Finite Group Databasebeta

← C139×#22174 #48016770

Subgroups — C139×#22174 #48016770

Order 35584.

964 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C139C211yesmaximal, characteristic, complemented
2C2×#435×C139C211yesmaximal, characteristic, complemented
3C4×#121×C139C211yesmaximal, characteristic
4#1924×C139C211yesmaximal, characteristic, complemented
5#1923×C139C211yesmaximal, characteristic, complemented
6#1917×C139C211yesmaximal, characteristic, complemented
7#1916×C139C211yesmaximal, characteristic, complemented
8#1870×C139C211yesmaximal, characteristic, complemented
9#1870×C139C211yesmaximal, characteristic, complemented
10#1870×C139C211yesmaximal, characteristic, complemented
11#1869×C139C211yesmaximal, characteristic, complemented
12#1851×C139C211yesmaximal, characteristic, complemented
13#1850×C139C211yesmaximal, characteristic, complemented
14#1797×C139C211yesmaximal, characteristic, complemented
15#1728×C139C211yesmaximal, characteristic, complemented
16C22×M16×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20C2×#121×C139C411yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C2×C4×D4×C139C2211yescharacteristic
24C22×C42×C139C2211yescharacteristic
25#436×C139—24no—
26#435×C139—24no—
27C2×C4⋊C8×C139C2211yescharacteristic
28C2×C4⋊C8×C139C2211yescharacteristic
29C2×C4⋊C8×C139C2211yescharacteristic
30C2×C4⋊C8×C139C2211yescharacteristic
31C2×C22⋊C8×C139C2211yescharacteristic
32C2×C22⋊C8×C139C2211yescharacteristic
33C2×C22⋊C8×C139C2211yescharacteristic
34C2×C22⋊C8×C139C2211yescharacteristic
35C2×C22⋊C8×C139C2211yescharacteristic
36C2×C22⋊C8×C139C2211yescharacteristic
37C2×C22⋊C8×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×#97×C139C2211yescharacteristic
40C2×C4×C8×C139C2211yescharacteristic
41#390×C139C411yescharacteristic
42#389×C139C411yescharacteristic
43#388×C139C411yescharacteristic
44#388×C139C411yescharacteristic
45#386×C139C411yescharacteristic
46#386×C139C411yescharacteristic
47#380×C139C411yescharacteristic
48C4×C4⋊C4×C139C2211yescharacteristic
49C4×C22⋊C4×C139C2211yescharacteristic
50C4×C22⋊C4×C139C2211yescharacteristic
51#336×C139C2211yescharacteristic
52#336×C139C2211yescharacteristic
53#336×C139C2211yescharacteristic
54#336×C139C2211yescharacteristic
55#336×C139C2211yescharacteristic
56#336×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×D4×C139C2×C411yescharacteristic
62C22×D4×C139C2×C411yescharacteristic
63C22×D4×C139C2×C411yescharacteristic
64C23×C4×C139C2×C411yescharacteristic
65C23×C4×C139C2×C411yescharacteristic
66C23×C4×C139C2311yescharacteristic
67C23×C4×C139C2311yescharacteristic
68C23×C4×C139C2311yescharacteristic
69C2×M16×C139—22no—
70C2×M16×C139—22no—
71C2×M16×C139—41no—
72C2×M16×C139—41no—
73C2×M16×C139—41no—
74C2×M16×C139—41no—
75C2×M16×C139—41no—
76C2×M16×C139—41no—
77C2×M16×C139D414yescomplemented
78C22×C8×C139—22no—
79C22×C8×C139—41no—
80C22×C8×C139—41no—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89#121×C139—24no—
90C4×D4×C139—22no—
91C4×D4×C139—22no—
92C4×D4×C139—22no—
93C4×D4×C139—22no—
94C4×D4×C139—41no—
95C4×D4×C139—41no—
96C2×C4⋊C4×C139C2×C411yescharacteristic
97C2×C4⋊C4×C139C2×C411yescharacteristic
98C2×C4⋊C4×C139C2×C411yescharacteristic
99C2×C4⋊C4×C139C2×C411yescharacteristic
100C2×C4⋊C4×C139C2×C411yescharacteristic
101C2×C22⋊C4×C139C2×C411yescharacteristic
102C2×C22⋊C4×C139C2×C411yescharacteristic
103C2×C22⋊C4×C139C2×C411yescharacteristic
104C2×C22⋊C4×C139C2×C411yescharacteristic
105C2×C22⋊C4×C139C2×C411yescharacteristic
106C2×C22⋊C4×C139C2×C411yescharacteristic
107C2×C22⋊C4×C139C2×C411yescharacteristic
108C2×C22⋊C4×C139C2×C411yescharacteristic
109C2×C22⋊C4×C139C2×C411yescharacteristic
110C2×C22⋊C4×C139C2×C411yescharacteristic
111C2×C42×C139—41no—
112C2×C42×C139—41no—
113C2×C42×C139C2×C411yescharacteristic
114C2×C42×C139C2×C411yescharacteristic
115C2×C42×C139C2311yescharacteristic
116C2×C42×C139C2311yescharacteristic
117C2×C42×C139C2311yescharacteristic
118C2×C42×C139C2311yescharacteristic
119C4⋊C8×C139—22no—
120C4⋊C8×C139—22no—
121C4⋊C8×C139—41no—
122C4⋊C8×C139—41no—
123C22⋊C8×C139—22no—
124C22⋊C8×C139—22no—
125C22⋊C8×C139—22no—
126C22⋊C8×C139—22no—
127C22⋊C8×C139—41no—
128C22⋊C8×C139—41no—
129C22⋊C8×C139—41no—
130C22⋊C8×C139—41no—
131#97×C139—22no—
132C4×C8×C139—22no—
133#95×C139C2×C411yescharacteristic
134#95×C139C2×C411yescharacteristic
135#95×C139C2×C411yescharacteristic
136#95×C139C2×C411yescharacteristic
137#95×C139C2×C411yescharacteristic
138#95×C139C2×C411yescharacteristic
139C24×C139C22×C411yescharacteristic
140C24×C139C22×C411yescharacteristic
141C24×C139C22×C411yescharacteristic
142C2×D4×C139—22no—
143C2×D4×C139—22no—
144C2×D4×C139—22no—
145C2×D4×C139—22no—
146C2×D4×C139—22no—
147C2×D4×C139—22no—
148C2×D4×C139—41no—
149C2×D4×C139—41no—
150C2×D4×C139—41no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—21no—
155C22×C4×C139—22no—
156C22×C4×C139—22no—
157C22×C4×C139—21no—
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—41no—
170C22×C4×C139—41no—
171C22×C4×C139—41no—
172C22×C4×C139—41no—
173C22×C4×C139C22×C411yescharacteristic
174C22×C4×C139C22×C411yescharacteristic
175C22×C4×C139C22×C411yescharacteristic
176C22×C4×C139C22×C411yescharacteristic
177C22×C4×C139C22×C411yescharacteristic
178C22×C4×C139C22×C411yescharacteristic
179C22×C4×C139C22×C411yescharacteristic
180C22×C4×C139C22×C411yescharacteristic
181C22×C4×C139C22×C411yescharacteristic
182C22×C4×C139C22×C411yescharacteristic
183C22×C4×C139C22×C411yescharacteristic
184C22×C4×C139C2×D412yes—
185C22×C4×C139#4112yes—
186C22×C4×C139C2411yescharacteristic
187M16×C139—44no—
188M16×C139—44no—
189M16×C139—44no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
197C2×C8×C139—21no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139—21no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—44no—
213C2×C8×C139C2×D412yes—
214C2×C8×C139C2×D412yes—
215C4⋊C4×C139—22no—
216C4⋊C4×C139—22no—
217C4⋊C4×C139—22no—
218C4⋊C4×C139—22no—
219C4⋊C4×C139—41no—
220C22⋊C4×C139—22no—
221C22⋊C4×C139—22no—
222C22⋊C4×C139—22no—
223C22⋊C4×C139—22no—
224C22⋊C4×C139—22no—
225C22⋊C4×C139—41no—
226C22⋊C4×C139—41no—
227C22⋊C4×C139—41no—
228C22⋊C4×C139—41no—
229C22⋊C4×C139M1614yescomplemented
230C42×C139—21no—
231C42×C139—21no—
232C42×C139—21no—
233C42×C139—21no—
234C42×C139—21no—
235C42×C139—21no—
236C42×C139—21no—
237C42×C139—21no—
238C42×C139—41no—
239C42×C139—41no—
240C23×C139—21no—
241C23×C139—21no—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—21no—
255C23×C139—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139C4×D412yes—
260C23×C139C2×M1612yes—
261C23×C139C23×C411yescharacteristic
262D4×C139—44no—
263D4×C139—44no—
264D4×C139—44no—
265C2×C4×C139—21no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—22no—
274C2×C4×C139—22no—
275C2×C4×C139—22no—
276C2×C4×C139—22no—
277C2×C4×C139—21no—
278C2×C4×C139—21no—
279C2×C4×C139—21no—
280C2×C4×C139—21no—
281C2×C4×C139—21no—
282C2×C4×C139—21no—
283C2×C4×C139—21no—
284C2×C4×C139—21no—
285C2×C4×C139—21no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—44no—
299C2×C4×C139—44no—
300C2×C4×C139—41no—
301C2×C4×C139—41no—
302C2×C4×C139—41no—
303C2×C4×C139—41no—
304C2×C4×C139—41no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139C4×D412yes—
309C2×C4×C139C2×M1612yes—
310C2×C4×C139C2×M1612yes—
311C2×C4×C139#13112yes—
312C2×C4×C139C22×D411yescharacteristic
313C2×C4×C139C2×#4111yescharacteristic
314C2×C4×C139H(5,𝔽2)11yescharacteristic
315C2×C4×C139H(5,𝔽2)11yescharacteristic
316C2×C4×C139H(5,𝔽2)11yescharacteristic
317C2×C4×C1392−1+411yescharacteristic
318C8×C139—22no—
319C8×C139—22no—
320C8×C139—41no—
321C8×C139—41no—
322C8×C139—41no—
323C8×C139—41no—
324C8×C139—41no—
325C8×C139—41no—
326C22×C139—22no—
327C22×C139—22no—
328C22×C139—22no—
329C22×C139—22no—
330C22×C139—22no—
331C22×C139—22no—
332C22×C139—41no—
333C22×C139—41no—
334C22×C139—41no—
335C22×C139—41no—
336C22×C139—41no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139—41no—
340C22×C139—41no—
341C22×C139—41no—
342C22×C139—41no—
343C22×C139—41no—
344C22×C139—41no—
345C22×C139—41no—
346C22×C139—41no—
347C22×C139C2×C4×D411yescharacteristic
348C22×C139#51811yescharacteristic
349C22×C139#52011yescharacteristic
350C22×C139C22×M1611yescharacteristic
351C22×C139C2×#13111yescharacteristic
352C22×C139#56811yescharacteristic
353C22×C139#56811yescharacteristic
354C4×C139—22no—
355C4×C139—22no—
356C4×C139—22no—
357C4×C139—22no—
358C4×C139—41no—
359C4×C139—41no—
360C4×C139—41no—
361C4×C139—41no—
362C4×C139—41no—
363C4×C139—41no—
364C4×C139—41no—
365C4×C139#53411yescharacteristic
366C4×C139#53711yescharacteristic
367C4×C139#53811yescharacteristic
368C4×C139#53911yescharacteristic
369C2×C139—42no—
370C2×C139—42no—
371C2×C139—81no—
372C2×C139#232511yescharacteristic
373C2×C139D4×M1611yescharacteristic
374C2×C139#293511yescharacteristic
375C2×C139#297411yescharacteristic
376C2×C139#297811yescharacteristic
377C2×C139#298911yescharacteristic
378C2×C139#299311yescharacteristic
379#22174C13911yesmaximal, characteristic, direct product factor, Sylow
380C139#2217411yescharacteristic, direct product factor, Sylow
381C2×#436C2×C13911yescharacteristic, complemented
382C2×#435C2×C13911yescharacteristic, complemented
383C4×#121C2×C13911yescharacteristic
384#1924C2×C13911yescharacteristic, complemented
385#1923C2×C13911yescharacteristic, complemented
386#1917C2×C13911yescharacteristic, complemented
387#1916C2×C13911yescharacteristic, complemented
388#1870C2×C13911yescharacteristic, complemented
389#1870C2×C13911yescharacteristic, complemented
390#1870C2×C13911yescharacteristic, complemented
391#1869C2×C13911yescharacteristic, complemented
392#1851C2×C13911yescharacteristic, complemented
393#1850C2×C13911yescharacteristic, complemented
394#1797C2×C13911yescharacteristic, complemented
395#1728C2×C13911yescharacteristic, complemented
396C22×M16C22×C13911yescharacteristic
397C22×M16C22×C13911yescharacteristic
398C22×M16C22×C13911yescharacteristic
399C23×C8C22×C13911yescharacteristic
400C2×#121C4×C13911yescharacteristic
401C2×C4×D4C22×C13911yescharacteristic
402C2×C4×D4C22×C13911yescharacteristic
403C2×C4×D4C22×C13911yescharacteristic
404C22×C42C22×C13911yescharacteristic
405#436—24no—
406#435—24no—
407C2×C4⋊C8C22×C13911yescharacteristic
408C2×C4⋊C8C22×C13911yescharacteristic
409C2×C4⋊C8C22×C13911yescharacteristic
410C2×C4⋊C8C22×C13911yescharacteristic
411C2×C22⋊C8C22×C13911yescharacteristic
412C2×C22⋊C8C22×C13911yescharacteristic
413C2×C22⋊C8C22×C13911yescharacteristic
414C2×C22⋊C8C22×C13911yescharacteristic
415C2×C22⋊C8C22×C13911yescharacteristic
416C2×C22⋊C8C22×C13911yescharacteristic
417C2×C22⋊C8C22×C13911yescharacteristic
418C2×C22⋊C8C22×C13911yescharacteristic
419C2×#97C22×C13911yescharacteristic
420C2×C4×C8C22×C13911yescharacteristic
421#390C4×C13911yescharacteristic
422#389C4×C13911yescharacteristic
423#388C4×C13911yescharacteristic
424#388C4×C13911yescharacteristic
425#386C4×C13911yescharacteristic
426#386C4×C13911yescharacteristic
427#380C4×C13911yescharacteristic
428C4×C4⋊C4C22×C13911yescharacteristic
429C4×C22⋊C4C22×C13911yescharacteristic
430C4×C22⋊C4C22×C13911yescharacteristic
431#336C22×C13911yescharacteristic
432#336C22×C13911yescharacteristic
433#336C22×C13911yescharacteristic
434#336C22×C13911yescharacteristic
435#336C22×C13911yescharacteristic
436#336C22×C13911yescharacteristic
437#336C22×C13911yescharacteristic
438#336C22×C13911yescharacteristic
439#336C22×C13911yescharacteristic
440#336C22×C13911yescharacteristic
441C22×D4C2×C4×C13911yescharacteristic
442C22×D4C2×C4×C13911yescharacteristic
443C22×D4C2×C4×C13911yescharacteristic
444C23×C4C2×C4×C13911yescharacteristic
445C23×C4C2×C4×C13911yescharacteristic
446C23×C4C23×C13911yescharacteristic
447C23×C4C23×C13911yescharacteristic
448C23×C4C23×C13911yescharacteristic
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—41no—
457C2×M16D4×C13914yescomplemented
458C22×C8—22no—
459C22×C8—41no—
460C22×C8—41no—
461C22×C8C23×C13911yescharacteristic
462C22×C8C23×C13911yescharacteristic
463C22×C8C23×C13911yescharacteristic
464C22×C8C23×C13911yescharacteristic
465C22×C8C23×C13911yescharacteristic
466C22×C8C23×C13911yescharacteristic
467C22×C8C23×C13911yescharacteristic
468C22×C8C23×C13911yescharacteristic
469#121—24no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C2×C4⋊C4C2×C4×C13911yescharacteristic
477C2×C4⋊C4C2×C4×C13911yescharacteristic
478C2×C4⋊C4C2×C4×C13911yescharacteristic
479C2×C4⋊C4C2×C4×C13911yescharacteristic
480C2×C4⋊C4C2×C4×C13911yescharacteristic
481C2×C22⋊C4C2×C4×C13911yescharacteristic
482C2×C22⋊C4C2×C4×C13911yescharacteristic
483C2×C22⋊C4C2×C4×C13911yescharacteristic
484C2×C22⋊C4C2×C4×C13911yescharacteristic
485C2×C22⋊C4C2×C4×C13911yescharacteristic
486C2×C22⋊C4C2×C4×C13911yescharacteristic
487C2×C22⋊C4C2×C4×C13911yescharacteristic
488C2×C22⋊C4C2×C4×C13911yescharacteristic
489C2×C22⋊C4C2×C4×C13911yescharacteristic
490C2×C22⋊C4C2×C4×C13911yescharacteristic
491C2×C42—41no—
492C2×C42—41no—
493C2×C42C2×C4×C13911yescharacteristic
494C2×C42C2×C4×C13911yescharacteristic
495C2×C42C23×C13911yescharacteristic
496C2×C42C23×C13911yescharacteristic
497C2×C42C23×C13911yescharacteristic
498C2×C42C23×C13911yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—41no—
502C4⋊C8—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508C22⋊C8—41no—
509C22⋊C8—41no—
510C22⋊C8—41no—
511#97—22no—
512C4×C8—22no—
513#95C2×C4×C13911yescharacteristic
514#95C2×C4×C13911yescharacteristic
515#95C2×C4×C13911yescharacteristic
516#95C2×C4×C13911yescharacteristic
517#95C2×C4×C13911yescharacteristic
518#95C2×C4×C13911yescharacteristic
519C24C22×C4×C13911yescharacteristic
520C24C22×C4×C13911yescharacteristic
521C24C22×C4×C13911yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4C22×C4×C13911yescharacteristic
554C22×C4C22×C4×C13911yescharacteristic
555C22×C4C22×C4×C13911yescharacteristic
556C22×C4C22×C4×C13911yescharacteristic
557C22×C4C22×C4×C13911yescharacteristic
558C22×C4C22×C4×C13911yescharacteristic
559C22×C4C22×C4×C13911yescharacteristic
560C22×C4C22×C4×C13911yescharacteristic
561C22×C4C22×C4×C13911yescharacteristic
562C22×C4C22×C4×C13911yescharacteristic
563C22×C4C22×C4×C13911yescharacteristic
564C22×C4C2×D4×C13912yes—
565C22×C4#41×C13912yes—
566C22×C4C24×C13911yescharacteristic
567M16—44no—
568M16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—44no—
593C2×C8C2×D4×C13912yes—
594C2×C8C2×D4×C13912yes—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4M16×C13914yescomplemented
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—41no—
619C42—41no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C4×D4×C13912yes—
640C23C2×M16×C13912yes—
641C23C23×C4×C13911yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C4×D4×C13912yes—
689C2×C4C2×M16×C13912yes—
690C2×C4C2×M16×C13912yes—
691C2×C4#131×C13912yes—
692C2×C4C22×D4×C13911yescharacteristic
693C2×C4C2×#41×C13911yescharacteristic
694C2×C4H(5,𝔽2)×C13911yescharacteristic
695C2×C4H(5,𝔽2)×C13911yescharacteristic
696C2×C4H(5,𝔽2)×C13911yescharacteristic
697C2×C42−1+4×C13911yescharacteristic
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C4×D4×C13911yescharacteristic
728C22#518×C13911yescharacteristic
729C22#520×C13911yescharacteristic
730C22C22×M16×C13911yescharacteristic
731C22C2×#131×C13911yescharacteristic
732C22#568×C13911yescharacteristic
733C22#568×C13911yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4#534×C13911yescharacteristic
746C4#537×C13911yescharacteristic
747C4#538×C13911yescharacteristic
748C4#539×C13911yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2#2325×C13911yescharacteristic
753C2D4×M16×C13911yescharacteristic
754C2#2935×C13911yescharacteristic
755C2#2974×C13911yescharacteristic
756C2#2978×C13911yescharacteristic
757C2#2989×C13911yescharacteristic
758C2#2993×C13911yescharacteristic
subgroupG/H
centerC22×C4×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC22×C4C24×C139
socleC23×C139C23×C4
prime radicalC2×#121×C139C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#436×C139C2semidirect
2. C2×#435×C139C2semidirect
4. #1924×C139C2semidirect
5. #1923×C139C2semidirect
6. #1917×C139C2semidirect
7. #1916×C139C2semidirect
8. #1870×C139C2semidirect
9. #1870×C139C2semidirect
10. #1870×C139C2semidirect
11. #1869×C139C2semidirect
12. #1851×C139C2semidirect
13. #1850×C139C2semidirect
14. #1797×C139C2semidirect
15. #1728×C139C2semidirect
77. C2×M16×C139D4semidirect
229. C22⋊C4×C139M16semidirect
379. #22174C139direct (N × H)
380. C139#22174direct (N × H)
381. C2×#436C2×C139semidirect
382. C2×#435C2×C139semidirect
384. #1924C2×C139semidirect
385. #1923C2×C139semidirect
386. #1917C2×C139semidirect
387. #1916C2×C139semidirect
388. #1870C2×C139semidirect
389. #1870C2×C139semidirect
390. #1870C2×C139semidirect
391. #1869C2×C139semidirect
392. #1851C2×C139semidirect
393. #1850C2×C139semidirect
394. #1797C2×C139semidirect
395. #1728C2×C139semidirect
457. C2×M16D4×C139semidirect
609. C22⋊C4M16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#436×C1392
C2×#435×C1392
C4×#121×C1392
#1924×C1392
#1923×C1392
#1917×C1392
#1916×C1392
#1870×C1392
#1869×C1392
#1851×C1392
#1850×C1392
#1797×C1392
#1728×C1392
#22174139