Finite Group Databasebeta

← C139×#36430 #48031026

Subgroups — C139×#36430 #48031026

Order 35584.

3182 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C211yesmaximal, characteristic, complemented
3C2×#548×C139C211yesmaximal, characteristic, complemented
4C2×C4×#41×C139C211yesmaximal, characteristic, complemented
5#2850×C139C213yesmaximal, complemented
6#2544×C139C213yesmaximal, complemented
7#2535×C139C213yesmaximal, complemented
8#2428×C139C213yesmaximal, complemented
9#2427×C139C213yesmaximal, complemented
10#2415×C139C213yesmaximal, complemented
11#2414×C139C213yesmaximal, complemented
12#2351×C139C211yesmaximal, characteristic, complemented
13#2341×C139C211yesmaximal, characteristic, complemented
14Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
15C4×#121×C139C213yesmaximal, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C23×Q8×C139C2211yescharacteristic
19#550×C139—28no—
20#548×C139—28no—
21#548×C139—28no—
22C2×#127×C139C2213yes—
23C2×#124×C139C2213yes—
24C2×#124×C139C2213yes—
25C2×C22⋊Q8×C139C2213yes—
26C2×C22⋊Q8×C139C2213yes—
27C2×#121×C139C2213yes—
28C2×#121×C139C2213yes—
29C2×#121×C139C2213yes—
30C2×#121×C139C2213yes—
31C2×#121×C139C2213yes—
32C4×#41×C139—28no—
33C2×C4×Q8×C139C2211yescharacteristic
34C2×C4×Q8×C139C2211yescharacteristic
35C2×C4×Q8×C139C2211yescharacteristic
36C2×C4×Q8×C139C2211yescharacteristic
37C2×C4×D4×C139C2213yes—
38C2×C4×D4×C139C2213yes—
39C2×C4×D4×C139C2213yes—
40C2×C4×D4×C139C2213yes—
41C2×C4×D4×C139C2213yes—
42C2×#117×C139C2213yes—
43C22×C42×C139C2213yes—
44#397×C139C2216yes—
45#394×C139C2216yes—
46#394×C139C2216yes—
47#392×C139C2216yes—
48#391×C139C2213yes—
49#391×C139C2213yes—
50#390×C139C2213yes—
51#390×C139C2213yes—
52#390×C139C2213yes—
53#389×C139C2213yes—
54#389×C139C2213yes—
55#389×C139C2213yes—
56#388×C139C2211yescharacteristic
57#388×C139C2213yes—
58#388×C139C2216yes—
59#386×C139C2213yes—
60#386×C139C2216yes—
61#386×C139C2213yes—
62#386×C139C2216yes—
63#382×C139C2213yes—
64#380×C139C2213yes—
65#380×C139C2213yes—
66#380×C139C2213yes—
67C4×C4⋊C4×C139C2213yes—
68C4×C22⋊C4×C139C2213yes—
69C4×C22⋊C4×C139C2213yes—
70C2×#41×C139—24no—
71C2×#41×C139—24no—
72C2×#41×C139—24no—
73C2×#41×C139—24no—
74C2×#41×C139—24no—
75C2×#41×C139D418yescomplemented
76C22×Q8×C139—24no—
77C22×Q8×C139—24no—
78C22×Q8×C139—24no—
79C22×Q8×C139C2313yes—
80C22×Q8×C139C2311yescharacteristic
81C22×D4×C139C2313yes—
82C22×D4×C139C2313yes—
83C22×D4×C139C2313yes—
84C22×D4×C139C2313yes—
85C22×D4×C139C2313yes—
86C22×D4×C139C2316yes—
87C23×C4×C139C2313yes—
88C23×C4×C139C2313yes—
89C23×C4×C139C2313yes—
90C23×C4×C139C2313yes—
91C23×C4×C139C2313yes—
92#127×C139—212no—
93#124×C139—212no—
94#124×C139—212no—
95C22⋊Q8×C139—212no—
96C22⋊Q8×C139—212no—
97#121×C139—212no—
98#121×C139—212no—
99#121×C139—212no—
100#121×C139—212no—
101#121×C139—212no—
102C4×Q8×C139—24no—
103C4×Q8×C139—24no—
104C4×Q8×C139—24no—
105C4×Q8×C139D418yescomplemented
106C4×D4×C139—212no—
107C4×D4×C139—212no—
108C4×D4×C139—212no—
109C4×D4×C139—212no—
110C4×D4×C139—212no—
111#117×C139—212no—
112C2×C4⋊C4×C139C2313yes—
113C2×C4⋊C4×C139C2313yes—
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2313yes—
116C2×C4⋊C4×C139C2313yes—
117C2×C4⋊C4×C139C2313yes—
118C2×C4⋊C4×C139C2313yes—
119C2×C4⋊C4×C139C2313yes—
120C2×C4⋊C4×C139C2313yes—
121C2×C22⋊C4×C139C2313yes—
122C2×C22⋊C4×C139C2316yes—
123C2×C22⋊C4×C139C2316yes—
124C2×C22⋊C4×C139C2311yescharacteristic
125C2×C22⋊C4×C139C2311yescharacteristic
126C2×C22⋊C4×C139C2313yes—
127C2×C22⋊C4×C139C2313yes—
128C2×C22⋊C4×C139C2313yes—
129C2×C22⋊C4×C139C2316yes—
130C2×C22⋊C4×C139C2313yes—
131C2×C22⋊C4×C139C2313yes—
132C2×C22⋊C4×C139C2313yes—
133C2×C22⋊C4×C139C2316yes—
134C2×C22⋊C4×C139C2311yescharacteristic
135C2×C42×C139—212no—
136C2×C42×C139C2311yescharacteristic
137C2×C42×C139C2313yes—
138C2×C42×C139C2313yes—
139C2×C42×C139C2313yes—
140C2×C42×C139C2313yes—
141C2×C42×C139C2313yes—
142#95×C139C2313yes—
143#95×C139C2316yes—
144#95×C139C2316yes—
145#95×C139C2311yescharacteristic
146#95×C139C2313yes—
147#95×C139C2313yes—
148#95×C139C2311yescharacteristic
149#95×C139C2313yes—
150C24×C139C2413yes—
151C24×C139C2413yes—
152C24×C139C2411yescharacteristic
153#41×C139—232no—
154#41×C139—416no—
155C2×Q8×C139—26no—
156C2×Q8×C139—26no—
157C2×Q8×C139—26no—
158C2×Q8×C139—416no—
159C2×Q8×C139C2×D414yes—
160C2×Q8×C139C2×D414yes—
161C2×Q8×C139#4114yes—
162C2×D4×C139—26no—
163C2×D4×C139—26no—
164C2×D4×C139—26no—
165C2×D4×C139—26no—
166C2×D4×C139—212no—
167C2×D4×C139—26no—
168C2×D4×C139—26no—
169C2×D4×C139—26no—
170C2×D4×C139—26no—
171C2×D4×C139—26no—
172C2×D4×C139—26no—
173C2×D4×C139—26no—
174C2×D4×C139—43no—
175C2×D4×C139—43no—
176C2×D4×C139—43no—
177C2×D4×C139—46no—
178C2×D4×C139—46no—
179C2×D4×C139C2×D4112yes—
180C22×C4×C139—26no—
181C22×C4×C139—26no—
182C22×C4×C139—26no—
183C22×C4×C139—26no—
184C22×C4×C139—26no—
185C22×C4×C139—26no—
186C22×C4×C139—26no—
187C22×C4×C139—26no—
188C22×C4×C139—26no—
189C22×C4×C139—26no—
190C22×C4×C139—26no—
191C22×C4×C139—43no—
192C22×C4×C139—43no—
193C22×C4×C139—43no—
194C22×C4×C139C2×D4112yes—
195C22×C4×C139C2413yes—
196C22×C4×C139C2413yes—
197C22×C4×C139C2413yes—
198C22×C4×C139C2413yes—
199C22×C4×C139C2411yescharacteristic
200C22×C4×C139C2411yescharacteristic
201C22×C4×C139C2411yescharacteristic
202C22×C4×C139C2413yes—
203C22×C4×C139C2411yescharacteristic
204C22×C4×C139C2411yescharacteristic
205C22×C4×C139C2411yescharacteristic
206C22×C4×C139C2413yes—
207C4⋊C4×C139—26no—
208C4⋊C4×C139—22no—
209C4⋊C4×C139—26no—
210C4⋊C4×C139—26no—
211C4⋊C4×C139—26no—
212C4⋊C4×C139—26no—
213C4⋊C4×C139—26no—
214C4⋊C4×C139—43no—
215C4⋊C4×C139C2×D4112yes—
216C22⋊C4×C139—26no—
217C22⋊C4×C139—26no—
218C22⋊C4×C139—212no—
219C22⋊C4×C139—212no—
220C22⋊C4×C139—22no—
221C22⋊C4×C139—22no—
222C22⋊C4×C139—26no—
223C22⋊C4×C139—26no—
224C22⋊C4×C139—212no—
225C22⋊C4×C139—26no—
226C22⋊C4×C139—43no—
227C22⋊C4×C139—46no—
228C22⋊C4×C139—43no—
229C22⋊C4×C139#4114yescomplemented
230C42×C139—22no—
231C42×C139—26no—
232C42×C139—26no—
233C42×C139—26no—
234C42×C139—26no—
235C42×C139C2×D4112yes—
236C23×C139—23no—
237C23×C139—21no—
238C23×C139—21no—
239C23×C139—21no—
240C23×C139—23no—
241C23×C139—23no—
242C23×C139—21no—
243C23×C139—23no—
244C23×C139—23no—
245C23×C139—23no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—23no—
249C23×C139—23no—
250C23×C139—23no—
251C23×C139—23no—
252C23×C139—23no—
253C23×C139—23no—
254C23×C139—23no—
255C23×C139C22×D416yes—
256C23×C139C2×#4112yes—
257C23×C139C2511yescharacteristic
258Q8×C139—412no—
259Q8×C139#121116yescomplemented
260D4×C139—224no—
261D4×C139—412no—
262D4×C139—412no—
263D4×C139—412no—
264D4×C139—412no—
265D4×C139—812no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
268C2×C4×C139—21no—
269C2×C4×C139—23no—
270C2×C4×C139—21no—
271C2×C4×C139—23no—
272C2×C4×C139—21no—
273C2×C4×C139—21no—
274C2×C4×C139—21no—
275C2×C4×C139—21no—
276C2×C4×C139—224no—
277C2×C4×C139—21no—
278C2×C4×C139—23no—
279C2×C4×C139—23no—
280C2×C4×C139—23no—
281C2×C4×C139—21no—
282C2×C4×C139—23no—
283C2×C4×C139—23no—
284C2×C4×C139—21no—
285C2×C4×C139—23no—
286C2×C4×C139—21no—
287C2×C4×C139—23no—
288C2×C4×C139—21no—
289C2×C4×C139—23no—
290C2×C4×C139—23no—
291C2×C4×C139—23no—
292C2×C4×C139—23no—
293C2×C4×C139—21no—
294C2×C4×C139—23no—
295C2×C4×C139—412no—
296C2×C4×C139—412no—
297C2×C4×C139—412no—
298C2×C4×C139—412no—
299C2×C4×C139C22×D412yes—
300C2×C4×C139C22×D416yes—
301C2×C4×C139C22×D412yes—
302C2×C4×C139C22×D416yes—
303C2×C4×C139C22×D416yes—
304C2×C4×C139C2×#4112yes—
305C2×C4×C139C2×#4112yes—
306C2×C4×C139C2×#4116yes—
307C22×C139—26no—
308C22×C139—22no—
309C22×C139—22no—
310C22×C139—26no—
311C22×C139—22no—
312C22×C139—26no—
313C22×C139—41no—
314C22×C139—43no—
315C22×C139—43no—
316C22×C139—43no—
317C22×C139—41no—
318C22×C139—41no—
319C22×C139—41no—
320C22×C139—43no—
321C22×C139—43no—
322C22×C139—43no—
323C22×C139—43no—
324C22×C139—43no—
325C22×C139—43no—
326C22×C139—43no—
327C22×C139—43no—
328C22×C139C23×D411yescharacteristic
329C22×C139C23×D411yescharacteristic
330C22×C139C22×#4111yescharacteristic
331C22×C139C22×#4111yescharacteristic
332C22×C139#58511yescharacteristic
333C22×C139#58511yescharacteristic
334C22×C139#58511yescharacteristic
335C4×C139—22no—
336C4×C139—22no—
337C4×C139—26no—
338C4×C139—22no—
339C4×C139—22no—
340C4×C139—41no—
341C4×C139—43no—
342C4×C139—43no—
343C4×C139—43no—
344C4×C139—41no—
345C4×C139—43no—
346C4×C139C2×#121112yes—
347C2×C139—46no—
348C2×C139—42no—
349C2×C139—83no—
350C2×C139C22×#12111yescharacteristic
351C2×C139D4×#4111yescharacteristic
352C2×C139D4×#4111yescharacteristic
353C2×C139#348011yescharacteristic
354C2×C139#348711yescharacteristic
355C2×C139#350011yescharacteristic
356C2×C139#352411yescharacteristic
357#36430C13911yesmaximal, characteristic, direct product factor, Sylow
358C139#3643011yescharacteristic, direct product factor, Sylow
359C2×#550C2×C13911yescharacteristic, complemented
360C2×#548C2×C13911yescharacteristic, complemented
361C2×#548C2×C13911yescharacteristic, complemented
362C2×C4×#41C2×C13911yescharacteristic, complemented
363#2850C2×C13913yescomplemented
364#2544C2×C13913yescomplemented
365#2535C2×C13913yescomplemented
366#2428C2×C13913yescomplemented
367#2427C2×C13913yescomplemented
368#2415C2×C13913yescomplemented
369#2414C2×C13913yescomplemented
370#2351C2×C13911yescharacteristic, complemented
371#2341C2×C13911yescharacteristic, complemented
372Q8×C22⋊C4C2×C13911yescharacteristic, complemented
373C4×#121C2×C13913yescomplemented
374C22×#41C22×C13911yescharacteristic
375C22×#41C22×C13911yescharacteristic
376C23×Q8C22×C13911yescharacteristic
377#550—28no—
378#548—28no—
379#548—28no—
380C2×#127C22×C13913yes—
381C2×#124C22×C13913yes—
382C2×#124C22×C13913yes—
383C2×C22⋊Q8C22×C13913yes—
384C2×C22⋊Q8C22×C13913yes—
385C2×#121C22×C13913yes—
386C2×#121C22×C13913yes—
387C2×#121C22×C13913yes—
388C2×#121C22×C13913yes—
389C2×#121C22×C13913yes—
390C4×#41—28no—
391C2×C4×Q8C22×C13911yescharacteristic
392C2×C4×Q8C22×C13911yescharacteristic
393C2×C4×Q8C22×C13911yescharacteristic
394C2×C4×Q8C22×C13911yescharacteristic
395C2×C4×D4C22×C13913yes—
396C2×C4×D4C22×C13913yes—
397C2×C4×D4C22×C13913yes—
398C2×C4×D4C22×C13913yes—
399C2×C4×D4C22×C13913yes—
400C2×#117C22×C13913yes—
401C22×C42C22×C13913yes—
402#397C22×C13916yes—
403#394C22×C13916yes—
404#394C22×C13916yes—
405#392C22×C13916yes—
406#391C22×C13913yes—
407#391C22×C13913yes—
408#390C22×C13913yes—
409#390C22×C13913yes—
410#390C22×C13913yes—
411#389C22×C13913yes—
412#389C22×C13913yes—
413#389C22×C13913yes—
414#388C22×C13913yes—
415#388C22×C13916yes—
416#388C22×C13911yescharacteristic
417#386C22×C13916yes—
418#386C22×C13916yes—
419#386C22×C13913yes—
420#386C22×C13913yes—
421#382C22×C13913yes—
422#380C22×C13913yes—
423#380C22×C13913yes—
424#380C22×C13913yes—
425C4×C4⋊C4C22×C13913yes—
426C4×C22⋊C4C22×C13913yes—
427C4×C22⋊C4C22×C13913yes—
428C2×#41—24no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41D4×C13918yescomplemented
434C22×Q8—24no—
435C22×Q8—24no—
436C22×Q8—24no—
437C22×Q8C23×C13913yes—
438C22×Q8C23×C13911yescharacteristic
439C22×D4C23×C13913yes—
440C22×D4C23×C13913yes—
441C22×D4C23×C13913yes—
442C22×D4C23×C13913yes—
443C22×D4C23×C13913yes—
444C22×D4C23×C13916yes—
445C23×C4C23×C13913yes—
446C23×C4C23×C13913yes—
447C23×C4C23×C13913yes—
448C23×C4C23×C13913yes—
449C23×C4C23×C13913yes—
450#127—212no—
451#124—212no—
452#124—212no—
453C22⋊Q8—212no—
454C22⋊Q8—212no—
455#121—212no—
456#121—212no—
457#121—212no—
458#121—212no—
459#121—212no—
460C4×Q8—24no—
461C4×Q8—24no—
462C4×Q8—24no—
463C4×Q8D4×C13918yescomplemented
464C4×D4—212no—
465C4×D4—212no—
466C4×D4—212no—
467C4×D4—212no—
468C4×D4—212no—
469#117—212no—
470C2×C4⋊C4C23×C13913yes—
471C2×C4⋊C4C23×C13911yescharacteristic
472C2×C4⋊C4C23×C13913yes—
473C2×C4⋊C4C23×C13913yes—
474C2×C4⋊C4C23×C13913yes—
475C2×C4⋊C4C23×C13913yes—
476C2×C4⋊C4C23×C13913yes—
477C2×C4⋊C4C23×C13913yes—
478C2×C4⋊C4C23×C13913yes—
479C2×C22⋊C4C23×C13916yes—
480C2×C22⋊C4C23×C13911yescharacteristic
481C2×C22⋊C4C23×C13911yescharacteristic
482C2×C22⋊C4C23×C13913yes—
483C2×C22⋊C4C23×C13913yes—
484C2×C22⋊C4C23×C13913yes—
485C2×C22⋊C4C23×C13913yes—
486C2×C22⋊C4C23×C13916yes—
487C2×C22⋊C4C23×C13916yes—
488C2×C22⋊C4C23×C13913yes—
489C2×C22⋊C4C23×C13913yes—
490C2×C22⋊C4C23×C13913yes—
491C2×C22⋊C4C23×C13916yes—
492C2×C22⋊C4C23×C13911yescharacteristic
493C2×C42—212no—
494C2×C42C23×C13913yes—
495C2×C42C23×C13913yes—
496C2×C42C23×C13913yes—
497C2×C42C23×C13913yes—
498C2×C42C23×C13911yescharacteristic
499C2×C42C23×C13913yes—
500#95C23×C13911yescharacteristic
501#95C23×C13913yes—
502#95C23×C13913yes—
503#95C23×C13913yes—
504#95C23×C13911yescharacteristic
505#95C23×C13913yes—
506#95C23×C13916yes—
507#95C23×C13916yes—
508C24C24×C13913yes—
509C24C24×C13913yes—
510C24C24×C13911yescharacteristic
511#41—232no—
512#41—416no—
513C2×Q8—26no—
514C2×Q8—26no—
515C2×Q8—26no—
516C2×Q8—416no—
517C2×Q8C2×D4×C13914yes—
518C2×Q8C2×D4×C13914yes—
519C2×Q8#41×C13914yes—
520C2×D4—26no—
521C2×D4—26no—
522C2×D4—26no—
523C2×D4—26no—
524C2×D4—212no—
525C2×D4—26no—
526C2×D4—26no—
527C2×D4—26no—
528C2×D4—26no—
529C2×D4—26no—
530C2×D4—26no—
531C2×D4—26no—
532C2×D4—43no—
533C2×D4—43no—
534C2×D4—43no—
535C2×D4—46no—
536C2×D4—46no—
537C2×D4C2×D4×C139112yes—
538C22×C4—26no—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—26no—
542C22×C4—26no—
543C22×C4—26no—
544C22×C4—26no—
545C22×C4—26no—
546C22×C4—26no—
547C22×C4—26no—
548C22×C4—26no—
549C22×C4—43no—
550C22×C4—43no—
551C22×C4—43no—
552C22×C4C2×D4×C139112yes—
553C22×C4C24×C13913yes—
554C22×C4C24×C13913yes—
555C22×C4C24×C13913yes—
556C22×C4C24×C13913yes—
557C22×C4C24×C13911yescharacteristic
558C22×C4C24×C13911yescharacteristic
559C22×C4C24×C13911yescharacteristic
560C22×C4C24×C13913yes—
561C22×C4C24×C13911yescharacteristic
562C22×C4C24×C13911yescharacteristic
563C22×C4C24×C13911yescharacteristic
564C22×C4C24×C13913yes—
565C4⋊C4—26no—
566C4⋊C4—22no—
567C4⋊C4—26no—
568C4⋊C4—26no—
569C4⋊C4—26no—
570C4⋊C4—26no—
571C4⋊C4—26no—
572C4⋊C4—43no—
573C4⋊C4C2×D4×C139112yes—
574C22⋊C4—26no—
575C22⋊C4—26no—
576C22⋊C4—212no—
577C22⋊C4—212no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—26no—
581C22⋊C4—26no—
582C22⋊C4—212no—
583C22⋊C4—26no—
584C22⋊C4—43no—
585C22⋊C4—46no—
586C22⋊C4—43no—
587C22⋊C4#41×C13914yescomplemented
588C42—22no—
589C42—26no—
590C42—26no—
591C42—26no—
592C42—26no—
593C42C2×D4×C139112yes—
594C23—23no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—23no—
599C23—23no—
600C23—21no—
601C23—23no—
602C23—23no—
603C23—23no—
604C23—21no—
605C23—21no—
606C23—23no—
607C23—23no—
608C23—23no—
609C23—23no—
610C23—23no—
611C23—23no—
612C23—23no—
613C23C22×D4×C13916yes—
614C23C2×#41×C13912yes—
615C23C25×C13911yescharacteristic
616Q8—412no—
617Q8#121×C139116yescomplemented
618D4—224no—
619D4—412no—
620D4—412no—
621D4—412no—
622D4—412no—
623D4—812no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—23no—
628C2×C4—21no—
629C2×C4—23no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—224no—
635C2×C4—21no—
636C2×C4—23no—
637C2×C4—23no—
638C2×C4—23no—
639C2×C4—21no—
640C2×C4—23no—
641C2×C4—23no—
642C2×C4—21no—
643C2×C4—23no—
644C2×C4—21no—
645C2×C4—23no—
646C2×C4—21no—
647C2×C4—23no—
648C2×C4—23no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—21no—
652C2×C4—23no—
653C2×C4—412no—
654C2×C4—412no—
655C2×C4—412no—
656C2×C4—412no—
657C2×C4C22×D4×C13912yes—
658C2×C4C22×D4×C13916yes—
659C2×C4C22×D4×C13912yes—
660C2×C4C22×D4×C13916yes—
661C2×C4C22×D4×C13916yes—
662C2×C4C2×#41×C13912yes—
663C2×C4C2×#41×C13912yes—
664C2×C4C2×#41×C13916yes—
665C22—26no—
666C22—22no—
667C22—22no—
668C22—26no—
669C22—22no—
670C22—26no—
671C22—41no—
672C22—43no—
673C22—43no—
674C22—43no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—43no—
679C22—43no—
680C22—43no—
681C22—43no—
682C22—43no—
683C22—43no—
684C22—43no—
685C22—43no—
686C22C23×D4×C13911yescharacteristic
687C22C23×D4×C13911yescharacteristic
688C22C22×#41×C13911yescharacteristic
689C22C22×#41×C13911yescharacteristic
690C22#585×C13911yescharacteristic
691C22#585×C13911yescharacteristic
692C22#585×C13911yescharacteristic
693C4—22no—
694C4—22no—
695C4—26no—
696C4—22no—
697C4—22no—
698C4—41no—
699C4—43no—
700C4—43no—
701C4—43no—
702C4—43no—
703C4—41no—
704C4C2×#121×C139112yes—
705C2—46no—
706C2—42no—
707C2—83no—
708C2C22×#121×C13911yescharacteristic
709C2D4×#41×C13911yescharacteristic
710C2D4×#41×C13911yescharacteristic
711C2#3480×C13911yescharacteristic
712C2#3487×C13911yescharacteristic
713C2#3500×C13911yescharacteristic
714C2#3524×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C139C2semidirect
2. C2×#548×C139C2semidirect
3. C2×#548×C139C2semidirect
4. C2×C4×#41×C139C2semidirect
5. #2850×C139C2semidirect
6. #2544×C139C2semidirect
7. #2535×C139C2semidirect
8. #2428×C139C2semidirect
9. #2427×C139C2semidirect
10. #2415×C139C2semidirect
11. #2414×C139C2semidirect
12. #2351×C139C2semidirect
13. #2341×C139C2semidirect
14. Q8×C22⋊C4×C139C2semidirect
15. C4×#121×C139C2semidirect
75. C2×#41×C139D4semidirect
105. C4×Q8×C139D4semidirect
229. C22⋊C4×C139#41semidirect
259. Q8×C139#121semidirect
357. #36430C139direct (N × H)
358. C139#36430direct (N × H)
359. C2×#550C2×C139semidirect
360. C2×#548C2×C139semidirect
361. C2×#548C2×C139semidirect
362. C2×C4×#41C2×C139semidirect
363. #2850C2×C139semidirect
364. #2544C2×C139semidirect
365. #2535C2×C139semidirect
366. #2428C2×C139semidirect
367. #2427C2×C139semidirect
368. #2415C2×C139semidirect
369. #2414C2×C139semidirect
370. #2351C2×C139semidirect
371. #2341C2×C139semidirect
372. Q8×C22⋊C4C2×C139semidirect
373. C4×#121C2×C139semidirect
433. C2×#41D4×C139semidirect
463. C4×Q8D4×C139semidirect
587. C22⋊C4#41×C139semidirect
617. Q8#121×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1392
C2×#548×C1392
C2×C4×#41×C1392
#2850×C1392
#2544×C1392
#2535×C1392
#2428×C1392
#2427×C1392
#2415×C1392
#2414×C1392
#2351×C1392
#2341×C1392
Q8×C22⋊C4×C1392
C4×#121×C1392
#36430139