Finite Group Databasebeta

← C139×#35589 #48030185

Subgroups — C139×#35589 #48030185

Order 35584.

1864 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2594×C139C212yesmaximal, complemented
2#2576×C139C212yesmaximal, complemented
3#2574×C139C212yesmaximal, complemented
4#2560×C139C212yesmaximal, complemented
5#2512×C139C211yesmaximal, characteristic, complemented
6#2507×C139C211yesmaximal, characteristic, complemented
7#2500×C139C211yesmaximal, characteristic, complemented
8#2494×C139C211yesmaximal, characteristic, complemented
9#2491×C139C211yesmaximal, characteristic, complemented
10#2485×C139C211yesmaximal, characteristic, complemented
11#2476×C139C212yesmaximal, complemented
12#2474×C139C212yesmaximal, complemented
13#2468×C139C212yesmaximal, complemented
14#2440×C139C211yesmaximal, characteristic, complemented
15#2427×C139C212yesmaximal, complemented
16#2416×C139C211yesmaximal, characteristic
17#2331×C139C211yesmaximal, characteristic, complemented
18#2324×C139C211yesmaximal, characteristic, complemented
19#2319×C139C211yesmaximal, characteristic, complemented
20C4×#121×C139C211yesmaximal, characteristic, complemented
21#2290×C139C211yesmaximal, characteristic, complemented
22#2285×C139C211yesmaximal, characteristic, complemented
23#2274×C139C211yesmaximal, characteristic, complemented
24C2×C4⋊Q8×C139C2211yescharacteristic
25C2×#126×C139C2212yes—
26C2×#124×C139C2212yes—
27C2×C22⋊Q8×C139C2212yes—
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2212yes—
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C2×C4×D4×C139C2212yes—
34C2×#117×C139C2211yescharacteristic
35C2×#117×C139C2211yescharacteristic
36C2×#117×C139C2212yes—
37C22×C4⋊C4×C139C2211yescharacteristic
38C22×C42×C139C2211yescharacteristic
39#401×C139C2212yes—
40#398×C139C2212yes—
41#398×C139C2212yes—
42#398×C139C2212yes—
43#397×C139C2212yes—
44#397×C139C2212yes—
45#397×C139C2212yes—
46#396×C139C2212yes—
47#396×C139C2212yes—
48#395×C139C2212yes—
49#394×C139C2212yes—
50#394×C139C2212yes—
51#394×C139C2212yes—
52#394×C139C2212yes—
53#394×C139C2212yes—
54#393×C139C2212yes—
55#391×C139C2212yes—
56#391×C139C2212yes—
57#390×C139C2211yescharacteristic
58#390×C139C2211yescharacteristic
59#390×C139C2211yescharacteristic
60#390×C139C2212yes—
61#390×C139C2211yescharacteristic
62#389×C139C2211yescharacteristic
63#389×C139C2211yescharacteristic
64#389×C139C2211yescharacteristic
65#389×C139C2211yescharacteristic
66#389×C139C2211yescharacteristic
67#389×C139C2211yescharacteristic
68#389×C139C2212yes—
69#388×C139C2212yes—
70#388×C139C2211yescharacteristic
71#388×C139C2211yescharacteristic
72#388×C139C2212yes—
73#388×C139C2212yes—
74#388×C139C2212yes—
75#388×C139C2212yes—
76#388×C139C2212yes—
77#388×C139C2212yes—
78#388×C139C2212yes—
79#388×C139C2212yes—
80#388×C139C2212yes—
81#387×C139C2211yescharacteristic
82#387×C139C2211yescharacteristic
83#387×C139C2212yes—
84#387×C139C2212yes—
85#387×C139C2212yes—
86#387×C139C2212yes—
87#387×C139C2212yes—
88#386×C139C2211yescharacteristic
89#386×C139C2211yescharacteristic
90#386×C139C2212yes—
91#386×C139C2212yes—
92#386×C139C2212yes—
93#385×C139C2211yescharacteristic
94#385×C139C2211yescharacteristic
95#385×C139C2212yes—
96#385×C139C2212yes—
97#384×C139C2211yescharacteristic
98#384×C139C2211yescharacteristic
99#382×C139C2212yes—
100#382×C139C2211yescharacteristic
101#381×C139C2212yes—
102#380×C139C2211yescharacteristic
103#380×C139C2212yes—
104#380×C139C2211yescharacteristic
105#380×C139C2211yescharacteristic
106#380×C139C2212yes—
107#380×C139C2211yescharacteristic
108C4×C4⋊C4×C139C2211yescharacteristic
109C4×C4⋊C4×C139C2211yescharacteristic
110C4×C4⋊C4×C139C2211yescharacteristic
111C4×C4⋊C4×C139C2211yescharacteristic
112C4×C4⋊C4×C139C2212yes—
113C4×C4⋊C4×C139C2212yes—
114C4×C4⋊C4×C139C2211yescharacteristic
115C4×C4⋊C4×C139C2212yes—
116C4×C4⋊C4×C139C2211yescharacteristic
117C4×C22⋊C4×C139C2212yes—
118C4×C22⋊C4×C139C2212yes—
119C4×C22⋊C4×C139C2211yescharacteristic
120C4×C22⋊C4×C139C2211yescharacteristic
121C4×C22⋊C4×C139C2212yes—
122#376×C139C2211yescharacteristic
123C22×Q8×C139C2312yes—
124C22×D4×C139C2311yescharacteristic
125C22×D4×C139C2312yes—
126C22×D4×C139C2311yescharacteristic
127C22×D4×C139C2312yes—
128C23×C4×C139C2311yescharacteristic
129C23×C4×C139C2311yescharacteristic
130C23×C4×C139C2311yescharacteristic
131C23×C4×C139C2311yescharacteristic
132C23×C4×C139C2312yes—
133C23×C4×C139C2312yes—
134C4⋊Q8×C139—24no—
135#126×C139—44no—
136#124×C139—44no—
137C22⋊Q8×C139—44no—
138#121×C139—24no—
139#121×C139—24no—
140#121×C139—44no—
141C4×D4×C139—24no—
142C4×D4×C139—24no—
143C4×D4×C139—44no—
144#117×C139—24no—
145#117×C139—24no—
146#117×C139—44no—
147C2×C4⋊C4×C139—24no—
148C2×C4⋊C4×C139C2312yes—
149C2×C4⋊C4×C139C2311yescharacteristic
150C2×C4⋊C4×C139C2311yescharacteristic
151C2×C4⋊C4×C139C2312yes—
152C2×C4⋊C4×C139C2312yes—
153C2×C4⋊C4×C139C2311yescharacteristic
154C2×C4⋊C4×C139C2312yes—
155C2×C4⋊C4×C139C2311yescharacteristic
156C2×C4⋊C4×C139C2311yescharacteristic
157C2×C4⋊C4×C139C2311yescharacteristic
158C2×C4⋊C4×C139C2311yescharacteristic
159C2×C4⋊C4×C139C2311yescharacteristic
160C2×C4⋊C4×C139C2311yescharacteristic
161C2×C4⋊C4×C139C2311yescharacteristic
162C2×C4⋊C4×C139C2311yescharacteristic
163C2×C4⋊C4×C139C2312yes—
164C2×C4⋊C4×C139C2312yes—
165C2×C4⋊C4×C139C2312yes—
166C2×C4⋊C4×C139C2312yes—
167C2×C4⋊C4×C139C2312yes—
168C2×C4⋊C4×C139C2312yes—
169C2×C4⋊C4×C139C2312yes—
170C2×C4⋊C4×C139C2312yes—
171C2×C4⋊C4×C139C2311yescharacteristic
172C2×C22⋊C4×C139C2312yes—
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×C139C2312yes—
181C2×C22⋊C4×C139C2311yescharacteristic
182C2×C22⋊C4×C139C2311yescharacteristic
183C2×C22⋊C4×C139C2311yescharacteristic
184C2×C22⋊C4×C139C2312yes—
185C2×C22⋊C4×C139C2311yescharacteristic
186C2×C22⋊C4×C139C2311yescharacteristic
187C2×C22⋊C4×C139C2312yes—
188C2×C22⋊C4×C139C2312yes—
189C2×C22⋊C4×C139C2312yes—
190C2×C22⋊C4×C139C2312yes—
191C2×C22⋊C4×C139C2312yes—
192C2×C22⋊C4×C139C2312yes—
193C2×C22⋊C4×C139C2312yes—
194C2×C22⋊C4×C139C2311yescharacteristic
195C2×C22⋊C4×C139C2312yes—
196C2×C42×C139—24no—
197C2×C42×C139C2311yescharacteristic
198C2×C42×C139C2311yescharacteristic
199C2×C42×C139C2311yescharacteristic
200C2×C42×C139C2311yescharacteristic
201C2×C42×C139C2312yes—
202C2×C42×C139C2311yescharacteristic
203C2×C42×C139C2311yescharacteristic
204C2×C42×C139C2312yes—
205C2×C42×C139C2312yes—
206C2×C42×C139C2312yes—
207C2×C42×C139C2312yes—
208C2×C42×C139C2312yes—
209C2×C42×C139C2311yescharacteristic
210#95×C139C2311yescharacteristic
211#95×C139C2312yes—
212#95×C139C2312yes—
213#95×C139C2312yes—
214#95×C139C2312yes—
215#95×C139C2311yescharacteristic
216#95×C139C2312yes—
217#95×C139C2312yes—
218#95×C139C2312yes—
219#95×C139C2312yes—
220#95×C139C2312yes—
221#95×C139C2312yes—
222#95×C139C2312yes—
223#95×C139C2311yescharacteristic
224#95×C139C2311yescharacteristic
225#95×C139C2312yes—
226#95×C139C2312yes—
227#95×C139C2311yescharacteristic
228#95×C139C2312yes—
229#95×C139C2311yescharacteristic
230#95×C139C2311yescharacteristic
231#95×C139C2311yescharacteristic
232#95×C139C2311yescharacteristic
233#95×C139C2312yes—
234#95×C139C2312yes—
235#95×C139C2311yescharacteristic
236#95×C139C2312yes—
237C24×C139C2412yes—
238C24×C139C2411yescharacteristic
239C24×C139C2411yescharacteristic
240C2×Q8×C139—24no—
241C2×Q8×C139—42no—
242C2×Q8×C139—42no—
243C2×D4×C139—22no—
244C2×D4×C139—22no—
245C2×D4×C139—24no—
246C2×D4×C139—24no—
247C2×D4×C139—22no—
248C2×D4×C139—24no—
249C2×D4×C139—22no—
250C2×D4×C139—22no—
251C2×D4×C139—42no—
252C2×D4×C139—41no—
253C2×D4×C139—42no—
254C2×D4×C139—42no—
255C22×C4×C139—22no—
256C22×C4×C139—22no—
257C22×C4×C139—22no—
258C22×C4×C139—22no—
259C22×C4×C139—22no—
260C22×C4×C139—22no—
261C22×C4×C139—22no—
262C22×C4×C139—22no—
263C22×C4×C139—22no—
264C22×C4×C139—22no—
265C22×C4×C139—24no—
266C22×C4×C139—24no—
267C22×C4×C139—41no—
268C22×C4×C139—42no—
269C22×C4×C139—42no—
270C22×C4×C139—42no—
271C22×C4×C139—42no—
272C22×C4×C139#4114yes—
273C22×C4×C139C2411yescharacteristic
274C22×C4×C139C2411yescharacteristic
275C22×C4×C139C2411yescharacteristic
276C22×C4×C139C2412yes—
277C22×C4×C139C2411yescharacteristic
278C22×C4×C139C2411yescharacteristic
279C22×C4×C139C2411yescharacteristic
280C22×C4×C139C2412yes—
281C22×C4×C139C2412yes—
282C22×C4×C139C2412yes—
283C22×C4×C139C2411yescharacteristic
284C22×C4×C139C2412yes—
285C22×C4×C139C2412yes—
286C22×C4×C139C2411yescharacteristic
287C22×C4×C139C2411yescharacteristic
288C22×C4×C139C2411yescharacteristic
289C22×C4×C139C2412yes—
290C22×C4×C139C2411yescharacteristic
291C22×C4×C139C2411yescharacteristic
292C22×C4×C139C2411yescharacteristic
293C4⋊C4×C139—24no—
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—24no—
303C4⋊C4×C139—22no—
304C4⋊C4×C139—24no—
305C4⋊C4×C139—24no—
306C4⋊C4×C139—22no—
307C4⋊C4×C139—22no—
308C4⋊C4×C139—42no—
309C4⋊C4×C139—42no—
310C4⋊C4×C139—42no—
311C4⋊C4×C139—42no—
312C4⋊C4×C139—42no—
313C4⋊C4×C139—42no—
314C4⋊C4×C139—42no—
315C4⋊C4×C139—42no—
316C4⋊C4×C139#4114yes—
317C22⋊C4×C139—24no—
318C22⋊C4×C139—22no—
319C22⋊C4×C139—24no—
320C22⋊C4×C139—24no—
321C22⋊C4×C139—22no—
322C22⋊C4×C139—22no—
323C22⋊C4×C139—22no—
324C22⋊C4×C139—22no—
325C22⋊C4×C139—24no—
326C22⋊C4×C139—24no—
327C22⋊C4×C139—24no—
328C22⋊C4×C139—24no—
329C22⋊C4×C139—22no—
330C22⋊C4×C139—22no—
331C22⋊C4×C139—24no—
332C22⋊C4×C139—41no—
333C22⋊C4×C139—42no—
334C22⋊C4×C139—42no—
335C22⋊C4×C139—42no—
336C22⋊C4×C139—42no—
337C22⋊C4×C139—42no—
338C22⋊C4×C139—42no—
339C22⋊C4×C139—42no—
340C22⋊C4×C139—42no—
341C42×C139—22no—
342C42×C139—22no—
343C42×C139—22no—
344C42×C139—24no—
345C42×C139—22no—
346C42×C139—22no—
347C42×C139—22no—
348C42×C139—42no—
349C42×C139—42no—
350C42×C139—42no—
351C42×C139—42no—
352C42×C139—42no—
353C42×C139#4114yes—
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—21no—
364C23×C139—21no—
365C23×C139—21no—
366C23×C139—22no—
367C23×C139—22no—
368C23×C139—22no—
369C23×C139—22no—
370C23×C139—22no—
371C23×C139—22no—
372C23×C139—22no—
373C23×C139C2×#4112yes—
374C23×C139H(5,𝔽2)12yes—
375C23×C139C2511yescharacteristic
376Q8×C139—84no—
377D4×C139—48no—
378D4×C139—44no—
379D4×C139—44no—
380D4×C139—84no—
381C2×C4×C139—28no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—21no—
385C2×C4×C139—21no—
386C2×C4×C139—21no—
387C2×C4×C139—21no—
388C2×C4×C139—22no—
389C2×C4×C139—22no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—28no—
395C2×C4×C139—21no—
396C2×C4×C139—21no—
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—22no—
400C2×C4×C139—22no—
401C2×C4×C139—21no—
402C2×C4×C139—21no—
403C2×C4×C139—21no—
404C2×C4×C139—21no—
405C2×C4×C139—21no—
406C2×C4×C139—22no—
407C2×C4×C139—22no—
408C2×C4×C139—22no—
409C2×C4×C139—22no—
410C2×C4×C139—21no—
411C2×C4×C139—22no—
412C2×C4×C139—22no—
413C2×C4×C139—21no—
414C2×C4×C139—22no—
415C2×C4×C139—22no—
416C2×C4×C139—22no—
417C2×C4×C139—22no—
418C2×C4×C139—21no—
419C2×C4×C139—21no—
420C2×C4×C139—21no—
421C2×C4×C139—22no—
422C2×C4×C139—22no—
423C2×C4×C139—21no—
424C2×C4×C139—22no—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—21no—
428C2×C4×C139—21no—
429C2×C4×C139—21no—
430C2×C4×C139—22no—
431C2×C4×C139—22no—
432C2×C4×C139—21no—
433C2×C4×C139—22no—
434C2×C4×C139—44no—
435C2×C4×C139—44no—
436C2×C4×C139—84no—
437C2×C4×C139—84no—
438C2×C4×C139C2×#4112yes—
439C2×C4×C139C2×#4112yes—
440C2×C4×C139C2×#4112yes—
441C2×C4×C139C2×#4114yes—
442C2×C4×C139C2×#4112yes—
443C2×C4×C139C2×#4112yes—
444C2×C4×C139C2×#4112yes—
445C2×C4×C139H(5,𝔽2)12yes—
446C2×C4×C1392−1+412yes—
447C22×C139—22no—
448C22×C139—22no—
449C22×C139—22no—
450C22×C139—22no—
451C22×C139—22no—
452C22×C139—22no—
453C22×C139—41no—
454C22×C139—41no—
455C22×C139—41no—
456C22×C139—41no—
457C22×C139—41no—
458C22×C139—41no—
459C22×C139—41no—
460C22×C139—41no—
461C22×C139—42no—
462C22×C139—42no—
463C22×C139—42no—
464C22×C139—42no—
465C22×C139—42no—
466C22×C139—42no—
467C22×C139—42no—
468C22×C139C22×#4111yescharacteristic
469C22×C139C22×#4111yescharacteristic
470C22×C139C22×#4111yescharacteristic
471C22×C139C2×H(5,𝔽2)11yescharacteristic
472C22×C139C2×H(5,𝔽2)11yescharacteristic
473C22×C139C2×2−1+411yescharacteristic
474C22×C139#58511yescharacteristic
475C4×C139—22no—
476C4×C139—22no—
477C4×C139—22no—
478C4×C139—22no—
479C4×C139—22no—
480C4×C139—24no—
481C4×C139—41no—
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—41no—
491C4×C139—42no—
492C4×C139—42no—
493C4×C139—41no—
494C4×C139#52914yes—
495C2×C139—42no—
496C2×C139—42no—
497C2×C139—82no—
498C2×C139C2×#52911yescharacteristic
499C2×C139#349211yescharacteristic
500C2×C139#349411yescharacteristic
501C2×C139#349411yescharacteristic
502C2×C139#351111yescharacteristic
503C2×C139#351811yescharacteristic
504C2×C139#351911yescharacteristic
505#35589C13911yesmaximal, characteristic, direct product factor, Sylow
506C139#3558911yescharacteristic, direct product factor, Sylow
507#2594C2×C13912yescomplemented
508#2576C2×C13912yescomplemented
509#2574C2×C13912yescomplemented
510#2560C2×C13912yescomplemented
511#2512C2×C13911yescharacteristic, complemented
512#2507C2×C13911yescharacteristic, complemented
513#2500C2×C13911yescharacteristic, complemented
514#2494C2×C13911yescharacteristic, complemented
515#2491C2×C13911yescharacteristic, complemented
516#2485C2×C13911yescharacteristic, complemented
517#2476C2×C13912yescomplemented
518#2474C2×C13912yescomplemented
519#2468C2×C13912yescomplemented
520#2440C2×C13911yescharacteristic, complemented
521#2427C2×C13912yescomplemented
522#2416C2×C13911yescharacteristic
523#2331C2×C13911yescharacteristic, complemented
524#2324C2×C13911yescharacteristic, complemented
525#2319C2×C13911yescharacteristic, complemented
526C4×#121C2×C13911yescharacteristic, complemented
527#2290C2×C13911yescharacteristic, complemented
528#2285C2×C13911yescharacteristic, complemented
529#2274C2×C13911yescharacteristic, complemented
530C2×C4⋊Q8C22×C13911yescharacteristic
531C2×#126C22×C13912yes—
532C2×#124C22×C13912yes—
533C2×C22⋊Q8C22×C13912yes—
534C2×#121C22×C13911yescharacteristic
535C2×#121C22×C13911yescharacteristic
536C2×#121C22×C13912yes—
537C2×C4×D4C22×C13911yescharacteristic
538C2×C4×D4C22×C13911yescharacteristic
539C2×C4×D4C22×C13912yes—
540C2×#117C22×C13911yescharacteristic
541C2×#117C22×C13911yescharacteristic
542C2×#117C22×C13912yes—
543C22×C4⋊C4C22×C13911yescharacteristic
544C22×C42C22×C13911yescharacteristic
545#401C22×C13912yes—
546#398C22×C13912yes—
547#398C22×C13912yes—
548#398C22×C13912yes—
549#397C22×C13912yes—
550#397C22×C13912yes—
551#397C22×C13912yes—
552#396C22×C13912yes—
553#396C22×C13912yes—
554#395C22×C13912yes—
555#394C22×C13912yes—
556#394C22×C13912yes—
557#394C22×C13912yes—
558#394C22×C13912yes—
559#394C22×C13912yes—
560#393C22×C13912yes—
561#391C22×C13912yes—
562#391C22×C13912yes—
563#390C22×C13912yes—
564#390C22×C13911yescharacteristic
565#390C22×C13911yescharacteristic
566#390C22×C13911yescharacteristic
567#390C22×C13911yescharacteristic
568#389C22×C13911yescharacteristic
569#389C22×C13911yescharacteristic
570#389C22×C13911yescharacteristic
571#389C22×C13911yescharacteristic
572#389C22×C13911yescharacteristic
573#389C22×C13912yes—
574#389C22×C13911yescharacteristic
575#388C22×C13911yescharacteristic
576#388C22×C13912yes—
577#388C22×C13912yes—
578#388C22×C13912yes—
579#388C22×C13912yes—
580#388C22×C13912yes—
581#388C22×C13911yescharacteristic
582#388C22×C13912yes—
583#388C22×C13912yes—
584#388C22×C13912yes—
585#388C22×C13912yes—
586#388C22×C13912yes—
587#387C22×C13912yes—
588#387C22×C13911yescharacteristic
589#387C22×C13912yes—
590#387C22×C13912yes—
591#387C22×C13912yes—
592#387C22×C13912yes—
593#387C22×C13911yescharacteristic
594#386C22×C13912yes—
595#386C22×C13912yes—
596#386C22×C13911yescharacteristic
597#386C22×C13912yes—
598#386C22×C13911yescharacteristic
599#385C22×C13912yes—
600#385C22×C13912yes—
601#385C22×C13911yescharacteristic
602#385C22×C13911yescharacteristic
603#384C22×C13911yescharacteristic
604#384C22×C13911yescharacteristic
605#382C22×C13912yes—
606#382C22×C13911yescharacteristic
607#381C22×C13912yes—
608#380C22×C13912yes—
609#380C22×C13911yescharacteristic
610#380C22×C13911yescharacteristic
611#380C22×C13912yes—
612#380C22×C13911yescharacteristic
613#380C22×C13911yescharacteristic
614C4×C4⋊C4C22×C13912yes—
615C4×C4⋊C4C22×C13912yes—
616C4×C4⋊C4C22×C13911yescharacteristic
617C4×C4⋊C4C22×C13911yescharacteristic
618C4×C4⋊C4C22×C13911yescharacteristic
619C4×C4⋊C4C22×C13912yes—
620C4×C4⋊C4C22×C13911yescharacteristic
621C4×C4⋊C4C22×C13911yescharacteristic
622C4×C4⋊C4C22×C13911yescharacteristic
623C4×C22⋊C4C22×C13912yes—
624C4×C22⋊C4C22×C13912yes—
625C4×C22⋊C4C22×C13912yes—
626C4×C22⋊C4C22×C13911yescharacteristic
627C4×C22⋊C4C22×C13911yescharacteristic
628#376C22×C13911yescharacteristic
629C22×Q8C23×C13912yes—
630C22×D4C23×C13911yescharacteristic
631C22×D4C23×C13912yes—
632C22×D4C23×C13911yescharacteristic
633C22×D4C23×C13912yes—
634C23×C4C23×C13911yescharacteristic
635C23×C4C23×C13911yescharacteristic
636C23×C4C23×C13911yescharacteristic
637C23×C4C23×C13911yescharacteristic
638C23×C4C23×C13912yes—
639C23×C4C23×C13912yes—
640C4⋊Q8—24no—
641#126—44no—
642#124—44no—
643C22⋊Q8—44no—
644#121—24no—
645#121—24no—
646#121—44no—
647C4×D4—24no—
648C4×D4—24no—
649C4×D4—44no—
650#117—24no—
651#117—24no—
652#117—44no—
653C2×C4⋊C4—24no—
654C2×C4⋊C4C23×C13911yescharacteristic
655C2×C4⋊C4C23×C13912yes—
656C2×C4⋊C4C23×C13911yescharacteristic
657C2×C4⋊C4C23×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C4⋊C4C23×C13912yes—
661C2×C4⋊C4C23×C13911yescharacteristic
662C2×C4⋊C4C23×C13911yescharacteristic
663C2×C4⋊C4C23×C13911yescharacteristic
664C2×C4⋊C4C23×C13912yes—
665C2×C4⋊C4C23×C13911yescharacteristic
666C2×C4⋊C4C23×C13911yescharacteristic
667C2×C4⋊C4C23×C13912yes—
668C2×C4⋊C4C23×C13911yescharacteristic
669C2×C4⋊C4C23×C13912yes—
670C2×C4⋊C4C23×C13912yes—
671C2×C4⋊C4C23×C13912yes—
672C2×C4⋊C4C23×C13912yes—
673C2×C4⋊C4C23×C13912yes—
674C2×C4⋊C4C23×C13912yes—
675C2×C4⋊C4C23×C13912yes—
676C2×C4⋊C4C23×C13912yes—
677C2×C4⋊C4C23×C13911yescharacteristic
678C2×C22⋊C4C23×C13912yes—
679C2×C22⋊C4C23×C13912yes—
680C2×C22⋊C4C23×C13911yescharacteristic
681C2×C22⋊C4C23×C13911yescharacteristic
682C2×C22⋊C4C23×C13912yes—
683C2×C22⋊C4C23×C13912yes—
684C2×C22⋊C4C23×C13911yescharacteristic
685C2×C22⋊C4C23×C13911yescharacteristic
686C2×C22⋊C4C23×C13912yes—
687C2×C22⋊C4C23×C13912yes—
688C2×C22⋊C4C23×C13912yes—
689C2×C22⋊C4C23×C13911yescharacteristic
690C2×C22⋊C4C23×C13911yescharacteristic
691C2×C22⋊C4C23×C13911yescharacteristic
692C2×C22⋊C4C23×C13912yes—
693C2×C22⋊C4C23×C13912yes—
694C2×C22⋊C4C23×C13912yes—
695C2×C22⋊C4C23×C13912yes—
696C2×C22⋊C4C23×C13912yes—
697C2×C22⋊C4C23×C13912yes—
698C2×C22⋊C4C23×C13912yes—
699C2×C22⋊C4C23×C13912yes—
700C2×C22⋊C4C23×C13911yescharacteristic
701C2×C22⋊C4C23×C13912yes—
702C2×C42—24no—
703C2×C42C23×C13911yescharacteristic
704C2×C42C23×C13912yes—
705C2×C42C23×C13911yescharacteristic
706C2×C42C23×C13911yescharacteristic
707C2×C42C23×C13911yescharacteristic
708C2×C42C23×C13911yescharacteristic
709C2×C42C23×C13911yescharacteristic
710C2×C42C23×C13912yes—
711C2×C42C23×C13912yes—
712C2×C42C23×C13912yes—
713C2×C42C23×C13912yes—
714C2×C42C23×C13912yes—
715C2×C42C23×C13911yescharacteristic
716#95C23×C13911yescharacteristic
717#95C23×C13911yescharacteristic
718#95C23×C13911yescharacteristic
719#95C23×C13911yescharacteristic
720#95C23×C13912yes—
721#95C23×C13912yes—
722#95C23×C13912yes—
723#95C23×C13912yes—
724#95C23×C13912yes—
725#95C23×C13912yes—
726#95C23×C13911yescharacteristic
727#95C23×C13911yescharacteristic
728#95C23×C13911yescharacteristic
729#95C23×C13911yescharacteristic
730#95C23×C13912yes—
731#95C23×C13912yes—
732#95C23×C13912yes—
733#95C23×C13911yescharacteristic
734#95C23×C13911yescharacteristic
735#95C23×C13912yes—
736#95C23×C13912yes—
737#95C23×C13912yes—
738#95C23×C13912yes—
739#95C23×C13912yes—
740#95C23×C13912yes—
741#95C23×C13912yes—
742#95C23×C13912yes—
743C24C24×C13912yes—
744C24C24×C13911yescharacteristic
745C24C24×C13911yescharacteristic
746C2×Q8—24no—
747C2×Q8—42no—
748C2×Q8—42no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—22no—
754C2×D4—24no—
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—42no—
758C2×D4—41no—
759C2×D4—42no—
760C2×D4—42no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—41no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4#41×C13914yes—
779C22×C4C24×C13911yescharacteristic
780C22×C4C24×C13911yescharacteristic
781C22×C4C24×C13911yescharacteristic
782C22×C4C24×C13912yes—
783C22×C4C24×C13911yescharacteristic
784C22×C4C24×C13911yescharacteristic
785C22×C4C24×C13911yescharacteristic
786C22×C4C24×C13912yes—
787C22×C4C24×C13912yes—
788C22×C4C24×C13912yes—
789C22×C4C24×C13911yescharacteristic
790C22×C4C24×C13912yes—
791C22×C4C24×C13912yes—
792C22×C4C24×C13911yescharacteristic
793C22×C4C24×C13911yescharacteristic
794C22×C4C24×C13911yescharacteristic
795C22×C4C24×C13912yes—
796C22×C4C24×C13911yescharacteristic
797C22×C4C24×C13911yescharacteristic
798C22×C4C24×C13911yescharacteristic
799C4⋊C4—24no—
800C4⋊C4—22no—
801C4⋊C4—22no—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—42no—
822C4⋊C4#41×C13914yes—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—22no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—22no—
836C22⋊C4—22no—
837C22⋊C4—24no—
838C22⋊C4—41no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—42no—
847C42—22no—
848C42—22no—
849C42—22no—
850C42—24no—
851C42—22no—
852C42—22no—
853C42—22no—
854C42—42no—
855C42—42no—
856C42—42no—
857C42—42no—
858C42—42no—
859C42#41×C13914yes—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23C2×#41×C13912yes—
880C23H(5,𝔽2)×C13912yes—
881C23C25×C13911yescharacteristic
882Q8—84no—
883D4—48no—
884D4—44no—
885D4—44no—
886D4—84no—
887C2×C4—28no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—28no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—44no—
941C2×C4—44no—
942C2×C4—84no—
943C2×C4—84no—
944C2×C4C2×#41×C13912yes—
945C2×C4C2×#41×C13912yes—
946C2×C4C2×#41×C13912yes—
947C2×C4C2×#41×C13914yes—
948C2×C4C2×#41×C13912yes—
949C2×C4C2×#41×C13912yes—
950C2×C4C2×#41×C13912yes—
951C2×C4H(5,𝔽2)×C13912yes—
952C2×C42−1+4×C13912yes—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22C22×#41×C13911yescharacteristic
975C22C22×#41×C13911yescharacteristic
976C22C22×#41×C13911yescharacteristic
977C22C2×H(5,𝔽2)×C13911yescharacteristic
978C22C2×H(5,𝔽2)×C13911yescharacteristic
979C22C2×2−1+4×C13911yescharacteristic
980C22#585×C13911yescharacteristic
981C4—22no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—22no—
986C4—24no—
987C4—41no—
988C4—41no—
989C4—42no—
990C4—41no—
991C4—42no—
992C4—41no—
993C4—42no—
994C4—41no—
995C4—42no—
996C4—41no—
997C4—42no—
998C4—41no—
999C4—42no—
1000C4#529×C13914yes—
1001C2—42no—
1002C2—42no—
1003C2—82no—
1004C2C2×#529×C13911yescharacteristic
1005C2#3492×C13911yescharacteristic
1006C2#3494×C13911yescharacteristic
1007C2#3494×C13911yescharacteristic
1008C2#3511×C13911yescharacteristic
1009C2#3518×C13911yescharacteristic
1010C2#3519×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radical#2416×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2594×C139C2semidirect
2. #2576×C139C2semidirect
3. #2574×C139C2semidirect
4. #2560×C139C2semidirect
5. #2512×C139C2semidirect
6. #2507×C139C2semidirect
7. #2500×C139C2semidirect
8. #2494×C139C2semidirect
9. #2491×C139C2semidirect
10. #2485×C139C2semidirect
11. #2476×C139C2semidirect
12. #2474×C139C2semidirect
13. #2468×C139C2semidirect
14. #2440×C139C2semidirect
15. #2427×C139C2semidirect
17. #2331×C139C2semidirect
18. #2324×C139C2semidirect
19. #2319×C139C2semidirect
20. C4×#121×C139C2semidirect
21. #2290×C139C2semidirect
22. #2285×C139C2semidirect
23. #2274×C139C2semidirect
505. #35589C139direct (N × H)
506. C139#35589direct (N × H)
507. #2594C2×C139semidirect
508. #2576C2×C139semidirect
509. #2574C2×C139semidirect
510. #2560C2×C139semidirect
511. #2512C2×C139semidirect
512. #2507C2×C139semidirect
513. #2500C2×C139semidirect
514. #2494C2×C139semidirect
515. #2491C2×C139semidirect
516. #2485C2×C139semidirect
517. #2476C2×C139semidirect
518. #2474C2×C139semidirect
519. #2468C2×C139semidirect
520. #2440C2×C139semidirect
521. #2427C2×C139semidirect
523. #2331C2×C139semidirect
524. #2324C2×C139semidirect
525. #2319C2×C139semidirect
526. C4×#121C2×C139semidirect
527. #2290C2×C139semidirect
528. #2285C2×C139semidirect
529. #2274C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2594×C1392
#2576×C1392
#2574×C1392
#2560×C1392
#2512×C1392
#2507×C1392
#2500×C1392
#2494×C1392
#2491×C1392
#2485×C1392
#2476×C1392
#2474×C1392
#2468×C1392
#2440×C1392
#2427×C1392
#2416×C1392
#2331×C1392
#2324×C1392
#2319×C1392
C4×#121×C1392
#2290×C1392
#2285×C1392
#2274×C1392
#35589139