Finite Group Databasebeta

← C139×#24512 #48019108

Subgroups — C139×#24512 #48019108

Order 35584.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic
2C2×#433×C139C211yesmaximal, characteristic, complemented
3#2624×C139C211yesmaximal, characteristic, complemented
4#2309×C139C211yesmaximal, characteristic, complemented
5#2067×C139C211yesmaximal, characteristic, complemented
6#2065×C139C211yesmaximal, characteristic, complemented
7#2054×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#1972×C139C211yesmaximal, characteristic, complemented
10#1970×C139C211yesmaximal, characteristic, complemented
11#1936×C139C211yesmaximal, characteristic, complemented
12#1934×C139C211yesmaximal, characteristic, complemented
13#1875×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#117×C139C2211yescharacteristic
21C2×#117×C139C2211yescharacteristic
22#447×C139—24no—
23#433×C139—24no—
24C2×#107×C139C2211yescharacteristic, complemented
25C2×#106×C139C2211yescharacteristic, complemented
26C2×C4⋊C8×C139C2211yescharacteristic, complemented
27C2×C4⋊C8×C139C2211yescharacteristic, complemented
28C2×#102×C139C2211yescharacteristic
29C2×#102×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic, complemented
35C2×#102×C139C2211yescharacteristic, complemented
36C2×C22⋊C8×C139C2211yescharacteristic
37C2×C22⋊C8×C139C2211yescharacteristic
38C2×#97×C139C2211yescharacteristic, complemented
39C2×C4×C8×C139C2211yescharacteristic, complemented
40#399×C139—21no—
41#397×C139—21no—
42#394×C139—21no—
43#394×C139—21no—
44#390×C139—21no—
45#390×C139—21no—
46#390×C139C2211yescharacteristic
47#390×C139C2211yescharacteristic
48#390×C139C2211yescharacteristic
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic, complemented
51#390×C139C2211yescharacteristic, complemented
52#389×C139C2211yescharacteristic, complemented
53#389×C139C2211yescharacteristic, complemented
54#380×C139C2211yescharacteristic
55#379×C139—21no—
56#379×C139—21no—
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61C25×C139—21no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—41no—
69C22×D4×C139—41no—
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C23×C4×C139C2311yescharacteristic
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—22no—
78C2×D8×C139—41no—
79C2×D8×C139—41no—
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84#121×C139—22no—
85#121×C139—22no—
86#117×C139—22no—
87#117×C139—22no—
88#117×C139—41no—
89#117×C139—41no—
90C2×C4⋊C4×C139—21no—
91C2×C4⋊C4×C139—21no—
92C2×C4⋊C4×C139D411yescharacteristic
93C2×C4⋊C4×C139D411yescharacteristic
94C2×C4⋊C4×C139C2311yescharacteristic
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C22⋊C4×C139—21no—
100C2×C22⋊C4×C139—21no—
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C22⋊C4×C139D411yescharacteristic
116C2×C42×C139—21no—
117C2×C42×C139C2311yescharacteristic
118C2×C42×C139C2311yescharacteristic
119#107×C139—41no—
120#106×C139—41no—
121C4⋊C8×C139—22no—
122C4⋊C8×C139—22no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—41no—
128#102×C139—41no—
129#102×C139—41no—
130#102×C139—41no—
131C22⋊C8×C139—22no—
132C22⋊C8×C139D414yes—
133#97×C139—22no—
134C4×C8×C139—22no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138C24×C139—24no—
139C24×C139—21no—
140C24×C139—21no—
141C24×C139—21no—
142C24×C139—42no—
143C24×C139—42no—
144C24×C139—81no—
145C24×C139—81no—
146C24×C139—81no—
147C24×C139—81no—
148C24×C139C2×D411yescharacteristic
149C2×D4×C139—24no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—44no—
167C2×D4×C139—44no—
168C2×D4×C139—44no—
169C2×D4×C139—44no—
170C2×D4×C139—42no—
171C2×D4×C139—42no—
172C2×D4×C139—42no—
173C2×D4×C139—81no—
174C2×D4×C139—81no—
175C2×D4×C139#4112yes—
176C2×D4×C139#4112yes—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139C2×D411yescharacteristic
187C22×C4×C139C2×D411yescharacteristic
188C22×C4×C139C2×D411yescharacteristic
189C22×C4×C139C2×D411yescharacteristic
190C22×C4×C139C2×D411yescharacteristic
191C22×C4×C139C2×D412yes—
192C22×C4×C139#4112yes—
193C22×C4×C139C2411yescharacteristic
194D8×C139—44no—
195D8×C139—44no—
196C2×C8×C139—21no—
197C2×C8×C139—21no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139—21no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139C2×D412yes—
207C2×C8×C139C2×D412yes—
208C4⋊C4×C139—22no—
209C4⋊C4×C139—22no—
210C4⋊C4×C139—21no—
211C4⋊C4×C139—21no—
212C4⋊C4×C139—21no—
213C4⋊C4×C139—21no—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—81no—
221C4⋊C4×C139—81no—
222C22⋊C4×C139—22no—
223C22⋊C4×C139—22no—
224C22⋊C4×C139—42no—
225C22⋊C4×C139—42no—
226C22⋊C4×C139—81no—
227C22⋊C4×C139—81no—
228C22⋊C4×C139—81no—
229C22⋊C4×C139—81no—
230C22⋊C4×C139—81no—
231C22⋊C4×C139—81no—
232C22⋊C4×C139—81no—
233C22⋊C4×C139—81no—
234C22⋊C4×C139—81no—
235C22⋊C4×C139—81no—
236C22⋊C4×C139—81no—
237C22⋊C4×C139—81no—
238C22⋊C4×C139—81no—
239C42×C139—21no—
240C42×C139—21no—
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—42no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—22no—
251C23×C139—22no—
252C23×C139—48no—
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×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—84no—
273C23×C139—84no—
274C23×C139—84no—
275C23×C139—84no—
276C23×C139—84no—
277C23×C139—84no—
278C23×C139#12112yes—
279C23×C139C22×D411yescharacteristic
280D4×C139—22no—
281D4×C139—22no—
282D4×C139—22no—
283D4×C139—22no—
284D4×C139—48no—
285D4×C139—41no—
286D4×C139—41no—
287D4×C139—41no—
288D4×C139—41no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—84no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—22no—
297C2×C4×C139—22no—
298C2×C4×C139—22no—
299C2×C4×C139—22no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
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—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139#12112yes—
328C2×C4×C139C22×D411yescharacteristic
329C2×C4×C139C2×#4111yescharacteristic
330C2×C4×C139C2×#4111yescharacteristic
331C2×C4×C139C2×#4111yescharacteristic
332C2×C4×C139H(5,𝔽2)11yescharacteristic
333C2×C4×C139H(5,𝔽2)11yescharacteristic
334C8×C139—22no—
335C8×C139—22no—
336C8×C139—41no—
337C8×C139—41no—
338C22×C139—22no—
339C22×C139—22no—
340C22×C139—22no—
341C22×C139—41no—
342C22×C139—41no—
343C22×C139—41no—
344C22×C139—41no—
345C22×C139—42no—
346C22×C139—42no—
347C22×C139—42no—
348C22×C139—42no—
349C22×C139—42no—
350C22×C139—42no—
351C22×C139—816no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—81no—
359C22×C139—81no—
360C22×C139—81no—
361C22×C139—81no—
362C22×C139—81no—
363C22×C139—81no—
364C22×C139—81no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139C2×#12111yescharacteristic
368C22×C139#52511yescharacteristic
369C22×C139#53511yescharacteristic
370C22×C139#57611yescharacteristic
371C22×C139#57611yescharacteristic
372C22×C139#57611yescharacteristic
373C22×C139#57711yescharacteristic
374C4×C139—22no—
375C4×C139—41no—
376C4×C139—41no—
377C4×C139—41no—
378C4×C139—41no—
379C4×C139—81no—
380C4×C139—81no—
381C4×C139—81no—
382C4×C139—81no—
383C4×C139—81no—
384C4×C139#54611yescharacteristic
385C4×C139#54611yescharacteristic
386C4×C139#55111yescharacteristic
387C4×C139#55111yescharacteristic
388C2×C139—42no—
389C2×C139—82no—
390C2×C139—82no—
391C2×C139—161no—
392C2×C139#241111yescharacteristic
393C2×C139#305811yescharacteristic
394C2×C139#306211yescharacteristic
395C2×C139#311811yescharacteristic
396C2×C139#312211yescharacteristic
397C2×C139#322011yescharacteristic
398C2×C139#322411yescharacteristic
399#24512C13911yesmaximal, characteristic, direct product factor, Sylow
400C139#2451211yescharacteristic, direct product factor, Sylow
401C2×#447C2×C13911yescharacteristic
402C2×#433C2×C13911yescharacteristic, complemented
403#2624C2×C13911yescharacteristic, complemented
404#2309C2×C13911yescharacteristic, complemented
405#2067C2×C13911yescharacteristic, complemented
406#2065C2×C13911yescharacteristic, complemented
407#2054C2×C13911yescharacteristic, complemented
408#2054C2×C13911yescharacteristic, complemented
409#1972C2×C13911yescharacteristic, complemented
410#1970C2×C13911yescharacteristic, complemented
411#1936C2×C13911yescharacteristic, complemented
412#1934C2×C13911yescharacteristic, complemented
413#1875C2×C13911yescharacteristic, complemented
414#1854C2×C13911yescharacteristic, complemented
415#1786C2×C13911yescharacteristic, complemented
416C23×D4C22×C13911yescharacteristic
417C22×D8C22×C13911yescharacteristic
418C22×D8C22×C13911yescharacteristic
419C2×#121C22×C13911yescharacteristic
420C2×#117C22×C13911yescharacteristic
421C2×#117C22×C13911yescharacteristic
422#447—24no—
423#433—24no—
424C2×#107C22×C13911yescharacteristic, complemented
425C2×#106C22×C13911yescharacteristic, complemented
426C2×C4⋊C8C22×C13911yescharacteristic, complemented
427C2×C4⋊C8C22×C13911yescharacteristic, complemented
428C2×#102C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×#102C22×C13911yescharacteristic
434C2×#102C22×C13911yescharacteristic, complemented
435C2×#102C22×C13911yescharacteristic, complemented
436C2×C22⋊C8C22×C13911yescharacteristic
437C2×C22⋊C8C22×C13911yescharacteristic
438C2×#97C22×C13911yescharacteristic, complemented
439C2×C4×C8C22×C13911yescharacteristic, complemented
440#399—21no—
441#397—21no—
442#394—21no—
443#394—21no—
444#390—21no—
445#390—21no—
446#390C22×C13911yescharacteristic
447#390C22×C13911yescharacteristic
448#390C22×C13911yescharacteristic
449#390C22×C13911yescharacteristic
450#390C22×C13911yescharacteristic, complemented
451#390C22×C13911yescharacteristic, complemented
452#389C22×C13911yescharacteristic, complemented
453#389C22×C13911yescharacteristic, complemented
454#380C22×C13911yescharacteristic
455#379—21no—
456#379—21no—
457#340C22×C13911yescharacteristic, complemented
458#340C22×C13911yescharacteristic, complemented
459#340C22×C13911yescharacteristic, complemented
460#340C22×C13911yescharacteristic, complemented
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C13911yescharacteristic
471C22×D4C23×C13911yescharacteristic
472C22×D4C23×C13911yescharacteristic
473C23×C4C23×C13911yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C13911yescharacteristic
481C22×C8C23×C13911yescharacteristic
482C22×C8C23×C13911yescharacteristic
483C22×C8C23×C13911yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
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×C4⋊C4C23×C13911yescharacteristic
498C2×C4⋊C4C23×C13911yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4D4×C13911yescharacteristic
515C2×C22⋊C4D4×C13911yescharacteristic
516C2×C42—21no—
517C2×C42C23×C13911yescharacteristic
518C2×C42C23×C13911yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C13914yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C13911yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
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—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C13912yes—
576C2×D4#41×C13912yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4C2×D4×C13911yescharacteristic
587C22×C4C2×D4×C13911yescharacteristic
588C22×C4C2×D4×C13911yescharacteristic
589C22×C4C2×D4×C13911yescharacteristic
590C22×C4C2×D4×C13911yescharacteristic
591C22×C4C2×D4×C13912yes—
592C22×C4#41×C13912yes—
593C22×C4C24×C13911yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C13912yes—
607C2×C8C2×D4×C13912yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C13912yes—
679C23C22×D4×C13911yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4#121×C13912yes—
728C2×C4C22×D4×C13911yescharacteristic
729C2×C4C2×#41×C13911yescharacteristic
730C2×C4C2×#41×C13911yescharacteristic
731C2×C4C2×#41×C13911yescharacteristic
732C2×C4H(5,𝔽2)×C13911yescharacteristic
733C2×C4H(5,𝔽2)×C13911yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C13911yescharacteristic
768C22#525×C13911yescharacteristic
769C22#535×C13911yescharacteristic
770C22#576×C13911yescharacteristic
771C22#576×C13911yescharacteristic
772C22#576×C13911yescharacteristic
773C22#577×C13911yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C13911yescharacteristic
785C4#546×C13911yescharacteristic
786C4#551×C13911yescharacteristic
787C4#551×C13911yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2#2411×C13911yescharacteristic
793C2#3058×C13911yescharacteristic
794C2#3062×C13911yescharacteristic
795C2#3118×C13911yescharacteristic
796C2#3122×C13911yescharacteristic
797C2#3220×C13911yescharacteristic
798C2#3224×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#433×C139C2semidirect
3. #2624×C139C2semidirect
4. #2309×C139C2semidirect
5. #2067×C139C2semidirect
6. #2065×C139C2semidirect
7. #2054×C139C2semidirect
8. #2054×C139C2semidirect
9. #1972×C139C2semidirect
10. #1970×C139C2semidirect
11. #1936×C139C2semidirect
12. #1934×C139C2semidirect
13. #1875×C139C2semidirect
14. #1854×C139C2semidirect
15. #1786×C139C2semidirect
24. C2×#107×C139C22semidirect
25. C2×#106×C139C22semidirect
26. C2×C4⋊C8×C139C22semidirect
27. C2×C4⋊C8×C139C22semidirect
34. C2×#102×C139C22semidirect
35. C2×#102×C139C22semidirect
38. C2×#97×C139C22semidirect
39. C2×C4×C8×C139C22semidirect
50. #390×C139C22semidirect
51. #390×C139C22semidirect
52. #389×C139C22semidirect
53. #389×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
399. #24512C139direct (N × H)
400. C139#24512direct (N × H)
402. C2×#433C2×C139semidirect
403. #2624C2×C139semidirect
404. #2309C2×C139semidirect
405. #2067C2×C139semidirect
406. #2065C2×C139semidirect
407. #2054C2×C139semidirect
408. #2054C2×C139semidirect
409. #1972C2×C139semidirect
410. #1970C2×C139semidirect
411. #1936C2×C139semidirect
412. #1934C2×C139semidirect
413. #1875C2×C139semidirect
414. #1854C2×C139semidirect
415. #1786C2×C139semidirect
424. C2×#107C22×C139semidirect
425. C2×#106C22×C139semidirect
426. C2×C4⋊C8C22×C139semidirect
427. C2×C4⋊C8C22×C139semidirect
434. C2×#102C22×C139semidirect
435. C2×#102C22×C139semidirect
438. C2×#97C22×C139semidirect
439. C2×C4×C8C22×C139semidirect
450. #390C22×C139semidirect
451. #390C22×C139semidirect
452. #389C22×C139semidirect
453. #389C22×C139semidirect
457. #340C22×C139semidirect
458. #340C22×C139semidirect
459. #340C22×C139semidirect
460. #340C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
C2×#433×C1392
#2624×C1392
#2309×C1392
#2067×C1392
#2065×C1392
#2054×C1392
#1972×C1392
#1970×C1392
#1936×C1392
#1934×C1392
#1875×C1392
#1854×C1392
#1786×C1392
#24512139