Finite Group Databasebeta

← #32019986

Subgroups — #32019986

Order 18176.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986121C211yesmaximal, characteristic, complemented
2C2×#17986116C211yesmaximal, characteristic, complemented
3#22597084C211yesmaximal, characteristic, complemented
4#22596908C211yesmaximal, characteristic, complemented
5#22589173C211yesmaximal, characteristic, complemented
6#22589116C211yesmaximal, characteristic, complemented
7#22589053C211yesmaximal, characteristic, complemented
8#22589046C211yesmaximal, characteristic, complemented
9#22588669C211yesmaximal, characteristic, complemented
10#22588669C211yesmaximal, characteristic, complemented
11#22588617C211yesmaximal, characteristic, complemented
12#22588617C211yesmaximal, characteristic, complemented
13#22588199C211yesmaximal, characteristic, complemented
14#22588150C211yesmaximal, characteristic, complemented
15C71×#3035C211yesmaximal, characteristic
16C2×#14556135C2211yescharacteristic
17C2×#14556135C2211yescharacteristic
18C2×#14556135C2211yescharacteristic
19C2×#14556135C2211yescharacteristic
20#17986121—24no—
21#17986116—24no—
22#17986077—21no—
23#17986071—21no—
24#17986071—21no—
25D4×C71⋊C8—21no—
26C2×#14556064C2211yescharacteristic
27C2×#14556064C2211yescharacteristic
28#17986026—21no—
29#17986026—21no—
30#17986026C2211yescharacteristic
31#17986026C2211yescharacteristic
32#17986023—21no—
33#17986023C2211yescharacteristic
34C2×C4⋊(C71⋊C8)—21no—
35C2×C4⋊(C71⋊C8)C2211yescharacteristic
36C2×#14556055C2211yescharacteristic
37C2×#14556055C2211yescharacteristic
38C2×#14556055C2211yescharacteristic
39C2×#14556055C2211yescharacteristic
40C2×#14556055C2211yescharacteristic
41C2×#14556055C2211yescharacteristic
42#17985966C2211yescharacteristic
43#17985966C2211yescharacteristic
44C4×#11765849C2211yescharacteristic
45C2×#14556038C2211yescharacteristic
46C2×C8×Dic71C2211yescharacteristic
47#17985845C2211yescharacteristic
48#17985764C2211yescharacteristic
49#17985764C2211yescharacteristic
50#17985758C2211yescharacteristic
51#17985758C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C2×#135×C71C2211yescharacteristic
55C2×#135×C71C2211yescharacteristic
56#532×C71C2211yescharacteristic
57C4×#41×C71C2211yescharacteristic
58#464×C71C411yescharacteristic, complemented
59#464×C71C411yescharacteristic, complemented
60#463×C71C411yescharacteristic, complemented
61#463×C71C411yescharacteristic, complemented
62#462×C71C411yescharacteristic, complemented
63#461×C71C411yescharacteristic, complemented
64#460×C71C411yescharacteristic, complemented
65#459×C71C411yescharacteristic, complemented
66C2×C4⋊C8×C71C2211yescharacteristic
67#416×C71C2211yescharacteristic
68#416×C71C2211yescharacteristic
69#14556135—22no—
70#14556135—22no—
71#14556135—22no—
72#14556135—22no—
73#14556135—41no—
74#14556135—41no—
75#14556135—41no—
76#14556135—41no—
77C2×#11765849—21no—
78C2×#11765849—21no—
79C2×#11765849—21no—
80C2×#11765849—21no—
81C2×#11765849C2311yescharacteristic
82C2×#11765849C2311yescharacteristic
83C2×#11765849C2311yescharacteristic
84C2×#11765849C2311yescharacteristic
85C22×C71⋊C8—21no—
86C22×C71⋊C8—21no—
87C22×C71⋊C8—21no—
88C22×C71⋊C8—21no—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C2×C4×Dic71C2311yescharacteristic
92C2×C4×Dic71C2311yescharacteristic
93#14556064—22no—
94#14556064—22no—
95C4⋊(C71⋊C8)—21no—
96C4⋊(C71⋊C8)—21no—
97C4⋊(C71⋊C8)—21no—
98C4⋊(C71⋊C8)—21no—
99C4⋊(C71⋊C8)—21no—
100C4⋊(C71⋊C8)—21no—
101C4⋊(C71⋊C8)D411yescharacteristic
102C4⋊(C71⋊C8)D411yescharacteristic
103C4⋊(C71⋊C8)D411yescharacteristic
104C4⋊(C71⋊C8)D411yescharacteristic
105#14556055—22no—
106#14556055—22no—
107#14556055—22no—
108#14556055—41no—
109#14556055—41no—
110#14556055D414yescomplemented
111C22⋊(C71⋊C8)—21no—
112C22⋊(C71⋊C8)—21no—
113C22⋊(C71⋊C8)—21no—
114C22⋊(C71⋊C8)—21no—
115#14556039—21no—
116#14556038—22no—
117C4×C71⋊C8—21no—
118C8×Dic71—22no—
119C71⋊#95—21no—
120C71⋊#95—21no—
121C2×#41×C71C2311yescharacteristic
122C2×#41×C71C2311yescharacteristic
123C2×#41×C71C2311yescharacteristic
124#135×C71—22no—
125#135×C71—22no—
126#135×C71—22no—
127#135×C71—22no—
128C2×Q16×C71C2×C411yescharacteristic
129C2×Q16×C71C2×C411yescharacteristic
130C2×SD16×C71C2×C411yescharacteristic
131C2×SD16×C71C2×C411yescharacteristic
132C2×SD16×C71C2×C411yescharacteristic
133C2×SD16×C71C2×C411yescharacteristic
134C2×D8×C71C2×C411yescharacteristic
135C2×D8×C71C2×C411yescharacteristic
136C22×C8×C71C2311yescharacteristic
137C22×C8×C71C2311yescharacteristic
138C4⋊Q8×C71C2×C411yescharacteristic
139#127×C71C2×C411yescharacteristic
140#124×C71C2×C411yescharacteristic
141#124×C71C2×C411yescharacteristic
142#121×C71—21no—
143#121×C71—21no—
144C4×Q8×C71C2×C411yescharacteristic
145C4×Q8×C71C2×C411yescharacteristic
146C4×D4×C71—21no—
147C4×D4×C71—21no—
148C4×D4×C71—21no—
149C4×D4×C71—21no—
150C4×D4×C71C2×C411yescharacteristic
151C4×D4×C71C2×C411yescharacteristic
152#117×C71—21no—
153#117×C71C2311yescharacteristic
154C2×C42×C71—21no—
155C2×C42×C71C2311yescharacteristic
156C4⋊C8×C71C2×C411yescharacteristic
157C4⋊C8×C71C2×C411yescharacteristic
158C4⋊C8×C71C2×C411yescharacteristic
159C4⋊C8×C71C2×C411yescharacteristic
160#103×C71C2×C411yescharacteristic
161#103×C71C2×C411yescharacteristic
162#103×C71C2×C411yescharacteristic
163#103×C71C2×C411yescharacteristic
164#102×C71C2×C411yescharacteristic
165#102×C71C2×C411yescharacteristic
166#102×C71C2×C411yescharacteristic
167#102×C71C2×C411yescharacteristic
168C22×Dic71—21no—
169C22×Dic71—21no—
170#11765849—21no—
171#11765849—21no—
172#11765849—21no—
173#11765849—21no—
174#11765849—21no—
175#11765849—21no—
176#11765849—21no—
177#11765849—42no—
178#11765849—42no—
179#11765849—42no—
180#11765849—42no—
181#11765849C2×D412yes—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—21no—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—42no—
191C2×C71⋊C8—42no—
192C2×C71⋊C8—42no—
193C2×C71⋊C8—42no—
194C2×C71⋊C8C2×D411yescharacteristic
195C2×C71⋊C8C2×D411yescharacteristic
196C2×C71⋊C8C2×D411yescharacteristic
197C2×C71⋊C8C2×D411yescharacteristic
198C4×Dic71—21no—
199C4×Dic71—21no—
200C4×Dic71—21no—
201C4×Dic71C2×D412yes—
202#41×C71—21no—
203#41×C71—21no—
204#41×C71—21no—
205#41×C71—21no—
206#41×C71—21no—
207#41×C71—21no—
208#41×C71—21no—
209#41×C71—21no—
210#41×C71—21no—
211#41×C71—21no—
212#41×C71C2×D412yes—
213#41×C71#4112yes—
214C2×Q8×C71C22×C411yescharacteristic
215C2×Q8×C71C22×C411yescharacteristic
216C2×Q8×C71C22×C411yescharacteristic
217C2×D4×C71—21no—
218C2×D4×C71—21no—
219C2×D4×C71—21no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71C22×C411yescharacteristic
223C2×D4×C71C22×C411yescharacteristic
224C2×D4×C71C22×C411yescharacteristic
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71#4111yescharacteristic
231C22×C4×C71#4111yescharacteristic
232C22×C4×C71C2411yescharacteristic
233Q16×C71—22no—
234Q16×C71—22no—
235SD16×C71—22no—
236SD16×C71—22no—
237SD16×C71—22no—
238SD16×C71—22no—
239D8×C71—22no—
240D8×C71—22no—
241C2×C8×C71—21no—
242C2×C8×C71—21no—
243C2×C8×C71—21no—
244C2×C8×C71—21no—
245C2×C8×C71C22×C411yescharacteristic
246C2×C8×C71C22×C411yescharacteristic
247C2×C8×C71C22×C411yescharacteristic
248C2×C8×C71C22×C411yescharacteristic
249C4⋊C4×C71—21no—
250C4⋊C4×C71—21no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—21no—
253C4⋊C4×C71C22×C411yescharacteristic
254C4⋊C4×C71C22×C411yescharacteristic
255C22⋊C4×C71—21no—
256C22⋊C4×C71—21no—
257C22⋊C4×C71—21no—
258C22⋊C4×C71—21no—
259C22⋊C4×C71—21no—
260C22⋊C4×C71—21no—
261C22⋊C4×C71—21no—
262C42×C71—21no—
263C42×C71—21no—
264C42×C71—21no—
265C42×C71C22×C411yescharacteristic
266C42×C71C22×C411yescharacteristic
267C42×C71C2×D411yescharacteristic
268C42×C71C2×D411yescharacteristic
269C23×C71—21no—
270C23×C71—21no—
271C23×C71—21no—
272C23×C71C2×#4111yescharacteristic
273Q8×C71—21no—
274Q8×C71—21no—
275Q8×C71—21no—
276Q8×C71—21no—
277Q8×C71—21no—
278Q8×C71C4×D412yes—
279D4×C71—22no—
280D4×C71—22no—
281D4×C71—21no—
282D4×C71—21no—
283D4×C71—21no—
284D4×C71—21no—
285D4×C71—21no—
286D4×C71—42no—
287D4×C71—41no—
288D4×C71—41no—
289D4×C71—41no—
290D4×C71—41no—
291D4×C71—81no—
292D4×C71C4×D412yes—
293C2×C4×C71—21no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—21no—
297C2×C4×C71—21no—
298C2×C4×C71—21no—
299C2×C4×C71—21no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—42no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—81no—
308C2×C4×C71C4×D411yescharacteristic
309C2×C4×C71C4×D411yescharacteristic
310C2×C4×C71C4×D411yescharacteristic
311C2×C4×C71C4×D411yescharacteristic
312C2×C4×C71C23×C411yescharacteristic
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C22×D411yescharacteristic
315C2×C4×C71C2×#4111yescharacteristic
316C2×C4×C71H(5,𝔽2)11yescharacteristic
317C2×C4×C712−1+411yescharacteristic
318C2×Dic71—22no—
319C2×Dic71—41no—
320C2×Dic71—41no—
321C2×Dic71—41no—
322C2×Dic71—41no—
323C2×Dic71—41no—
324C8×C71—21no—
325C8×C71—21no—
326C8×C71—21no—
327C8×C71—21no—
328C71⋊C8—21no—
329C71⋊C8—21no—
330C71⋊C8—21no—
331C71⋊C8—21no—
332C71⋊C8—22no—
333C71⋊C8—41no—
334C71⋊C8—41no—
335C71⋊C8—41no—
336C22×C71—21no—
337C22×C71—21no—
338C22×C71—22no—
339C22×C71—41no—
340C22×C71—41no—
341C22×C71—41no—
342C22×C71—41no—
343C22×C71—41no—
344C22×C71—41no—
345C22×C71—41no—
346C22×C71—41no—
347C22×C71C2×C4×D411yescharacteristic
348C22×C71#54711yescharacteristic
349C22×C71#55311yescharacteristic
350C4×C71—22no—
351C4×C71—21no—
352C4×C71—21no—
353C4×C71—21no—
354C4×C71—21no—
355C4×C71—41no—
356C4×C71—41no—
357C4×C71—41no—
358C4×C71—41no—
359C4×C71C2×C4×D411yescharacteristic
360C4×C71#52011yescharacteristic
361C4×C71D4211yescharacteristic
362C4×C71#54811yescharacteristic
363Dic71—42no—
364Dic71—81no—
365#23017—711nomaximal, Sylow
366C2×C71—21no—
367C2×C71—21no—
368C2×C71—42no—
369C2×C71—81no—
370C2×C71—81no—
371C2×C71#236111yescharacteristic
372C2×C71#295511yescharacteristic
373C2×C71#295711yescharacteristic
374#3035D7111yescharacteristic
375C2×#444—711no—
376C2×#443—711no—
377#2935—711no—
378#2906—711no—
379#1963—711no—
380#1950—711no—
381#1938—711no—
382#1937—711no—
383#1876—711no—
384#1876—711no—
385#1866—711no—
386#1866—711no—
387#1768—711no—
388#1759—711no—
389C71#2301711yescharacteristic, complemented, Sylow
390C2×#135C2×D7111yescharacteristic
391C2×#135C2×D7111yescharacteristic
392C2×#131—711no—
393C2×#131—711no—
394C2×#131—711no—
395C2×#131—711no—
396#532C2×D7111yescharacteristic
397C4×#41C2×D7111yescharacteristic
398#464Dic7111yescharacteristic, complemented
399#464Dic7111yescharacteristic, complemented
400#463Dic7111yescharacteristic, complemented
401#463Dic7111yescharacteristic, complemented
402#462Dic7111yescharacteristic, complemented
403#461Dic7111yescharacteristic, complemented
404#460Dic7111yescharacteristic, complemented
405#459Dic7111yescharacteristic, complemented
406#444—1424no—
407#443—1424no—
408#436—1421no—
409#435—1421no—
410#435—1421no—
411C8×D4—1421no—
412C2×#108—711no—
413C2×#108—711no—
414#424—711no—
415#424—711no—
416#424—1421no—
417#424—1421no—
418#423—711no—
419#423—1421no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—1421no—
422C2×C4⋊C8C2×D7111yescharacteristic
423C2×#104—711no—
424C2×#104—711no—
425C2×#104—711no—
426C2×#104—711no—
427C2×#104—711no—
428C2×#104—711no—
429#416C2×D7111yescharacteristic
430#416C2×D7111yescharacteristic
431#408—711no—
432#408—711no—
433C4×M16—711no—
434C2×#97—711no—
435C2×C4×C8—711no—
436#376—711no—
437#341—711no—
438#341—711no—
439#339—711no—
440#339—711no—
441#336—711no—
442#336—711no—
443C2×#41C22×D7111yescharacteristic
444C2×#41C22×D7111yescharacteristic
445C2×#41C22×D7111yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×Dic7111yescharacteristic
451C2×Q16C2×Dic7111yescharacteristic
452C2×SD16C2×Dic7111yescharacteristic
453C2×SD16C2×Dic7111yescharacteristic
454C2×SD16C2×Dic7111yescharacteristic
455C2×SD16C2×Dic7111yescharacteristic
456C2×D8C2×Dic7111yescharacteristic
457C2×D8C2×Dic7111yescharacteristic
458#131—2841no—
459#131—2841no—
460#131—2841no—
461#131—2841no—
462#131—1422no—
463#131—1422no—
464#131—1422no—
465#131—1422no—
466C2×M16—711no—
467C2×M16—711no—
468C2×M16—711no—
469C2×M16—711no—
470C2×M16—1421no—
471C2×M16—1421no—
472C2×M16—1421no—
473C2×M16—1421no—
474C22×C8—711no—
475C22×C8—711no—
476C22×C8—1421no—
477C22×C8—1421no—
478C22×C8—1421no—
479C22×C8—1421no—
480C22×C8C22×D7111yescharacteristic
481C22×C8C22×D7111yescharacteristic
482C4⋊Q8C2×Dic7111yescharacteristic
483#127C2×Dic7111yescharacteristic
484#124C2×Dic7111yescharacteristic
485#124C2×Dic7111yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×Dic7111yescharacteristic
489C4×Q8C2×Dic7111yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×Dic7111yescharacteristic
495C4×D4C2×Dic7111yescharacteristic
496#117—21no—
497#117C22×D7111yescharacteristic
498C2×C42—21no—
499C2×C42—711no—
500C2×C42—711no—
501C2×C42C22×D7111yescharacteristic
502#108—1422no—
503#108—1422no—
504C4⋊C8—711no—
505C4⋊C8—711no—
506C4⋊C8—711no—
507C4⋊C8—711no—
508C4⋊C8—1421no—
509C4⋊C8—1421no—
510C4⋊C8—1421no—
511C4⋊C8—1421no—
512C4⋊C8—1421no—
513C4⋊C8—1421no—
514C4⋊C8C2×Dic7111yescharacteristic
515C4⋊C8C2×Dic7111yescharacteristic
516C4⋊C8C2×Dic7111yescharacteristic
517C4⋊C8C2×Dic7111yescharacteristic
518#104—2841no—
519#104—2841no—
520#104—714no—
521#104—1422no—
522#104—1422no—
523#104—1422no—
524#103C2×Dic7111yescharacteristic
525#103C2×Dic7111yescharacteristic
526#103C2×Dic7111yescharacteristic
527#103C2×Dic7111yescharacteristic
528#102C2×Dic7111yescharacteristic
529#102C2×Dic7111yescharacteristic
530#102C2×Dic7111yescharacteristic
531#102C2×Dic7111yescharacteristic
532C22⋊C8—1421no—
533C22⋊C8—1421no—
534C22⋊C8—1421no—
535C22⋊C8—1421no—
536#97—1422no—
537#97—1421no—
538C4×C8—1422no—
539C4×C8—1421no—
540#95—1421no—
541#95—1421no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41D4×D7112yes—
553#41#1176586412yes—
554C2×Q8C22×Dic7111yescharacteristic
555C2×Q8C22×Dic7111yescharacteristic
556C2×Q8C22×Dic7111yescharacteristic
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×Dic7111yescharacteristic
563C2×D4C22×Dic7111yescharacteristic
564C2×D4C22×Dic7111yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—1421no—
571C22×C4—1421no—
572C22×C4#1176586411yescharacteristic
573C22×C4#1176586411yescharacteristic
574C22×C4C23×D7111yescharacteristic
575Q16—22no—
576Q16—22no—
577SD16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581D8—22no—
582D8—22no—
583M16—2842no—
584M16—2842no—
585M16—2842no—
586M16—2842no—
587M16—712no—
588M16—1421no—
589M16—1421no—
590M16—1421no—
591M16—1421no—
592M16—1421no—
593M16—1421no—
594M16—1421no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—2842no—
600C2×C8—2842no—
601C2×C8—2842no—
602C2×C8—2842no—
603C2×C8—711no—
604C2×C8—711no—
605C2×C8—711no—
606C2×C8—711no—
607C2×C8—1421no—
608C2×C8—1421no—
609C2×C8—1421no—
610C2×C8—1421no—
611C2×C8—1421no—
612C2×C8—1421no—
613C2×C8—1421no—
614C2×C8—1421no—
615C2×C8C22×Dic7111yescharacteristic
616C2×C8C22×Dic7111yescharacteristic
617C2×C8C22×Dic7111yescharacteristic
618C2×C8C22×Dic7111yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C22×Dic7111yescharacteristic
624C4⋊C4C22×Dic7111yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—712no—
636C42—1421no—
637C42—1421no—
638C42—1421no—
639C42C22×Dic7111yescharacteristic
640C42C22×Dic7111yescharacteristic
641C42D4×D7111yescharacteristic
642C42D4×D7111yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23C2×#1176586411yescharacteristic
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8D4×Dic7112yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4D4×Dic7112yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—2841no—
683C2×C4—2841no—
684C2×C4—2841no—
685C2×C4—2841no—
686C2×C4—2841no—
687C2×C4—1422no—
688C2×C4D4×Dic7111yescharacteristic
689C2×C4D4×Dic7111yescharacteristic
690C2×C4D4×Dic7111yescharacteristic
691C2×C4D4×Dic7111yescharacteristic
692C2×C4C23×Dic7111yescharacteristic
693C2×C4C2×D4×D7111yescharacteristic
694C2×C4C2×D4×D7111yescharacteristic
695C2×C4C2×#1176586411yescharacteristic
696C2×C4#1455617411yescharacteristic
697C2×C4#1455617511yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—2841no—
703C8—2841no—
704C8—2841no—
705C8—1421no—
706C8—1421no—
707C8—1421no—
708C8—1422no—
709C8—1421no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×D4×Dic7111yescharacteristic
722C22#1798664911yescharacteristic
723C22#1798670111yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—2842no—
734C4—5681no—
735C4C2×D4×Dic7111yescharacteristic
736C4#1798648211yescharacteristic
737C4#1798663311yescharacteristic
738C4#1798665511yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—81no—
743C2—81no—
744C2#2259136011yescharacteristic
745C2#2259724311yescharacteristic
746C2#2259725711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3035C2
socleC22×C71C2×C4×D4
cosocleC22×C4×C71C24
hypercenter#3035D71
hypocenterC71#23017
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#17986121C2semidirect
2. C2×#17986116C2semidirect
3. #22597084C2semidirect
4. #22596908C2semidirect
5. #22589173C2semidirect
6. #22589116C2semidirect
7. #22589053C2semidirect
8. #22589046C2semidirect
9. #22588669C2semidirect
10. #22588669C2semidirect
11. #22588617C2semidirect
12. #22588617C2semidirect
13. #22588199C2semidirect
14. #22588150C2semidirect
58. #464×C71C4semidirect
59. #464×C71C4semidirect
60. #463×C71C4semidirect
61. #463×C71C4semidirect
62. #462×C71C4semidirect
63. #461×C71C4semidirect
64. #460×C71C4semidirect
65. #459×C71C4semidirect
110. #14556055D4semidirect
389. C71#23017semidirect
398. #464Dic71semidirect
399. #464Dic71semidirect
400. #463Dic71semidirect
401. #463Dic71semidirect
402. #462Dic71semidirect
403. #461Dic71semidirect
404. #460Dic71semidirect
405. #459Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179861212
C2×#179861162
#225970842
#225969082
#225891732
#225891162
#225890532
#225890462
#225886692
#225886172
#225881992
#225881502
C71×#30352
#2301771