Finite Group Databasebeta

← C139×#24362 #48018958

Subgroups — C139×#24362 #48018958

Order 35584.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C139C211yesmaximal, characteristic, complemented
2C2×#464×C139C211yesmaximal, characteristic, complemented
3C2×#460×C139C211yesmaximal, characteristic, complemented
4C2×#449×C139C211yesmaximal, characteristic, complemented
5#2431×C139C211yesmaximal, characteristic, complemented
6#2341×C139C211yesmaximal, characteristic, complemented
7#2055×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2012×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1893×C139C211yesmaximal, characteristic, complemented
12#1880×C139C211yesmaximal, characteristic, complemented
13#1878×C139C211yesmaximal, characteristic, complemented
14#1850×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C2×#135×C139—24no—
19C2×#135×C139—24no—
20C2×#135×C139—24no—
21C22×Q16×C139C2211yescharacteristic
22C22×SD16×C139C2211yescharacteristic
23C22×SD16×C139C2211yescharacteristic
24C22×SD16×C139C2211yescharacteristic
25C22×D8×C139C2211yescharacteristic
26C22×D8×C139C2211yescharacteristic
27C23×C8×C139C2211yescharacteristic
28C2×#127×C139C2211yescharacteristic
29C2×#124×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×C4×Q8×C139C2211yescharacteristic
32C2×C4×Q8×C139C2211yescharacteristic
33#464×C139—24no—
34#460×C139—24no—
35#449×C139—24no—
36C2×C4⋊C8×C139C2211yescharacteristic
37C2×C4⋊C8×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#103×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47#392×C139—21no—
48#392×C139—21no—
49#391×C139C2211yescharacteristic
50#390×C139—21no—
51#390×C139—21no—
52#390×C139C2211yescharacteristic
53#390×C139C2211yescharacteristic
54#390×C139C2211yescharacteristic
55#386×C139—21no—
56#386×C139—21no—
57#380×C139—21no—
58#380×C139C2211yescharacteristic
59C4×C22⋊C4×C139—21no—
60C4×C22⋊C4×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63#336×C139C2211yescharacteristic
64#336×C139C2211yescharacteristic
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—22no—
72C2×#41×C139—41no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C2×#41×C139—41no—
76C2×#41×C139D414yescomplemented
77C22×Q8×C139C2311yescharacteristic
78C22×Q8×C139C2311yescharacteristic
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139—21no—
83C22×D4×C139—21no—
84C22×D4×C139C2311yescharacteristic
85C22×D4×C139C2311yescharacteristic
86C22×D4×C139C2311yescharacteristic
87C23×C4×C139—21no—
88C23×C4×C139—21no—
89C23×C4×C139C2311yescharacteristic
90#135×C139—232no—
91C2×Q16×C139—22no—
92C2×Q16×C139—22no—
93C2×Q16×C139D414yescomplemented
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×SD16×C139—22no—
98C2×SD16×C139—22no—
99C2×SD16×C139—22no—
100C2×SD16×C139—22no—
101C2×SD16×C139—22no—
102C2×SD16×C139D414yescomplemented
103C2×D8×C139—22no—
104C2×D8×C139—22no—
105C2×D8×C139—22no—
106C2×D8×C139—22no—
107C2×D8×C139—41no—
108C2×D8×C139—41no—
109C22×C8×C139—22no—
110C22×C8×C139—22no—
111C22×C8×C139—22no—
112C22×C8×C139C2311yescharacteristic
113C22×C8×C139C2311yescharacteristic
114C22×C8×C139C2311yescharacteristic
115C22×C8×C139C2311yescharacteristic
116#127×C139—22no—
117#127×C139—41no—
118#124×C139—22no—
119#124×C139—41no—
120#121×C139—22no—
121#121×C139—22no—
122C4×Q8×C139—22no—
123C4×Q8×C139—22no—
124C4×Q8×C139—41no—
125C4×Q8×C139—41no—
126C2×C4⋊C4×C139—21no—
127C2×C4⋊C4×C139—21no—
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C4⋊C4×C139C2311yescharacteristic
130C2×C4⋊C4×C139C2311yescharacteristic
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139—21no—
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139D411yescharacteristic
142C2×C22⋊C4×C139D411yescharacteristic
143C2×C42×C139—21no—
144C2×C42×C139—21no—
145C2×C42×C139C2311yescharacteristic
146C2×C42×C139C2311yescharacteristic
147C4⋊C8×C139—22no—
148C4⋊C8×C139—22no—
149#103×C139—22no—
150#103×C139—22no—
151#103×C139—41no—
152#102×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—41no—
157C22⋊C8×C139—22no—
158#95×C139—21no—
159#95×C139—21no—
160#95×C139—21no—
161#95×C139D411yescharacteristic
162#95×C139D411yescharacteristic
163C24×C139—21no—
164C24×C139—21no—
165C24×C139—21no—
166C24×C139C2×D411yescharacteristic
167#41×C139—28no—
168#41×C139—28no—
169#41×C139—44no—
170#41×C139—44no—
171#41×C139—44no—
172#41×C139—44no—
173#41×C139—44no—
174#41×C139—44no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139C2×D412yes—
184C2×Q8×C139C2×D412yes—
185C2×Q8×C139C2×D412yes—
186C2×Q8×C139C2×D412yes—
187C2×D4×C139—24no—
188C2×D4×C139—21no—
189C2×D4×C139—21no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—42no—
205C2×D4×C139—42no—
206C2×D4×C139—42no—
207C2×D4×C139—42no—
208C2×D4×C139—42no—
209C2×D4×C139—42no—
210C2×D4×C139—42no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—81no—
215C2×D4×C139—81no—
216C2×D4×C139—81no—
217C2×D4×C139—81no—
218C2×D4×C139C2×D412yes—
219C2×D4×C139C2×D412yes—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—24no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—42no—
231C22×C4×C139—42no—
232C22×C4×C139—42no—
233C22×C4×C139—42no—
234C22×C4×C139—42no—
235C22×C4×C139C2×D411yescharacteristic
236C22×C4×C139C2×D411yescharacteristic
237C22×C4×C139C2×D411yescharacteristic
238C22×C4×C139C2×D411yescharacteristic
239C22×C4×C139C2×D412yes—
240C22×C4×C139C2×D411yescharacteristic
241C22×C4×C139#4112yes—
242C22×C4×C139C2411yescharacteristic
243Q16×C139—28no—
244SD16×C139—28no—
245SD16×C139—28no—
246SD16×C139—44no—
247D8×C139—28no—
248D8×C139—44no—
249C2×C8×C139—28no—
250C2×C8×C139—21no—
251C2×C8×C139—21no—
252C2×C8×C139—21no—
253C2×C8×C139—21no—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139C2×D412yes—
261C2×C8×C139C2×D412yes—
262C4⋊C4×C139—21no—
263C4⋊C4×C139—21no—
264C4⋊C4×C139—21no—
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—42no—
269C4⋊C4×C139—42no—
270C22⋊C4×C139—22no—
271C22⋊C4×C139—41no—
272C22⋊C4×C139—42no—
273C22⋊C4×C139—42no—
274C22⋊C4×C139—42no—
275C22⋊C4×C139—42no—
276C22⋊C4×C139—42no—
277C22⋊C4×C139—81no—
278C22⋊C4×C139—81no—
279C22⋊C4×C139—81no—
280C22⋊C4×C139—81no—
281C22⋊C4×C139—81no—
282C42×C139—21no—
283C42×C139—21no—
284C42×C139—21no—
285C42×C139—21no—
286C42×C139—42no—
287C42×C139—42no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—22no—
295C23×C139—22no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139#12112yes—
316C23×C139C22×D411yescharacteristic
317Q8×C139—22no—
318Q8×C139—22no—
319Q8×C139—22no—
320Q8×C139—22no—
321Q8×C139—22no—
322Q8×C139—41no—
323Q8×C139—41no—
324Q8×C139#12014yes—
325D4×C139—22no—
326D4×C139—22no—
327D4×C139—22no—
328D4×C139—22no—
329D4×C139—48no—
330D4×C139—48no—
331D4×C139—41no—
332D4×C139—41no—
333D4×C139—41no—
334D4×C139—41no—
335D4×C139—41no—
336D4×C139—41no—
337D4×C139—41no—
338D4×C139—41no—
339D4×C139—84no—
340D4×C139—84no—
341D4×C139—84no—
342C2×C4×C139—22no—
343C2×C4×C139—21no—
344C2×C4×C139—22no—
345C2×C4×C139—22no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
351C2×C4×C139—22no—
352C2×C4×C139—22no—
353C2×C4×C139—21no—
354C2×C4×C139—21no—
355C2×C4×C139—21no—
356C2×C4×C139—22no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—21no—
363C2×C4×C139—48no—
364C2×C4×C139—48no—
365C2×C4×C139—41no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139#12112yes—
377C2×C4×C139#13512yescomplemented
378C2×C4×C139C22×D411yescharacteristic
379C2×C4×C139C22×D411yescharacteristic
380C2×C4×C139C22×D411yescharacteristic
381C2×C4×C139C2×#4111yescharacteristic
382C2×C4×C139H(5,𝔽2)11yescharacteristic
383C2×C4×C139H(5,𝔽2)11yescharacteristic
384C8×C139—22no—
385C8×C139—22no—
386C8×C139—41no—
387C8×C139—41no—
388C22×C139—22no—
389C22×C139—22no—
390C22×C139—22no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—41no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—42no—
398C22×C139—42no—
399C22×C139—42no—
400C22×C139—42no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139—81no—
414C22×C139—81no—
415C22×C139—81no—
416C22×C139C2×#12111yescharacteristic
417C22×C139D4211yescharacteristic
418C22×C139D4211yescharacteristic
419C22×C139C2×#13511yescharacteristic
420C22×C139#57511yescharacteristic
421C22×C139#57611yescharacteristic
422C22×C139#57711yescharacteristic
423C4×C139—22no—
424C4×C139—24no—
425C4×C139—22no—
426C4×C139—42no—
427C4×C139—41no—
428C4×C139—41no—
429C4×C139—41no—
430C4×C139—81no—
431C4×C139—81no—
432C4×C139—81no—
433C4×C139C2×#12011yescharacteristic
434C4×C139#53411yescharacteristic
435C4×C139#54611yescharacteristic
436C4×C139#54611yescharacteristic
437C2×C139—42no—
438C2×C139—82no—
439C2×C139—82no—
440C2×C139—161no—
441C2×C139#241011yescharacteristic
442C2×C139#303511yescharacteristic
443C2×C139#304511yescharacteristic
444C2×C139#326811yescharacteristic
445C2×C139#327111yescharacteristic
446C2×C139#328211yescharacteristic
447C2×C139#328711yescharacteristic
448#24362C13911yesmaximal, characteristic, direct product factor, Sylow
449C139#2436211yescharacteristic, direct product factor, Sylow
450C22×#135C2×C13911yescharacteristic, complemented
451C2×#464C2×C13911yescharacteristic, complemented
452C2×#460C2×C13911yescharacteristic, complemented
453C2×#449C2×C13911yescharacteristic, complemented
454#2431C2×C13911yescharacteristic, complemented
455#2341C2×C13911yescharacteristic, complemented
456#2055C2×C13911yescharacteristic, complemented
457#2054C2×C13911yescharacteristic, complemented
458#2012C2×C13911yescharacteristic, complemented
459#2011C2×C13911yescharacteristic, complemented
460#1893C2×C13911yescharacteristic, complemented
461#1880C2×C13911yescharacteristic, complemented
462#1878C2×C13911yescharacteristic, complemented
463#1850C2×C13911yescharacteristic, complemented
464#1788C2×C13911yescharacteristic, complemented
465C22×#41C22×C13911yescharacteristic
466C22×#41C22×C13911yescharacteristic
467C2×#135—24no—
468C2×#135—24no—
469C2×#135—24no—
470C22×Q16C22×C13911yescharacteristic
471C22×SD16C22×C13911yescharacteristic
472C22×SD16C22×C13911yescharacteristic
473C22×SD16C22×C13911yescharacteristic
474C22×D8C22×C13911yescharacteristic
475C22×D8C22×C13911yescharacteristic
476C23×C8C22×C13911yescharacteristic
477C2×#127C22×C13911yescharacteristic
478C2×#124C22×C13911yescharacteristic
479C2×#121C22×C13911yescharacteristic
480C2×C4×Q8C22×C13911yescharacteristic
481C2×C4×Q8C22×C13911yescharacteristic
482#464—24no—
483#460—24no—
484#449—24no—
485C2×C4⋊C8C22×C13911yescharacteristic
486C2×C4⋊C8C22×C13911yescharacteristic
487C2×#103C22×C13911yescharacteristic
488C2×#103C22×C13911yescharacteristic
489C2×#103C22×C13911yescharacteristic
490C2×#102C22×C13911yescharacteristic
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic
493C2×#102C22×C13911yescharacteristic
494C2×#102C22×C13911yescharacteristic
495C2×C22⋊C8C22×C13911yescharacteristic
496#392—21no—
497#392—21no—
498#391C22×C13911yescharacteristic
499#390—21no—
500#390—21no—
501#390C22×C13911yescharacteristic
502#390C22×C13911yescharacteristic
503#390C22×C13911yescharacteristic
504#386—21no—
505#386—21no—
506#380—21no—
507#380C22×C13911yescharacteristic
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C13911yescharacteristic
510#340C22×C13911yescharacteristic
511#340C22×C13911yescharacteristic
512#336C22×C13911yescharacteristic
513#336C22×C13911yescharacteristic
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C13914yescomplemented
526C22×Q8C23×C13911yescharacteristic
527C22×Q8C23×C13911yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C23×C13911yescharacteristic
534C22×D4C23×C13911yescharacteristic
535C22×D4C23×C13911yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C13911yescharacteristic
539#135—232no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16D4×C13914yescomplemented
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16D4×C13914yescomplemented
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8C23×C13911yescharacteristic
562C22×C8C23×C13911yescharacteristic
563C22×C8C23×C13911yescharacteristic
564C22×C8C23×C13911yescharacteristic
565#127—22no—
566#127—41no—
567#124—22no—
568#124—41no—
569#121—22no—
570#121—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4C23×C13911yescharacteristic
578C2×C4⋊C4C23×C13911yescharacteristic
579C2×C4⋊C4C23×C13911yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C13911yescharacteristic
591C2×C22⋊C4D4×C13911yescharacteristic
592C2×C42—21no—
593C2×C42—21no—
594C2×C42C23×C13911yescharacteristic
595C2×C42C23×C13911yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95D4×C13911yescharacteristic
611#95D4×C13911yescharacteristic
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C13911yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C13912yes—
633C2×Q8C2×D4×C13912yes—
634C2×Q8C2×D4×C13912yes—
635C2×Q8C2×D4×C13912yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C13912yes—
668C2×D4C2×D4×C13912yes—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C13911yescharacteristic
685C22×C4C2×D4×C13911yescharacteristic
686C22×C4C2×D4×C13911yescharacteristic
687C22×C4C2×D4×C13911yescharacteristic
688C22×C4C2×D4×C13912yes—
689C22×C4C2×D4×C13911yescharacteristic
690C22×C4#41×C13912yes—
691C22×C4C24×C13911yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C13912yes—
710C2×C8C2×D4×C13912yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23#121×C13912yes—
765C23C22×D4×C13911yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8#120×C13914yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4#121×C13912yes—
826C2×C4#135×C13912yescomplemented
827C2×C4C22×D4×C13911yescharacteristic
828C2×C4C22×D4×C13911yescharacteristic
829C2×C4C22×D4×C13911yescharacteristic
830C2×C4C2×#41×C13911yescharacteristic
831C2×C4H(5,𝔽2)×C13911yescharacteristic
832C2×C4H(5,𝔽2)×C13911yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#121×C13911yescharacteristic
866C22D42×C13911yescharacteristic
867C22D42×C13911yescharacteristic
868C22C2×#135×C13911yescharacteristic
869C22#575×C13911yescharacteristic
870C22#576×C13911yescharacteristic
871C22#577×C13911yescharacteristic
872C4—22no—
873C4—22no—
874C4—24no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×#120×C13911yescharacteristic
883C4#534×C13911yescharacteristic
884C4#546×C13911yescharacteristic
885C4#546×C13911yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2#2410×C13911yescharacteristic
891C2#3035×C13911yescharacteristic
892C2#3045×C13911yescharacteristic
893C2#3268×C13911yescharacteristic
894C2#3271×C13911yescharacteristic
895C2#3282×C13911yescharacteristic
896C2#3287×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. C22×#135×C139C2semidirect
2. C2×#464×C139C2semidirect
3. C2×#460×C139C2semidirect
4. C2×#449×C139C2semidirect
5. #2431×C139C2semidirect
6. #2341×C139C2semidirect
7. #2055×C139C2semidirect
8. #2054×C139C2semidirect
9. #2012×C139C2semidirect
10. #2011×C139C2semidirect
11. #1893×C139C2semidirect
12. #1880×C139C2semidirect
13. #1878×C139C2semidirect
14. #1850×C139C2semidirect
15. #1788×C139C2semidirect
76. C2×#41×C139D4semidirect
93. C2×Q16×C139D4semidirect
102. C2×SD16×C139D4semidirect
377. C2×C4×C139#135semidirect
448. #24362C139direct (N × H)
449. C139#24362direct (N × H)
450. C22×#135C2×C139semidirect
451. C2×#464C2×C139semidirect
452. C2×#460C2×C139semidirect
453. C2×#449C2×C139semidirect
454. #2431C2×C139semidirect
455. #2341C2×C139semidirect
456. #2055C2×C139semidirect
457. #2054C2×C139semidirect
458. #2012C2×C139semidirect
459. #2011C2×C139semidirect
460. #1893C2×C139semidirect
461. #1880C2×C139semidirect
462. #1878C2×C139semidirect
463. #1850C2×C139semidirect
464. #1788C2×C139semidirect
525. C2×#41D4×C139semidirect
542. C2×Q16D4×C139semidirect
551. C2×SD16D4×C139semidirect
826. C2×C4#135×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1392
C2×#464×C1392
C2×#460×C1392
C2×#449×C1392
#2431×C1392
#2341×C1392
#2055×C1392
#2054×C1392
#2012×C1392
#2011×C1392
#1893×C1392
#1880×C1392
#1878×C1392
#1850×C1392
#1788×C1392
#24362139