Finite Group Databasebeta

← C139×#24390 #48018986

Subgroups — C139×#24390 #48018986

Order 35584.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C139C211yesmaximal, characteristic, complemented
2C2×#469×C139C211yesmaximal, characteristic, complemented
3C2×#466×C139C211yesmaximal, characteristic, complemented
4C2×#447×C139C211yesmaximal, characteristic, complemented
5C2×#408×C139C211yesmaximal, characteristic, complemented
6#2615×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1999×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1893×C139C211yesmaximal, characteristic, complemented
13#1875×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic, complemented
21C23×C8×C139C2211yescharacteristic, complemented
22#535×C139—24no—
23#535×C139—24no—
24C2×#127×C139—21no—
25C2×#124×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×#121×C139C2211yescharacteristic, complemented
32C2×#121×C139C2211yescharacteristic, complemented
33C2×#120×C139—21no—
34C2×#120×C139—21no—
35C2×#117×C139C2211yescharacteristic
36#469×C139—24no—
37#466×C139—24no—
38#447×C139—24no—
39C2×#107×C139C2211yescharacteristic, complemented
40C2×#106×C139C2211yescharacteristic, complemented
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic, complemented
48C2×#102×C139C2211yescharacteristic, complemented
49#408×C139—24no—
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic, complemented
54#393×C139—21no—
55#392×C139—21no—
56#392×C139—21no—
57#392×C139—21no—
58#380×C139C2211yescharacteristic
59#380×C139C2211yescharacteristic, complemented
60#380×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×C139C2211yescharacteristic, complemented
65C25×C139—21no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C22×Q8×C139D411yescharacteristic
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—22no—
78C22×D4×C139—22no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139—21no—
83C22×D4×C139—22no—
84C22×D4×C139—22no—
85C22×D4×C139—41no—
86C22×D4×C139—41no—
87C22×D4×C139D411yescharacteristic
88C22×D4×C139D411yescharacteristic
89C22×D4×C139D411yescharacteristic
90C22×D4×C139C2311yescharacteristic
91C22×D4×C139C2311yescharacteristic
92C22×D4×C139C2311yescharacteristic
93C23×C4×C139C2311yescharacteristic
94C23×C4×C139C2311yescharacteristic
95C23×C4×C139C2311yescharacteristic
96C2×D8×C139—22no—
97C2×D8×C139—22no—
98C2×D8×C139—22no—
99C2×D8×C139—22no—
100C2×D8×C139—41no—
101C2×D8×C139—41no—
102C2×M16×C139—22no—
103C2×M16×C139—22no—
104C2×M16×C139—41no—
105C22×C8×C139—22no—
106C22×C8×C139—22no—
107C22×C8×C139—41no—
108C22×C8×C139C2311yescharacteristic
109C22×C8×C139C2311yescharacteristic
110C22×C8×C139C2311yescharacteristic
111C22×C8×C139C2311yescharacteristic
112#127×C139—28no—
113#124×C139—28no—
114#121×C139—22no—
115#121×C139—22no—
116#121×C139—22no—
117#121×C139—22no—
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139—22no—
124#121×C139—41no—
125#121×C139—41no—
126#121×C139D414yescomplemented
127#121×C139D414yescomplemented
128#120×C139—28no—
129#120×C139—28no—
130#117×C139—22no—
131#117×C139—22no—
132C2×C4⋊C4×C139C2311yescharacteristic
133C2×C4⋊C4×C139C2311yescharacteristic
134C2×C4⋊C4×C139C2311yescharacteristic
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C4⋊C4×C139C2311yescharacteristic
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139—21no—
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—21no—
144C2×C22⋊C4×C139—21no—
145C2×C22⋊C4×C139—21no—
146C2×C22⋊C4×C139—21no—
147C2×C22⋊C4×C139—21no—
148C2×C42×C139—21no—
149#107×C139—22no—
150#106×C139—22no—
151#102×C139—22no—
152#102×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—22no—
157#102×C139—41no—
158#102×C139—41no—
159C22⋊C8×C139—22no—
160C22⋊C8×C139—22no—
161C22⋊C8×C139—22no—
162C22⋊C8×C139D414yescomplemented
163#95×C139—21no—
164#95×C139—21no—
165#95×C139—21no—
166C24×C139—24no—
167C24×C139—21no—
168C24×C139—21no—
169C24×C139—21no—
170C24×C139—42no—
171C24×C139—42no—
172C24×C139—81no—
173C24×C139—81no—
174C24×C139—81no—
175C24×C139—81no—
176C24×C139C2×D411yescharacteristic
177C24×C139C2×D411yescharacteristic
178C24×C139C2×D411yescharacteristic
179#41×C139—44no—
180#41×C139—44no—
181#41×C139—44no—
182#41×C139—44no—
183C2×Q8×C139—22no—
184C2×Q8×C139—22no—
185C2×Q8×C139—41no—
186C2×D4×C139—24no—
187C2×D4×C139—22no—
188C2×D4×C139—22no—
189C2×D4×C139—22no—
190C2×D4×C139—22no—
191C2×D4×C139—24no—
192C2×D4×C139—24no—
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—22no—
196C2×D4×C139—22no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—21no—
213C2×D4×C139—44no—
214C2×D4×C139—44no—
215C2×D4×C139—44no—
216C2×D4×C139—44no—
217C2×D4×C139—41no—
218C2×D4×C139—41no—
219C2×D4×C139—41no—
220C2×D4×C139—42no—
221C2×D4×C139—42no—
222C2×D4×C139—42no—
223C2×D4×C139—42no—
224C2×D4×C139—42no—
225C2×D4×C139—81no—
226C2×D4×C139—81no—
227C2×D4×C139—81no—
228C2×D4×C139—81no—
229C2×D4×C139—81no—
230C2×D4×C139—81no—
231C2×D4×C139—81no—
232C2×D4×C139—81no—
233C2×D4×C139—81no—
234C2×D4×C139—81no—
235C2×D4×C139—81no—
236C2×D4×C139—81no—
237C2×D4×C139—81no—
238C2×D4×C139—81no—
239C2×D4×C139C2×D412yes—
240C2×D4×C139C2×D412yes—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—21no—
249C22×C4×C139—21no—
250C22×C4×C139—21no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139C2×D411yescharacteristic
261C22×C4×C139C2×D411yescharacteristic
262C22×C4×C139C2×D412yes—
263C22×C4×C139C2×D412yes—
264C22×C4×C139C2×D411yescharacteristic
265C22×C4×C139C2×D412yes—
266C22×C4×C139#4112yes—
267C22×C4×C139C2411yescharacteristic
268D8×C139—44no—
269D8×C139—44no—
270M16×C139—44no—
271C2×C8×C139—21no—
272C2×C8×C139—21no—
273C2×C8×C139—21no—
274C2×C8×C139—21no—
275C2×C8×C139—21no—
276C2×C8×C139—21no—
277C2×C8×C139—21no—
278C2×C8×C139—21no—
279C2×C8×C139—21no—
280C2×C8×C139—21no—
281C2×C8×C139—44no—
282C2×C8×C139C2×D412yes—
283C2×C8×C139C2×D412yes—
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139—21no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139—21no—
289C4⋊C4×C139—21no—
290C4⋊C4×C139—21no—
291C4⋊C4×C139—21no—
292C4⋊C4×C139C2×D412yes—
293C4⋊C4×C139C2×D412yes—
294C22⋊C4×C139—24no—
295C22⋊C4×C139—24no—
296C22⋊C4×C139—24no—
297C22⋊C4×C139—24no—
298C22⋊C4×C139—24no—
299C22⋊C4×C139—42no—
300C22⋊C4×C139—42no—
301C22⋊C4×C139—42no—
302C22⋊C4×C139—81no—
303C22⋊C4×C139—81no—
304C22⋊C4×C139—81no—
305C42×C139—24no—
306C23×C139—21no—
307C23×C139—21no—
308C23×C139—21no—
309C23×C139—21no—
310C23×C139—21no—
311C23×C139—21no—
312C23×C139—21no—
313C23×C139—21no—
314C23×C139—21no—
315C23×C139—21no—
316C23×C139—21no—
317C23×C139—21no—
318C23×C139—22no—
319C23×C139—22no—
320C23×C139—21no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—21no—
324C23×C139—21no—
325C23×C139—21no—
326C23×C139—21no—
327C23×C139—48no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—41no—
333C23×C139—41no—
334C23×C139—41no—
335C23×C139—41no—
336C23×C139—41no—
337C23×C139—41no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—84no—
348C23×C139—84no—
349C23×C139—84no—
350C23×C139—84no—
351C23×C139—84no—
352C23×C139—84no—
353C23×C139#12012yes—
354C23×C139#12112yes—
355C23×C139C22×D411yescharacteristic
356Q8×C139—44no—
357D4×C139—22no—
358D4×C139—22no—
359D4×C139—22no—
360D4×C139—22no—
361D4×C139—44no—
362D4×C139—44no—
363D4×C139—48no—
364D4×C139—44no—
365D4×C139—41no—
366D4×C139—41no—
367D4×C139—41no—
368D4×C139—41no—
369D4×C139—41no—
370D4×C139—41no—
371D4×C139—41no—
372D4×C139—41no—
373D4×C139—84no—
374D4×C139—84no—
375D4×C139—84no—
376D4×C139—84no—
377D4×C139—84no—
378D4×C139—84no—
379D4×C139—84no—
380C2×C4×C139—21no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—22no—
385C2×C4×C139—22no—
386C2×C4×C139—22no—
387C2×C4×C139—22no—
388C2×C4×C139—22no—
389C2×C4×C139—22no—
390C2×C4×C139—22no—
391C2×C4×C139—22no—
392C2×C4×C139—22no—
393C2×C4×C139—22no—
394C2×C4×C139—21no—
395C2×C4×C139—21no—
396C2×C4×C139—21no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139—41no—
409C2×C4×C139—41no—
410C2×C4×C139—41no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
413C2×C4×C139—41no—
414C2×C4×C139#12012yes—
415C2×C4×C139#12112yes—
416C2×C4×C139C22×D411yescharacteristic
417C2×C4×C139C22×D411yescharacteristic
418C2×C4×C139C22×D411yescharacteristic
419C2×C4×C139C2×#4111yescharacteristic
420C2×C4×C139H(5,𝔽2)11yescharacteristic
421C2×C4×C139H(5,𝔽2)11yescharacteristic
422C8×C139—22no—
423C8×C139—22no—
424C8×C139—41no—
425C8×C139—41no—
426C22×C139—22no—
427C22×C139—22no—
428C22×C139—22no—
429C22×C139—22no—
430C22×C139—22no—
431C22×C139—22no—
432C22×C139—41no—
433C22×C139—41no—
434C22×C139—41no—
435C22×C139—41no—
436C22×C139—41no—
437C22×C139—41no—
438C22×C139—41no—
439C22×C139—41no—
440C22×C139—41no—
441C22×C139—42no—
442C22×C139—42no—
443C22×C139—41no—
444C22×C139—41no—
445C22×C139—41no—
446C22×C139—42no—
447C22×C139—42no—
448C22×C139—41no—
449C22×C139—42no—
450C22×C139—42no—
451C22×C139—41no—
452C22×C139—41no—
453C22×C139—816no—
454C22×C139—81no—
455C22×C139—81no—
456C22×C139—81no—
457C22×C139—81no—
458C22×C139—81no—
459C22×C139—81no—
460C22×C139—81no—
461C22×C139—81no—
462C22×C139—81no—
463C22×C139—81no—
464C22×C139—81no—
465C22×C139—81no—
466C22×C139—81no—
467C22×C139—81no—
468C22×C139—81no—
469C22×C139C2×#12011yescharacteristic
470C22×C139C2×#12111yescharacteristic
471C22×C139#53411yescharacteristic
472C22×C139#57611yescharacteristic
473C22×C139#57611yescharacteristic
474C22×C139#57611yescharacteristic
475C22×C139#57711yescharacteristic
476C4×C139—22no—
477C4×C139—22no—
478C4×C139—41no—
479C4×C139—42no—
480C4×C139—42no—
481C4×C139—81no—
482C4×C139—81no—
483C4×C139—81no—
484C4×C139D4211yescharacteristic
485C4×C139D4211yescharacteristic
486C4×C139#54611yescharacteristic
487C4×C139#54611yescharacteristic
488C2×C139—42no—
489C2×C139—42no—
490C2×C139—81no—
491C2×C139—82no—
492C2×C139—82no—
493C2×C139—161no—
494C2×C139#241011yescharacteristic
495C2×C139#300811yescharacteristic
496C2×C139#301211yescharacteristic
497C2×C139#305811yescharacteristic
498C2×C139#306211yescharacteristic
499C2×C139#319811yescharacteristic
500C2×C139#319911yescharacteristic
501#24390C13911yesmaximal, characteristic, direct product factor, Sylow
502C139#2439011yescharacteristic, direct product factor, Sylow
503C2×#535C2×C13911yescharacteristic, complemented
504C2×#469C2×C13911yescharacteristic, complemented
505C2×#466C2×C13911yescharacteristic, complemented
506C2×#447C2×C13911yescharacteristic, complemented
507C2×#408C2×C13911yescharacteristic, complemented
508#2615C2×C13911yescharacteristic, complemented
509#2034C2×C13911yescharacteristic, complemented
510#2033C2×C13911yescharacteristic, complemented
511#1999C2×C13911yescharacteristic, complemented
512#1999C2×C13911yescharacteristic, complemented
513#1895C2×C13911yescharacteristic, complemented
514#1893C2×C13911yescharacteristic, complemented
515#1875C2×C13911yescharacteristic, complemented
516#1854C2×C13911yescharacteristic, complemented
517#1786C2×C13911yescharacteristic, complemented
518C22×#41C22×C13911yescharacteristic
519C23×D4C22×C13911yescharacteristic
520C22×D8C22×C13911yescharacteristic
521C22×D8C22×C13911yescharacteristic
522C22×M16C22×C13911yescharacteristic, complemented
523C23×C8C22×C13911yescharacteristic, complemented
524#535—24no—
525#535—24no—
526C2×#127—21no—
527C2×#124—21no—
528C2×#121C22×C13911yescharacteristic
529C2×#121C22×C13911yescharacteristic
530C2×#121C22×C13911yescharacteristic
531C2×#121C22×C13911yescharacteristic
532C2×#121C22×C13911yescharacteristic
533C2×#121C22×C13911yescharacteristic, complemented
534C2×#121C22×C13911yescharacteristic, complemented
535C2×#120—21no—
536C2×#120—21no—
537C2×#117C22×C13911yescharacteristic
538#469—24no—
539#466—24no—
540#447—24no—
541C2×#107C22×C13911yescharacteristic, complemented
542C2×#106C22×C13911yescharacteristic, complemented
543C2×#102C22×C13911yescharacteristic
544C2×#102C22×C13911yescharacteristic
545C2×#102C22×C13911yescharacteristic
546C2×#102C22×C13911yescharacteristic
547C2×#102C22×C13911yescharacteristic
548C2×#102C22×C13911yescharacteristic
549C2×#102C22×C13911yescharacteristic, complemented
550C2×#102C22×C13911yescharacteristic, complemented
551#408—24no—
552C2×C22⋊C8C22×C13911yescharacteristic
553C2×C22⋊C8C22×C13911yescharacteristic
554C2×C22⋊C8C22×C13911yescharacteristic, complemented
555C2×C22⋊C8C22×C13911yescharacteristic, complemented
556#393—21no—
557#392—21no—
558#392—21no—
559#392—21no—
560#380C22×C13911yescharacteristic
561#380C22×C13911yescharacteristic, complemented
562#380C22×C13911yescharacteristic, complemented
563#340C22×C13911yescharacteristic, complemented
564#340C22×C13911yescharacteristic, complemented
565#340C22×C13911yescharacteristic, complemented
566#340C22×C13911yescharacteristic, complemented
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C13911yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C13911yescharacteristic
590C22×D4D4×C13911yescharacteristic
591C22×D4D4×C13911yescharacteristic
592C22×D4C23×C13911yescharacteristic
593C22×D4C23×C13911yescharacteristic
594C22×D4C23×C13911yescharacteristic
595C23×C4C23×C13911yescharacteristic
596C23×C4C23×C13911yescharacteristic
597C23×C4C23×C13911yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C13911yescharacteristic
611C22×C8C23×C13911yescharacteristic
612C22×C8C23×C13911yescharacteristic
613C22×C8C23×C13911yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C13914yescomplemented
629#121D4×C13914yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C13911yescharacteristic
635C2×C4⋊C4C23×C13911yescharacteristic
636C2×C4⋊C4C23×C13911yescharacteristic
637C2×C4⋊C4C23×C13911yescharacteristic
638C2×C4⋊C4C23×C13911yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C13914yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C13911yescharacteristic
679C24C2×D4×C13911yescharacteristic
680C24C2×D4×C13911yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C13912yes—
742C2×D4C2×D4×C13912yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C13911yescharacteristic
763C22×C4C2×D4×C13911yescharacteristic
764C22×C4C2×D4×C13912yes—
765C22×C4C2×D4×C13912yes—
766C22×C4C2×D4×C13911yescharacteristic
767C22×C4C2×D4×C13912yes—
768C22×C4#41×C13912yes—
769C22×C4C24×C13911yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C13912yes—
785C2×C8C2×D4×C13912yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C13912yes—
795C4⋊C4C2×D4×C13912yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C13912yes—
856C23#121×C13912yes—
857C23C22×D4×C13911yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C13912yes—
917C2×C4#121×C13912yes—
918C2×C4C22×D4×C13911yescharacteristic
919C2×C4C22×D4×C13911yescharacteristic
920C2×C4C22×D4×C13911yescharacteristic
921C2×C4C2×#41×C13911yescharacteristic
922C2×C4H(5,𝔽2)×C13911yescharacteristic
923C2×C4H(5,𝔽2)×C13911yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C13911yescharacteristic
972C22C2×#121×C13911yescharacteristic
973C22#534×C13911yescharacteristic
974C22#576×C13911yescharacteristic
975C22#576×C13911yescharacteristic
976C22#576×C13911yescharacteristic
977C22#577×C13911yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C13911yescharacteristic
987C4D42×C13911yescharacteristic
988C4#546×C13911yescharacteristic
989C4#546×C13911yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2#2410×C13911yescharacteristic
997C2#3008×C13911yescharacteristic
998C2#3012×C13911yescharacteristic
999C2#3058×C13911yescharacteristic
1000C2#3062×C13911yescharacteristic
1001C2#3198×C13911yescharacteristic
1002C2#3199×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C139C2semidirect
2. C2×#469×C139C2semidirect
3. C2×#466×C139C2semidirect
4. C2×#447×C139C2semidirect
5. C2×#408×C139C2semidirect
6. #2615×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1999×C139C2semidirect
10. #1999×C139C2semidirect
11. #1895×C139C2semidirect
12. #1893×C139C2semidirect
13. #1875×C139C2semidirect
14. #1854×C139C2semidirect
15. #1786×C139C2semidirect
20. C22×M16×C139C22semidirect
21. C23×C8×C139C22semidirect
31. C2×#121×C139C22semidirect
32. C2×#121×C139C22semidirect
39. C2×#107×C139C22semidirect
40. C2×#106×C139C22semidirect
47. C2×#102×C139C22semidirect
48. C2×#102×C139C22semidirect
52. C2×C22⋊C8×C139C22semidirect
53. C2×C22⋊C8×C139C22semidirect
59. #380×C139C22semidirect
60. #380×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
126. #121×C139D4semidirect
127. #121×C139D4semidirect
162. C22⋊C8×C139D4semidirect
501. #24390C139direct (N × H)
502. C139#24390direct (N × H)
503. C2×#535C2×C139semidirect
504. C2×#469C2×C139semidirect
505. C2×#466C2×C139semidirect
506. C2×#447C2×C139semidirect
507. C2×#408C2×C139semidirect
508. #2615C2×C139semidirect
509. #2034C2×C139semidirect
510. #2033C2×C139semidirect
511. #1999C2×C139semidirect
512. #1999C2×C139semidirect
513. #1895C2×C139semidirect
514. #1893C2×C139semidirect
515. #1875C2×C139semidirect
516. #1854C2×C139semidirect
517. #1786C2×C139semidirect
522. C22×M16C22×C139semidirect
523. C23×C8C22×C139semidirect
533. C2×#121C22×C139semidirect
534. C2×#121C22×C139semidirect
541. C2×#107C22×C139semidirect
542. C2×#106C22×C139semidirect
549. C2×#102C22×C139semidirect
550. C2×#102C22×C139semidirect
554. C2×C22⋊C8C22×C139semidirect
555. C2×C22⋊C8C22×C139semidirect
561. #380C22×C139semidirect
562. #380C22×C139semidirect
563. #340C22×C139semidirect
564. #340C22×C139semidirect
565. #340C22×C139semidirect
566. #340C22×C139semidirect
628. #121D4×C139semidirect
629. #121D4×C139semidirect
664. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1392
C2×#469×C1392
C2×#466×C1392
C2×#447×C1392
C2×#408×C1392
#2615×C1392
#2034×C1392
#2033×C1392
#1999×C1392
#1895×C1392
#1893×C1392
#1875×C1392
#1854×C1392
#1786×C1392
#24390139