Finite Group Databasebeta

← C107×#9079 #41035043

Subgroups — C107×#9079 #41035043

Order 27392.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C107C211yesmaximal, characteristic, complemented
2C2×#386×C107C211yesmaximal, characteristic
3C107×#1779C211yesmaximal, characteristic, complemented
4C2×#323×C107C212yesmaximal, complemented
5C107×#1280C212yesmaximal, complemented
6C23×D4×C107C411yescharacteristic
7C24×C4×C107C2211yescharacteristic
8C23×C8×C107—21no—
9C22×C22⋊C4×C107C411yescharacteristic
10C22×C22⋊C4×C107C411yescharacteristic
11C22×C22⋊C4×C107C2211yescharacteristic
12C2×C22⋊C8×C107—21no—
13C2×C22⋊C8×C107—24no—
14C2×C22⋊C8×C107—21no—
15C2×C22⋊C8×C107—21no—
16C2×C22⋊C8×C107C2212yes—
17C2×C22⋊C8×C107C2212yes—
18#386×C107—21no—
19#386×C107—21no—
20#386×C107—21no—
21#386×C107—21no—
22C2×#95×C107C411yescharacteristic
23C2×#95×C107C2211yescharacteristic
24#323×C107—24no—
25C25×C107C2×C411yescharacteristic
26C25×C107C2×C411yescharacteristic
27C22×D4×C107—21no—
28C22×D4×C107—21no—
29C22×D4×C107—22no—
30C22×D4×C107—42no—
31C22×D4×C107—42no—
32C22×D4×C107C814yescomplemented
33C23×C4×C107—22no—
34C23×C4×C107—22no—
35C23×C4×C107—42no—
36C23×C4×C107—42no—
37C23×C4×C107C2×C411yescharacteristic
38C23×C4×C107C2×C411yescharacteristic
39C23×C4×C107C2×C411yescharacteristic
40C23×C4×C107C2×C411yescharacteristic
41C23×C4×C107D411yescharacteristic
42C23×C4×C107D411yescharacteristic
43C23×C4×C107D411yescharacteristic
44C23×C4×C107D411yescharacteristic
45C23×C4×C107C2311yescharacteristic
46C22×C8×C107—24no—
47C22×C8×C107—22no—
48C22×C8×C107—22no—
49C22×C8×C107—42no—
50C22×C8×C107—42no—
51C2×C22⋊C4×C107—21no—
52C2×C22⋊C4×C107—21no—
53C2×C22⋊C4×C107—21no—
54C2×C22⋊C4×C107—21no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—22no—
58C2×C22⋊C4×C107—22no—
59C2×C22⋊C4×C107—42no—
60C2×C22⋊C4×C107—42no—
61C22⋊C8×C107—24no—
62C22⋊C8×C107—22no—
63C22⋊C8×C107—22no—
64C22⋊C8×C107—22no—
65C22⋊C8×C107—42no—
66C22⋊C8×C107—42no—
67C22⋊C8×C107D414yescomplemented
68#95×C107—21no—
69#95×C107—21no—
70#95×C107—21no—
71#95×C107—21no—
72C24×C107—22no—
73C24×C107—22no—
74C24×C107—22no—
75C24×C107—22no—
76C24×C107—21no—
77C24×C107—21no—
78C24×C107—22no—
79C24×C107—22no—
80C24×C107—41no—
81C24×C107—41no—
82C24×C107—41no—
83C24×C107—41no—
84C24×C107—41no—
85C24×C107—41no—
86C24×C107C22⋊C411yescharacteristic
87C24×C107C22⋊C411yescharacteristic
88C24×C107C2×C812yes—
89C24×C107C2×C812yescomplemented
90C24×C107M1612yes—
91C24×C107C22×C411yescharacteristic
92C2×D4×C107—24no—
93C2×D4×C107—24no—
94C2×D4×C107—48no—
95C2×D4×C107—42no—
96C2×D4×C107—42no—
97C2×D4×C107—42no—
98C2×D4×C107—42no—
99C2×D4×C107—48no—
100C22×C4×C107—22no—
101C22×C4×C107—22no—
102C22×C4×C107—21no—
103C22×C4×C107—21no—
104C22×C4×C107—22no—
105C22×C4×C107—21no—
106C22×C4×C107—22no—
107C22×C4×C107—21no—
108C22×C4×C107—22no—
109C22×C4×C107—22no—
110C22×C4×C107—21no—
111C22×C4×C107—22no—
112C22×C4×C107—22no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—22no—
117C22×C4×C107—22no—
118C22×C4×C107—41no—
119C22×C4×C107—41no—
120C22×C4×C107—41no—
121C22×C4×C107—41no—
122C22×C4×C107—41no—
123C22×C4×C107—41no—
124C22×C4×C107—41no—
125C22×C4×C107—48no—
126C22×C4×C107—48no—
127C22×C4×C107—41no—
128C22×C4×C107—41no—
129C22×C4×C107—41no—
130C22×C4×C107—41no—
131C22×C4×C107—41no—
132C22×C4×C107—41no—
133C22×C4×C107C22⋊C411yescharacteristic
134C22×C4×C107C22⋊C411yescharacteristic
135C22×C4×C107C2×C812yescomplemented
136C22×C4×C107C2×D411yescharacteristic
137C22×C4×C107C2×D411yescharacteristic
138C22×C4×C107C2×D412yes—
139C22×C4×C107#4112yes—
140C2×C8×C107—24no—
141C2×C8×C107—48no—
142C2×C8×C107—42no—
143C2×C8×C107—42no—
144C2×C8×C107—42no—
145C2×C8×C107—42no—
146C2×C8×C107—42no—
147C22⋊C4×C107—42no—
148C22⋊C4×C107—42no—
149C22⋊C4×C107—42no—
150C22⋊C4×C107—42no—
151C22⋊C4×C107—41no—
152C22⋊C4×C107—42no—
153C22⋊C4×C107—41no—
154C23×C107—21no—
155C23×C107—21no—
156C23×C107—21no—
157C23×C107—21no—
158C23×C107—21no—
159C23×C107—21no—
160C23×C107—21no—
161C23×C107—21no—
162C23×C107—24no—
163C23×C107—24no—
164C23×C107—21no—
165C23×C107—21no—
166C23×C107—21no—
167C23×C107—21no—
168C23×C107—21no—
169C23×C107—21no—
170C23×C107—24no—
171C23×C107—24no—
172C23×C107—22no—
173C23×C107—24no—
174C23×C107—42no—
175C23×C107—42no—
176C23×C107—44no—
177C23×C107—44no—
178C23×C107—44no—
179C23×C107—44no—
180C23×C107—42no—
181C23×C107—42no—
182C23×C107—42no—
183C23×C107—42no—
184C23×C107—41no—
185C23×C107—41no—
186C23×C107—41no—
187C23×C107—41no—
188C23×C107—41no—
189C23×C107—41no—
190C23×C107—42no—
191C23×C107—82no—
192C23×C107—82no—
193C23×C107—82no—
194C23×C107—82no—
195C23×C107C22⋊C812yes—
196C23×C107C22⋊C812yes—
197C23×C107#9912yes—
198C23×C107#10012yes—
199C23×C107C2×C22⋊C411yescharacteristic
200C23×C107C4×D412yes—
201C23×C107C22×C811yescharacteristic
202C23×C107C2×M1611yescharacteristic
203C23×C107#13112yes—
204D4×C107—48no—
205D4×C107—48no—
206C2×C4×C107—24no—
207C2×C4×C107—24no—
208C2×C4×C107—21no—
209C2×C4×C107—21no—
210C2×C4×C107—21no—
211C2×C4×C107—21no—
212C2×C4×C107—21no—
213C2×C4×C107—21no—
214C2×C4×C107—21no—
215C2×C4×C107—22no—
216C2×C4×C107—21no—
217C2×C4×C107—21no—
218C2×C4×C107—42no—
219C2×C4×C107—42no—
220C2×C4×C107—44no—
221C2×C4×C107—44no—
222C2×C4×C107—44no—
223C2×C4×C107—42no—
224C2×C4×C107—42no—
225C2×C4×C107—42no—
226C2×C4×C107—41no—
227C2×C4×C107—41no—
228C2×C4×C107—42no—
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—82no—
236C2×C4×C107—82no—
237C2×C4×C107#9912yes—
238C2×C4×C107#12011yescharacteristic
239C2×C4×C107#12112yes—
240C2×C4×C107#12311yescharacteristic
241C8×C107—44no—
242C8×C107—82no—
243C22×C107—22no—
244C22×C107—22no—
245C22×C107—22no—
246C22×C107—22no—
247C22×C107—22no—
248C22×C107—21no—
249C22×C107—21no—
250C22×C107—21no—
251C22×C107—21no—
252C22×C107—22no—
253C22×C107—22no—
254C22×C107—22no—
255C22×C107—22no—
256C22×C107—22no—
257C22×C107—22no—
258C22×C107—22no—
259C22×C107—22no—
260C22×C107—48no—
261C22×C107—48no—
262C22×C107—41no—
263C22×C107—41no—
264C22×C107—41no—
265C22×C107—41no—
266C22×C107—42no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—84no—
270C22×C107—84no—
271C22×C107—81no—
272C22×C107—81no—
273C22×C107—81no—
274C22×C107—81no—
275C22×C107#32314yescomplemented
276C22×C107#38611yescharacteristic
277C22×C107C2×C22⋊C811yescharacteristic
278C22×C107#40811yescharacteristic
279C22×C107C2×#9911yescharacteristic
280C22×C107C2×#9911yescharacteristic
281C22×C107C2×#10011yescharacteristic
282C22×C107#41311yescharacteristic
283C22×C107C8×D412yes—
284C22×C107#43512yes—
285C4×C107—21no—
286C4×C107—22no—
287C4×C107—22no—
288C4×C107—21no—
289C4×C107—41no—
290C4×C107—42no—
291C4×C107—81no—
292C4×C107—81no—
293#9079C10711yesmaximal, characteristic, direct product factor, Sylow
294C2×C107—22no—
295C2×C107—22no—
296C2×C107—24no—
297C2×C107—42no—
298C2×C107—82no—
299C2×C107C2×#32311yescharacteristic
300C2×C107#145911yescharacteristic
301C2×C107#146811yescharacteristic
302C2×C107#147111yescharacteristic
303C2×C107#186911yescharacteristic
304C2×C107#189811yescharacteristic
305C2×C107#190011yescharacteristic
306C22×C22⋊C8C2×C10711yescharacteristic, complemented
307C2×#386C2×C10711yescharacteristic
308#1779C2×C10711yescharacteristic, complemented
309C2×#323C2×C10712yescomplemented
310#1280C2×C10712yescomplemented
311C107#907911yescharacteristic, direct product factor, Sylow
312C23×D4C4×C10711yescharacteristic
313C24×C4C22×C10711yescharacteristic
314C23×C8—21no—
315C22×C22⋊C4C4×C10711yescharacteristic
316C22×C22⋊C4C4×C10711yescharacteristic
317C22×C22⋊C4C22×C10711yescharacteristic
318C2×C22⋊C8—21no—
319C2×C22⋊C8—24no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8—21no—
322C2×C22⋊C8C22×C10712yes—
323C2×C22⋊C8C22×C10712yes—
324#386—21no—
325#386—21no—
326#386—21no—
327#386—21no—
328C2×#95C4×C10711yescharacteristic
329C2×#95C22×C10711yescharacteristic
330#323—24no—
331C25C2×C4×C10711yescharacteristic
332C25C2×C4×C10711yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4C8×C10714yescomplemented
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C10711yescharacteristic
344C23×C4C2×C4×C10711yescharacteristic
345C23×C4C2×C4×C10711yescharacteristic
346C23×C4C2×C4×C10711yescharacteristic
347C23×C4D4×C10711yescharacteristic
348C23×C4D4×C10711yescharacteristic
349C23×C4D4×C10711yescharacteristic
350C23×C4D4×C10711yescharacteristic
351C23×C4C23×C10711yescharacteristic
352C22×C8—24no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—42no—
356C22×C8—42no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C10714yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24C22⋊C4×C10711yescharacteristic
393C24C22⋊C4×C10711yescharacteristic
394C24C2×C8×C10712yes—
395C24C2×C8×C10712yescomplemented
396C24M16×C10712yes—
397C24C22×C4×C10711yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—48no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C10711yescharacteristic
440C22×C4C22⋊C4×C10711yescharacteristic
441C22×C4C2×C8×C10712yescomplemented
442C22×C4C2×D4×C10711yescharacteristic
443C22×C4C2×D4×C10711yescharacteristic
444C22×C4C2×D4×C10712yes—
445C22×C4#41×C10712yes—
446C2×C8—24no—
447C2×C8—48no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23C22⋊C8×C10712yes—
502C23C22⋊C8×C10712yes—
503C23#99×C10712yes—
504C23#100×C10712yes—
505C23C2×C22⋊C4×C10711yescharacteristic
506C23C4×D4×C10712yes—
507C23C22×C8×C10711yescharacteristic
508C23C2×M16×C10711yescharacteristic
509C23#131×C10712yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C10712yes—
544C2×C4#120×C10711yescharacteristic
545C2×C4#121×C10712yes—
546C2×C4#123×C10711yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22#323×C10714yescomplemented
582C22#386×C10711yescharacteristic
583C22C2×C22⋊C8×C10711yescharacteristic
584C22#408×C10711yescharacteristic
585C22C2×#99×C10711yescharacteristic
586C22C2×#99×C10711yescharacteristic
587C22C2×#100×C10711yescharacteristic
588C22#413×C10711yescharacteristic
589C22C8×D4×C10712yes—
590C22#435×C10712yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—42no—
603C2—82no—
604C2C2×#323×C10711yescharacteristic
605C2C107×#145911yescharacteristic
606C2C107×#146811yescharacteristic
607C2C107×#147111yescharacteristic
608C2C107×#186911yescharacteristic
609C2C107×#189811yescharacteristic
610C2C107×#190011yescharacteristic
subgroupG/H
center, socleC23×C107C2×C22⋊C4
commutatorC23C22×C8×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC23×D4×C107C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C24×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C107C2semidirect
3. C107×#1779C2semidirect
4. C2×#323×C107C2semidirect
5. C107×#1280C2semidirect
32. C22×D4×C107C8semidirect
67. C22⋊C8×C107D4semidirect
89. C24×C107C2×C8semidirect
135. C22×C4×C107C2×C8semidirect
275. C22×C107#323semidirect
293. #9079C107direct (N × H)
306. C22×C22⋊C8C2×C107semidirect
308. #1779C2×C107semidirect
309. C2×#323C2×C107semidirect
310. #1280C2×C107semidirect
311. C107#9079direct (N × H)
338. C22×D4C8×C107semidirect
373. C22⋊C8D4×C107semidirect
395. C24C2×C8×C107semidirect
441. C22×C4C2×C8×C107semidirect
581. C22#323×C107semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1072
C2×#386×C1072
C107×#17792
C2×#323×C1072
C107×#12802
#9079107