Finite Group Databasebeta

← C139×#22889 #48017485

Subgroups — C139×#22889 #48017485

Order 35584.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3002×C139C211yesmaximal, characteristic
2C2×#443×C139C211yesmaximal, characteristic, complemented
3#2933×C139C211yesmaximal, characteristic, complemented
4C2×#421×C139C211yesmaximal, characteristic, complemented
5#2880×C139C211yesmaximal, characteristic, complemented
6#1975×C139C211yesmaximal, characteristic, complemented
7#1937×C139C211yesmaximal, characteristic, complemented
8#1929×C139C211yesmaximal, characteristic, complemented
9#1897×C139C211yesmaximal, characteristic, complemented
10#1876×C139C211yesmaximal, characteristic, complemented
11#1876×C139C211yesmaximal, characteristic, complemented
12#1866×C139C211yesmaximal, characteristic, complemented
13#1855×C139C211yesmaximal, characteristic, complemented
14#1765×C139C211yesmaximal, characteristic, complemented
15#1750×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#135×C139C2211yescharacteristic
18C2×#135×C139C2211yescharacteristic
19C2×#131×C139C2211yescharacteristic
20C2×#131×C139C2211yescharacteristic
21C2×#131×C139C2211yescharacteristic, complemented
22C22×M16×C139C2211yescharacteristic
23#525×C139C2211yescharacteristic
24C2×#117×C139C2211yescharacteristic
25#452×C139C411yescharacteristic, complemented
26#452×C139C411yescharacteristic, complemented
27#451×C139C411yescharacteristic, complemented
28#450×C139C411yescharacteristic, complemented
29#449×C139C411yescharacteristic, complemented
30#449×C139C411yescharacteristic, complemented
31#448×C139C411yescharacteristic, complemented
32#447×C139C411yescharacteristic, complemented
33#443×C139—24no—
34#436×C139—21no—
35#435×C139—21no—
36#435×C139—21no—
37C8×D4×C139—21no—
38C2×#108×C139C2211yescharacteristic, complemented
39C2×#108×C139C2211yescharacteristic, complemented
40#424×C139C2211yescharacteristic, complemented
41#421×C139—24no—
42C2×#104×C139C2211yescharacteristic
43C2×#104×C139C2211yescharacteristic
44C2×#104×C139C2211yescharacteristic
45C2×#104×C139C2211yescharacteristic
46C2×#104×C139C2211yescharacteristic, complemented
47C2×#104×C139C2211yescharacteristic, complemented
48#416×C139C2211yescharacteristic
49#416×C139C2211yescharacteristic
50#408×C139—21no—
51#408×C139—21no—
52#408×C139C2211yescharacteristic
53#408×C139C2211yescharacteristic
54#408×C139C2211yescharacteristic, complemented
55#407×C139—21no—
56#407×C139C2211yescharacteristic
57C2×C22⋊C8×C139—21no—
58C2×C22⋊C8×C139C2211yescharacteristic
59C2×C22⋊C8×C139C2211yescharacteristic
60#405×C139C2211yescharacteristic, complemented
61C2×#97×C139C2211yescharacteristic, complemented
62C2×C4×C8×C139C2211yescharacteristic, complemented
63#341×C139C2211yescharacteristic, complemented
64#341×C139C2211yescharacteristic, complemented
65#339×C139C2211yescharacteristic, complemented
66#339×C139C2211yescharacteristic, complemented
67#336×C139C2211yescharacteristic, complemented
68#336×C139C2211yescharacteristic, complemented
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71C2×#41×C139—22no—
72C2×#41×C139—22no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C2×#41×C139C2×C411yescharacteristic
76C2×#41×C139C2×C411yescharacteristic
77C2×#41×C139C2311yescharacteristic
78C2×#41×C139C2311yescharacteristic
79C2×#41×C139C2311yescharacteristic
80C22×Q8×C139C2×C411yescharacteristic
81C22×D4×C139—21no—
82C22×D4×C139C2×C411yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139C2311yescharacteristic
85#135×C139—22no—
86#135×C139—22no—
87#135×C139—41no—
88#135×C139—41no—
89C2×Q16×C139C2×C411yescharacteristic
90C2×Q16×C139C2×C411yescharacteristic
91C2×SD16×C139C2×C411yescharacteristic
92C2×SD16×C139C2×C411yescharacteristic
93C2×SD16×C139C2×C411yescharacteristic
94C2×SD16×C139C2×C411yescharacteristic
95C2×D8×C139C2×C411yescharacteristic
96C2×D8×C139C2×C411yescharacteristic
97#131×C139—22no—
98#131×C139—22no—
99#131×C139—22no—
100#131×C139—41no—
101#131×C139—41no—
102#131×C139—41no—
103C2×M16×C139—21no—
104C2×M16×C139—21no—
105C2×M16×C139—21no—
106C2×M16×C139—21no—
107C2×M16×C139—22no—
108C2×M16×C139—41no—
109C2×M16×C139C2311yescharacteristic
110C2×M16×C139C2311yescharacteristic
111C2×M16×C139C2311yescharacteristic
112C2×M16×C139C2311yescharacteristic
113C22×C8×C139—21no—
114C22×C8×C139—21no—
115C22×C8×C139—21no—
116C22×C8×C139—21no—
117C22×C8×C139C2311yescharacteristic
118C22×C8×C139C2311yescharacteristic
119C22×C8×C139C2311yescharacteristic
120C22×C8×C139C2311yescharacteristic
121#123×C139—21no—
122C22⋊Q8×C139C2×C411yescharacteristic
123C22⋊Q8×C139C2×C411yescharacteristic
124#121×C139C2×C411yescharacteristic
125#121×C139C2×C411yescharacteristic
126#120×C139—21no—
127C4×D4×C139—21no—
128C4×D4×C139—21no—
129#117×C139—22no—
130#117×C139—41no—
131#117×C139C2311yescharacteristic
132C2×C4⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C42×C139C2311yescharacteristic
135C2×C42×C139C2311yescharacteristic
136#108×C139—22no—
137#108×C139—41no—
138C4⋊C8×C139—21no—
139C4⋊C8×C139—21no—
140#104×C139—22no—
141#104×C139—22no—
142#104×C139—22no—
143#104×C139—22no—
144#104×C139—41no—
145#104×C139D414yescomplemented
146#103×C139C2×C411yescharacteristic
147#103×C139C2×C411yescharacteristic
148#103×C139C2×C411yescharacteristic
149#103×C139C2×C411yescharacteristic
150#102×C139C2×C411yescharacteristic
151#102×C139C2×C411yescharacteristic
152#102×C139C2×C411yescharacteristic
153#102×C139C2×C411yescharacteristic
154C22⋊C8×C139—21no—
155C22⋊C8×C139—21no—
156C22⋊C8×C139—21no—
157C22⋊C8×C139—21no—
158C22⋊C8×C139—21no—
159C22⋊C8×C139—21no—
160C22⋊C8×C139—21no—
161C22⋊C8×C139—21no—
162C22⋊C8×C139C2×C411yescharacteristic
163C22⋊C8×C139C2×C411yescharacteristic
164C22⋊C8×C139C2×C411yescharacteristic
165C22⋊C8×C139C2×C411yescharacteristic
166C22⋊C8×C139D411yescharacteristic
167C22⋊C8×C139D411yescharacteristic
168C22⋊C8×C139D411yescharacteristic
169C22⋊C8×C139D411yescharacteristic
170#97×C139—21no—
171#97×C139—41no—
172C4×C8×C139—21no—
173C4×C8×C139—22no—
174C24×C139—21no—
175C24×C139#4111yescharacteristic
176#41×C139—21no—
177#41×C139—21no—
178#41×C139—22no—
179#41×C139—22no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—21no—
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—21no—
186#41×C139—21no—
187#41×C139—21no—
188#41×C139—42no—
189#41×C139—42no—
190#41×C139—41no—
191#41×C139—41no—
192#41×C139—42no—
193#41×C139—42no—
194#41×C139C2×D412yes—
195#41×C139#4112yes—
196C2×Q8×C139—21no—
197C2×Q8×C139—22no—
198C2×Q8×C139—41no—
199C2×Q8×C139C22×C411yescharacteristic
200C2×Q8×C139C22×C411yescharacteristic
201C2×Q8×C139C22×C411yescharacteristic
202C2×D4×C139—21no—
203C2×D4×C139—22no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—41no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139C22×C411yescharacteristic
215C2×D4×C139C22×C411yescharacteristic
216C2×D4×C139C22×C411yescharacteristic
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—42no—
230C22×C4×C139—42no—
231C22×C4×C139C22×C411yescharacteristic
232C22×C4×C139C22×C411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D411yescharacteristic
235C22×C4×C139#4111yescharacteristic
236C22×C4×C139C2411yescharacteristic
237Q16×C139—22no—
238Q16×C139—41no—
239SD16×C139—22no—
240SD16×C139—22no—
241SD16×C139—41no—
242SD16×C139—41no—
243D8×C139—22no—
244D8×C139—41no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—42no—
253M16×C139—42no—
254M16×C139—42no—
255M16×C139—42no—
256M16×C139C2×D412yes—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
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—42no—
270C2×C8×C139—42no—
271C2×C8×C139—42no—
272C2×C8×C139—42no—
273C2×C8×C139C22×C411yescharacteristic
274C2×C8×C139C22×C411yescharacteristic
275C2×C8×C139C22×C411yescharacteristic
276C2×C8×C139C22×C411yescharacteristic
277C2×C8×C139C2×D411yescharacteristic
278C2×C8×C139C2×D411yescharacteristic
279C2×C8×C139C2×D411yescharacteristic
280C2×C8×C139C2×D411yescharacteristic
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—42no—
284C4⋊C4×C139C22×C411yescharacteristic
285C4⋊C4×C139C22×C411yescharacteristic
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—42no—
292C42×C139—21no—
293C42×C139—21no—
294C42×C139—21no—
295C42×C139—21no—
296C42×C139C2×D412yes—
297C23×C139—21no—
298C23×C139—21no—
299C23×C139—21no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—42no—
305C23×C139—42no—
306C23×C139—81no—
307C23×C139C4×D411yescharacteristic
308C23×C139C4×D411yescharacteristic
309C23×C139C2×#4111yescharacteristic
310Q8×C139—21no—
311Q8×C139—21no—
312Q8×C139—21no—
313Q8×C139—21no—
314Q8×C139—21no—
315Q8×C139—42no—
316Q8×C139C4×D412yes—
317D4×C139—22no—
318D4×C139—22no—
319D4×C139—21no—
320D4×C139—21no—
321D4×C139—21no—
322D4×C139—21no—
323D4×C139—21no—
324D4×C139—42no—
325D4×C139—42no—
326D4×C139—42no—
327D4×C139—42no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—41no—
332D4×C139—81no—
333D4×C139C4×D412yes—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—22no—
343C2×C4×C139—21no—
344C2×C4×C139—22no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—21no—
350C2×C4×C139—21no—
351C2×C4×C139—22no—
352C2×C4×C139—42no—
353C2×C4×C139—42no—
354C2×C4×C139—42no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139C4×D411yescharacteristic
365C2×C4×C139C4×D411yescharacteristic
366C2×C4×C139C23×C411yescharacteristic
367C2×C4×C139C22×D411yescharacteristic
368C2×C4×C139C22×D411yescharacteristic
369C2×C4×C139C2×#4111yescharacteristic
370C2×C4×C139H(5,𝔽2)11yescharacteristic
371C2×C4×C139H(5,𝔽2)11yescharacteristic
372C8×C139—21no—
373C8×C139—21no—
374C8×C139—21no—
375C8×C139—21no—
376C8×C139—21no—
377C8×C139—21no—
378C8×C139—22no—
379C8×C139—21no—
380C8×C139—21no—
381C8×C139—41no—
382C8×C139—41no—
383C8×C139—41no—
384C22×C139—21no—
385C22×C139—21no—
386C22×C139—21no—
387C22×C139—21no—
388C22×C139—22no—
389C22×C139—21no—
390C22×C139—21no—
391C22×C139—21no—
392C22×C139—21no—
393C22×C139—41no—
394C22×C139—41no—
395C22×C139—41no—
396C22×C139—41no—
397C22×C139—41no—
398C22×C139—41no—
399C22×C139—41no—
400C22×C139—41no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—84no—
404C22×C139C2×C4×D411yescharacteristic
405C22×C139#54611yescharacteristic
406C22×C139#55111yescharacteristic
407C4×C139—21no—
408C4×C139—21no—
409C4×C139—22no—
410C4×C139—42no—
411C4×C139—41no—
412C4×C139—41no—
413C4×C139—41no—
414C4×C139—41no—
415C4×C139—81no—
416C4×C139C2×C4×D411yescharacteristic
417C4×C139#51811yescharacteristic
418C4×C139D4211yescharacteristic
419C4×C139#54611yescharacteristic
420C2×C139—21no—
421C2×C139—21no—
422C2×C139—41no—
423C2×C139—41no—
424C2×C139—42no—
425C2×C139—81no—
426C2×C139—81no—
427C2×C139#235811yescharacteristic
428C2×C139#295511yescharacteristic
429C2×C139#295711yescharacteristic
430#22889C13911yesmaximal, characteristic, direct product factor, Sylow
431C139#2288911yescharacteristic, direct product factor, Sylow
432#3002C2×C13911yescharacteristic
433C2×#443C2×C13911yescharacteristic, complemented
434#2933C2×C13911yescharacteristic, complemented
435C2×#421C2×C13911yescharacteristic, complemented
436#2880C2×C13911yescharacteristic, complemented
437#1975C2×C13911yescharacteristic, complemented
438#1937C2×C13911yescharacteristic, complemented
439#1929C2×C13911yescharacteristic, complemented
440#1897C2×C13911yescharacteristic, complemented
441#1876C2×C13911yescharacteristic, complemented
442#1876C2×C13911yescharacteristic, complemented
443#1866C2×C13911yescharacteristic, complemented
444#1855C2×C13911yescharacteristic, complemented
445#1765C2×C13911yescharacteristic, complemented
446#1750C2×C13911yescharacteristic, complemented
447C22×#41C22×C13911yescharacteristic
448C2×#135C22×C13911yescharacteristic
449C2×#135C22×C13911yescharacteristic
450C2×#131C22×C13911yescharacteristic
451C2×#131C22×C13911yescharacteristic
452C2×#131C22×C13911yescharacteristic, complemented
453C22×M16C22×C13911yescharacteristic
454#525C22×C13911yescharacteristic
455C2×#117C22×C13911yescharacteristic
456#452C4×C13911yescharacteristic, complemented
457#452C4×C13911yescharacteristic, complemented
458#451C4×C13911yescharacteristic, complemented
459#450C4×C13911yescharacteristic, complemented
460#449C4×C13911yescharacteristic, complemented
461#449C4×C13911yescharacteristic, complemented
462#448C4×C13911yescharacteristic, complemented
463#447C4×C13911yescharacteristic, complemented
464#443—24no—
465#436—21no—
466#435—21no—
467#435—21no—
468C8×D4—21no—
469C2×#108C22×C13911yescharacteristic, complemented
470C2×#108C22×C13911yescharacteristic, complemented
471#424C22×C13911yescharacteristic, complemented
472#421—24no—
473C2×#104C22×C13911yescharacteristic
474C2×#104C22×C13911yescharacteristic
475C2×#104C22×C13911yescharacteristic
476C2×#104C22×C13911yescharacteristic
477C2×#104C22×C13911yescharacteristic, complemented
478C2×#104C22×C13911yescharacteristic, complemented
479#416C22×C13911yescharacteristic
480#416C22×C13911yescharacteristic
481#408—21no—
482#408—21no—
483#408C22×C13911yescharacteristic
484#408C22×C13911yescharacteristic
485#408C22×C13911yescharacteristic, complemented
486#407—21no—
487#407C22×C13911yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8C22×C13911yescharacteristic
490C2×C22⋊C8C22×C13911yescharacteristic
491#405C22×C13911yescharacteristic, complemented
492C2×#97C22×C13911yescharacteristic, complemented
493C2×C4×C8C22×C13911yescharacteristic, complemented
494#341C22×C13911yescharacteristic, complemented
495#341C22×C13911yescharacteristic, complemented
496#339C22×C13911yescharacteristic, complemented
497#339C22×C13911yescharacteristic, complemented
498#336C22×C13911yescharacteristic, complemented
499#336C22×C13911yescharacteristic, complemented
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×C4×C13911yescharacteristic
507C2×#41C2×C4×C13911yescharacteristic
508C2×#41C23×C13911yescharacteristic
509C2×#41C23×C13911yescharacteristic
510C2×#41C23×C13911yescharacteristic
511C22×Q8C2×C4×C13911yescharacteristic
512C22×D4—21no—
513C22×D4C2×C4×C13911yescharacteristic
514C23×C4—21no—
515C23×C4C23×C13911yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×C4×C13911yescharacteristic
521C2×Q16C2×C4×C13911yescharacteristic
522C2×SD16C2×C4×C13911yescharacteristic
523C2×SD16C2×C4×C13911yescharacteristic
524C2×SD16C2×C4×C13911yescharacteristic
525C2×SD16C2×C4×C13911yescharacteristic
526C2×D8C2×C4×C13911yescharacteristic
527C2×D8C2×C4×C13911yescharacteristic
528#131—22no—
529#131—22no—
530#131—22no—
531#131—41no—
532#131—41no—
533#131—41no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16C23×C13911yescharacteristic
541C2×M16C23×C13911yescharacteristic
542C2×M16C23×C13911yescharacteristic
543C2×M16C23×C13911yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—21no—
547C22×C8—21no—
548C22×C8C23×C13911yescharacteristic
549C22×C8C23×C13911yescharacteristic
550C22×C8C23×C13911yescharacteristic
551C22×C8C23×C13911yescharacteristic
552#123—21no—
553C22⋊Q8C2×C4×C13911yescharacteristic
554C22⋊Q8C2×C4×C13911yescharacteristic
555#121C2×C4×C13911yescharacteristic
556#121C2×C4×C13911yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C23×C13911yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C23×C13911yescharacteristic
566C2×C42C23×C13911yescharacteristic
567#108—22no—
568#108—41no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—22no—
573#104—22no—
574#104—22no—
575#104—41no—
576#104D4×C13914yescomplemented
577#103C2×C4×C13911yescharacteristic
578#103C2×C4×C13911yescharacteristic
579#103C2×C4×C13911yescharacteristic
580#103C2×C4×C13911yescharacteristic
581#102C2×C4×C13911yescharacteristic
582#102C2×C4×C13911yescharacteristic
583#102C2×C4×C13911yescharacteristic
584#102C2×C4×C13911yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8C2×C4×C13911yescharacteristic
594C22⋊C8C2×C4×C13911yescharacteristic
595C22⋊C8C2×C4×C13911yescharacteristic
596C22⋊C8C2×C4×C13911yescharacteristic
597C22⋊C8D4×C13911yescharacteristic
598C22⋊C8D4×C13911yescharacteristic
599C22⋊C8D4×C13911yescharacteristic
600C22⋊C8D4×C13911yescharacteristic
601#97—21no—
602#97—41no—
603C4×C8—21no—
604C4×C8—22no—
605C24—21no—
606C24#41×C13911yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41C2×D4×C13912yes—
626#41#41×C13912yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×C4×C13911yescharacteristic
631C2×Q8C22×C4×C13911yescharacteristic
632C2×Q8C22×C4×C13911yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×C4×C13911yescharacteristic
646C2×D4C22×C4×C13911yescharacteristic
647C2×D4C22×C4×C13911yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4C22×C4×C13911yescharacteristic
663C22×C4C22×C4×C13911yescharacteristic
664C22×C4C2×D4×C13911yescharacteristic
665C22×C4C2×D4×C13911yescharacteristic
666C22×C4#41×C13911yescharacteristic
667C22×C4C24×C13911yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C13912yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8C22×C4×C13911yescharacteristic
705C2×C8C22×C4×C13911yescharacteristic
706C2×C8C22×C4×C13911yescharacteristic
707C2×C8C22×C4×C13911yescharacteristic
708C2×C8C2×D4×C13911yescharacteristic
709C2×C8C2×D4×C13911yescharacteristic
710C2×C8C2×D4×C13911yescharacteristic
711C2×C8C2×D4×C13911yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C22×C4×C13911yescharacteristic
716C4⋊C4C22×C4×C13911yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C13912yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23C4×D4×C13911yescharacteristic
739C23C4×D4×C13911yescharacteristic
740C23C2×#41×C13911yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8C4×D4×C13912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4C4×D4×C13912yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4C4×D4×C13911yescharacteristic
796C2×C4C4×D4×C13911yescharacteristic
797C2×C4C23×C4×C13911yescharacteristic
798C2×C4C22×D4×C13911yescharacteristic
799C2×C4C22×D4×C13911yescharacteristic
800C2×C4C2×#41×C13911yescharacteristic
801C2×C4H(5,𝔽2)×C13911yescharacteristic
802C2×C4H(5,𝔽2)×C13911yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×C4×D4×C13911yescharacteristic
836C22#546×C13911yescharacteristic
837C22#551×C13911yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—42no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—81no—
847C4C2×C4×D4×C13911yescharacteristic
848C4#518×C13911yescharacteristic
849C4D42×C13911yescharacteristic
850C4#546×C13911yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2358×C13911yescharacteristic
859C2#2955×C13911yescharacteristic
860C2#2957×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
socleC22×C139C2×C4×D4
prime radical#3002×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C22⋊C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C139C2semidirect
3. #2933×C139C2semidirect
4. C2×#421×C139C2semidirect
5. #2880×C139C2semidirect
6. #1975×C139C2semidirect
7. #1937×C139C2semidirect
8. #1929×C139C2semidirect
9. #1897×C139C2semidirect
10. #1876×C139C2semidirect
11. #1876×C139C2semidirect
12. #1866×C139C2semidirect
13. #1855×C139C2semidirect
14. #1765×C139C2semidirect
15. #1750×C139C2semidirect
21. C2×#131×C139C22semidirect
25. #452×C139C4semidirect
26. #452×C139C4semidirect
27. #451×C139C4semidirect
28. #450×C139C4semidirect
29. #449×C139C4semidirect
30. #449×C139C4semidirect
31. #448×C139C4semidirect
32. #447×C139C4semidirect
38. C2×#108×C139C22semidirect
39. C2×#108×C139C22semidirect
40. #424×C139C22semidirect
46. C2×#104×C139C22semidirect
47. C2×#104×C139C22semidirect
54. #408×C139C22semidirect
60. #405×C139C22semidirect
61. C2×#97×C139C22semidirect
62. C2×C4×C8×C139C22semidirect
63. #341×C139C22semidirect
64. #341×C139C22semidirect
65. #339×C139C22semidirect
66. #339×C139C22semidirect
67. #336×C139C22semidirect
68. #336×C139C22semidirect
145. #104×C139D4semidirect
430. #22889C139direct (N × H)
431. C139#22889direct (N × H)
433. C2×#443C2×C139semidirect
434. #2933C2×C139semidirect
435. C2×#421C2×C139semidirect
436. #2880C2×C139semidirect
437. #1975C2×C139semidirect
438. #1937C2×C139semidirect
439. #1929C2×C139semidirect
440. #1897C2×C139semidirect
441. #1876C2×C139semidirect
442. #1876C2×C139semidirect
443. #1866C2×C139semidirect
444. #1855C2×C139semidirect
445. #1765C2×C139semidirect
446. #1750C2×C139semidirect
452. C2×#131C22×C139semidirect
456. #452C4×C139semidirect
457. #452C4×C139semidirect
458. #451C4×C139semidirect
459. #450C4×C139semidirect
460. #449C4×C139semidirect
461. #449C4×C139semidirect
462. #448C4×C139semidirect
463. #447C4×C139semidirect
469. C2×#108C22×C139semidirect
470. C2×#108C22×C139semidirect
471. #424C22×C139semidirect
477. C2×#104C22×C139semidirect
478. C2×#104C22×C139semidirect
485. #408C22×C139semidirect
491. #405C22×C139semidirect
492. C2×#97C22×C139semidirect
493. C2×C4×C8C22×C139semidirect
494. #341C22×C139semidirect
495. #341C22×C139semidirect
496. #339C22×C139semidirect
497. #339C22×C139semidirect
498. #336C22×C139semidirect
499. #336C22×C139semidirect
576. #104D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3002×C1392
C2×#443×C1392
#2933×C1392
C2×#421×C1392
#2880×C1392
#1975×C1392
#1937×C1392
#1929×C1392
#1897×C1392
#1876×C1392
#1866×C1392
#1855×C1392
#1765×C1392
#1750×C1392
#22889139