Finite Group Databasebeta

← C139×#36297 #48030893

Subgroups — C139×#36297 #48030893

Order 35584.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2866×C139C212yesmaximal, complemented
2#2854×C139C211yesmaximal, characteristic, complemented
3#2530×C139C212yesmaximal, complemented
4#2526×C139C212yesmaximal, complemented
5#2516×C139C212yesmaximal, complemented
6#2513×C139C211yesmaximal, characteristic, complemented
7#2509×C139C211yesmaximal, characteristic, complemented
8#2497×C139C211yesmaximal, characteristic, complemented
9#2490×C139C211yesmaximal, characteristic, complemented
10#2471×C139C212yesmaximal, complemented
11#2470×C139C212yesmaximal, complemented
12#2457×C139C212yesmaximal, complemented
13#2441×C139C211yesmaximal, characteristic, complemented
14#2414×C139C211yesmaximal, characteristic
15#2370×C139C211yesmaximal, characteristic, complemented
16#2363×C139C211yesmaximal, characteristic, complemented
17#2361×C139C211yesmaximal, characteristic, complemented
18#2354×C139C211yesmaximal, characteristic, complemented
19#2352×C139C211yesmaximal, characteristic, complemented
20#2344×C139C211yesmaximal, characteristic, complemented
21C4×#123×C139C211yesmaximal, characteristic, complemented
22#2293×C139C212yesmaximal, complemented
23C4×#117×C139C211yesmaximal, characteristic, complemented
24C2×#125×C139C2211yescharacteristic
25C2×#123×C139C2211yescharacteristic
26C2×#123×C139C2212yes—
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×C4×D4×C139C2212yes—
30C2×C4×D4×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C2×#117×C139C2211yescharacteristic
33C2×#117×C139C2211yescharacteristic
34C2×#117×C139C2212yes—
35C2×#117×C139C2212yes—
36C22×C4⋊C4×C139C2211yescharacteristic
37C22×C42×C139C2211yescharacteristic
38#400×C139C2212yes—
39#400×C139C2212yes—
40#400×C139C2212yes—
41#399×C139C2212yes—
42#397×C139C2212yes—
43#397×C139C2212yes—
44#397×C139C2212yes—
45#396×C139C2212yes—
46#396×C139C2212yes—
47#394×C139C2212yes—
48#394×C139C2212yes—
49#392×C139C2212yes—
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#390×C139C2212yes—
54#390×C139C2212yes—
55#390×C139C2212yes—
56#390×C139C2211yescharacteristic
57#389×C139C2211yescharacteristic
58#389×C139C2212yes—
59#389×C139C2212yes—
60#389×C139C2212yes—
61#389×C139C2211yescharacteristic
62#389×C139C2211yescharacteristic
63#389×C139C2211yescharacteristic
64#389×C139C2211yescharacteristic
65#389×C139C2211yescharacteristic
66#388×C139C2212yes—
67#388×C139C2212yes—
68#388×C139C2212yes—
69#388×C139C2212yes—
70#388×C139C2212yes—
71#388×C139C2211yescharacteristic
72#388×C139C2212yes—
73#388×C139C2212yes—
74#388×C139C2212yes—
75#388×C139C2211yescharacteristic
76#388×C139C2212yes—
77#388×C139C2212yes—
78#388×C139C2212yes—
79#388×C139C2212yes—
80#387×C139C2212yes—
81#387×C139C2212yes—
82#387×C139C2212yes—
83#387×C139C2211yescharacteristic
84#387×C139C2212yes—
85#387×C139C2212yes—
86#387×C139C2211yescharacteristic
87#387×C139C2212yes—
88#387×C139C2212yes—
89#387×C139C2212yes—
90#386×C139C2212yes—
91#386×C139C2212yes—
92#386×C139C2211yescharacteristic
93#386×C139C2212yes—
94#386×C139C2212yes—
95#385×C139C2212yes—
96#385×C139C2211yescharacteristic
97#384×C139C2211yescharacteristic
98#382×C139C2211yescharacteristic
99#381×C139C2211yescharacteristic
100#381×C139C2212yes—
101#380×C139C2212yes—
102#380×C139C2211yescharacteristic
103#380×C139C2211yescharacteristic
104#380×C139C2211yescharacteristic
105C4×C4⋊C4×C139C2211yescharacteristic
106C4×C4⋊C4×C139C2211yescharacteristic
107C4×C4⋊C4×C139C2212yes—
108C4×C4⋊C4×C139C2211yescharacteristic
109C4×C4⋊C4×C139C2211yescharacteristic
110C4×C4⋊C4×C139C2211yescharacteristic
111C4×C4⋊C4×C139C2211yescharacteristic
112C4×C4⋊C4×C139C2211yescharacteristic
113C4×C4⋊C4×C139C2211yescharacteristic
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
121#376×C139C2212yes—
122C43×C139C2212yes—
123C22×D4×C139C2311yescharacteristic
124C22×D4×C139C2312yes—
125C22×D4×C139C2311yescharacteristic
126C22×D4×C139C2312yes—
127C23×C4×C139C2311yescharacteristic
128C23×C4×C139C2311yescharacteristic
129C23×C4×C139C2311yescharacteristic
130C23×C4×C139C2312yes—
131C23×C4×C139C2312yes—
132C23×C4×C139C2311yescharacteristic
133#125×C139—24no—
134#123×C139—24no—
135#123×C139—44no—
136#121×C139—24no—
137#121×C139—24no—
138C4×D4×C139—24no—
139C4×D4×C139—24no—
140C4×D4×C139—28no—
141#117×C139—24no—
142#117×C139—24no—
143#117×C139—44no—
144#117×C139—44no—
145C2×C4⋊C4×C139—24no—
146C2×C4⋊C4×C139C2312yes—
147C2×C4⋊C4×C139C2312yes—
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×C139C2311yescharacteristic
165C2×C4⋊C4×C139C2312yes—
166C2×C4⋊C4×C139C2312yes—
167C2×C4⋊C4×C139C2311yescharacteristic
168C2×C4⋊C4×C139C2311yescharacteristic
169C2×C22⋊C4×C139C2311yescharacteristic
170C2×C22⋊C4×C139C2312yes—
171C2×C22⋊C4×C139C2312yes—
172C2×C22⋊C4×C139C2311yescharacteristic
173C2×C22⋊C4×C139C2312yes—
174C2×C22⋊C4×C139C2312yes—
175C2×C22⋊C4×C139C2311yescharacteristic
176C2×C22⋊C4×C139C2311yescharacteristic
177C2×C22⋊C4×C139C2312yes—
178C2×C22⋊C4×C139C2312yes—
179C2×C22⋊C4×C139C2312yes—
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×C139C2312yes—
189C2×C22⋊C4×C139C2312yes—
190C2×C22⋊C4×C139C2312yes—
191C2×C22⋊C4×C139C2311yescharacteristic
192C2×C22⋊C4×C139C2311yescharacteristic
193C2×C42×C139—24no—
194C2×C42×C139C2311yescharacteristic
195C2×C42×C139C2311yescharacteristic
196C2×C42×C139C2311yescharacteristic
197C2×C42×C139C2311yescharacteristic
198C2×C42×C139C2312yes—
199C2×C42×C139C2312yes—
200C2×C42×C139C2312yes—
201C2×C42×C139C2312yes—
202C2×C42×C139C2311yescharacteristic
203C2×C42×C139C2311yescharacteristic
204C2×C42×C139C2311yescharacteristic
205C2×C42×C139C2312yes—
206C2×C42×C139C2312yes—
207C2×C42×C139C2312yes—
208C2×C42×C139C2312yes—
209#95×C139C2312yes—
210#95×C139C2312yes—
211#95×C139C2311yescharacteristic
212#95×C139C2311yescharacteristic
213#95×C139C2312yes—
214#95×C139C2312yes—
215#95×C139C2312yes—
216#95×C139C2312yes—
217#95×C139C2312yes—
218#95×C139C2311yescharacteristic
219#95×C139C2312yes—
220#95×C139C2311yescharacteristic
221#95×C139C2312yes—
222#95×C139C2312yes—
223#95×C139C2312yes—
224#95×C139C2312yes—
225#95×C139C2312yes—
226#95×C139C2311yescharacteristic
227#95×C139C2312yes—
228#95×C139C2311yescharacteristic
229#95×C139C2311yescharacteristic
230#95×C139C2311yescharacteristic
231#95×C139C2311yescharacteristic
232#95×C139C2312yes—
233#95×C139C2312yes—
234#95×C139C2311yescharacteristic
235#95×C139C2312yes—
236C24×C139C2412yes—
237C24×C139C2411yescharacteristic
238C24×C139C2411yescharacteristic
239C2×D4×C139—24no—
240C2×D4×C139—22no—
241C2×D4×C139—22no—
242C2×D4×C139—24no—
243C2×D4×C139—22no—
244C2×D4×C139—24no—
245C2×D4×C139—22no—
246C2×D4×C139—22no—
247C2×D4×C139—42no—
248C2×D4×C139—41no—
249C2×D4×C139—42no—
250C2×D4×C139—42no—
251C22×C4×C139—22no—
252C22×C4×C139—22no—
253C22×C4×C139—22no—
254C22×C4×C139—22no—
255C22×C4×C139—24no—
256C22×C4×C139—24no—
257C22×C4×C139—22no—
258C22×C4×C139—24no—
259C22×C4×C139—24no—
260C22×C4×C139—22no—
261C22×C4×C139—22no—
262C22×C4×C139—22no—
263C22×C4×C139—22no—
264C22×C4×C139—42no—
265C22×C4×C139—42no—
266C22×C4×C139—41no—
267C22×C4×C139—41no—
268C22×C4×C139#4114yes—
269C22×C4×C139C2411yescharacteristic
270C22×C4×C139C2411yescharacteristic
271C22×C4×C139C2411yescharacteristic
272C22×C4×C139C2412yes—
273C22×C4×C139C2411yescharacteristic
274C22×C4×C139C2411yescharacteristic
275C22×C4×C139C2411yescharacteristic
276C22×C4×C139C2412yes—
277C22×C4×C139C2412yes—
278C22×C4×C139C2411yescharacteristic
279C22×C4×C139C2412yes—
280C22×C4×C139C2411yescharacteristic
281C22×C4×C139C2412yes—
282C22×C4×C139C2411yescharacteristic
283C22×C4×C139C2411yescharacteristic
284C22×C4×C139C2412yes—
285C22×C4×C139C2412yes—
286C22×C4×C139C2411yescharacteristic
287C22×C4×C139C2411yescharacteristic
288C22×C4×C139C2411yescharacteristic
289C4⋊C4×C139—24no—
290C4⋊C4×C139—22no—
291C4⋊C4×C139—22no—
292C4⋊C4×C139—22no—
293C4⋊C4×C139—24no—
294C4⋊C4×C139—22no—
295C4⋊C4×C139—22no—
296C4⋊C4×C139—22no—
297C4⋊C4×C139—22no—
298C4⋊C4×C139—24no—
299C4⋊C4×C139—24no—
300C4⋊C4×C139—22no—
301C4⋊C4×C139—22no—
302C4⋊C4×C139—24no—
303C4⋊C4×C139—42no—
304C4⋊C4×C139—42no—
305C4⋊C4×C139—42no—
306C4⋊C4×C139—41no—
307C4⋊C4×C139—42no—
308C4⋊C4×C139—42no—
309C4⋊C4×C139—42no—
310C4⋊C4×C139#4114yes—
311C4⋊C4×C139#4114yes—
312C22⋊C4×C139—22no—
313C22⋊C4×C139—22no—
314C22⋊C4×C139—24no—
315C22⋊C4×C139—24no—
316C22⋊C4×C139—22no—
317C22⋊C4×C139—24no—
318C22⋊C4×C139—24no—
319C22⋊C4×C139—24no—
320C22⋊C4×C139—24no—
321C22⋊C4×C139—22no—
322C22⋊C4×C139—22no—
323C22⋊C4×C139—24no—
324C22⋊C4×C139—42no—
325C22⋊C4×C139—42no—
326C22⋊C4×C139—42no—
327C22⋊C4×C139—42no—
328C22⋊C4×C139—41no—
329C22⋊C4×C139—42no—
330C22⋊C4×C139—41no—
331C22⋊C4×C139—42no—
332C22⋊C4×C139—42no—
333C22⋊C4×C139—42no—
334C22⋊C4×C139—42no—
335C22⋊C4×C139#4114yes—
336C42×C139—22no—
337C42×C139—22no—
338C42×C139—22no—
339C42×C139—22no—
340C42×C139—24no—
341C42×C139—24no—
342C42×C139—24no—
343C42×C139—22no—
344C42×C139—22no—
345C42×C139—22no—
346C42×C139—24no—
347C42×C139—42no—
348C42×C139—42no—
349C42×C139—42no—
350C42×C139—42no—
351C23×C139—21no—
352C23×C139—21no—
353C23×C139—21no—
354C23×C139—21no—
355C23×C139—21no—
356C23×C139—21no—
357C23×C139—21no—
358C23×C139—21no—
359C23×C139—21no—
360C23×C139—21no—
361C23×C139—21no—
362C23×C139—21no—
363C23×C139—22no—
364C23×C139—22no—
365C23×C139—22no—
366C23×C139—22no—
367C23×C139—22no—
368C23×C139—22no—
369C23×C139—22no—
370C23×C139C2×#4112yes—
371C23×C139C2×#4112yes—
372C23×C139C2511yescharacteristic
373D4×C139—48no—
374D4×C139—44no—
375D4×C139—44no—
376D4×C139—84no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—21no—
381C2×C4×C139—22no—
382C2×C4×C139—21no—
383C2×C4×C139—22no—
384C2×C4×C139—22no—
385C2×C4×C139—21no—
386C2×C4×C139—21no—
387C2×C4×C139—21no—
388C2×C4×C139—22no—
389C2×C4×C139—28no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—22no—
395C2×C4×C139—22no—
396C2×C4×C139—21no—
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—21no—
402C2×C4×C139—21no—
403C2×C4×C139—22no—
404C2×C4×C139—22no—
405C2×C4×C139—22no—
406C2×C4×C139—21no—
407C2×C4×C139—22no—
408C2×C4×C139—21no—
409C2×C4×C139—22no—
410C2×C4×C139—21no—
411C2×C4×C139—21no—
412C2×C4×C139—22no—
413C2×C4×C139—22no—
414C2×C4×C139—22no—
415C2×C4×C139—21no—
416C2×C4×C139—22no—
417C2×C4×C139—22no—
418C2×C4×C139—22no—
419C2×C4×C139—21no—
420C2×C4×C139—21no—
421C2×C4×C139—22no—
422C2×C4×C139—21no—
423C2×C4×C139—21no—
424C2×C4×C139—21no—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—21no—
428C2×C4×C139—22no—
429C2×C4×C139—48no—
430C2×C4×C139—44no—
431C2×C4×C139—48no—
432C2×C4×C139—44no—
433C2×C4×C139—44no—
434C2×C4×C139C2×#4112yes—
435C2×C4×C139C2×#4112yes—
436C2×C4×C139C2×#4114yes—
437C2×C4×C139C2×#4114yes—
438C2×C4×C139C2×#4112yes—
439C2×C4×C139C2×#4112yes—
440C2×C4×C139C2×#4112yes—
441C2×C4×C139C2×#4112yes—
442C2×C4×C139H(5,𝔽2)12yes—
443C22×C139—22no—
444C22×C139—22no—
445C22×C139—22no—
446C22×C139—22no—
447C22×C139—22no—
448C22×C139—22no—
449C22×C139—41no—
450C22×C139—41no—
451C22×C139—41no—
452C22×C139—41no—
453C22×C139—41no—
454C22×C139—41no—
455C22×C139—41no—
456C22×C139—41no—
457C22×C139—42no—
458C22×C139—42no—
459C22×C139—42no—
460C22×C139—42no—
461C22×C139—42no—
462C22×C139—42no—
463C22×C139—42no—
464C22×C139C22×#4111yescharacteristic
465C22×C139C22×#4111yescharacteristic
466C22×C139C22×#4111yescharacteristic
467C22×C139C22×#4111yescharacteristic
468C22×C139C2×H(5,𝔽2)11yescharacteristic
469C22×C139#58511yescharacteristic
470C22×C139#58511yescharacteristic
471C4×C139—22no—
472C4×C139—22no—
473C4×C139—24no—
474C4×C139—24no—
475C4×C139—22no—
476C4×C139—22no—
477C4×C139—41no—
478C4×C139—41no—
479C4×C139—41no—
480C4×C139—41no—
481C4×C139—42no—
482C4×C139—41no—
483C4×C139—41no—
484C4×C139—42no—
485C4×C139—42no—
486C4×C139—41no—
487C4×C139—42no—
488C4×C139—41no—
489C4×C139—42no—
490C4×C139#52914yes—
491C2×C139—42no—
492C2×C139—42no—
493C2×C139—82no—
494C2×C139C2×#52911yescharacteristic
495C2×C139#347511yescharacteristic
496C2×C139#347511yescharacteristic
497C2×C139#348111yescharacteristic
498C2×C139#349411yescharacteristic
499C2×C139#351711yescharacteristic
500C2×C139#352411yescharacteristic
501#36297C13911yesmaximal, characteristic, direct product factor, Sylow
502C139#3629711yescharacteristic, direct product factor, Sylow
503#2866C2×C13912yescomplemented
504#2854C2×C13911yescharacteristic, complemented
505#2530C2×C13912yescomplemented
506#2526C2×C13912yescomplemented
507#2516C2×C13912yescomplemented
508#2513C2×C13911yescharacteristic, complemented
509#2509C2×C13911yescharacteristic, complemented
510#2497C2×C13911yescharacteristic, complemented
511#2490C2×C13911yescharacteristic, complemented
512#2471C2×C13912yescomplemented
513#2470C2×C13912yescomplemented
514#2457C2×C13912yescomplemented
515#2441C2×C13911yescharacteristic, complemented
516#2414C2×C13911yescharacteristic
517#2370C2×C13911yescharacteristic, complemented
518#2363C2×C13911yescharacteristic, complemented
519#2361C2×C13911yescharacteristic, complemented
520#2354C2×C13911yescharacteristic, complemented
521#2352C2×C13911yescharacteristic, complemented
522#2344C2×C13911yescharacteristic, complemented
523C4×#123C2×C13911yescharacteristic, complemented
524#2293C2×C13912yescomplemented
525C4×#117C2×C13911yescharacteristic, complemented
526C2×#125C22×C13911yescharacteristic
527C2×#123C22×C13911yescharacteristic
528C2×#123C22×C13912yes—
529C2×#121C22×C13911yescharacteristic
530C2×#121C22×C13911yescharacteristic
531C2×C4×D4C22×C13911yescharacteristic
532C2×C4×D4C22×C13911yescharacteristic
533C2×C4×D4C22×C13912yes—
534C2×#117C22×C13911yescharacteristic
535C2×#117C22×C13911yescharacteristic
536C2×#117C22×C13912yes—
537C2×#117C22×C13912yes—
538C22×C4⋊C4C22×C13911yescharacteristic
539C22×C42C22×C13911yescharacteristic
540#400C22×C13912yes—
541#400C22×C13912yes—
542#400C22×C13912yes—
543#399C22×C13912yes—
544#397C22×C13912yes—
545#397C22×C13912yes—
546#397C22×C13912yes—
547#396C22×C13912yes—
548#396C22×C13912yes—
549#394C22×C13912yes—
550#394C22×C13912yes—
551#392C22×C13912yes—
552#390C22×C13911yescharacteristic
553#390C22×C13911yescharacteristic
554#390C22×C13911yescharacteristic
555#390C22×C13912yes—
556#390C22×C13911yescharacteristic
557#390C22×C13912yes—
558#390C22×C13912yes—
559#389C22×C13911yescharacteristic
560#389C22×C13911yescharacteristic
561#389C22×C13911yescharacteristic
562#389C22×C13911yescharacteristic
563#389C22×C13911yescharacteristic
564#389C22×C13911yescharacteristic
565#389C22×C13912yes—
566#389C22×C13912yes—
567#389C22×C13912yes—
568#388C22×C13912yes—
569#388C22×C13912yes—
570#388C22×C13912yes—
571#388C22×C13912yes—
572#388C22×C13912yes—
573#388C22×C13912yes—
574#388C22×C13912yes—
575#388C22×C13912yes—
576#388C22×C13912yes—
577#388C22×C13912yes—
578#388C22×C13912yes—
579#388C22×C13912yes—
580#388C22×C13911yescharacteristic
581#388C22×C13911yescharacteristic
582#387C22×C13912yes—
583#387C22×C13912yes—
584#387C22×C13912yes—
585#387C22×C13911yescharacteristic
586#387C22×C13912yes—
587#387C22×C13912yes—
588#387C22×C13912yes—
589#387C22×C13912yes—
590#387C22×C13912yes—
591#387C22×C13911yescharacteristic
592#386C22×C13912yes—
593#386C22×C13912yes—
594#386C22×C13912yes—
595#386C22×C13912yes—
596#386C22×C13911yescharacteristic
597#385C22×C13912yes—
598#385C22×C13911yescharacteristic
599#384C22×C13911yescharacteristic
600#382C22×C13911yescharacteristic
601#381C22×C13912yes—
602#381C22×C13911yescharacteristic
603#380C22×C13911yescharacteristic
604#380C22×C13911yescharacteristic
605#380C22×C13911yescharacteristic
606#380C22×C13912yes—
607C4×C4⋊C4C22×C13911yescharacteristic
608C4×C4⋊C4C22×C13911yescharacteristic
609C4×C4⋊C4C22×C13911yescharacteristic
610C4×C4⋊C4C22×C13911yescharacteristic
611C4×C4⋊C4C22×C13911yescharacteristic
612C4×C4⋊C4C22×C13911yescharacteristic
613C4×C4⋊C4C22×C13912yes—
614C4×C4⋊C4C22×C13911yescharacteristic
615C4×C4⋊C4C22×C13911yescharacteristic
616C4×C22⋊C4C22×C13911yescharacteristic
617C4×C22⋊C4C22×C13912yes—
618C4×C22⋊C4C22×C13911yescharacteristic
619C4×C22⋊C4C22×C13911yescharacteristic
620C4×C22⋊C4C22×C13912yes—
621C4×C22⋊C4C22×C13912yes—
622C4×C22⋊C4C22×C13912yes—
623#376C22×C13912yes—
624C43C22×C13912yes—
625C22×D4C23×C13911yescharacteristic
626C22×D4C23×C13912yes—
627C22×D4C23×C13911yescharacteristic
628C22×D4C23×C13912yes—
629C23×C4C23×C13911yescharacteristic
630C23×C4C23×C13912yes—
631C23×C4C23×C13912yes—
632C23×C4C23×C13911yescharacteristic
633C23×C4C23×C13911yescharacteristic
634C23×C4C23×C13911yescharacteristic
635#125—24no—
636#123—24no—
637#123—44no—
638#121—24no—
639#121—24no—
640C4×D4—24no—
641C4×D4—24no—
642C4×D4—28no—
643#117—24no—
644#117—24no—
645#117—44no—
646#117—44no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4C23×C13911yescharacteristic
649C2×C4⋊C4C23×C13912yes—
650C2×C4⋊C4C23×C13911yescharacteristic
651C2×C4⋊C4C23×C13912yes—
652C2×C4⋊C4C23×C13911yescharacteristic
653C2×C4⋊C4C23×C13911yescharacteristic
654C2×C4⋊C4C23×C13912yes—
655C2×C4⋊C4C23×C13911yescharacteristic
656C2×C4⋊C4C23×C13911yescharacteristic
657C2×C4⋊C4C23×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C4⋊C4C23×C13912yes—
661C2×C4⋊C4C23×C13912yes—
662C2×C4⋊C4C23×C13912yes—
663C2×C4⋊C4C23×C13912yes—
664C2×C4⋊C4C23×C13912yes—
665C2×C4⋊C4C23×C13911yescharacteristic
666C2×C4⋊C4C23×C13912yes—
667C2×C4⋊C4C23×C13912yes—
668C2×C4⋊C4C23×C13912yes—
669C2×C4⋊C4C23×C13911yescharacteristic
670C2×C4⋊C4C23×C13911yescharacteristic
671C2×C22⋊C4C23×C13911yescharacteristic
672C2×C22⋊C4C23×C13912yes—
673C2×C22⋊C4C23×C13912yes—
674C2×C22⋊C4C23×C13912yes—
675C2×C22⋊C4C23×C13911yescharacteristic
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×C13912yes—
684C2×C22⋊C4C23×C13912yes—
685C2×C22⋊C4C23×C13912yes—
686C2×C22⋊C4C23×C13912yes—
687C2×C22⋊C4C23×C13912yes—
688C2×C22⋊C4C23×C13911yescharacteristic
689C2×C22⋊C4C23×C13911yescharacteristic
690C2×C22⋊C4C23×C13912yes—
691C2×C22⋊C4C23×C13912yes—
692C2×C22⋊C4C23×C13912yes—
693C2×C22⋊C4C23×C13912yes—
694C2×C22⋊C4C23×C13911yescharacteristic
695C2×C42—24no—
696C2×C42C23×C13912yes—
697C2×C42C23×C13912yes—
698C2×C42C23×C13912yes—
699C2×C42C23×C13912yes—
700C2×C42C23×C13911yescharacteristic
701C2×C42C23×C13911yescharacteristic
702C2×C42C23×C13911yescharacteristic
703C2×C42C23×C13911yescharacteristic
704C2×C42C23×C13911yescharacteristic
705C2×C42C23×C13911yescharacteristic
706C2×C42C23×C13911yescharacteristic
707C2×C42C23×C13912yes—
708C2×C42C23×C13912yes—
709C2×C42C23×C13912yes—
710C2×C42C23×C13912yes—
711#95C23×C13912yes—
712#95C23×C13912yes—
713#95C23×C13912yes—
714#95C23×C13912yes—
715#95C23×C13911yescharacteristic
716#95C23×C13912yes—
717#95C23×C13911yescharacteristic
718#95C23×C13911yescharacteristic
719#95C23×C13912yes—
720#95C23×C13911yescharacteristic
721#95C23×C13911yescharacteristic
722#95C23×C13912yes—
723#95C23×C13911yescharacteristic
724#95C23×C13911yescharacteristic
725#95C23×C13912yes—
726#95C23×C13912yes—
727#95C23×C13911yescharacteristic
728#95C23×C13911yescharacteristic
729#95C23×C13911yescharacteristic
730#95C23×C13912yes—
731#95C23×C13912yes—
732#95C23×C13912yes—
733#95C23×C13912yes—
734#95C23×C13912yes—
735#95C23×C13912yes—
736#95C23×C13912yes—
737#95C23×C13912yes—
738C24C24×C13912yes—
739C24C24×C13911yescharacteristic
740C24C24×C13911yescharacteristic
741C2×D4—24no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—24no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—42no—
750C2×D4—41no—
751C2×D4—42no—
752C2×D4—42no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4#41×C13914yes—
771C22×C4C24×C13911yescharacteristic
772C22×C4C24×C13911yescharacteristic
773C22×C4C24×C13911yescharacteristic
774C22×C4C24×C13912yes—
775C22×C4C24×C13911yescharacteristic
776C22×C4C24×C13911yescharacteristic
777C22×C4C24×C13911yescharacteristic
778C22×C4C24×C13912yes—
779C22×C4C24×C13912yes—
780C22×C4C24×C13911yescharacteristic
781C22×C4C24×C13912yes—
782C22×C4C24×C13911yescharacteristic
783C22×C4C24×C13912yes—
784C22×C4C24×C13911yescharacteristic
785C22×C4C24×C13911yescharacteristic
786C22×C4C24×C13912yes—
787C22×C4C24×C13912yes—
788C22×C4C24×C13911yescharacteristic
789C22×C4C24×C13911yescharacteristic
790C22×C4C24×C13911yescharacteristic
791C4⋊C4—24no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—24no—
805C4⋊C4—42no—
806C4⋊C4—42no—
807C4⋊C4—42no—
808C4⋊C4—41no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4#41×C13914yes—
813C4⋊C4#41×C13914yes—
814C22⋊C4—22no—
815C22⋊C4—22no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—41no—
831C22⋊C4—42no—
832C22⋊C4—41no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—42no—
836C22⋊C4—42no—
837C22⋊C4#41×C13914yes—
838C42—22no—
839C42—22no—
840C42—22no—
841C42—22no—
842C42—24no—
843C42—24no—
844C42—24no—
845C42—22no—
846C42—22no—
847C42—22no—
848C42—24no—
849C42—42no—
850C42—42no—
851C42—42no—
852C42—42no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23C2×#41×C13912yes—
873C23C2×#41×C13912yes—
874C23C25×C13911yescharacteristic
875D4—48no—
876D4—44no—
877D4—44no—
878D4—84no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—22no—
891C2×C4—28no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—48no—
932C2×C4—44no—
933C2×C4—48no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4C2×#41×C13912yes—
937C2×C4C2×#41×C13912yes—
938C2×C4C2×#41×C13914yes—
939C2×C4C2×#41×C13914yes—
940C2×C4C2×#41×C13912yes—
941C2×C4C2×#41×C13912yes—
942C2×C4C2×#41×C13912yes—
943C2×C4C2×#41×C13912yes—
944C2×C4H(5,𝔽2)×C13912yes—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C22×#41×C13911yescharacteristic
967C22C22×#41×C13911yescharacteristic
968C22C22×#41×C13911yescharacteristic
969C22C22×#41×C13911yescharacteristic
970C22C2×H(5,𝔽2)×C13911yescharacteristic
971C22#585×C13911yescharacteristic
972C22#585×C13911yescharacteristic
973C4—22no—
974C4—22no—
975C4—24no—
976C4—24no—
977C4—22no—
978C4—22no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—41no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—42no—
990C4—41no—
991C4—42no—
992C4#529×C13914yes—
993C2—42no—
994C2—42no—
995C2—82no—
996C2C2×#529×C13911yescharacteristic
997C2#3475×C13911yescharacteristic
998C2#3475×C13911yescharacteristic
999C2#3481×C13911yescharacteristic
1000C2#3494×C13911yescharacteristic
1001C2#3517×C13911yescharacteristic
1002C2#3524×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radical#2414×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2866×C139C2semidirect
2. #2854×C139C2semidirect
3. #2530×C139C2semidirect
4. #2526×C139C2semidirect
5. #2516×C139C2semidirect
6. #2513×C139C2semidirect
7. #2509×C139C2semidirect
8. #2497×C139C2semidirect
9. #2490×C139C2semidirect
10. #2471×C139C2semidirect
11. #2470×C139C2semidirect
12. #2457×C139C2semidirect
13. #2441×C139C2semidirect
15. #2370×C139C2semidirect
16. #2363×C139C2semidirect
17. #2361×C139C2semidirect
18. #2354×C139C2semidirect
19. #2352×C139C2semidirect
20. #2344×C139C2semidirect
21. C4×#123×C139C2semidirect
22. #2293×C139C2semidirect
23. C4×#117×C139C2semidirect
501. #36297C139direct (N × H)
502. C139#36297direct (N × H)
503. #2866C2×C139semidirect
504. #2854C2×C139semidirect
505. #2530C2×C139semidirect
506. #2526C2×C139semidirect
507. #2516C2×C139semidirect
508. #2513C2×C139semidirect
509. #2509C2×C139semidirect
510. #2497C2×C139semidirect
511. #2490C2×C139semidirect
512. #2471C2×C139semidirect
513. #2470C2×C139semidirect
514. #2457C2×C139semidirect
515. #2441C2×C139semidirect
517. #2370C2×C139semidirect
518. #2363C2×C139semidirect
519. #2361C2×C139semidirect
520. #2354C2×C139semidirect
521. #2352C2×C139semidirect
522. #2344C2×C139semidirect
523. C4×#123C2×C139semidirect
524. #2293C2×C139semidirect
525. C4×#117C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2866×C1392
#2854×C1392
#2530×C1392
#2526×C1392
#2516×C1392
#2513×C1392
#2509×C1392
#2497×C1392
#2490×C1392
#2471×C1392
#2470×C1392
#2457×C1392
#2441×C1392
#2414×C1392
#2370×C1392
#2363×C1392
#2361×C1392
#2354×C1392
#2352×C1392
#2344×C1392
C4×#123×C1392
#2293×C1392
C4×#117×C1392
#36297139