Finite Group Databasebeta

← C139×#26926 #48021522

Subgroups — C139×#26926 #48021522

Order 35584.

1082 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×#480×C139C211yesmaximal, characteristic, complemented
2C2×#459×C139C211yesmaximal, characteristic, complemented
3#2428×C139C211yesmaximal, characteristic, complemented
4#2361×C139C211yesmaximal, characteristic, complemented
5#2086×C139C211yesmaximal, characteristic, complemented
6#2041×C139C211yesmaximal, characteristic, complemented
7#1999×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1970×C139C211yesmaximal, characteristic, complemented
10#1925×C139C211yesmaximal, characteristic, complemented
11#1923×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1874×C139C211yesmaximal, characteristic, complemented
14#1862×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C2×#127×C139C2211yescharacteristic
19C2×#121×C139—21no—
20C2×#121×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×#121×C139C2211yescharacteristic
23C2×C4×D4×C139—21no—
24C2×C4×D4×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C22×C4⋊C4×C139C2211yescharacteristic
27#480×C139—24no—
28#459×C139—24no—
29C2×#107×C139C2211yescharacteristic
30C2×#107×C139C2211yescharacteristic
31C2×C4⋊C8×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×C22⋊C8×C139C2211yescharacteristic
41C2×C22⋊C8×C139C2211yescharacteristic
42C2×C4×C8×C139C2211yescharacteristic
43#394×C139—21no—
44#392×C139—21no—
45#390×C139C2211yescharacteristic
46#390×C139C2211yescharacteristic
47#389×C139C2211yescharacteristic
48#389×C139C2211yescharacteristic
49#388×C139—21no—
50#386×C139—21no—
51#386×C139—21no—
52#385×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C23×C4×C139—21no—
70C23×C4×C139—21no—
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—
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83#127×C139—22no—
84#127×C139—41no—
85#121×C139—22no—
86#121×C139—22no—
87#121×C139—22no—
88#121×C139—22no—
89#121×C139—41no—
90#121×C139—41no—
91#121×C139—44no—
92C4×D4×C139—22no—
93C4×D4×C139—22no—
94C4×D4×C139—41no—
95C4×D4×C139—41no—
96C4×D4×C139—44no—
97C2×C4⋊C4×C139—22no—
98C2×C4⋊C4×C139—21no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139—21no—
101C2×C4⋊C4×C139—41no—
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
117C2×C22⋊C4×C139D411yescharacteristic
118C2×C42×C139—21no—
119C2×C42×C139C2311yescharacteristic
120C2×C42×C139C2311yescharacteristic
121#107×C139—22no—
122#107×C139—22no—
123C4⋊C8×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—22no—
128#102×C139—22no—
129#102×C139—41no—
130#102×C139—41no—
131#102×C139D414yescomplemented
132C22⋊C8×C139—22no—
133C22⋊C8×C139—41no—
134C4×C8×C139—41no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139D411yescharacteristic
139#95×C139D411yescharacteristic
140C24×C139—21no—
141C24×C139—21no—
142C24×C139—21no—
143C24×C139C2×D411yescharacteristic
144C2×D4×C139—24no—
145C2×D4×C139—21no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
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—42no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—42no—
167C2×D4×C139—42no—
168C2×D4×C139—42no—
169C2×D4×C139—42no—
170C2×D4×C139—42no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139—81no—
174C2×D4×C139—81no—
175C2×D4×C139C2×D412yes—
176C2×D4×C139#4112yes—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
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—42no—
189C22×C4×C139—42no—
190C22×C4×C139—42no—
191C22×C4×C139—42no—
192C22×C4×C139—42no—
193C22×C4×C139—42no—
194C22×C4×C139—81no—
195C22×C4×C139—81no—
196C22×C4×C139—81no—
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D411yescharacteristic
202C22×C4×C139C2411yescharacteristic
203D8×C139—44no—
204D8×C139—44no—
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—21no—
215C2×C8×C139—21no—
216C2×C8×C139C2×D412yes—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—42no—
225C4⋊C4×C139—42no—
226C4⋊C4×C139—42no—
227C4⋊C4×C139C2×D412yes—
228C4⋊C4×C139#4112yes—
229C4⋊C4×C139#4112yes—
230C22⋊C4×C139—24no—
231C22⋊C4×C139—41no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—81no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139D814yescomplemented
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—21no—
244C42×C139—21no—
245C42×C139—42no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—22no—
253C23×C139—22no—
254C23×C139—41no—
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×C139C2×D812yes—
274C23×C139C22×D411yescharacteristic
275D4×C139—22no—
276D4×C139—22no—
277D4×C139—22no—
278D4×C139—22no—
279D4×C139—48no—
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—84no—
289D4×C139—84no—
290D4×C139—84no—
291D4×C139—84no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—22no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—22no—
301C2×C4×C139—21no—
302C2×C4×C139—22no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—41no—
309C2×C4×C139—41no—
310C2×C4×C139—41no—
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—84no—
325C2×C4×C139—84no—
326C2×C4×C139—84no—
327C2×C4×C139C2×D812yes—
328C2×C4×C139C2×D812yes—
329C2×C4×C139C22×D411yescharacteristic
330C2×C4×C139C2×#4111yescharacteristic
331C2×C4×C139C2×#4111yescharacteristic
332C2×C4×C139C2×#4111yescharacteristic
333C2×C4×C139H(5,𝔽2)11yescharacteristic
334C2×C4×C139H(5,𝔽2)11yescharacteristic
335C8×C139—22no—
336C8×C139—41no—
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—42no—
350C22×C139—42no—
351C22×C139—42no—
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×C139#52511yescharacteristic
368C22×C139D4211yescharacteristic
369C22×C139#54611yescharacteristic
370C22×C139C22×D811yescharacteristic
371C22×C139#57511yescharacteristic
372C22×C139#57611yescharacteristic
373C22×C139#57711yescharacteristic
374C4×C139—22no—
375C4×C139—22no—
376C4×C139—42no—
377C4×C139—41no—
378C4×C139—41no—
379C4×C139—42no—
380C4×C139—42no—
381C4×C139—41no—
382C4×C139—81no—
383C4×C139—81no—
384C4×C139#53211yescharacteristic
385C4×C139#54011yescharacteristic
386C4×C139#54611yescharacteristic
387C4×C139#55311yescharacteristic
388C2×C139—42no—
389C2×C139—82no—
390C2×C139—82no—
391C2×C139—161no—
392C2×C139#246411yescharacteristic
393C2×C139#310011yescharacteristic
394C2×C139#311911yescharacteristic
395C2×C139#327511yescharacteristic
396C2×C139D4×D811yescharacteristic
397C2×C139#329411yescharacteristic
398C2×C139#330911yescharacteristic
399#26926C13911yesmaximal, characteristic, direct product factor, Sylow
400C139#2692611yescharacteristic, direct product factor, Sylow
401C2×#480C2×C13911yescharacteristic, complemented
402C2×#459C2×C13911yescharacteristic, complemented
403#2428C2×C13911yescharacteristic, complemented
404#2361C2×C13911yescharacteristic, complemented
405#2086C2×C13911yescharacteristic, complemented
406#2041C2×C13911yescharacteristic, complemented
407#1999C2×C13911yescharacteristic, complemented
408#1999C2×C13911yescharacteristic, complemented
409#1970C2×C13911yescharacteristic, complemented
410#1925C2×C13911yescharacteristic, complemented
411#1923C2×C13911yescharacteristic, complemented
412#1879C2×C13911yescharacteristic, complemented
413#1874C2×C13911yescharacteristic, complemented
414#1862C2×C13911yescharacteristic, complemented
415C4×#102C2×C13911yescharacteristic, complemented
416C22×D8C22×C13911yescharacteristic
417C22×D8C22×C13911yescharacteristic
418C2×#127C22×C13911yescharacteristic
419C2×#121—21no—
420C2×#121C22×C13911yescharacteristic
421C2×#121C22×C13911yescharacteristic
422C2×#121C22×C13911yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4C22×C13911yescharacteristic
425C2×C4×D4C22×C13911yescharacteristic
426C22×C4⋊C4C22×C13911yescharacteristic
427#480—24no—
428#459—24no—
429C2×#107C22×C13911yescharacteristic
430C2×#107C22×C13911yescharacteristic
431C2×C4⋊C8C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×#102C22×C13911yescharacteristic
434C2×#102C22×C13911yescharacteristic
435C2×#102C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×#102C22×C13911yescharacteristic
438C2×#102C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×C22⋊C8C22×C13911yescharacteristic
441C2×C22⋊C8C22×C13911yescharacteristic
442C2×C4×C8C22×C13911yescharacteristic
443#394—21no—
444#392—21no—
445#390C22×C13911yescharacteristic
446#390C22×C13911yescharacteristic
447#389C22×C13911yescharacteristic
448#389C22×C13911yescharacteristic
449#388—21no—
450#386—21no—
451#386—21no—
452#385—21no—
453C4×C4⋊C4C22×C13911yescharacteristic
454C4×C22⋊C4C22×C13911yescharacteristic
455#340C22×C13911yescharacteristic
456#340C22×C13911yescharacteristic
457#340C22×C13911yescharacteristic
458#340C22×C13911yescharacteristic
459#336C22×C13911yescharacteristic
460#336C22×C13911yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C13911yescharacteristic
467C22×D4C23×C13911yescharacteristic
468C22×D4C23×C13911yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C13911yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C13911yescharacteristic
480C22×C8C23×C13911yescharacteristic
481C22×C8C23×C13911yescharacteristic
482C22×C8C23×C13911yescharacteristic
483#127—22no—
484#127—41no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—44no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C4×D4—44no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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⋊C4D4×C13911yescharacteristic
517C2×C22⋊C4D4×C13911yescharacteristic
518C2×C42—21no—
519C2×C42C23×C13911yescharacteristic
520C2×C42C23×C13911yescharacteristic
521#107—22no—
522#107—22no—
523C4⋊C8—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—41no—
530#102—41no—
531#102D4×C13914yescomplemented
532C22⋊C8—22no—
533C22⋊C8—41no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95D4×C13911yescharacteristic
539#95D4×C13911yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C13911yescharacteristic
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
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—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C2×D4×C13912yes—
576C2×D4#41×C13912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C13911yescharacteristic
598C22×C4C2×D4×C13911yescharacteristic
599C22×C4C2×D4×C13911yescharacteristic
600C22×C4C2×D4×C13911yescharacteristic
601C22×C4C2×D4×C13911yescharacteristic
602C22×C4C24×C13911yescharacteristic
603D8—44no—
604D8—44no—
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—21no—
615C2×C8—21no—
616C2×C8C2×D4×C13912yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C13912yes—
628C4⋊C4#41×C13912yes—
629C4⋊C4#41×C13912yes—
630C22⋊C4—24no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4D8×C13914yescomplemented
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—41no—
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—
673C23C2×D8×C13912yes—
674C23C22×D4×C13911yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
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—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×D8×C13912yes—
728C2×C4C2×D8×C13912yes—
729C2×C4C22×D4×C13911yescharacteristic
730C2×C4C2×#41×C13911yescharacteristic
731C2×C4C2×#41×C13911yescharacteristic
732C2×C4C2×#41×C13911yescharacteristic
733C2×C4H(5,𝔽2)×C13911yescharacteristic
734C2×C4H(5,𝔽2)×C13911yescharacteristic
735C8—22no—
736C8—41no—
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—42no—
750C22—42no—
751C22—42no—
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—
767C22#525×C13911yescharacteristic
768C22D42×C13911yescharacteristic
769C22#546×C13911yescharacteristic
770C22C22×D8×C13911yescharacteristic
771C22#575×C13911yescharacteristic
772C22#576×C13911yescharacteristic
773C22#577×C13911yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4#532×C13911yescharacteristic
785C4#540×C13911yescharacteristic
786C4#546×C13911yescharacteristic
787C4#553×C13911yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2#2464×C13911yescharacteristic
793C2#3100×C13911yescharacteristic
794C2#3119×C13911yescharacteristic
795C2#3275×C13911yescharacteristic
796C2D4×D8×C13911yescharacteristic
797C2#3294×C13911yescharacteristic
798C2#3309×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#480×C139C2semidirect
2. C2×#459×C139C2semidirect
3. #2428×C139C2semidirect
4. #2361×C139C2semidirect
5. #2086×C139C2semidirect
6. #2041×C139C2semidirect
7. #1999×C139C2semidirect
8. #1999×C139C2semidirect
9. #1970×C139C2semidirect
10. #1925×C139C2semidirect
11. #1923×C139C2semidirect
12. #1879×C139C2semidirect
13. #1874×C139C2semidirect
14. #1862×C139C2semidirect
15. C4×#102×C139C2semidirect
131. #102×C139D4semidirect
240. C22⋊C4×C139D8semidirect
399. #26926C139direct (N × H)
400. C139#26926direct (N × H)
401. C2×#480C2×C139semidirect
402. C2×#459C2×C139semidirect
403. #2428C2×C139semidirect
404. #2361C2×C139semidirect
405. #2086C2×C139semidirect
406. #2041C2×C139semidirect
407. #1999C2×C139semidirect
408. #1999C2×C139semidirect
409. #1970C2×C139semidirect
410. #1925C2×C139semidirect
411. #1923C2×C139semidirect
412. #1879C2×C139semidirect
413. #1874C2×C139semidirect
414. #1862C2×C139semidirect
415. C4×#102C2×C139semidirect
531. #102D4×C139semidirect
640. C22⋊C4D8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1392
C2×#459×C1392
#2428×C1392
#2361×C1392
#2086×C1392
#2041×C1392
#1999×C1392
#1970×C1392
#1925×C1392
#1923×C1392
#1879×C1392
#1874×C1392
#1862×C1392
C4×#102×C1392
#26926139