227C4⋊C4×C107—22no—
228C4⋊C4×C107—22no—
229C4⋊C4×C107—22no—
230C4⋊C4×C107—42no—
231C4⋊C4×C107—42no—
232C4⋊C4×C107C2×D412yes—
233C4⋊C4×C107C2×D412yes—
234C22⋊C4×C107—24no—
235C22⋊C4×C107—24no—
236C22⋊C4×C107—24no—
237C22⋊C4×C107—24no—
238C22⋊C4×C107—24no—
239C22⋊C4×C107—44no—
240C22⋊C4×C107—44no—
241C42×C107—24no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—28no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107—21no—
254C23×C107—21no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—22no—
260C23×C107—44no—
261C23×C107—44no—
262C23×C107—44no—
263C23×C107—44no—
264C23×C107—44no—
265C23×C107—44no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107#12012yes—
273C23×C107#12112yes—
274C23×C107#12312yes—
275C23×C107AGL(1,ℤ/8)12yes—
276C23×C107#13712yes—
277C23×C107C22×D411yescharacteristic
278Q8×C107—22no—
279Q8×C107—22no—
280Q8×C107—41no—
281Q8×C107—41no—
282D4×C107—22no—
283D4×C107—22no—
284D4×C107—48no—
285D4×C107—48no—
286D4×C107—48no—
287D4×C107—41no—
288D4×C107—41no—
289C2×C4×C107—22no—
290C2×C4×C107—22no—
291C2×C4×C107—21no—
292C2×C4×C107—21no—
293C2×C4×C107—22no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—41no—
299C2×C4×C107—41no—
300C2×C4×C107—41no—
301C2×C4×C107—41no—
302C2×C4×C107—41no—
303C2×C4×C107—41no—
304C2×C4×C107—44no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—41no—
308C2×C4×C107—41no—
309C2×C4×C107—41no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—44no—
314C2×C4×C107—44no—
315C2×C4×C107—48no—
316C2×C4×C107—42no—
317C2×C4×C107—42no—
318C2×C4×C107—42no—
319C2×C4×C107—42no—
320C2×C4×C107—42no—
321C2×C4×C107—42no—
322C2×C4×C107—84no—
323C2×C4×C107—84no—
324C2×C4×C107#12012yes—
325C2×C4×C107#12114yes—
326C2×C4×C107#12114yes—
327C2×C4×C107#12112yes—
328C2×C4×C107#12314yes—
329C2×C4×C107#12312yes—
330C2×C4×C107#12414yes—
331C2×C4×C107C22×D411yescharacteristic
332C2×C4×C107C22×D411yescharacteristic
333C2×C4×C107C22×D411yescharacteristic
334C2×C4×C107C2×#4111yescharacteristic
335C2×C4×C107C2×#4111yescharacteristic
336C2×C4×C107C2×#4111yescharacteristic
337C8×C107—24no—
338C8×C107—42no—
339C22×C107—22no—
340C22×C107—22no—
341C22×C107—22no—
342C22×C107—22no—
343C22×C107—22no—
344C22×C107—22no—
345C22×C107—22no—
346C22×C107—22no—
347C22×C107—22no—
348C22×C107—22no—
349C22×C107—22no—
350C22×C107—22no—
351C22×C107—416no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—41no—
356C22×C107—41no—
357C22×C107—41no—
358C22×C107—41no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—42no—
362C22×C107—42no—
363C22×C107—81no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107#39414yes—
368C22×C107C2×#12011yescharacteristic
369C22×C107C2×#12111yescharacteristic
370C22×C107C2×#12311yescharacteristic
371C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C107C2×#13711yescharacteristic
373C22×C107#57511yescharacteristic
374C22×C107#57511yescharacteristic
375C4×C107—41no—
376C4×C107—41no—
377C4×C107—42no—
378C4×C107—42no—
379C4×C107—42no—
380C4×C107—82no—
381C4×C107—82no—
382C4×C107#39414yes—
383C4×C107C2×#12111yescharacteristic
384C4×C107C2×#12111yescharacteristic
385C4×C107C2×#12311yescharacteristic
386C4×C107C2×#12411yescharacteristic
387#23482C10711yesmaximal, characteristic, direct product factor, Sylow
388C2×C107—24no—
389C2×C107—42no—
390C2×C107—42no—
391C2×C107—82no—
392C2×C107C2×#39411yescharacteristic
393C2×C107#300611yescharacteristic
394C2×C107#300711yescharacteristic
395C2×C107#305511yescharacteristic
396C2×C107#305611yescharacteristic
397C2×C107#309211yescharacteristic
398C2×C107#309311yescharacteristic
399C2×#525C2×C10711yescharacteristic
400C2×#428C2×C10711yescharacteristic, complemented
401C2×#417C2×C10711yescharacteristic, complemented
402C2×#417C2×C10711yescharacteristic, complemented
403C2×#407C2×C10711yescharacteristic, complemented
404C2×#380C2×C10711yescharacteristic, complemented
405#2036C2×C10712yescomplemented
406#2035C2×C10712yescomplemented
407#2034C2×C10712yescomplemented
408#2033C2×C10712yescomplemented
409#1736C2×C10711yescharacteristic, complemented
410C107#2348211yescharacteristic, direct product factor, Sylow
411C22×#41C22×C10711yescharacteristic
412C24×C4C22×C10711yescharacteristic
413C22×M16C22×C10711yescharacteristic
414C22×M16C22×C10711yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C10711yescharacteristic
419C2×C22⋊Q8C22×C10711yescharacteristic
420C2×#121C22×C10711yescharacteristic
421C2×#121C22×C10711yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C10711yescharacteristic
426C22×C4⋊C4C22×C10711yescharacteristic
427C22×C4⋊C4C22×C10711yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C10712yescomplemented
431C2×#106C22×C10712yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C10712yescomplemented
435C2×#103C22×C10712yescomplemented
436C2×#102C22×C10712yescomplemented
437C2×#102C22×C10712yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C10712yes—
440C2×C22⋊C8C22×C10712yes—
441#380—21no—
442#380—21no—
443#380C22×C10712yes—
444#380C22×C10712yes—
445C2×#95—21no—
446#340C22×C10712yescomplemented
447#340C22×C10712yescomplemented
448C25D4×C10711yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C10714yes—
455C22×Q8C23×C10711yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C10711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C10711yescharacteristic
470C23×C4D4×C10711yescharacteristic
471C23×C4D4×C10711yescharacteristic
472C23×C4C23×C10711yescharacteristic
473C23×C4C23×C10711yescharacteristic
474C23×C4C23×C10711yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C10714yescomplemented
481C22×C8C23×C10712yes—
482C22×C8C23×C10712yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C10714yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C10712yes—
506C2×C4⋊C4C23×C10712yes—
507C2×C4⋊C4C23×C10711yescharacteristic
508C2×C4⋊C4C23×C10711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C10711yescharacteristic
537C24C2×D4×C10711yescharacteristic
538C24C2×D4×C10711yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C10712yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C10712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
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—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C10711yescharacteristic
604C22×C4C2×D4×C10711yescharacteristic
605C22×C4C2×D4×C10711yescharacteristic
606C22×C4C2×D4×C10712yes—
607C22×C4C2×D4×C10712yes—
608C22×C4C2×D4×C10712yes—
609C22×C4#41×C10712yes—
610C22×C4#41×C10712yes—
611C22×C4#41×C10712yes—
612C22×C4C24×C10711yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C10714yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C10712yes—
632C4⋊C4C2×D4×C10712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C10712yes—
672C23#121×C10712yes—
673C23#123×C10712yes—
674C23AGL(1,ℤ/8)×C10712yes—
675C23#137×C10712yes—
676C23C22×D4×C10711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C10712yes—
724C2×C4#121×C10712yes—
725C2×C4#121×C10714yes—
726C2×C4#121×C10714yes—
727C2×C4#123×C10712yes—
728C2×C4#123×C10714yes—
729C2×C4#124×C10714yes—
730C2×C4C22×D4×C10711yescharacteristic
731C2×C4C22×D4×C10711yescharacteristic
732C2×C4C22×D4×C10711yescharacteristic
733C2×C4C2×#41×C10711yescharacteristic
734C2×C4C2×#41×C10711yescharacteristic
735C2×C4C2×#41×C10711yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C10714yes—
767C22C2×#120×C10711yescharacteristic
768C22C2×#121×C10711yescharacteristic
769C22C2×#123×C10711yescharacteristic
770C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
771C22C2×#137×C10711yescharacteristic
772C22#575×C10711yescharacteristic
773C22#575×C10711yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C10714yes—
782C4C2×#121×C10711yescharacteristic
783C4C2×#121×C10711yescharacteristic
784C4C2×#123×C10711yescharacteristic
785C4C2×#124×C10711yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C10711yescharacteristic
791C2C107×#300611yescharacteristic
792C2C107×#300711yescharacteristic
793C2C107×#305511yescharacteristic
794C2C107×#305611yescharacteristic
795C2C107×#309211yescharacteristic
796C2C107×#309311yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#525×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C107C2semidirect
3. C2×#417×C107C2semidirect
4. C2×#417×C107C2semidirect
5. C2×#407×C107C2semidirect
6. C2×#380×C107C2semidirect
7. C107×#2036C2semidirect
8. C107×#2035C2semidirect
9. C107×#2034C2semidirect
10. C107×#2033C2semidirect
11. C107×#1736C2semidirect
31. C2×#107×C107C22semidirect
32. C2×#106×C107C22semidirect
35. C2×#103×C107C22semidirect
36. C2×#103×C107C22semidirect
37. C2×#102×C107C22semidirect
38. C2×#102×C107C22semidirect
47. #340×C107C22semidirect
48. #340×C107C22semidirect
81. C2×M16×C107D4semidirect
387. #23482C107direct (N × H)
400. C2×#428C2×C107semidirect
401. C2×#417C2×C107semidirect
402. C2×#417C2×C107semidirect
403. C2×#407C2×C107semidirect
404. C2×#380C2×C107semidirect
405. #2036C2×C107semidirect
406. #2035C2×C107semidirect
407. #2034C2×C107semidirect
408. #2033C2×C107semidirect
409. #1736C2×C107semidirect
410. C107#23482direct (N × H)
430. C2×#107C22×C107semidirect
431. C2×#106C22×C107semidirect
434. C2×#103C22×C107semidirect
435. C2×#103C22×C107semidirect
436. C2×#102C22×C107semidirect
437. C2×#102C22×C107semidirect
446. #340C22×C107semidirect
447. #340C22×C107semidirect
480. C2×M16D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1072
C2×#428×C1072
C2×#417×C1072
C2×#407×C1072
C2×#380×C1072
C107×#20362
C107×#20352
C107×#20342
C107×#20332
C107×#17362
#23482107