Finite Group Databasebeta

← C107×#13422 #41039386

Subgroups — C107×#13422 #41039386

Order 27392.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2669C211yesmaximal, characteristic
2C2×#353×C107C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C107C211yesmaximal, characteristic, complemented
4C107×#1889C211yesmaximal, characteristic, complemented
5C107×#1887C211yesmaximal, characteristic, complemented
6C107×#1867C211yesmaximal, characteristic, complemented
7C107×#1390C211yesmaximal, characteristic, complemented
8C2×#127×C107C2211yescharacteristic
9C2×#121×C107—21no—
10C2×#120×C107—21no—
11C2×#120×C107C2211yescharacteristic
12#518×C107C2211yescharacteristic
13#418×C107—21no—
14C2×#100×C107C2211yescharacteristic
15C2×#99×C107C2211yescharacteristic
16C2×#99×C107C2211yescharacteristic
17#394×C107—21no—
18#392×C107—21no—
19#392×C107—21no—
20#388×C107—21no—
21#386×C107C2211yescharacteristic
22#385×C107—21no—
23#379×C107—21no—
24#353×C107—22no—
25AΣL(1,𝔽16)×C107—22no—
26#342×C107—21no—
27#342×C107—21no—
28#339×C107—21no—
29C25×C107D411yescharacteristic
30C22×D4×C107—21no—
31C22×D4×C107—21no—
32C22×D4×C107—21no—
33C22×D4×C107—21no—
34C22×D4×C107—21no—
35C22×D4×C107D411yescharacteristic
36C22×D4×C107C2311yescharacteristic
37C23×C4×C107D411yescharacteristic
38C2×M16×C107—21no—
39#127×C107—21no—
40#127×C107—21no—
41#127×C107—21no—
42#127×C107—21no—
43#121×C107—44no—
44#120×C107—21no—
45#120×C107—21no—
46#120×C107—21no—
47#120×C107—21no—
48#120×C107—44no—
49C4×D4×C107—41no—
50C4×D4×C107—41no—
51#117×C107—21no—
52C2×C4⋊C4×C107—21no—
53C2×C4⋊C4×C107—41no—
54C2×C22⋊C4×C107—21no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C22⋊C4×C107—21no—
60C2×C22⋊C4×C107—21no—
61C2×C22⋊C4×C107—21no—
62C2×C22⋊C4×C107—21no—
63C2×C22⋊C4×C107—21no—
64C2×C22⋊C4×C107—41no—
65C2×C22⋊C4×C107—41no—
66C2×C22⋊C4×C107D411yescharacteristic
67C2×C22⋊C4×C107D411yescharacteristic
68C2×C42×C107D411yescharacteristic
69#102×C107—41no—
70#102×C107—41no—
71#100×C107—21no—
72#100×C107—21no—
73#99×C107—21no—
74#99×C107—21no—
75#99×C107—21no—
76#99×C107D412yescomplemented
77#95×C107—21no—
78#95×C107—21no—
79#95×C107—41no—
80C24×C107—21no—
81C24×C107—21no—
82C24×C107—21no—
83C24×C107—21no—
84C24×C107—41no—
85C24×C107—42no—
86C24×C107—41no—
87C24×C107—81no—
88C24×C107C2×D411yescharacteristic
89C24×C107C2×D411yescharacteristic
90C2×D4×C107—21no—
91C2×D4×C107—21no—
92C2×D4×C107—41no—
93C2×D4×C107—41no—
94C2×D4×C107—41no—
95C2×D4×C107—41no—
96C2×D4×C107—42no—
97C2×D4×C107—42no—
98C2×D4×C107—42no—
99C2×D4×C107—42no—
100C2×D4×C107—42no—
101C2×D4×C107—42no—
102C2×D4×C107—41no—
103C2×D4×C107—41no—
104C2×D4×C107—41no—
105C2×D4×C107—41no—
106C2×D4×C107—41no—
107C2×D4×C107—41no—
108C2×D4×C107—81no—
109C2×D4×C107—81no—
110C2×D4×C107—81no—
111C2×D4×C107—81no—
112C2×D4×C107—81no—
113C2×D4×C107—81no—
114C2×D4×C107C2×D411yescharacteristic
115C2×D4×C107#4111yescharacteristic
116C2×D4×C107#4111yescharacteristic
117C2×D4×C107#4111yescharacteristic
118C22×C4×C107—21no—
119C22×C4×C107—21no—
120C22×C4×C107—21no—
121C22×C4×C107—21no—
122C22×C4×C107—21no—
123C22×C4×C107—21no—
124C22×C4×C107—21no—
125C22×C4×C107—21no—
126C22×C4×C107—42no—
127C22×C4×C107—41no—
128C22×C4×C107—41no—
129C22×C4×C107—41no—
130C22×C4×C107C2×D411yescharacteristic
131M16×C107—41no—
132M16×C107—41no—
133C2×C8×C107—41no—
134C4⋊C4×C107—21no—
135C4⋊C4×C107—21no—
136C4⋊C4×C107—42no—
137C4⋊C4×C107—82no—
138C22⋊C4×C107—24no—
139C22⋊C4×C107—22no—
140C22⋊C4×C107—21no—
141C22⋊C4×C107—21no—
142C22⋊C4×C107—42no—
143C22⋊C4×C107—42no—
144C22⋊C4×C107—42no—
145C22⋊C4×C107—41no—
146C22⋊C4×C107—41no—
147C22⋊C4×C107—41no—
148C22⋊C4×C107—41no—
149C22⋊C4×C107—41no—
150C22⋊C4×C107—41no—
151C22⋊C4×C107—41no—
152C22⋊C4×C107—41no—
153C22⋊C4×C107—41no—
154C22⋊C4×C107—81no—
155C22⋊C4×C107—82no—
156C22⋊C4×C107—82no—
157C42×C107—21no—
158C42×C107—21no—
159C42×C107—41no—
160C23×C107—21no—
161C23×C107—21no—
162C23×C107—21no—
163C23×C107—21no—
164C23×C107—22no—
165C23×C107—41no—
166C23×C107—41no—
167C23×C107—41no—
168C23×C107—41no—
169C23×C107—41no—
170C23×C107—41no—
171C23×C107—41no—
172C23×C107—42no—
173C23×C107—41no—
174C23×C107—41no—
175C23×C107—41no—
176C23×C107—41no—
177C23×C107—42no—
178C23×C107—42no—
179C23×C107—41no—
180C23×C107—41no—
181C23×C107—41no—
182C23×C107—41no—
183C23×C107—41no—
184C23×C107—41no—
185C23×C107—81no—
186C23×C107—82no—
187C23×C107—81no—
188C23×C107—82no—
189C23×C107—84no—
190C23×C107—81no—
191C23×C107#12011yescharacteristic
192C23×C107#12111yescharacteristic
193C23×C107#12111yescharacteristic
194C23×C107#12311yescharacteristic
195C23×C107#12411yescharacteristic
196D4×C107—41no—
197D4×C107—41no—
198D4×C107—41no—
199D4×C107—41no—
200D4×C107—42no—
201D4×C107—81no—
202D4×C107—82no—
203D4×C107—82no—
204D4×C107—82no—
205D4×C107—82no—
206D4×C107—84no—
207D4×C107—82no—
208D4×C107—82no—
209D4×C107—84no—
210C2×C4×C107—21no—
211C2×C4×C107—21no—
212C2×C4×C107—22no—
213C2×C4×C107—22no—
214C2×C4×C107—41no—
215C2×C4×C107—41no—
216C2×C4×C107—41no—
217C2×C4×C107—41no—
218C2×C4×C107—42no—
219C2×C4×C107—42no—
220C2×C4×C107—41no—
221C2×C4×C107—41no—
222C2×C4×C107—41no—
223C2×C4×C107—41no—
224C2×C4×C107—41no—
225C2×C4×C107—41no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—81no—
229C2×C4×C107—81no—
230C2×C4×C107—81no—
231C2×C4×C107—81no—
232C2×C4×C107—81no—
233C2×C4×C107—81no—
234C2×C4×C107—81no—
235C2×C4×C107—81no—
236C2×C4×C107—81no—
237C2×C4×C107—81no—
238C2×C4×C107#12111yescharacteristic
239C2×C4×C107#12311yescharacteristic
240C8×C107—81no—
241C22×C107—21no—
242C22×C107—21no—
243C22×C107—21no—
244C22×C107—21no—
245C22×C107—21no—
246C22×C107—21no—
247C22×C107—41no—
248C22×C107—41no—
249C22×C107—41no—
250C22×C107—41no—
251C22×C107—42no—
252C22×C107—42no—
253C22×C107—41no—
254C22×C107—41no—
255C22×C107—41no—
256C22×C107—41no—
257C22×C107—44no—
258C22×C107—42no—
259C22×C107—81no—
260C22×C107—81no—
261C22×C107—81no—
262C22×C107—81no—
263C22×C107—81no—
264C22×C107—81no—
265C22×C107—81no—
266C22×C107—81no—
267C22×C107—82no—
268C22×C107—82no—
269C22×C107—82no—
270C22×C107—81no—
271C22×C107—81no—
272C22×C107—81no—
273C22×C107—81no—
274C22×C107—81no—
275C22×C107#39411yescharacteristic
276C22×C107B(4,𝔽2)11yescharacteristic
277C22×C107#45811yescharacteristic
278C4×C107—21no—
279C4×C107—21no—
280C4×C107—42no—
281C4×C107—42no—
282C4×C107—81no—
283C4×C107—81no—
284C4×C107—82no—
285C4×C107—81no—
286C4×C107—81no—
287C4×C107—161no—
288#13422C10711yesmaximal, characteristic, direct product factor, Sylow
289C2×C107—21no—
290C2×C107—21no—
291C2×C107—41no—
292C2×C107—41no—
293C2×C107—41no—
294C2×C107—41no—
295C2×C107—82no—
296C2×C107—161no—
297C2×C107#204411yescharacteristic
298C2×C107#219611yescharacteristic
299C2×C107#220011yescharacteristic
300#2669C2×C10711yescharacteristic
301C2×#353C2×C10711yescharacteristic, complemented
302C2×AΣL(1,𝔽16)C2×C10711yescharacteristic, complemented
303#1889C2×C10711yescharacteristic, complemented
304#1887C2×C10711yescharacteristic, complemented
305#1867C2×C10711yescharacteristic, complemented
306#1390C2×C10711yescharacteristic, complemented
307C107#1342211yescharacteristic, direct product factor, Sylow
308C2×#127C22×C10711yescharacteristic
309C2×#121—21no—
310C2×#120—21no—
311C2×#120C22×C10711yescharacteristic
312#518C22×C10711yescharacteristic
313#418—21no—
314C2×#100C22×C10711yescharacteristic
315C2×#99C22×C10711yescharacteristic
316C2×#99C22×C10711yescharacteristic
317#394—21no—
318#392—21no—
319#392—21no—
320#388—21no—
321#386C22×C10711yescharacteristic
322#385—21no—
323#379—21no—
324#353—22no—
325AΣL(1,𝔽16)—22no—
326#342—21no—
327#342—21no—
328#339—21no—
329C25D4×C10711yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C10711yescharacteristic
336C22×D4C23×C10711yescharacteristic
337C23×C4D4×C10711yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C10711yescharacteristic
367C2×C22⋊C4D4×C10711yescharacteristic
368C2×C42D4×C10711yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C10712yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C10711yescharacteristic
389C24C2×D4×C10711yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C10711yescharacteristic
415C2×D4#41×C10711yescharacteristic
416C2×D4#41×C10711yescharacteristic
417C2×D4#41×C10711yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C10711yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C10711yescharacteristic
492C23#121×C10711yescharacteristic
493C23#121×C10711yescharacteristic
494C23#123×C10711yescharacteristic
495C23#124×C10711yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C10711yescharacteristic
539C2×C4#123×C10711yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#394×C10711yescharacteristic
576C22B(4,𝔽2)×C10711yescharacteristic
577C22#458×C10711yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2C107×#204411yescharacteristic
597C2C107×#219611yescharacteristic
598C2C107×#220011yescharacteristic
subgroupG/H
center, socleC22×C107B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C107
prime radicalC107×#2669C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C107C2semidirect
3. C2×AΣL(1,𝔽16)×C107C2semidirect
4. C107×#1889C2semidirect
5. C107×#1887C2semidirect
6. C107×#1867C2semidirect
7. C107×#1390C2semidirect
76. #99×C107D4semidirect
288. #13422C107direct (N × H)
301. C2×#353C2×C107semidirect
302. C2×AΣL(1,𝔽16)C2×C107semidirect
303. #1889C2×C107semidirect
304. #1887C2×C107semidirect
305. #1867C2×C107semidirect
306. #1390C2×C107semidirect
307. C107#13422direct (N × H)
376. #99D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#26692
C2×#353×C1072
C2×AΣL(1,𝔽16)×C1072
C107×#18892
C107×#18872
C107×#18672
C107×#13902
#13422107