Finite Group Databasebeta

← C139×#18416 #48013012

Subgroups — C139×#18416 #48013012

Order 35584.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3535×C139C211yesmaximal, characteristic, complemented
2#3194×C139C211yesmaximal, characteristic, complemented
3#3187×C139C211yesmaximal, characteristic, complemented
4#2661×C139C211yesmaximal, characteristic, complemented
5#1612×C139C211yesmaximal, characteristic, complemented
6#1611×C139C211yesmaximal, characteristic, complemented
7#1609×C139C211yesmaximal, characteristic, complemented
8#1608×C139C211yesmaximal, characteristic, complemented
9#1600×C139C211yesmaximal, characteristic, complemented
10#1599×C139C211yesmaximal, characteristic, complemented
11#1597×C139C211yesmaximal, characteristic, complemented
12#1596×C139C211yesmaximal, characteristic, complemented
13#1508×C139C211yesmaximal, characteristic, complemented
14#1501×C139C211yesmaximal, characteristic, complemented
15#1468×C139C211yesmaximal, characteristic, complemented
16#563×C139—21no—
17#562×C139—21no—
18#554×C139—21no—
19#552×C139—21no—
20#551×C139—21no—
21#551×C139—21no—
22#547×C139—21no—
23#546×C139—21no—
24#544×C139C2211yescharacteristic
25#543×C139C2211yescharacteristic
26#542×C139—21no—
27#539×C139—21no—
28#539×C139—21no—
29#539×C139C2211yescharacteristic
30#538×C139C2211yescharacteristic
31#536×C139—21no—
32#525×C139C2211yescharacteristic
33C2×#123×C139C2211yescharacteristic
34C2×C22⋊Q8×C139C2211yescharacteristic
35C2×#121×C139C2211yescharacteristic
36#483×C139C2211yescharacteristic
37#483×C139C2211yescharacteristic
38#483×C139C2211yescharacteristic
39#482×C139—21no—
40#481×C139—21no—
41#480×C139C2211yescharacteristic
42#469×C139—21no—
43#468×C139—21no—
44#465×C139—21no—
45#465×C139—21no—
46#450×C139C2211yescharacteristic
47#450×C139C2211yescharacteristic
48#450×C139C2211yescharacteristic
49#449×C139—21no—
50#448×C139—21no—
51#447×C139C2211yescharacteristic
52#407×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54#398×C139C2211yescharacteristic
55#397×C139C2211yescharacteristic
56#394×C139—21no—
57#394×C139C2211yescharacteristic
58#392×C139—21no—
59#392×C139C2211yescharacteristic
60#390×C139—21no—
61#388×C139—21no—
62C4×C22⋊C4×C139C2211yescharacteristic
63#328×C139C2211yescharacteristic
64#328×C139C2211yescharacteristic
65#328×C139C2211yescharacteristic
66#328×C139C2211yescharacteristic
67#328×C139C2211yescharacteristic
68#328×C139C2211yescharacteristic
69#327×C139C2211yescharacteristic
70#327×C139C2211yescharacteristic
71#324×C139C2211yescharacteristic
72#324×C139C2211yescharacteristic
73#323×C139C2211yescharacteristic
74#323×C139C2211yescharacteristic
75C2×#41×C139—21no—
76C2×#41×C139D411yescharacteristic, complemented
77C22×Q8×C139D411yescharacteristic, complemented
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139D411yescharacteristic
81C22×D4×C139C2311yescharacteristic
82C23×C4×C139C2311yescharacteristic
83C2×SD16×C139—21no—
84C2×SD16×C139—21no—
85C2×SD16×C139—21no—
86C2×D8×C139—21no—
87C2×M16×C139—21no—
88C22×C8×C139—21no—
89C4⋊Q8×C139—21no—
90C4⋊Q8×C139—21no—
91C4⋊Q8×C139—21no—
92#126×C139—21no—
93#126×C139—21no—
94#126×C139—21no—
95#126×C139—21no—
96#126×C139—21no—
97#126×C139—21no—
98#125×C139—21no—
99#125×C139—21no—
100#125×C139—21no—
101#125×C139—21no—
102#125×C139—21no—
103#124×C139—21no—
104#124×C139—21no—
105#124×C139—21no—
106#124×C139—21no—
107#123×C139—21no—
108#123×C139—21no—
109#123×C139—21no—
110#123×C139—21no—
111#123×C139—21no—
112#123×C139—21no—
113#123×C139—21no—
114#123×C139—21no—
115#123×C139—21no—
116#123×C139—21no—
117#123×C139—21no—
118#123×C139—21no—
119#123×C139—21no—
120#123×C139—21no—
121C22⋊Q8×C139—21no—
122C22⋊Q8×C139—21no—
123C22⋊Q8×C139—21no—
124C22⋊Q8×C139—21no—
125C22⋊Q8×C139—21no—
126C22⋊Q8×C139—21no—
127C22⋊Q8×C139—21no—
128C22⋊Q8×C139—21no—
129C22⋊Q8×C139—21no—
130C22⋊Q8×C139—21no—
131C22⋊Q8×C139—21no—
132C22⋊Q8×C139—21no—
133C22⋊Q8×C139—21no—
134C22⋊Q8×C139—21no—
135C22⋊Q8×C139D411yescharacteristic, complemented
136C22⋊Q8×C139D411yescharacteristic, complemented
137C22⋊Q8×C139D411yescharacteristic, complemented
138C22⋊Q8×C139C2311yescharacteristic
139C22⋊Q8×C139C2311yescharacteristic
140C22⋊Q8×C139C2311yescharacteristic
141#121×C139—21no—
142#121×C139—21no—
143#121×C139—21no—
144#121×C139—21no—
145#121×C139—21no—
146#121×C139—21no—
147#121×C139—21no—
148#121×C139—21no—
149#121×C139D411yescharacteristic, complemented
150#121×C139C2311yescharacteristic
151#120×C139—21no—
152#120×C139—21no—
153C4×Q8×C139—21no—
154C4×D4×C139—21no—
155C4×D4×C139—21no—
156C4×D4×C139—21no—
157C4×D4×C139—21no—
158C4×D4×C139—21no—
159C4×D4×C139—21no—
160C4×D4×C139—21no—
161#117×C139—21no—
162#117×C139—21no—
163#117×C139—21no—
164#117×C139D411yescharacteristic, complemented
165C2×C4⋊C4×C139—21no—
166C2×C4⋊C4×C139—21no—
167C2×C4⋊C4×C139—21no—
168C2×C4⋊C4×C139D411yescharacteristic
169C2×C4⋊C4×C139D411yescharacteristic, complemented
170C2×C4⋊C4×C139C2311yescharacteristic
171C2×C4⋊C4×C139C2311yescharacteristic
172C2×C22⋊C4×C139—21no—
173C2×C22⋊C4×C139—21no—
174C2×C22⋊C4×C139—21no—
175C2×C22⋊C4×C139—21no—
176C2×C22⋊C4×C139—21no—
177C2×C22⋊C4×C139—21no—
178C2×C22⋊C4×C139—21no—
179C2×C22⋊C4×C139—21no—
180C2×C22⋊C4×C139D411yescharacteristic
181C2×C22⋊C4×C139D411yescharacteristic
182C2×C22⋊C4×C139C2311yescharacteristic
183C2×C42×C139—21no—
184#107×C139—21no—
185#106×C139—21no—
186#106×C139—21no—
187#106×C139—21no—
188#103×C139—21no—
189#103×C139—21no—
190#103×C139—21no—
191#102×C139—21no—
192#102×C139—21no—
193#102×C139—21no—
194#102×C139—21no—
195#102×C139—21no—
196C22⋊C8×C139—21no—
197C22⋊C8×C139—21no—
198C22⋊C8×C139C2311yescharacteristic
199C22⋊C8×C139C2311yescharacteristic
200C22⋊C8×C139C2311yescharacteristic
201C22⋊C8×C139C2311yescharacteristic
202#95×C139—21no—
203#95×C139—21no—
204#95×C139C2311yescharacteristic
205#95×C139C2311yescharacteristic
206C24×C139—21no—
207C24×C139C2×D411yescharacteristic
208C24×C139C2×D411yescharacteristic
209#41×C139—82no—
210#41×C139—81no—
211C2×Q8×C139—21no—
212C2×Q8×C139—21no—
213C2×Q8×C139—21no—
214C2×Q8×C139—81no—
215C2×Q8×C139C2×D411yescharacteristic
216C2×Q8×C139C2×D411yescharacteristic
217C2×Q8×C139C2×D411yescharacteristic
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—42no—
228C2×D4×C139—41no—
229C2×D4×C139—41no—
230C2×D4×C139—81no—
231C2×D4×C139—81no—
232C2×D4×C139—81no—
233C2×D4×C139—81no—
234C2×D4×C139—81no—
235C2×D4×C139—81no—
236C2×D4×C139C2×D411yescharacteristic
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—81no—
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2×D411yescharacteristic
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139C2×D411yescharacteristic
253C22×C4×C139C2×D411yescharacteristic
254C22×C4×C139C2×D411yescharacteristic
255C22×C4×C139C2×D411yescharacteristic
256C22×C4×C139C2411yescharacteristic
257SD16×C139—81no—
258SD16×C139—81no—
259SD16×C139—81no—
260D8×C139—81no—
261M16×C139—81no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—81no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139—21no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139—21no—
289C4⋊C4×C139—21no—
290C4⋊C4×C139—21no—
291C4⋊C4×C139—21no—
292C4⋊C4×C139—81no—
293C4⋊C4×C139C2×D411yescharacteristic
294C4⋊C4×C139C2×D411yescharacteristic
295C4⋊C4×C139C2×D411yescharacteristic
296C4⋊C4×C139C2×D411yescharacteristic
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—21no—
304C22⋊C4×C139—21no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—21no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—21no—
312C22⋊C4×C139—21no—
313C22⋊C4×C139—21no—
314C22⋊C4×C139—21no—
315C22⋊C4×C139—21no—
316C22⋊C4×C139—21no—
317C22⋊C4×C139—21no—
318C22⋊C4×C139—21no—
319C22⋊C4×C139—21no—
320C22⋊C4×C139—42no—
321C22⋊C4×C139—42no—
322C22⋊C4×C139—41no—
323C22⋊C4×C139—41no—
324C22⋊C4×C139—81no—
325C22⋊C4×C139—81no—
326C22⋊C4×C139—81no—
327C42×C139—21no—
328C42×C139—21no—
329C42×C139—21no—
330C42×C139—21no—
331C42×C139—21no—
332C42×C139—81no—
333C23×C139—21no—
334C23×C139—21no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—21no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—41no—
348C23×C139—41no—
349C23×C139—41no—
350C23×C139#12011yescharacteristic
351C23×C139#12011yescharacteristic
352C23×C139C22×D411yescharacteristic
353Q8×C139—41no—
354Q8×C139—41no—
355Q8×C139—41no—
356Q8×C139—81no—
357Q8×C139—81no—
358Q8×C139—81no—
359D4×C139—41no—
360D4×C139—41no—
361D4×C139—41no—
362D4×C139—41no—
363D4×C139—41no—
364D4×C139—42no—
365D4×C139—42no—
366D4×C139—41no—
367D4×C139—41no—
368D4×C139—81no—
369D4×C139—81no—
370D4×C139—81no—
371D4×C139—81no—
372D4×C139—84no—
373D4×C139—82no—
374D4×C139—82no—
375C2×C4×C139—22no—
376C2×C4×C139—21no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
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—21no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—42no—
396C2×C4×C139—41no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—81no—
406C2×C4×C139—81no—
407C2×C4×C139—81no—
408C2×C4×C139—81no—
409C2×C4×C139—81no—
410C2×C4×C139—81no—
411C2×C4×C139#12011yescharacteristic
412C2×C4×C139#12011yescharacteristic
413C2×C4×C139C22×D411yescharacteristic
414C2×C4×C139C22×D411yescharacteristic
415C8×C139—41no—
416C8×C139—41no—
417C8×C139—41no—
418C8×C139—41no—
419C22×C139—21no—
420C22×C139—21no—
421C22×C139—21no—
422C22×C139—21no—
423C22×C139—21no—
424C22×C139—21no—
425C22×C139—21no—
426C22×C139—21no—
427C22×C139—41no—
428C22×C139—41no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—41no—
432C22×C139—41no—
433C22×C139—81no—
434C22×C139—81no—
435C22×C139—81no—
436C22×C139—81no—
437C22×C139—81no—
438C22×C139—81no—
439C22×C139—81no—
440C22×C139—81no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139C2×#12011yescharacteristic
445C22×C139#57711yescharacteristic
446C22×C139#57711yescharacteristic
447C4×C139—21no—
448C4×C139—21no—
449C4×C139—21no—
450C4×C139—21no—
451C4×C139—42no—
452C4×C139—41no—
453C4×C139—41no—
454C4×C139—41no—
455C4×C139—41no—
456C4×C139—41no—
457C4×C139—41no—
458C4×C139—41no—
459C4×C139—41no—
460C4×C139—41no—
461C4×C139—41no—
462C4×C139—81no—
463C4×C139—81no—
464C2×C139—21no—
465C2×C139—21no—
466C2×C139—41no—
467C2×C139—41no—
468C2×C139—81no—
469C2×C139—81no—
470C2×C139—161no—
471C2×C139#301011yescharacteristic
472C2×C139#301811yescharacteristic
473C2×C139#302611yescharacteristic
474#18416C13911yesmaximal, characteristic, direct product factor, Sylow
475C139#1841611yescharacteristic, direct product factor, Sylow
476#3535C2×C13911yescharacteristic, complemented
477#3194C2×C13911yescharacteristic, complemented
478#3187C2×C13911yescharacteristic, complemented
479#2661C2×C13911yescharacteristic, complemented
480#1612C2×C13911yescharacteristic, complemented
481#1611C2×C13911yescharacteristic, complemented
482#1609C2×C13911yescharacteristic, complemented
483#1608C2×C13911yescharacteristic, complemented
484#1600C2×C13911yescharacteristic, complemented
485#1599C2×C13911yescharacteristic, complemented
486#1597C2×C13911yescharacteristic, complemented
487#1596C2×C13911yescharacteristic, complemented
488#1508C2×C13911yescharacteristic, complemented
489#1501C2×C13911yescharacteristic, complemented
490#1468C2×C13911yescharacteristic, complemented
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C13911yescharacteristic
500#543C22×C13911yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C13911yescharacteristic
505#538C22×C13911yescharacteristic
506#536—21no—
507#525C22×C13911yescharacteristic
508C2×#123C22×C13911yescharacteristic
509C2×C22⋊Q8C22×C13911yescharacteristic
510C2×#121C22×C13911yescharacteristic
511#483C22×C13911yescharacteristic
512#483C22×C13911yescharacteristic
513#483C22×C13911yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C13911yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C13911yescharacteristic
522#450C22×C13911yescharacteristic
523#450C22×C13911yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C13911yescharacteristic
527#407C22×C13911yescharacteristic
528C2×C22⋊C8C22×C13911yescharacteristic
529#398C22×C13911yescharacteristic
530#397C22×C13911yescharacteristic
531#394—21no—
532#394C22×C13911yescharacteristic
533#392—21no—
534#392C22×C13911yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C13911yescharacteristic
538#328C22×C13911yescharacteristic
539#328C22×C13911yescharacteristic
540#328C22×C13911yescharacteristic
541#328C22×C13911yescharacteristic
542#328C22×C13911yescharacteristic
543#328C22×C13911yescharacteristic
544#327C22×C13911yescharacteristic
545#327C22×C13911yescharacteristic
546#324C22×C13911yescharacteristic
547#324C22×C13911yescharacteristic
548#323C22×C13911yescharacteristic
549#323C22×C13911yescharacteristic
550C2×#41—21no—
551C2×#41D4×C13911yescharacteristic, complemented
552C22×Q8D4×C13911yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C13911yescharacteristic
556C22×D4C23×C13911yescharacteristic
557C23×C4C23×C13911yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C13911yescharacteristic, complemented
611C22⋊Q8D4×C13911yescharacteristic, complemented
612C22⋊Q8D4×C13911yescharacteristic, complemented
613C22⋊Q8C23×C13911yescharacteristic
614C22⋊Q8C23×C13911yescharacteristic
615C22⋊Q8C23×C13911yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C13911yescharacteristic, complemented
625#121C23×C13911yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C13911yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C13911yescharacteristic
644C2×C4⋊C4D4×C13911yescharacteristic, complemented
645C2×C4⋊C4C23×C13911yescharacteristic
646C2×C4⋊C4C23×C13911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C13911yescharacteristic
656C2×C22⋊C4D4×C13911yescharacteristic
657C2×C22⋊C4C23×C13911yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C13911yescharacteristic
674C22⋊C8C23×C13911yescharacteristic
675C22⋊C8C23×C13911yescharacteristic
676C22⋊C8C23×C13911yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C13911yescharacteristic
680#95C23×C13911yescharacteristic
681C24—21no—
682C24C2×D4×C13911yescharacteristic
683C24C2×D4×C13911yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C13911yescharacteristic
691C2×Q8C2×D4×C13911yescharacteristic
692C2×Q8C2×D4×C13911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C13911yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C13911yescharacteristic
724C22×C4C2×D4×C13911yescharacteristic
725C22×C4C2×D4×C13911yescharacteristic
726C22×C4C2×D4×C13911yescharacteristic
727C22×C4C2×D4×C13911yescharacteristic
728C22×C4C2×D4×C13911yescharacteristic
729C22×C4C2×D4×C13911yescharacteristic
730C22×C4C2×D4×C13911yescharacteristic
731C22×C4C24×C13911yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C13911yescharacteristic
769C4⋊C4C2×D4×C13911yescharacteristic
770C4⋊C4C2×D4×C13911yescharacteristic
771C4⋊C4C2×D4×C13911yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C13911yescharacteristic
826C23#120×C13911yescharacteristic
827C23C22×D4×C13911yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C13911yescharacteristic
887C2×C4#120×C13911yescharacteristic
888C2×C4C22×D4×C13911yescharacteristic
889C2×C4C22×D4×C13911yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C13911yescharacteristic
920C22#577×C13911yescharacteristic
921C22#577×C13911yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2#3010×C13911yescharacteristic
947C2#3018×C13911yescharacteristic
948C2#3026×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3535×C139C2semidirect
2. #3194×C139C2semidirect
3. #3187×C139C2semidirect
4. #2661×C139C2semidirect
5. #1612×C139C2semidirect
6. #1611×C139C2semidirect
7. #1609×C139C2semidirect
8. #1608×C139C2semidirect
9. #1600×C139C2semidirect
10. #1599×C139C2semidirect
11. #1597×C139C2semidirect
12. #1596×C139C2semidirect
13. #1508×C139C2semidirect
14. #1501×C139C2semidirect
15. #1468×C139C2semidirect
76. C2×#41×C139D4semidirect
77. C22×Q8×C139D4semidirect
135. C22⋊Q8×C139D4semidirect
136. C22⋊Q8×C139D4semidirect
137. C22⋊Q8×C139D4semidirect
149. #121×C139D4semidirect
164. #117×C139D4semidirect
169. C2×C4⋊C4×C139D4semidirect
474. #18416C139direct (N × H)
475. C139#18416direct (N × H)
476. #3535C2×C139semidirect
477. #3194C2×C139semidirect
478. #3187C2×C139semidirect
479. #2661C2×C139semidirect
480. #1612C2×C139semidirect
481. #1611C2×C139semidirect
482. #1609C2×C139semidirect
483. #1608C2×C139semidirect
484. #1600C2×C139semidirect
485. #1599C2×C139semidirect
486. #1597C2×C139semidirect
487. #1596C2×C139semidirect
488. #1508C2×C139semidirect
489. #1501C2×C139semidirect
490. #1468C2×C139semidirect
551. C2×#41D4×C139semidirect
552. C22×Q8D4×C139semidirect
610. C22⋊Q8D4×C139semidirect
611. C22⋊Q8D4×C139semidirect
612. C22⋊Q8D4×C139semidirect
624. #121D4×C139semidirect
639. #117D4×C139semidirect
644. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3535×C1392
#3194×C1392
#3187×C1392
#2661×C1392
#1612×C1392
#1611×C1392
#1609×C1392
#1608×C1392
#1600×C1392
#1599×C1392
#1597×C1392
#1596×C1392
#1508×C1392
#1501×C1392
#1468×C1392
#18416139