Finite Group Databasebeta

← C107×#10745 #41036709

Subgroups — C107×#10745 #41036709

Order 27392.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C107C211yesmaximal, characteristic
2C22×#99×C107C211yesmaximal, characteristic
3C2×#386×C107C211yesmaximal, characteristic
4C2×#342×C107C212yesmaximal, complemented
5C107×C22⋊#95C212yesmaximal, complemented
6C23×D4×C107C2211yescharacteristic
7C24×C4×C107C2211yescharacteristic
8#518×C107—22no—
9#518×C107—24no—
10#518×C107C414yescomplemented
11C2×C4×D4×C107—24no—
12C2×#117×C107—21no—
13C22×C22⋊C4×C107—21no—
14C22×C22⋊C4×C107—21no—
15C22×C22⋊C4×C107C2212yes—
16C22×C22⋊C4×C107C2211yescharacteristic
17C22×C22⋊C4×C107C2212yes—
18C2×#99×C107—22no—
19C2×#99×C107—22no—
20C2×#99×C107C414yescomplemented
21#386×C107—22no—
22#386×C107C414yescomplemented
23C2×#95×C107—21no—
24C2×#95×C107—24no—
25#342×C107—24no—
26C25×C107D411yescharacteristic
27C25×C107C2311yescharacteristic
28C22×D4×C107—22no—
29C22×D4×C107—22no—
30C22×D4×C107—22no—
31C22×D4×C107—22no—
32C22×D4×C107C2×C412yes—
33C22×D4×C107C2×C412yes—
34C22×D4×C107C2×C412yes—
35C22×D4×C107D412yes—
36C22×D4×C107D412yes—
37C22×D4×C107Q812yes—
38C23×C4×C107—22no—
39C23×C4×C107—21no—
40C23×C4×C107—22no—
41C23×C4×C107—22no—
42C23×C4×C107—21no—
43C23×C4×C107—21no—
44C23×C4×C107—22no—
45C23×C4×C107—44no—
46C23×C4×C107C2×C412yescomplemented
47C23×C4×C107D411yescharacteristic
48C23×C4×C107D414yes—
49C4×D4×C107—216no—
50C4×D4×C107—216no—
51#117×C107—24no—
52#117×C107—24no—
53C2×C4⋊C4×C107—22no—
54C2×C22⋊C4×C107—22no—
55C2×C22⋊C4×C107—24no—
56C2×C22⋊C4×C107—24no—
57C2×C22⋊C4×C107—22no—
58C2×C22⋊C4×C107—22no—
59C2×C22⋊C4×C107—22no—
60C2×C22⋊C4×C107—22no—
61C2×C22⋊C4×C107—22no—
62C2×C22⋊C4×C107—22no—
63C2×C22⋊C4×C107—22no—
64C2×C22⋊C4×C107—22no—
65C2×C22⋊C4×C107—22no—
66C2×C22⋊C4×C107—22no—
67C2×C22⋊C4×C107—24no—
68C2×C22⋊C4×C107—21no—
69C2×C22⋊C4×C107—22no—
70C2×C22⋊C4×C107—44no—
71C2×C22⋊C4×C107C2×C414yes—
72C2×C22⋊C4×C107C2×C412yescomplemented
73C2×C22⋊C4×C107C2×C414yescomplemented
74C2×C22⋊C4×C107D414yes—
75C2×C42×C107—22no—
76#99×C107—28no—
77#95×C107—24no—
78#95×C107—48no—
79C24×C107—21no—
80C24×C107—21no—
81C24×C107—21no—
82C24×C107—21no—
83C24×C107—42no—
84C24×C107—42no—
85C24×C107—42no—
86C24×C107—42no—
87C24×C107C22⋊C412yes—
88C24×C107C22⋊C412yes—
89C24×C107C4⋊C412yes—
90C24×C107C22×C411yescharacteristic
91C24×C107C22×C411yescharacteristic
92C24×C107C22×C411yescharacteristic
93C24×C107C2×D411yescharacteristic
94C24×C107C2×D412yes—
95C24×C107C2×D411yescharacteristic
96C24×C107C2×D411yescharacteristic
97C24×C107C2×D412yes—
98C24×C107C2×Q811yescharacteristic
99C24×C107#4112yes—
100C24×C107#4112yes—
101C2×D4×C107—24no—
102C2×D4×C107—24no—
103C2×D4×C107—24no—
104C2×D4×C107—24no—
105C2×D4×C107—24no—
106C2×D4×C107—24no—
107C2×D4×C107—24no—
108C2×D4×C107—24no—
109C2×D4×C107—24no—
110C2×D4×C107—24no—
111C2×D4×C107—24no—
112C2×D4×C107—24no—
113C2×D4×C107C4214yes—
114C2×D4×C107C22⋊C414yes—
115C2×D4×C107C4⋊C414yes—
116C2×D4×C107C4⋊C414yes—
117C22×C4×C107—21no—
118C22×C4×C107—21no—
119C22×C4×C107—21no—
120C22×C4×C107—21no—
121C22×C4×C107—28no—
122C22×C4×C107—24no—
123C22×C4×C107—22no—
124C22×C4×C107—24no—
125C22×C4×C107—24no—
126C22×C4×C107—28no—
127C22×C4×C107—24no—
128C22×C4×C107—22no—
129C22×C4×C107—24no—
130C22×C4×C107—44no—
131C22×C4×C107—44no—
132C22×C4×C107—48no—
133C22×C4×C107—44no—
134C22×C4×C107—42no—
135C22×C4×C107—41no—
136C22×C4×C107—42no—
137C22×C4×C107—41no—
138C22×C4×C107—44no—
139C22×C4×C107—44no—
140C22×C4×C107—44no—
141C22×C4×C107—42no—
142C22×C4×C107—44no—
143C22×C4×C107—42no—
144C22×C4×C107—41no—
145C22×C4×C107—42no—
146C22×C4×C107—42no—
147C22×C4×C107—41no—
148C22×C4×C107—82no—
149C22×C4×C107—82no—
150C22×C4×C107C22⋊C412yes—
151C22×C4×C107C22⋊C412yes—
152C22×C4×C107C22⋊C418yescomplemented
153C22×C4×C107C4⋊C412yes—
154C4⋊C4×C107—28no—
155C22⋊C4×C107—28no—
156C22⋊C4×C107—24no—
157C22⋊C4×C107—24no—
158C22⋊C4×C107—24no—
159C22⋊C4×C107—24no—
160C22⋊C4×C107—24no—
161C22⋊C4×C107—24no—
162C22⋊C4×C107—24no—
163C22⋊C4×C107—48no—
164C22⋊C4×C107—42no—
165C22⋊C4×C107—42no—
166C22⋊C4×C107—42no—
167C42×C107—28no—
168C23×C107—24no—
169C23×C107—22no—
170C23×C107—24no—
171C23×C107—22no—
172C23×C107—22no—
173C23×C107—22no—
174C23×C107—22no—
175C23×C107—22no—
176C23×C107—22no—
177C23×C107—22no—
178C23×C107—41no—
179C23×C107—41no—
180C23×C107—42no—
181C23×C107—42no—
182C23×C107—41no—
183C23×C107—42no—
184C23×C107—41no—
185C23×C107—44no—
186C23×C107—42no—
187C23×C107—42no—
188C23×C107—44no—
189C23×C107—42no—
190C23×C107—42no—
191C23×C107—42no—
192C23×C107—44no—
193C23×C107—44no—
194C23×C107—42no—
195C23×C107—42no—
196C23×C107—82no—
197C23×C107—81no—
198C23×C107—81no—
199C23×C107—82no—
200C23×C107#9514yescomplemented
201C23×C107C2×C4211yescharacteristic
202C23×C107C2×C22⋊C411yescharacteristic
203C23×C107C2×C22⋊C411yescharacteristic
204C23×C107C2×C22⋊C412yes—
205C23×C107C2×C22⋊C411yescharacteristic
206C23×C107C2×C4⋊C411yescharacteristic
207C23×C107C2×C4⋊C411yescharacteristic
208C23×C107C2×C4⋊C411yescharacteristic
209C23×C107#11712yes—
210C23×C107C4×D412yes—
211C23×C107C4×D412yes—
212C23×C107C4×D412yes—
213C23×C107C4×D412yes—
214C23×C107#12011yescharacteristic
215C23×C107#12012yes—
216C23×C107#12011yescharacteristic
217C23×C107#12112yes—
218C23×C107#12112yes—
219C23×C107C22⋊Q812yes—
220C23×C107C22⋊Q812yes—
221C23×C107#12311yescharacteristic
222C23×C107#12311yescharacteristic
223C23×C107#12312yes—
224D4×C107—28no—
225D4×C107—28no—
226D4×C107—28no—
227D4×C107—28no—
228C2×C4×C107—22no—
229C2×C4×C107—22no—
230C2×C4×C107—22no—
231C2×C4×C107—22no—
232C2×C4×C107—22no—
233C2×C4×C107—22no—
234C2×C4×C107—24no—
235C2×C4×C107—28no—
236C2×C4×C107—28no—
237C2×C4×C107—42no—
238C2×C4×C107—44no—
239C2×C4×C107—48no—
240C2×C4×C107—44no—
241C2×C4×C107—42no—
242C2×C4×C107—44no—
243C2×C4×C107—44no—
244C2×C4×C107—44no—
245C2×C4×C107—48no—
246C2×C4×C107—42no—
247C2×C4×C107—48no—
248C2×C4×C107—42no—
249C2×C4×C107—42no—
250C2×C4×C107—44no—
251C2×C4×C107—84no—
252C2×C4×C107—88no—
253C2×C4×C107—82no—
254C2×C4×C107—82no—
255C2×C4×C107—82no—
256C2×C4×C107—84no—
257C2×C4×C107—82no—
258C2×C4×C107#9514yescomplemented
259C22×C107—24no—
260C22×C107—22no—
261C22×C107—22no—
262C22×C107—24no—
263C22×C107—21no—
264C22×C107—22no—
265C22×C107—22no—
266C22×C107—21no—
267C22×C107—21no—
268C22×C107—22no—
269C22×C107—21no—
270C22×C107—22no—
271C22×C107—24no—
272C22×C107—24no—
273C22×C107—22no—
274C22×C107—22no—
275C22×C107—24no—
276C22×C107—41no—
277C22×C107—41no—
278C22×C107—41no—
279C22×C107—41no—
280C22×C107—42no—
281C22×C107—42no—
282C22×C107—42no—
283C22×C107—42no—
284C22×C107—42no—
285C22×C107—42no—
286C22×C107—44no—
287C22×C107—44no—
288C22×C107—42no—
289C22×C107—42no—
290C22×C107—44no—
291C22×C107—82no—
292C22×C107—82no—
293C22×C107—82no—
294C22×C107C2×#9511yescharacteristic
295C22×C107C4×C22⋊C412yes—
296C22×C107#37911yescharacteristic
297C22×C107#38012yes—
298C22×C107#38111yescharacteristic
299C22×C107#38511yescharacteristic
300C22×C107#38512yes—
301C22×C107#38511yescharacteristic
302C22×C107#38611yescharacteristic
303C22×C107#38612yes—
304C22×C107#38611yescharacteristic
305C22×C107B(4,𝔽2)12yes—
306C22×C107#45812yes—
307C4×C107—24no—
308C4×C107—44no—
309C4×C107—48no—
310C4×C107—82no—
311C4×C107—84no—
312#10745C10711yesmaximal, characteristic, direct product factor, Sylow
313C2×C107—21no—
314C2×C107—22no—
315C2×C107—21no—
316C2×C107—21no—
317C2×C107—21no—
318C2×C107—22no—
319C2×C107—22no—
320C2×C107—22no—
321C2×C107—44no—
322C2×C107C22⋊#9511yescharacteristic
323C2×C107#179012yes—
324C2×C107#186712yes—
325C2×C107#188911yescharacteristic
326C2×C107#189011yescharacteristic
327C2×#518C2×C10711yescharacteristic
328C22×#99C2×C10711yescharacteristic
329C2×#386C2×C10711yescharacteristic
330C2×#342C2×C10712yescomplemented
331C22⋊#95C2×C10712yescomplemented
332C107#1074511yescharacteristic, direct product factor, Sylow
333C23×D4C22×C10711yescharacteristic
334C24×C4C22×C10711yescharacteristic
335#518—22no—
336#518—24no—
337#518C4×C10714yescomplemented
338C2×C4×D4—24no—
339C2×#117—21no—
340C22×C22⋊C4—21no—
341C22×C22⋊C4—21no—
342C22×C22⋊C4C22×C10712yes—
343C22×C22⋊C4C22×C10711yescharacteristic
344C22×C22⋊C4C22×C10712yes—
345C2×#99—22no—
346C2×#99—22no—
347C2×#99C4×C10714yescomplemented
348#386—22no—
349#386C4×C10714yescomplemented
350C2×#95—21no—
351C2×#95—24no—
352#342—24no—
353C25D4×C10711yescharacteristic
354C25C23×C10711yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C10712yes—
360C22×D4C2×C4×C10712yes—
361C22×D4C2×C4×C10712yes—
362C22×D4D4×C10712yes—
363C22×D4D4×C10712yes—
364C22×D4Q8×C10712yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—44no—
373C23×C4C2×C4×C10712yescomplemented
374C23×C4D4×C10711yescharacteristic
375C23×C4D4×C10714yes—
376C4×D4—216no—
377C4×D4—216no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×C4×C10714yes—
399C2×C22⋊C4C2×C4×C10712yescomplemented
400C2×C22⋊C4C2×C4×C10714yescomplemented
401C2×C22⋊C4D4×C10714yes—
402C2×C42—22no—
403#99—28no—
404#95—24no—
405#95—48no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C10712yes—
415C24C22⋊C4×C10712yes—
416C24C4⋊C4×C10712yes—
417C24C22×C4×C10711yescharacteristic
418C24C22×C4×C10711yescharacteristic
419C24C22×C4×C10711yescharacteristic
420C24C2×D4×C10711yescharacteristic
421C24C2×D4×C10712yes—
422C24C2×D4×C10711yescharacteristic
423C24C2×D4×C10711yescharacteristic
424C24C2×D4×C10712yes—
425C24C2×Q8×C10711yescharacteristic
426C24#41×C10712yes—
427C24#41×C10712yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C10714yes—
441C2×D4C22⋊C4×C10714yes—
442C2×D4C4⋊C4×C10714yes—
443C2×D4C4⋊C4×C10714yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C10712yes—
478C22×C4C22⋊C4×C10712yes—
479C22×C4C22⋊C4×C10718yescomplemented
480C22×C4C4⋊C4×C10712yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—44no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—81no—
525C23—81no—
526C23—82no—
527C23#95×C10714yescomplemented
528C23C2×C42×C10711yescharacteristic
529C23C2×C22⋊C4×C10711yescharacteristic
530C23C2×C22⋊C4×C10711yescharacteristic
531C23C2×C22⋊C4×C10712yes—
532C23C2×C22⋊C4×C10711yescharacteristic
533C23C2×C4⋊C4×C10711yescharacteristic
534C23C2×C4⋊C4×C10711yescharacteristic
535C23C2×C4⋊C4×C10711yescharacteristic
536C23#117×C10712yes—
537C23C4×D4×C10712yes—
538C23C4×D4×C10712yes—
539C23C4×D4×C10712yes—
540C23C4×D4×C10712yes—
541C23#120×C10711yescharacteristic
542C23#120×C10712yes—
543C23#120×C10711yescharacteristic
544C23#121×C10712yes—
545C23#121×C10712yes—
546C23C22⋊Q8×C10712yes—
547C23C22⋊Q8×C10712yes—
548C23#123×C10711yescharacteristic
549C23#123×C10711yescharacteristic
550C23#123×C10712yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—84no—
584C2×C4—82no—
585C2×C4#95×C10714yescomplemented
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—21no—
591C22—22no—
592C22—22no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—22no—
598C22—24no—
599C22—24no—
600C22—22no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—44no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×#95×C10711yescharacteristic
622C22C4×C22⋊C4×C10712yes—
623C22#379×C10711yescharacteristic
624C22#380×C10712yes—
625C22#381×C10711yescharacteristic
626C22#385×C10711yescharacteristic
627C22#385×C10712yes—
628C22#385×C10711yescharacteristic
629C22#386×C10711yescharacteristic
630C22#386×C10712yes—
631C22#386×C10711yescharacteristic
632C22B(4,𝔽2)×C10712yes—
633C22#458×C10712yes—
634C4—24no—
635C4—44no—
636C4—48no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C107×C22⋊#9511yescharacteristic
649C2C107×#179012yes—
650C2C107×#186712yes—
651C2C107×#188911yescharacteristic
652C2C107×#189011yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutatorC23C2×C42×C107
Frattini, cosocleC25C23×C107
prime radicalC23×D4×C107C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#342×C107C2semidirect
5. C107×C22⋊#95C2semidirect
10. #518×C107C4semidirect
20. C2×#99×C107C4semidirect
22. #386×C107C4semidirect
46. C23×C4×C107C2×C4semidirect
72. C2×C22⋊C4×C107C2×C4semidirect
73. C2×C22⋊C4×C107C2×C4semidirect
152. C22×C4×C107C22⋊C4semidirect
200. C23×C107#95semidirect
258. C2×C4×C107#95semidirect
312. #10745C107direct (N × H)
330. C2×#342C2×C107semidirect
331. C22⋊#95C2×C107semidirect
332. C107#10745direct (N × H)
337. #518C4×C107semidirect
347. C2×#99C4×C107semidirect
349. #386C4×C107semidirect
373. C23×C4C2×C4×C107semidirect
399. C2×C22⋊C4C2×C4×C107semidirect
400. C2×C22⋊C4C2×C4×C107semidirect
479. C22×C4C22⋊C4×C107semidirect
527. C23#95×C107semidirect
585. C2×C4#95×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1072
C22×#99×C1072
C2×#386×C1072
C2×#342×C1072
C107×C22⋊#952
#10745107