Finite Group Databasebeta

← C139×#25377 #48019973

Subgroups — C139×#25377 #48019973

Order 35584.

1022 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#497×C139C211yesmaximal, characteristic, complemented
2C2×#464×C139C211yesmaximal, characteristic, complemented
3C2×#460×C139C211yesmaximal, characteristic
4C2×#461×C139C211yesmaximal, characteristic, complemented
5#2544×C139C211yesmaximal, characteristic
6#2365×C139C211yesmaximal, characteristic, complemented
7#2056×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2015×C139C211yesmaximal, characteristic, complemented
10#2014×C139C211yesmaximal, characteristic
11#1983×C139C211yesmaximal, characteristic, complemented
12#1940×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic, complemented
14#1878×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139C2211yescharacteristic
17C22×Q16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21C22×SD16×C139C2211yescharacteristic
22C2×C4⋊Q8×C139C2211yescharacteristic
23C2×#127×C139C2211yescharacteristic
24C2×#124×C139C2211yescharacteristic
25C2×#124×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29#497×C139—24no—
30#464×C139—24no—
31#461×C139—24no—
32#460×C139—24no—
33C2×C4⋊C8×C139C2211yescharacteristic
34C2×C4⋊C8×C139C2211yescharacteristic
35C2×C4⋊C8×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#97×C139C2211yescharacteristic
45#394×C139—21no—
46#394×C139—21no—
47#391×C139C2211yescharacteristic
48#391×C139C2211yescharacteristic
49#391×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic
51#389×C139—21no—
52#387×C139—21no—
53#387×C139—21no—
54#386×C139—21no—
55#386×C139—21no—
56C4×C4⋊C4×C139—21no—
57C4×C4⋊C4×C139C2211yescharacteristic
58C4×C4⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×Q8×C139C2311yescharacteristic
65C22×Q8×C139C2311yescharacteristic
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C23×C4×C139—21no—
71C2×Q16×C139—22no—
72C2×Q16×C139—22no—
73C2×Q16×C139—22no—
74C2×Q16×C139—22no—
75C2×Q16×C139—41no—
76C2×Q16×C139—41no—
77C2×SD16×C139—22no—
78C2×SD16×C139—22no—
79C2×SD16×C139—22no—
80C2×SD16×C139—22no—
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—41no—
86C2×SD16×C139—41no—
87C2×SD16×C139—41no—
88C2×SD16×C139—41no—
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C4⋊Q8×C139—22no—
94C4⋊Q8×C139D414yescomplemented
95#127×C139—22no—
96#127×C139—41no—
97#124×C139—22no—
98#124×C139—22no—
99#124×C139—22no—
100#124×C139—41no—
101C4×Q8×C139—22no—
102C4×Q8×C139—22no—
103C4×Q8×C139—41no—
104C4×Q8×C139—41no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139D411yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C42×C139—21no—
124C2×C42×C139—21no—
125C2×C42×C139—21no—
126C2×C42×C139C2311yescharacteristic
127C2×C42×C139C2311yescharacteristic
128C2×C42×C139C2311yescharacteristic
129C4⋊C8×C139—22no—
130C4⋊C8×C139—22no—
131C4⋊C8×C139—22no—
132#103×C139—22no—
133#103×C139—22no—
134#103×C139—22no—
135#103×C139—41no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—41no—
139#102×C139D414yes—
140#97×C139—22no—
141#95×C139—21no—
142#95×C139—21no—
143#95×C139—21no—
144#95×C139—21no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139D411yescharacteristic
149#95×C139D411yescharacteristic
150C24×C139—21no—
151C24×C139—21no—
152C2×Q8×C139—21no—
153C2×Q8×C139—21no—
154C2×Q8×C139—21no—
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—21no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139C2×D412yes—
169C2×Q8×C139C2×D412yes—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—42no—
182C2×D4×C139—42no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—81no—
186C2×D4×C139—81no—
187C2×D4×C139C2×D412yes—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—42no—
195C22×C4×C139—81no—
196C22×C4×C139—81no—
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D411yescharacteristic
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139C2411yescharacteristic
204Q16×C139—44no—
205Q16×C139—44no—
206SD16×C139—44no—
207SD16×C139—44no—
208SD16×C139—44no—
209SD16×C139—44no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139—21no—
220C2×C8×C139C2×D412yes—
221C2×C8×C139#4112yes—
222C4⋊C4×C139—24no—
223C4⋊C4×C139—24no—
224C4⋊C4×C139—22no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—41no—
231C4⋊C4×C139—42no—
232C4⋊C4×C139—42no—
233C4⋊C4×C139C2×D412yes—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—42no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139—81no—
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—21no—
244C42×C139—21no—
245C42×C139—42no—
246C42×C139—42no—
247C42×C139—42no—
248C42×C139C2×D412yes—
249C42×C139#4112yes—
250C23×C139—22no—
251C23×C139—41no—
252C23×C139—41no—
253C23×C139—41no—
254C23×C139—41no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139—41no—
263C23×C139—41no—
264C23×C139C22×D411yescharacteristic
265Q8×C139—22no—
266Q8×C139—22no—
267Q8×C139—22no—
268Q8×C139—22no—
269Q8×C139—41no—
270Q8×C139—41no—
271Q8×C139—41no—
272Q8×C139—41no—
273Q8×C139—41no—
274Q8×C139—41no—
275Q8×C139—41no—
276Q8×C139—41no—
277D4×C139—22no—
278D4×C139—22no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
283D4×C139—41no—
284D4×C139—41no—
285D4×C139—84no—
286D4×C139—84no—
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—22no—
294C2×C4×C139—22no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—22no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
309C2×C4×C139—41no—
310C2×C4×C139—41no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—84no—
321C2×C4×C139#12112yes—
322C2×C4×C139#12112yes—
323C2×C4×C139#13712yes—
324C2×C4×C139C22×D411yescharacteristic
325C2×C4×C139C22×D411yescharacteristic
326C2×C4×C139C2×#4111yescharacteristic
327C2×C4×C139C2×#4111yescharacteristic
328C2×C4×C139H(5,𝔽2)11yescharacteristic
329C2×C4×C139H(5,𝔽2)11yescharacteristic
330C8×C139—22no—
331C8×C139—22no—
332C8×C139—41no—
333C8×C139—41no—
334C22×C139—42no—
335C22×C139—42no—
336C22×C139—42no—
337C22×C139—81no—
338C22×C139—81no—
339C22×C139—81no—
340C22×C139—81no—
341C22×C139—81no—
342C22×C139—81no—
343C22×C139—81no—
344C22×C139—81no—
345C22×C139—81no—
346C22×C139—81no—
347C22×C139—81no—
348C22×C139C2×#12111yescharacteristic
349C22×C139D4211yescharacteristic
350C22×C139#55011yescharacteristic
351C22×C139C2×#13711yescharacteristic
352C22×C139#57511yescharacteristic
353C22×C139#57711yescharacteristic
354C22×C139#57711yescharacteristic
355C4×C139—22no—
356C4×C139—22no—
357C4×C139—22no—
358C4×C139—42no—
359C4×C139—42no—
360C4×C139—41no—
361C4×C139—41no—
362C4×C139—41no—
363C4×C139—42no—
364C4×C139—81no—
365C4×C139—81no—
366C4×C139—81no—
367C4×C139#53211yescharacteristic
368C4×C139#54011yescharacteristic
369C4×C139D4211yescharacteristic
370C4×C139#54611yescharacteristic
371C2×C139—82no—
372C2×C139—161no—
373C2×C139#242811yescharacteristic
374C2×C139#303711yescharacteristic
375C2×C139#304311yescharacteristic
376C2×C139#326611yescharacteristic
377C2×C139#326711yescharacteristic
378C2×C139#340011yescharacteristic
379C2×C139#340111yescharacteristic
380#25377C13911yesmaximal, characteristic, direct product factor, Sylow
381C139#2537711yescharacteristic, direct product factor, Sylow
382C2×#497C2×C13911yescharacteristic, complemented
383C2×#464C2×C13911yescharacteristic, complemented
384C2×#460C2×C13911yescharacteristic
385C2×#461C2×C13911yescharacteristic, complemented
386#2544C2×C13911yescharacteristic
387#2365C2×C13911yescharacteristic, complemented
388#2056C2×C13911yescharacteristic, complemented
389#2055C2×C13911yescharacteristic, complemented
390#2015C2×C13911yescharacteristic, complemented
391#2014C2×C13911yescharacteristic
392#1983C2×C13911yescharacteristic, complemented
393#1940C2×C13911yescharacteristic, complemented
394#1880C2×C13911yescharacteristic, complemented
395#1878C2×C13911yescharacteristic, complemented
396#1762C2×C13911yescharacteristic, complemented
397C22×Q16C22×C13911yescharacteristic
398C22×Q16C22×C13911yescharacteristic
399C22×SD16C22×C13911yescharacteristic
400C22×SD16C22×C13911yescharacteristic
401C22×SD16C22×C13911yescharacteristic
402C22×SD16C22×C13911yescharacteristic
403C2×C4⋊Q8C22×C13911yescharacteristic
404C2×#127C22×C13911yescharacteristic
405C2×#124C22×C13911yescharacteristic
406C2×#124C22×C13911yescharacteristic
407C2×C4×Q8C22×C13911yescharacteristic
408C2×C4×Q8C22×C13911yescharacteristic
409C2×C4×D4C22×C13911yescharacteristic
410#497—24no—
411#464—24no—
412#461—24no—
413#460—24no—
414C2×C4⋊C8C22×C13911yescharacteristic
415C2×C4⋊C8C22×C13911yescharacteristic
416C2×C4⋊C8C22×C13911yescharacteristic
417C2×#103C22×C13911yescharacteristic
418C2×#103C22×C13911yescharacteristic
419C2×#103C22×C13911yescharacteristic
420C2×#103C22×C13911yescharacteristic
421C2×#102C22×C13911yescharacteristic
422C2×#102C22×C13911yescharacteristic
423C2×#102C22×C13911yescharacteristic
424C2×#102C22×C13911yescharacteristic
425C2×#97C22×C13911yescharacteristic
426#394—21no—
427#394—21no—
428#391C22×C13911yescharacteristic
429#391C22×C13911yescharacteristic
430#391C22×C13911yescharacteristic
431#390C22×C13911yescharacteristic
432#389—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4C22×C13911yescharacteristic
439C4×C4⋊C4C22×C13911yescharacteristic
440#340C22×C13911yescharacteristic
441#340C22×C13911yescharacteristic
442#336C22×C13911yescharacteristic
443#336C22×C13911yescharacteristic
444C22×Q8C23×C13911yescharacteristic
445C22×Q8C23×C13911yescharacteristic
446C22×Q8C23×C13911yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C13911yescharacteristic
450C22×D4C23×C13911yescharacteristic
451C23×C4—21no—
452C2×Q16—22no—
453C2×Q16—22no—
454C2×Q16—22no—
455C2×Q16—22no—
456C2×Q16—41no—
457C2×Q16—41no—
458C2×SD16—22no—
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—22no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—41no—
467C2×SD16—41no—
468C2×SD16—41no—
469C2×SD16—41no—
470C22×C8C23×C13911yescharacteristic
471C22×C8C23×C13911yescharacteristic
472C22×C8C23×C13911yescharacteristic
473C22×C8C23×C13911yescharacteristic
474C4⋊Q8—22no—
475C4⋊Q8D4×C13914yescomplemented
476#127—22no—
477#127—41no—
478#124—22no—
479#124—22no—
480#124—22no—
481#124—41no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—41no—
485C4×Q8—41no—
486C4×D4—22no—
487C4×D4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C13911yescharacteristic
493C2×C4⋊C4D4×C13911yescharacteristic
494C2×C4⋊C4C23×C13911yescharacteristic
495C2×C4⋊C4C23×C13911yescharacteristic
496C2×C4⋊C4C23×C13911yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42C23×C13911yescharacteristic
508C2×C42C23×C13911yescharacteristic
509C2×C42C23×C13911yescharacteristic
510C4⋊C8—22no—
511C4⋊C8—22no—
512C4⋊C8—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—41no—
517#102—22no—
518#102—22no—
519#102—41no—
520#102D4×C13914yes—
521#97—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95D4×C13911yescharacteristic
530#95D4×C13911yescharacteristic
531C24—21no—
532C24—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×D4×C13912yes—
550C2×Q8C2×D4×C13912yes—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C2×D4×C13912yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4C2×D4×C13911yescharacteristic
579C22×C4C2×D4×C13911yescharacteristic
580C22×C4C2×D4×C13911yescharacteristic
581C22×C4C2×D4×C13911yescharacteristic
582C22×C4C2×D4×C13911yescharacteristic
583C22×C4C2×D4×C13911yescharacteristic
584C22×C4C24×C13911yescharacteristic
585Q16—44no—
586Q16—44no—
587SD16—44no—
588SD16—44no—
589SD16—44no—
590SD16—44no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8C2×D4×C13912yes—
602C2×C8#41×C13912yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—41no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4C2×D4×C13912yes—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—42no—
627C42—42no—
628C42—42no—
629C42C2×D4×C13912yes—
630C42#41×C13912yes—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C22×D4×C13911yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658D4—22no—
659D4—22no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—84no—
667D4—84no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4#121×C13912yes—
703C2×C4#121×C13912yes—
704C2×C4#137×C13912yes—
705C2×C4C22×D4×C13911yescharacteristic
706C2×C4C22×D4×C13911yescharacteristic
707C2×C4C2×#41×C13911yescharacteristic
708C2×C4C2×#41×C13911yescharacteristic
709C2×C4H(5,𝔽2)×C13911yescharacteristic
710C2×C4H(5,𝔽2)×C13911yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×#121×C13911yescharacteristic
730C22D42×C13911yescharacteristic
731C22#550×C13911yescharacteristic
732C22C2×#137×C13911yescharacteristic
733C22#575×C13911yescharacteristic
734C22#577×C13911yescharacteristic
735C22#577×C13911yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—42no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4#532×C13911yescharacteristic
749C4#540×C13911yescharacteristic
750C4D42×C13911yescharacteristic
751C4#546×C13911yescharacteristic
752C2—82no—
753C2—161no—
754C2#2428×C13911yescharacteristic
755C2#3037×C13911yescharacteristic
756C2#3043×C13911yescharacteristic
757C2#3266×C13911yescharacteristic
758C2#3267×C13911yescharacteristic
759C2#3400×C13911yescharacteristic
760C2#3401×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#127×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#497×C139C2semidirect
2. C2×#464×C139C2semidirect
4. C2×#461×C139C2semidirect
6. #2365×C139C2semidirect
7. #2056×C139C2semidirect
8. #2055×C139C2semidirect
9. #2015×C139C2semidirect
11. #1983×C139C2semidirect
12. #1940×C139C2semidirect
13. #1880×C139C2semidirect
14. #1878×C139C2semidirect
15. #1762×C139C2semidirect
94. C4⋊Q8×C139D4semidirect
380. #25377C139direct (N × H)
381. C139#25377direct (N × H)
382. C2×#497C2×C139semidirect
383. C2×#464C2×C139semidirect
385. C2×#461C2×C139semidirect
387. #2365C2×C139semidirect
388. #2056C2×C139semidirect
389. #2055C2×C139semidirect
390. #2015C2×C139semidirect
392. #1983C2×C139semidirect
393. #1940C2×C139semidirect
394. #1880C2×C139semidirect
395. #1878C2×C139semidirect
396. #1762C2×C139semidirect
475. C4⋊Q8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#497×C1392
C2×#464×C1392
C2×#460×C1392
C2×#461×C1392
#2544×C1392
#2365×C1392
#2056×C1392
#2055×C1392
#2015×C1392
#2014×C1392
#1983×C1392
#1940×C1392
#1880×C1392
#1878×C1392
#1762×C1392
#25377139