Finite Group Databasebeta

← C107×#29397 #41055361

Subgroups — C107×#29397 #41055361

Order 27392.

722 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C107C211yesmaximal, characteristic, complemented
2C107×#2293C211yesmaximal, characteristic
3C107×#2085C211yesmaximal, characteristic, complemented
4C107×#2073C211yesmaximal, characteristic
5C107×#2059C211yesmaximal, characteristic, complemented
6C107×#2025C211yesmaximal, characteristic
7C107×#1926C211yesmaximal, characteristic
8C107×#1925C211yesmaximal, characteristic
9C107×#1921C211yesmaximal, characteristic, complemented
10C107×#1920C211yesmaximal, characteristic, complemented
11C107×#1920C211yesmaximal, characteristic, complemented
12C107×#1918C211yesmaximal, characteristic, complemented
13C107×#1864C211yesmaximal, characteristic
14C107×#1862C211yesmaximal, characteristic
15C107×#1839C211yesmaximal, characteristic, complemented
16C2×#125×C107C2211yescharacteristic
17C2×C4×D4×C107C2211yescharacteristic
18C2×#117×C107—21no—
19C2×#107×C107C2211yescharacteristic
20C2×#107×C107C2211yescharacteristic
21C2×#106×C107C2211yescharacteristic
22C2×#106×C107C2211yescharacteristic
23C2×#102×C107C2211yescharacteristic
24C2×#102×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27#390×C107C2211yescharacteristic
28#390×C107C2211yescharacteristic
29#389×C107C2211yescharacteristic
30#389×C107C2211yescharacteristic
31#389×C107C2211yescharacteristic
32#389×C107C2211yescharacteristic
33#388×C107—21no—
34#388×C107—21no—
35#387×C107—21no—
36#387×C107—21no—
37#382×C107C2211yescharacteristic
38C4×C4⋊C4×C107—21no—
39C4×C4⋊C4×C107—21no—
40C4×C4⋊C4×C107C2211yescharacteristic
41C4×C4⋊C4×C107C2211yescharacteristic
42C4×C4⋊C4×C107C2211yescharacteristic
43C4×C22⋊C4×C107—21no—
44C43×C107C2211yescharacteristic
45#340×C107C2211yescharacteristic
46#340×C107C2211yescharacteristic
47#340×C107C2211yescharacteristic
48#340×C107C2211yescharacteristic
49#340×C107C2211yescharacteristic
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#336×C107C2211yescharacteristic
54#336×C107C2211yescharacteristic
55#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×D4×C107C2311yescharacteristic
60C23×C4×C107—21no—
61C22×C8×C107C2311yescharacteristic
62C22×C8×C107C2311yescharacteristic
63C22×C8×C107C2311yescharacteristic
64C22×C8×C107C2311yescharacteristic
65#125×C107—22no—
66#125×C107—22no—
67C4×D4×C107—22no—
68C4×D4×C107—22no—
69#117×C107—44no—
70C2×C4⋊C4×C107—21no—
71C2×C4⋊C4×C107—21no—
72C2×C4⋊C4×C107—21no—
73C2×C4⋊C4×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C4⋊C4×C107—21no—
76C2×C4⋊C4×C107C2311yescharacteristic
77C2×C4⋊C4×C107C2311yescharacteristic
78C2×C4⋊C4×C107C2311yescharacteristic
79C2×C4⋊C4×C107C2311yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C22⋊C4×C107—21no—
84C2×C22⋊C4×C107—21no—
85C2×C22⋊C4×C107—21no—
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C42×C107—21no—
89C2×C42×C107—21no—
90C2×C42×C107—21no—
91C2×C42×C107D411yescharacteristic
92C2×C42×C107D411yescharacteristic
93C2×C42×C107D411yescharacteristic
94C2×C42×C107D411yescharacteristic
95C2×C42×C107C2311yescharacteristic
96C2×C42×C107C2311yescharacteristic
97C2×C42×C107C2311yescharacteristic
98#107×C107—22no—
99#107×C107—22no—
100#106×C107—22no—
101#106×C107—22no—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107—22no—
105#102×C107—22no—
106#95×C107—21no—
107#95×C107—21no—
108#95×C107—21no—
109#95×C107—21no—
110#95×C107—21no—
111#95×C107—21no—
112#95×C107—21no—
113#95×C107—21no—
114#95×C107—21no—
115C24×C107—21no—
116C2×D4×C107—21no—
117C2×D4×C107—21no—
118C2×D4×C107—21no—
119C2×D4×C107—21no—
120C2×D4×C107—21no—
121C2×D4×C107#4112yes—
122C22×C4×C107—24no—
123C22×C4×C107—21no—
124C22×C4×C107—21no—
125C22×C4×C107—21no—
126C22×C4×C107—21no—
127C22×C4×C107—21no—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—42no—
131C22×C4×C107—42no—
132C22×C4×C107C2×D411yescharacteristic
133C22×C4×C107C2×D411yescharacteristic
134C22×C4×C107C2×D411yescharacteristic
135C22×C4×C107C2×D411yescharacteristic
136C22×C4×C107C2×D411yescharacteristic
137C22×C4×C107C2×D411yescharacteristic
138C22×C4×C107C2411yescharacteristic
139C2×C8×C107—21no—
140C2×C8×C107—21no—
141C2×C8×C107—21no—
142C2×C8×C107—21no—
143C2×C8×C107—21no—
144C2×C8×C107—21no—
145C2×C8×C107—21no—
146C2×C8×C107—21no—
147C2×C8×C107—21no—
148C2×C8×C107—21no—
149C2×C8×C107—21no—
150C2×C8×C107—21no—
151C4⋊C4×C107—24no—
152C4⋊C4×C107—24no—
153C4⋊C4×C107—21no—
154C4⋊C4×C107—21no—
155C4⋊C4×C107—21no—
156C4⋊C4×C107—21no—
157C4⋊C4×C107—21no—
158C4⋊C4×C107—21no—
159C4⋊C4×C107—21no—
160C4⋊C4×C107—21no—
161C4⋊C4×C107—21no—
162C4⋊C4×C107—21no—
163C4⋊C4×C107—21no—
164C4⋊C4×C107—42no—
165C4⋊C4×C107—42no—
166C4⋊C4×C107—42no—
167C4⋊C4×C107—42no—
168C4⋊C4×C107#4112yes—
169C4⋊C4×C107#4112yes—
170C4⋊C4×C107#4112yes—
171C22⋊C4×C107—24no—
172C22⋊C4×C107—42no—
173C22⋊C4×C107—42no—
174C22⋊C4×C107—42no—
175C22⋊C4×C107—42no—
176C42×C107—22no—
177C42×C107—22no—
178C42×C107—21no—
179C42×C107—21no—
180C42×C107—21no—
181C42×C107—21no—
182C42×C107—21no—
183C42×C107—21no—
184C42×C107—41no—
185C42×C107—41no—
186C42×C107—42no—
187C42×C107—42no—
188C42×C107—42no—
189C23×C107—22no—
190C23×C107—41no—
191C23×C107—41no—
192C23×C107—41no—
193C23×C107—41no—
194C23×C107—41no—
195C23×C107—41no—
196C23×C107C22×D411yescharacteristic
197D4×C107—22no—
198D4×C107—22no—
199D4×C107—41no—
200D4×C107—41no—
201C2×C4×C107—21no—
202C2×C4×C107—21no—
203C2×C4×C107—21no—
204C2×C4×C107—21no—
205C2×C4×C107—21no—
206C2×C4×C107—21no—
207C2×C4×C107—21no—
208C2×C4×C107—22no—
209C2×C4×C107—22no—
210C2×C4×C107—22no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—48no—
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—41no—
229C2×C4×C107—41no—
230C2×C4×C107—41no—
231C2×C4×C107—41no—
232C2×C4×C107—41no—
233C2×C4×C107—41no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107#13512yes—
240C2×C4×C107AGL(1,ℤ/8)12yes—
241C2×C4×C107C2×#4111yescharacteristic
242C2×C4×C107C2×#4111yescharacteristic
243C2×C4×C107C2×#4111yescharacteristic
244C2×C4×C107C2×#4111yescharacteristic
245C2×C4×C1072−1+411yescharacteristic
246C2×C4×C1072−1+411yescharacteristic
247C8×C107—41no—
248C8×C107—41no—
249C8×C107—41no—
250C8×C107—41no—
251C22×C107—42no—
252C22×C107—42no—
253C22×C107—42no—
254C22×C107—81no—
255C22×C107—81no—
256C22×C107—81no—
257C22×C107—81no—
258C22×C107#52511yescharacteristic
259C22×C107#52511yescharacteristic
260C22×C107#53611yescharacteristic
261C22×C107C2×#13511yescharacteristic
262C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C107#57511yescharacteristic
264C22×C107#57511yescharacteristic
265C4×C107—22no—
266C4×C107—22no—
267C4×C107—41no—
268C4×C107—41no—
269C4×C107—42no—
270C4×C107—41no—
271C4×C107—42no—
272C4×C107—42no—
273C4×C107—41no—
274C4×C107—81no—
275C4×C107—81no—
276C4×C107—81no—
277C4×C107—81no—
278C4×C107#55211yescharacteristic
279C4×C107#55211yescharacteristic
280C4×C107#55611yescharacteristic
281C4×C107#55611yescharacteristic
282#29397C10711yesmaximal, characteristic, direct product factor, Sylow
283C2×C107—82no—
284C2×C107#259911yescharacteristic
285C2×C107#310211yescharacteristic
286C2×C107#310611yescharacteristic
287C2×C107#311111yescharacteristic
288C2×C107#311411yescharacteristic
289C2×C107#323211yescharacteristic
290C2×C107#323511yescharacteristic
291C4×#125C2×C10711yescharacteristic, complemented
292#2293C2×C10711yescharacteristic
293#2085C2×C10711yescharacteristic, complemented
294#2073C2×C10711yescharacteristic
295#2059C2×C10711yescharacteristic, complemented
296#2025C2×C10711yescharacteristic
297#1926C2×C10711yescharacteristic
298#1925C2×C10711yescharacteristic
299#1921C2×C10711yescharacteristic, complemented
300#1920C2×C10711yescharacteristic, complemented
301#1920C2×C10711yescharacteristic, complemented
302#1918C2×C10711yescharacteristic, complemented
303#1864C2×C10711yescharacteristic
304#1862C2×C10711yescharacteristic
305#1839C2×C10711yescharacteristic, complemented
306C107#2939711yescharacteristic, direct product factor, Sylow
307C2×#125C22×C10711yescharacteristic
308C2×C4×D4C22×C10711yescharacteristic
309C2×#117—21no—
310C2×#107C22×C10711yescharacteristic
311C2×#107C22×C10711yescharacteristic
312C2×#106C22×C10711yescharacteristic
313C2×#106C22×C10711yescharacteristic
314C2×#102C22×C10711yescharacteristic
315C2×#102C22×C10711yescharacteristic
316C2×#102C22×C10711yescharacteristic
317C2×#102C22×C10711yescharacteristic
318#390C22×C10711yescharacteristic
319#390C22×C10711yescharacteristic
320#389C22×C10711yescharacteristic
321#389C22×C10711yescharacteristic
322#389C22×C10711yescharacteristic
323#389C22×C10711yescharacteristic
324#388—21no—
325#388—21no—
326#387—21no—
327#387—21no—
328#382C22×C10711yescharacteristic
329C4×C4⋊C4—21no—
330C4×C4⋊C4—21no—
331C4×C4⋊C4C22×C10711yescharacteristic
332C4×C4⋊C4C22×C10711yescharacteristic
333C4×C4⋊C4C22×C10711yescharacteristic
334C4×C22⋊C4—21no—
335C43C22×C10711yescharacteristic
336#340C22×C10711yescharacteristic
337#340C22×C10711yescharacteristic
338#340C22×C10711yescharacteristic
339#340C22×C10711yescharacteristic
340#340C22×C10711yescharacteristic
341#340C22×C10711yescharacteristic
342#340C22×C10711yescharacteristic
343#340C22×C10711yescharacteristic
344#336C22×C10711yescharacteristic
345#336C22×C10711yescharacteristic
346#336C22×C10711yescharacteristic
347#336C22×C10711yescharacteristic
348#336C22×C10711yescharacteristic
349#336C22×C10711yescharacteristic
350C22×D4C23×C10711yescharacteristic
351C23×C4—21no—
352C22×C8C23×C10711yescharacteristic
353C22×C8C23×C10711yescharacteristic
354C22×C8C23×C10711yescharacteristic
355C22×C8C23×C10711yescharacteristic
356#125—22no—
357#125—22no—
358C4×D4—22no—
359C4×D4—22no—
360#117—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C10711yescharacteristic
368C2×C4⋊C4C23×C10711yescharacteristic
369C2×C4⋊C4C23×C10711yescharacteristic
370C2×C4⋊C4C23×C10711yescharacteristic
371C2×C4⋊C4C23×C10711yescharacteristic
372C2×C4⋊C4C23×C10711yescharacteristic
373C2×C4⋊C4C23×C10711yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42D4×C10711yescharacteristic
383C2×C42D4×C10711yescharacteristic
384C2×C42D4×C10711yescharacteristic
385C2×C42D4×C10711yescharacteristic
386C2×C42C23×C10711yescharacteristic
387C2×C42C23×C10711yescharacteristic
388C2×C42C23×C10711yescharacteristic
389#107—22no—
390#107—22no—
391#106—22no—
392#106—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406C24—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#41×C10712yes—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4C2×D4×C10711yescharacteristic
424C22×C4C2×D4×C10711yescharacteristic
425C22×C4C2×D4×C10711yescharacteristic
426C22×C4C2×D4×C10711yescharacteristic
427C22×C4C2×D4×C10711yescharacteristic
428C22×C4C2×D4×C10711yescharacteristic
429C22×C4C24×C10711yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4#41×C10712yes—
460C4⋊C4#41×C10712yes—
461C4⋊C4#41×C10712yes—
462C22⋊C4—24no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—42no—
478C42—42no—
479C42—42no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C22×D4×C10711yescharacteristic
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—48no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
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—41no—
529C2×C4—41no—
530C2×C4#135×C10712yes—
531C2×C4AGL(1,ℤ/8)×C10712yes—
532C2×C4C2×#41×C10711yescharacteristic
533C2×C4C2×#41×C10711yescharacteristic
534C2×C4C2×#41×C10711yescharacteristic
535C2×C4C2×#41×C10711yescharacteristic
536C2×C42−1+4×C10711yescharacteristic
537C2×C42−1+4×C10711yescharacteristic
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22#525×C10711yescharacteristic
550C22#525×C10711yescharacteristic
551C22#536×C10711yescharacteristic
552C22C2×#135×C10711yescharacteristic
553C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
554C22#575×C10711yescharacteristic
555C22#575×C10711yescharacteristic
556C4—22no—
557C4—22no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4#552×C10711yescharacteristic
570C4#552×C10711yescharacteristic
571C4#556×C10711yescharacteristic
572C4#556×C10711yescharacteristic
573C2—82no—
574C2C107×#259911yescharacteristic
575C2C107×#310211yescharacteristic
576C2C107×#310611yescharacteristic
577C2C107×#311111yescharacteristic
578C2C107×#311411yescharacteristic
579C2C107×#323211yescharacteristic
580C2C107×#323511yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×#125×C107C2semidirect
3. C107×#2085C2semidirect
5. C107×#2059C2semidirect
9. C107×#1921C2semidirect
10. C107×#1920C2semidirect
11. C107×#1920C2semidirect
12. C107×#1918C2semidirect
15. C107×#1839C2semidirect
282. #29397C107direct (N × H)
291. C4×#125C2×C107semidirect
293. #2085C2×C107semidirect
295. #2059C2×C107semidirect
299. #1921C2×C107semidirect
300. #1920C2×C107semidirect
301. #1920C2×C107semidirect
302. #1918C2×C107semidirect
305. #1839C2×C107semidirect
306. C107#29397direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C1072
C107×#22932
C107×#20852
C107×#20732
C107×#20592
C107×#20252
C107×#19262
C107×#19252
C107×#19212
C107×#19202
C107×#19182
C107×#18642
C107×#18622
C107×#18392
#29397107