Finite Group Databasebeta

← C107×#18169 #41044133

Subgroups — C107×#18169 #41044133

Order 27392.

1144 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3490C211yesmaximal, characteristic
2C107×#3092C212yesmaximal, complemented
3C2×#397×C107C211yesmaximal, characteristic, complemented
4C107×#1612C214yesmaximal, complemented
5C107×#1608C212yesmaximal, complemented
6C107×#1607C212yesmaximal, complemented
7C107×#1504C212yesmaximal, complemented
8C107×#1462C211yesmaximal, characteristic, complemented
9#551×C107—22no—
10#551×C107—22no—
11#546×C107—22no—
12#546×C107—22no—
13#543×C107C2211yescharacteristic
14#538×C107—21no—
15#538×C107C2212yes—
16#534×C107C2211yescharacteristic
17#525×C107—21no—
18#525×C107C2212yes—
19C2×#120×C107—21no—
20#518×C107—21no—
21C22×C4⋊C4×C107C2211yescharacteristic, complemented
22C22×C22⋊C4×C107—21no—
23C22×C22⋊C4×C107C2211yescharacteristic
24#484×C107—22no—
25#483×C107C2214yescomplemented
26#481×C107—22no—
27#480×C107C2214yescomplemented
28#428×C107—22no—
29#417×C107—22no—
30#407×C107C2212yescomplemented
31#397×C107—21no—
32#397×C107—21no—
33#397×C107C2212yes—
34#397×C107C2212yescomplemented
35C2×#95×C107—21no—
36C2×#95×C107C2211yescharacteristic, complemented
37#328×C107C2214yescomplemented
38#327×C107C2214yescomplemented
39#323×C107C2212yes—
40#323×C107C2212yescomplemented
41C25×C107D411yescharacteristic
42C2×#41×C107—21no—
43C2×#41×C107D412yes—
44C22×D4×C107—21no—
45C22×D4×C107—21no—
46C22×D4×C107—21no—
47C23×C4×C107—21no—
48C23×C4×C107—21no—
49C23×C4×C107D411yescharacteristic
50C23×C4×C107C2311yescharacteristic
51C2×M16×C107—22no—
52#126×C107—22no—
53#126×C107—22no—
54#124×C107—22no—
55#124×C107—22no—
56#123×C107—22no—
57#123×C107—22no—
58#123×C107—22no—
59#123×C107—22no—
60#123×C107—22no—
61C22⋊Q8×C107—21no—
62C22⋊Q8×C107—22no—
63C22⋊Q8×C107—21no—
64C22⋊Q8×C107—22no—
65C22⋊Q8×C107D412yes—
66C22⋊Q8×C107C2312yes—
67#121×C107—21no—
68#121×C107—22no—
69#121×C107—22no—
70#121×C107—21no—
71#121×C107D412yes—
72#121×C107C2312yes—
73#120×C107—22no—
74#120×C107—22no—
75#120×C107—22no—
76#120×C107—22no—
77#120×C107—22no—
78C4×D4×C107—22no—
79C4×D4×C107—22no—
80C4×D4×C107—22no—
81C4×D4×C107—22no—
82C4×D4×C107—22no—
83C4×D4×C107—22no—
84#117×C107—22no—
85#117×C107—21no—
86#117×C107D412yes—
87C2×C4⋊C4×C107—22no—
88C2×C4⋊C4×C107—22no—
89C2×C4⋊C4×C107—21no—
90C2×C4⋊C4×C107C2312yes—
91C2×C22⋊C4×C107—22no—
92C2×C22⋊C4×C107—21no—
93C2×C22⋊C4×C107—21no—
94C2×C22⋊C4×C107—21no—
95C2×C22⋊C4×C107—22no—
96C2×C22⋊C4×C107—22no—
97C2×C22⋊C4×C107—22no—
98C2×C22⋊C4×C107—22no—
99C2×C22⋊C4×C107—44no—
100C2×C22⋊C4×C107D411yescharacteristic
101C2×C22⋊C4×C107D411yescharacteristic
102C2×C22⋊C4×C107C2311yescharacteristic
103C2×C22⋊C4×C107C2311yescharacteristic
104#107×C107—24no—
105#106×C107—24no—
106#103×C107—24no—
107#102×C107—24no—
108C22⋊C8×C107—22no—
109C22⋊C8×C107C2314yes—
110#95×C107—22no—
111#95×C107—22no—
112#95×C107—21no—
113#95×C107C2312yes—
114C24×C107—21no—
115C24×C107—22no—
116C24×C107—21no—
117C24×C107—21no—
118C24×C107—41no—
119C24×C107—42no—
120C24×C107—42no—
121C24×C107C2×D411yescharacteristic
122C24×C107C2×D411yescharacteristic
123C24×C107C2×D411yescharacteristic
124#41×C107—44no—
125#41×C107—82no—
126C2×Q8×C107—21no—
127C2×Q8×C107C2×D412yes—
128C2×D4×C107—22no—
129C2×D4×C107—22no—
130C2×D4×C107—22no—
131C2×D4×C107—22no—
132C2×D4×C107—21no—
133C2×D4×C107—22no—
134C2×D4×C107—22no—
135C2×D4×C107—42no—
136C2×D4×C107—42no—
137C2×D4×C107—82no—
138C2×D4×C107—82no—
139C2×D4×C107C2×D412yes—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—21no—
144C22×C4×C107—22no—
145C22×C4×C107—21no—
146C22×C4×C107—22no—
147C22×C4×C107—22no—
148C22×C4×C107—22no—
149C22×C4×C107—42no—
150C22×C4×C107—42no—
151C22×C4×C107—42no—
152C22×C4×C107—42no—
153C22×C4×C107—42no—
154C22×C4×C107—42no—
155C22×C4×C107—42no—
156C22×C4×C107—41no—
157C22×C4×C107—41no—
158C22×C4×C107C2×D412yes—
159C22×C4×C107C2×D411yescharacteristic
160C22×C4×C107C2×D411yescharacteristic
161C22×C4×C107C2×D411yescharacteristic
162C22×C4×C107C2×D412yes—
163C22×C4×C107C2411yescharacteristic
164M16×C107—44no—
165C2×C8×C107—24no—
166C4⋊C4×C107—22no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—22no—
170C4⋊C4×C107—22no—
171C4⋊C4×C107—22no—
172C4⋊C4×C107—24no—
173C4⋊C4×C107—42no—
174C4⋊C4×C107C2×D412yes—
175C4⋊C4×C107C2×D412yes—
176C22⋊C4×C107—22no—
177C22⋊C4×C107—22no—
178C22⋊C4×C107—22no—
179C22⋊C4×C107—22no—
180C22⋊C4×C107—22no—
181C22⋊C4×C107—22no—
182C22⋊C4×C107—22no—
183C22⋊C4×C107—22no—
184C22⋊C4×C107—22no—
185C22⋊C4×C107—22no—
186C22⋊C4×C107—22no—
187C22⋊C4×C107—22no—
188C22⋊C4×C107—22no—
189C22⋊C4×C107—22no—
190C22⋊C4×C107—44no—
191C22⋊C4×C107—44no—
192C42×C107—22no—
193C42×C107—22no—
194C23×C107—21no—
195C23×C107—21no—
196C23×C107—22no—
197C23×C107—22no—
198C23×C107—21no—
199C23×C107—21no—
200C23×C107—21no—
201C23×C107—22no—
202C23×C107—21no—
203C23×C107—21no—
204C23×C107—42no—
205C23×C107—42no—
206C23×C107—41no—
207C23×C107—41no—
208C23×C107—41no—
209C23×C107—41no—
210C23×C107—48no—
211C23×C107—42no—
212C23×C107—42no—
213C23×C107—42no—
214C23×C107—81no—
215C23×C107—81no—
216C23×C107—84no—
217C23×C107—81no—
218C23×C107—81no—
219C23×C107#12011yescharacteristic
220C23×C107#12011yescharacteristic
221C23×C107AGL(1,ℤ/8)12yes—
222C23×C107C22×D411yescharacteristic
223Q8×C107—42no—
224Q8×C107—81no—
225D4×C107—42no—
226D4×C107—44no—
227D4×C107—42no—
228D4×C107—42no—
229D4×C107—44no—
230D4×C107—44no—
231D4×C107—82no—
232D4×C107—82no—
233D4×C107—81no—
234C2×C4×C107—24no—
235C2×C4×C107—22no—
236C2×C4×C107—21no—
237C2×C4×C107—22no—
238C2×C4×C107—22no—
239C2×C4×C107—21no—
240C2×C4×C107—42no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—42no—
244C2×C4×C107—42no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—42no—
248C2×C4×C107—42no—
249C2×C4×C107—42no—
250C2×C4×C107—42no—
251C2×C4×C107—42no—
252C2×C4×C107—42no—
253C2×C4×C107—82no—
254C2×C4×C107—81no—
255C2×C4×C107—81no—
256C2×C4×C107—81no—
257C2×C4×C107—82no—
258C2×C4×C107—84no—
259C2×C4×C107—82no—
260C2×C4×C107—82no—
261C2×C4×C107#12012yes—
262C2×C4×C107C22×D412yes—
263C8×C107—44no—
264C22×C107—24no—
265C22×C107—24no—
266C22×C107—21no—
267C22×C107—21no—
268C22×C107—21no—
269C22×C107—21no—
270C22×C107—21no—
271C22×C107—21no—
272C22×C107—22no—
273C22×C107—42no—
274C22×C107—42no—
275C22×C107—41no—
276C22×C107—41no—
277C22×C107—42no—
278C22×C107—41no—
279C22×C107—42no—
280C22×C107—41no—
281C22×C107—42no—
282C22×C107—41no—
283C22×C107—81no—
284C22×C107—84no—
285C22×C107—84no—
286C22×C107—81no—
287C22×C107—162no—
288C22×C107#45512yes—
289C22×C107#45812yes—
290C22×C107C2×#12011yescharacteristic
291C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C107#57511yescharacteristic
293C4×C107—22no—
294C4×C107—22no—
295C4×C107—42no—
296C4×C107—41no—
297C4×C107—41no—
298C4×C107—42no—
299C4×C107—42no—
300C4×C107—82no—
301C4×C107—82no—
302#18169C10711yesmaximal, characteristic, direct product factor, Sylow
303C2×C107—21no—
304C2×C107—21no—
305C2×C107—22no—
306C2×C107—22no—
307C2×C107—42no—
308C2×C107—81no—
309C2×C107—82no—
310C2×C107#300611yescharacteristic
311C2×C107C2×#45511yescharacteristic
312C2×C107C2×#45811yescharacteristic
313#3490C2×C10711yescharacteristic
314#3092C2×C10712yescomplemented
315C2×#397C2×C10711yescharacteristic, complemented
316#1612C2×C10714yescomplemented
317#1608C2×C10712yescomplemented
318#1607C2×C10712yescomplemented
319#1504C2×C10712yescomplemented
320#1462C2×C10711yescharacteristic, complemented
321C107#1816911yescharacteristic, direct product factor, Sylow
322#551—22no—
323#551—22no—
324#546—22no—
325#546—22no—
326#543C22×C10711yescharacteristic
327#538—21no—
328#538C22×C10712yes—
329#534C22×C10711yescharacteristic
330#525—21no—
331#525C22×C10712yes—
332C2×#120—21no—
333#518—21no—
334C22×C4⋊C4C22×C10711yescharacteristic, complemented
335C22×C22⋊C4—21no—
336C22×C22⋊C4C22×C10711yescharacteristic
337#484—22no—
338#483C22×C10714yescomplemented
339#481—22no—
340#480C22×C10714yescomplemented
341#428—22no—
342#417—22no—
343#407C22×C10712yescomplemented
344#397—21no—
345#397—21no—
346#397C22×C10712yes—
347#397C22×C10712yescomplemented
348C2×#95—21no—
349C2×#95C22×C10711yescharacteristic, complemented
350#328C22×C10714yescomplemented
351#327C22×C10714yescomplemented
352#323C22×C10712yes—
353#323C22×C10712yescomplemented
354C25D4×C10711yescharacteristic
355C2×#41—21no—
356C2×#41D4×C10712yes—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4D4×C10711yescharacteristic
363C23×C4C23×C10711yescharacteristic
364C2×M16—22no—
365#126—22no—
366#126—22no—
367#124—22no—
368#124—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8D4×C10712yes—
379C22⋊Q8C23×C10712yes—
380#121—21no—
381#121—22no—
382#121—22no—
383#121—21no—
384#121D4×C10712yes—
385#121C23×C10712yes—
386#120—22no—
387#120—22no—
388#120—22no—
389#120—22no—
390#120—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397#117—22no—
398#117—21no—
399#117D4×C10712yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4C23×C10712yes—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4D4×C10711yescharacteristic
414C2×C22⋊C4D4×C10711yescharacteristic
415C2×C22⋊C4C23×C10711yescharacteristic
416C2×C22⋊C4C23×C10711yescharacteristic
417#107—24no—
418#106—24no—
419#103—24no—
420#102—24no—
421C22⋊C8—22no—
422C22⋊C8C23×C10714yes—
423#95—22no—
424#95—22no—
425#95—21no—
426#95C23×C10712yes—
427C24—21no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—41no—
432C24—42no—
433C24—42no—
434C24C2×D4×C10711yescharacteristic
435C24C2×D4×C10711yescharacteristic
436C24C2×D4×C10711yescharacteristic
437#41—44no—
438#41—82no—
439C2×Q8—21no—
440C2×Q8C2×D4×C10712yes—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—82no—
451C2×D4—82no—
452C2×D4C2×D4×C10712yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4C2×D4×C10712yes—
472C22×C4C2×D4×C10711yescharacteristic
473C22×C4C2×D4×C10711yescharacteristic
474C22×C4C2×D4×C10711yescharacteristic
475C22×C4C2×D4×C10712yes—
476C22×C4C24×C10711yescharacteristic
477M16—44no—
478C2×C8—24no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—24no—
486C4⋊C4—42no—
487C4⋊C4C2×D4×C10712yes—
488C4⋊C4C2×D4×C10712yes—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—44no—
504C22⋊C4—44no—
505C42—22no—
506C42—22no—
507C23—22no—
508C23—22no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—21no—
516C23—21no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—48no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—81no—
528C23—81no—
529C23—84no—
530C23—81no—
531C23—81no—
532C23#120×C10711yescharacteristic
533C23#120×C10711yescharacteristic
534C23AGL(1,ℤ/8)×C10712yes—
535C23C22×D4×C10711yescharacteristic
536Q8—42no—
537Q8—81no—
538D4—42no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—42no—
543D4—42no—
544D4—82no—
545D4—82no—
546D4—81no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—82no—
571C2×C4—84no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#120×C10712yes—
575C2×C4C22×D4×C10712yes—
576C8—44no—
577C22—24no—
578C22—24no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—81no—
597C22—84no—
598C22—84no—
599C22—81no—
600C22—162no—
601C22#455×C10712yes—
602C22#458×C10712yes—
603C22C2×#120×C10711yescharacteristic
604C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
605C22#575×C10711yescharacteristic
606C4—22no—
607C4—22no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—42no—
613C4—82no—
614C4—82no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—42no—
620C2—81no—
621C2—82no—
622C2C107×#300611yescharacteristic
623C2C2×#455×C10711yescharacteristic
624C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3490C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3092C2semidirect
3. C2×#397×C107C2semidirect
4. C107×#1612C2semidirect
5. C107×#1608C2semidirect
6. C107×#1607C2semidirect
7. C107×#1504C2semidirect
8. C107×#1462C2semidirect
21. C22×C4⋊C4×C107C22semidirect
25. #483×C107C22semidirect
27. #480×C107C22semidirect
30. #407×C107C22semidirect
34. #397×C107C22semidirect
36. C2×#95×C107C22semidirect
37. #328×C107C22semidirect
38. #327×C107C22semidirect
40. #323×C107C22semidirect
302. #18169C107direct (N × H)
314. #3092C2×C107semidirect
315. C2×#397C2×C107semidirect
316. #1612C2×C107semidirect
317. #1608C2×C107semidirect
318. #1607C2×C107semidirect
319. #1504C2×C107semidirect
320. #1462C2×C107semidirect
321. C107#18169direct (N × H)
334. C22×C4⋊C4C22×C107semidirect
338. #483C22×C107semidirect
340. #480C22×C107semidirect
343. #407C22×C107semidirect
347. #397C22×C107semidirect
349. C2×#95C22×C107semidirect
350. #328C22×C107semidirect
351. #327C22×C107semidirect
353. #323C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34902
C107×#30922
C2×#397×C1072
C107×#16122
C107×#16082
C107×#16072
C107×#15042
C107×#14622
#18169107