Finite Group Databasebeta

← C2×C107×#1390 #41038536

Subgroups — C2×C107×#1390 #41038536

Order 27392.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C107C211yesmaximal, characteristic
2C22×#99×C107C211yesmaximal, characteristic
3C2×#386×C107C211yesmaximal, characteristic
4C107×#1390C214yesmaximal, direct product factor
5C23×D4×C107C2211yescharacteristic
6C24×C4×C107C411yescharacteristic, complemented
7C22×M16×C107—21no—
8C22×C22⋊C4×C107—21no—
9C22×C22⋊C4×C107—21no—
10C22×C22⋊C4×C107C411yescharacteristic, complemented
11C2×#100×C107—21no—
12C2×#100×C107—22no—
13C2×#100×C107C414yescomplemented
14C2×#100×C107C2212yes—
15C2×#99×C107—21no—
16C2×#99×C107—22no—
17C2×#99×C107C414yescomplemented
18C2×#99×C107C2212yes—
19#386×C107—21no—
20#386×C107—21no—
21#386×C107C412yescomplemented
22#386×C107C2212yes—
23C2×#95×C107—21no—
24C25×C107C2×C411yescharacteristic
25C25×C107D411yescharacteristic
26C22×D4×C107—42no—
27C22×D4×C107—41no—
28C22×D4×C107—41no—
29C22×D4×C107C2×C411yescharacteristic
30C22×D4×C107C2×C412yes—
31C22×D4×C107C2×C412yes—
32C22×D4×C107D411yescharacteristic
33C22×D4×C107D412yes—
34C22×D4×C107D411yescharacteristic
35C22×D4×C107Q812yes—
36C22×D4×C107C2311yescharacteristic
37C23×C4×C107—21no—
38C23×C4×C107—21no—
39C23×C4×C107—21no—
40C23×C4×C107—44no—
41C23×C4×C107—41no—
42C23×C4×C107—41no—
43C23×C4×C107—41no—
44C23×C4×C107C2×C412yescomplemented
45C23×C4×C107D411yescharacteristic
46C2×M16×C107—24no—
47C2×M16×C107—22no—
48C2×M16×C107—42no—
49C2×M16×C107—41no—
50C22×C8×C107—41no—
51C2×C22⋊C4×C107—24no—
52C2×C22⋊C4×C107—22no—
53C2×C22⋊C4×C107—21no—
54C2×C22⋊C4×C107—22no—
55C2×C22⋊C4×C107—22no—
56C2×C22⋊C4×C107—44no—
57C2×C22⋊C4×C107—41no—
58C2×C22⋊C4×C107—42no—
59C2×C22⋊C4×C107—42no—
60C2×C22⋊C4×C107C2×C412yescomplemented
61#100×C107—24no—
62#100×C107—22no—
63#100×C107C2×C414yescomplemented
64#99×C107—24no—
65#99×C107—22no—
66#99×C107C2×C414yescomplemented
67#95×C107—22no—
68#95×C107—22no—
69C24×C107—22no—
70C24×C107—21no—
71C24×C107—21no—
72C24×C107—21no—
73C24×C107—22no—
74C24×C107—21no—
75C24×C107—42no—
76C24×C107—42no—
77C24×C107—42no—
78C24×C107—42no—
79C24×C107C4212yes—
80C24×C107C22⋊C412yes—
81C24×C107C22⋊C411yescharacteristic
82C24×C107C22⋊C411yescharacteristic
83C24×C107C22⋊C411yescharacteristic
84C24×C107C4⋊C412yes—
85C24×C107C4⋊C412yes—
86C24×C107C22×C411yescharacteristic
87C24×C107C2×D411yescharacteristic
88C2×D4×C107—42no—
89C2×D4×C107—42no—
90C2×D4×C107—42no—
91C2×D4×C107—42no—
92C2×D4×C107—41no—
93C2×D4×C107—41no—
94C2×D4×C107—42no—
95C2×D4×C107—42no—
96C2×D4×C107—41no—
97C2×D4×C107—41no—
98C2×D4×C107—41no—
99C2×D4×C107—41no—
100C2×D4×C107—42no—
101C2×D4×C107—42no—
102C2×D4×C107—41no—
103C2×D4×C107—41no—
104C2×D4×C107C4212yes—
105C2×D4×C107C22⋊C412yes—
106C2×D4×C107C22⋊C412yes—
107C2×D4×C107C4⋊C412yes—
108C2×D4×C107C4⋊C412yes—
109C2×D4×C107C4⋊C412yes—
110C2×D4×C107C22×C411yescharacteristic
111C2×D4×C107C22×C411yescharacteristic
112C2×D4×C107C2×D411yescharacteristic
113C2×D4×C107C2×Q811yescharacteristic
114C22×C4×C107—22no—
115C22×C4×C107—21no—
116C22×C4×C107—21no—
117C22×C4×C107—24no—
118C22×C4×C107—22no—
119C22×C4×C107—22no—
120C22×C4×C107—44no—
121C22×C4×C107—44no—
122C22×C4×C107—42no—
123C22×C4×C107—42no—
124C22×C4×C107—48no—
125C22×C4×C107—44no—
126C22×C4×C107—41no—
127C22×C4×C107—41no—
128C22×C4×C107—42no—
129C22×C4×C107—44no—
130C22×C4×C107—44no—
131C22×C4×C107—42no—
132C22×C4×C107—42no—
133C22×C4×C107—42no—
134C22×C4×C107—42no—
135C22×C4×C107—82no—
136C22×C4×C107—82no—
137C22×C4×C107C22⋊C411yescharacteristic
138C22×C4×C107C22⋊C412yes—
139C22×C4×C107C4⋊C412yes—
140C22×C4×C107C2×D411yescharacteristic
141M16×C107—24no—
142M16×C107—44no—
143M16×C107—42no—
144C2×C8×C107—44no—
145C2×C8×C107—42no—
146C22⋊C4×C107—24no—
147C22⋊C4×C107—44no—
148C22⋊C4×C107—44no—
149C22⋊C4×C107—44no—
150C22⋊C4×C107—42no—
151C22⋊C4×C107—42no—
152C22⋊C4×C107—42no—
153C23×C107—22no—
154C23×C107—22no—
155C23×C107—22no—
156C23×C107—22no—
157C23×C107—22no—
158C23×C107—22no—
159C23×C107—22no—
160C23×C107—22no—
161C23×C107—21no—
162C23×C107—21no—
163C23×C107—21no—
164C23×C107—21no—
165C23×C107—21no—
166C23×C107—21no—
167C23×C107—22no—
168C23×C107—22no—
169C23×C107—21no—
170C23×C107—21no—
171C23×C107—41no—
172C23×C107—41no—
173C23×C107—44no—
174C23×C107—41no—
175C23×C107—44no—
176C23×C107—41no—
177C23×C107—42no—
178C23×C107—42no—
179C23×C107—48no—
180C23×C107—41no—
181C23×C107—41no—
182C23×C107—41no—
183C23×C107—44no—
184C23×C107—44no—
185C23×C107—41no—
186C23×C107—42no—
187C23×C107—42no—
188C23×C107—42no—
189C23×C107—42no—
190C23×C107—81no—
191C23×C107—81no—
192C23×C107—84no—
193C23×C107#9512yes—
194C23×C107#9512yes—
195C23×C107#9512yes—
196C23×C107#9911yescharacteristic
197C23×C107#9912yes—
198C23×C107#9911yescharacteristic
199C23×C107C2×C4211yescharacteristic
200C23×C107C2×C22⋊C411yescharacteristic
201C23×C107C2×C22⋊C411yescharacteristic
202C23×C107C2×C4⋊C411yescharacteristic
203C23×C107C2×C4⋊C411yescharacteristic
204D4×C107—42no—
205D4×C107—42no—
206D4×C107—42no—
207D4×C107—42no—
208D4×C107—42no—
209D4×C107—42no—
210D4×C107—41no—
211D4×C107—41no—
212D4×C107—41no—
213D4×C107—41no—
214C2×C4×C107—22no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—21no—
222C2×C4×C107—24no—
223C2×C4×C107—42no—
224C2×C4×C107—44no—
225C2×C4×C107—48no—
226C2×C4×C107—44no—
227C2×C4×C107—44no—
228C2×C4×C107—42no—
229C2×C4×C107—44no—
230C2×C4×C107—44no—
231C2×C4×C107—42no—
232C2×C4×C107—42no—
233C2×C4×C107—42no—
234C2×C4×C107—84no—
235C2×C4×C107—82no—
236C2×C4×C107—82no—
237C2×C4×C107—88no—
238C2×C4×C107#9512yes—
239C2×C4×C107C2×C22⋊C411yescharacteristic
240C2×C4×C107C2×C4⋊C411yescharacteristic
241C8×C107—44no—
242C22×C107—21no—
243C22×C107—21no—
244C22×C107—21no—
245C22×C107—21no—
246C22×C107—24no—
247C22×C107—24no—
248C22×C107—21no—
249C22×C107—22no—
250C22×C107—22no—
251C22×C107—21no—
252C22×C107—21no—
253C22×C107—21no—
254C22×C107—42no—
255C22×C107—42no—
256C22×C107—41no—
257C22×C107—41no—
258C22×C107—41no—
259C22×C107—41no—
260C22×C107—42no—
261C22×C107—42no—
262C22×C107—44no—
263C22×C107—44no—
264C22×C107—41no—
265C22×C107—41no—
266C22×C107—41no—
267C22×C107—41no—
268C22×C107—41no—
269C22×C107—41no—
270C22×C107—41no—
271C22×C107—41no—
272C22×C107—44no—
273C22×C107—44no—
274C22×C107—44no—
275C22×C107—44no—
276C22×C107—81no—
277C22×C107—81no—
278C22×C107—82no—
279C22×C107—82no—
280C22×C107#34212yes—
281C22×C107#34212yes—
282C22×C107AΣL(1,𝔽16)12yes—
283C22×C107#35212yes—
284C22×C107C2×#9511yescharacteristic
285C22×C107C2×#9911yescharacteristic
286C22×C107C2×#9911yescharacteristic
287C4×C107—21no—
288C4×C107—22no—
289C4×C107—21no—
290C4×C107—44no—
291C4×C107—82no—
292C4×C107—84no—
293C2×#1390C10711yesmaximal, characteristic, direct product factor, Sylow
294C2×C107—21no—
295C2×C107—21no—
296C2×C107—22no—
297C2×C107—41no—
298C2×C107—42no—
299C2×C107—41no—
300C2×C107—41no—
301C2×C107—42no—
302C2×C107—41no—
303C2×C107#139014yesdirect product factor
304C2×C107C2×#34211yescharacteristic
305C2×C107C2×AΣL(1,𝔽16)11yescharacteristic
306C2×C107C2×#35211yescharacteristic
307C22×#100C2×C10711yescharacteristic
308C22×#99C2×C10711yescharacteristic
309C2×#386C2×C10711yescharacteristic
310#1390C2×C10714yesdirect product factor
311C107C2×#139011yescharacteristic, direct product factor, Sylow
312C23×D4C22×C10711yescharacteristic
313C24×C4C4×C10711yescharacteristic, complemented
314C22×M16—21no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4—21no—
317C22×C22⋊C4C4×C10711yescharacteristic, complemented
318C2×#100—21no—
319C2×#100—22no—
320C2×#100C4×C10714yescomplemented
321C2×#100C22×C10712yes—
322C2×#99—21no—
323C2×#99—22no—
324C2×#99C4×C10714yescomplemented
325C2×#99C22×C10712yes—
326#386—21no—
327#386—21no—
328#386C4×C10712yescomplemented
329#386C22×C10712yes—
330C2×#95—21no—
331C25C2×C4×C10711yescharacteristic
332C25D4×C10711yescharacteristic
333C22×D4—41no—
334C22×D4—42no—
335C22×D4—41no—
336C22×D4C2×C4×C10711yescharacteristic
337C22×D4C2×C4×C10712yes—
338C22×D4C2×C4×C10712yes—
339C22×D4D4×C10711yescharacteristic
340C22×D4D4×C10712yes—
341C22×D4D4×C10711yescharacteristic
342C22×D4Q8×C10712yes—
343C22×D4C23×C10711yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C10712yescomplemented
352C23×C4D4×C10711yescharacteristic
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—42no—
356C2×M16—41no—
357C22×C8—41no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4C2×C4×C10712yescomplemented
368#100—24no—
369#100—22no—
370#100C2×C4×C10714yescomplemented
371#99—24no—
372#99—22no—
373#99C2×C4×C10714yescomplemented
374#95—22no—
375#95—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—21no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C42×C10712yes—
387C24C22⋊C4×C10711yescharacteristic
388C24C22⋊C4×C10712yes—
389C24C22⋊C4×C10711yescharacteristic
390C24C22⋊C4×C10711yescharacteristic
391C24C4⋊C4×C10712yes—
392C24C4⋊C4×C10712yes—
393C24C22×C4×C10711yescharacteristic
394C24C2×D4×C10711yescharacteristic
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C42×C10712yes—
412C2×D4C22⋊C4×C10712yes—
413C2×D4C22⋊C4×C10712yes—
414C2×D4C4⋊C4×C10712yes—
415C2×D4C4⋊C4×C10712yes—
416C2×D4C4⋊C4×C10712yes—
417C2×D4C22×C4×C10711yescharacteristic
418C2×D4C22×C4×C10711yescharacteristic
419C2×D4C2×D4×C10711yescharacteristic
420C2×D4C2×Q8×C10711yescharacteristic
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C22⋊C4×C10711yescharacteristic
445C22×C4C22⋊C4×C10712yes—
446C22×C4C4⋊C4×C10712yes—
447C22×C4C2×D4×C10711yescharacteristic
448M16—24no—
449M16—44no—
450M16—42no—
451C2×C8—44no—
452C2×C8—42no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—44no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—41no—
479C23—41no—
480C23—44no—
481C23—41no—
482C23—44no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—84no—
500C23#95×C10712yes—
501C23#95×C10712yes—
502C23#95×C10712yes—
503C23#99×C10711yescharacteristic
504C23#99×C10712yes—
505C23#99×C10711yescharacteristic
506C23C2×C42×C10711yescharacteristic
507C23C2×C22⋊C4×C10711yescharacteristic
508C23C2×C22⋊C4×C10711yescharacteristic
509C23C2×C4⋊C4×C10711yescharacteristic
510C23C2×C4⋊C4×C10711yescharacteristic
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4#95×C10712yes—
546C2×C4C2×C22⋊C4×C10711yescharacteristic
547C2×C4C2×C4⋊C4×C10711yescharacteristic
548C8—44no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—81no—
584C22—81no—
585C22—82no—
586C22—82no—
587C22#342×C10712yes—
588C22#342×C10712yes—
589C22AΣL(1,𝔽16)×C10712yes—
590C22#352×C10712yes—
591C22C2×#95×C10711yescharacteristic
592C22C2×#99×C10711yescharacteristic
593C22C2×#99×C10711yescharacteristic
594C4—21no—
595C4—22no—
596C4—21no—
597C4—44no—
598C4—82no—
599C4—84no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—42no—
605C2—41no—
606C2—41no—
607C2—42no—
608C2—41no—
609C2C107×#139014yesdirect product factor
610C2C2×#342×C10711yescharacteristic
611C2C2×AΣL(1,𝔽16)×C10711yescharacteristic
612C2C2×#352×C10711yescharacteristic
subgroupG/H
center, socleC23×C107#99
commutatorC23C2×C42×C107
Frattini, cosocleC22×D4C23×C107
prime radicalC23×D4×C107C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C107 ◁ C23×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C107×#1390C2direct (N × H)
6. C24×C4×C107C4semidirect
10. C22×C22⋊C4×C107C4semidirect
13. C2×#100×C107C4semidirect
17. C2×#99×C107C4semidirect
21. #386×C107C4semidirect
44. C23×C4×C107C2×C4semidirect
60. C2×C22⋊C4×C107C2×C4semidirect
63. #100×C107C2×C4semidirect
66. #99×C107C2×C4semidirect
293. C2×#1390C107direct (N × H)
303. C2×C107#1390direct (N × H)
310. #1390C2×C107direct (N × H)
311. C107C2×#1390direct (N × H)
313. C24×C4C4×C107semidirect
317. C22×C22⋊C4C4×C107semidirect
320. C2×#100C4×C107semidirect
324. C2×#99C4×C107semidirect
328. #386C4×C107semidirect
351. C23×C4C2×C4×C107semidirect
367. C2×C22⋊C4C2×C4×C107semidirect
370. #100C2×C4×C107semidirect
373. #99C2×C4×C107semidirect
609. C2C107×#1390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#100×C1072
C22×#99×C1072
C2×#386×C1072
C107×#13902
C2×#1390107