Finite Group Databasebeta

← C139×#24403 #48018999

Subgroups — C139×#24403 #48018999

Order 35584.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic
2C2×#473×C139C211yesmaximal, characteristic, complemented
3C2×#471×C139C211yesmaximal, characteristic, complemented
4#3007×C139C211yesmaximal, characteristic, complemented
5C2×#452×C139C211yesmaximal, characteristic, complemented
6#2880×C139C211yesmaximal, characteristic, complemented
7#2052×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2020×C139C211yesmaximal, characteristic, complemented
10#2019×C139C211yesmaximal, characteristic, complemented
11#1908×C139C211yesmaximal, characteristic, complemented
12#1907×C139C211yesmaximal, characteristic, complemented
13#1901×C139C211yesmaximal, characteristic, complemented
14#1855×C139C211yesmaximal, characteristic, complemented
15#1785×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18#575×C139—24no—
19#575×C139—24no—
20C2×#137×C139—21no—
21C2×#137×C139C2211yescharacteristic
22C2×#137×C139C2211yescharacteristic
23C2×#137×C139C2211yescharacteristic
24C2×#137×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139—21no—
26C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
28C2×#135×C139—21no—
29C2×#135×C139—21no—
30C22×Q16×C139C2211yescharacteristic, complemented
31C22×SD16×C139C2211yescharacteristic, complemented
32C2×#131×C139C2211yescharacteristic
33C2×#131×C139C2211yescharacteristic
34C22×M16×C139C2211yescharacteristic
35C2×C22⋊Q8×C139C2211yescharacteristic
36#473×C139—24no—
37#471×C139—24no—
38#452×C139—21no—
39#452×C139—21no—
40#452×C139—21no—
41#452×C139—21no—
42#452×C139—21no—
43#452×C139—21no—
44#451×C139—21no—
45#450×C139—21no—
46C2×#108×C139C2211yescharacteristic, complemented
47C2×#108×C139C2211yescharacteristic, complemented
48#417×C139C2211yescharacteristic
49#417×C139C2211yescharacteristic
50C2×#103×C139C2211yescharacteristic, complemented
51C2×#102×C139C2211yescharacteristic, complemented
52C2×#101×C139C2211yescharacteristic, complemented
53C2×#101×C139C2211yescharacteristic, complemented
54C2×#101×C139C2211yescharacteristic, complemented
55C2×#101×C139C2211yescharacteristic, complemented
56C2×#100×C139C2211yescharacteristic, complemented
57C2×#100×C139C2211yescharacteristic, complemented
58#408×C139—21no—
59#408×C139—21no—
60#408×C139C2211yescharacteristic
61#408×C139C2211yescharacteristic
62#407×C139—21no—
63#407×C139C2211yescharacteristic
64#407×C139C2211yescharacteristic
65C2×C22⋊C8×C139—21no—
66C2×C22⋊C8×C139C2211yescharacteristic
67#343×C139C2211yescharacteristic, complemented
68#343×C139C2211yescharacteristic, complemented
69#341×C139C2211yescharacteristic, complemented
70#341×C139C2211yescharacteristic, complemented
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—22no—
74C2×#41×C139—22no—
75C2×#41×C139—22no—
76C2×#41×C139—22no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—41no—
82C2×#41×C139—41no—
83C2×#41×C139—41no—
84C2×#41×C139—41no—
85C2×#41×C139D411yescharacteristic
86C2×#41×C139D411yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C22×Q8×C139D411yescharacteristic
90C22×Q8×C139C2311yescharacteristic
91C22×Q8×C139C2311yescharacteristic
92C22×D4×C139—21no—
93C22×D4×C139—21no—
94C22×D4×C139D411yescharacteristic
95C22×D4×C139C2311yescharacteristic
96C23×C4×C139—21no—
97C23×C4×C139—21no—
98C23×C4×C139C2311yescharacteristic
99#137×C139—28no—
100#137×C139—22no—
101#137×C139—22no—
102#137×C139—22no—
103#137×C139—22no—
104#137×C139—22no—
105#137×C139—41no—
106#137×C139—41no—
107#137×C139D414yes—
108AGL(1,ℤ/8)×C139—28no—
109AGL(1,ℤ/8)×C139—22no—
110AGL(1,ℤ/8)×C139—22no—
111AGL(1,ℤ/8)×C139—22no—
112AGL(1,ℤ/8)×C139D414yes—
113#135×C139—28no—
114#135×C139—28no—
115C2×Q16×C139—21no—
116C2×Q16×C139—21no—
117C2×Q16×C139—21no—
118C2×Q16×C139—21no—
119C2×Q16×C139—22no—
120C2×Q16×C139—21no—
121C2×Q16×C139—21no—
122C2×Q16×C139—41no—
123C2×SD16×C139—21no—
124C2×SD16×C139—21no—
125C2×SD16×C139—21no—
126C2×SD16×C139—21no—
127C2×SD16×C139—21no—
128C2×SD16×C139—21no—
129C2×SD16×C139—22no—
130C2×SD16×C139—21no—
131C2×SD16×C139—21no—
132C2×SD16×C139—41no—
133C2×D8×C139—21no—
134C2×D8×C139—21no—
135#131×C139—22no—
136#131×C139—22no—
137#131×C139—41no—
138#131×C139—41no—
139C2×M16×C139—21no—
140C2×M16×C139—22no—
141C2×M16×C139—22no—
142C2×M16×C139—21no—
143C2×M16×C139—21no—
144C2×M16×C139C2311yescharacteristic
145C2×M16×C139C2311yescharacteristic
146C2×M16×C139C2311yescharacteristic
147C2×M16×C139C2311yescharacteristic
148C2×M16×C139C2311yescharacteristic
149C2×M16×C139C2311yescharacteristic
150C22×C8×C139—21no—
151C22×C8×C139—21no—
152C22×C8×C139—21no—
153C22×C8×C139C2311yescharacteristic
154C22×C8×C139C2311yescharacteristic
155C22⋊Q8×C139—21no—
156C22⋊Q8×C139—21no—
157C22⋊Q8×C139—21no—
158C22⋊Q8×C139—21no—
159C2×C4⋊C4×C139—21no—
160C2×C4⋊C4×C139C2311yescharacteristic
161C2×C22⋊C4×C139—21no—
162#108×C139—22no—
163#108×C139—22no—
164#103×C139—21no—
165#103×C139—21no—
166#103×C139—21no—
167#103×C139—21no—
168#102×C139—21no—
169#102×C139—21no—
170#102×C139—21no—
171#102×C139—21no—
172#101×C139—22no—
173#101×C139—22no—
174#101×C139—22no—
175#101×C139—41no—
176#100×C139—22no—
177#100×C139—41no—
178C22⋊C8×C139—21no—
179C22⋊C8×C139—21no—
180C22⋊C8×C139—21no—
181C22⋊C8×C139—21no—
182C22⋊C8×C139—21no—
183C22⋊C8×C139—21no—
184C22⋊C8×C139—21no—
185C22⋊C8×C139—21no—
186C22⋊C8×C139D411yescharacteristic
187C22⋊C8×C139D411yescharacteristic
188C22⋊C8×C139D411yescharacteristic
189C22⋊C8×C139D411yescharacteristic
190C24×C139—21no—
191C24×C139—21no—
192C24×C139#4111yescharacteristic
193#41×C139—21no—
194#41×C139—21no—
195#41×C139—24no—
196#41×C139—24no—
197#41×C139—22no—
198#41×C139—22no—
199#41×C139—21no—
200#41×C139—21no—
201#41×C139—21no—
202#41×C139—21no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—41no—
206#41×C139—41no—
207#41×C139—42no—
208#41×C139—42no—
209#41×C139—42no—
210#41×C139—42no—
211#41×C139—42no—
212#41×C139—42no—
213#41×C139—42no—
214#41×C139—42no—
215#41×C139C2×D412yes—
216#41×C139C2×D412yes—
217C2×Q8×C139—21no—
218C2×Q8×C139—21no—
219C2×Q8×C139—22no—
220C2×Q8×C139—21no—
221C2×Q8×C139—21no—
222C2×Q8×C139—21no—
223C2×Q8×C139—21no—
224C2×Q8×C139—21no—
225C2×Q8×C139—21no—
226C2×Q8×C139—21no—
227C2×Q8×C139—21no—
228C2×Q8×C139—21no—
229C2×Q8×C139—21no—
230C2×Q8×C139—41no—
231C2×Q8×C139C2×D412yes—
232C2×Q8×C139C2×D411yescharacteristic
233C2×Q8×C139C2×D411yescharacteristic
234C2×D4×C139—21no—
235C2×D4×C139—22no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—21no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—21no—
243C2×D4×C139—21no—
244C2×D4×C139—21no—
245C2×D4×C139—41no—
246C2×D4×C139—42no—
247C2×D4×C139—42no—
248C2×D4×C139—42no—
249C2×D4×C139—42no—
250C2×D4×C139—41no—
251C2×D4×C139—41no—
252C2×D4×C139C2×D412yes—
253C2×D4×C139C2×D411yescharacteristic
254C2×D4×C139C2×D411yescharacteristic
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—21no—
265C22×C4×C139—21no—
266C22×C4×C139—21no—
267C22×C4×C139—42no—
268C22×C4×C139—42no—
269C22×C4×C139—42no—
270C22×C4×C139—42no—
271C22×C4×C139—41no—
272C22×C4×C139—41no—
273C22×C4×C139C2×D411yescharacteristic
274C22×C4×C139C2×D411yescharacteristic
275C22×C4×C139C2×D411yescharacteristic
276C22×C4×C139C2×D411yescharacteristic
277C22×C4×C139#4111yescharacteristic
278C22×C4×C139C2411yescharacteristic
279Q16×C139—24no—
280Q16×C139—24no—
281Q16×C139—42no—
282Q16×C139—42no—
283Q16×C139—42no—
284Q16×C139—42no—
285SD16×C139—24no—
286SD16×C139—24no—
287SD16×C139—24no—
288SD16×C139—24no—
289SD16×C139—42no—
290SD16×C139—42no—
291SD16×C139—42no—
292SD16×C139—42no—
293D8×C139—24no—
294D8×C139—24no—
295M16×C139—24no—
296M16×C139—21no—
297M16×C139—21no—
298M16×C139—21no—
299M16×C139—21no—
300M16×C139—21no—
301M16×C139—21no—
302M16×C139—21no—
303M16×C139—21no—
304M16×C139—21no—
305M16×C139—21no—
306M16×C139—42no—
307M16×C139—42no—
308M16×C139C2×D412yes—
309M16×C139C2×D412yes—
310C2×C8×C139—24no—
311C2×C8×C139—21no—
312C2×C8×C139—21no—
313C2×C8×C139—21no—
314C2×C8×C139—21no—
315C2×C8×C139—21no—
316C2×C8×C139—21no—
317C2×C8×C139—21no—
318C2×C8×C139—21no—
319C2×C8×C139—21no—
320C2×C8×C139—21no—
321C2×C8×C139—42no—
322C2×C8×C139—42no—
323C2×C8×C139C2×D411yescharacteristic
324C2×C8×C139C2×D411yescharacteristic
325C2×C8×C139C2×D411yescharacteristic
326C2×C8×C139C2×D411yescharacteristic
327C4⋊C4×C139—21no—
328C4⋊C4×C139—21no—
329C4⋊C4×C139—41no—
330C4⋊C4×C139—41no—
331C22⋊C4×C139—41no—
332C22⋊C4×C139—41no—
333C23×C139—21no—
334C23×C139—21no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—22no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—42no—
341C23×C139—42no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—81no—
345C23×C139—81no—
346C23×C139—81no—
347C23×C139#12111yescharacteristic
348C23×C139#12111yescharacteristic
349C23×C139C2×#4111yescharacteristic
350Q8×C139—21no—
351Q8×C139—21no—
352Q8×C139—22no—
353Q8×C139—21no—
354Q8×C139—22no—
355Q8×C139—42no—
356Q8×C139—41no—
357Q8×C139—41no—
358Q8×C139—41no—
359Q8×C139—41no—
360Q8×C139—41no—
361Q8×C139—41no—
362Q8×C139#12012yes—
363D4×C139—22no—
364D4×C139—22no—
365D4×C139—21no—
366D4×C139—22no—
367D4×C139—21no—
368D4×C139—21no—
369D4×C139—22no—
370D4×C139—42no—
371D4×C139—42no—
372D4×C139—42no—
373D4×C139—44no—
374D4×C139—44no—
375D4×C139—41no—
376D4×C139—41no—
377D4×C139—41no—
378D4×C139—41no—
379D4×C139#12012yes—
380C2×C4×C139—21no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—21no—
385C2×C4×C139—21no—
386C2×C4×C139—21no—
387C2×C4×C139—22no—
388C2×C4×C139—22no—
389C2×C4×C139—21no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—22no—
395C2×C4×C139—42no—
396C2×C4×C139—42no—
397C2×C4×C139—42no—
398C2×C4×C139—44no—
399C2×C4×C139—44no—
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—81no—
409C2×C4×C139#12111yescharacteristic
410C2×C4×C139#12111yescharacteristic
411C2×C4×C139C22×D411yescharacteristic
412C2×C4×C139C22×D411yescharacteristic
413C2×C4×C139C22×D411yescharacteristic
414C2×C4×C139C22×D411yescharacteristic
415C2×C4×C139H(5,𝔽2)11yescharacteristic
416C2×C4×C139H(5,𝔽2)11yescharacteristic
417C8×C139—22no—
418C8×C139—22no—
419C8×C139—21no—
420C8×C139—21no—
421C8×C139—21no—
422C8×C139—21no—
423C8×C139—41no—
424C8×C139—41no—
425C8×C139—41no—
426C8×C139—41no—
427C22×C139—21no—
428C22×C139—21no—
429C22×C139—21no—
430C22×C139—21no—
431C22×C139—22no—
432C22×C139—21no—
433C22×C139—21no—
434C22×C139—21no—
435C22×C139—21no—
436C22×C139—41no—
437C22×C139—41no—
438C22×C139—41no—
439C22×C139—42no—
440C22×C139—41no—
441C22×C139—41no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—82no—
445C22×C139—82no—
446C22×C139—84no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139C2×#12111yescharacteristic
450C22×C139#54611yescharacteristic
451C22×C139#54611yescharacteristic
452C4×C139—21no—
453C4×C139—21no—
454C4×C139—22no—
455C4×C139—41no—
456C4×C139—42no—
457C4×C139—81no—
458C4×C139—81no—
459C4×C139C2×#12011yescharacteristic
460C4×C139#53411yescharacteristic
461C4×C139D4211yescharacteristic
462C4×C139D4211yescharacteristic
463C2×C139—21no—
464C2×C139—21no—
465C2×C139—41no—
466C2×C139—41no—
467C2×C139—42no—
468C2×C139—81no—
469C2×C139—82no—
470C2×C139#241011yescharacteristic
471C2×C139#306711yescharacteristic
472C2×C139#306911yescharacteristic
473#24403C13911yesmaximal, characteristic, direct product factor, Sylow
474C139#2440311yescharacteristic, direct product factor, Sylow
475C2×#575C2×C13911yescharacteristic
476C2×#473C2×C13911yescharacteristic, complemented
477C2×#471C2×C13911yescharacteristic, complemented
478#3007C2×C13911yescharacteristic, complemented
479C2×#452C2×C13911yescharacteristic, complemented
480#2880C2×C13911yescharacteristic, complemented
481#2052C2×C13911yescharacteristic, complemented
482#2051C2×C13911yescharacteristic, complemented
483#2020C2×C13911yescharacteristic, complemented
484#2019C2×C13911yescharacteristic, complemented
485#1908C2×C13911yescharacteristic, complemented
486#1907C2×C13911yescharacteristic, complemented
487#1901C2×C13911yescharacteristic, complemented
488#1855C2×C13911yescharacteristic, complemented
489#1785C2×C13911yescharacteristic, complemented
490C22×#41C22×C13911yescharacteristic
491C22×#41C22×C13911yescharacteristic
492#575—24no—
493#575—24no—
494C2×#137—21no—
495C2×#137C22×C13911yescharacteristic
496C2×#137C22×C13911yescharacteristic
497C2×#137C22×C13911yescharacteristic
498C2×#137C22×C13911yescharacteristic
499C2×AGL(1,ℤ/8)—21no—
500C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
501C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
502C2×#135—21no—
503C2×#135—21no—
504C22×Q16C22×C13911yescharacteristic, complemented
505C22×SD16C22×C13911yescharacteristic, complemented
506C2×#131C22×C13911yescharacteristic
507C2×#131C22×C13911yescharacteristic
508C22×M16C22×C13911yescharacteristic
509C2×C22⋊Q8C22×C13911yescharacteristic
510#473—24no—
511#471—24no—
512#452—21no—
513#452—21no—
514#452—21no—
515#452—21no—
516#452—21no—
517#452—21no—
518#451—21no—
519#450—21no—
520C2×#108C22×C13911yescharacteristic, complemented
521C2×#108C22×C13911yescharacteristic, complemented
522#417C22×C13911yescharacteristic
523#417C22×C13911yescharacteristic
524C2×#103C22×C13911yescharacteristic, complemented
525C2×#102C22×C13911yescharacteristic, complemented
526C2×#101C22×C13911yescharacteristic, complemented
527C2×#101C22×C13911yescharacteristic, complemented
528C2×#101C22×C13911yescharacteristic, complemented
529C2×#101C22×C13911yescharacteristic, complemented
530C2×#100C22×C13911yescharacteristic, complemented
531C2×#100C22×C13911yescharacteristic, complemented
532#408—21no—
533#408—21no—
534#408C22×C13911yescharacteristic
535#408C22×C13911yescharacteristic
536#407—21no—
537#407C22×C13911yescharacteristic
538#407C22×C13911yescharacteristic
539C2×C22⋊C8—21no—
540C2×C22⋊C8C22×C13911yescharacteristic
541#343C22×C13911yescharacteristic, complemented
542#343C22×C13911yescharacteristic, complemented
543#341C22×C13911yescharacteristic, complemented
544#341C22×C13911yescharacteristic, complemented
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41D4×C13911yescharacteristic
560C2×#41D4×C13911yescharacteristic
561C2×#41C23×C13911yescharacteristic
562C2×#41C23×C13911yescharacteristic
563C22×Q8D4×C13911yescharacteristic
564C22×Q8C23×C13911yescharacteristic
565C22×Q8C23×C13911yescharacteristic
566C22×D4—21no—
567C22×D4—21no—
568C22×D4D4×C13911yescharacteristic
569C22×D4C23×C13911yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C13911yescharacteristic
573#137—28no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—22no—
579#137—41no—
580#137—41no—
581#137D4×C13914yes—
582AGL(1,ℤ/8)—28no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)—22no—
586AGL(1,ℤ/8)D4×C13914yes—
587#135—28no—
588#135—28no—
589C2×Q16—21no—
590C2×Q16—21no—
591C2×Q16—22no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—21no—
596C2×Q16—41no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—22no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—41no—
607C2×D8—21no—
608C2×D8—21no—
609#131—22no—
610#131—22no—
611#131—41no—
612#131—41no—
613C2×M16—21no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—21no—
617C2×M16—21no—
618C2×M16C23×C13911yescharacteristic
619C2×M16C23×C13911yescharacteristic
620C2×M16C23×C13911yescharacteristic
621C2×M16C23×C13911yescharacteristic
622C2×M16C23×C13911yescharacteristic
623C2×M16C23×C13911yescharacteristic
624C22×C8—21no—
625C22×C8—21no—
626C22×C8—21no—
627C22×C8C23×C13911yescharacteristic
628C22×C8C23×C13911yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4C23×C13911yescharacteristic
635C2×C22⋊C4—21no—
636#108—22no—
637#108—22no—
638#103—21no—
639#103—21no—
640#103—21no—
641#103—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#102—21no—
646#101—22no—
647#101—22no—
648#101—22no—
649#101—41no—
650#100—22no—
651#100—41no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8—21no—
660C22⋊C8D4×C13911yescharacteristic
661C22⋊C8D4×C13911yescharacteristic
662C22⋊C8D4×C13911yescharacteristic
663C22⋊C8D4×C13911yescharacteristic
664C24—21no—
665C24—21no—
666C24#41×C13911yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C13912yes—
690#41C2×D4×C13912yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C13912yes—
706C2×Q8C2×D4×C13911yescharacteristic
707C2×Q8C2×D4×C13911yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C13912yes—
727C2×D4C2×D4×C13911yescharacteristic
728C2×D4C2×D4×C13911yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C13911yescharacteristic
748C22×C4C2×D4×C13911yescharacteristic
749C22×C4C2×D4×C13911yescharacteristic
750C22×C4C2×D4×C13911yescharacteristic
751C22×C4#41×C13911yescharacteristic
752C22×C4C24×C13911yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C13912yes—
783M16C2×D4×C13912yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C13911yescharacteristic
798C2×C8C2×D4×C13911yescharacteristic
799C2×C8C2×D4×C13911yescharacteristic
800C2×C8C2×D4×C13911yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23#121×C13911yescharacteristic
822C23#121×C13911yescharacteristic
823C23C2×#41×C13911yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8#120×C13912yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4#120×C13912yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—81no—
883C2×C4#121×C13911yescharacteristic
884C2×C4#121×C13911yescharacteristic
885C2×C4C22×D4×C13911yescharacteristic
886C2×C4C22×D4×C13911yescharacteristic
887C2×C4C22×D4×C13911yescharacteristic
888C2×C4C22×D4×C13911yescharacteristic
889C2×C4H(5,𝔽2)×C13911yescharacteristic
890C2×C4H(5,𝔽2)×C13911yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—22no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×#121×C13911yescharacteristic
924C22#546×C13911yescharacteristic
925C22#546×C13911yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#120×C13911yescharacteristic
934C4#534×C13911yescharacteristic
935C4D42×C13911yescharacteristic
936C4D42×C13911yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2410×C13911yescharacteristic
945C2#3067×C13911yescharacteristic
946C2#3069×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#575×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#473×C139C2semidirect
3. C2×#471×C139C2semidirect
4. #3007×C139C2semidirect
5. C2×#452×C139C2semidirect
6. #2880×C139C2semidirect
7. #2052×C139C2semidirect
8. #2051×C139C2semidirect
9. #2020×C139C2semidirect
10. #2019×C139C2semidirect
11. #1908×C139C2semidirect
12. #1907×C139C2semidirect
13. #1901×C139C2semidirect
14. #1855×C139C2semidirect
15. #1785×C139C2semidirect
30. C22×Q16×C139C22semidirect
31. C22×SD16×C139C22semidirect
46. C2×#108×C139C22semidirect
47. C2×#108×C139C22semidirect
50. C2×#103×C139C22semidirect
51. C2×#102×C139C22semidirect
52. C2×#101×C139C22semidirect
53. C2×#101×C139C22semidirect
54. C2×#101×C139C22semidirect
55. C2×#101×C139C22semidirect
56. C2×#100×C139C22semidirect
57. C2×#100×C139C22semidirect
67. #343×C139C22semidirect
68. #343×C139C22semidirect
69. #341×C139C22semidirect
70. #341×C139C22semidirect
473. #24403C139direct (N × H)
474. C139#24403direct (N × H)
476. C2×#473C2×C139semidirect
477. C2×#471C2×C139semidirect
478. #3007C2×C139semidirect
479. C2×#452C2×C139semidirect
480. #2880C2×C139semidirect
481. #2052C2×C139semidirect
482. #2051C2×C139semidirect
483. #2020C2×C139semidirect
484. #2019C2×C139semidirect
485. #1908C2×C139semidirect
486. #1907C2×C139semidirect
487. #1901C2×C139semidirect
488. #1855C2×C139semidirect
489. #1785C2×C139semidirect
504. C22×Q16C22×C139semidirect
505. C22×SD16C22×C139semidirect
520. C2×#108C22×C139semidirect
521. C2×#108C22×C139semidirect
524. C2×#103C22×C139semidirect
525. C2×#102C22×C139semidirect
526. C2×#101C22×C139semidirect
527. C2×#101C22×C139semidirect
528. C2×#101C22×C139semidirect
529. C2×#101C22×C139semidirect
530. C2×#100C22×C139semidirect
531. C2×#100C22×C139semidirect
541. #343C22×C139semidirect
542. #343C22×C139semidirect
543. #341C22×C139semidirect
544. #341C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1392
C2×#473×C1392
C2×#471×C1392
#3007×C1392
C2×#452×C1392
#2880×C1392
#2052×C1392
#2051×C1392
#2020×C1392
#2019×C1392
#1908×C1392
#1907×C1392
#1901×C1392
#1855×C1392
#1785×C1392
#24403139