Finite Group Databasebeta

← C139×#25174 #48019770

Subgroups — C139×#25174 #48019770

Order 35584.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C139C211yesmaximal, characteristic, complemented
2C2×#449×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×#442×C139C211yesmaximal, characteristic, complemented
5#2428×C139C211yesmaximal, characteristic, complemented
6#2339×C139C211yesmaximal, characteristic, complemented
7#2066×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#2033×C139C211yesmaximal, characteristic, complemented
10#2014×C139C211yesmaximal, characteristic, complemented
11#1973×C139C211yesmaximal, characteristic, complemented
12#1924×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1877×C139C211yesmaximal, characteristic, complemented
15#1862×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#121×C139—21no—
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×C4×D4×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28#459×C139—24no—
29#449×C139—24no—
30#449×C139—24no—
31#442×C139—24no—
32C2×#107×C139C2211yescharacteristic
33C2×#106×C139C2211yescharacteristic
34C2×C4⋊C8×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×#97×C139C2211yescharacteristic
46#394×C139—21no—
47#392×C139—21no—
48#391×C139C2211yescharacteristic
49#391×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#389×C139C2211yescharacteristic
52#386×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#381×C139—21no—
56#380×C139C2211yescharacteristic
57C4×C22⋊C4×C139C2211yescharacteristic
58C2×#95×C139—21no—
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C22×Q8×C139C2311yescharacteristic
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139C2311yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78C23×C4×C139—21no—
79C23×C4×C139—21no—
80C23×C4×C139—21no—
81C23×C4×C139—21no—
82C23×C4×C139C2311yescharacteristic
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—22no—
86C2×SD16×C139—22no—
87C2×SD16×C139—41no—
88C2×SD16×C139—41no—
89C2×D8×C139—22no—
90C2×D8×C139—22no—
91C2×D8×C139—22no—
92C2×D8×C139—22no—
93C2×D8×C139—22no—
94C2×D8×C139D414yescomplemented
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99#127×C139—22no—
100#127×C139—41no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—44no—
104#121×C139—41no—
105#121×C139—41no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108C4×D4×C139—22no—
109C4×D4×C139—41no—
110C4×D4×C139—41no—
111C4×D4×C139—41no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139D411yescharacteristic
126C2×C22⋊C4×C139D411yescharacteristic
127C2×C42×C139C2311yescharacteristic
128C2×C42×C139C2311yescharacteristic
129#107×C139—41no—
130#106×C139—22no—
131C4⋊C8×C139—22no—
132#103×C139—22no—
133#103×C139—22no—
134#102×C139—22no—
135#102×C139—22no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—41no—
139#102×C139D414yescomplemented
140C22⋊C8×C139—22no—
141C22⋊C8×C139—22no—
142#97×C139—22no—
143#95×C139—21no—
144#95×C139—21no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139D411yescharacteristic
150#95×C139D411yescharacteristic
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139C2×D411yescharacteristic
155#41×C139—44no—
156#41×C139—44no—
157#41×C139—44no—
158#41×C139—44no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139#4112yes—
165C2×D4×C139—24no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—42no—
181C2×D4×C139—42no—
182C2×D4×C139—42no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139—81no—
193C2×D4×C139—81no—
194C2×D4×C139C2×D412yes—
195C2×D4×C139C2×D412yes—
196C2×D4×C139C2×D412yes—
197C2×D4×C139#4112yes—
198C22×C4×C139—24no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—42no—
211C22×C4×C139—42no—
212C22×C4×C139—42no—
213C22×C4×C139—42no—
214C22×C4×C139—42no—
215C22×C4×C139—42no—
216C22×C4×C139—42no—
217C22×C4×C139—42no—
218C22×C4×C139—81no—
219C22×C4×C139—81no—
220C22×C4×C139—81no—
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139C2×D411yescharacteristic
225C22×C4×C139C2×D411yescharacteristic
226C22×C4×C139C2411yescharacteristic
227SD16×C139—44no—
228SD16×C139—44no—
229D8×C139—28no—
230D8×C139—44no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139C2×D412yes—
242C2×C8×C139C2×D412yes—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—42no—
251C4⋊C4×C139C2×D412yes—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—41no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—81no—
261C22⋊C4×C139—81no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—21no—
265C42×C139—21no—
266C23×C139—22no—
267C23×C139—22no—
268C23×C139—22no—
269C23×C139—21no—
270C23×C139—22no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139C22×D411yescharacteristic
295Q8×C139—22no—
296Q8×C139—22no—
297Q8×C139—41no—
298Q8×C139—41no—
299D4×C139—22no—
300D4×C139—22no—
301D4×C139—22no—
302D4×C139—22no—
303D4×C139—22no—
304D4×C139—48no—
305D4×C139—41no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—41no—
309D4×C139—41no—
310D4×C139—41no—
311D4×C139—84no—
312D4×C139—84no—
313D4×C139—84no—
314D4×C139—84no—
315D4×C139#12114yescomplemented
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—22no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—22no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—48no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—84no—
351C2×C4×C139—84no—
352C2×C4×C139—84no—
353C2×C4×C139AGL(1,ℤ/8)12yes—
354C2×C4×C139C22×D411yescharacteristic
355C2×C4×C139C22×D411yescharacteristic
356C2×C4×C139C2×#4111yescharacteristic
357C2×C4×C139C2×#4111yescharacteristic
358C2×C4×C139H(5,𝔽2)11yescharacteristic
359C2×C4×C139H(5,𝔽2)11yescharacteristic
360C8×C139—22no—
361C8×C139—22no—
362C8×C139—41no—
363C8×C139—41no—
364C22×C139—24no—
365C22×C139—42no—
366C22×C139—42no—
367C22×C139—42no—
368C22×C139—42no—
369C22×C139—42no—
370C22×C139—42no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—41no—
374C22×C139—42no—
375C22×C139—41no—
376C22×C139—42no—
377C22×C139—42no—
378C22×C139—41no—
379C22×C139—41no—
380C22×C139—41no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139#52511yescharacteristic
393C22×C139D4211yescharacteristic
394C22×C139D4211yescharacteristic
395C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C139#57511yescharacteristic
397C22×C139#57611yescharacteristic
398C22×C139#57711yescharacteristic
399C4×C139—22no—
400C4×C139—41no—
401C4×C139—42no—
402C4×C139—41no—
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—42no—
406C4×C139—81no—
407C4×C139—81no—
408C4×C139—81no—
409C4×C139C2×#12111yescharacteristic
410C4×C139#53811yescharacteristic
411C4×C139#54611yescharacteristic
412C4×C139#54611yescharacteristic
413C2×C139—44no—
414C2×C139—81no—
415C2×C139—82no—
416C2×C139—161no—
417C2×C139#242411yescharacteristic
418C2×C139#311511yescharacteristic
419C2×C139#311911yescharacteristic
420C2×C139#326411yescharacteristic
421C2×C139#326711yescharacteristic
422C2×C139#326811yescharacteristic
423C2×C139#327211yescharacteristic
424#25174C13911yesmaximal, characteristic, direct product factor, Sylow
425C139#2517411yescharacteristic, direct product factor, Sylow
426C2×#459C2×C13911yescharacteristic, complemented
427C2×#449C2×C13911yescharacteristic, complemented
428C2×#449C2×C13911yescharacteristic, complemented
429C2×#442C2×C13911yescharacteristic, complemented
430#2428C2×C13911yescharacteristic, complemented
431#2339C2×C13911yescharacteristic, complemented
432#2066C2×C13911yescharacteristic, complemented
433#2034C2×C13911yescharacteristic, complemented
434#2033C2×C13911yescharacteristic, complemented
435#2014C2×C13911yescharacteristic, complemented
436#1973C2×C13911yescharacteristic, complemented
437#1924C2×C13911yescharacteristic, complemented
438#1879C2×C13911yescharacteristic, complemented
439#1877C2×C13911yescharacteristic, complemented
440#1862C2×C13911yescharacteristic, complemented
441C22×#41C22×C13911yescharacteristic
442C22×SD16C22×C13911yescharacteristic
443C22×SD16C22×C13911yescharacteristic
444C22×D8C22×C13911yescharacteristic
445C22×D8C22×C13911yescharacteristic
446C2×#127C22×C13911yescharacteristic
447C2×#121—21no—
448C2×#121C22×C13911yescharacteristic
449C2×#121C22×C13911yescharacteristic
450C2×C4×D4C22×C13911yescharacteristic
451C2×C4×D4C22×C13911yescharacteristic
452C2×C4×D4C22×C13911yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456#442—24no—
457C2×#107C22×C13911yescharacteristic
458C2×#106C22×C13911yescharacteristic
459C2×C4⋊C8C22×C13911yescharacteristic
460C2×#103C22×C13911yescharacteristic
461C2×#103C22×C13911yescharacteristic
462C2×#102C22×C13911yescharacteristic
463C2×#102C22×C13911yescharacteristic
464C2×#102C22×C13911yescharacteristic
465C2×#102C22×C13911yescharacteristic
466C2×#102C22×C13911yescharacteristic
467C2×#102C22×C13911yescharacteristic
468C2×C22⋊C8C22×C13911yescharacteristic
469C2×C22⋊C8C22×C13911yescharacteristic
470C2×#97C22×C13911yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C13911yescharacteristic
474#391C22×C13911yescharacteristic
475#390C22×C13911yescharacteristic
476#389C22×C13911yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C13911yescharacteristic
482C4×C22⋊C4C22×C13911yescharacteristic
483C2×#95—21no—
484#340C22×C13911yescharacteristic
485#340C22×C13911yescharacteristic
486#336C22×C13911yescharacteristic
487#336C22×C13911yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C13911yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C13911yescharacteristic
501C22×D4C23×C13911yescharacteristic
502C22×D4C23×C13911yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C13911yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C13914yescomplemented
520C22×C8C23×C13911yescharacteristic
521C22×C8C23×C13911yescharacteristic
522C22×C8C23×C13911yescharacteristic
523C22×C8C23×C13911yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C13911yescharacteristic
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C4⋊C4C23×C13911yescharacteristic
541C2×C4⋊C4C23×C13911yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C13911yescharacteristic
551C2×C22⋊C4D4×C13911yescharacteristic
552C2×C42C23×C13911yescharacteristic
553C2×C42C23×C13911yescharacteristic
554#107—41no—
555#106—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C13914yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567#97—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C13911yescharacteristic
575#95D4×C13911yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C13911yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C13912yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C13912yes—
620C2×D4C2×D4×C13912yes—
621C2×D4C2×D4×C13912yes—
622C2×D4#41×C13912yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C13911yescharacteristic
647C22×C4C2×D4×C13911yescharacteristic
648C22×C4C2×D4×C13911yescharacteristic
649C22×C4C2×D4×C13911yescharacteristic
650C22×C4C2×D4×C13911yescharacteristic
651C22×C4C24×C13911yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C13912yes—
667C2×C8C2×D4×C13912yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C13912yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C13911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C13914yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4AGL(1,ℤ/8)×C13912yes—
779C2×C4C22×D4×C13911yescharacteristic
780C2×C4C22×D4×C13911yescharacteristic
781C2×C4C2×#41×C13911yescharacteristic
782C2×C4C2×#41×C13911yescharacteristic
783C2×C4H(5,𝔽2)×C13911yescharacteristic
784C2×C4H(5,𝔽2)×C13911yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C13911yescharacteristic
818C22D42×C13911yescharacteristic
819C22D42×C13911yescharacteristic
820C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
821C22#575×C13911yescharacteristic
822C22#576×C13911yescharacteristic
823C22#577×C13911yescharacteristic
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C13911yescharacteristic
835C4#538×C13911yescharacteristic
836C4#546×C13911yescharacteristic
837C4#546×C13911yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2#2424×C13911yescharacteristic
843C2#3115×C13911yescharacteristic
844C2#3119×C13911yescharacteristic
845C2#3264×C13911yescharacteristic
846C2#3267×C13911yescharacteristic
847C2#3268×C13911yescharacteristic
848C2#3272×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×#459×C139C2semidirect
2. C2×#449×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×#442×C139C2semidirect
5. #2428×C139C2semidirect
6. #2339×C139C2semidirect
7. #2066×C139C2semidirect
8. #2034×C139C2semidirect
9. #2033×C139C2semidirect
10. #2014×C139C2semidirect
11. #1973×C139C2semidirect
12. #1924×C139C2semidirect
13. #1879×C139C2semidirect
14. #1877×C139C2semidirect
15. #1862×C139C2semidirect
94. C2×D8×C139D4semidirect
139. #102×C139D4semidirect
315. D4×C139#121semidirect
424. #25174C139direct (N × H)
425. C139#25174direct (N × H)
426. C2×#459C2×C139semidirect
427. C2×#449C2×C139semidirect
428. C2×#449C2×C139semidirect
429. C2×#442C2×C139semidirect
430. #2428C2×C139semidirect
431. #2339C2×C139semidirect
432. #2066C2×C139semidirect
433. #2034C2×C139semidirect
434. #2033C2×C139semidirect
435. #2014C2×C139semidirect
436. #1973C2×C139semidirect
437. #1924C2×C139semidirect
438. #1879C2×C139semidirect
439. #1877C2×C139semidirect
440. #1862C2×C139semidirect
519. C2×D8D4×C139semidirect
564. #102D4×C139semidirect
740. D4#121×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1392
C2×#449×C1392
C2×#442×C1392
#2428×C1392
#2339×C1392
#2066×C1392
#2034×C1392
#2033×C1392
#2014×C1392
#1973×C1392
#1924×C1392
#1879×C1392
#1877×C1392
#1862×C1392
#25174139