Finite Group Databasebeta

← C139×#35831 #48030427

Subgroups — C139×#35831 #48030427

Order 35584.

3148 conjugacy classes of subgroups.

The subgroup lattice has 712 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×#520×C139C211yesmaximal, characteristic, complemented
5#2620×C139C213yesmaximal, complemented
6#2544×C139C213yesmaximal, complemented
7#2537×C139C213yesmaximal, complemented
8#2428×C139C213yesmaximal, complemented
9#2427×C139C213yesmaximal, complemented
10#2417×C139C213yesmaximal, complemented
11#2416×C139C213yesmaximal, complemented
12#2392×C139C213yesmaximal, complemented
13Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
14#2341×C139C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C139C211yesmaximal, characteristic, 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×C139C2216yes—
32#520×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×C4⋊C4×C139C2213yes—
44#398×C139C2213yes—
45#397×C139C2213yes—
46#396×C139C2213yes—
47#396×C139C2216yes—
48#396×C139C2211yescharacteristic
49#394×C139C2213yes—
50#394×C139C2216yes—
51#394×C139C2213yes—
52#394×C139C2216yes—
53#394×C139C2213yes—
54#392×C139C2213yes—
55#391×C139C2213yes—
56#391×C139C2213yes—
57#390×C139C2213yes—
58#390×C139C2213yes—
59#389×C139C2213yes—
60#389×C139C2213yes—
61#386×C139C2216yes—
62#386×C139C2216yes—
63#384×C139C2213yes—
64#380×C139C2213yes—
65#380×C139C2213yes—
66#380×C139C2216yes—
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×C139C2316yes—
91#127×C139—212no—
92#124×C139—212no—
93#124×C139—212no—
94C22⋊Q8×C139—212no—
95C22⋊Q8×C139—212no—
96#121×C139—212no—
97#121×C139—212no—
98#121×C139—212no—
99#121×C139—212no—
100#121×C139—412no—
101C4×Q8×C139—24no—
102C4×Q8×C139—24no—
103C4×Q8×C139—24no—
104C4×Q8×C139D418yescomplemented
105C4×D4×C139—212no—
106C4×D4×C139—212no—
107C4×D4×C139—212no—
108C4×D4×C139—212no—
109C4×D4×C139—212no—
110#117×C139—212no—
111C2×C4⋊C4×C139—212no—
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2313yes—
114C2×C4⋊C4×C139C2313yes—
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2313yes—
118C2×C4⋊C4×C139C2313yes—
119C2×C4⋊C4×C139C2313yes—
120C2×C4⋊C4×C139C2313yes—
121C2×C4⋊C4×C139C2316yes—
122C2×C4⋊C4×C139C2313yes—
123C2×C4⋊C4×C139C2313yes—
124C2×C22⋊C4×C139C2313yes—
125C2×C22⋊C4×C139C2311yescharacteristic
126C2×C22⋊C4×C139C2311yescharacteristic
127C2×C22⋊C4×C139C2313yes—
128C2×C22⋊C4×C139C2316yes—
129C2×C22⋊C4×C139C2311yescharacteristic
130C2×C22⋊C4×C139C2313yes—
131C2×C22⋊C4×C139C2313yes—
132C2×C22⋊C4×C139C2313yes—
133C2×C22⋊C4×C139C2313yes—
134C2×C22⋊C4×C139C2313yes—
135C2×C22⋊C4×C139C2316yes—
136C2×C22⋊C4×C139C2316yes—
137C2×C22⋊C4×C139C2313yes—
138C2×C22⋊C4×C139C2313yes—
139C2×C42×C139C2313yes—
140C2×C42×C139C2313yes—
141C2×C42×C139C2313yes—
142C2×C42×C139C2313yes—
143#95×C139C2311yescharacteristic
144#95×C139C2313yes—
145#95×C139C2316yes—
146#95×C139C2313yes—
147#95×C139C2313yes—
148#95×C139C2313yes—
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—212no—
189C22×C4×C139—46no—
190C22×C4×C139—46no—
191C22×C4×C139C2×D4112yes—
192C22×C4×C139C2411yescharacteristic
193C22×C4×C139C2411yescharacteristic
194C22×C4×C139C2413yes—
195C22×C4×C139C2413yes—
196C22×C4×C139C2413yes—
197C22×C4×C139C2411yescharacteristic
198C22×C4×C139C2413yes—
199C22×C4×C139C2413yes—
200C22×C4×C139C2411yescharacteristic
201C22×C4×C139C2411yescharacteristic
202C22×C4×C139C2411yescharacteristic
203C22×C4×C139C2413yes—
204C4⋊C4×C139—26no—
205C4⋊C4×C139—26no—
206C4⋊C4×C139—22no—
207C4⋊C4×C139—22no—
208C4⋊C4×C139—26no—
209C4⋊C4×C139—26no—
210C4⋊C4×C139—26no—
211C4⋊C4×C139—26no—
212C4⋊C4×C139—22no—
213C4⋊C4×C139—43no—
214C4⋊C4×C139—46no—
215C4⋊C4×C139C2×D4112yes—
216C22⋊C4×C139—26no—
217C22⋊C4×C139—26no—
218C22⋊C4×C139—212no—
219C22⋊C4×C139—26no—
220C22⋊C4×C139—26no—
221C22⋊C4×C139—26no—
222C22⋊C4×C139—22no—
223C22⋊C4×C139—22no—
224C22⋊C4×C139—26no—
225C22⋊C4×C139—26no—
226C22⋊C4×C139—212no—
227C22⋊C4×C139—22no—
228C22⋊C4×C139—43no—
229C22⋊C4×C139—43no—
230C22⋊C4×C139—46no—
231C42×C139—26no—
232C42×C139—26no—
233C42×C139—26no—
234C42×C139C2×D4112yes—
235C23×C139—23no—
236C23×C139—21no—
237C23×C139—21no—
238C23×C139—21no—
239C23×C139—23no—
240C23×C139—23no—
241C23×C139—21no—
242C23×C139—23no—
243C23×C139—23no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—23no—
247C23×C139—23no—
248C23×C139—23no—
249C23×C139—23no—
250C23×C139—23no—
251C23×C139—23no—
252C23×C139—23no—
253C23×C139—23no—
254C23×C139C22×D416yes—
255C23×C139H(5,𝔽2)12yes—
256C23×C139C2511yescharacteristic
257Q8×C139—412no—
258Q8×C139#121116yescomplemented
259D4×C139—224no—
260D4×C139—412no—
261D4×C139—412no—
262D4×C139—412no—
263D4×C139—412no—
264D4×C139—812no—
265C2×C4×C139—21no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
268C2×C4×C139—23no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—23no—
272C2×C4×C139—21no—
273C2×C4×C139—224no—
274C2×C4×C139—21no—
275C2×C4×C139—21no—
276C2×C4×C139—23no—
277C2×C4×C139—23no—
278C2×C4×C139—23no—
279C2×C4×C139—21no—
280C2×C4×C139—23no—
281C2×C4×C139—23no—
282C2×C4×C139—21no—
283C2×C4×C139—21no—
284C2×C4×C139—23no—
285C2×C4×C139—23no—
286C2×C4×C139—23no—
287C2×C4×C139—23no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—23no—
293C2×C4×C139—23no—
294C2×C4×C139—23no—
295C2×C4×C139—412no—
296C2×C4×C139—412no—
297C2×C4×C139—812no—
298C2×C4×C139C22×D412yes—
299C2×C4×C139C22×D416yes—
300C2×C4×C139C22×D412yes—
301C2×C4×C139C22×D416yes—
302C2×C4×C139C22×D416yes—
303C2×C4×C139C2×#4116yes—
304C2×C4×C1392−1+412yes—
305C22×C139—26no—
306C22×C139—22no—
307C22×C139—22no—
308C22×C139—26no—
309C22×C139—26no—
310C22×C139—22no—
311C22×C139—41no—
312C22×C139—43no—
313C22×C139—41no—
314C22×C139—43no—
315C22×C139—41no—
316C22×C139—43no—
317C22×C139—41no—
318C22×C139—43no—
319C22×C139—43no—
320C22×C139—43no—
321C22×C139—43no—
322C22×C139—43no—
323C22×C139—43no—
324C22×C139—43no—
325C22×C139—43no—
326C22×C139C23×D411yescharacteristic
327C22×C139C23×D411yescharacteristic
328C22×C139C22×#4111yescharacteristic
329C22×C139C2×H(5,𝔽2)11yescharacteristic
330C22×C139C2×2−1+411yescharacteristic
331C22×C139#58511yescharacteristic
332C22×C139#58511yescharacteristic
333C4×C139—22no—
334C4×C139—26no—
335C4×C139—22no—
336C4×C139—22no—
337C4×C139—41no—
338C4×C139—43no—
339C4×C139—43no—
340C4×C139—43no—
341C4×C139—43no—
342C4×C139—41no—
343C4×C139—41no—
344C4×C139C2×#121112yes—
345C2×C139—46no—
346C2×C139—42no—
347C2×C139—83no—
348C2×C139C22×#12111yescharacteristic
349C2×C139#348811yescharacteristic
350C2×C139#348811yescharacteristic
351C2×C139#348911yescharacteristic
352C2×C139#349711yescharacteristic
353C2×C139#352211yescharacteristic
354C2×C139#352411yescharacteristic
355#35831C13911yesmaximal, characteristic, direct product factor, Sylow
356C139#3583111yescharacteristic, direct product factor, Sylow
357C2×#550C2×C13911yescharacteristic, complemented
358C2×#548C2×C13911yescharacteristic, complemented
359C2×#548C2×C13911yescharacteristic, complemented
360C2×#520C2×C13911yescharacteristic, complemented
361#2620C2×C13913yescomplemented
362#2544C2×C13913yescomplemented
363#2537C2×C13913yescomplemented
364#2428C2×C13913yescomplemented
365#2427C2×C13913yescomplemented
366#2417C2×C13913yescomplemented
367#2416C2×C13913yescomplemented
368#2392C2×C13913yescomplemented
369Q8×C4⋊C4C2×C13911yescharacteristic, complemented
370#2341C2×C13911yescharacteristic, complemented
371Q8×C22⋊C4C2×C13911yescharacteristic, complemented
372C22×#41C22×C13911yescharacteristic
373C22×#41C22×C13911yescharacteristic
374C23×Q8C22×C13911yescharacteristic
375#550—28no—
376#548—28no—
377#548—28no—
378C2×#127C22×C13913yes—
379C2×#124C22×C13913yes—
380C2×#124C22×C13913yes—
381C2×C22⋊Q8C22×C13913yes—
382C2×C22⋊Q8C22×C13913yes—
383C2×#121C22×C13913yes—
384C2×#121C22×C13913yes—
385C2×#121C22×C13913yes—
386C2×#121C22×C13913yes—
387C2×#121C22×C13916yes—
388#520—28no—
389C2×C4×Q8C22×C13911yescharacteristic
390C2×C4×Q8C22×C13911yescharacteristic
391C2×C4×Q8C22×C13911yescharacteristic
392C2×C4×Q8C22×C13911yescharacteristic
393C2×C4×D4C22×C13913yes—
394C2×C4×D4C22×C13913yes—
395C2×C4×D4C22×C13913yes—
396C2×C4×D4C22×C13913yes—
397C2×C4×D4C22×C13913yes—
398C2×#117C22×C13913yes—
399C22×C4⋊C4C22×C13913yes—
400#398C22×C13913yes—
401#397C22×C13913yes—
402#396C22×C13913yes—
403#396C22×C13916yes—
404#396C22×C13911yescharacteristic
405#394C22×C13916yes—
406#394C22×C13916yes—
407#394C22×C13913yes—
408#394C22×C13913yes—
409#394C22×C13913yes—
410#392C22×C13913yes—
411#391C22×C13913yes—
412#391C22×C13913yes—
413#390C22×C13913yes—
414#390C22×C13913yes—
415#389C22×C13913yes—
416#389C22×C13913yes—
417#386C22×C13916yes—
418#386C22×C13916yes—
419#384C22×C13913yes—
420#380C22×C13913yes—
421#380C22×C13913yes—
422#380C22×C13916yes—
423C4×C4⋊C4C22×C13913yes—
424C4×C22⋊C4C22×C13913yes—
425C4×C22⋊C4C22×C13913yes—
426C2×#41—24no—
427C2×#41—24no—
428C2×#41—24no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41D4×C13918yescomplemented
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C23×C13913yes—
436C22×Q8C23×C13911yescharacteristic
437C22×D4C23×C13913yes—
438C22×D4C23×C13913yes—
439C22×D4C23×C13913yes—
440C22×D4C23×C13913yes—
441C22×D4C23×C13913yes—
442C22×D4C23×C13916yes—
443C23×C4C23×C13913yes—
444C23×C4C23×C13913yes—
445C23×C4C23×C13913yes—
446C23×C4C23×C13916yes—
447#127—212no—
448#124—212no—
449#124—212no—
450C22⋊Q8—212no—
451C22⋊Q8—212no—
452#121—212no—
453#121—212no—
454#121—212no—
455#121—212no—
456#121—412no—
457C4×Q8—24no—
458C4×Q8—24no—
459C4×Q8—24no—
460C4×Q8D4×C13918yescomplemented
461C4×D4—212no—
462C4×D4—212no—
463C4×D4—212no—
464C4×D4—212no—
465C4×D4—212no—
466#117—212no—
467C2×C4⋊C4—212no—
468C2×C4⋊C4C23×C13913yes—
469C2×C4⋊C4C23×C13913yes—
470C2×C4⋊C4C23×C13911yescharacteristic
471C2×C4⋊C4C23×C13911yescharacteristic
472C2×C4⋊C4C23×C13913yes—
473C2×C4⋊C4C23×C13913yes—
474C2×C4⋊C4C23×C13913yes—
475C2×C4⋊C4C23×C13913yes—
476C2×C4⋊C4C23×C13911yescharacteristic
477C2×C4⋊C4C23×C13916yes—
478C2×C4⋊C4C23×C13913yes—
479C2×C4⋊C4C23×C13913yes—
480C2×C22⋊C4C23×C13913yes—
481C2×C22⋊C4C23×C13913yes—
482C2×C22⋊C4C23×C13911yescharacteristic
483C2×C22⋊C4C23×C13911yescharacteristic
484C2×C22⋊C4C23×C13913yes—
485C2×C22⋊C4C23×C13913yes—
486C2×C22⋊C4C23×C13913yes—
487C2×C22⋊C4C23×C13913yes—
488C2×C22⋊C4C23×C13913yes—
489C2×C22⋊C4C23×C13916yes—
490C2×C22⋊C4C23×C13916yes—
491C2×C22⋊C4C23×C13911yescharacteristic
492C2×C22⋊C4C23×C13916yes—
493C2×C22⋊C4C23×C13913yes—
494C2×C22⋊C4C23×C13913yes—
495C2×C42C23×C13913yes—
496C2×C42C23×C13913yes—
497C2×C42C23×C13913yes—
498C2×C42C23×C13913yes—
499#95C23×C13911yescharacteristic
500#95C23×C13913yes—
501#95C23×C13913yes—
502#95C23×C13913yes—
503#95C23×C13913yes—
504#95C23×C13913yes—
505#95C23×C13916yes—
506C24C24×C13913yes—
507C24C24×C13913yes—
508C24C24×C13911yescharacteristic
509#41—232no—
510#41—416no—
511C2×Q8—26no—
512C2×Q8—26no—
513C2×Q8—26no—
514C2×Q8—416no—
515C2×Q8C2×D4×C13914yes—
516C2×Q8C2×D4×C13914yes—
517C2×Q8#41×C13914yes—
518C2×D4—26no—
519C2×D4—26no—
520C2×D4—26no—
521C2×D4—26no—
522C2×D4—212no—
523C2×D4—26no—
524C2×D4—26no—
525C2×D4—26no—
526C2×D4—26no—
527C2×D4—26no—
528C2×D4—26no—
529C2×D4—26no—
530C2×D4—43no—
531C2×D4—43no—
532C2×D4—43no—
533C2×D4—46no—
534C2×D4—46no—
535C2×D4C2×D4×C139112yes—
536C22×C4—26no—
537C22×C4—26no—
538C22×C4—26no—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—26no—
542C22×C4—26no—
543C22×C4—26no—
544C22×C4—212no—
545C22×C4—46no—
546C22×C4—46no—
547C22×C4C2×D4×C139112yes—
548C22×C4C24×C13911yescharacteristic
549C22×C4C24×C13911yescharacteristic
550C22×C4C24×C13913yes—
551C22×C4C24×C13913yes—
552C22×C4C24×C13913yes—
553C22×C4C24×C13911yescharacteristic
554C22×C4C24×C13913yes—
555C22×C4C24×C13913yes—
556C22×C4C24×C13911yescharacteristic
557C22×C4C24×C13911yescharacteristic
558C22×C4C24×C13911yescharacteristic
559C22×C4C24×C13913yes—
560C4⋊C4—26no—
561C4⋊C4—26no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—26no—
565C4⋊C4—26no—
566C4⋊C4—26no—
567C4⋊C4—26no—
568C4⋊C4—22no—
569C4⋊C4—43no—
570C4⋊C4—46no—
571C4⋊C4C2×D4×C139112yes—
572C22⋊C4—26no—
573C22⋊C4—26no—
574C22⋊C4—212no—
575C22⋊C4—26no—
576C22⋊C4—26no—
577C22⋊C4—26no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—26no—
581C22⋊C4—26no—
582C22⋊C4—212no—
583C22⋊C4—22no—
584C22⋊C4—43no—
585C22⋊C4—43no—
586C22⋊C4—46no—
587C42—26no—
588C42—26no—
589C42—26no—
590C42C2×D4×C139112yes—
591C23—23no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—23no—
596C23—23no—
597C23—21no—
598C23—23no—
599C23—23no—
600C23—21no—
601C23—21no—
602C23—23no—
603C23—23no—
604C23—23no—
605C23—23no—
606C23—23no—
607C23—23no—
608C23—23no—
609C23—23no—
610C23C22×D4×C13916yes—
611C23H(5,𝔽2)×C13912yes—
612C23C25×C13911yescharacteristic
613Q8—412no—
614Q8#121×C139116yescomplemented
615D4—224no—
616D4—412no—
617D4—412no—
618D4—412no—
619D4—412no—
620D4—812no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—23no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—23no—
628C2×C4—21no—
629C2×C4—224no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—23no—
633C2×C4—23no—
634C2×C4—23no—
635C2×C4—21no—
636C2×C4—23no—
637C2×C4—23no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—23no—
641C2×C4—23no—
642C2×C4—23no—
643C2×C4—23no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—23no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—412no—
652C2×C4—412no—
653C2×C4—812no—
654C2×C4C22×D4×C13912yes—
655C2×C4C22×D4×C13916yes—
656C2×C4C22×D4×C13912yes—
657C2×C4C22×D4×C13916yes—
658C2×C4C22×D4×C13916yes—
659C2×C4C2×#41×C13916yes—
660C2×C42−1+4×C13912yes—
661C22—26no—
662C22—22no—
663C22—22no—
664C22—26no—
665C22—26no—
666C22—22no—
667C22—41no—
668C22—43no—
669C22—41no—
670C22—43no—
671C22—41no—
672C22—43no—
673C22—41no—
674C22—43no—
675C22—43no—
676C22—43no—
677C22—43no—
678C22—43no—
679C22—43no—
680C22—43no—
681C22—43no—
682C22C23×D4×C13911yescharacteristic
683C22C23×D4×C13911yescharacteristic
684C22C22×#41×C13911yescharacteristic
685C22C2×H(5,𝔽2)×C13911yescharacteristic
686C22C2×2−1+4×C13911yescharacteristic
687C22#585×C13911yescharacteristic
688C22#585×C13911yescharacteristic
689C4—22no—
690C4—26no—
691C4—22no—
692C4—22no—
693C4—41no—
694C4—43no—
695C4—43no—
696C4—43no—
697C4—43no—
698C4—41no—
699C4—41no—
700C4C2×#121×C139112yes—
701C2—46no—
702C2—42no—
703C2—83no—
704C2C22×#121×C13911yescharacteristic
705C2#3488×C13911yescharacteristic
706C2#3488×C13911yescharacteristic
707C2#3489×C13911yescharacteristic
708C2#3497×C13911yescharacteristic
709C2#3522×C13911yescharacteristic
710C2#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×#520×C139C2semidirect
5. #2620×C139C2semidirect
6. #2544×C139C2semidirect
7. #2537×C139C2semidirect
8. #2428×C139C2semidirect
9. #2427×C139C2semidirect
10. #2417×C139C2semidirect
11. #2416×C139C2semidirect
12. #2392×C139C2semidirect
13. Q8×C4⋊C4×C139C2semidirect
14. #2341×C139C2semidirect
15. Q8×C22⋊C4×C139C2semidirect
75. C2×#41×C139D4semidirect
104. C4×Q8×C139D4semidirect
258. Q8×C139#121semidirect
355. #35831C139direct (N × H)
356. C139#35831direct (N × H)
357. C2×#550C2×C139semidirect
358. C2×#548C2×C139semidirect
359. C2×#548C2×C139semidirect
360. C2×#520C2×C139semidirect
361. #2620C2×C139semidirect
362. #2544C2×C139semidirect
363. #2537C2×C139semidirect
364. #2428C2×C139semidirect
365. #2427C2×C139semidirect
366. #2417C2×C139semidirect
367. #2416C2×C139semidirect
368. #2392C2×C139semidirect
369. Q8×C4⋊C4C2×C139semidirect
370. #2341C2×C139semidirect
371. Q8×C22⋊C4C2×C139semidirect
431. C2×#41D4×C139semidirect
460. C4×Q8D4×C139semidirect
614. 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×#520×C1392
#2620×C1392
#2544×C1392
#2537×C1392
#2428×C1392
#2427×C1392
#2417×C1392
#2416×C1392
#2392×C1392
Q8×C4⋊C4×C1392
#2341×C1392
Q8×C22⋊C4×C1392
#35831139