Finite Group Databasebeta

← C139×#22056 #48016652

Subgroups — C139×#22056 #48016652

Order 35584.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic
2#2324×C139C211yesmaximal, characteristic, complemented
3#2309×C139C211yesmaximal, characteristic, complemented
4#1972×C139C211yesmaximal, characteristic, complemented
5#1970×C139C211yesmaximal, characteristic, complemented
6#1936×C139C211yesmaximal, characteristic, complemented
7#1934×C139C211yesmaximal, characteristic, complemented
8#1926×C139C211yesmaximal, characteristic, complemented
9#1925×C139C211yesmaximal, characteristic, complemented
10#1879×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1875×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15#1750×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×C4×D4×C139C2211yescharacteristic, complemented
21C2×#117×C139C2211yescharacteristic
22C2×#117×C139C2211yescharacteristic
23#447×C139C418yescomplemented
24C2×#107×C139C2211yescharacteristic, complemented
25C2×#106×C139C2211yescharacteristic, complemented
26C2×#102×C139C2211yescharacteristic
27C2×#102×C139C2211yescharacteristic
28C2×#102×C139C2211yescharacteristic
29C2×#102×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic, complemented
33C2×#102×C139C2211yescharacteristic, complemented
34C2×C22⋊C8×C139C2211yescharacteristic
35C2×C22⋊C8×C139C2211yescharacteristic
36C2×#97×C139C2211yescharacteristic, complemented
37C2×C4×C8×C139C2211yescharacteristic, complemented
38#390×C139—21no—
39#390×C139—21no—
40#390×C139—21no—
41#390×C139C2211yescharacteristic
42#390×C139C2211yescharacteristic
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic, complemented
46#389×C139C2211yescharacteristic, complemented
47#388×C139—21no—
48#386×C139—21no—
49#385×C139—21no—
50#380×C139C2211yescharacteristic
51#379×C139—21no—
52#379×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic, complemented
54#340×C139C2211yescharacteristic, complemented
55#340×C139C2211yescharacteristic, complemented
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#336×C139C2211yescharacteristic, complemented
59#336×C139C2211yescharacteristic, complemented
60C25×C139—21no—
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—22no—
64C22×D4×C139—41no—
65C22×D4×C139—41no—
66C22×D4×C139—41no—
67C22×D4×C139—41no—
68C22×D4×C139C2×C414yescomplemented
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C23×C4×C139—21no—
73C23×C4×C139C2311yescharacteristic
74C2×D8×C139—41no—
75C2×D8×C139—41no—
76C2×D8×C139—41no—
77C2×D8×C139—41no—
78C2×D8×C139C2×C414yes—
79C2×D8×C139C2×C414yes—
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84#121×C139—22no—
85#121×C139C2×C414yes—
86C4×D4×C139—41no—
87C4×D4×C139—41no—
88#117×C139—41no—
89#117×C139—41no—
90#117×C139—41no—
91#117×C139—41no—
92C2×C4⋊C4×C139—21no—
93C2×C4⋊C4×C139D411yescharacteristic
94C2×C4⋊C4×C139D411yescharacteristic
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C22⋊C4×C139—21no—
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
115C2×C22⋊C4×C139D411yescharacteristic
116C2×C42×C139—21no—
117C2×C42×C139—21no—
118C2×C42×C139C2311yescharacteristic
119C2×C42×C139C2311yescharacteristic
120#107×C139—41no—
121#106×C139—41no—
122#102×C139—41no—
123#102×C139—41no—
124#102×C139—41no—
125#102×C139—41no—
126#102×C139—41no—
127#102×C139—41no—
128#102×C139C2×C414yescomplemented
129#102×C139C2×C414yescomplemented
130C22⋊C8×C139—22no—
131C22⋊C8×C139C2×C414yescomplemented
132#97×C139—41no—
133C4×C8×C139—41no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137C24×C139—21no—
138C24×C139—21no—
139C24×C139—21no—
140C24×C139—24no—
141C24×C139—42no—
142C24×C139—42no—
143C24×C139—81no—
144C24×C139—81no—
145C24×C139—81no—
146C24×C139—81no—
147C24×C139C2×D411yescharacteristic
148C2×D4×C139—24no—
149C2×D4×C139—24no—
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—44no—
166C2×D4×C139—44no—
167C2×D4×C139—42no—
168C2×D4×C139—42no—
169C2×D4×C139—44no—
170C2×D4×C139—44no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139C22×C412yes—
174C2×D4×C139C22×C412yes—
175C2×D4×C139C22×C412yes—
176C22×C4×C139—21no—
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—42no—
186C22×C4×C139—81no—
187C22×C4×C139—81no—
188C22×C4×C139C22×C412yes—
189C22×C4×C139C2×D411yescharacteristic
190C22×C4×C139C2×D411yescharacteristic
191C22×C4×C139C2×D411yescharacteristic
192C22×C4×C139C2×D411yescharacteristic
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139#4112yes—
195C22×C4×C139C2411yescharacteristic
196D8×C139—44no—
197D8×C139—44no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139—21no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139C22×C412yes—
209C2×C8×C139C22×C412yes—
210C4⋊C4×C139—21no—
211C4⋊C4×C139—21no—
212C4⋊C4×C139—21no—
213C4⋊C4×C139—21no—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—41no—
220C4⋊C4×C139—41no—
221C4⋊C4×C139—81no—
222C4⋊C4×C139C22×C412yes—
223C22⋊C4×C139—24no—
224C22⋊C4×C139—41no—
225C22⋊C4×C139—41no—
226C22⋊C4×C139—42no—
227C22⋊C4×C139—42no—
228C22⋊C4×C139—81no—
229C22⋊C4×C139—81no—
230C22⋊C4×C139—81no—
231C22⋊C4×C139—81no—
232C22⋊C4×C139—81no—
233C22⋊C4×C139—81no—
234C22⋊C4×C139—81no—
235C22⋊C4×C139—81no—
236C22⋊C4×C139—81no—
237C22⋊C4×C139—81no—
238C22⋊C4×C139—81no—
239C42×C139—21no—
240C42×C139—21no—
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—42no—
244C42×C139—81no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—22no—
252C23×C139—22no—
253C23×C139—22no—
254C23×C139—48no—
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—84no—
274C23×C139—84no—
275C23×C139—84no—
276C23×C139—84no—
277C23×C139—84no—
278C23×C139—84no—
279C23×C139C4×D412yes—
280C23×C139C22×D411yescharacteristic
281D4×C139—22no—
282D4×C139—22no—
283D4×C139—22no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—48no—
288D4×C139—41no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—84no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—22no—
298C2×C4×C139—22no—
299C2×C4×C139—22no—
300C2×C4×C139—22no—
301C2×C4×C139—22no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
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—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—84no—
329C2×C4×C139C4×D412yes—
330C2×C4×C139C23×C411yescharacteristic
331C2×C4×C139C2×#4111yescharacteristic
332C2×C4×C139H(5,𝔽2)11yescharacteristic
333C2×C4×C139H(5,𝔽2)11yescharacteristic
334C2×C4×C139H(5,𝔽2)11yescharacteristic
335C2×C4×C139H(5,𝔽2)11yescharacteristic
336C8×C139—22no—
337C8×C139—22no—
338C8×C139—41no—
339C8×C139—41no—
340C22×C139—22no—
341C22×C139—22no—
342C22×C139—22no—
343C22×C139—41no—
344C22×C139—41no—
345C22×C139—41no—
346C22×C139—41no—
347C22×C139—42no—
348C22×C139—42no—
349C22×C139—42no—
350C22×C139—42no—
351C22×C139—42no—
352C22×C139—42no—
353C22×C139—42no—
354C22×C139—42no—
355C22×C139—42no—
356C22×C139—816no—
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—81no—
368C22×C139—81no—
369C22×C139C2×C4×D411yescharacteristic
370C22×C139#53411yescharacteristic
371C22×C139#53511yescharacteristic
372C22×C139#57611yescharacteristic
373C22×C139#57611yescharacteristic
374C22×C139#57611yescharacteristic
375C22×C139#57711yescharacteristic
376C4×C139—22no—
377C4×C139—41no—
378C4×C139—41no—
379C4×C139—41no—
380C4×C139—41no—
381C4×C139—42no—
382C4×C139—81no—
383C4×C139—81no—
384C4×C139—81no—
385C4×C139—81no—
386C4×C139#51811yescharacteristic
387C4×C139#51811yescharacteristic
388C4×C139#53811yescharacteristic
389C4×C139#53811yescharacteristic
390C2×C139—42no—
391C2×C139—82no—
392C2×C139—82no—
393C2×C139—82no—
394C2×C139#232111yescharacteristic
395C2×C139#294611yescharacteristic
396C2×C139#294811yescharacteristic
397C2×C139#319811yescharacteristic
398C2×C139#319911yescharacteristic
399C2×C139#322011yescharacteristic
400C2×C139#322411yescharacteristic
401#22056C13911yesmaximal, characteristic, direct product factor, Sylow
402C139#2205611yescharacteristic, direct product factor, Sylow
403C2×#447C2×C13911yescharacteristic
404#2324C2×C13911yescharacteristic, complemented
405#2309C2×C13911yescharacteristic, complemented
406#1972C2×C13911yescharacteristic, complemented
407#1970C2×C13911yescharacteristic, complemented
408#1936C2×C13911yescharacteristic, complemented
409#1934C2×C13911yescharacteristic, complemented
410#1926C2×C13911yescharacteristic, complemented
411#1925C2×C13911yescharacteristic, complemented
412#1879C2×C13911yescharacteristic, complemented
413#1879C2×C13911yescharacteristic, complemented
414#1875C2×C13911yescharacteristic, complemented
415#1854C2×C13911yescharacteristic, complemented
416#1786C2×C13911yescharacteristic, complemented
417#1750C2×C13911yescharacteristic, complemented
418C23×D4C22×C13911yescharacteristic
419C22×D8C22×C13911yescharacteristic
420C22×D8C22×C13911yescharacteristic
421C2×#121C22×C13911yescharacteristic
422C2×C4×D4C22×C13911yescharacteristic, complemented
423C2×#117C22×C13911yescharacteristic
424C2×#117C22×C13911yescharacteristic
425#447C4×C13918yescomplemented
426C2×#107C22×C13911yescharacteristic, complemented
427C2×#106C22×C13911yescharacteristic, complemented
428C2×#102C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×#102C22×C13911yescharacteristic
434C2×#102C22×C13911yescharacteristic, complemented
435C2×#102C22×C13911yescharacteristic, complemented
436C2×C22⋊C8C22×C13911yescharacteristic
437C2×C22⋊C8C22×C13911yescharacteristic
438C2×#97C22×C13911yescharacteristic, complemented
439C2×C4×C8C22×C13911yescharacteristic, complemented
440#390—21no—
441#390—21no—
442#390—21no—
443#390C22×C13911yescharacteristic
444#390C22×C13911yescharacteristic
445#390C22×C13911yescharacteristic
446#390C22×C13911yescharacteristic
447#390C22×C13911yescharacteristic, complemented
448#389C22×C13911yescharacteristic, complemented
449#388—21no—
450#386—21no—
451#385—21no—
452#380C22×C13911yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4C22×C13911yescharacteristic, complemented
456#340C22×C13911yescharacteristic, complemented
457#340C22×C13911yescharacteristic, complemented
458#340C22×C13911yescharacteristic, complemented
459#340C22×C13911yescharacteristic, complemented
460#336C22×C13911yescharacteristic, complemented
461#336C22×C13911yescharacteristic, complemented
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C13914yescomplemented
471C22×D4C23×C13911yescharacteristic
472C22×D4C23×C13911yescharacteristic
473C22×D4C23×C13911yescharacteristic
474C23×C4—21no—
475C23×C4C23×C13911yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C13914yes—
481C2×D8C2×C4×C13914yes—
482C22×C8C23×C13911yescharacteristic
483C22×C8C23×C13911yescharacteristic
484C22×C8C23×C13911yescharacteristic
485C22×C8C23×C13911yescharacteristic
486#121—22no—
487#121C2×C4×C13914yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C13911yescharacteristic
496C2×C4⋊C4D4×C13911yescharacteristic
497C2×C4⋊C4C23×C13911yescharacteristic
498C2×C4⋊C4C23×C13911yescharacteristic
499C2×C4⋊C4C23×C13911yescharacteristic
500C2×C4⋊C4C23×C13911yescharacteristic
501C2×C4⋊C4C23×C13911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
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×C42—21no—
520C2×C42C23×C13911yescharacteristic
521C2×C42C23×C13911yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C13914yescomplemented
531#102C2×C4×C13914yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C13914yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C13911yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
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—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C13912yes—
576C2×D4C22×C4×C13912yes—
577C2×D4C22×C4×C13912yes—
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—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C13912yes—
591C22×C4C2×D4×C13911yescharacteristic
592C22×C4C2×D4×C13911yescharacteristic
593C22×C4C2×D4×C13911yescharacteristic
594C22×C4C2×D4×C13911yescharacteristic
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4#41×C13912yes—
597C22×C4C24×C13911yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C13912yes—
611C2×C8C22×C4×C13912yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C13912yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
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—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C13912yes—
682C23C22×D4×C13911yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
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—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C13912yes—
732C2×C4C23×C4×C13911yescharacteristic
733C2×C4C2×#41×C13911yescharacteristic
734C2×C4H(5,𝔽2)×C13911yescharacteristic
735C2×C4H(5,𝔽2)×C13911yescharacteristic
736C2×C4H(5,𝔽2)×C13911yescharacteristic
737C2×C4H(5,𝔽2)×C13911yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C13911yescharacteristic
772C22#534×C13911yescharacteristic
773C22#535×C13911yescharacteristic
774C22#576×C13911yescharacteristic
775C22#576×C13911yescharacteristic
776C22#576×C13911yescharacteristic
777C22#577×C13911yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4#518×C13911yescharacteristic
789C4#518×C13911yescharacteristic
790C4#538×C13911yescharacteristic
791C4#538×C13911yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2#2321×C13911yescharacteristic
797C2#2946×C13911yescharacteristic
798C2#2948×C13911yescharacteristic
799C2#3198×C13911yescharacteristic
800C2#3199×C13911yescharacteristic
801C2#3220×C13911yescharacteristic
802C2#3224×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2324×C139C2semidirect
3. #2309×C139C2semidirect
4. #1972×C139C2semidirect
5. #1970×C139C2semidirect
6. #1936×C139C2semidirect
7. #1934×C139C2semidirect
8. #1926×C139C2semidirect
9. #1925×C139C2semidirect
10. #1879×C139C2semidirect
11. #1879×C139C2semidirect
12. #1875×C139C2semidirect
13. #1854×C139C2semidirect
14. #1786×C139C2semidirect
15. #1750×C139C2semidirect
20. C2×C4×D4×C139C22semidirect
23. #447×C139C4semidirect
24. C2×#107×C139C22semidirect
25. C2×#106×C139C22semidirect
32. C2×#102×C139C22semidirect
33. C2×#102×C139C22semidirect
36. C2×#97×C139C22semidirect
37. C2×C4×C8×C139C22semidirect
45. #390×C139C22semidirect
46. #389×C139C22semidirect
53. C4×C4⋊C4×C139C22semidirect
54. #340×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #336×C139C22semidirect
59. #336×C139C22semidirect
68. C22×D4×C139C2×C4semidirect
128. #102×C139C2×C4semidirect
129. #102×C139C2×C4semidirect
131. C22⋊C8×C139C2×C4semidirect
401. #22056C139direct (N × H)
402. C139#22056direct (N × H)
404. #2324C2×C139semidirect
405. #2309C2×C139semidirect
406. #1972C2×C139semidirect
407. #1970C2×C139semidirect
408. #1936C2×C139semidirect
409. #1934C2×C139semidirect
410. #1926C2×C139semidirect
411. #1925C2×C139semidirect
412. #1879C2×C139semidirect
413. #1879C2×C139semidirect
414. #1875C2×C139semidirect
415. #1854C2×C139semidirect
416. #1786C2×C139semidirect
417. #1750C2×C139semidirect
422. C2×C4×D4C22×C139semidirect
425. #447C4×C139semidirect
426. C2×#107C22×C139semidirect
427. C2×#106C22×C139semidirect
434. C2×#102C22×C139semidirect
435. C2×#102C22×C139semidirect
438. C2×#97C22×C139semidirect
439. C2×C4×C8C22×C139semidirect
447. #390C22×C139semidirect
448. #389C22×C139semidirect
455. C4×C4⋊C4C22×C139semidirect
456. #340C22×C139semidirect
457. #340C22×C139semidirect
458. #340C22×C139semidirect
459. #340C22×C139semidirect
460. #336C22×C139semidirect
461. #336C22×C139semidirect
470. C22×D4C2×C4×C139semidirect
530. #102C2×C4×C139semidirect
531. #102C2×C4×C139semidirect
533. C22⋊C8C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
#2324×C1392
#2309×C1392
#1972×C1392
#1970×C1392
#1936×C1392
#1934×C1392
#1926×C1392
#1925×C1392
#1879×C1392
#1875×C1392
#1854×C1392
#1786×C1392
#1750×C1392
#22056139