Finite Group Databasebeta

← C107×#26028 #41051992

Subgroups — C107×#26028 #41051992

Order 27392.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2550C211yesmaximal, characteristic, complemented
2C107×#2357C211yesmaximal, characteristic
3C107×#2067C211yesmaximal, characteristic
4C107×#2065C211yesmaximal, characteristic
5C107×#2025C211yesmaximal, characteristic
6C107×#2023C211yesmaximal, characteristic
7C107×#1989C211yesmaximal, characteristic, complemented
8C107×#1988C211yesmaximal, characteristic, complemented
9C107×#1949C211yesmaximal, characteristic, complemented
10C107×#1939C211yesmaximal, characteristic, complemented
11C107×#1921C211yesmaximal, characteristic, complemented
12C107×#1920C211yesmaximal, characteristic, complemented
13C107×#1835C211yesmaximal, characteristic, complemented
14C107×#1804C211yesmaximal, characteristic
15C4×#102×C107C211yesmaximal, characteristic
16C2×C4⋊Q8×C107C2211yescharacteristic
17C2×#125×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×#107×C107C2211yescharacteristic
20C2×#106×C107C2211yescharacteristic
21C2×C4⋊C8×C107C2211yescharacteristic
22C2×C4⋊C8×C107C2211yescharacteristic
23C2×C4⋊C8×C107C2211yescharacteristic
24C2×#102×C107C2211yescharacteristic
25C2×#102×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×C4×C8×C107C2211yescharacteristic
29#398×C107—21no—
30#395×C107—21no—
31#391×C107—21no—
32#390×C107C2211yescharacteristic
33#390×C107C2211yescharacteristic
34#389×C107—21no—
35#389×C107C2211yescharacteristic
36#389×C107C2211yescharacteristic
37#388×C107—21no—
38#388×C107—21no—
39#382×C107C2211yescharacteristic
40#382×C107C2211yescharacteristic
41#381×C107—21no—
42C4×C4⋊C4×C107C2211yescharacteristic
43C4×C4⋊C4×C107C2211yescharacteristic
44C4×C4⋊C4×C107C2211yescharacteristic
45C4×C4⋊C4×C107C2211yescharacteristic
46C4×C22⋊C4×C107—21no—
47#340×C107C2211yescharacteristic
48#340×C107C2211yescharacteristic
49#340×C107C2211yescharacteristic
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107—21no—
60C22×D4×C107C2311yescharacteristic
61C23×C4×C107—21no—
62C22×C8×C107C2311yescharacteristic
63C22×C8×C107C2311yescharacteristic
64C22×C8×C107C2311yescharacteristic
65C22×C8×C107C2311yescharacteristic
66C4⋊Q8×C107—22no—
67C4⋊Q8×C107—41no—
68#125×C107—22no—
69#125×C107—41no—
70C4×D4×C107—22no—
71C4×D4×C107Q814yescomplemented
72C2×C4⋊C4×C107—21no—
73C2×C4⋊C4×C107—21no—
74C2×C4⋊C4×C107—21no—
75C2×C4⋊C4×C107—21no—
76C2×C4⋊C4×C107—21no—
77C2×C4⋊C4×C107D411yescharacteristic
78C2×C4⋊C4×C107D411yescharacteristic
79C2×C4⋊C4×C107C2311yescharacteristic
80C2×C4⋊C4×C107C2311yescharacteristic
81C2×C4⋊C4×C107C2311yescharacteristic
82C2×C4⋊C4×C107C2311yescharacteristic
83C2×C4⋊C4×C107C2311yescharacteristic
84C2×C4⋊C4×C107C2311yescharacteristic
85C2×C4⋊C4×C107C2311yescharacteristic
86C2×C22⋊C4×C107—21no—
87C2×C22⋊C4×C107—21no—
88C2×C22⋊C4×C107—21no—
89C2×C22⋊C4×C107—21no—
90C2×C22⋊C4×C107—21no—
91C2×C42×C107—21no—
92C2×C42×C107—21no—
93C2×C42×C107—21no—
94C2×C42×C107C2311yescharacteristic
95C2×C42×C107C2311yescharacteristic
96C2×C42×C107C2311yescharacteristic
97#107×C107—22no—
98#106×C107—22no—
99C4⋊C8×C107—22no—
100C4⋊C8×C107—41no—
101C4⋊C8×C107—41no—
102#102×C107—22no—
103#102×C107—22no—
104#102×C107—41no—
105#102×C107—41no—
106C4×C8×C107—22no—
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—
115#95×C107—21no—
116#95×C107D411yescharacteristic
117#95×C107D411yescharacteristic
118C24×C107—21no—
119C2×Q8×C107—42no—
120C2×Q8×C107—42no—
121C2×Q8×C107—81no—
122C2×D4×C107—21no—
123C2×D4×C107—21no—
124C2×D4×C107—21no—
125C2×D4×C107—21no—
126C2×D4×C107—21no—
127C2×D4×C107C2×Q812yes—
128C22×C4×C107—21no—
129C22×C4×C107—21no—
130C22×C4×C107—21no—
131C22×C4×C107—24no—
132C22×C4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—21no—
136C22×C4×C107—81no—
137C22×C4×C107—81no—
138C22×C4×C107C2×D411yescharacteristic
139C22×C4×C107C2×D411yescharacteristic
140C22×C4×C107C2×D411yescharacteristic
141C22×C4×C107C2×D411yescharacteristic
142C22×C4×C107C2×D411yescharacteristic
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2411yescharacteristic
145C2×C8×C107—21no—
146C2×C8×C107—21no—
147C2×C8×C107—21no—
148C2×C8×C107—21no—
149C2×C8×C107—21no—
150C2×C8×C107—21no—
151C2×C8×C107—21no—
152C2×C8×C107—21no—
153C2×C8×C107—21no—
154C2×C8×C107—21no—
155C2×C8×C107—21no—
156C2×C8×C107—21no—
157C4⋊C4×C107—22no—
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—21no—
165C4⋊C4×C107—21no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—41no—
170C4⋊C4×C107—42no—
171C4⋊C4×C107—42no—
172C4⋊C4×C107—42no—
173C4⋊C4×C107—42no—
174C4⋊C4×C107—81no—
175C4⋊C4×C107C2×Q812yes—
176C4⋊C4×C107#4112yes—
177C4⋊C4×C107#4112yes—
178C22⋊C4×C107—24no—
179C22⋊C4×C107—42no—
180C22⋊C4×C107—42no—
181C22⋊C4×C107—81no—
182C22⋊C4×C107—81no—
183C42×C107—21no—
184C42×C107—21no—
185C42×C107—21no—
186C42×C107—21no—
187C42×C107—81no—
188C42×C107—81no—
189C42×C107—81no—
190C42×C107C2×Q812yes—
191C42×C107#4112yes—
192C23×C107—22no—
193C23×C107—41no—
194C23×C107—41no—
195C23×C107—41no—
196C23×C107—41no—
197C23×C107—41no—
198C23×C107—41no—
199C23×C107C22×D411yescharacteristic
200Q8×C107—84no—
201D4×C107—22no—
202D4×C107—22no—
203D4×C107—41no—
204D4×C107—41no—
205C2×C4×C107—21no—
206C2×C4×C107—21no—
207C2×C4×C107—21no—
208C2×C4×C107—21no—
209C2×C4×C107—21no—
210C2×C4×C107—21no—
211C2×C4×C107—22no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—21no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—21no—
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—41no—
240C2×C4×C107—41no—
241C2×C4×C107—84no—
242C2×C4×C107C22⋊Q812yes—
243C2×C4×C107C22⋊Q812yes—
244C2×C4×C107#13512yes—
245C2×C4×C107C22×Q811yescharacteristic
246C2×C4×C107C2×#4111yescharacteristic
247C2×C4×C107C2×#4111yescharacteristic
248C2×C4×C107C2×#4111yescharacteristic
249C2×C4×C107H(5,𝔽2)11yescharacteristic
250C2×C4×C1072−1+411yescharacteristic
251C8×C107—41no—
252C8×C107—41no—
253C8×C107—41no—
254C8×C107—41no—
255C22×C107—42no—
256C22×C107—42no—
257C22×C107—42no—
258C22×C107—81no—
259C22×C107—81no—
260C22×C107—81no—
261C22×C107—81no—
262C22×C107C2×C22⋊Q811yescharacteristic
263C22×C107#54611yescharacteristic
264C22×C107#54811yescharacteristic
265C22×C107C2×#13511yescharacteristic
266C22×C107#57511yescharacteristic
267C22×C107#57611yescharacteristic
268C22×C107#57711yescharacteristic
269C4×C107—22no—
270C4×C107—22no—
271C4×C107—22no—
272C4×C107—42no—
273C4×C107—42no—
274C4×C107—41no—
275C4×C107—42no—
276C4×C107—41no—
277C4×C107—41no—
278C4×C107—81no—
279C4×C107—81no—
280C4×C107—81no—
281C4×C107—81no—
282C4×C107#53311yescharacteristic
283C4×C107#54411yescharacteristic
284C4×C107#55511yescharacteristic
285C4×C107#55611yescharacteristic
286#26028C10711yesmaximal, characteristic, direct product factor, Sylow
287C2×C107—82no—
288C2×C107#243911yescharacteristic
289C2×C107#307611yescharacteristic
290C2×C107#308111yescharacteristic
291C2×C107#329711yescharacteristic
292C2×C107#332611yescharacteristic
293C2×C107#336511yescharacteristic
294C2×C107#337011yescharacteristic
295#2550C2×C10711yescharacteristic, complemented
296#2357C2×C10711yescharacteristic
297#2067C2×C10711yescharacteristic
298#2065C2×C10711yescharacteristic
299#2025C2×C10711yescharacteristic
300#2023C2×C10711yescharacteristic
301#1989C2×C10711yescharacteristic, complemented
302#1988C2×C10711yescharacteristic, complemented
303#1949C2×C10711yescharacteristic, complemented
304#1939C2×C10711yescharacteristic, complemented
305#1921C2×C10711yescharacteristic, complemented
306#1920C2×C10711yescharacteristic, complemented
307#1835C2×C10711yescharacteristic, complemented
308#1804C2×C10711yescharacteristic
309C4×#102C2×C10711yescharacteristic
310C107#2602811yescharacteristic, direct product factor, Sylow
311C2×C4⋊Q8C22×C10711yescharacteristic
312C2×#125C22×C10711yescharacteristic
313C2×C4×D4C22×C10711yescharacteristic
314C2×#107C22×C10711yescharacteristic
315C2×#106C22×C10711yescharacteristic
316C2×C4⋊C8C22×C10711yescharacteristic
317C2×C4⋊C8C22×C10711yescharacteristic
318C2×C4⋊C8C22×C10711yescharacteristic
319C2×#102C22×C10711yescharacteristic
320C2×#102C22×C10711yescharacteristic
321C2×#102C22×C10711yescharacteristic
322C2×#102C22×C10711yescharacteristic
323C2×C4×C8C22×C10711yescharacteristic
324#398—21no—
325#395—21no—
326#391—21no—
327#390C22×C10711yescharacteristic
328#390C22×C10711yescharacteristic
329#389—21no—
330#389C22×C10711yescharacteristic
331#389C22×C10711yescharacteristic
332#388—21no—
333#388—21no—
334#382C22×C10711yescharacteristic
335#382C22×C10711yescharacteristic
336#381—21no—
337C4×C4⋊C4C22×C10711yescharacteristic
338C4×C4⋊C4C22×C10711yescharacteristic
339C4×C4⋊C4C22×C10711yescharacteristic
340C4×C4⋊C4C22×C10711yescharacteristic
341C4×C22⋊C4—21no—
342#340C22×C10711yescharacteristic
343#340C22×C10711yescharacteristic
344#340C22×C10711yescharacteristic
345#340C22×C10711yescharacteristic
346#340C22×C10711yescharacteristic
347#340C22×C10711yescharacteristic
348#340C22×C10711yescharacteristic
349#340C22×C10711yescharacteristic
350#340C22×C10711yescharacteristic
351#340C22×C10711yescharacteristic
352#336C22×C10711yescharacteristic
353#336C22×C10711yescharacteristic
354C22×Q8—21no—
355C22×D4C23×C10711yescharacteristic
356C23×C4—21no—
357C22×C8C23×C10711yescharacteristic
358C22×C8C23×C10711yescharacteristic
359C22×C8C23×C10711yescharacteristic
360C22×C8C23×C10711yescharacteristic
361C4⋊Q8—22no—
362C4⋊Q8—41no—
363#125—22no—
364#125—41no—
365C4×D4—22no—
366C4×D4Q8×C10714yescomplemented
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4D4×C10711yescharacteristic
373C2×C4⋊C4D4×C10711yescharacteristic
374C2×C4⋊C4C23×C10711yescharacteristic
375C2×C4⋊C4C23×C10711yescharacteristic
376C2×C4⋊C4C23×C10711yescharacteristic
377C2×C4⋊C4C23×C10711yescharacteristic
378C2×C4⋊C4C23×C10711yescharacteristic
379C2×C4⋊C4C23×C10711yescharacteristic
380C2×C4⋊C4C23×C10711yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C10711yescharacteristic
390C2×C42C23×C10711yescharacteristic
391C2×C42C23×C10711yescharacteristic
392#107—22no—
393#106—22no—
394C4⋊C8—22no—
395C4⋊C8—41no—
396C4⋊C8—41no—
397#102—22no—
398#102—22no—
399#102—41no—
400#102—41no—
401C4×C8—22no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95D4×C10711yescharacteristic
412#95D4×C10711yescharacteristic
413C24—21no—
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8—81no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Q8×C10712yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4C2×D4×C10711yescharacteristic
434C22×C4C2×D4×C10711yescharacteristic
435C22×C4C2×D4×C10711yescharacteristic
436C22×C4C2×D4×C10711yescharacteristic
437C22×C4C2×D4×C10711yescharacteristic
438C22×C4C2×D4×C10711yescharacteristic
439C22×C4C24×C10711yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4C2×Q8×C10712yes—
471C4⋊C4#41×C10712yes—
472C4⋊C4#41×C10712yes—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—81no—
484C42—81no—
485C42C2×Q8×C10712yes—
486C42#41×C10712yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×D4×C10711yescharacteristic
495Q8—84no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
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—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—84no—
537C2×C4C22⋊Q8×C10712yes—
538C2×C4C22⋊Q8×C10712yes—
539C2×C4#135×C10712yes—
540C2×C4C22×Q8×C10711yescharacteristic
541C2×C4C2×#41×C10711yescharacteristic
542C2×C4C2×#41×C10711yescharacteristic
543C2×C4C2×#41×C10711yescharacteristic
544C2×C4H(5,𝔽2)×C10711yescharacteristic
545C2×C42−1+4×C10711yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C22⋊Q8×C10711yescharacteristic
558C22#546×C10711yescharacteristic
559C22#548×C10711yescharacteristic
560C22C2×#135×C10711yescharacteristic
561C22#575×C10711yescharacteristic
562C22#576×C10711yescharacteristic
563C22#577×C10711yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C10711yescharacteristic
578C4#544×C10711yescharacteristic
579C4#555×C10711yescharacteristic
580C4#556×C10711yescharacteristic
581C2—82no—
582C2C107×#243911yescharacteristic
583C2C107×#307611yescharacteristic
584C2C107×#308111yescharacteristic
585C2C107×#329711yescharacteristic
586C2C107×#332611yescharacteristic
587C2C107×#336511yescharacteristic
588C2C107×#337011yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2550C2semidirect
7. C107×#1989C2semidirect
8. C107×#1988C2semidirect
9. C107×#1949C2semidirect
10. C107×#1939C2semidirect
11. C107×#1921C2semidirect
12. C107×#1920C2semidirect
13. C107×#1835C2semidirect
71. C4×D4×C107Q8semidirect
286. #26028C107direct (N × H)
295. #2550C2×C107semidirect
301. #1989C2×C107semidirect
302. #1988C2×C107semidirect
303. #1949C2×C107semidirect
304. #1939C2×C107semidirect
305. #1921C2×C107semidirect
306. #1920C2×C107semidirect
307. #1835C2×C107semidirect
310. C107#26028direct (N × H)
366. C4×D4Q8×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#25502
C107×#23572
C107×#20672
C107×#20652
C107×#20252
C107×#20232
C107×#19892
C107×#19882
C107×#19492
C107×#19392
C107×#19212
C107×#19202
C107×#18352
C107×#18042
C4×#102×C1072
#26028107