Finite Group Databasebeta

← C139×#35771 #48030367

Subgroups — C139×#35771 #48030367

Order 35584.

2948 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C211yesmaximal, characteristic, complemented
3C2×#548×C139C211yesmaximal, characteristic, complemented
4C2×#519×C139C211yesmaximal, characteristic, complemented
5#2620×C139C213yesmaximal, complemented
6#2545×C139C213yesmaximal, complemented
7#2538×C139C213yesmaximal, complemented
8#2429×C139C213yesmaximal, complemented
9#2426×C139C213yesmaximal, complemented
10#2415×C139C213yesmaximal, complemented
11#2414×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
17C23×Q8×C139C2211yescharacteristic
18C23×Q8×C139C2211yescharacteristic
19D4×Q8×C139—28no—
20#548×C139—28no—
21#548×C139—28no—
22C2×C4⋊Q8×C139C2213yes—
23C2×#124×C139C2213yes—
24C2×#124×C139C2213yes—
25C2×C22⋊Q8×C139C2213yes—
26C2×C22⋊Q8×C139C2213yes—
27C2×C22⋊Q8×C139C2213yes—
28C2×C22⋊Q8×C139C2213yes—
29C2×#121×C139C2213yes—
30C2×#121×C139C2213yes—
31#519×C139—28no—
32C2×C4×Q8×C139C2213yes—
33C2×C4×Q8×C139C2211yescharacteristic
34C2×C4×Q8×C139C2211yescharacteristic
35C2×C4×Q8×C139C2211yescharacteristic
36C2×C4×Q8×C139C2213yes—
37C2×C4×Q8×C139C2211yescharacteristic
38C2×C4×D4×C139C2213yes—
39C2×C4×D4×C139C2213yes—
40C2×C4×D4×C139C2213yes—
41C2×#117×C139C2213yes—
42C2×#117×C139C2213yes—
43#398×C139C2213yes—
44#397×C139C2213yes—
45#396×C139C2213yes—
46#396×C139C2216yes—
47#396×C139C2213yes—
48#396×C139C2216yes—
49#394×C139C2213yes—
50#394×C139C2216yes—
51#394×C139C2211yescharacteristic
52#394×C139C2213yes—
53#392×C139C2213yes—
54#391×C139C2213yes—
55#391×C139C2213yes—
56#390×C139C2216yes—
57#390×C139C2213yes—
58#390×C139C2213yes—
59#389×C139C2216yes—
60#389×C139C2213yes—
61#389×C139C2213yes—
62#388×C139C2216yes—
63#388×C139C2216yes—
64#384×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—
73C22×Q8×C139—24no—
74C22×Q8×C139—24no—
75C22×Q8×C139—24no—
76C22×Q8×C139—24no—
77C22×Q8×C139—24no—
78C22×Q8×C139D418yescomplemented
79C22×Q8×C139C2313yes—
80C22×Q8×C139C2313yes—
81C22×Q8×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2313yes—
84C22×D4×C139C2313yes—
85C22×D4×C139C2313yes—
86C23×C4×C139C2313yes—
87C23×C4×C139C2313yes—
88C23×C4×C139C2313yes—
89C4⋊Q8×C139—212no—
90#124×C139—212no—
91#124×C139—212no—
92C22⋊Q8×C139—212no—
93C22⋊Q8×C139—212no—
94C22⋊Q8×C139—212no—
95C22⋊Q8×C139—212no—
96#121×C139—212no—
97#121×C139—212no—
98C4×Q8×C139—24no—
99C4×Q8×C139—24no—
100C4×Q8×C139—24no—
101C4×Q8×C139—212no—
102C4×Q8×C139—212no—
103C4×Q8×C139D418yescomplemented
104C4×D4×C139—212no—
105C4×D4×C139—212no—
106C4×D4×C139—212no—
107#117×C139—212no—
108#117×C139—212no—
109C2×C4⋊C4×C139C2313yes—
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2313yes—
112C2×C4⋊C4×C139C2316yes—
113C2×C4⋊C4×C139C2313yes—
114C2×C4⋊C4×C139C2313yes—
115C2×C4⋊C4×C139C2313yes—
116C2×C4⋊C4×C139C2313yes—
117C2×C4⋊C4×C139C2313yes—
118C2×C4⋊C4×C139C2313yes—
119C2×C4⋊C4×C139C2313yes—
120C2×C4⋊C4×C139C2316yes—
121C2×C4⋊C4×C139C2313yes—
122C2×C22⋊C4×C139C2311yescharacteristic
123C2×C22⋊C4×C139C2313yes—
124C2×C22⋊C4×C139C2316yes—
125C2×C22⋊C4×C139C2313yes—
126C2×C22⋊C4×C139C2313yes—
127C2×C22⋊C4×C139C2316yes—
128C2×C22⋊C4×C139C2313yes—
129C2×C22⋊C4×C139C2311yescharacteristic
130C2×C22⋊C4×C139C2313yes—
131C2×C22⋊C4×C139C2313yes—
132C2×C22⋊C4×C139C2311yescharacteristic
133C2×C22⋊C4×C139C2311yescharacteristic
134C2×C22⋊C4×C139C2313yes—
135C2×C22⋊C4×C139C2313yes—
136C2×C22⋊C4×C139C2316yes—
137C2×C42×C139C2313yes—
138C2×C42×C139C2316yes—
139C2×C42×C139C2313yes—
140C2×C42×C139C2313yes—
141C2×C42×C139C2313yes—
142#95×C139C2313yes—
143#95×C139C2313yes—
144#95×C139C2313yes—
145#95×C139C2316yes—
146#95×C139C2313yes—
147#95×C139C2311yescharacteristic
148#95×C139C2313yes—
149C24×C139C2413yes—
150C24×C139C2411yescharacteristic
151C24×C139C2411yescharacteristic
152#41×C139—416no—
153C2×Q8×C139—232no—
154C2×Q8×C139—26no—
155C2×Q8×C139—26no—
156C2×Q8×C139—26no—
157C2×Q8×C139—26no—
158C2×Q8×C139—26no—
159C2×Q8×C139—416no—
160C2×Q8×C139C2×D4112yes—
161C2×Q8×C139C2×D414yes—
162C2×Q8×C139C2×D414yes—
163C2×Q8×C139#4114yes—
164C2×D4×C139—22no—
165C2×D4×C139—22no—
166C2×D4×C139—26no—
167C2×D4×C139—26no—
168C2×D4×C139—26no—
169C2×D4×C139—26no—
170C2×D4×C139—26no—
171C2×D4×C139—26no—
172C2×D4×C139—22no—
173C2×D4×C139—43no—
174C2×D4×C139—43no—
175C2×D4×C139—43no—
176C22×C4×C139—26no—
177C22×C4×C139—26no—
178C22×C4×C139—26no—
179C22×C4×C139—26no—
180C22×C4×C139—26no—
181C22×C4×C139—26no—
182C22×C4×C139—26no—
183C22×C4×C139—26no—
184C22×C4×C139C2×D4112yes—
185C22×C4×C139C2411yescharacteristic
186C22×C4×C139C2411yescharacteristic
187C22×C4×C139C2413yes—
188C22×C4×C139C2413yes—
189C22×C4×C139C2413yes—
190C22×C4×C139C2411yescharacteristic
191C22×C4×C139C2413yes—
192C22×C4×C139C2413yes—
193C22×C4×C139C2411yescharacteristic
194C22×C4×C139C2413yes—
195C22×C4×C139C2411yescharacteristic
196C22×C4×C139C2413yes—
197C4⋊C4×C139—26no—
198C4⋊C4×C139—26no—
199C4⋊C4×C139—26no—
200C4⋊C4×C139—26no—
201C4⋊C4×C139—26no—
202C4⋊C4×C139—26no—
203C4⋊C4×C139—26no—
204C4⋊C4×C139—26no—
205C4⋊C4×C139—212no—
206C4⋊C4×C139—22no—
207C4⋊C4×C139—43no—
208C4⋊C4×C139—46no—
209C4⋊C4×C139C2×D4112yes—
210C22⋊C4×C139—22no—
211C22⋊C4×C139—26no—
212C22⋊C4×C139—22no—
213C22⋊C4×C139—26no—
214C22⋊C4×C139—22no—
215C22⋊C4×C139—22no—
216C22⋊C4×C139—26no—
217C22⋊C4×C139—26no—
218C22⋊C4×C139—26no—
219C22⋊C4×C139—212no—
220C22⋊C4×C139—212no—
221C22⋊C4×C139—26no—
222C22⋊C4×C139—46no—
223C22⋊C4×C139—43no—
224C22⋊C4×C139—43no—
225C42×C139—212no—
226C42×C139—26no—
227C42×C139—26no—
228C42×C139—26no—
229C42×C139C2×D4112yes—
230C23×C139—21no—
231C23×C139—21no—
232C23×C139—21no—
233C23×C139—21no—
234C23×C139—21no—
235C23×C139—21no—
236C23×C139—21no—
237C23×C139—21no—
238C23×C139—21no—
239C23×C139—21no—
240C23×C139—21no—
241C23×C139—21no—
242C23×C139—23no—
243C23×C139—23no—
244C23×C139—23no—
245C23×C139—23no—
246C23×C139—23no—
247C23×C139—23no—
248C23×C139—23no—
249C23×C139C22×D412yes—
250C23×C1392−1+412yes—
251C23×C139C2511yescharacteristic
252Q8×C139—224no—
253Q8×C139—412no—
254Q8×C139#121116yes—
255D4×C139—28no—
256D4×C139—412no—
257D4×C139—412no—
258D4×C139—412no—
259C2×C4×C139—21no—
260C2×C4×C139—23no—
261C2×C4×C139—23no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—23no—
265C2×C4×C139—21no—
266C2×C4×C139—23no—
267C2×C4×C139—224no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—23no—
271C2×C4×C139—23no—
272C2×C4×C139—23no—
273C2×C4×C139—23no—
274C2×C4×C139—21no—
275C2×C4×C139—21no—
276C2×C4×C139—23no—
277C2×C4×C139—21no—
278C2×C4×C139—23no—
279C2×C4×C139—21no—
280C2×C4×C139—21no—
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—23no—
289C2×C4×C139—412no—
290C2×C4×C139—412no—
291C2×C4×C139C22×D416yes—
292C2×C4×C139C22×D412yes—
293C2×C4×C139C22×D416yes—
294C2×C4×C139C22×D416yes—
295C2×C4×C139C22×D416yes—
296C2×C4×C139C2×#4116yes—
297C2×C4×C1392−1+412yes—
298C22×C139—22no—
299C22×C139—22no—
300C22×C139—22no—
301C22×C139—22no—
302C22×C139—22no—
303C22×C139—22no—
304C22×C139—41no—
305C22×C139—41no—
306C22×C139—41no—
307C22×C139—41no—
308C22×C139—41no—
309C22×C139—41no—
310C22×C139—41no—
311C22×C139—41no—
312C22×C139—43no—
313C22×C139—43no—
314C22×C139—43no—
315C22×C139—43no—
316C22×C139—43no—
317C22×C139—43no—
318C22×C139—43no—
319C22×C139C23×D411yescharacteristic
320C22×C139C23×D411yescharacteristic
321C22×C139C22×#4111yescharacteristic
322C22×C139C2×2−1+411yescharacteristic
323C22×C139C2×2−1+411yescharacteristic
324C22×C139#58511yescharacteristic
325C22×C139#58511yescharacteristic
326C4×C139—26no—
327C4×C139—22no—
328C4×C139—26no—
329C4×C139—22no—
330C4×C139—41no—
331C4×C139—43no—
332C4×C139—41no—
333C4×C139—43no—
334C4×C139—43no—
335C4×C139—41no—
336C4×C139—43no—
337C4×C139C2×#121112yes—
338C2×C139—42no—
339C2×C139—42no—
340C2×C139—83no—
341C2×C139C22×#12111yescharacteristic
342C2×C139#348611yescharacteristic
343C2×C139#348711yescharacteristic
344C2×C139#348911yescharacteristic
345C2×C139#349711yescharacteristic
346C2×C139#351611yescharacteristic
347C2×C139#351811yescharacteristic
348#35771C13911yesmaximal, characteristic, direct product factor, Sylow
349C139#3577111yescharacteristic, direct product factor, Sylow
350C2×D4×Q8C2×C13911yescharacteristic, complemented
351C2×#548C2×C13911yescharacteristic, complemented
352C2×#548C2×C13911yescharacteristic, complemented
353C2×#519C2×C13911yescharacteristic, complemented
354#2620C2×C13913yescomplemented
355#2545C2×C13913yescomplemented
356#2538C2×C13913yescomplemented
357#2429C2×C13913yescomplemented
358#2426C2×C13913yescomplemented
359#2415C2×C13913yescomplemented
360#2414C2×C13913yescomplemented
361#2392C2×C13913yescomplemented
362Q8×C4⋊C4C2×C13911yescharacteristic, complemented
363#2341C2×C13911yescharacteristic, complemented
364Q8×C22⋊C4C2×C13911yescharacteristic, complemented
365C22×#41C22×C13911yescharacteristic
366C23×Q8C22×C13911yescharacteristic
367C23×Q8C22×C13911yescharacteristic
368D4×Q8—28no—
369#548—28no—
370#548—28no—
371C2×C4⋊Q8C22×C13913yes—
372C2×#124C22×C13913yes—
373C2×#124C22×C13913yes—
374C2×C22⋊Q8C22×C13913yes—
375C2×C22⋊Q8C22×C13913yes—
376C2×C22⋊Q8C22×C13913yes—
377C2×C22⋊Q8C22×C13913yes—
378C2×#121C22×C13913yes—
379C2×#121C22×C13913yes—
380#519—28no—
381C2×C4×Q8C22×C13911yescharacteristic
382C2×C4×Q8C22×C13911yescharacteristic
383C2×C4×Q8C22×C13911yescharacteristic
384C2×C4×Q8C22×C13913yes—
385C2×C4×Q8C22×C13913yes—
386C2×C4×Q8C22×C13911yescharacteristic
387C2×C4×D4C22×C13913yes—
388C2×C4×D4C22×C13913yes—
389C2×C4×D4C22×C13913yes—
390C2×#117C22×C13913yes—
391C2×#117C22×C13913yes—
392#398C22×C13913yes—
393#397C22×C13913yes—
394#396C22×C13916yes—
395#396C22×C13916yes—
396#396C22×C13913yes—
397#396C22×C13913yes—
398#394C22×C13913yes—
399#394C22×C13916yes—
400#394C22×C13911yescharacteristic
401#394C22×C13913yes—
402#392C22×C13913yes—
403#391C22×C13913yes—
404#391C22×C13913yes—
405#390C22×C13913yes—
406#390C22×C13913yes—
407#390C22×C13916yes—
408#389C22×C13913yes—
409#389C22×C13913yes—
410#389C22×C13916yes—
411#388C22×C13916yes—
412#388C22×C13916yes—
413#384C22×C13913yes—
414#380C22×C13913yes—
415#380C22×C13913yes—
416C4×C4⋊C4C22×C13913yes—
417C4×C22⋊C4C22×C13913yes—
418C4×C22⋊C4C22×C13913yes—
419C2×#41—24no—
420C2×#41—24no—
421C2×#41—24no—
422C22×Q8—24no—
423C22×Q8—24no—
424C22×Q8—24no—
425C22×Q8—24no—
426C22×Q8—24no—
427C22×Q8D4×C13918yescomplemented
428C22×Q8C23×C13913yes—
429C22×Q8C23×C13913yes—
430C22×Q8C23×C13911yescharacteristic
431C22×D4C23×C13911yescharacteristic
432C22×D4C23×C13913yes—
433C22×D4C23×C13913yes—
434C22×D4C23×C13913yes—
435C23×C4C23×C13913yes—
436C23×C4C23×C13913yes—
437C23×C4C23×C13913yes—
438C4⋊Q8—212no—
439#124—212no—
440#124—212no—
441C22⋊Q8—212no—
442C22⋊Q8—212no—
443C22⋊Q8—212no—
444C22⋊Q8—212no—
445#121—212no—
446#121—212no—
447C4×Q8—24no—
448C4×Q8—24no—
449C4×Q8—24no—
450C4×Q8—212no—
451C4×Q8—212no—
452C4×Q8D4×C13918yescomplemented
453C4×D4—212no—
454C4×D4—212no—
455C4×D4—212no—
456#117—212no—
457#117—212no—
458C2×C4⋊C4C23×C13913yes—
459C2×C4⋊C4C23×C13913yes—
460C2×C4⋊C4C23×C13913yes—
461C2×C4⋊C4C23×C13913yes—
462C2×C4⋊C4C23×C13913yes—
463C2×C4⋊C4C23×C13913yes—
464C2×C4⋊C4C23×C13913yes—
465C2×C4⋊C4C23×C13913yes—
466C2×C4⋊C4C23×C13916yes—
467C2×C4⋊C4C23×C13911yescharacteristic
468C2×C4⋊C4C23×C13913yes—
469C2×C4⋊C4C23×C13916yes—
470C2×C4⋊C4C23×C13913yes—
471C2×C22⋊C4C23×C13913yes—
472C2×C22⋊C4C23×C13911yescharacteristic
473C2×C22⋊C4C23×C13911yescharacteristic
474C2×C22⋊C4C23×C13911yescharacteristic
475C2×C22⋊C4C23×C13913yes—
476C2×C22⋊C4C23×C13913yes—
477C2×C22⋊C4C23×C13913yes—
478C2×C22⋊C4C23×C13913yes—
479C2×C22⋊C4C23×C13916yes—
480C2×C22⋊C4C23×C13916yes—
481C2×C22⋊C4C23×C13911yescharacteristic
482C2×C22⋊C4C23×C13913yes—
483C2×C22⋊C4C23×C13913yes—
484C2×C22⋊C4C23×C13913yes—
485C2×C22⋊C4C23×C13916yes—
486C2×C42C23×C13913yes—
487C2×C42C23×C13916yes—
488C2×C42C23×C13913yes—
489C2×C42C23×C13913yes—
490C2×C42C23×C13913yes—
491#95C23×C13911yescharacteristic
492#95C23×C13913yes—
493#95C23×C13913yes—
494#95C23×C13913yes—
495#95C23×C13913yes—
496#95C23×C13913yes—
497#95C23×C13916yes—
498C24C24×C13913yes—
499C24C24×C13911yescharacteristic
500C24C24×C13911yescharacteristic
501#41—416no—
502C2×Q8—232no—
503C2×Q8—26no—
504C2×Q8—26no—
505C2×Q8—26no—
506C2×Q8—26no—
507C2×Q8—26no—
508C2×Q8—416no—
509C2×Q8C2×D4×C139112yes—
510C2×Q8C2×D4×C13914yes—
511C2×Q8C2×D4×C13914yes—
512C2×Q8#41×C13914yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—26no—
516C2×D4—26no—
517C2×D4—26no—
518C2×D4—26no—
519C2×D4—26no—
520C2×D4—26no—
521C2×D4—22no—
522C2×D4—43no—
523C2×D4—43no—
524C2×D4—43no—
525C22×C4—26no—
526C22×C4—26no—
527C22×C4—26no—
528C22×C4—26no—
529C22×C4—26no—
530C22×C4—26no—
531C22×C4—26no—
532C22×C4—26no—
533C22×C4C2×D4×C139112yes—
534C22×C4C24×C13911yescharacteristic
535C22×C4C24×C13911yescharacteristic
536C22×C4C24×C13913yes—
537C22×C4C24×C13913yes—
538C22×C4C24×C13913yes—
539C22×C4C24×C13911yescharacteristic
540C22×C4C24×C13913yes—
541C22×C4C24×C13913yes—
542C22×C4C24×C13911yescharacteristic
543C22×C4C24×C13913yes—
544C22×C4C24×C13911yescharacteristic
545C22×C4C24×C13913yes—
546C4⋊C4—26no—
547C4⋊C4—26no—
548C4⋊C4—26no—
549C4⋊C4—26no—
550C4⋊C4—26no—
551C4⋊C4—26no—
552C4⋊C4—26no—
553C4⋊C4—26no—
554C4⋊C4—212no—
555C4⋊C4—22no—
556C4⋊C4—43no—
557C4⋊C4—46no—
558C4⋊C4C2×D4×C139112yes—
559C22⋊C4—22no—
560C22⋊C4—26no—
561C22⋊C4—22no—
562C22⋊C4—26no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—26no—
566C22⋊C4—26no—
567C22⋊C4—26no—
568C22⋊C4—212no—
569C22⋊C4—212no—
570C22⋊C4—26no—
571C22⋊C4—46no—
572C22⋊C4—43no—
573C22⋊C4—43no—
574C42—212no—
575C42—26no—
576C42—26no—
577C42—26no—
578C42C2×D4×C139112yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—23no—
592C23—23no—
593C23—23no—
594C23—23no—
595C23—23no—
596C23—23no—
597C23—23no—
598C23C22×D4×C13912yes—
599C232−1+4×C13912yes—
600C23C25×C13911yescharacteristic
601Q8—224no—
602Q8—412no—
603Q8#121×C139116yes—
604D4—28no—
605D4—412no—
606D4—412no—
607D4—412no—
608C2×C4—21no—
609C2×C4—23no—
610C2×C4—23no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—23no—
614C2×C4—21no—
615C2×C4—23no—
616C2×C4—224no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—23no—
620C2×C4—23no—
621C2×C4—23no—
622C2×C4—23no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—23no—
626C2×C4—21no—
627C2×C4—23no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—23no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—23no—
634C2×C4—23no—
635C2×C4—23no—
636C2×C4—23no—
637C2×C4—23no—
638C2×C4—412no—
639C2×C4—412no—
640C2×C4C22×D4×C13916yes—
641C2×C4C22×D4×C13912yes—
642C2×C4C22×D4×C13916yes—
643C2×C4C22×D4×C13916yes—
644C2×C4C22×D4×C13916yes—
645C2×C4C2×#41×C13916yes—
646C2×C42−1+4×C13912yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—43no—
662C22—43no—
663C22—43no—
664C22—43no—
665C22—43no—
666C22—43no—
667C22—43no—
668C22C23×D4×C13911yescharacteristic
669C22C23×D4×C13911yescharacteristic
670C22C22×#41×C13911yescharacteristic
671C22C2×2−1+4×C13911yescharacteristic
672C22C2×2−1+4×C13911yescharacteristic
673C22#585×C13911yescharacteristic
674C22#585×C13911yescharacteristic
675C4—26no—
676C4—22no—
677C4—26no—
678C4—22no—
679C4—41no—
680C4—43no—
681C4—41no—
682C4—43no—
683C4—43no—
684C4—41no—
685C4—43no—
686C4C2×#121×C139112yes—
687C2—42no—
688C2—42no—
689C2—83no—
690C2C22×#121×C13911yescharacteristic
691C2#3486×C13911yescharacteristic
692C2#3487×C13911yescharacteristic
693C2#3489×C13911yescharacteristic
694C2#3497×C13911yescharacteristic
695C2#3516×C13911yescharacteristic
696C2#3518×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×D4×Q8×C139C2semidirect
2. C2×#548×C139C2semidirect
3. C2×#548×C139C2semidirect
4. C2×#519×C139C2semidirect
5. #2620×C139C2semidirect
6. #2545×C139C2semidirect
7. #2538×C139C2semidirect
8. #2429×C139C2semidirect
9. #2426×C139C2semidirect
10. #2415×C139C2semidirect
11. #2414×C139C2semidirect
12. #2392×C139C2semidirect
13. Q8×C4⋊C4×C139C2semidirect
14. #2341×C139C2semidirect
15. Q8×C22⋊C4×C139C2semidirect
78. C22×Q8×C139D4semidirect
103. C4×Q8×C139D4semidirect
348. #35771C139direct (N × H)
349. C139#35771direct (N × H)
350. C2×D4×Q8C2×C139semidirect
351. C2×#548C2×C139semidirect
352. C2×#548C2×C139semidirect
353. C2×#519C2×C139semidirect
354. #2620C2×C139semidirect
355. #2545C2×C139semidirect
356. #2538C2×C139semidirect
357. #2429C2×C139semidirect
358. #2426C2×C139semidirect
359. #2415C2×C139semidirect
360. #2414C2×C139semidirect
361. #2392C2×C139semidirect
362. Q8×C4⋊C4C2×C139semidirect
363. #2341C2×C139semidirect
364. Q8×C22⋊C4C2×C139semidirect
427. C22×Q8D4×C139semidirect
452. C4×Q8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1392
C2×#548×C1392
C2×#519×C1392
#2620×C1392
#2545×C1392
#2538×C1392
#2429×C1392
#2426×C1392
#2415×C1392
#2414×C1392
#2392×C1392
Q8×C4⋊C4×C1392
#2341×C1392
Q8×C22⋊C4×C1392
#35771139