Finite Group Databasebeta

← C139×#24762 #48019358

Subgroups — C139×#24762 #48019358

Order 35584.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#466×C139C211yesmaximal, characteristic, complemented
3C2×#459×C139C211yesmaximal, characteristic, complemented
4C2×#424×C139C211yesmaximal, characteristic, complemented
5#2619×C139C211yesmaximal, characteristic, complemented
6#2324×C139C211yesmaximal, characteristic, complemented
7#2067×C139C211yesmaximal, characteristic, complemented
8#2065×C139C211yesmaximal, characteristic, complemented
9#2054×C139C211yesmaximal, characteristic, complemented
10#2054×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1893×C139C211yesmaximal, characteristic, complemented
15#1804×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20C2×#127×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×C4×D4×C139C2211yescharacteristic
25C2×#117×C139C2211yescharacteristic
26#469×C139—24no—
27#466×C139—24no—
28#459×C139—24no—
29C2×#107×C139C2211yescharacteristic
30C2×#106×C139C2211yescharacteristic
31#424×C139—24no—
32C2×C4⋊C8×C139C2211yescharacteristic
33C2×C4⋊C8×C139C2211yescharacteristic
34C2×C4⋊C8×C139C2211yescharacteristic
35C2×C4⋊C8×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44#394×C139—21no—
45#394×C139—21no—
46#392×C139—21no—
47#392×C139—21no—
48#390×C139—21no—
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#388×C139—21no—
54#386×C139—21no—
55#385×C139—21no—
56#382×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58C4×C4⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139C2311yescharacteristic
73C2×D8×C139—22no—
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—41no—
78C2×D8×C139—41no—
79C2×M16×C139—22no—
80C2×M16×C139—22no—
81C2×M16×C139—41no—
82C22×C8×C139—22no—
83C22×C8×C139—22no—
84C22×C8×C139—41no—
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89#127×C139—22no—
90#127×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—22no—
94#121×C139—22no—
95#121×C139—22no—
96#121×C139D414yescomplemented
97C4×D4×C139—22no—
98C4×D4×C139—22no—
99#117×C139—22no—
100#117×C139—22no—
101C2×C4⋊C4×C139—21no—
102C2×C4⋊C4×C139D411yescharacteristic
103C2×C4⋊C4×C139D411yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C4⋊C4×C139C2311yescharacteristic
108C2×C4⋊C4×C139C2311yescharacteristic
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139D411yescharacteristic
121C2×C22⋊C4×C139D411yescharacteristic
122C2×C42×C139—21no—
123C2×C42×C139C2311yescharacteristic
124C2×C42×C139C2311yescharacteristic
125#107×C139—22no—
126#106×C139—22no—
127C4⋊C8×C139—22no—
128C4⋊C8×C139—22no—
129C4⋊C8×C139—22no—
130C4⋊C8×C139D414yescomplemented
131#102×C139—22no—
132#102×C139—22no—
133#102×C139—22no—
134#102×C139—22no—
135#102×C139—22no—
136#102×C139—22no—
137#102×C139—41no—
138#102×C139—41no—
139#95×C139—21no—
140#95×C139—21no—
141#95×C139—21no—
142#95×C139—21no—
143#95×C139—21no—
144C24×C139—21no—
145C24×C139—21no—
146C24×C139—21no—
147C24×C139C2×D411yescharacteristic
148C2×D4×C139—24no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—42no—
167C2×D4×C139—42no—
168C2×D4×C139—42no—
169C2×D4×C139—42no—
170C2×D4×C139—81no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139—81no—
174C2×D4×C139—81no—
175C2×D4×C139—81no—
176C2×D4×C139—81no—
177C2×D4×C139—81no—
178C2×D4×C139—81no—
179C2×D4×C139—81no—
180C2×D4×C139C2×D412yes—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—42no—
191C22×C4×C139—81no—
192C22×C4×C139—81no—
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D412yes—
199C22×C4×C139#4112yes—
200C22×C4×C139C2411yescharacteristic
201D8×C139—44no—
202D8×C139—44no—
203M16×C139—44no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—44no—
215C2×C8×C139C2×D412yes—
216C2×C8×C139C2×D412yes—
217C4⋊C4×C139—22no—
218C4⋊C4×C139—22no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—81no—
229C4⋊C4×C139C2×D412yes—
230C22⋊C4×C139—24no—
231C22⋊C4×C139—22no—
232C22⋊C4×C139—22no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—81no—
237C22⋊C4×C139—81no—
238C22⋊C4×C139—81no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139—81no—
241C22⋊C4×C139—81no—
242C22⋊C4×C139—81no—
243C42×C139—21no—
244C42×C139—21no—
245C42×C139—81no—
246C42×C139C2×D412yes—
247C42×C139#4112yes—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—22no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139—41no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139#12112yes—
276C23×C139C22×D411yescharacteristic
277D4×C139—22no—
278D4×C139—22no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
283D4×C139—41no—
284D4×C139—41no—
285D4×C139—41no—
286D4×C139—41no—
287D4×C139—41no—
288D4×C139—41no—
289D4×C139—84no—
290D4×C139—84no—
291D4×C139—84no—
292D4×C139—84no—
293D4×C139—84no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—22no—
301C2×C4×C139—22no—
302C2×C4×C139—22no—
303C2×C4×C139—22no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—22no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—84no—
326C2×C4×C139#12112yes—
327C2×C4×C139#12112yes—
328C2×C4×C139#12112yes—
329C2×C4×C139C22×D411yescharacteristic
330C2×C4×C139C22×D411yescharacteristic
331C2×C4×C139C2×#4111yescharacteristic
332C2×C4×C139C2×#4111yescharacteristic
333C2×C4×C139H(5,𝔽2)11yescharacteristic
334C2×C4×C1392−1+411yescharacteristic
335C8×C139—22no—
336C8×C139—22no—
337C8×C139—41no—
338C8×C139—41no—
339C22×C139—22no—
340C22×C139—22no—
341C22×C139—22no—
342C22×C139—41no—
343C22×C139—41no—
344C22×C139—41no—
345C22×C139—41no—
346C22×C139—42no—
347C22×C139—42no—
348C22×C139—42no—
349C22×C139—81no—
350C22×C139—81no—
351C22×C139—81no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—81no—
359C22×C139—81no—
360C22×C139—81no—
361C22×C139—81no—
362C22×C139—81no—
363C22×C139—81no—
364C22×C139—81no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139C2×#12111yescharacteristic
368C22×C139C2×#12111yescharacteristic
369C22×C139#53711yescharacteristic
370C22×C139#57611yescharacteristic
371C22×C139#57611yescharacteristic
372C22×C139#57611yescharacteristic
373C22×C139#57711yescharacteristic
374C4×C139—22no—
375C4×C139—22no—
376C4×C139—22no—
377C4×C139—42no—
378C4×C139—41no—
379C4×C139—41no—
380C4×C139—81no—
381C4×C139—81no—
382C4×C139—81no—
383C4×C139—81no—
384C4×C139D4211yescharacteristic
385C4×C139#54711yescharacteristic
386C4×C139#54811yescharacteristic
387C4×C139#55311yescharacteristic
388C2×C139—42no—
389C2×C139—82no—
390C2×C139—161no—
391C2×C139—161no—
392C2×C139#241611yescharacteristic
393C2×C139#304111yescharacteristic
394C2×C139#304511yescharacteristic
395C2×C139#305811yescharacteristic
396C2×C139#306211yescharacteristic
397C2×C139#325711yescharacteristic
398C2×C139#325911yescharacteristic
399#24762C13911yesmaximal, characteristic, direct product factor, Sylow
400C139#2476211yescharacteristic, direct product factor, Sylow
401C2×#469C2×C13911yescharacteristic, complemented
402C2×#466C2×C13911yescharacteristic, complemented
403C2×#459C2×C13911yescharacteristic, complemented
404C2×#424C2×C13911yescharacteristic, complemented
405#2619C2×C13911yescharacteristic, complemented
406#2324C2×C13911yescharacteristic, complemented
407#2067C2×C13911yescharacteristic, complemented
408#2065C2×C13911yescharacteristic, complemented
409#2054C2×C13911yescharacteristic, complemented
410#2054C2×C13911yescharacteristic, complemented
411#1982C2×C13911yescharacteristic, complemented
412#1949C2×C13911yescharacteristic, complemented
413#1895C2×C13911yescharacteristic, complemented
414#1893C2×C13911yescharacteristic, complemented
415#1804C2×C13911yescharacteristic, complemented
416C22×D8C22×C13911yescharacteristic
417C22×D8C22×C13911yescharacteristic
418C22×M16C22×C13911yescharacteristic
419C23×C8C22×C13911yescharacteristic
420C2×#127C22×C13911yescharacteristic
421C2×#121C22×C13911yescharacteristic
422C2×#121C22×C13911yescharacteristic
423C2×#121C22×C13911yescharacteristic
424C2×C4×D4C22×C13911yescharacteristic
425C2×#117C22×C13911yescharacteristic
426#469—24no—
427#466—24no—
428#459—24no—
429C2×#107C22×C13911yescharacteristic
430C2×#106C22×C13911yescharacteristic
431#424—24no—
432C2×C4⋊C8C22×C13911yescharacteristic
433C2×C4⋊C8C22×C13911yescharacteristic
434C2×C4⋊C8C22×C13911yescharacteristic
435C2×C4⋊C8C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×#102C22×C13911yescharacteristic
438C2×#102C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×#102C22×C13911yescharacteristic
442C2×#102C22×C13911yescharacteristic
443C2×#102C22×C13911yescharacteristic
444#394—21no—
445#394—21no—
446#392—21no—
447#392—21no—
448#390—21no—
449#390C22×C13911yescharacteristic
450#390C22×C13911yescharacteristic
451#390C22×C13911yescharacteristic
452#389C22×C13911yescharacteristic
453#388—21no—
454#386—21no—
455#385—21no—
456#382C22×C13911yescharacteristic
457#380C22×C13911yescharacteristic
458C4×C4⋊C4C22×C13911yescharacteristic
459#340C22×C13911yescharacteristic
460#340C22×C13911yescharacteristic
461#340C22×C13911yescharacteristic
462#340C22×C13911yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C23×C13911yescharacteristic
469C22×D4C23×C13911yescharacteristic
470C22×D4C23×C13911yescharacteristic
471C23×C4—21no—
472C23×C4C23×C13911yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C13911yescharacteristic
486C22×C8C23×C13911yescharacteristic
487C22×C8C23×C13911yescharacteristic
488C22×C8C23×C13911yescharacteristic
489#127—22no—
490#127—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121D4×C13914yescomplemented
497C4×D4—22no—
498C4×D4—22no—
499#117—22no—
500#117—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C13911yescharacteristic
503C2×C4⋊C4D4×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
507C2×C4⋊C4C23×C13911yescharacteristic
508C2×C4⋊C4C23×C13911yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C13911yescharacteristic
521C2×C22⋊C4D4×C13911yescharacteristic
522C2×C42—21no—
523C2×C42C23×C13911yescharacteristic
524C2×C42C23×C13911yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8D4×C13914yescomplemented
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C2×D4×C13911yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C13912yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C13911yescharacteristic
594C22×C4C2×D4×C13911yescharacteristic
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4C2×D4×C13911yescharacteristic
597C22×C4C2×D4×C13911yescharacteristic
598C22×C4C2×D4×C13912yes—
599C22×C4#41×C13912yes—
600C22×C4C24×C13911yescharacteristic
601D8—44no—
602D8—44no—
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—44no—
615C2×C8C2×D4×C13912yes—
616C2×C8C2×D4×C13912yes—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—81no—
629C4⋊C4C2×D4×C13912yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42C2×D4×C13912yes—
647C42#41×C13912yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#121×C13912yes—
676C23C22×D4×C13911yescharacteristic
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4#121×C13912yes—
727C2×C4#121×C13912yes—
728C2×C4#121×C13912yes—
729C2×C4C22×D4×C13911yescharacteristic
730C2×C4C22×D4×C13911yescharacteristic
731C2×C4C2×#41×C13911yescharacteristic
732C2×C4C2×#41×C13911yescharacteristic
733C2×C4H(5,𝔽2)×C13911yescharacteristic
734C2×C42−1+4×C13911yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C13911yescharacteristic
768C22C2×#121×C13911yescharacteristic
769C22#537×C13911yescharacteristic
770C22#576×C13911yescharacteristic
771C22#576×C13911yescharacteristic
772C22#576×C13911yescharacteristic
773C22#577×C13911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4D42×C13911yescharacteristic
785C4#547×C13911yescharacteristic
786C4#548×C13911yescharacteristic
787C4#553×C13911yescharacteristic
788C2—42no—
789C2—82no—
790C2—161no—
791C2—161no—
792C2#2416×C13911yescharacteristic
793C2#3041×C13911yescharacteristic
794C2#3045×C13911yescharacteristic
795C2#3058×C13911yescharacteristic
796C2#3062×C13911yescharacteristic
797C2#3257×C13911yescharacteristic
798C2#3259×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C139C2semidirect
2. C2×#466×C139C2semidirect
3. C2×#459×C139C2semidirect
4. C2×#424×C139C2semidirect
5. #2619×C139C2semidirect
6. #2324×C139C2semidirect
7. #2067×C139C2semidirect
8. #2065×C139C2semidirect
9. #2054×C139C2semidirect
10. #2054×C139C2semidirect
11. #1982×C139C2semidirect
12. #1949×C139C2semidirect
13. #1895×C139C2semidirect
14. #1893×C139C2semidirect
15. #1804×C139C2semidirect
96. #121×C139D4semidirect
130. C4⋊C8×C139D4semidirect
399. #24762C139direct (N × H)
400. C139#24762direct (N × H)
401. C2×#469C2×C139semidirect
402. C2×#466C2×C139semidirect
403. C2×#459C2×C139semidirect
404. C2×#424C2×C139semidirect
405. #2619C2×C139semidirect
406. #2324C2×C139semidirect
407. #2067C2×C139semidirect
408. #2065C2×C139semidirect
409. #2054C2×C139semidirect
410. #2054C2×C139semidirect
411. #1982C2×C139semidirect
412. #1949C2×C139semidirect
413. #1895C2×C139semidirect
414. #1893C2×C139semidirect
415. #1804C2×C139semidirect
496. #121D4×C139semidirect
530. C4⋊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×#466×C1392
C2×#459×C1392
C2×#424×C1392
#2619×C1392
#2324×C1392
#2067×C1392
#2065×C1392
#2054×C1392
#1982×C1392
#1949×C1392
#1895×C1392
#1893×C1392
#1804×C1392
#24762139