Finite Group Databasebeta

← C107×#26375 #41052339

Subgroups — C107×#26375 #41052339

Order 27392.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C107C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C107C211yesmaximal, characteristic
3C107×#2454C211yesmaximal, characteristic
4C107×#2351C211yesmaximal, characteristic, complemented
5C107×#2092C211yesmaximal, characteristic
6C107×#2085C211yesmaximal, characteristic, complemented
7C107×#2065C211yesmaximal, characteristic
8C107×#2059C211yesmaximal, characteristic, complemented
9C107×#1941C211yesmaximal, characteristic, complemented
10C107×#1916C211yesmaximal, characteristic, complemented
11C107×#1880C211yesmaximal, characteristic
12C107×#1880C211yesmaximal, characteristic
13C107×#1865C211yesmaximal, characteristic, complemented
14C107×#1863C211yesmaximal, characteristic, complemented
15C107×#1862C211yesmaximal, characteristic
16C22×SD16×C107C2211yescharacteristic
17C2×#125×C107C2211yescharacteristic
18C2×C4×Q8×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic
21C2×C4×D4×C107C2211yescharacteristic
22#479×C107—24no—
23C4×SD16×C107—24no—
24C2×#107×C107C2211yescharacteristic
25C2×#107×C107C2211yescharacteristic
26C2×#106×C107C2211yescharacteristic
27C2×#106×C107C2211yescharacteristic
28C2×#106×C107C2211yescharacteristic
29C2×C4⋊C8×C107C2211yescharacteristic
30C2×#103×C107C2211yescharacteristic
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×C4×C8×C107C2211yescharacteristic
37#399×C107—21no—
38#396×C107—21no—
39#390×C107C2211yescharacteristic
40#390×C107C2211yescharacteristic
41#389×C107—21no—
42#389×C107—21no—
43#389×C107C2211yescharacteristic
44#389×C107C2211yescharacteristic
45#389×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#385×C107—21no—
48#382×C107—21no—
49#382×C107C2211yescharacteristic
50#380×C107—21no—
51C4×C4⋊C4×C107—21no—
52C4×C4⋊C4×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61C22×Q8×C107C2311yescharacteristic
62C22×D4×C107C2311yescharacteristic
63C23×C4×C107—21no—
64C2×SD16×C107—22no—
65C2×SD16×C107—22no—
66C2×SD16×C107Q814yes—
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C22×C8×C107C2311yescharacteristic
70C22×C8×C107C2311yescharacteristic
71#125×C107—22no—
72#125×C107—41no—
73C4×Q8×C107—22no—
74C4×Q8×C107—22no—
75C4×Q8×C107—22no—
76C4×Q8×C107—22no—
77C4×Q8×C107—41no—
78C4×Q8×C107—41no—
79C4×D4×C107—22no—
80C4×D4×C107—41no—
81C2×C4⋊C4×C107—21no—
82C2×C4⋊C4×C107—21no—
83C2×C4⋊C4×C107—21no—
84C2×C4⋊C4×C107—21no—
85C2×C4⋊C4×C107—21no—
86C2×C4⋊C4×C107—21no—
87C2×C4⋊C4×C107—21no—
88C2×C4⋊C4×C107—21no—
89C2×C4⋊C4×C107—21no—
90C2×C4⋊C4×C107D411yescharacteristic
91C2×C4⋊C4×C107D411yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C42×C107—21no—
104C2×C42×C107—21no—
105C2×C42×C107—21no—
106C2×C42×C107C2311yescharacteristic
107C2×C42×C107C2311yescharacteristic
108C2×C42×C107C2311yescharacteristic
109#107×C107—22no—
110#107×C107—41no—
111#106×C107—22no—
112#106×C107—22no—
113#106×C107—22no—
114C4⋊C8×C107—22no—
115#103×C107—22no—
116#103×C107—22no—
117#103×C107D414yes—
118#102×C107—22no—
119#102×C107—22no—
120#102×C107—41no—
121C4×C8×C107—22no—
122#95×C107—21no—
123#95×C107—21no—
124#95×C107—21no—
125#95×C107—21no—
126#95×C107—21no—
127#95×C107—21no—
128#95×C107D411yescharacteristic
129#95×C107D411yescharacteristic
130C24×C107—21no—
131C2×Q8×C107—21no—
132C2×Q8×C107—21no—
133C2×Q8×C107—21no—
134C2×Q8×C107C2×D412yes—
135C2×Q8×C107C2×Q812yes—
136C2×Q8×C107#4112yes—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107—21no—
140C2×D4×C107—21no—
141C2×D4×C107—21no—
142C2×D4×C107C2×Q812yes—
143C22×C4×C107—21no—
144C22×C4×C107—21no—
145C22×C4×C107—21no—
146C22×C4×C107—21no—
147C22×C4×C107—21no—
148C22×C4×C107—21no—
149C22×C4×C107—21no—
150C22×C4×C107—42no—
151C22×C4×C107—42no—
152C22×C4×C107—81no—
153C22×C4×C107C2×D411yescharacteristic
154C22×C4×C107C2×D411yescharacteristic
155C22×C4×C107C2×D411yescharacteristic
156C22×C4×C107C2×D411yescharacteristic
157C22×C4×C107C2×D411yescharacteristic
158C22×C4×C107C2×D411yescharacteristic
159C22×C4×C107C2411yescharacteristic
160SD16×C107—28no—
161C2×C8×C107—21no—
162C2×C8×C107—21no—
163C2×C8×C107—21no—
164C2×C8×C107—21no—
165C2×C8×C107—21no—
166C2×C8×C107—21no—
167C2×C8×C107—21no—
168C2×C8×C107—21no—
169C2×C8×C107—21no—
170C2×C8×C107—21no—
171C2×C8×C107C2×D412yes—
172C2×C8×C107C2×Q812yes—
173C4⋊C4×C107—24no—
174C4⋊C4×C107—22no—
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—21no—
180C4⋊C4×C107—21no—
181C4⋊C4×C107—21no—
182C4⋊C4×C107—21no—
183C4⋊C4×C107—21no—
184C4⋊C4×C107—21no—
185C4⋊C4×C107—41no—
186C4⋊C4×C107—42no—
187C4⋊C4×C107—42no—
188C4⋊C4×C107—42no—
189C4⋊C4×C107—42no—
190C4⋊C4×C107—42no—
191C4⋊C4×C107—42no—
192C4⋊C4×C107—81no—
193C4⋊C4×C107—81no—
194C4⋊C4×C107C2×D412yes—
195C4⋊C4×C107#4112yes—
196C22⋊C4×C107—42no—
197C22⋊C4×C107—42no—
198C22⋊C4×C107—81no—
199C22⋊C4×C107—81no—
200C22⋊C4×C107—81no—
201C42×C107—24no—
202C42×C107—21no—
203C42×C107—21no—
204C42×C107—21no—
205C42×C107—21no—
206C42×C107—21no—
207C42×C107—21no—
208C42×C107—42no—
209C42×C107—42no—
210C23×C107—22no—
211C23×C107—41no—
212C23×C107—41no—
213C23×C107—41no—
214C23×C107—41no—
215C23×C107—41no—
216C23×C107—41no—
217C23×C107C22×D411yescharacteristic
218Q8×C107—22no—
219Q8×C107—22no—
220Q8×C107—22no—
221Q8×C107C22⋊Q814yes—
222D4×C107—22no—
223D4×C107—22no—
224D4×C107—41no—
225D4×C107—41no—
226C2×C4×C107—22no—
227C2×C4×C107—21no—
228C2×C4×C107—22no—
229C2×C4×C107—22no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—22no—
234C2×C4×C107—21no—
235C2×C4×C107—21no—
236C2×C4×C107—21no—
237C2×C4×C107—22no—
238C2×C4×C107—21no—
239C2×C4×C107—21no—
240C2×C4×C107—21no—
241C2×C4×C107—21no—
242C2×C4×C107—21no—
243C2×C4×C107—21no—
244C2×C4×C107—21no—
245C2×C4×C107—21no—
246C2×C4×C107—21no—
247C2×C4×C107—21no—
248C2×C4×C107—41no—
249C2×C4×C107—41no—
250C2×C4×C107—41no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107—41no—
256C2×C4×C107—41no—
257C2×C4×C107—41no—
258C2×C4×C107—41no—
259C2×C4×C107—41no—
260C2×C4×C107—41no—
261C2×C4×C107—41no—
262C2×C4×C107—41no—
263C2×C4×C107—41no—
264C2×C4×C107—84no—
265C2×C4×C107#13512yes—
266C2×C4×C107C22×D411yescharacteristic
267C2×C4×C107C22×Q811yescharacteristic
268C2×C4×C107C2×#4111yescharacteristic
269C2×C4×C107C2×#4111yescharacteristic
270C2×C4×C107H(5,𝔽2)11yescharacteristic
271C2×C4×C1072−1+411yescharacteristic
272C8×C107—22no—
273C8×C107—22no—
274C8×C107—41no—
275C8×C107—41no—
276C22×C107—42no—
277C22×C107—42no—
278C22×C107—42no—
279C22×C107—81no—
280C22×C107—81no—
281C22×C107—81no—
282C22×C107—81no—
283C22×C107#52511yescharacteristic
284C22×C107D4211yescharacteristic
285C22×C107D4×Q811yescharacteristic
286C22×C107C2×#13511yescharacteristic
287C22×C107#57511yescharacteristic
288C22×C107#57711yescharacteristic
289C22×C107#57711yescharacteristic
290C4×C107—24no—
291C4×C107—22no—
292C4×C107—41no—
293C4×C107—42no—
294C4×C107—41no—
295C4×C107—41no—
296C4×C107—41no—
297C4×C107—41no—
298C4×C107—42no—
299C4×C107—81no—
300C4×C107—81no—
301C4×C107—81no—
302C4×C107—81no—
303C4×C107C2×C22⋊Q811yescharacteristic
304C4×C107#53911yescharacteristic
305C4×C107#54711yescharacteristic
306C4×C107#55411yescharacteristic
307#26375C10711yesmaximal, characteristic, direct product factor, Sylow
308C2×C107—82no—
309C2×C107#244911yescharacteristic
310C2×C107#310211yescharacteristic
311C2×C107#312611yescharacteristic
312C2×C107#327111yescharacteristic
313C2×C107#328211yescharacteristic
314C2×C107#338111yescharacteristic
315C2×C107#338811yescharacteristic
316C2×#479C2×C10711yescharacteristic, complemented
317C2×C4×SD16C2×C10711yescharacteristic
318#2454C2×C10711yescharacteristic
319#2351C2×C10711yescharacteristic, complemented
320#2092C2×C10711yescharacteristic
321#2085C2×C10711yescharacteristic, complemented
322#2065C2×C10711yescharacteristic
323#2059C2×C10711yescharacteristic, complemented
324#1941C2×C10711yescharacteristic, complemented
325#1916C2×C10711yescharacteristic, complemented
326#1880C2×C10711yescharacteristic
327#1880C2×C10711yescharacteristic
328#1865C2×C10711yescharacteristic, complemented
329#1863C2×C10711yescharacteristic, complemented
330#1862C2×C10711yescharacteristic
331C107#2637511yescharacteristic, direct product factor, Sylow
332C22×SD16C22×C10711yescharacteristic
333C2×#125C22×C10711yescharacteristic
334C2×C4×Q8C22×C10711yescharacteristic
335C2×C4×Q8C22×C10711yescharacteristic
336C2×C4×Q8C22×C10711yescharacteristic
337C2×C4×D4C22×C10711yescharacteristic
338#479—24no—
339C4×SD16—24no—
340C2×#107C22×C10711yescharacteristic
341C2×#107C22×C10711yescharacteristic
342C2×#106C22×C10711yescharacteristic
343C2×#106C22×C10711yescharacteristic
344C2×#106C22×C10711yescharacteristic
345C2×C4⋊C8C22×C10711yescharacteristic
346C2×#103C22×C10711yescharacteristic
347C2×#103C22×C10711yescharacteristic
348C2×#103C22×C10711yescharacteristic
349C2×#102C22×C10711yescharacteristic
350C2×#102C22×C10711yescharacteristic
351C2×#102C22×C10711yescharacteristic
352C2×C4×C8C22×C10711yescharacteristic
353#399—21no—
354#396—21no—
355#390C22×C10711yescharacteristic
356#390C22×C10711yescharacteristic
357#389—21no—
358#389—21no—
359#389C22×C10711yescharacteristic
360#389C22×C10711yescharacteristic
361#389C22×C10711yescharacteristic
362#389C22×C10711yescharacteristic
363#385—21no—
364#382—21no—
365#382C22×C10711yescharacteristic
366#380—21no—
367C4×C4⋊C4—21no—
368C4×C4⋊C4C22×C10711yescharacteristic
369#340C22×C10711yescharacteristic
370#340C22×C10711yescharacteristic
371#340C22×C10711yescharacteristic
372#340C22×C10711yescharacteristic
373#336C22×C10711yescharacteristic
374#336C22×C10711yescharacteristic
375#336C22×C10711yescharacteristic
376#336C22×C10711yescharacteristic
377C22×Q8C23×C10711yescharacteristic
378C22×D4C23×C10711yescharacteristic
379C23×C4—21no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16Q8×C10714yes—
383C22×C8C23×C10711yescharacteristic
384C22×C8C23×C10711yescharacteristic
385C22×C8C23×C10711yescharacteristic
386C22×C8C23×C10711yescharacteristic
387#125—22no—
388#125—41no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—41no—
394C4×Q8—41no—
395C4×D4—22no—
396C4×D4—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C10711yescharacteristic
407C2×C4⋊C4D4×C10711yescharacteristic
408C2×C4⋊C4C23×C10711yescharacteristic
409C2×C4⋊C4C23×C10711yescharacteristic
410C2×C4⋊C4C23×C10711yescharacteristic
411C2×C4⋊C4C23×C10711yescharacteristic
412C2×C4⋊C4C23×C10711yescharacteristic
413C2×C4⋊C4C23×C10711yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C23×C10711yescharacteristic
423C2×C42C23×C10711yescharacteristic
424C2×C42C23×C10711yescharacteristic
425#107—22no—
426#107—41no—
427#106—22no—
428#106—22no—
429#106—22no—
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103D4×C10714yes—
434#102—22no—
435#102—22no—
436#102—41no—
437C4×C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95D4×C10711yescharacteristic
445#95D4×C10711yescharacteristic
446C24—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C10712yes—
451C2×Q8C2×Q8×C10712yes—
452C2×Q8#41×C10712yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×Q8×C10712yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4C2×D4×C10711yescharacteristic
470C22×C4C2×D4×C10711yescharacteristic
471C22×C4C2×D4×C10711yescharacteristic
472C22×C4C2×D4×C10711yescharacteristic
473C22×C4C2×D4×C10711yescharacteristic
474C22×C4C2×D4×C10711yescharacteristic
475C22×C4C24×C10711yescharacteristic
476SD16—28no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×D4×C10712yes—
488C2×C8C2×Q8×C10712yes—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4C2×D4×C10712yes—
511C4⋊C4#41×C10712yes—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C22⋊C4—81no—
517C42—24no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—42no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23C22×D4×C10711yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8C22⋊Q8×C10714yes—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4#135×C10712yes—
582C2×C4C22×D4×C10711yescharacteristic
583C2×C4C22×Q8×C10711yescharacteristic
584C2×C4C2×#41×C10711yescharacteristic
585C2×C4C2×#41×C10711yescharacteristic
586C2×C4H(5,𝔽2)×C10711yescharacteristic
587C2×C42−1+4×C10711yescharacteristic
588C8—22no—
589C8—22no—
590C8—41no—
591C8—41no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#525×C10711yescharacteristic
600C22D42×C10711yescharacteristic
601C22D4×Q8×C10711yescharacteristic
602C22C2×#135×C10711yescharacteristic
603C22#575×C10711yescharacteristic
604C22#577×C10711yescharacteristic
605C22#577×C10711yescharacteristic
606C4—24no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4C2×C22⋊Q8×C10711yescharacteristic
620C4#539×C10711yescharacteristic
621C4#547×C10711yescharacteristic
622C4#554×C10711yescharacteristic
623C2—82no—
624C2C107×#244911yescharacteristic
625C2C107×#310211yescharacteristic
626C2C107×#312611yescharacteristic
627C2C107×#327111yescharacteristic
628C2C107×#328211yescharacteristic
629C2C107×#338111yescharacteristic
630C2C107×#338811yescharacteristic
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. C2×#479×C107C2semidirect
4. C107×#2351C2semidirect
6. C107×#2085C2semidirect
8. C107×#2059C2semidirect
9. C107×#1941C2semidirect
10. C107×#1916C2semidirect
13. C107×#1865C2semidirect
14. C107×#1863C2semidirect
307. #26375C107direct (N × H)
316. C2×#479C2×C107semidirect
319. #2351C2×C107semidirect
321. #2085C2×C107semidirect
323. #2059C2×C107semidirect
324. #1941C2×C107semidirect
325. #1916C2×C107semidirect
328. #1865C2×C107semidirect
329. #1863C2×C107semidirect
331. C107#26375direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#479×C1072
C2×C4×SD16×C1072
C107×#24542
C107×#23512
C107×#20922
C107×#20852
C107×#20652
C107×#20592
C107×#19412
C107×#19162
C107×#18802
C107×#18652
C107×#18632
C107×#18622
#26375107