Finite Group Databasebeta

← C139×#25087 #48019683

Subgroups — C139×#25087 #48019683

Order 35584.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C139C211yesmaximal, characteristic, complemented
2C2×#463×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×#416×C139C211yesmaximal, characteristic, complemented
5#2431×C139C211yesmaximal, characteristic, complemented
6#2363×C139C211yesmaximal, characteristic, complemented
7#2067×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2042×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1928×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1875×C139C211yesmaximal, characteristic, complemented
15#1850×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C23×C8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#124×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×#117×C139C2211yescharacteristic
27#466×C139—24no—
28#463×C139—24no—
29#449×C139—24no—
30C2×#107×C139C2211yescharacteristic
31C2×C4⋊C8×C139C2211yescharacteristic
32C2×C4⋊C8×C139C2211yescharacteristic
33#416×C139—24no—
34C2×#103×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×#102×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45#392×C139—21no—
46#392×C139—21no—
47#391×C139C2211yescharacteristic
48#390×C139—21no—
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#389×C139C2211yescharacteristic
52#388×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#386×C139—21no—
56C4×C4⋊C4×C139C2211yescharacteristic
57C4×C22⋊C4×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
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×C139C2311yescharacteristic
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—41no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—22no—
87C2×D8×C139—22no—
88C2×D8×C139—41no—
89C2×D8×C139—41no—
90C22×C8×C139—22no—
91C22×C8×C139—22no—
92C22×C8×C139—41no—
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97#127×C139—22no—
98#127×C139—41no—
99#124×C139—22no—
100#124×C139—41no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139D414yescomplemented
105C4×D4×C139—22no—
106C4×D4×C139—41no—
107#117×C139—22no—
108#117×C139—41no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
125C2×C22⋊C4×C139D411yescharacteristic
126C2×C42×C139—21no—
127C2×C42×C139—21no—
128C2×C42×C139C2311yescharacteristic
129C2×C42×C139C2311yescharacteristic
130#107×C139—22no—
131C4⋊C8×C139—22no—
132C4⋊C8×C139—41no—
133#103×C139—22no—
134#103×C139—22no—
135#103×C139D414yescomplemented
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—41no—
143C22⋊C8×C139—22no—
144#95×C139—21no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139D411yescharacteristic
149#95×C139D411yescharacteristic
150C24×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139C2×D411yescharacteristic
154#41×C139—28no—
155#41×C139—44no—
156#41×C139—44no—
157#41×C139—44no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139C2×D412yes—
164C2×D4×C139—24no—
165C2×D4×C139—21no—
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—21no—
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—81no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139—81no—
193C2×D4×C139—81no—
194C2×D4×C139—81no—
195C2×D4×C139C2×D412yes—
196C2×D4×C139#4112yes—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
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—42no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139—42no—
210C22×C4×C139—42no—
211C22×C4×C139—81no—
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D412yes—
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139#4112yes—
219C22×C4×C139C2411yescharacteristic
220SD16×C139—44no—
221D8×C139—44no—
222D8×C139—44no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—44no—
235C2×C8×C139C2×D412yes—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—81no—
243C4⋊C4×C139C2×D412yes—
244C4⋊C4×C139C2×D412yes—
245C22⋊C4×C139—24no—
246C22⋊C4×C139—22no—
247C22⋊C4×C139—41no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—81no—
255C22⋊C4×C139—81no—
256C22⋊C4×C139—81no—
257C42×C139—21no—
258C42×C139—21no—
259C42×C139—21no—
260C42×C139—21no—
261C42×C139—42no—
262C42×C139—81no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—22no—
270C23×C139—22no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
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#12112yes—
291C23×C139C22×D411yescharacteristic
292Q8×C139—22no—
293Q8×C139—22no—
294Q8×C139—41no—
295Q8×C139—41no—
296D4×C139—22no—
297D4×C139—22no—
298D4×C139—22no—
299D4×C139—22no—
300D4×C139—48no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—41no—
304D4×C139—41no—
305D4×C139—41no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—41no—
309D4×C139—84no—
310D4×C139—84no—
311D4×C139—84no—
312D4×C139—84no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—22no—
318C2×C4×C139—22no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—22no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
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—21no—
333C2×C4×C139—48no—
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—84no—
347C2×C4×C139#12112yes—
348C2×C4×C139#13512yes—
349C2×C4×C139C22×D411yescharacteristic
350C2×C4×C139C22×D411yescharacteristic
351C2×C4×C139C2×#4111yescharacteristic
352C2×C4×C139C2×#4111yescharacteristic
353C2×C4×C139H(5,𝔽2)11yescharacteristic
354C2×C4×C139H(5,𝔽2)11yescharacteristic
355C8×C139—22no—
356C8×C139—41no—
357C8×C139—41no—
358C8×C139—41no—
359C22×C139—22no—
360C22×C139—22no—
361C22×C139—22no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—42no—
367C22×C139—42no—
368C22×C139—42no—
369C22×C139—42no—
370C22×C139—42no—
371C22×C139—42no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139C2×#12111yescharacteristic
388C22×C139D4211yescharacteristic
389C22×C139#54611yescharacteristic
390C22×C139C2×#13511yescharacteristic
391C22×C139#57511yescharacteristic
392C22×C139#57611yescharacteristic
393C22×C139#57611yescharacteristic
394C4×C139—22no—
395C4×C139—22no—
396C4×C139—42no—
397C4×C139—41no—
398C4×C139—42no—
399C4×C139—41no—
400C4×C139—42no—
401C4×C139—41no—
402C4×C139—81no—
403C4×C139—81no—
404C4×C139#52511yescharacteristic
405C4×C139#53811yescharacteristic
406C4×C139D4211yescharacteristic
407C4×C139#54611yescharacteristic
408C2×C139—42no—
409C2×C139—82no—
410C2×C139—82no—
411C2×C139—161no—
412C2×C139#242411yescharacteristic
413C2×C139#303511yescharacteristic
414C2×C139#304111yescharacteristic
415C2×C139#326811yescharacteristic
416C2×C139#328711yescharacteristic
417C2×C139#329711yescharacteristic
418C2×C139#331911yescharacteristic
419#25087C13911yesmaximal, characteristic, direct product factor, Sylow
420C139#2508711yescharacteristic, direct product factor, Sylow
421C2×#466C2×C13911yescharacteristic, complemented
422C2×#463C2×C13911yescharacteristic, complemented
423C2×#449C2×C13911yescharacteristic, complemented
424C2×#416C2×C13911yescharacteristic, complemented
425#2431C2×C13911yescharacteristic, complemented
426#2363C2×C13911yescharacteristic, complemented
427#2067C2×C13911yescharacteristic, complemented
428#2055C2×C13911yescharacteristic, complemented
429#2042C2×C13911yescharacteristic, complemented
430#2011C2×C13911yescharacteristic, complemented
431#1982C2×C13911yescharacteristic, complemented
432#1928C2×C13911yescharacteristic, complemented
433#1879C2×C13911yescharacteristic, complemented
434#1875C2×C13911yescharacteristic, complemented
435#1850C2×C13911yescharacteristic, complemented
436C22×#41C22×C13911yescharacteristic
437C22×SD16C22×C13911yescharacteristic
438C22×D8C22×C13911yescharacteristic
439C22×D8C22×C13911yescharacteristic
440C23×C8C22×C13911yescharacteristic
441C2×#127C22×C13911yescharacteristic
442C2×#124C22×C13911yescharacteristic
443C2×#121C22×C13911yescharacteristic
444C2×#121C22×C13911yescharacteristic
445C2×C4×D4C22×C13911yescharacteristic
446C2×#117C22×C13911yescharacteristic
447#466—24no—
448#463—24no—
449#449—24no—
450C2×#107C22×C13911yescharacteristic
451C2×C4⋊C8C22×C13911yescharacteristic
452C2×C4⋊C8C22×C13911yescharacteristic
453#416—24no—
454C2×#103C22×C13911yescharacteristic
455C2×#103C22×C13911yescharacteristic
456C2×#103C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×#102C22×C13911yescharacteristic
459C2×#102C22×C13911yescharacteristic
460C2×#102C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×#102C22×C13911yescharacteristic
463C2×#102C22×C13911yescharacteristic
464C2×C22⋊C8C22×C13911yescharacteristic
465#392—21no—
466#392—21no—
467#391C22×C13911yescharacteristic
468#390—21no—
469#390C22×C13911yescharacteristic
470#390C22×C13911yescharacteristic
471#389C22×C13911yescharacteristic
472#388—21no—
473#386—21no—
474#386—21no—
475#386—21no—
476C4×C4⋊C4C22×C13911yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4C22×C13911yescharacteristic
479#340C22×C13911yescharacteristic
480#340C22×C13911yescharacteristic
481#336C22×C13911yescharacteristic
482#336C22×C13911yescharacteristic
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C13911yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C13911yescharacteristic
496C22×D4C23×C13911yescharacteristic
497C22×D4C23×C13911yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C13911yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C13911yescharacteristic
514C22×C8C23×C13911yescharacteristic
515C22×C8C23×C13911yescharacteristic
516C22×C8C23×C13911yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C13914yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C13911yescharacteristic
531C2×C4⋊C4C23×C13911yescharacteristic
532C2×C4⋊C4C23×C13911yescharacteristic
533C2×C4⋊C4C23×C13911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C13911yescharacteristic
545C2×C22⋊C4D4×C13911yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C13911yescharacteristic
549C2×C42C23×C13911yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C13914yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C13911yescharacteristic
569#95D4×C13911yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C13911yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C13912yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
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—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C13912yes—
616C2×D4#41×C13912yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13911yescharacteristic
634C22×C4C2×D4×C13911yescharacteristic
635C22×C4C2×D4×C13911yescharacteristic
636C22×C4C2×D4×C13912yes—
637C22×C4C2×D4×C13911yescharacteristic
638C22×C4#41×C13912yes—
639C22×C4C24×C13911yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C13912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C13912yes—
664C4⋊C4C2×D4×C13912yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#121×C13912yes—
711C23C22×D4×C13911yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
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—84no—
767C2×C4#121×C13912yes—
768C2×C4#135×C13912yes—
769C2×C4C22×D4×C13911yescharacteristic
770C2×C4C22×D4×C13911yescharacteristic
771C2×C4C2×#41×C13911yescharacteristic
772C2×C4C2×#41×C13911yescharacteristic
773C2×C4H(5,𝔽2)×C13911yescharacteristic
774C2×C4H(5,𝔽2)×C13911yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C13911yescharacteristic
808C22D42×C13911yescharacteristic
809C22#546×C13911yescharacteristic
810C22C2×#135×C13911yescharacteristic
811C22#575×C13911yescharacteristic
812C22#576×C13911yescharacteristic
813C22#576×C13911yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—42no—
818C4—41no—
819C4—42no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—81no—
824C4#525×C13911yescharacteristic
825C4#538×C13911yescharacteristic
826C4D42×C13911yescharacteristic
827C4#546×C13911yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2#2424×C13911yescharacteristic
833C2#3035×C13911yescharacteristic
834C2#3041×C13911yescharacteristic
835C2#3268×C13911yescharacteristic
836C2#3287×C13911yescharacteristic
837C2#3297×C13911yescharacteristic
838C2#3319×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×#466×C139C2semidirect
2. C2×#463×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×#416×C139C2semidirect
5. #2431×C139C2semidirect
6. #2363×C139C2semidirect
7. #2067×C139C2semidirect
8. #2055×C139C2semidirect
9. #2042×C139C2semidirect
10. #2011×C139C2semidirect
11. #1982×C139C2semidirect
12. #1928×C139C2semidirect
13. #1879×C139C2semidirect
14. #1875×C139C2semidirect
15. #1850×C139C2semidirect
104. #121×C139D4semidirect
135. #103×C139D4semidirect
419. #25087C139direct (N × H)
420. C139#25087direct (N × H)
421. C2×#466C2×C139semidirect
422. C2×#463C2×C139semidirect
423. C2×#449C2×C139semidirect
424. C2×#416C2×C139semidirect
425. #2431C2×C139semidirect
426. #2363C2×C139semidirect
427. #2067C2×C139semidirect
428. #2055C2×C139semidirect
429. #2042C2×C139semidirect
430. #2011C2×C139semidirect
431. #1982C2×C139semidirect
432. #1928C2×C139semidirect
433. #1879C2×C139semidirect
434. #1875C2×C139semidirect
435. #1850C2×C139semidirect
524. #121D4×C139semidirect
555. #103D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1392
C2×#463×C1392
C2×#449×C1392
C2×#416×C1392
#2431×C1392
#2363×C1392
#2067×C1392
#2055×C1392
#2042×C1392
#2011×C1392
#1982×C1392
#1928×C1392
#1879×C1392
#1875×C1392
#1850×C1392
#25087139