Finite Group Databasebeta

← C139×#25132 #48019728

Subgroups — C139×#25132 #48019728

Order 35584.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#447×C139C211yesmaximal, characteristic, complemented
3C2×#436×C139C211yesmaximal, characteristic, complemented
4C2×#418×C139C211yesmaximal, characteristic, complemented
5#2414×C139C211yesmaximal, characteristic, complemented
6#2408×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2033×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1970×C139C211yesmaximal, characteristic, complemented
12#1934×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1895×C139C211yesmaximal, characteristic, complemented
15#1854×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic, complemented
21C2×#121×C139C2211yescharacteristic
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic, complemented
25C2×#120×C139—21no—
26C2×C4×D4×C139C2211yescharacteristic
27C2×#117×C139C2211yescharacteristic
28#469×C139—24no—
29#447×C139—24no—
30#436×C139—24no—
31C2×#107×C139C2211yescharacteristic, complemented
32C2×#106×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34#418×C139—24no—
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic, complemented
42C2×#102×C139C2211yescharacteristic, complemented
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic, complemented
45C2×C4×C8×C139C2211yescharacteristic, complemented
46#394×C139—21no—
47#394×C139—21no—
48#392×C139—21no—
49#392×C139—21no—
50#390×C139—21no—
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#390×C139C2211yescharacteristic, complemented
54#389×C139C2211yescharacteristic, complemented
55#388×C139—21no—
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic, complemented
58#379×C139—21no—
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—22no—
71C22×D4×C139—21no—
72C22×D4×C139—22no—
73C22×D4×C139—41no—
74C22×D4×C139—41no—
75C22×D4×C139D411yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78C22×D4×C139C2311yescharacteristic
79C23×C4×C139C2311yescharacteristic
80C23×C4×C139C2311yescharacteristic
81C2×D8×C139—22no—
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—41no—
86C2×D8×C139—41no—
87C2×M16×C139—22no—
88C2×M16×C139—22no—
89C2×M16×C139—22no—
90C2×M16×C139—22no—
91C2×M16×C139—41no—
92C2×M16×C139—41no—
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—41no—
103#121×C139—41no—
104#121×C139—41no—
105#120×C139—44no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108#117×C139—22no—
109#117×C139—41no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139D411yescharacteristic
131C2×C22⋊C4×C139D411yescharacteristic
132C2×C42×C139—21no—
133C2×C42×C139C2311yescharacteristic
134#107×C139—41no—
135#106×C139—22no—
136C4⋊C8×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144#102×C139D414yescomplemented
145C22⋊C8×C139—22no—
146C22⋊C8×C139D414yescomplemented
147C4×C8×C139—22no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—42no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—81no—
160C24×C139—81no—
161C24×C139C2×D411yescharacteristic
162C24×C139C2×D411yescharacteristic
163C2×D4×C139—28no—
164C2×D4×C139—22no—
165C2×D4×C139—22no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—44no—
183C2×D4×C139—44no—
184C2×D4×C139—41no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—44no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—81no—
197C2×D4×C139—81no—
198C2×D4×C139—81no—
199C2×D4×C139—81no—
200C2×D4×C139—81no—
201C2×D4×C139C2×D412yes—
202C2×D4×C139#4112yes—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2×D411yescharacteristic
221C22×C4×C139C2×D412yes—
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139#4112yes—
224C22×C4×C139C2411yescharacteristic
225D8×C139—44no—
226D8×C139—44no—
227M16×C139—44no—
228M16×C139—44no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139C2×D412yes—
239C2×C8×C139C2×D412yes—
240C2×C8×C139C2×D412yes—
241C4⋊C4×C139—22no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—81no—
252C4⋊C4×C139C2×D412yes—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—42no—
263C22⋊C4×C139—42no—
264C22⋊C4×C139—81no—
265C22⋊C4×C139—81no—
266C22⋊C4×C139—81no—
267C22⋊C4×C139—81no—
268C42×C139—21no—
269C42×C139—21no—
270C42×C139—42no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—22no—
279C23×C139—21no—
280C23×C139—22no—
281C23×C139—21no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—48no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—84no—
307C23×C139—84no—
308C23×C139—84no—
309C23×C139—84no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139#12112yes—
313C23×C139C22×D411yescharacteristic
314D4×C139—22no—
315D4×C139—22no—
316D4×C139—22no—
317D4×C139—22no—
318D4×C139—44no—
319D4×C139—48no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—84no—
329D4×C139—84no—
330D4×C139—84no—
331D4×C139—84no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—22no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—22no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139#12112yes—
366C2×C4×C139AGL(1,ℤ/8)12yes—
367C2×C4×C139C22×D411yescharacteristic
368C2×C4×C139C22×D411yescharacteristic
369C2×C4×C139C2×#4111yescharacteristic
370C2×C4×C139C2×#4111yescharacteristic
371C2×C4×C139H(5,𝔽2)11yescharacteristic
372C2×C4×C139H(5,𝔽2)11yescharacteristic
373C8×C139—22no—
374C8×C139—22no—
375C8×C139—22no—
376C8×C139—41no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—42no—
386C22×C139—42no—
387C22×C139—41no—
388C22×C139—42no—
389C22×C139—41no—
390C22×C139—42no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—42no—
395C22×C139—41no—
396C22×C139—42no—
397C22×C139—816no—
398C22×C139—81no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139C2×#12111yescharacteristic
414C22×C139D4211yescharacteristic
415C22×C139#54611yescharacteristic
416C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C139#57511yescharacteristic
418C22×C139#57611yescharacteristic
419C22×C139#57611yescharacteristic
420C4×C139—22no—
421C4×C139—22no—
422C4×C139—41no—
423C4×C139—42no—
424C4×C139—41no—
425C4×C139—81no—
426C4×C139—81no—
427C4×C139—81no—
428C4×C139—81no—
429C4×C139#52511yescharacteristic
430C4×C139#53811yescharacteristic
431C4×C139D4211yescharacteristic
432C4×C139#54611yescharacteristic
433C2×C139—42no—
434C2×C139—81no—
435C2×C139—82no—
436C2×C139—82no—
437C2×C139—161no—
438C2×C139#242411yescharacteristic
439C2×C139#305511yescharacteristic
440C2×C139#305811yescharacteristic
441C2×C139#327311yescharacteristic
442C2×C139#327411yescharacteristic
443C2×C139#332211yescharacteristic
444C2×C139#332511yescharacteristic
445#25132C13911yesmaximal, characteristic, direct product factor, Sylow
446C139#2513211yescharacteristic, direct product factor, Sylow
447C2×#469C2×C13911yescharacteristic, complemented
448C2×#447C2×C13911yescharacteristic, complemented
449C2×#436C2×C13911yescharacteristic, complemented
450C2×#418C2×C13911yescharacteristic, complemented
451#2414C2×C13911yescharacteristic, complemented
452#2408C2×C13911yescharacteristic, complemented
453#2065C2×C13911yescharacteristic, complemented
454#2054C2×C13911yescharacteristic, complemented
455#2033C2×C13911yescharacteristic, complemented
456#1999C2×C13911yescharacteristic, complemented
457#1970C2×C13911yescharacteristic, complemented
458#1934C2×C13911yescharacteristic, complemented
459#1895C2×C13911yescharacteristic, complemented
460#1895C2×C13911yescharacteristic, complemented
461#1854C2×C13911yescharacteristic, complemented
462C23×D4C22×C13911yescharacteristic
463C22×D8C22×C13911yescharacteristic
464C22×D8C22×C13911yescharacteristic
465C22×M16C22×C13911yescharacteristic
466C22×M16C22×C13911yescharacteristic, complemented
467C2×#121C22×C13911yescharacteristic
468C2×#121C22×C13911yescharacteristic
469C2×#121C22×C13911yescharacteristic
470C2×#121C22×C13911yescharacteristic, complemented
471C2×#120—21no—
472C2×C4×D4C22×C13911yescharacteristic
473C2×#117C22×C13911yescharacteristic
474#469—24no—
475#447—24no—
476#436—24no—
477C2×#107C22×C13911yescharacteristic, complemented
478C2×#106C22×C13911yescharacteristic, complemented
479C2×C4⋊C8C22×C13911yescharacteristic, complemented
480#418—24no—
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×#102C22×C13911yescharacteristic
484C2×#102C22×C13911yescharacteristic
485C2×#102C22×C13911yescharacteristic
486C2×#102C22×C13911yescharacteristic
487C2×#102C22×C13911yescharacteristic, complemented
488C2×#102C22×C13911yescharacteristic, complemented
489C2×C22⋊C8C22×C13911yescharacteristic
490C2×C22⋊C8C22×C13911yescharacteristic, complemented
491C2×C4×C8C22×C13911yescharacteristic, complemented
492#394—21no—
493#394—21no—
494#392—21no—
495#392—21no—
496#390—21no—
497#390C22×C13911yescharacteristic
498#390C22×C13911yescharacteristic
499#390C22×C13911yescharacteristic, complemented
500#389C22×C13911yescharacteristic, complemented
501#388—21no—
502#380C22×C13911yescharacteristic
503#380C22×C13911yescharacteristic, complemented
504#379—21no—
505#340C22×C13911yescharacteristic, complemented
506#340C22×C13911yescharacteristic, complemented
507#340C22×C13911yescharacteristic, complemented
508#340C22×C13911yescharacteristic, complemented
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C13911yescharacteristic
522C22×D4C23×C13911yescharacteristic
523C22×D4C23×C13911yescharacteristic
524C22×D4C23×C13911yescharacteristic
525C23×C4C23×C13911yescharacteristic
526C23×C4C23×C13911yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C13911yescharacteristic
540C22×C8C23×C13911yescharacteristic
541C22×C8C23×C13911yescharacteristic
542C22×C8C23×C13911yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C13911yescharacteristic
558C2×C4⋊C4C23×C13911yescharacteristic
559C2×C4⋊C4C23×C13911yescharacteristic
560C2×C4⋊C4C23×C13911yescharacteristic
561C2×C4⋊C4C23×C13911yescharacteristic
562C2×C4⋊C4C23×C13911yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C13911yescharacteristic
577C2×C22⋊C4D4×C13911yescharacteristic
578C2×C42—21no—
579C2×C42C23×C13911yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C13914yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C13914yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C13911yescharacteristic
608C24C2×D4×C13911yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C13912yes—
648C2×D4#41×C13912yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C13911yescharacteristic
665C22×C4C2×D4×C13911yescharacteristic
666C22×C4C2×D4×C13911yescharacteristic
667C22×C4C2×D4×C13912yes—
668C22×C4C2×D4×C13911yescharacteristic
669C22×C4#41×C13912yes—
670C22×C4C24×C13911yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C13912yes—
685C2×C8C2×D4×C13912yes—
686C2×C8C2×D4×C13912yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C13912yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C13912yes—
759C23C22×D4×C13911yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C13912yes—
812C2×C4AGL(1,ℤ/8)×C13912yes—
813C2×C4C22×D4×C13911yescharacteristic
814C2×C4C22×D4×C13911yescharacteristic
815C2×C4C2×#41×C13911yescharacteristic
816C2×C4C2×#41×C13911yescharacteristic
817C2×C4H(5,𝔽2)×C13911yescharacteristic
818C2×C4H(5,𝔽2)×C13911yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C13911yescharacteristic
860C22D42×C13911yescharacteristic
861C22#546×C13911yescharacteristic
862C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
863C22#575×C13911yescharacteristic
864C22#576×C13911yescharacteristic
865C22#576×C13911yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—41no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4#525×C13911yescharacteristic
876C4#538×C13911yescharacteristic
877C4D42×C13911yescharacteristic
878C4#546×C13911yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2#2424×C13911yescharacteristic
885C2#3055×C13911yescharacteristic
886C2#3058×C13911yescharacteristic
887C2#3273×C13911yescharacteristic
888C2#3274×C13911yescharacteristic
889C2#3322×C13911yescharacteristic
890C2#3325×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C139C2semidirect
2. C2×#447×C139C2semidirect
3. C2×#436×C139C2semidirect
4. C2×#418×C139C2semidirect
5. #2414×C139C2semidirect
6. #2408×C139C2semidirect
7. #2065×C139C2semidirect
8. #2054×C139C2semidirect
9. #2033×C139C2semidirect
10. #1999×C139C2semidirect
11. #1970×C139C2semidirect
12. #1934×C139C2semidirect
13. #1895×C139C2semidirect
14. #1895×C139C2semidirect
15. #1854×C139C2semidirect
20. C22×M16×C139C22semidirect
24. C2×#121×C139C22semidirect
31. C2×#107×C139C22semidirect
32. C2×#106×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
41. C2×#102×C139C22semidirect
42. C2×#102×C139C22semidirect
44. C2×C22⋊C8×C139C22semidirect
45. C2×C4×C8×C139C22semidirect
53. #390×C139C22semidirect
54. #389×C139C22semidirect
57. #380×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
144. #102×C139D4semidirect
146. C22⋊C8×C139D4semidirect
445. #25132C139direct (N × H)
446. C139#25132direct (N × H)
447. C2×#469C2×C139semidirect
448. C2×#447C2×C139semidirect
449. C2×#436C2×C139semidirect
450. C2×#418C2×C139semidirect
451. #2414C2×C139semidirect
452. #2408C2×C139semidirect
453. #2065C2×C139semidirect
454. #2054C2×C139semidirect
455. #2033C2×C139semidirect
456. #1999C2×C139semidirect
457. #1970C2×C139semidirect
458. #1934C2×C139semidirect
459. #1895C2×C139semidirect
460. #1895C2×C139semidirect
461. #1854C2×C139semidirect
466. C22×M16C22×C139semidirect
470. C2×#121C22×C139semidirect
477. C2×#107C22×C139semidirect
478. C2×#106C22×C139semidirect
479. C2×C4⋊C8C22×C139semidirect
487. C2×#102C22×C139semidirect
488. C2×#102C22×C139semidirect
490. C2×C22⋊C8C22×C139semidirect
491. C2×C4×C8C22×C139semidirect
499. #390C22×C139semidirect
500. #389C22×C139semidirect
503. #380C22×C139semidirect
505. #340C22×C139semidirect
506. #340C22×C139semidirect
507. #340C22×C139semidirect
508. #340C22×C139semidirect
590. #102D4×C139semidirect
592. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1392
C2×#447×C1392
C2×#436×C1392
C2×#418×C1392
#2414×C1392
#2408×C1392
#2065×C1392
#2054×C1392
#2033×C1392
#1999×C1392
#1970×C1392
#1934×C1392
#1895×C1392
#1854×C1392
#25132139