Finite Group Databasebeta

← C139×#36526 #48031122

Subgroups — C139×#36526 #48031122

Order 35584.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2864×C139C211yesmaximal, characteristic, complemented
2#2852×C139C212yesmaximal, complemented
3#2597×C139C212yesmaximal, complemented
4#2580×C139C211yesmaximal, characteristic, complemented
5#2578×C139C212yesmaximal, complemented
6#2575×C139C212yesmaximal, complemented
7#2557×C139C212yesmaximal, complemented
8#2535×C139C211yesmaximal, characteristic
9#2523×C139C212yesmaximal, complemented
10#2496×C139C211yesmaximal, characteristic, complemented
11#2495×C139C211yesmaximal, characteristic, complemented
12#2467×C139C212yesmaximal, complemented
13#2422×C139C211yesmaximal, characteristic, complemented
14#2420×C139C211yesmaximal, characteristic, complemented
15#2363×C139C211yesmaximal, characteristic, complemented
16#2361×C139C211yesmaximal, characteristic, complemented
17#2355×C139C211yesmaximal, characteristic, complemented
18#2352×C139C211yesmaximal, characteristic, complemented
19#2347×C139C211yesmaximal, characteristic, complemented
20#2345×C139C211yesmaximal, characteristic, complemented
21C4×#124×C139C211yesmaximal, characteristic, complemented
22C4×#123×C139C212yesmaximal, complemented
23C42×D4×C139C211yesmaximal, characteristic, complemented
24C2×#126×C139C2212yes—
25C2×#124×C139C2211yescharacteristic
26C2×#123×C139C2212yes—
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×C4×Q8×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C2×C4×D4×C139C2211yescharacteristic
34C2×C4×D4×C139C2212yes—
35C2×#117×C139C2211yescharacteristic
36C22×C4⋊C4×C139C2211yescharacteristic
37C22×C42×C139C2212yes—
38#400×C139C2212yes—
39#400×C139C2212yes—
40#399×C139C2212yes—
41#397×C139C2212yes—
42#397×C139C2212yes—
43#397×C139C2212yes—
44#397×C139C2212yes—
45#397×C139C2212yes—
46#394×C139C2212yes—
47#394×C139C2212yes—
48#393×C139C2212yes—
49#392×C139C2212yes—
50#391×C139C2211yescharacteristic
51#391×C139C2212yes—
52#390×C139C2212yes—
53#390×C139C2211yescharacteristic
54#390×C139C2211yescharacteristic
55#390×C139C2211yescharacteristic
56#389×C139C2211yescharacteristic
57#389×C139C2211yescharacteristic
58#389×C139C2211yescharacteristic
59#389×C139C2211yescharacteristic
60#389×C139C2211yescharacteristic
61#389×C139C2211yescharacteristic
62#388×C139C2211yescharacteristic
63#388×C139C2212yes—
64#388×C139C2212yes—
65#388×C139C2211yescharacteristic
66#388×C139C2211yescharacteristic
67#388×C139C2211yescharacteristic
68#388×C139C2212yes—
69#388×C139C2212yes—
70#388×C139C2212yes—
71#388×C139C2212yes—
72#387×C139C2212yes—
73#387×C139C2212yes—
74#387×C139C2212yes—
75#387×C139C2212yes—
76#387×C139C2212yes—
77#387×C139C2212yes—
78#387×C139C2212yes—
79#387×C139C2212yes—
80#387×C139C2212yes—
81#387×C139C2212yes—
82#386×C139C2212yes—
83#386×C139C2212yes—
84#386×C139C2212yes—
85#386×C139C2212yes—
86#386×C139C2212yes—
87#386×C139C2212yes—
88#385×C139C2212yes—
89#385×C139C2212yes—
90#385×C139C2212yes—
91#385×C139C2212yes—
92#384×C139C2211yescharacteristic
93#383×C139C2212yes—
94#383×C139C2212yes—
95#382×C139C2211yescharacteristic
96#382×C139C2211yescharacteristic
97#382×C139C2211yescharacteristic
98#382×C139C2211yescharacteristic
99#381×C139C2212yes—
100#380×C139C2211yescharacteristic
101#380×C139C2211yescharacteristic
102#380×C139C2212yes—
103#380×C139C2211yescharacteristic
104#380×C139C2211yescharacteristic
105C4×C4⋊C4×C139C2211yescharacteristic
106C4×C4⋊C4×C139C2211yescharacteristic
107C4×C4⋊C4×C139C2211yescharacteristic
108C4×C4⋊C4×C139C2212yes—
109C4×C4⋊C4×C139C2212yes—
110C4×C4⋊C4×C139C2211yescharacteristic
111C4×C4⋊C4×C139C2211yescharacteristic
112C4×C22⋊C4×C139C2212yes—
113C4×C22⋊C4×C139C2212yes—
114C4×C22⋊C4×C139C2212yes—
115C4×C22⋊C4×C139C2212yes—
116C4×C22⋊C4×C139C2212yes—
117C4×C22⋊C4×C139C2212yes—
118C4×C22⋊C4×C139C2211yescharacteristic
119C4×C22⋊C4×C139C2211yescharacteristic
120C4×C22⋊C4×C139C2211yescharacteristic
121C4×C22⋊C4×C139C2211yescharacteristic
122C43×C139C2211yescharacteristic
123C22×Q8×C139C2311yescharacteristic
124C22×D4×C139C2312yes—
125C22×D4×C139C2311yescharacteristic
126C22×D4×C139C2311yescharacteristic
127C22×D4×C139C2312yes—
128C23×C4×C139C2311yescharacteristic
129C23×C4×C139C2311yescharacteristic
130C23×C4×C139C2312yes—
131C23×C4×C139C2312yes—
132C23×C4×C139C2312yes—
133C23×C4×C139C2312yes—
134#126×C139—44no—
135#124×C139—24no—
136#123×C139—28no—
137#121×C139—24no—
138#121×C139—24no—
139C4×Q8×C139—24no—
140C4×D4×C139—24no—
141C4×D4×C139—24no—
142C4×D4×C139—24no—
143C4×D4×C139—24no—
144C4×D4×C139—44no—
145#117×C139—24no—
146C2×C4⋊C4×C139—24no—
147C2×C4⋊C4×C139C2311yescharacteristic
148C2×C4⋊C4×C139C2312yes—
149C2×C4⋊C4×C139C2311yescharacteristic
150C2×C4⋊C4×C139C2311yescharacteristic
151C2×C4⋊C4×C139C2312yes—
152C2×C4⋊C4×C139C2311yescharacteristic
153C2×C4⋊C4×C139C2312yes—
154C2×C4⋊C4×C139C2311yescharacteristic
155C2×C4⋊C4×C139C2311yescharacteristic
156C2×C4⋊C4×C139C2311yescharacteristic
157C2×C4⋊C4×C139C2311yescharacteristic
158C2×C4⋊C4×C139C2311yescharacteristic
159C2×C4⋊C4×C139C2311yescharacteristic
160C2×C4⋊C4×C139C2312yes—
161C2×C4⋊C4×C139C2312yes—
162C2×C4⋊C4×C139C2312yes—
163C2×C4⋊C4×C139C2312yes—
164C2×C4⋊C4×C139C2312yes—
165C2×C4⋊C4×C139C2312yes—
166C2×C4⋊C4×C139C2311yescharacteristic
167C2×C22⋊C4×C139C2312yes—
168C2×C22⋊C4×C139C2312yes—
169C2×C22⋊C4×C139C2312yes—
170C2×C22⋊C4×C139C2311yescharacteristic
171C2×C22⋊C4×C139C2311yescharacteristic
172C2×C22⋊C4×C139C2312yes—
173C2×C22⋊C4×C139C2312yes—
174C2×C22⋊C4×C139C2312yes—
175C2×C22⋊C4×C139C2312yes—
176C2×C22⋊C4×C139C2311yescharacteristic
177C2×C22⋊C4×C139C2311yescharacteristic
178C2×C22⋊C4×C139C2312yes—
179C2×C22⋊C4×C139C2311yescharacteristic
180C2×C22⋊C4×C139C2311yescharacteristic
181C2×C22⋊C4×C139C2311yescharacteristic
182C2×C22⋊C4×C139C2312yes—
183C2×C22⋊C4×C139C2312yes—
184C2×C22⋊C4×C139C2312yes—
185C2×C22⋊C4×C139C2312yes—
186C2×C22⋊C4×C139C2312yes—
187C2×C22⋊C4×C139C2312yes—
188C2×C22⋊C4×C139C2311yescharacteristic
189C2×C22⋊C4×C139C2311yescharacteristic
190C2×C22⋊C4×C139C2311yescharacteristic
191C2×C42×C139—44no—
192C2×C42×C139C2311yescharacteristic
193C2×C42×C139C2312yes—
194C2×C42×C139C2312yes—
195C2×C42×C139C2311yescharacteristic
196C2×C42×C139C2311yescharacteristic
197C2×C42×C139C2311yescharacteristic
198C2×C42×C139C2311yescharacteristic
199C2×C42×C139C2311yescharacteristic
200C2×C42×C139C2312yes—
201C2×C42×C139C2312yes—
202C2×C42×C139C2312yes—
203C2×C42×C139C2311yescharacteristic
204C2×C42×C139C2311yescharacteristic
205C2×C42×C139C2312yes—
206C2×C42×C139C2311yescharacteristic
207#95×C139C2312yes—
208#95×C139C2311yescharacteristic
209#95×C139C2311yescharacteristic
210#95×C139C2312yes—
211#95×C139C2312yes—
212#95×C139C2312yes—
213#95×C139C2312yes—
214#95×C139C2312yes—
215#95×C139C2312yes—
216#95×C139C2312yes—
217#95×C139C2312yes—
218#95×C139C2312yes—
219#95×C139C2312yes—
220#95×C139C2312yes—
221#95×C139C2311yescharacteristic
222#95×C139C2311yescharacteristic
223#95×C139C2312yes—
224#95×C139C2311yescharacteristic
225#95×C139C2312yes—
226#95×C139C2312yes—
227#95×C139C2311yescharacteristic
228#95×C139C2312yes—
229#95×C139C2311yescharacteristic
230#95×C139C2312yes—
231#95×C139C2311yescharacteristic
232#95×C139C2312yes—
233#95×C139C2312yes—
234#95×C139C2312yes—
235#95×C139C2312yes—
236C24×C139C2411yescharacteristic
237C24×C139C2412yes—
238C24×C139C2411yescharacteristic
239C2×Q8×C139—22no—
240C2×Q8×C139—22no—
241C2×Q8×C139—41no—
242C2×D4×C139—24no—
243C2×D4×C139—24no—
244C2×D4×C139—22no—
245C2×D4×C139—24no—
246C2×D4×C139—22no—
247C2×D4×C139—22no—
248C2×D4×C139—22no—
249C2×D4×C139—42no—
250C2×D4×C139—41no—
251C2×D4×C139—42no—
252C2×D4×C139—42no—
253C2×D4×C139#4114yes—
254C22×C4×C139—24no—
255C22×C4×C139—22no—
256C22×C4×C139—22no—
257C22×C4×C139—24no—
258C22×C4×C139—24no—
259C22×C4×C139—22no—
260C22×C4×C139—22no—
261C22×C4×C139—22no—
262C22×C4×C139—22no—
263C22×C4×C139—24no—
264C22×C4×C139—24no—
265C22×C4×C139—24no—
266C22×C4×C139—42no—
267C22×C4×C139—42no—
268C22×C4×C139—42no—
269C22×C4×C139—42no—
270C22×C4×C139—42no—
271C22×C4×C139—42no—
272C22×C4×C139C2411yescharacteristic
273C22×C4×C139C2411yescharacteristic
274C22×C4×C139C2412yes—
275C22×C4×C139C2411yescharacteristic
276C22×C4×C139C2411yescharacteristic
277C22×C4×C139C2411yescharacteristic
278C22×C4×C139C2412yes—
279C22×C4×C139C2412yes—
280C22×C4×C139C2412yes—
281C22×C4×C139C2412yes—
282C22×C4×C139C2412yes—
283C22×C4×C139C2411yescharacteristic
284C22×C4×C139C2411yescharacteristic
285C22×C4×C139C2411yescharacteristic
286C22×C4×C139C2411yescharacteristic
287C22×C4×C139C2411yescharacteristic
288C22×C4×C139C2412yes—
289C22×C4×C139C2411yescharacteristic
290C22×C4×C139C2411yescharacteristic
291C22×C4×C139C2411yescharacteristic
292C4⋊C4×C139—24no—
293C4⋊C4×C139—22no—
294C4⋊C4×C139—22no—
295C4⋊C4×C139—22no—
296C4⋊C4×C139—22no—
297C4⋊C4×C139—22no—
298C4⋊C4×C139—22no—
299C4⋊C4×C139—22no—
300C4⋊C4×C139—22no—
301C4⋊C4×C139—22no—
302C4⋊C4×C139—22no—
303C4⋊C4×C139—24no—
304C4⋊C4×C139—24no—
305C4⋊C4×C139—24no—
306C4⋊C4×C139—42no—
307C4⋊C4×C139—42no—
308C4⋊C4×C139—42no—
309C4⋊C4×C139—42no—
310C4⋊C4×C139—42no—
311C4⋊C4×C139#4114yes—
312C22⋊C4×C139—24no—
313C22⋊C4×C139—24no—
314C22⋊C4×C139—24no—
315C22⋊C4×C139—24no—
316C22⋊C4×C139—22no—
317C22⋊C4×C139—24no—
318C22⋊C4×C139—24no—
319C22⋊C4×C139—22no—
320C22⋊C4×C139—22no—
321C22⋊C4×C139—24no—
322C22⋊C4×C139—24no—
323C22⋊C4×C139—22no—
324C22⋊C4×C139—22no—
325C22⋊C4×C139—22no—
326C22⋊C4×C139—22no—
327C22⋊C4×C139—41no—
328C22⋊C4×C139—41no—
329C22⋊C4×C139—42no—
330C22⋊C4×C139—42no—
331C22⋊C4×C139—42no—
332C22⋊C4×C139—42no—
333C22⋊C4×C139—42no—
334C22⋊C4×C139—42no—
335C22⋊C4×C139#4114yes—
336C42×C139—24no—
337C42×C139—22no—
338C42×C139—22no—
339C42×C139—22no—
340C42×C139—22no—
341C42×C139—22no—
342C42×C139—22no—
343C42×C139—24no—
344C42×C139—42no—
345C42×C139—42no—
346C42×C139—42no—
347C42×C139—41no—
348C42×C139—41no—
349C42×C139—42no—
350C42×C139#4114yes—
351C23×C139—22no—
352C23×C139—22no—
353C23×C139—21no—
354C23×C139—22no—
355C23×C139—21no—
356C23×C139—21no—
357C23×C139—21no—
358C23×C139—22no—
359C23×C139—21no—
360C23×C139—22no—
361C23×C139—22no—
362C23×C139—21no—
363C23×C139—21no—
364C23×C139—21no—
365C23×C139—21no—
366C23×C139—21no—
367C23×C139—21no—
368C23×C139—21no—
369C23×C139—21no—
370C23×C139C2×#4112yes—
371C23×C139C2×#4114yes—
372C23×C139C2511yescharacteristic
373Q8×C139—44no—
374D4×C139—28no—
375D4×C139—44no—
376D4×C139—48no—
377D4×C139—84no—
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—22no—
385C2×C4×C139—21no—
386C2×C4×C139—21no—
387C2×C4×C139—21no—
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—21no—
396C2×C4×C139—21no—
397C2×C4×C139—21no—
398C2×C4×C139—22no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—21no—
402C2×C4×C139—21no—
403C2×C4×C139—21no—
404C2×C4×C139—22no—
405C2×C4×C139—22no—
406C2×C4×C139—22no—
407C2×C4×C139—22no—
408C2×C4×C139—22no—
409C2×C4×C139—21no—
410C2×C4×C139—22no—
411C2×C4×C139—22no—
412C2×C4×C139—22no—
413C2×C4×C139—22no—
414C2×C4×C139—21no—
415C2×C4×C139—22no—
416C2×C4×C139—21no—
417C2×C4×C139—22no—
418C2×C4×C139—21no—
419C2×C4×C139—21no—
420C2×C4×C139—21no—
421C2×C4×C139—22no—
422C2×C4×C139—21no—
423C2×C4×C139—21no—
424C2×C4×C139—22no—
425C2×C4×C139—21no—
426C2×C4×C139—22no—
427C2×C4×C139—22no—
428C2×C4×C139—22no—
429C2×C4×C139—48no—
430C2×C4×C139—48no—
431C2×C4×C139—48no—
432C2×C4×C139—44no—
433C2×C4×C139—44no—
434C2×C4×C139—84no—
435C2×C4×C139C2×#4114yes—
436C2×C4×C139C2×#4112yes—
437C2×C4×C139C2×#4112yes—
438C2×C4×C139C2×#4112yes—
439C2×C4×C139C2×#4112yes—
440C2×C4×C139C2×#4112yes—
441C2×C4×C139C2×#4112yes—
442C2×C4×C139C2×#4112yes—
443C2×C4×C139H(5,𝔽2)12yes—
444C22×C139—24no—
445C22×C139—22no—
446C22×C139—22no—
447C22×C139—24no—
448C22×C139—22no—
449C22×C139—24no—
450C22×C139—41no—
451C22×C139—42no—
452C22×C139—42no—
453C22×C139—42no—
454C22×C139—41no—
455C22×C139—42no—
456C22×C139—41no—
457C22×C139—41no—
458C22×C139—41no—
459C22×C139—41no—
460C22×C139—41no—
461C22×C139—41no—
462C22×C139—41no—
463C22×C139—41no—
464C22×C139—41no—
465C22×C139C22×#4111yescharacteristic
466C22×C139C22×#4111yescharacteristic
467C22×C139C22×#4111yescharacteristic
468C22×C139C22×#4111yescharacteristic
469C22×C139C2×H(5,𝔽2)11yescharacteristic
470C22×C139#58511yescharacteristic
471C22×C139#58511yescharacteristic
472C4×C139—22no—
473C4×C139—22no—
474C4×C139—22no—
475C4×C139—22no—
476C4×C139—22no—
477C4×C139—24no—
478C4×C139—41no—
479C4×C139—41no—
480C4×C139—41no—
481C4×C139—41no—
482C4×C139—42no—
483C4×C139—42no—
484C4×C139—42no—
485C4×C139—41no—
486C4×C139—41no—
487C4×C139—42no—
488C4×C139—42no—
489C4×C139—41no—
490C4×C139—42no—
491C4×C139#52914yes—
492C2×C139—44no—
493C2×C139—42no—
494C2×C139—81no—
495C2×C139C2×#52911yescharacteristic
496C2×C139#347511yescharacteristic
497C2×C139#348011yescharacteristic
498C2×C139#348111yescharacteristic
499C2×C139#350611yescharacteristic
500C2×C139#351311yescharacteristic
501C2×C139#352111yescharacteristic
502#36526C13911yesmaximal, characteristic, direct product factor, Sylow
503C139#3652611yescharacteristic, direct product factor, Sylow
504#2864C2×C13911yescharacteristic, complemented
505#2852C2×C13912yescomplemented
506#2597C2×C13912yescomplemented
507#2580C2×C13911yescharacteristic, complemented
508#2578C2×C13912yescomplemented
509#2575C2×C13912yescomplemented
510#2557C2×C13912yescomplemented
511#2535C2×C13911yescharacteristic
512#2523C2×C13912yescomplemented
513#2496C2×C13911yescharacteristic, complemented
514#2495C2×C13911yescharacteristic, complemented
515#2467C2×C13912yescomplemented
516#2422C2×C13911yescharacteristic, complemented
517#2420C2×C13911yescharacteristic, complemented
518#2363C2×C13911yescharacteristic, complemented
519#2361C2×C13911yescharacteristic, complemented
520#2355C2×C13911yescharacteristic, complemented
521#2352C2×C13911yescharacteristic, complemented
522#2347C2×C13911yescharacteristic, complemented
523#2345C2×C13911yescharacteristic, complemented
524C4×#124C2×C13911yescharacteristic, complemented
525C4×#123C2×C13912yescomplemented
526C42×D4C2×C13911yescharacteristic, complemented
527C2×#126C22×C13912yes—
528C2×#124C22×C13911yescharacteristic
529C2×#123C22×C13912yes—
530C2×#121C22×C13911yescharacteristic
531C2×#121C22×C13911yescharacteristic
532C2×C4×Q8C22×C13911yescharacteristic
533C2×C4×D4C22×C13911yescharacteristic
534C2×C4×D4C22×C13911yescharacteristic
535C2×C4×D4C22×C13911yescharacteristic
536C2×C4×D4C22×C13911yescharacteristic
537C2×C4×D4C22×C13912yes—
538C2×#117C22×C13911yescharacteristic
539C22×C4⋊C4C22×C13911yescharacteristic
540C22×C42C22×C13912yes—
541#400C22×C13912yes—
542#400C22×C13912yes—
543#399C22×C13912yes—
544#397C22×C13912yes—
545#397C22×C13912yes—
546#397C22×C13912yes—
547#397C22×C13912yes—
548#397C22×C13912yes—
549#394C22×C13912yes—
550#394C22×C13912yes—
551#393C22×C13912yes—
552#392C22×C13912yes—
553#391C22×C13912yes—
554#391C22×C13911yescharacteristic
555#390C22×C13911yescharacteristic
556#390C22×C13911yescharacteristic
557#390C22×C13912yes—
558#390C22×C13911yescharacteristic
559#389C22×C13911yescharacteristic
560#389C22×C13911yescharacteristic
561#389C22×C13911yescharacteristic
562#389C22×C13911yescharacteristic
563#389C22×C13911yescharacteristic
564#389C22×C13911yescharacteristic
565#388C22×C13912yes—
566#388C22×C13912yes—
567#388C22×C13911yescharacteristic
568#388C22×C13911yescharacteristic
569#388C22×C13912yes—
570#388C22×C13912yes—
571#388C22×C13911yescharacteristic
572#388C22×C13912yes—
573#388C22×C13912yes—
574#388C22×C13911yescharacteristic
575#387C22×C13912yes—
576#387C22×C13912yes—
577#387C22×C13912yes—
578#387C22×C13912yes—
579#387C22×C13912yes—
580#387C22×C13912yes—
581#387C22×C13912yes—
582#387C22×C13912yes—
583#387C22×C13912yes—
584#387C22×C13912yes—
585#386C22×C13912yes—
586#386C22×C13912yes—
587#386C22×C13912yes—
588#386C22×C13912yes—
589#386C22×C13912yes—
590#386C22×C13912yes—
591#385C22×C13912yes—
592#385C22×C13912yes—
593#385C22×C13912yes—
594#385C22×C13912yes—
595#384C22×C13911yescharacteristic
596#383C22×C13912yes—
597#383C22×C13912yes—
598#382C22×C13911yescharacteristic
599#382C22×C13911yescharacteristic
600#382C22×C13911yescharacteristic
601#382C22×C13911yescharacteristic
602#381C22×C13912yes—
603#380C22×C13912yes—
604#380C22×C13911yescharacteristic
605#380C22×C13911yescharacteristic
606#380C22×C13911yescharacteristic
607#380C22×C13911yescharacteristic
608C4×C4⋊C4C22×C13912yes—
609C4×C4⋊C4C22×C13912yes—
610C4×C4⋊C4C22×C13911yescharacteristic
611C4×C4⋊C4C22×C13911yescharacteristic
612C4×C4⋊C4C22×C13911yescharacteristic
613C4×C4⋊C4C22×C13911yescharacteristic
614C4×C4⋊C4C22×C13911yescharacteristic
615C4×C22⋊C4C22×C13912yes—
616C4×C22⋊C4C22×C13912yes—
617C4×C22⋊C4C22×C13912yes—
618C4×C22⋊C4C22×C13911yescharacteristic
619C4×C22⋊C4C22×C13912yes—
620C4×C22⋊C4C22×C13911yescharacteristic
621C4×C22⋊C4C22×C13911yescharacteristic
622C4×C22⋊C4C22×C13911yescharacteristic
623C4×C22⋊C4C22×C13912yes—
624C4×C22⋊C4C22×C13912yes—
625C43C22×C13911yescharacteristic
626C22×Q8C23×C13911yescharacteristic
627C22×D4C23×C13912yes—
628C22×D4C23×C13911yescharacteristic
629C22×D4C23×C13911yescharacteristic
630C22×D4C23×C13912yes—
631C23×C4C23×C13911yescharacteristic
632C23×C4C23×C13911yescharacteristic
633C23×C4C23×C13912yes—
634C23×C4C23×C13912yes—
635C23×C4C23×C13912yes—
636C23×C4C23×C13912yes—
637#126—44no—
638#124—24no—
639#123—28no—
640#121—24no—
641#121—24no—
642C4×Q8—24no—
643C4×D4—24no—
644C4×D4—24no—
645C4×D4—24no—
646C4×D4—24no—
647C4×D4—44no—
648#117—24no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4C23×C13911yescharacteristic
651C2×C4⋊C4C23×C13912yes—
652C2×C4⋊C4C23×C13911yescharacteristic
653C2×C4⋊C4C23×C13912yes—
654C2×C4⋊C4C23×C13911yescharacteristic
655C2×C4⋊C4C23×C13911yescharacteristic
656C2×C4⋊C4C23×C13911yescharacteristic
657C2×C4⋊C4C23×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C4⋊C4C23×C13911yescharacteristic
661C2×C4⋊C4C23×C13911yescharacteristic
662C2×C4⋊C4C23×C13912yes—
663C2×C4⋊C4C23×C13912yes—
664C2×C4⋊C4C23×C13912yes—
665C2×C4⋊C4C23×C13912yes—
666C2×C4⋊C4C23×C13912yes—
667C2×C4⋊C4C23×C13912yes—
668C2×C4⋊C4C23×C13912yes—
669C2×C4⋊C4C23×C13911yescharacteristic
670C2×C22⋊C4C23×C13912yes—
671C2×C22⋊C4C23×C13911yescharacteristic
672C2×C22⋊C4C23×C13911yescharacteristic
673C2×C22⋊C4C23×C13912yes—
674C2×C22⋊C4C23×C13912yes—
675C2×C22⋊C4C23×C13912yes—
676C2×C22⋊C4C23×C13911yescharacteristic
677C2×C22⋊C4C23×C13912yes—
678C2×C22⋊C4C23×C13912yes—
679C2×C22⋊C4C23×C13912yes—
680C2×C22⋊C4C23×C13912yes—
681C2×C22⋊C4C23×C13911yescharacteristic
682C2×C22⋊C4C23×C13911yescharacteristic
683C2×C22⋊C4C23×C13911yescharacteristic
684C2×C22⋊C4C23×C13911yescharacteristic
685C2×C22⋊C4C23×C13912yes—
686C2×C22⋊C4C23×C13912yes—
687C2×C22⋊C4C23×C13912yes—
688C2×C22⋊C4C23×C13912yes—
689C2×C22⋊C4C23×C13911yescharacteristic
690C2×C22⋊C4C23×C13911yescharacteristic
691C2×C22⋊C4C23×C13912yes—
692C2×C22⋊C4C23×C13912yes—
693C2×C22⋊C4C23×C13911yescharacteristic
694C2×C42—44no—
695C2×C42C23×C13912yes—
696C2×C42C23×C13911yescharacteristic
697C2×C42C23×C13911yescharacteristic
698C2×C42C23×C13911yescharacteristic
699C2×C42C23×C13911yescharacteristic
700C2×C42C23×C13911yescharacteristic
701C2×C42C23×C13912yes—
702C2×C42C23×C13911yescharacteristic
703C2×C42C23×C13912yes—
704C2×C42C23×C13911yescharacteristic
705C2×C42C23×C13911yescharacteristic
706C2×C42C23×C13912yes—
707C2×C42C23×C13912yes—
708C2×C42C23×C13912yes—
709C2×C42C23×C13911yescharacteristic
710#95C23×C13911yescharacteristic
711#95C23×C13912yes—
712#95C23×C13912yes—
713#95C23×C13912yes—
714#95C23×C13911yescharacteristic
715#95C23×C13912yes—
716#95C23×C13912yes—
717#95C23×C13911yescharacteristic
718#95C23×C13912yes—
719#95C23×C13911yescharacteristic
720#95C23×C13911yescharacteristic
721#95C23×C13911yescharacteristic
722#95C23×C13911yescharacteristic
723#95C23×C13912yes—
724#95C23×C13912yes—
725#95C23×C13911yescharacteristic
726#95C23×C13912yes—
727#95C23×C13912yes—
728#95C23×C13912yes—
729#95C23×C13912yes—
730#95C23×C13912yes—
731#95C23×C13912yes—
732#95C23×C13912yes—
733#95C23×C13912yes—
734#95C23×C13912yes—
735#95C23×C13912yes—
736#95C23×C13912yes—
737#95C23×C13912yes—
738#95C23×C13912yes—
739C24C24×C13911yescharacteristic
740C24C24×C13912yes—
741C24C24×C13911yescharacteristic
742C2×Q8—22no—
743C2×Q8—22no—
744C2×Q8—41no—
745C2×D4—24no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—24no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—22no—
752C2×D4—42no—
753C2×D4—41no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4#41×C13914yes—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4C24×C13911yescharacteristic
776C22×C4C24×C13911yescharacteristic
777C22×C4C24×C13912yes—
778C22×C4C24×C13911yescharacteristic
779C22×C4C24×C13911yescharacteristic
780C22×C4C24×C13911yescharacteristic
781C22×C4C24×C13912yes—
782C22×C4C24×C13912yes—
783C22×C4C24×C13912yes—
784C22×C4C24×C13912yes—
785C22×C4C24×C13912yes—
786C22×C4C24×C13911yescharacteristic
787C22×C4C24×C13911yescharacteristic
788C22×C4C24×C13911yescharacteristic
789C22×C4C24×C13911yescharacteristic
790C22×C4C24×C13911yescharacteristic
791C22×C4C24×C13912yes—
792C22×C4C24×C13911yescharacteristic
793C22×C4C24×C13911yescharacteristic
794C22×C4C24×C13911yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—42no—
814C4⋊C4#41×C13914yes—
815C22⋊C4—24no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—22no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—41no—
831C22⋊C4—41no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4—42no—
838C22⋊C4#41×C13914yes—
839C42—24no—
840C42—22no—
841C42—22no—
842C42—22no—
843C42—22no—
844C42—22no—
845C42—22no—
846C42—24no—
847C42—42no—
848C42—42no—
849C42—42no—
850C42—41no—
851C42—41no—
852C42—42no—
853C42#41×C13914yes—
854C23—22no—
855C23—22no—
856C23—21no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—22no—
862C23—21no—
863C23—22no—
864C23—22no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23C2×#41×C13912yes—
874C23C2×#41×C13914yes—
875C23C25×C13911yescharacteristic
876Q8—44no—
877D4—28no—
878D4—44no—
879D4—48no—
880D4—84no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—84no—
938C2×C4C2×#41×C13914yes—
939C2×C4C2×#41×C13912yes—
940C2×C4C2×#41×C13912yes—
941C2×C4C2×#41×C13912yes—
942C2×C4C2×#41×C13912yes—
943C2×C4C2×#41×C13912yes—
944C2×C4C2×#41×C13912yes—
945C2×C4C2×#41×C13912yes—
946C2×C4H(5,𝔽2)×C13912yes—
947C22—24no—
948C22—22no—
949C22—22no—
950C22—24no—
951C22—22no—
952C22—24no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22C22×#41×C13911yescharacteristic
969C22C22×#41×C13911yescharacteristic
970C22C22×#41×C13911yescharacteristic
971C22C22×#41×C13911yescharacteristic
972C22C2×H(5,𝔽2)×C13911yescharacteristic
973C22#585×C13911yescharacteristic
974C22#585×C13911yescharacteristic
975C4—22no—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—24no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—41no—
990C4—41no—
991C4—42no—
992C4—42no—
993C4—41no—
994C4#529×C13914yes—
995C2—44no—
996C2—42no—
997C2—81no—
998C2C2×#529×C13911yescharacteristic
999C2#3475×C13911yescharacteristic
1000C2#3480×C13911yescharacteristic
1001C2#3481×C13911yescharacteristic
1002C2#3506×C13911yescharacteristic
1003C2#3513×C13911yescharacteristic
1004C2#3521×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radical#2535×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2864×C139C2semidirect
2. #2852×C139C2semidirect
3. #2597×C139C2semidirect
4. #2580×C139C2semidirect
5. #2578×C139C2semidirect
6. #2575×C139C2semidirect
7. #2557×C139C2semidirect
9. #2523×C139C2semidirect
10. #2496×C139C2semidirect
11. #2495×C139C2semidirect
12. #2467×C139C2semidirect
13. #2422×C139C2semidirect
14. #2420×C139C2semidirect
15. #2363×C139C2semidirect
16. #2361×C139C2semidirect
17. #2355×C139C2semidirect
18. #2352×C139C2semidirect
19. #2347×C139C2semidirect
20. #2345×C139C2semidirect
21. C4×#124×C139C2semidirect
22. C4×#123×C139C2semidirect
23. C42×D4×C139C2semidirect
502. #36526C139direct (N × H)
503. C139#36526direct (N × H)
504. #2864C2×C139semidirect
505. #2852C2×C139semidirect
506. #2597C2×C139semidirect
507. #2580C2×C139semidirect
508. #2578C2×C139semidirect
509. #2575C2×C139semidirect
510. #2557C2×C139semidirect
512. #2523C2×C139semidirect
513. #2496C2×C139semidirect
514. #2495C2×C139semidirect
515. #2467C2×C139semidirect
516. #2422C2×C139semidirect
517. #2420C2×C139semidirect
518. #2363C2×C139semidirect
519. #2361C2×C139semidirect
520. #2355C2×C139semidirect
521. #2352C2×C139semidirect
522. #2347C2×C139semidirect
523. #2345C2×C139semidirect
524. C4×#124C2×C139semidirect
525. C4×#123C2×C139semidirect
526. C42×D4C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2864×C1392
#2852×C1392
#2597×C1392
#2580×C1392
#2578×C1392
#2575×C1392
#2557×C1392
#2535×C1392
#2523×C1392
#2496×C1392
#2495×C1392
#2467×C1392
#2422×C1392
#2420×C1392
#2363×C1392
#2361×C1392
#2355×C1392
#2352×C1392
#2347×C1392
#2345×C1392
C4×#124×C1392
C4×#123×C1392
C42×D4×C1392
#36526139