Finite Group Databasebeta

← C139×#17521 #48012117

Subgroups — C139×#17521 #48012117

Order 35584.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3481×C139C211yesmaximal, characteristic
2#2990×C139C211yesmaximal, characteristic, complemented
3#2922×C139C211yesmaximal, characteristic, complemented
4#1496×C139C211yesmaximal, characteristic, complemented
5#1495×C139C211yesmaximal, characteristic, complemented
6#1494×C139C211yesmaximal, characteristic, complemented
7#1490×C139C211yesmaximal, characteristic, complemented
8#1488×C139C211yesmaximal, characteristic, complemented
9#1486×C139C211yesmaximal, characteristic, complemented
10#1483×C139C211yesmaximal, characteristic, complemented
11#1482×C139C211yesmaximal, characteristic, complemented
12#1480×C139C211yesmaximal, characteristic, complemented
13#1478×C139C211yesmaximal, characteristic, complemented
14#1477×C139C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C139C211yesmaximal, characteristic, complemented
16#559×C139C411yescharacteristic
17#554×C139C411yescharacteristic
18#554×C139C411yescharacteristic
19#553×C139—21no—
20#553×C139C411yescharacteristic
21#553×C139C411yescharacteristic
22#551×C139—21no—
23#551×C139—21no—
24#546×C139—21no—
25#546×C139C411yescharacteristic
26#546×C139C411yescharacteristic
27D42×C139C411yescharacteristic
28#532×C139C2211yescharacteristic
29#529×C139—21no—
30#529×C139C2211yescharacteristic
31#529×C139C2211yescharacteristic
32#525×C139—21no—
33#525×C139—21no—
34C4×#41×C139C2211yescharacteristic
35C4×#41×C139C2211yescharacteristic
36C2×C4×D4×C139—21no—
37C2×C4×D4×C139C2211yescharacteristic
38C2×C4×D4×C139C2211yescharacteristic
39#446×C139—21no—
40#435×C139—21no—
41#435×C139—21no—
42C8×D4×C139—21no—
43#433×C139—21no—
44#433×C139—21no—
45#432×C139C2211yescharacteristic, complemented
46#432×C139C2211yescharacteristic, complemented
47#431×C139C2211yescharacteristic, complemented
48#431×C139C2211yescharacteristic, complemented
49#431×C139C2211yescharacteristic, complemented
50#431×C139C2211yescharacteristic, complemented
51#431×C139C2211yescharacteristic, complemented
52#424×C139—21no—
53#423×C139C2211yescharacteristic, complemented
54C2×C4⋊C8×C139C2211yescharacteristic, complemented
55C2×C4⋊C8×C139C2211yescharacteristic, complemented
56#408×C139—21no—
57C4×M16×C139C2211yescharacteristic, complemented
58C2×C4×C8×C139C2211yescharacteristic, complemented
59Q8⋊C8×C139C2211yescharacteristic, complemented
60Q8⋊C8×C139C2211yescharacteristic, complemented
61Q8⋊C8×C139C2211yescharacteristic, complemented
62Q8⋊C8×C139C2211yescharacteristic, complemented
63D4⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66D4⋊C8×C139C2211yescharacteristic
67D4⋊C8×C139C2211yescharacteristic, complemented
68D4⋊C8×C139C2211yescharacteristic, complemented
69D4⋊C8×C139C2211yescharacteristic, complemented
70D4⋊C8×C139C2211yescharacteristic, complemented
71D4⋊C8×C139C2211yescharacteristic, complemented
72D4⋊C8×C139C2211yescharacteristic, complemented
73D4⋊C8×C139C2211yescharacteristic, complemented
74D4⋊C8×C139C2211yescharacteristic, complemented
75C2×#41×C139—21no—
76C2×#41×C139C2×C411yescharacteristic
77C2×#41×C139D411yescharacteristic
78C22×D4×C139—21no—
79C22×D4×C139C2×C411yescharacteristic
80C22×D4×C139C2×C411yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139—21no—
83C2×M16×C139—21no—
84C2×M16×C139—21no—
85C22×C8×C139—21no—
86C22×C8×C139—21no—
87C22×C8×C139—21no—
88C4⋊Q8×C139C2×C411yescharacteristic
89#127×C139C2×C411yescharacteristic
90#126×C139—21no—
91#126×C139—21no—
92#126×C139—21no—
93#126×C139—21no—
94#125×C139—21no—
95#125×C139C2×C411yescharacteristic
96#125×C139C2×C411yescharacteristic
97#124×C139—21no—
98#124×C139—21no—
99#124×C139C2×C411yescharacteristic
100#124×C139C2×C411yescharacteristic
101#123×C139—21no—
102#123×C139—21no—
103#123×C139—21no—
104#123×C139—21no—
105#123×C139—21no—
106#123×C139—21no—
107#123×C139—21no—
108#123×C139—21no—
109C22⋊Q8×C139—21no—
110C22⋊Q8×C139—21no—
111C22⋊Q8×C139—21no—
112C22⋊Q8×C139—21no—
113C22⋊Q8×C139—21no—
114C22⋊Q8×C139C2×C411yescharacteristic
115C22⋊Q8×C139C2×C411yescharacteristic
116#121×C139—21no—
117#121×C139—21no—
118#121×C139—21no—
119#121×C139—21no—
120#121×C139—21no—
121#121×C139—21no—
122#121×C139C2×C411yescharacteristic
123#121×C139C2×C411yescharacteristic
124#121×C139C2×C411yescharacteristic
125#121×C139C2×C411yescharacteristic
126#120×C139—21no—
127#120×C139—21no—
128#120×C139—21no—
129#120×C139—21no—
130C4×Q8×C139C2×C411yescharacteristic
131C4×Q8×C139C2×C411yescharacteristic
132C4×Q8×C139D411yescharacteristic
133C4×Q8×C139C2311yescharacteristic
134C4×D4×C139—21no—
135C4×D4×C139—21no—
136C4×D4×C139—21no—
137C4×D4×C139—21no—
138C4×D4×C139—21no—
139C4×D4×C139—21no—
140C4×D4×C139—21no—
141C4×D4×C139—21no—
142C4×D4×C139—21no—
143C4×D4×C139—21no—
144C4×D4×C139—21no—
145C4×D4×C139—21no—
146C4×D4×C139—21no—
147C4×D4×C139C2×C411yescharacteristic
148C4×D4×C139C2×C411yescharacteristic
149C4×D4×C139C2×C411yescharacteristic
150C4×D4×C139C2×C411yescharacteristic
151C4×D4×C139C2×C411yescharacteristic
152C4×D4×C139C2×C411yescharacteristic
153C4×D4×C139C2×C411yescharacteristic
154C4×D4×C139C2×C411yescharacteristic
155C4×D4×C139D411yescharacteristic
156C4×D4×C139D411yescharacteristic
157C4×D4×C139D411yescharacteristic
158C4×D4×C139C2311yescharacteristic
159C4×D4×C139C2311yescharacteristic
160C4×D4×C139C2311yescharacteristic
161#117×C139—21no—
162#117×C139—21no—
163#117×C139—21no—
164#117×C139C2×C411yescharacteristic
165#117×C139D411yescharacteristic
166#117×C139D411yescharacteristic
167#117×C139D411yescharacteristic
168C2×C4⋊C4×C139—21no—
169C2×C4⋊C4×C139C2×C411yescharacteristic
170C2×C4⋊C4×C139C2×C411yescharacteristic
171C2×C22⋊C4×C139—21no—
172C2×C22⋊C4×C139—21no—
173C2×C22⋊C4×C139—21no—
174C2×C22⋊C4×C139—21no—
175C2×C42×C139—21no—
176C2×C42×C139C2311yescharacteristic
177C2×C42×C139C2311yescharacteristic
178C2×C42×C139C2311yescharacteristic
179C4⋊C8×C139—21no—
180C4⋊C8×C139—21no—
181C4⋊C8×C139—21no—
182C4⋊C8×C139—21no—
183C4⋊C8×C139—21no—
184C4⋊C8×C139—21no—
185C4⋊C8×C139—21no—
186C4⋊C8×C139C2311yescharacteristic
187C4⋊C8×C139C2311yescharacteristic
188C4⋊C8×C139C2311yescharacteristic
189C4⋊C8×C139C2311yescharacteristic
190C22⋊C8×C139—21no—
191C22⋊C8×C139—21no—
192C22⋊C8×C139—21no—
193C22⋊C8×C139—21no—
194C22⋊C8×C139—21no—
195C22⋊C8×C139—21no—
196C22⋊C8×C139—21no—
197#97×C139—21no—
198#97×C139—21no—
199#97×C139—21no—
200C4×C8×C139—21no—
201C4×C8×C139—21no—
202C4×C8×C139C2311yescharacteristic
203C4×C8×C139C2311yescharacteristic
204C4×C8×C139C2311yescharacteristic
205C4×C8×C139C2311yescharacteristic
206C24×C139—21no—
207C24×C139—21no—
208#41×C139—22no—
209#41×C139—42no—
210#41×C139—41no—
211#41×C139—81no—
212#41×C139—81no—
213C2×Q8×C139—21no—
214C2×Q8×C139C22⋊C411yescharacteristic
215C2×Q8×C139C22×C411yescharacteristic
216C2×D4×C139—22no—
217C2×D4×C139—22no—
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—41no—
228C2×D4×C139—41no—
229C2×D4×C139—44no—
230C2×D4×C139C22⋊C411yescharacteristic
231C2×D4×C139C22⋊C411yescharacteristic
232C2×D4×C139C22⋊C411yescharacteristic
233C2×D4×C139C22×C411yescharacteristic
234C2×D4×C139C22×C411yescharacteristic
235C2×D4×C139C22×C411yescharacteristic
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—81no—
248C22×C4×C139—81no—
249C22×C4×C139—81no—
250C22×C4×C139—81no—
251C22×C4×C139C22×C411yescharacteristic
252C22×C4×C139C22×C411yescharacteristic
253C22×C4×C139C22×C411yescharacteristic
254C22×C4×C139C2×D411yescharacteristic
255C22×C4×C139C2×D411yescharacteristic
256C22×C4×C139C2×D411yescharacteristic
257C22×C4×C139C2×D411yescharacteristic
258C22×C4×C139C2×D411yescharacteristic
259C22×C4×C139C2×D411yescharacteristic
260M16×C139—42no—
261M16×C139—81no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—42no—
271C2×C8×C139—81no—
272C2×C8×C139—81no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139C22⋊C411yescharacteristic
285C4⋊C4×C139C22⋊C411yescharacteristic
286C4⋊C4×C139C22⋊C411yescharacteristic
287C4⋊C4×C139C22⋊C411yescharacteristic
288C4⋊C4×C139C22⋊C411yescharacteristic
289C4⋊C4×C139C22⋊C411yescharacteristic
290C4⋊C4×C139C22×C411yescharacteristic
291C4⋊C4×C139C22×C411yescharacteristic
292C4⋊C4×C139C22×C411yescharacteristic
293C4⋊C4×C139C22×C411yescharacteristic
294C22⋊C4×C139—21no—
295C22⋊C4×C139—21no—
296C22⋊C4×C139—21no—
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—21no—
304C22⋊C4×C139—21no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—21no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—21no—
312C22⋊C4×C139—21no—
313C22⋊C4×C139C22⋊C411yescharacteristic
314C22⋊C4×C139C22⋊C411yescharacteristic
315C22⋊C4×C139C22⋊C411yescharacteristic
316C22⋊C4×C139C22⋊C411yescharacteristic
317C22⋊C4×C139C22⋊C411yescharacteristic
318C22⋊C4×C139C22⋊C411yescharacteristic
319C42×C139—21no—
320C42×C139—21no—
321C42×C139—21no—
322C42×C139C22×C411yescharacteristic
323C42×C139C22×C411yescharacteristic
324C42×C139C22×C411yescharacteristic
325C42×C139C2×D411yescharacteristic
326C42×C139C2×D411yescharacteristic
327C42×C139C2×D411yescharacteristic
328C42×C139C2×D411yescharacteristic
329C42×C139C2×D411yescharacteristic
330C42×C139C2×D411yescharacteristic
331C42×C139C2411yescharacteristic
332C23×C139—21no—
333C23×C139—21no—
334C23×C139—21no—
335C23×C139—42no—
336C23×C139—42no—
337C23×C139—42no—
338C23×C139—42no—
339C23×C139—81no—
340C23×C139—81no—
341C23×C139C2×C22⋊C411yescharacteristic
342C23×C139C2×C22⋊C411yescharacteristic
343C23×C139C2×C22⋊C411yescharacteristic
344Q8×C139—21no—
345Q8×C139—21no—
346Q8×C139—41no—
347Q8×C139—81no—
348D4×C139—22no—
349D4×C139—22no—
350D4×C139—21no—
351D4×C139—21no—
352D4×C139—21no—
353D4×C139—21no—
354D4×C139—21no—
355D4×C139—41no—
356D4×C139—42no—
357D4×C139—42no—
358D4×C139—42no—
359D4×C139—42no—
360D4×C139—42no—
361D4×C139—42no—
362D4×C139—81no—
363D4×C139—81no—
364D4×C139—81no—
365D4×C139#13112yes—
366C2×C4×C139—22no—
367C2×C4×C139—21no—
368C2×C4×C139—21no—
369C2×C4×C139—21no—
370C2×C4×C139—21no—
371C2×C4×C139—21no—
372C2×C4×C139—21no—
373C2×C4×C139—21no—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—21no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—21no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—42no—
387C2×C4×C139—42no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—81no—
395C2×C4×C139—81no—
396C2×C4×C139—81no—
397C2×C4×C139—81no—
398C2×C4×C139—81no—
399C2×C4×C139—81no—
400C2×C4×C139C2×C22⋊C411yescharacteristic
401C2×C4×C139C2×C22⋊C411yescharacteristic
402C2×C4×C139C2×C22⋊C411yescharacteristic
403C2×C4×C139C2×C22⋊C411yescharacteristic
404C2×C4×C139C2×C22⋊C411yescharacteristic
405C2×C4×C139C2×C22⋊C411yescharacteristic
406C2×C4×C139C2×C22⋊C411yescharacteristic
407C2×C4×C139C2×C22⋊C411yescharacteristic
408C2×C4×C139C2×C22⋊C411yescharacteristic
409C2×C4×C139C23×C411yescharacteristic
410C2×C4×C139C22×D411yescharacteristic
411C2×C4×C139C22×D411yescharacteristic
412C8×C139—41no—
413C8×C139—41no—
414C8×C139—41no—
415C8×C139—41no—
416C8×C139—41no—
417C8×C139—41no—
418C8×C139—41no—
419C8×C139—41no—
420C22×C139—21no—
421C22×C139—21no—
422C22×C139—21no—
423C22×C139—21no—
424C22×C139—22no—
425C22×C139—21no—
426C22×C139—21no—
427C22×C139—21no—
428C22×C139—21no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—41no—
432C22×C139—41no—
433C22×C139—41no—
434C22×C139—41no—
435C22×C139—41no—
436C22×C139—41no—
437C22×C139—84no—
438C22×C139—84no—
439C22×C139#42112yes—
440C22×C139C22×C22⋊C411yescharacteristic
441C4×C139—21no—
442C4×C139—21no—
443C4×C139—21no—
444C4×C139—21no—
445C4×C139—21no—
446C4×C139—21no—
447C4×C139—21no—
448C4×C139—21no—
449C4×C139—21no—
450C4×C139—21no—
451C4×C139—41no—
452C4×C139—41no—
453C4×C139—41no—
454C4×C139—41no—
455C4×C139—41no—
456C4×C139C2×#13111yescharacteristic
457C4×C139#56811yescharacteristic
458C4×C139#57611yescharacteristic
459C4×C139#57711yescharacteristic
460C2×C139—22no—
461C2×C139—41no—
462C2×C139—41no—
463C2×C139—42no—
464C2×C139—81no—
465C2×C139—81no—
466C2×C139#288011yescharacteristic
467C2×C139#289711yescharacteristic
468C2×C139C2×#42111yescharacteristic
469#17521C13911yesmaximal, characteristic, direct product factor, Sylow
470C139#1752111yescharacteristic, direct product factor, Sylow
471#3481C2×C13911yescharacteristic
472#2990C2×C13911yescharacteristic, complemented
473#2922C2×C13911yescharacteristic, complemented
474#1496C2×C13911yescharacteristic, complemented
475#1495C2×C13911yescharacteristic, complemented
476#1494C2×C13911yescharacteristic, complemented
477#1490C2×C13911yescharacteristic, complemented
478#1488C2×C13911yescharacteristic, complemented
479#1486C2×C13911yescharacteristic, complemented
480#1483C2×C13911yescharacteristic, complemented
481#1482C2×C13911yescharacteristic, complemented
482#1480C2×C13911yescharacteristic, complemented
483#1478C2×C13911yescharacteristic, complemented
484#1477C2×C13911yescharacteristic, complemented
485C2×D4⋊C8C2×C13911yescharacteristic, complemented
486#559C4×C13911yescharacteristic
487#554C4×C13911yescharacteristic
488#554C4×C13911yescharacteristic
489#553—21no—
490#553C4×C13911yescharacteristic
491#553C4×C13911yescharacteristic
492#551—21no—
493#551—21no—
494#546—21no—
495#546C4×C13911yescharacteristic
496#546C4×C13911yescharacteristic
497D42C4×C13911yescharacteristic
498#532C22×C13911yescharacteristic
499#529—21no—
500#529C22×C13911yescharacteristic
501#529C22×C13911yescharacteristic
502#525—21no—
503#525—21no—
504C4×#41C22×C13911yescharacteristic
505C4×#41C22×C13911yescharacteristic
506C2×C4×D4—21no—
507C2×C4×D4C22×C13911yescharacteristic
508C2×C4×D4C22×C13911yescharacteristic
509#446—21no—
510#435—21no—
511#435—21no—
512C8×D4—21no—
513#433—21no—
514#433—21no—
515#432C22×C13911yescharacteristic, complemented
516#432C22×C13911yescharacteristic, complemented
517#431C22×C13911yescharacteristic, complemented
518#431C22×C13911yescharacteristic, complemented
519#431C22×C13911yescharacteristic, complemented
520#431C22×C13911yescharacteristic, complemented
521#431C22×C13911yescharacteristic, complemented
522#424—21no—
523#423C22×C13911yescharacteristic, complemented
524C2×C4⋊C8C22×C13911yescharacteristic, complemented
525C2×C4⋊C8C22×C13911yescharacteristic, complemented
526#408—21no—
527C4×M16C22×C13911yescharacteristic, complemented
528C2×C4×C8C22×C13911yescharacteristic, complemented
529Q8⋊C8C22×C13911yescharacteristic, complemented
530Q8⋊C8C22×C13911yescharacteristic, complemented
531Q8⋊C8C22×C13911yescharacteristic, complemented
532Q8⋊C8C22×C13911yescharacteristic, complemented
533D4⋊C8C22×C13911yescharacteristic
534D4⋊C8C22×C13911yescharacteristic
535D4⋊C8C22×C13911yescharacteristic
536D4⋊C8C22×C13911yescharacteristic
537D4⋊C8C22×C13911yescharacteristic, complemented
538D4⋊C8C22×C13911yescharacteristic, complemented
539D4⋊C8C22×C13911yescharacteristic, complemented
540D4⋊C8C22×C13911yescharacteristic, complemented
541D4⋊C8C22×C13911yescharacteristic, complemented
542D4⋊C8C22×C13911yescharacteristic, complemented
543D4⋊C8C22×C13911yescharacteristic, complemented
544D4⋊C8C22×C13911yescharacteristic, complemented
545C2×#41—21no—
546C2×#41C2×C4×C13911yescharacteristic
547C2×#41D4×C13911yescharacteristic
548C22×D4—21no—
549C22×D4C2×C4×C13911yescharacteristic
550C22×D4C2×C4×C13911yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C2×M16—21no—
554C2×M16—21no—
555C22×C8—21no—
556C22×C8—21no—
557C22×C8—21no—
558C4⋊Q8C2×C4×C13911yescharacteristic
559#127C2×C4×C13911yescharacteristic
560#126—21no—
561#126—21no—
562#126—21no—
563#126—21no—
564#125—21no—
565#125C2×C4×C13911yescharacteristic
566#125C2×C4×C13911yescharacteristic
567#124—21no—
568#124—21no—
569#124C2×C4×C13911yescharacteristic
570#124C2×C4×C13911yescharacteristic
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8C2×C4×C13911yescharacteristic
585C22⋊Q8C2×C4×C13911yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121C2×C4×C13911yescharacteristic
593#121C2×C4×C13911yescharacteristic
594#121C2×C4×C13911yescharacteristic
595#121C2×C4×C13911yescharacteristic
596#120—21no—
597#120—21no—
598#120—21no—
599#120—21no—
600C4×Q8C2×C4×C13911yescharacteristic
601C4×Q8C2×C4×C13911yescharacteristic
602C4×Q8D4×C13911yescharacteristic
603C4×Q8C23×C13911yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4C2×C4×C13911yescharacteristic
618C4×D4C2×C4×C13911yescharacteristic
619C4×D4C2×C4×C13911yescharacteristic
620C4×D4C2×C4×C13911yescharacteristic
621C4×D4C2×C4×C13911yescharacteristic
622C4×D4C2×C4×C13911yescharacteristic
623C4×D4C2×C4×C13911yescharacteristic
624C4×D4C2×C4×C13911yescharacteristic
625C4×D4D4×C13911yescharacteristic
626C4×D4D4×C13911yescharacteristic
627C4×D4D4×C13911yescharacteristic
628C4×D4C23×C13911yescharacteristic
629C4×D4C23×C13911yescharacteristic
630C4×D4C23×C13911yescharacteristic
631#117—21no—
632#117—21no—
633#117—21no—
634#117C2×C4×C13911yescharacteristic
635#117D4×C13911yescharacteristic
636#117D4×C13911yescharacteristic
637#117D4×C13911yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4C2×C4×C13911yescharacteristic
640C2×C4⋊C4C2×C4×C13911yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C42—21no—
646C2×C42C23×C13911yescharacteristic
647C2×C42C23×C13911yescharacteristic
648C2×C42C23×C13911yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—21no—
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—21no—
656C4⋊C8C23×C13911yescharacteristic
657C4⋊C8C23×C13911yescharacteristic
658C4⋊C8C23×C13911yescharacteristic
659C4⋊C8C23×C13911yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667#97—21no—
668#97—21no—
669#97—21no—
670C4×C8—21no—
671C4×C8—21no—
672C4×C8C23×C13911yescharacteristic
673C4×C8C23×C13911yescharacteristic
674C4×C8C23×C13911yescharacteristic
675C4×C8C23×C13911yescharacteristic
676C24—21no—
677C24—21no—
678#41—22no—
679#41—42no—
680#41—41no—
681#41—81no—
682#41—81no—
683C2×Q8—21no—
684C2×Q8C22⋊C4×C13911yescharacteristic
685C2×Q8C22×C4×C13911yescharacteristic
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4C22⋊C4×C13911yescharacteristic
701C2×D4C22⋊C4×C13911yescharacteristic
702C2×D4C22⋊C4×C13911yescharacteristic
703C2×D4C22×C4×C13911yescharacteristic
704C2×D4C22×C4×C13911yescharacteristic
705C2×D4C22×C4×C13911yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4C22×C4×C13911yescharacteristic
722C22×C4C22×C4×C13911yescharacteristic
723C22×C4C22×C4×C13911yescharacteristic
724C22×C4C2×D4×C13911yescharacteristic
725C22×C4C2×D4×C13911yescharacteristic
726C22×C4C2×D4×C13911yescharacteristic
727C22×C4C2×D4×C13911yescharacteristic
728C22×C4C2×D4×C13911yescharacteristic
729C22×C4C2×D4×C13911yescharacteristic
730M16—42no—
731M16—81no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C2×C8—81no—
742C2×C8—81no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4C22⋊C4×C13911yescharacteristic
755C4⋊C4C22⋊C4×C13911yescharacteristic
756C4⋊C4C22⋊C4×C13911yescharacteristic
757C4⋊C4C22⋊C4×C13911yescharacteristic
758C4⋊C4C22⋊C4×C13911yescharacteristic
759C4⋊C4C22⋊C4×C13911yescharacteristic
760C4⋊C4C22×C4×C13911yescharacteristic
761C4⋊C4C22×C4×C13911yescharacteristic
762C4⋊C4C22×C4×C13911yescharacteristic
763C4⋊C4C22×C4×C13911yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4C22⋊C4×C13911yescharacteristic
784C22⋊C4C22⋊C4×C13911yescharacteristic
785C22⋊C4C22⋊C4×C13911yescharacteristic
786C22⋊C4C22⋊C4×C13911yescharacteristic
787C22⋊C4C22⋊C4×C13911yescharacteristic
788C22⋊C4C22⋊C4×C13911yescharacteristic
789C42—21no—
790C42—21no—
791C42—21no—
792C42C22×C4×C13911yescharacteristic
793C42C22×C4×C13911yescharacteristic
794C42C22×C4×C13911yescharacteristic
795C42C2×D4×C13911yescharacteristic
796C42C2×D4×C13911yescharacteristic
797C42C2×D4×C13911yescharacteristic
798C42C2×D4×C13911yescharacteristic
799C42C2×D4×C13911yescharacteristic
800C42C2×D4×C13911yescharacteristic
801C42C24×C13911yescharacteristic
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23C2×C22⋊C4×C13911yescharacteristic
812C23C2×C22⋊C4×C13911yescharacteristic
813C23C2×C22⋊C4×C13911yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—81no—
818D4—22no—
819D4—22no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—21no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—42no—
831D4—42no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4#131×C13912yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4C2×C22⋊C4×C13911yescharacteristic
871C2×C4C2×C22⋊C4×C13911yescharacteristic
872C2×C4C2×C22⋊C4×C13911yescharacteristic
873C2×C4C2×C22⋊C4×C13911yescharacteristic
874C2×C4C2×C22⋊C4×C13911yescharacteristic
875C2×C4C2×C22⋊C4×C13911yescharacteristic
876C2×C4C2×C22⋊C4×C13911yescharacteristic
877C2×C4C2×C22⋊C4×C13911yescharacteristic
878C2×C4C2×C22⋊C4×C13911yescharacteristic
879C2×C4C23×C4×C13911yescharacteristic
880C2×C4C22×D4×C13911yescharacteristic
881C2×C4C22×D4×C13911yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—84no—
908C22—84no—
909C22#421×C13912yes—
910C22C22×C22⋊C4×C13911yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×#131×C13911yescharacteristic
927C4#568×C13911yescharacteristic
928C4#576×C13911yescharacteristic
929C4#577×C13911yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—42no—
934C2—81no—
935C2—81no—
936C2#2880×C13911yescharacteristic
937C2#2897×C13911yescharacteristic
938C2C2×#421×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC42C24×C139
socleC22×C139C22×C22⋊C4
prime radical#3481×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C4×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2990×C139C2semidirect
3. #2922×C139C2semidirect
4. #1496×C139C2semidirect
5. #1495×C139C2semidirect
6. #1494×C139C2semidirect
7. #1490×C139C2semidirect
8. #1488×C139C2semidirect
9. #1486×C139C2semidirect
10. #1483×C139C2semidirect
11. #1482×C139C2semidirect
12. #1480×C139C2semidirect
13. #1478×C139C2semidirect
14. #1477×C139C2semidirect
15. C2×D4⋊C8×C139C2semidirect
45. #432×C139C22semidirect
46. #432×C139C22semidirect
47. #431×C139C22semidirect
48. #431×C139C22semidirect
49. #431×C139C22semidirect
50. #431×C139C22semidirect
51. #431×C139C22semidirect
53. #423×C139C22semidirect
54. C2×C4⋊C8×C139C22semidirect
55. C2×C4⋊C8×C139C22semidirect
57. C4×M16×C139C22semidirect
58. C2×C4×C8×C139C22semidirect
59. Q8⋊C8×C139C22semidirect
60. Q8⋊C8×C139C22semidirect
61. Q8⋊C8×C139C22semidirect
62. Q8⋊C8×C139C22semidirect
67. D4⋊C8×C139C22semidirect
68. D4⋊C8×C139C22semidirect
69. D4⋊C8×C139C22semidirect
70. D4⋊C8×C139C22semidirect
71. D4⋊C8×C139C22semidirect
72. D4⋊C8×C139C22semidirect
73. D4⋊C8×C139C22semidirect
74. D4⋊C8×C139C22semidirect
469. #17521C139direct (N × H)
470. C139#17521direct (N × H)
472. #2990C2×C139semidirect
473. #2922C2×C139semidirect
474. #1496C2×C139semidirect
475. #1495C2×C139semidirect
476. #1494C2×C139semidirect
477. #1490C2×C139semidirect
478. #1488C2×C139semidirect
479. #1486C2×C139semidirect
480. #1483C2×C139semidirect
481. #1482C2×C139semidirect
482. #1480C2×C139semidirect
483. #1478C2×C139semidirect
484. #1477C2×C139semidirect
485. C2×D4⋊C8C2×C139semidirect
515. #432C22×C139semidirect
516. #432C22×C139semidirect
517. #431C22×C139semidirect
518. #431C22×C139semidirect
519. #431C22×C139semidirect
520. #431C22×C139semidirect
521. #431C22×C139semidirect
523. #423C22×C139semidirect
524. C2×C4⋊C8C22×C139semidirect
525. C2×C4⋊C8C22×C139semidirect
527. C4×M16C22×C139semidirect
528. C2×C4×C8C22×C139semidirect
529. Q8⋊C8C22×C139semidirect
530. Q8⋊C8C22×C139semidirect
531. Q8⋊C8C22×C139semidirect
532. Q8⋊C8C22×C139semidirect
537. D4⋊C8C22×C139semidirect
538. D4⋊C8C22×C139semidirect
539. D4⋊C8C22×C139semidirect
540. D4⋊C8C22×C139semidirect
541. D4⋊C8C22×C139semidirect
542. D4⋊C8C22×C139semidirect
543. D4⋊C8C22×C139semidirect
544. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3481×C1392
#2990×C1392
#2922×C1392
#1496×C1392
#1495×C1392
#1494×C1392
#1490×C1392
#1488×C1392
#1486×C1392
#1483×C1392
#1482×C1392
#1480×C1392
#1478×C1392
#1477×C1392
C2×D4⋊C8×C1392
#17521139