Finite Group Databasebeta

← C139×#36434 #48031030

Subgroups — C139×#36434 #48031030

Order 35584.

3086 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C211yesmaximal, characteristic, complemented
3C2×#548×C139C211yesmaximal, characteristic, complemented
4C22×C4×Q8×C139C211yesmaximal, characteristic, complemented
5#2850×C139C213yesmaximal, complemented
6#2545×C139C213yesmaximal, complemented
7#2536×C139C213yesmaximal, complemented
8#2429×C139C213yesmaximal, complemented
9#2426×C139C213yesmaximal, complemented
10#2417×C139C213yesmaximal, complemented
11#2416×C139C213yesmaximal, complemented
12#2351×C139C211yesmaximal, characteristic, complemented
13#2341×C139C211yesmaximal, characteristic, complemented
14Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
15C4×#121×C139C213yesmaximal, complemented
16C22×#41×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18C23×Q8×C139C2211yescharacteristic
19D4×Q8×C139—28no—
20#548×C139—28no—
21#548×C139—28no—
22C2×C4⋊Q8×C139C2213yes—
23C2×#124×C139C2213yes—
24C2×#124×C139C2213yes—
25C2×C22⋊Q8×C139C2213yes—
26C2×C22⋊Q8×C139C2213yes—
27C2×C22⋊Q8×C139C2213yes—
28C2×C22⋊Q8×C139C2213yes—
29C2×#121×C139C2213yes—
30C2×#121×C139C2213yes—
31C2×#121×C139C2213yes—
32C2×C4×Q8×C139—28no—
33C2×C4×Q8×C139C2213yes—
34C2×C4×Q8×C139C2211yescharacteristic
35C2×C4×Q8×C139C2211yescharacteristic
36C2×C4×Q8×C139C2211yescharacteristic
37C2×C4×Q8×C139C2213yes—
38C2×C4×Q8×C139C2211yescharacteristic
39C2×C4×D4×C139C2213yes—
40C2×C4×D4×C139C2213yes—
41C2×C4×D4×C139C2213yes—
42C22×C4⋊C4×C139C2213yes—
43C22×C42×C139C2213yes—
44#398×C139C2216yes—
45#396×C139C2216yes—
46#396×C139C2216yes—
47#394×C139C2216yes—
48#391×C139C2213yes—
49#391×C139C2213yes—
50#390×C139C2213yes—
51#390×C139C2213yes—
52#390×C139C2213yes—
53#389×C139C2213yes—
54#389×C139C2213yes—
55#389×C139C2213yes—
56#388×C139C2213yes—
57#388×C139C2216yes—
58#388×C139C2213yes—
59#388×C139C2216yes—
60#386×C139C2211yescharacteristic
61#386×C139C2213yes—
62#386×C139C2216yes—
63#382×C139C2213yes—
64#380×C139C2213yes—
65#380×C139C2213yes—
66#380×C139C2213yes—
67C4×C4⋊C4×C139C2213yes—
68C4×C22⋊C4×C139C2213yes—
69C4×C22⋊C4×C139C2213yes—
70C2×#41×C139—24no—
71C2×#41×C139—24no—
72C2×#41×C139—24no—
73C22×Q8×C139—24no—
74C22×Q8×C139—24no—
75C22×Q8×C139—24no—
76C22×Q8×C139—24no—
77C22×Q8×C139—24no—
78C22×Q8×C139D418yescomplemented
79C22×Q8×C139C2313yes—
80C22×Q8×C139C2313yes—
81C22×Q8×C139C2311yescharacteristic
82C22×D4×C139C2313yes—
83C22×D4×C139C2313yes—
84C22×D4×C139C2313yes—
85C22×D4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2313yes—
88C23×C4×C139C2313yes—
89C23×C4×C139C2313yes—
90C23×C4×C139C2313yes—
91C4⋊Q8×C139—212no—
92#124×C139—212no—
93#124×C139—212no—
94C22⋊Q8×C139—212no—
95C22⋊Q8×C139—212no—
96C22⋊Q8×C139—212no—
97C22⋊Q8×C139—212no—
98#121×C139—212no—
99#121×C139—212no—
100#121×C139—212no—
101C4×Q8×C139—24no—
102C4×Q8×C139—24no—
103C4×Q8×C139—24no—
104C4×Q8×C139—212no—
105C4×Q8×C139—212no—
106C4×Q8×C139D418yescomplemented
107C4×D4×C139—212no—
108C4×D4×C139—212no—
109C4×D4×C139—212no—
110C2×C4⋊C4×C139—212no—
111C2×C4⋊C4×C139C2316yes—
112C2×C4⋊C4×C139C2313yes—
113C2×C4⋊C4×C139C2313yes—
114C2×C4⋊C4×C139C2316yes—
115C2×C4⋊C4×C139C2313yes—
116C2×C4⋊C4×C139C2313yes—
117C2×C4⋊C4×C139C2313yes—
118C2×C4⋊C4×C139C2313yes—
119C2×C4⋊C4×C139C2313yes—
120C2×C4⋊C4×C139C2313yes—
121C2×C4⋊C4×C139C2313yes—
122C2×C22⋊C4×C139C2313yes—
123C2×C22⋊C4×C139C2316yes—
124C2×C22⋊C4×C139C2313yes—
125C2×C22⋊C4×C139C2316yes—
126C2×C22⋊C4×C139C2311yescharacteristic
127C2×C22⋊C4×C139C2311yescharacteristic
128C2×C22⋊C4×C139C2313yes—
129C2×C22⋊C4×C139C2313yes—
130C2×C22⋊C4×C139C2313yes—
131C2×C22⋊C4×C139C2313yes—
132C2×C22⋊C4×C139C2311yescharacteristic
133C2×C22⋊C4×C139C2313yes—
134C2×C22⋊C4×C139C2316yes—
135C2×C42×C139—212no—
136C2×C42×C139C2313yes—
137C2×C42×C139C2313yes—
138C2×C42×C139C2313yes—
139C2×C42×C139C2313yes—
140C2×C42×C139C2313yes—
141C2×C42×C139C2313yes—
142#95×C139C2313yes—
143#95×C139C2316yes—
144#95×C139C2313yes—
145#95×C139C2316yes—
146#95×C139C2311yescharacteristic
147#95×C139C2313yes—
148#95×C139C2311yescharacteristic
149#95×C139C2313yes—
150C24×C139C2413yes—
151C24×C139C2411yescharacteristic
152C24×C139C2411yescharacteristic
153#41×C139—416no—
154C2×Q8×C139—232no—
155C2×Q8×C139—26no—
156C2×Q8×C139—26no—
157C2×Q8×C139—26no—
158C2×Q8×C139—26no—
159C2×Q8×C139—26no—
160C2×Q8×C139—416no—
161C2×Q8×C139C2×D4112yes—
162C2×Q8×C139C2×D414yes—
163C2×Q8×C139C2×D414yes—
164C2×Q8×C139#4114yes—
165C2×D4×C139—22no—
166C2×D4×C139—22no—
167C2×D4×C139—26no—
168C2×D4×C139—26no—
169C2×D4×C139—26no—
170C2×D4×C139—26no—
171C2×D4×C139—26no—
172C2×D4×C139—26no—
173C2×D4×C139—26no—
174C2×D4×C139—26no—
175C2×D4×C139—43no—
176C2×D4×C139#4114yescomplemented
177C22×C4×C139—22no—
178C22×C4×C139—22no—
179C22×C4×C139—26no—
180C22×C4×C139—26no—
181C22×C4×C139—22no—
182C22×C4×C139—26no—
183C22×C4×C139—26no—
184C22×C4×C139—26no—
185C22×C4×C139—26no—
186C22×C4×C139—26no—
187C22×C4×C139—26no—
188C22×C4×C139—26no—
189C22×C4×C139—26no—
190C22×C4×C139—43no—
191C22×C4×C139C2×D4112yes—
192C22×C4×C139C2413yes—
193C22×C4×C139C2411yescharacteristic
194C22×C4×C139C2413yes—
195C22×C4×C139C2413yes—
196C22×C4×C139C2413yes—
197C22×C4×C139C2411yescharacteristic
198C22×C4×C139C2411yescharacteristic
199C22×C4×C139C2413yes—
200C22×C4×C139C2413yes—
201C22×C4×C139C2411yescharacteristic
202C22×C4×C139C2411yescharacteristic
203C22×C4×C139C2413yes—
204C4⋊C4×C139—212no—
205C4⋊C4×C139—26no—
206C4⋊C4×C139—26no—
207C4⋊C4×C139—26no—
208C4⋊C4×C139—26no—
209C4⋊C4×C139—26no—
210C4⋊C4×C139—26no—
211C4⋊C4×C139—212no—
212C4⋊C4×C139—26no—
213C4⋊C4×C139—43no—
214C4⋊C4×C139C2×D4112yes—
215C22⋊C4×C139—22no—
216C22⋊C4×C139—26no—
217C22⋊C4×C139—26no—
218C22⋊C4×C139—22no—
219C22⋊C4×C139—26no—
220C22⋊C4×C139—26no—
221C22⋊C4×C139—26no—
222C22⋊C4×C139—212no—
223C22⋊C4×C139—212no—
224C22⋊C4×C139—26no—
225C22⋊C4×C139—22no—
226C22⋊C4×C139—26no—
227C22⋊C4×C139—46no—
228C42×C139—26no—
229C42×C139—26no—
230C42×C139—26no—
231C42×C139—26no—
232C42×C139—26no—
233C42×C139C2×D4112yes—
234C23×C139—21no—
235C23×C139—21no—
236C23×C139—21no—
237C23×C139—21no—
238C23×C139—21no—
239C23×C139—21no—
240C23×C139—21no—
241C23×C139—21no—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—23no—
245C23×C139—23no—
246C23×C139—23no—
247C23×C139—23no—
248C23×C139—23no—
249C23×C139—23no—
250C23×C139—23no—
251C23×C139C22×D412yes—
252C23×C139C2×#4112yes—
253C23×C139C2×#4112yes—
254C23×C1392−1+412yes—
255C23×C139C2511yescharacteristic
256Q8×C139—224no—
257Q8×C139—412no—
258Q8×C139#121116yescomplemented
259D4×C139—28no—
260D4×C139—412no—
261D4×C139—412no—
262D4×C139—412no—
263C2×C4×C139—28no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—23no—
267C2×C4×C139—23no—
268C2×C4×C139—23no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—23no—
274C2×C4×C139—224no—
275C2×C4×C139—21no—
276C2×C4×C139—23no—
277C2×C4×C139—23no—
278C2×C4×C139—23no—
279C2×C4×C139—23no—
280C2×C4×C139—21no—
281C2×C4×C139—21no—
282C2×C4×C139—23no—
283C2×C4×C139—23no—
284C2×C4×C139—23no—
285C2×C4×C139—21no—
286C2×C4×C139—23no—
287C2×C4×C139—21no—
288C2×C4×C139—23no—
289C2×C4×C139—23no—
290C2×C4×C139—23no—
291C2×C4×C139—23no—
292C2×C4×C139—21no—
293C2×C4×C139—412no—
294C2×C4×C139—412no—
295C2×C4×C139—412no—
296C2×C4×C139C22×D412yes—
297C2×C4×C139C22×D416yes—
298C2×C4×C139C22×D416yes—
299C2×C4×C139C22×D416yes—
300C2×C4×C139C22×D416yes—
301C2×C4×C139C2×#4112yes—
302C2×C4×C139C2×#4116yes—
303C2×C4×C1392−1+412yes—
304C22×C139—22no—
305C22×C139—22no—
306C22×C139—22no—
307C22×C139—22no—
308C22×C139—22no—
309C22×C139—22no—
310C22×C139—22no—
311C22×C139—22no—
312C22×C139—22no—
313C22×C139—41no—
314C22×C139—41no—
315C22×C139—41no—
316C22×C139—41no—
317C22×C139—43no—
318C22×C139—43no—
319C22×C139—43no—
320C22×C139—43no—
321C22×C139—43no—
322C22×C139—43no—
323C22×C139—43no—
324C22×C139#54814yescomplemented
325C22×C139C23×D411yescharacteristic
326C22×C139C23×D411yescharacteristic
327C22×C139C22×#4111yescharacteristic
328C22×C139C22×#4111yescharacteristic
329C22×C139C2×2−1+411yescharacteristic
330C22×C139C2×2−1+411yescharacteristic
331C22×C139#58511yescharacteristic
332C4×C139—26no—
333C4×C139—22no—
334C4×C139—26no—
335C4×C139—22no—
336C4×C139—22no—
337C4×C139—41no—
338C4×C139—43no—
339C4×C139—43no—
340C4×C139—43no—
341C4×C139—41no—
342C4×C139—43no—
343C4×C139C2×#121112yes—
344C2×C139—24no—
345C2×C139—42no—
346C2×C139—83no—
347C2×C139C22×#12111yescharacteristic
348C2×C139C2×#54811yescharacteristic
349C2×C139D4×#4111yescharacteristic
350C2×C139#348211yescharacteristic
351C2×C139#348611yescharacteristic
352C2×C139#349711yescharacteristic
353C2×C139#351611yescharacteristic
354#36434C13911yesmaximal, characteristic, direct product factor, Sylow
355C139#3643411yescharacteristic, direct product factor, Sylow
356C2×D4×Q8C2×C13911yescharacteristic, complemented
357C2×#548C2×C13911yescharacteristic, complemented
358C2×#548C2×C13911yescharacteristic, complemented
359C22×C4×Q8C2×C13911yescharacteristic, complemented
360#2850C2×C13913yescomplemented
361#2545C2×C13913yescomplemented
362#2536C2×C13913yescomplemented
363#2429C2×C13913yescomplemented
364#2426C2×C13913yescomplemented
365#2417C2×C13913yescomplemented
366#2416C2×C13913yescomplemented
367#2351C2×C13911yescharacteristic, complemented
368#2341C2×C13911yescharacteristic, complemented
369Q8×C22⋊C4C2×C13911yescharacteristic, complemented
370C4×#121C2×C13913yescomplemented
371C22×#41C22×C13911yescharacteristic
372C23×Q8C22×C13911yescharacteristic
373C23×Q8C22×C13911yescharacteristic
374D4×Q8—28no—
375#548—28no—
376#548—28no—
377C2×C4⋊Q8C22×C13913yes—
378C2×#124C22×C13913yes—
379C2×#124C22×C13913yes—
380C2×C22⋊Q8C22×C13913yes—
381C2×C22⋊Q8C22×C13913yes—
382C2×C22⋊Q8C22×C13913yes—
383C2×C22⋊Q8C22×C13913yes—
384C2×#121C22×C13913yes—
385C2×#121C22×C13913yes—
386C2×#121C22×C13913yes—
387C2×C4×Q8—28no—
388C2×C4×Q8C22×C13911yescharacteristic
389C2×C4×Q8C22×C13911yescharacteristic
390C2×C4×Q8C22×C13911yescharacteristic
391C2×C4×Q8C22×C13913yes—
392C2×C4×Q8C22×C13913yes—
393C2×C4×Q8C22×C13911yescharacteristic
394C2×C4×D4C22×C13913yes—
395C2×C4×D4C22×C13913yes—
396C2×C4×D4C22×C13913yes—
397C22×C4⋊C4C22×C13913yes—
398C22×C42C22×C13913yes—
399#398C22×C13916yes—
400#396C22×C13916yes—
401#396C22×C13916yes—
402#394C22×C13916yes—
403#391C22×C13913yes—
404#391C22×C13913yes—
405#390C22×C13913yes—
406#390C22×C13913yes—
407#390C22×C13913yes—
408#389C22×C13913yes—
409#389C22×C13913yes—
410#389C22×C13913yes—
411#388C22×C13916yes—
412#388C22×C13916yes—
413#388C22×C13913yes—
414#388C22×C13913yes—
415#386C22×C13913yes—
416#386C22×C13916yes—
417#386C22×C13911yescharacteristic
418#382C22×C13913yes—
419#380C22×C13913yes—
420#380C22×C13913yes—
421#380C22×C13913yes—
422C4×C4⋊C4C22×C13913yes—
423C4×C22⋊C4C22×C13913yes—
424C4×C22⋊C4C22×C13913yes—
425C2×#41—24no—
426C2×#41—24no—
427C2×#41—24no—
428C22×Q8—24no—
429C22×Q8—24no—
430C22×Q8—24no—
431C22×Q8—24no—
432C22×Q8—24no—
433C22×Q8D4×C13918yescomplemented
434C22×Q8C23×C13913yes—
435C22×Q8C23×C13913yes—
436C22×Q8C23×C13911yescharacteristic
437C22×D4C23×C13913yes—
438C22×D4C23×C13913yes—
439C22×D4C23×C13913yes—
440C22×D4C23×C13911yescharacteristic
441C23×C4C23×C13913yes—
442C23×C4C23×C13913yes—
443C23×C4C23×C13911yescharacteristic
444C23×C4C23×C13913yes—
445C23×C4C23×C13913yes—
446C4⋊Q8—212no—
447#124—212no—
448#124—212no—
449C22⋊Q8—212no—
450C22⋊Q8—212no—
451C22⋊Q8—212no—
452C22⋊Q8—212no—
453#121—212no—
454#121—212no—
455#121—212no—
456C4×Q8—24no—
457C4×Q8—24no—
458C4×Q8—24no—
459C4×Q8—212no—
460C4×Q8—212no—
461C4×Q8D4×C13918yescomplemented
462C4×D4—212no—
463C4×D4—212no—
464C4×D4—212no—
465C2×C4⋊C4—212no—
466C2×C4⋊C4C23×C13913yes—
467C2×C4⋊C4C23×C13916yes—
468C2×C4⋊C4C23×C13913yes—
469C2×C4⋊C4C23×C13913yes—
470C2×C4⋊C4C23×C13913yes—
471C2×C4⋊C4C23×C13913yes—
472C2×C4⋊C4C23×C13913yes—
473C2×C4⋊C4C23×C13913yes—
474C2×C4⋊C4C23×C13916yes—
475C2×C4⋊C4C23×C13913yes—
476C2×C4⋊C4C23×C13913yes—
477C2×C22⋊C4C23×C13911yescharacteristic
478C2×C22⋊C4C23×C13911yescharacteristic
479C2×C22⋊C4C23×C13913yes—
480C2×C22⋊C4C23×C13913yes—
481C2×C22⋊C4C23×C13913yes—
482C2×C22⋊C4C23×C13913yes—
483C2×C22⋊C4C23×C13916yes—
484C2×C22⋊C4C23×C13916yes—
485C2×C22⋊C4C23×C13913yes—
486C2×C22⋊C4C23×C13913yes—
487C2×C22⋊C4C23×C13911yescharacteristic
488C2×C22⋊C4C23×C13913yes—
489C2×C22⋊C4C23×C13916yes—
490C2×C42—212no—
491C2×C42C23×C13913yes—
492C2×C42C23×C13913yes—
493C2×C42C23×C13913yes—
494C2×C42C23×C13913yes—
495C2×C42C23×C13913yes—
496C2×C42C23×C13913yes—
497#95C23×C13911yescharacteristic
498#95C23×C13913yes—
499#95C23×C13913yes—
500#95C23×C13913yes—
501#95C23×C13911yescharacteristic
502#95C23×C13913yes—
503#95C23×C13916yes—
504#95C23×C13916yes—
505C24C24×C13913yes—
506C24C24×C13911yescharacteristic
507C24C24×C13911yescharacteristic
508#41—416no—
509C2×Q8—232no—
510C2×Q8—26no—
511C2×Q8—26no—
512C2×Q8—26no—
513C2×Q8—26no—
514C2×Q8—26no—
515C2×Q8—416no—
516C2×Q8C2×D4×C139112yes—
517C2×Q8C2×D4×C13914yes—
518C2×Q8C2×D4×C13914yes—
519C2×Q8#41×C13914yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—26no—
523C2×D4—26no—
524C2×D4—26no—
525C2×D4—26no—
526C2×D4—26no—
527C2×D4—26no—
528C2×D4—26no—
529C2×D4—26no—
530C2×D4—43no—
531C2×D4#41×C13914yescomplemented
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—26no—
535C22×C4—26no—
536C22×C4—22no—
537C22×C4—26no—
538C22×C4—26no—
539C22×C4—26no—
540C22×C4—26no—
541C22×C4—26no—
542C22×C4—26no—
543C22×C4—26no—
544C22×C4—26no—
545C22×C4—43no—
546C22×C4C2×D4×C139112yes—
547C22×C4C24×C13913yes—
548C22×C4C24×C13911yescharacteristic
549C22×C4C24×C13913yes—
550C22×C4C24×C13913yes—
551C22×C4C24×C13913yes—
552C22×C4C24×C13911yescharacteristic
553C22×C4C24×C13911yescharacteristic
554C22×C4C24×C13913yes—
555C22×C4C24×C13913yes—
556C22×C4C24×C13911yescharacteristic
557C22×C4C24×C13911yescharacteristic
558C22×C4C24×C13913yes—
559C4⋊C4—212no—
560C4⋊C4—26no—
561C4⋊C4—26no—
562C4⋊C4—26no—
563C4⋊C4—26no—
564C4⋊C4—26no—
565C4⋊C4—26no—
566C4⋊C4—212no—
567C4⋊C4—26no—
568C4⋊C4—43no—
569C4⋊C4C2×D4×C139112yes—
570C22⋊C4—22no—
571C22⋊C4—26no—
572C22⋊C4—26no—
573C22⋊C4—22no—
574C22⋊C4—26no—
575C22⋊C4—26no—
576C22⋊C4—26no—
577C22⋊C4—212no—
578C22⋊C4—212no—
579C22⋊C4—26no—
580C22⋊C4—22no—
581C22⋊C4—26no—
582C22⋊C4—46no—
583C42—26no—
584C42—26no—
585C42—26no—
586C42—26no—
587C42—26no—
588C42C2×D4×C139112yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—23no—
600C23—23no—
601C23—23no—
602C23—23no—
603C23—23no—
604C23—23no—
605C23—23no—
606C23C22×D4×C13912yes—
607C23C2×#41×C13912yes—
608C23C2×#41×C13912yes—
609C232−1+4×C13912yes—
610C23C25×C13911yescharacteristic
611Q8—224no—
612Q8—412no—
613Q8#121×C139116yescomplemented
614D4—28no—
615D4—412no—
616D4—412no—
617D4—412no—
618C2×C4—28no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—23no—
622C2×C4—23no—
623C2×C4—23no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—23no—
629C2×C4—224no—
630C2×C4—21no—
631C2×C4—23no—
632C2×C4—23no—
633C2×C4—23no—
634C2×C4—23no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—23no—
638C2×C4—23no—
639C2×C4—23no—
640C2×C4—21no—
641C2×C4—23no—
642C2×C4—21no—
643C2×C4—23no—
644C2×C4—23no—
645C2×C4—23no—
646C2×C4—23no—
647C2×C4—21no—
648C2×C4—412no—
649C2×C4—412no—
650C2×C4—412no—
651C2×C4C22×D4×C13912yes—
652C2×C4C22×D4×C13916yes—
653C2×C4C22×D4×C13916yes—
654C2×C4C22×D4×C13916yes—
655C2×C4C22×D4×C13916yes—
656C2×C4C2×#41×C13912yes—
657C2×C4C2×#41×C13916yes—
658C2×C42−1+4×C13912yes—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—43no—
673C22—43no—
674C22—43no—
675C22—43no—
676C22—43no—
677C22—43no—
678C22—43no—
679C22#548×C13914yescomplemented
680C22C23×D4×C13911yescharacteristic
681C22C23×D4×C13911yescharacteristic
682C22C22×#41×C13911yescharacteristic
683C22C22×#41×C13911yescharacteristic
684C22C2×2−1+4×C13911yescharacteristic
685C22C2×2−1+4×C13911yescharacteristic
686C22#585×C13911yescharacteristic
687C4—26no—
688C4—22no—
689C4—26no—
690C4—22no—
691C4—22no—
692C4—41no—
693C4—43no—
694C4—43no—
695C4—43no—
696C4—41no—
697C4—43no—
698C4C2×#121×C139112yes—
699C2—24no—
700C2—42no—
701C2—83no—
702C2C22×#121×C13911yescharacteristic
703C2C2×#548×C13911yescharacteristic
704C2D4×#41×C13911yescharacteristic
705C2#3482×C13911yescharacteristic
706C2#3486×C13911yescharacteristic
707C2#3497×C13911yescharacteristic
708C2#3516×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C139C2semidirect
2. C2×#548×C139C2semidirect
3. C2×#548×C139C2semidirect
4. C22×C4×Q8×C139C2semidirect
5. #2850×C139C2semidirect
6. #2545×C139C2semidirect
7. #2536×C139C2semidirect
8. #2429×C139C2semidirect
9. #2426×C139C2semidirect
10. #2417×C139C2semidirect
11. #2416×C139C2semidirect
12. #2351×C139C2semidirect
13. #2341×C139C2semidirect
14. Q8×C22⋊C4×C139C2semidirect
15. C4×#121×C139C2semidirect
78. C22×Q8×C139D4semidirect
106. C4×Q8×C139D4semidirect
176. C2×D4×C139#41semidirect
258. Q8×C139#121semidirect
324. C22×C139#548semidirect
354. #36434C139direct (N × H)
355. C139#36434direct (N × H)
356. C2×D4×Q8C2×C139semidirect
357. C2×#548C2×C139semidirect
358. C2×#548C2×C139semidirect
359. C22×C4×Q8C2×C139semidirect
360. #2850C2×C139semidirect
361. #2545C2×C139semidirect
362. #2536C2×C139semidirect
363. #2429C2×C139semidirect
364. #2426C2×C139semidirect
365. #2417C2×C139semidirect
366. #2416C2×C139semidirect
367. #2351C2×C139semidirect
368. #2341C2×C139semidirect
369. Q8×C22⋊C4C2×C139semidirect
370. C4×#121C2×C139semidirect
433. C22×Q8D4×C139semidirect
461. C4×Q8D4×C139semidirect
531. C2×D4#41×C139semidirect
613. Q8#121×C139semidirect
679. C22#548×C139semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1392
C2×#548×C1392
C22×C4×Q8×C1392
#2850×C1392
#2545×C1392
#2536×C1392
#2429×C1392
#2426×C1392
#2417×C1392
#2416×C1392
#2351×C1392
#2341×C1392
Q8×C22⋊C4×C1392
C4×#121×C1392
#36434139