Finite Group Databasebeta

← C139×#35621 #48030217

Subgroups — C139×#35621 #48030217

Order 35584.

2974 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C139C211yesmaximal, characteristic, complemented
2C2×#536×C139C211yesmaximal, characteristic, complemented
3C2×#532×C139C211yesmaximal, characteristic
4C2×#520×C139C211yesmaximal, characteristic, complemented
5#2547×C139C212yesmaximal, complemented
6#2546×C139C212yesmaximal, complemented
7#2545×C139C212yesmaximal, complemented
8#2544×C139C212yesmaximal, complemented
9#2425×C139C218yesmaximal, complemented
10#2417×C139C214yesmaximal, complemented
11#2415×C139C214yesmaximal, complemented
12#2311×C139C211yesmaximal, characteristic, complemented
13#2296×C139C211yesmaximal, characteristic, complemented
14C2×#391×C139C211yesmaximal, characteristic, complemented
15C22×#41×C139C2211yescharacteristic
16C22×#41×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18#536×C139—28no—
19#536×C139—28no—
20#532×C139—28no—
21C2×C4⋊Q8×C139C2212yes—
22C2×C4⋊Q8×C139C2211yescharacteristic
23C2×C4⋊Q8×C139C2212yes—
24C2×#127×C139C2211yescharacteristic
25C2×#124×C139C2212yes—
26C2×#124×C139C2212yes—
27C2×#124×C139C2211yescharacteristic
28C2×#124×C139C2211yescharacteristic
29C2×#123×C139C2214yes—
30C2×#123×C139C2214yes—
31C2×C22⋊Q8×C139C2212yes—
32C2×C22⋊Q8×C139C2214yes—
33C2×C22⋊Q8×C139C2212yes—
34C2×#121×C139C2214yes—
35#520×C139—28no—
36C2×C4×Q8×C139C2212yes—
37C2×C4×D4×C139C2212yes—
38C2×C4×D4×C139C2214yes—
39C2×C4×D4×C139C2214yes—
40C2×#117×C139C2211yescharacteristic
41C2×#117×C139C2212yes—
42C2×#117×C139C2211yescharacteristic
43C22×C4⋊C4×C139C2211yescharacteristic
44C22×C4⋊C4×C139C2212yes—
45C22×C42×C139C2211yescharacteristic
46#398×C139C2218yes—
47#397×C139C2218yes—
48#396×C139C2218yes—
49#394×C139C2218yes—
50#391×C139C2212yes—
51#391×C139C2212yes—
52#391×C139C2212yes—
53#391×C139C2214yes—
54#390×C139C2212yes—
55#389×C139C2218yes—
56#389×C139C2212yes—
57#389×C139C2212yes—
58#388×C139C2218yes—
59#386×C139C2218yes—
60#386×C139C2214yes—
61#385×C139C2214yes—
62#380×C139C2218yes—
63#380×C139C2214yes—
64C4×C4⋊C4×C139C2212yes—
65C4×C4⋊C4×C139C2212yes—
66C2×#95×C139C2214yes—
67C2×#41×C139—24no—
68C2×#41×C139—24no—
69C2×#41×C139—24no—
70C2×#41×C139—24no—
71C2×#41×C139—24no—
72C2×#41×C139D418yes—
73C22×Q8×C139—24no—
74C22×Q8×C139—24no—
75C22×Q8×C139—24no—
76C22×Q8×C139C2312yes—
77C22×Q8×C139C2312yes—
78C22×Q8×C139C2311yescharacteristic
79C22×Q8×C139C2311yescharacteristic
80C22×D4×C139C2312yes—
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2314yes—
83C22×D4×C139C2312yes—
84C22×D4×C139C2311yescharacteristic
85C23×C4×C139C2312yes—
86C23×C4×C139C2312yes—
87C23×C4×C139C2312yes—
88C23×C4×C139C2312yes—
89C23×C4×C139C2312yes—
90C23×C4×C139C2314yes—
91C23×C4×C139C2311yescharacteristic
92C4⋊Q8×C139—24no—
93C4⋊Q8×C139—28no—
94C4⋊Q8×C139—28no—
95#127×C139—24no—
96#124×C139—24no—
97#124×C139—24no—
98#124×C139—28no—
99#124×C139—28no—
100#123×C139—216no—
101#123×C139—216no—
102C22⋊Q8×C139—216no—
103C22⋊Q8×C139—28no—
104C22⋊Q8×C139—28no—
105#121×C139—216no—
106C4×Q8×C139—28no—
107C4×D4×C139—216no—
108C4×D4×C139—216no—
109C4×D4×C139—28no—
110#117×C139—24no—
111#117×C139—28no—
112#117×C139D418yescomplemented
113C2×C4⋊C4×C139—24no—
114C2×C4⋊C4×C139—28no—
115C2×C4⋊C4×C139C2314yes—
116C2×C4⋊C4×C139C2318yes—
117C2×C4⋊C4×C139C2314yes—
118C2×C4⋊C4×C139C2314yes—
119C2×C4⋊C4×C139C2314yes—
120C2×C4⋊C4×C139C2312yes—
121C2×C4⋊C4×C139C2312yes—
122C2×C4⋊C4×C139C2312yes—
123C2×C4⋊C4×C139C2314yes—
124C2×C4⋊C4×C139C2314yes—
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C22⋊C4×C139C2314yes—
128C2×C22⋊C4×C139C2314yes—
129C2×C22⋊C4×C139C2314yes—
130C2×C22⋊C4×C139C2314yes—
131C2×C22⋊C4×C139C2318yes—
132C2×C22⋊C4×C139C2312yes—
133C2×C22⋊C4×C139C2314yes—
134C2×C22⋊C4×C139C2318yes—
135C2×C22⋊C4×C139C2312yes—
136C2×C42×C139—24no—
137C2×C42×C139C2312yes—
138C2×C42×C139C2311yescharacteristic
139C2×C42×C139C2311yescharacteristic
140C2×C42×C139C2314yes—
141C2×C42×C139C2312yes—
142C2×C42×C139C2312yes—
143#95×C139C2318yes—
144#95×C139C2314yes—
145#95×C139C2318yes—
146#95×C139C2314yes—
147#95×C139C2318yes—
148C24×C139C2412yes—
149C24×C139C2412yes—
150C24×C139C2411yescharacteristic
151#41×C139—232no—
152#41×C139—416no—
153C2×Q8×C139—22no—
154C2×Q8×C139—24no—
155C2×Q8×C139—24no—
156C2×Q8×C139—24no—
157C2×Q8×C139—24no—
158C2×Q8×C139—22no—
159C2×Q8×C139—22no—
160C2×Q8×C139—22no—
161C2×Q8×C139—24no—
162C2×Q8×C139—24no—
163C2×Q8×C139—22no—
164C2×Q8×C139—416no—
165C2×Q8×C139C2×D414yes—
166C2×D4×C139—24no—
167C2×D4×C139—24no—
168C2×D4×C139—28no—
169C2×D4×C139—24no—
170C2×D4×C139—24no—
171C2×D4×C139—24no—
172C2×D4×C139—22no—
173C2×D4×C139—22no—
174C2×D4×C139—22no—
175C2×D4×C139—22no—
176C2×D4×C139—22no—
177C2×D4×C139—28no—
178C2×D4×C139—44no—
179C2×D4×C139C2×D418yes—
180C2×D4×C139C2×D414yes—
181C22×C4×C139—24no—
182C22×C4×C139—24no—
183C22×C4×C139—24no—
184C22×C4×C139—24no—
185C22×C4×C139—24no—
186C22×C4×C139—24no—
187C22×C4×C139—24no—
188C22×C4×C139—24no—
189C22×C4×C139—24no—
190C22×C4×C139—24no—
191C22×C4×C139—24no—
192C22×C4×C139—28no—
193C22×C4×C139—42no—
194C22×C4×C139—48no—
195C22×C4×C139—44no—
196C22×C4×C139C2×D418yes—
197C22×C4×C139C2×D414yes—
198C22×C4×C139C2×D414yes—
199C22×C4×C139#4114yes—
200C22×C4×C139C2412yes—
201C22×C4×C139C2414yes—
202C22×C4×C139C2414yes—
203C22×C4×C139C2414yes—
204C22×C4×C139C2412yes—
205C22×C4×C139C2412yes—
206C22×C4×C139C2412yes—
207C22×C4×C139C2412yes—
208C22×C4×C139C2412yes—
209C22×C4×C139C2411yescharacteristic
210C22×C4×C139C2411yescharacteristic
211C4⋊C4×C139—24no—
212C4⋊C4×C139—28no—
213C4⋊C4×C139—24no—
214C4⋊C4×C139—24no—
215C4⋊C4×C139—28no—
216C4⋊C4×C139—216no—
217C4⋊C4×C139—28no—
218C4⋊C4×C139—28no—
219C4⋊C4×C139—28no—
220C4⋊C4×C139—44no—
221C4⋊C4×C139C2×D414yes—
222C4⋊C4×C139C2×D414yes—
223C22⋊C4×C139—24no—
224C22⋊C4×C139—28no—
225C22⋊C4×C139—216no—
226C22⋊C4×C139—28no—
227C22⋊C4×C139—28no—
228C22⋊C4×C139—28no—
229C22⋊C4×C139—28no—
230C22⋊C4×C139—48no—
231C22⋊C4×C139C2×D418yes—
232C42×C139—24no—
233C42×C139—22no—
234C42×C139—22no—
235C42×C139—28no—
236C42×C139—24no—
237C42×C139C2×D418yes—
238C23×C139—22no—
239C23×C139—22no—
240C23×C139—22no—
241C23×C139—22no—
242C23×C139—24no—
243C23×C139—24no—
244C23×C139—22no—
245C23×C139—22no—
246C23×C139—22no—
247C23×C139—24no—
248C23×C139—24no—
249C23×C139C22×D414yes—
250C23×C139C22×D412yes—
251C23×C139C22×D412yes—
252C23×C139C2×#4112yes—
253C23×C139C2511yescharacteristic
254Q8×C139—28no—
255Q8×C139—48no—
256Q8×C139—48no—
257Q8×C139—44no—
258D4×C139—216no—
259D4×C139—28no—
260D4×C139—416no—
261D4×C139—48no—
262D4×C139—44no—
263C2×C4×C139—22no—
264C2×C4×C139—22no—
265C2×C4×C139—22no—
266C2×C4×C139—24no—
267C2×C4×C139—24no—
268C2×C4×C139—22no—
269C2×C4×C139—216no—
270C2×C4×C139—22no—
271C2×C4×C139—24no—
272C2×C4×C139—24no—
273C2×C4×C139—22no—
274C2×C4×C139—24no—
275C2×C4×C139—24no—
276C2×C4×C139—22no—
277C2×C4×C139—22no—
278C2×C4×C139—24no—
279C2×C4×C139—24no—
280C2×C4×C139—22no—
281C2×C4×C139—24no—
282C2×C4×C139—28no—
283C2×C4×C139—22no—
284C2×C4×C139—48no—
285C2×C4×C139—48no—
286C2×C4×C139—48no—
287C2×C4×C139—88no—
288C2×C4×C139—84no—
289C2×C4×C139#121116yes—
290C2×C4×C139C22×D414yes—
291C2×C4×C139C22×D414yes—
292C2×C4×C139C22×D414yes—
293C2×C4×C139C22×D412yes—
294C2×C4×C139C22×D412yes—
295C2×C4×C139C22×D412yes—
296C2×C4×C139C22×D412yes—
297C2×C4×C139C2×#4112yes—
298C2×C4×C139C2×#4112yes—
299C2×C4×C1392−1+414yes—
300C22×C139—24no—
301C22×C139—22no—
302C22×C139—22no—
303C22×C139—24no—
304C22×C139—24no—
305C22×C139—28no—
306C22×C139—42no—
307C22×C139—42no—
308C22×C139—44no—
309C22×C139—42no—
310C22×C139—44no—
311C22×C139—42no—
312C22×C139—42no—
313C22×C139—44no—
314C22×C139C2×#12114yes—
315C22×C139C23×D411yescharacteristic
316C22×C139C23×D411yescharacteristic
317C22×C139C22×#4111yescharacteristic
318C22×C139C2×2−1+412yes—
319C22×C139#58512yes—
320C4×C139—24no—
321C4×C139—24no—
322C4×C139—24no—
323C4×C139—24no—
324C4×C139—42no—
325C4×C139—44no—
326C4×C139—44no—
327C4×C139—42no—
328C4×C139—44no—
329C4×C139C2×#12114yes—
330C4×C139C2×#12114yes—
331C2×C139—24no—
332C2×C139—44no—
333C2×C139—82no—
334C2×C139C22×#12111yescharacteristic
335C2×C139#348912yes—
336C2×C139#349911yescharacteristic
337C2×C139#350011yescharacteristic
338C2×C139#350712yes—
339#35621C13911yesmaximal, characteristic, direct product factor, Sylow
340C139#3562111yescharacteristic, direct product factor, Sylow
341C2×#536C2×C13911yescharacteristic, complemented
342C2×#536C2×C13911yescharacteristic, complemented
343C2×#532C2×C13911yescharacteristic
344C2×#520C2×C13911yescharacteristic, complemented
345#2547C2×C13912yescomplemented
346#2546C2×C13912yescomplemented
347#2545C2×C13912yescomplemented
348#2544C2×C13912yescomplemented
349#2425C2×C13918yescomplemented
350#2417C2×C13914yescomplemented
351#2415C2×C13914yescomplemented
352#2311C2×C13911yescharacteristic, complemented
353#2296C2×C13911yescharacteristic, complemented
354C2×#391C2×C13911yescharacteristic, complemented
355C22×#41C22×C13911yescharacteristic
356C22×#41C22×C13911yescharacteristic
357C23×Q8C22×C13911yescharacteristic
358#536—28no—
359#536—28no—
360#532—28no—
361C2×C4⋊Q8C22×C13911yescharacteristic
362C2×C4⋊Q8C22×C13912yes—
363C2×C4⋊Q8C22×C13912yes—
364C2×#127C22×C13911yescharacteristic
365C2×#124C22×C13911yescharacteristic
366C2×#124C22×C13911yescharacteristic
367C2×#124C22×C13912yes—
368C2×#124C22×C13912yes—
369C2×#123C22×C13914yes—
370C2×#123C22×C13914yes—
371C2×C22⋊Q8C22×C13912yes—
372C2×C22⋊Q8C22×C13914yes—
373C2×C22⋊Q8C22×C13912yes—
374C2×#121C22×C13914yes—
375#520—28no—
376C2×C4×Q8C22×C13912yes—
377C2×C4×D4C22×C13914yes—
378C2×C4×D4C22×C13912yes—
379C2×C4×D4C22×C13914yes—
380C2×#117C22×C13911yescharacteristic
381C2×#117C22×C13912yes—
382C2×#117C22×C13911yescharacteristic
383C22×C4⋊C4C22×C13911yescharacteristic
384C22×C4⋊C4C22×C13912yes—
385C22×C42C22×C13911yescharacteristic
386#398C22×C13918yes—
387#397C22×C13918yes—
388#396C22×C13918yes—
389#394C22×C13918yes—
390#391C22×C13912yes—
391#391C22×C13914yes—
392#391C22×C13912yes—
393#391C22×C13912yes—
394#390C22×C13912yes—
395#389C22×C13912yes—
396#389C22×C13918yes—
397#389C22×C13912yes—
398#388C22×C13918yes—
399#386C22×C13914yes—
400#386C22×C13918yes—
401#385C22×C13914yes—
402#380C22×C13914yes—
403#380C22×C13918yes—
404C4×C4⋊C4C22×C13912yes—
405C4×C4⋊C4C22×C13912yes—
406C2×#95C22×C13914yes—
407C2×#41—24no—
408C2×#41—24no—
409C2×#41—24no—
410C2×#41—24no—
411C2×#41—24no—
412C2×#41D4×C13918yes—
413C22×Q8—24no—
414C22×Q8—24no—
415C22×Q8—24no—
416C22×Q8C23×C13912yes—
417C22×Q8C23×C13912yes—
418C22×Q8C23×C13911yescharacteristic
419C22×Q8C23×C13911yescharacteristic
420C22×D4C23×C13912yes—
421C22×D4C23×C13911yescharacteristic
422C22×D4C23×C13914yes—
423C22×D4C23×C13912yes—
424C22×D4C23×C13911yescharacteristic
425C23×C4C23×C13912yes—
426C23×C4C23×C13912yes—
427C23×C4C23×C13912yes—
428C23×C4C23×C13912yes—
429C23×C4C23×C13912yes—
430C23×C4C23×C13914yes—
431C23×C4C23×C13911yescharacteristic
432C4⋊Q8—24no—
433C4⋊Q8—28no—
434C4⋊Q8—28no—
435#127—24no—
436#124—24no—
437#124—24no—
438#124—28no—
439#124—28no—
440#123—216no—
441#123—216no—
442C22⋊Q8—216no—
443C22⋊Q8—28no—
444C22⋊Q8—28no—
445#121—216no—
446C4×Q8—28no—
447C4×D4—216no—
448C4×D4—216no—
449C4×D4—28no—
450#117—24no—
451#117—28no—
452#117D4×C13918yescomplemented
453C2×C4⋊C4—24no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4C23×C13912yes—
456C2×C4⋊C4C23×C13912yes—
457C2×C4⋊C4C23×C13914yes—
458C2×C4⋊C4C23×C13912yes—
459C2×C4⋊C4C23×C13914yes—
460C2×C4⋊C4C23×C13914yes—
461C2×C4⋊C4C23×C13918yes—
462C2×C4⋊C4C23×C13914yes—
463C2×C4⋊C4C23×C13914yes—
464C2×C4⋊C4C23×C13914yes—
465C2×C4⋊C4C23×C13911yescharacteristic
466C2×C4⋊C4C23×C13911yescharacteristic
467C2×C22⋊C4C23×C13914yes—
468C2×C22⋊C4C23×C13912yes—
469C2×C22⋊C4C23×C13914yes—
470C2×C22⋊C4C23×C13914yes—
471C2×C22⋊C4C23×C13918yes—
472C2×C22⋊C4C23×C13914yes—
473C2×C22⋊C4C23×C13914yes—
474C2×C22⋊C4C23×C13918yes—
475C2×C22⋊C4C23×C13912yes—
476C2×C42—24no—
477C2×C42C23×C13914yes—
478C2×C42C23×C13912yes—
479C2×C42C23×C13912yes—
480C2×C42C23×C13911yescharacteristic
481C2×C42C23×C13911yescharacteristic
482C2×C42C23×C13912yes—
483#95C23×C13918yes—
484#95C23×C13918yes—
485#95C23×C13914yes—
486#95C23×C13914yes—
487#95C23×C13918yes—
488C24C24×C13912yes—
489C24C24×C13912yes—
490C24C24×C13911yescharacteristic
491#41—232no—
492#41—416no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—22no—
504C2×Q8—416no—
505C2×Q8C2×D4×C13914yes—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—28no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—28no—
518C2×D4—44no—
519C2×D4C2×D4×C13918yes—
520C2×D4C2×D4×C13914yes—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—28no—
533C22×C4—42no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4C2×D4×C13918yes—
537C22×C4C2×D4×C13914yes—
538C22×C4C2×D4×C13914yes—
539C22×C4#41×C13914yes—
540C22×C4C24×C13912yes—
541C22×C4C24×C13914yes—
542C22×C4C24×C13914yes—
543C22×C4C24×C13914yes—
544C22×C4C24×C13912yes—
545C22×C4C24×C13912yes—
546C22×C4C24×C13912yes—
547C22×C4C24×C13912yes—
548C22×C4C24×C13912yes—
549C22×C4C24×C13911yescharacteristic
550C22×C4C24×C13911yescharacteristic
551C4⋊C4—24no—
552C4⋊C4—28no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—28no—
556C4⋊C4—216no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—44no—
561C4⋊C4C2×D4×C13914yes—
562C4⋊C4C2×D4×C13914yes—
563C22⋊C4—24no—
564C22⋊C4—28no—
565C22⋊C4—216no—
566C22⋊C4—28no—
567C22⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—48no—
571C22⋊C4C2×D4×C13918yes—
572C42—24no—
573C42—22no—
574C42—22no—
575C42—28no—
576C42—24no—
577C42C2×D4×C13918yes—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23C22×D4×C13914yes—
590C23C22×D4×C13912yes—
591C23C22×D4×C13912yes—
592C23C2×#41×C13912yes—
593C23C25×C13911yescharacteristic
594Q8—28no—
595Q8—48no—
596Q8—48no—
597Q8—44no—
598D4—216no—
599D4—28no—
600D4—416no—
601D4—48no—
602D4—44no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—216no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—48no—
625C2×C4—48no—
626C2×C4—48no—
627C2×C4—88no—
628C2×C4—84no—
629C2×C4#121×C139116yes—
630C2×C4C22×D4×C13914yes—
631C2×C4C22×D4×C13914yes—
632C2×C4C22×D4×C13914yes—
633C2×C4C22×D4×C13912yes—
634C2×C4C22×D4×C13912yes—
635C2×C4C22×D4×C13912yes—
636C2×C4C22×D4×C13912yes—
637C2×C4C2×#41×C13912yes—
638C2×C4C2×#41×C13912yes—
639C2×C42−1+4×C13914yes—
640C22—24no—
641C22—22no—
642C22—22no—
643C22—24no—
644C22—24no—
645C22—28no—
646C22—42no—
647C22—42no—
648C22—44no—
649C22—42no—
650C22—44no—
651C22—42no—
652C22—42no—
653C22—44no—
654C22C2×#121×C13914yes—
655C22C23×D4×C13911yescharacteristic
656C22C23×D4×C13911yescharacteristic
657C22C22×#41×C13911yescharacteristic
658C22C2×2−1+4×C13912yes—
659C22#585×C13912yes—
660C4—24no—
661C4—24no—
662C4—24no—
663C4—24no—
664C4—42no—
665C4—44no—
666C4—42no—
667C4—44no—
668C4—44no—
669C4C2×#121×C13914yes—
670C4C2×#121×C13914yes—
671C2—24no—
672C2—44no—
673C2—82no—
674C2C22×#121×C13911yescharacteristic
675C2#3489×C13912yes—
676C2#3499×C13911yescharacteristic
677C2#3500×C13911yescharacteristic
678C2#3507×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC2×#532×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#536×C139C2semidirect
2. C2×#536×C139C2semidirect
4. C2×#520×C139C2semidirect
5. #2547×C139C2semidirect
6. #2546×C139C2semidirect
7. #2545×C139C2semidirect
8. #2544×C139C2semidirect
9. #2425×C139C2semidirect
10. #2417×C139C2semidirect
11. #2415×C139C2semidirect
12. #2311×C139C2semidirect
13. #2296×C139C2semidirect
14. C2×#391×C139C2semidirect
112. #117×C139D4semidirect
339. #35621C139direct (N × H)
340. C139#35621direct (N × H)
341. C2×#536C2×C139semidirect
342. C2×#536C2×C139semidirect
344. C2×#520C2×C139semidirect
345. #2547C2×C139semidirect
346. #2546C2×C139semidirect
347. #2545C2×C139semidirect
348. #2544C2×C139semidirect
349. #2425C2×C139semidirect
350. #2417C2×C139semidirect
351. #2415C2×C139semidirect
352. #2311C2×C139semidirect
353. #2296C2×C139semidirect
354. C2×#391C2×C139semidirect
452. #117D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1392
C2×#532×C1392
C2×#520×C1392
#2547×C1392
#2546×C1392
#2545×C1392
#2544×C1392
#2425×C1392
#2417×C1392
#2415×C1392
#2311×C1392
#2296×C1392
C2×#391×C1392
#35621139