Finite Group Databasebeta

← C107×#13877 #41039841

Subgroups — C107×#13877 #41039841

Order 27392.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C107C211yesmaximal, characteristic
2C23×C22⋊C4×C107C211yesmaximal, characteristic
3C2×#385×C107C212yesmaximal, complemented
4C2×#380×C107C212yesmaximal, complemented
5C2×#379×C107C211yesmaximal, characteristic
6C107×#1439C214yesmaximal, complemented
7C107×C22⋊#95C212yesmaximal, complemented
8C107×C22⋊#95C212yesmaximal, complemented
9C26×C107C2211yescharacteristic
10C24×C4×C107C2212yes—
11C24×C4×C107C2212yes—
12C22×C4⋊C4×C107C2214yescomplemented
13C22×C22⋊C4×C107—24no—
14C22×C22⋊C4×C107—28no—
15C22×C22⋊C4×C107—28no—
16C22×C22⋊C4×C107C418yescomplemented
17C22×C22⋊C4×C107C2212yes—
18C22×C22⋊C4×C107C2211yescharacteristic
19C22×C22⋊C4×C107C2212yes—
20C22×C22⋊C4×C107C2211yescharacteristic
21C22×C22⋊C4×C107C2211yescharacteristic
22C22×C22⋊C4×C107C2212yes—
23C22×C22⋊C4×C107C2212yes—
24C22×C22⋊C4×C107C2212yes—
25C22×C22⋊C4×C107C2211yescharacteristic
26#385×C107—28no—
27#380×C107—28no—
28#379×C107—24no—
29C2×#95×C107C2214yescomplemented
30C2×#95×C107C2214yescomplemented
31C2×#95×C107C2214yescomplemented
32C25×C107—24no—
33C25×C107—24no—
34C25×C107—24no—
35C25×C107—24no—
36C25×C107—44no—
37C25×C107C2×C414yes—
38C25×C107D414yes—
39C25×C107Q814yes—
40C25×C107C2311yescharacteristic
41C25×C107C2311yescharacteristic
42C25×C107C2311yescharacteristic
43C23×C4×C107—24no—
44C23×C4×C107—24no—
45C23×C4×C107—24no—
46C23×C4×C107—28no—
47C23×C4×C107—28no—
48C23×C4×C107—24no—
49C23×C4×C107—24no—
50C23×C4×C107—44no—
51C23×C4×C107—44no—
52C23×C4×C107C2×C418yescomplemented
53C23×C4×C107C2312yes—
54C23×C4×C107C2312yes—
55C23×C4×C107C2312yes—
56C23×C4×C107C2314yes—
57C23×C4×C107C2312yes—
58C2×C4⋊C4×C107—28no—
59C2×C4⋊C4×C107—28no—
60C2×C4⋊C4×C107—44no—
61C2×C22⋊C4×C107—232no—
62C2×C22⋊C4×C107—24no—
63C2×C22⋊C4×C107—24no—
64C2×C22⋊C4×C107—24no—
65C2×C22⋊C4×C107—24no—
66C2×C22⋊C4×C107—28no—
67C2×C22⋊C4×C107—28no—
68C2×C22⋊C4×C107—232no—
69C2×C22⋊C4×C107—24no—
70C2×C22⋊C4×C107—22no—
71C2×C22⋊C4×C107—24no—
72C2×C22⋊C4×C107—22no—
73C2×C22⋊C4×C107—24no—
74C2×C22⋊C4×C107—24no—
75C2×C22⋊C4×C107—24no—
76C2×C22⋊C4×C107—24no—
77C2×C22⋊C4×C107—44no—
78C2×C22⋊C4×C107C2×C414yes—
79C2×C22⋊C4×C107C2×C414yes—
80C2×C22⋊C4×C107C2×C418yescomplemented
81C2×C22⋊C4×C107D418yes—
82C2×C22⋊C4×C107D418yes—
83#95×C107—28no—
84#95×C107—28no—
85#95×C107—44no—
86C24×C107—22no—
87C24×C107—22no—
88C24×C107—22no—
89C24×C107—22no—
90C24×C107—24no—
91C24×C107—24no—
92C24×C107—28no—
93C24×C107—28no—
94C24×C107—216no—
95C24×C107—28no—
96C24×C107—216no—
97C24×C107—216no—
98C24×C107—216no—
99C24×C107—28no—
100C24×C107—22no—
101C24×C107—22no—
102C24×C107—22no—
103C24×C107—22no—
104C24×C107—24no—
105C24×C107—48no—
106C24×C107—48no—
107C24×C107—48no—
108C24×C107—416no—
109C24×C107—416no—
110C24×C107—416no—
111C24×C107—416no—
112C24×C107C4⋊C4116yescomplemented
113C24×C107C22×C412yes—
114C24×C107C22×C412yes—
115C24×C107C22×C412yes—
116C24×C107C2×D412yes—
117C24×C107C2×D414yes—
118C24×C107C2×D412yes—
119C24×C107C2×D412yes—
120C24×C107C2×D414yes—
121C24×C107C2×Q812yes—
122C24×C107C2×Q812yes—
123C24×C107C2×Q812yes—
124C24×C107#4114yes—
125C24×C107#4114yes—
126C24×C107C2411yescharacteristic
127C22×C4×C107—22no—
128C22×C4×C107—22no—
129C22×C4×C107—24no—
130C22×C4×C107—216no—
131C22×C4×C107—216no—
132C22×C4×C107—22no—
133C22×C4×C107—24no—
134C22×C4×C107—24no—
135C22×C4×C107—24no—
136C22×C4×C107—24no—
137C22×C4×C107—22no—
138C22×C4×C107—24no—
139C22×C4×C107—24no—
140C22×C4×C107—24no—
141C22×C4×C107—24no—
142C22×C4×C107—216no—
143C22×C4×C107—22no—
144C22×C4×C107—24no—
145C22×C4×C107—22no—
146C22×C4×C107—22no—
147C22×C4×C107—22no—
148C22×C4×C107—22no—
149C22×C4×C107—22no—
150C22×C4×C107—24no—
151C22×C4×C107—24no—
152C22×C4×C107—24no—
153C22×C4×C107—48no—
154C22×C4×C107—416no—
155C22×C4×C107—416no—
156C22×C4×C107—416no—
157C22×C4×C107—416no—
158C22×C4×C107—48no—
159C22×C4×C107—48no—
160C22×C4×C107C22×C414yes—
161C22×C4×C107C22×C414yes—
162C22×C4×C107C2×D418yes—
163C22×C4×C107C2×D418yes—
164C4⋊C4×C107—416no—
165C22⋊C4×C107—216no—
166C22⋊C4×C107—28no—
167C22⋊C4×C107—216no—
168C22⋊C4×C107—216no—
169C22⋊C4×C107—48no—
170C22⋊C4×C107—44no—
171C22⋊C4×C107—48no—
172C22⋊C4×C107—44no—
173C22⋊C4×C107C22⋊C4116yescomplemented
174C23×C107—22no—
175C23×C107—22no—
176C23×C107—24no—
177C23×C107—24no—
178C23×C107—24no—
179C23×C107—22no—
180C23×C107—24no—
181C23×C107—24no—
182C23×C107—24no—
183C23×C107—22no—
184C23×C107—24no—
185C23×C107—24no—
186C23×C107—24no—
187C23×C107—24no—
188C23×C107—28no—
189C23×C107—28no—
190C23×C107—28no—
191C23×C107—28no—
192C23×C107—28no—
193C23×C107—28no—
194C23×C107—28no—
195C23×C107—28no—
196C23×C107—22no—
197C23×C107—22no—
198C23×C107—24no—
199C23×C107—24no—
200C23×C107—22no—
201C23×C107—24no—
202C23×C107—24no—
203C23×C107—24no—
204C23×C107—22no—
205C23×C107—24no—
206C23×C107—24no—
207C23×C107—232no—
208C23×C107—232no—
209C23×C107—416no—
210C23×C107—432no—
211C23×C107—432no—
212C23×C107—432no—
213C23×C107—432no—
214C23×C107—464no—
215C23×C107—44no—
216C23×C107—44no—
217C23×C107—44no—
218C23×C107—44no—
219C23×C107C2×C22⋊C414yes—
220C23×C107C2×C4⋊C414yes—
221C23×C107C2×C4⋊C414yes—
222C23×C107C2×C4⋊C414yes—
223C23×C107#11714yes—
224C23×C107C4×D418yes—
225C23×C107#12014yes—
226C23×C107#12118yes—
227C23×C107C22⋊Q818yes—
228C23×C107C22⋊Q818yes—
229C23×C107#12314yes—
230C23×C107C23×C411yescharacteristic
231C23×C107C22×D412yes—
232C23×C107C22×D411yescharacteristic
233C23×C107C22×D412yes—
234C23×C107C22×Q811yescharacteristic
235C23×C107C2×#4112yes—
236C23×C107C2×#4112yes—
237C23×C107H(5,𝔽2)14yes—
238C2×C4×C107—24no—
239C2×C4×C107—24no—
240C2×C4×C107—28no—
241C2×C4×C107—28no—
242C2×C4×C107—24no—
243C2×C4×C107—24no—
244C2×C4×C107—24no—
245C2×C4×C107—28no—
246C2×C4×C107—28no—
247C2×C4×C107—28no—
248C2×C4×C107—432no—
249C2×C4×C107—432no—
250C2×C4×C107—44no—
251C2×C4×C107—44no—
252C2×C4×C107—44no—
253C2×C4×C107—44no—
254C2×C4×C107—44no—
255C2×C4×C107—44no—
256C2×C4×C107—42no—
257C2×C4×C107—42no—
258C2×C4×C107—42no—
259C2×C4×C107—42no—
260C2×C4×C107—42no—
261C2×C4×C107—42no—
262C2×C4×C107—44no—
263C2×C4×C107—44no—
264C2×C4×C107—44no—
265C2×C4×C107—44no—
266C2×C4×C107C2×C22⋊C418yescomplemented
267C22×C107—24no—
268C22×C107—24no—
269C22×C107—28no—
270C22×C107—28no—
271C22×C107—28no—
272C22×C107—28no—
273C22×C107—28no—
274C22×C107—28no—
275C22×C107—28no—
276C22×C107—28no—
277C22×C107—216no—
278C22×C107—216no—
279C22×C107—24no—
280C22×C107—24no—
281C22×C107—24no—
282C22×C107—24no—
283C22×C107—24no—
284C22×C107—464no—
285C22×C107—44no—
286C22×C107—44no—
287C22×C107—44no—
288C22×C107—44no—
289C22×C107—48no—
290C22×C107#38018yescomplemented
291C22×C107#38518yescomplemented
292C22×C107C22×C22⋊C411yescharacteristic
293C22×C107C22×C4⋊C411yescharacteristic
294C22×C107C2×#11711yescharacteristic
295C22×C107C2×C4×D412yes—
296C22×C107#51812yes—
297C22×C107C2×#12011yescharacteristic
298C22×C107C2×#12112yes—
299C22×C107C2×C22⋊Q812yes—
300C22×C107C2×C22⋊Q812yes—
301C22×C107C2×#12311yescharacteristic
302C22×C107#53412yes—
303C22×C107#54312yes—
304C22×C107D4214yes—
305C22×C107#54614yes—
306C22×C107#54614yes—
307C22×C107#55114yes—
308C4×C107—28no—
309C4×C107—44no—
310C4×C107—48no—
311C4×C107—82no—
312C4×C107—82no—
313#13877C10711yesmaximal, characteristic, direct product factor, Sylow
314C2×C107—28no—
315C2×C107—28no—
316C2×C107—44no—
317C2×C107C2×#38011yescharacteristic
318C2×C107C2×#38511yescharacteristic
319C2×C107#231511yescharacteristic
320C2×C107D4×C22⋊C412yes—
321C2×C107#234212yes—
322C2×C107#241012yes—
323C2×C107#241212yes—
324C2×C107#243714yes—
325C23×C22⋊C4C2×C10711yescharacteristic
326C23×C22⋊C4C2×C10711yescharacteristic
327C2×#385C2×C10712yescomplemented
328C2×#380C2×C10712yescomplemented
329C2×#379C2×C10711yescharacteristic
330#1439C2×C10714yescomplemented
331C22⋊#95C2×C10712yescomplemented
332C22⋊#95C2×C10712yescomplemented
333C107#1387711yescharacteristic, direct product factor, Sylow
334C26C22×C10711yescharacteristic
335C24×C4C22×C10712yes—
336C24×C4C22×C10712yes—
337C22×C4⋊C4C22×C10714yescomplemented
338C22×C22⋊C4—24no—
339C22×C22⋊C4—28no—
340C22×C22⋊C4—28no—
341C22×C22⋊C4C4×C10718yescomplemented
342C22×C22⋊C4C22×C10712yes—
343C22×C22⋊C4C22×C10711yescharacteristic
344C22×C22⋊C4C22×C10712yes—
345C22×C22⋊C4C22×C10711yescharacteristic
346C22×C22⋊C4C22×C10711yescharacteristic
347C22×C22⋊C4C22×C10712yes—
348C22×C22⋊C4C22×C10712yes—
349C22×C22⋊C4C22×C10712yes—
350C22×C22⋊C4C22×C10711yescharacteristic
351#385—28no—
352#380—28no—
353#379—24no—
354C2×#95C22×C10714yescomplemented
355C2×#95C22×C10714yescomplemented
356C2×#95C22×C10714yescomplemented
357C25—24no—
358C25—24no—
359C25—24no—
360C25—24no—
361C25—44no—
362C25C2×C4×C10714yes—
363C25D4×C10714yes—
364C25Q8×C10714yes—
365C25C23×C10711yescharacteristic
366C25C23×C10711yescharacteristic
367C25C23×C10711yescharacteristic
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—28no—
372C23×C4—28no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4C2×C4×C10718yescomplemented
378C23×C4C23×C10712yes—
379C23×C4C23×C10712yes—
380C23×C4C23×C10712yes—
381C23×C4C23×C10714yes—
382C23×C4C23×C10712yes—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—44no—
386C2×C22⋊C4—232no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—232no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4C2×C4×C10714yes—
404C2×C22⋊C4C2×C4×C10714yes—
405C2×C22⋊C4C2×C4×C10718yescomplemented
406C2×C22⋊C4D4×C10718yes—
407C2×C22⋊C4D4×C10718yes—
408#95—28no—
409#95—28no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—216no—
423C24—216no—
424C24—28no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24—416no—
437C24C4⋊C4×C107116yescomplemented
438C24C22×C4×C10712yes—
439C24C22×C4×C10712yes—
440C24C22×C4×C10712yes—
441C24C2×D4×C10712yes—
442C24C2×D4×C10714yes—
443C24C2×D4×C10712yes—
444C24C2×D4×C10712yes—
445C24C2×D4×C10714yes—
446C24C2×Q8×C10712yes—
447C24C2×Q8×C10712yes—
448C24C2×Q8×C10712yes—
449C24#41×C10714yes—
450C24#41×C10714yes—
451C24C24×C10711yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—216no—
456C22×C4—216no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—416no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—416no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4C22×C4×C10714yes—
486C22×C4C22×C4×C10714yes—
487C22×C4C2×D4×C10718yes—
488C22×C4C2×D4×C10718yes—
489C4⋊C4—416no—
490C22⋊C4—216no—
491C22⋊C4—28no—
492C22⋊C4—216no—
493C22⋊C4—216no—
494C22⋊C4—48no—
495C22⋊C4—44no—
496C22⋊C4—48no—
497C22⋊C4—44no—
498C22⋊C4C22⋊C4×C107116yescomplemented
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—22no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—232no—
522C23—232no—
523C23—22no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—22no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—22no—
532C23—24no—
533C23—24no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—464no—
538C23—432no—
539C23—432no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23C2×C22⋊C4×C10714yes—
545C23C2×C4⋊C4×C10714yes—
546C23C2×C4⋊C4×C10714yes—
547C23C2×C4⋊C4×C10714yes—
548C23#117×C10714yes—
549C23C4×D4×C10718yes—
550C23#120×C10714yes—
551C23#121×C10718yes—
552C23C22⋊Q8×C10718yes—
553C23C22⋊Q8×C10718yes—
554C23#123×C10714yes—
555C23C23×C4×C10711yescharacteristic
556C23C22×D4×C10712yes—
557C23C22×D4×C10711yescharacteristic
558C23C22×D4×C10712yes—
559C23C22×Q8×C10711yescharacteristic
560C23C2×#41×C10712yes—
561C23C2×#41×C10712yes—
562C23H(5,𝔽2)×C10714yes—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—28no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4C2×C22⋊C4×C10718yescomplemented
592C22—28no—
593C22—28no—
594C22—28no—
595C22—28no—
596C22—216no—
597C22—216no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—24no—
602C22—28no—
603C22—28no—
604C22—28no—
605C22—28no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—48no—
613C22—44no—
614C22—44no—
615C22#380×C10718yescomplemented
616C22#385×C10718yescomplemented
617C22C22×C22⋊C4×C10711yescharacteristic
618C22C22×C4⋊C4×C10711yescharacteristic
619C22C2×#117×C10711yescharacteristic
620C22C2×C4×D4×C10712yes—
621C22#518×C10712yes—
622C22C2×#120×C10711yescharacteristic
623C22C2×#121×C10712yes—
624C22C2×C22⋊Q8×C10712yes—
625C22C2×C22⋊Q8×C10712yes—
626C22C2×#123×C10711yescharacteristic
627C22#534×C10712yes—
628C22#543×C10712yes—
629C22D42×C10714yes—
630C22#546×C10714yes—
631C22#546×C10714yes—
632C22#551×C10714yes—
633C4—28no—
634C4—48no—
635C4—44no—
636C4—82no—
637C4—82no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#380×C10711yescharacteristic
642C2C2×#385×C10711yescharacteristic
643C2C107×#231511yescharacteristic
644C2D4×C22⋊C4×C10712yes—
645C2C107×#234212yes—
646C2C107×#241012yes—
647C2C107×#241212yes—
648C2C107×#243714yes—
subgroupG/H
center, socleC24×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC24C24×C107
prime radicalC26×C107C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#385×C107C2semidirect
4. C2×#380×C107C2semidirect
6. C107×#1439C2semidirect
7. C107×C22⋊#95C2semidirect
8. C107×C22⋊#95C2semidirect
12. C22×C4⋊C4×C107C22semidirect
16. C22×C22⋊C4×C107C4semidirect
29. C2×#95×C107C22semidirect
30. C2×#95×C107C22semidirect
31. C2×#95×C107C22semidirect
52. C23×C4×C107C2×C4semidirect
80. C2×C22⋊C4×C107C2×C4semidirect
112. C24×C107C4⋊C4semidirect
173. C22⋊C4×C107C22⋊C4semidirect
266. C2×C4×C107C2×C22⋊C4semidirect
290. C22×C107#380semidirect
291. C22×C107#385semidirect
313. #13877C107direct (N × H)
327. C2×#385C2×C107semidirect
328. C2×#380C2×C107semidirect
330. #1439C2×C107semidirect
331. C22⋊#95C2×C107semidirect
332. C22⋊#95C2×C107semidirect
333. C107#13877direct (N × H)
337. C22×C4⋊C4C22×C107semidirect
341. C22×C22⋊C4C4×C107semidirect
354. C2×#95C22×C107semidirect
355. C2×#95C22×C107semidirect
356. C2×#95C22×C107semidirect
377. C23×C4C2×C4×C107semidirect
405. C2×C22⋊C4C2×C4×C107semidirect
437. C24C4⋊C4×C107semidirect
498. C22⋊C4C22⋊C4×C107semidirect
591. C2×C4C2×C22⋊C4×C107semidirect
615. C22#380×C107semidirect
616. C22#385×C107semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1072
C2×#385×C1072
C2×#380×C1072
C2×#379×C1072
C107×#14392
C107×C22⋊#952
#13877107