Finite Group Databasebeta

← C2×#11744279 #14267643

Subgroups — C2×#11744279 #14267643

Order 1792.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×2−1+4C211yesmaximal, characteristic, complemented
2C2×#90620C211yesmaximal, characteristic, complemented
3C2×C7×#578C211yesmaximal, characteristic, complemented
4C2×#90529C211yesmaximal, characteristic, complemented
5C2×#90528C211yesmaximal, characteristic, complemented
6#11744279C2132yesmaximal, direct product factor
7C2×#90470C213yesmaximal, complemented
8C2×#90469C213yesmaximal, complemented
9C2×#90468C213yesmaximal, complemented
10C2×D7×#137C213yesmaximal, complemented
11C2×#90461C213yesmaximal, complemented
12C2×#90459C213yesmaximal, complemented
13C2×#90457C213yesmaximal, complemented
14C22×#6481C213yesmaximal, complemented
15C2×#90442C211yesmaximal, characteristic, complemented
16C2×#90441C211yesmaximal, characteristic, complemented
17C2×C7×2−1+4C2211yescharacteristic, complemented
18C2×C7×2−1+4C2211yescharacteristic, complemented
19#90620—28no—
20#90620C22116yescomplemented
21D7×2−1+4—28no—
22D7×2−1+4C22116yescomplemented
23C2×#6554—23no—
24C2×#6554C2213yescomplemented
25C2×#6554C2211yescharacteristic, complemented
26C2×#6553—23no—
27C2×#6553C2213yescomplemented
28C2×#6553C2211yescharacteristic, complemented
29C2×D7×#41—23no—
30C2×D7×#41—23no—
31C2×D7×#41C2213yes—
32C2×D7×#41C2211yescharacteristic
33C2×D7×#41C2213yescomplemented
34C2×#6551—21no—
35C2×#6551—21no—
36C2×#6551C2213yescomplemented
37C2×#6551C2213yescomplemented
38C22×#1161—21no—
39C22×#1161C2213yes—
40C22×Q8×D7—21no—
41C22×Q8×D7C2213yescomplemented
42C7×#578C22116yescomplemented
43C2×C7×#137C2213yescomplemented
44C2×C7×#137C2213yescomplemented
45C2×C7×#135C2213yescomplemented
46C22×C7×Q16C2213yescomplemented
47C2×C7×#131C2211yescharacteristic, complemented
48#90529C22116yescomplemented
49#90528C22116yescomplemented
50C2×#6514C2213yescomplemented
51C2×#6513C2213yescomplemented
52C2×#6513C2213yescomplemented
53C2×#6512C2213yescomplemented
54C2×#6511C2211yescharacteristic, complemented
55C22×#1144C2213yescomplemented
56C2×#6505C2213yescomplemented
57C2×#6505C2213yescomplemented
58C22×#1143C2213yescomplemented
59#90470C22148yescomplemented
60#90469C22148yescomplemented
61#90468C22148yescomplemented
62D7×#137C22148yescomplemented
63#90461C22148yescomplemented
64#90459C22148yescomplemented
65#90457C22148yescomplemented
66C2×#6482C2216yescomplemented
67C2×#6481C2216yescomplemented
68C2×#6481C2216yescomplemented
69C2×#6481C2213yescomplemented
70C2×#6481C2216yescomplemented
71C2×#6481C2213yescomplemented
72C2×#6481C22148yescomplemented
73C2×D7×Q16C2216yescomplemented
74C2×#6479C2216yescomplemented
75C2×#6478C2213yescomplemented
76C2×#6478C2213yescomplemented
77C2×#6477C2213yescomplemented
78C2×#6477C2213yescomplemented
79C2×D7×SD16C2216yescomplemented
80C2×#6474C2211yescharacteristic, complemented
81C2×#6474C2213yescomplemented
82#90442C22116yescomplemented
83#90441C22116yescomplemented
84C2×#6472C2213yescomplemented
85C2×#6471C2213yescomplemented
86C2×#6470C2213yescomplemented
87C2×D7×M16C2213yescomplemented
88C2×#6467C2213yescomplemented
89C22×#1132C2213yescomplemented
90C2×#6464C2213yescomplemented
91C22×#1131C2213yescomplemented
92C2×#3586—71nomaximal, Sylow
93C7×2−1+4—24no—
94C7×2−1+4—24no—
95C7×2−1+4C2318yescomplemented
96C7×2−1+4C2318yescomplemented
97C2×C7×#41—23no—
98C2×C7×#41—23no—
99C2×C7×#41C2313yes—
100C2×C7×#41C2313yes—
101C2×C7×#41C2311yescharacteristic
102C22×C7×Q8—21no—
103C22×C7×Q8—21no—
104C22×C7×Q8C2313yes—
105C22×C7×Q8C2313yes—
106#6554—24no—
107#6554—248no—
108#6554—212no—
109#6554C23124yescomplemented
110#6554C2318yescomplemented
111#6553—24no—
112#6553—248no—
113#6553—212no—
114#6553C23124yescomplemented
115#6553C2318yescomplemented
116D7×#41—248no—
117D7×#41—248no—
118D7×#41—212no—
119D7×#41—212no—
120D7×#41D418yes—
121D7×#41C23124yes—
122D7×#41C2318yes—
123D7×#41C23124yescomplemented
124#6551—216no—
125#6551—216no—
126#6551—212no—
127#6551—212no—
128#6551C23124yescomplemented
129#6551C23124yescomplemented
130C2×#1161—21no—
131C2×#1161—216no—
132C2×#1161—23no—
133C2×#1161—23no—
134C2×#1161—23no—
135C2×#1161—23no—
136C2×#1161—212no—
137C2×#1161D411yescharacteristic
138C2×#1161C2313yes—
139C2×#1161C2313yes—
140C2×#1161C2316yes—
141C2×#1161C23124yes—
142C2×Q8×D7—21no—
143C2×Q8×D7—216no—
144C2×Q8×D7—23no—
145C2×Q8×D7—23no—
146C2×Q8×D7—212no—
147C2×Q8×D7—23no—
148C2×Q8×D7—23no—
149C2×Q8×D7D411yescharacteristic
150C2×Q8×D7C2316yes—
151C2×Q8×D7C2313yes—
152C2×Q8×D7C2313yes—
153C2×Q8×D7C23124yescomplemented
154C2×#1159—23no—
155C2×#1159—26no—
156C2×#1159—23no—
157C2×#1159—23no—
158C2×#1159D413yes—
159C2×#1159C2311yescharacteristic
160C2×#1159C2313yes—
161C2×D4×D7—23no—
162C2×D4×D7—23no—
163C2×D4×D7—23no—
164C2×D4×D7—26no—
165C2×D4×D7D413yes—
166C2×D4×D7C2313yes—
167C2×D4×D7C2311yescharacteristic
168C2×#1157—26no—
169C2×#1157—26no—
170C2×#1157—23no—
171C2×#1157—23no—
172C2×#1157—23no—
173C2×#1157—23no—
174C2×#1157C2313yes—
175C2×#1157C2313yes—
176C2×#1157C2313yes—
177C22×D28—23no—
178C22×D28—23no—
179C22×D28C2313yes—
180C22×C4×D7—23no—
181C22×C4×D7—23no—
182C22×C4×D7—23no—
183C22×C4×D7—23no—
184C22×C4×D7C2313yes—
185C22×Dic14—23no—
186C22×Dic14—23no—
187C22×Dic14C2313yes—
188C7×#137C23124yescomplemented
189C7×#137C23124yescomplemented
190C7×#135C23124yescomplemented
191C2×C7×Q16C2316yes—
192C2×C7×Q16C2313yes—
193C2×C7×Q16C23124yescomplemented
194C2×C7×SD16C2313yes—
195C2×C7×SD16C2313yes—
196C2×C7×D8C2311yescharacteristic
197C7×#131C2318yescomplemented
198C2×C7×M16C2313yes—
199C22×C7×C8C2313yes—
200#6514C23124yescomplemented
201#6513C23124yescomplemented
202#6513C23124yescomplemented
203#6512C23124yescomplemented
204#6511C2318yescomplemented
205C2×#1144C2313yes—
206C2×#1144C2313yes—
207C2×#1144C2316yes—
208C2×#1144C23124yescomplemented
209#6505C23124yescomplemented
210#6505C23124yescomplemented
211C2×#1143C2316yes—
212C2×#1143C2313yes—
213C2×#1143C2313yes—
214C2×#1143C23124yescomplemented
215C2×#1142C2313yes—
216C2×#1142C2311yescharacteristic
217C2×#1141C2311yescharacteristic
218C2×#1141C2313yes—
219C2×#1136C2313yes—
220C22×C7⋊C8C2313yes—
221#6482C23148yescomplemented
222#6481C23124yescomplemented
223#6481C23148yescomplemented
224#6481C23148yescomplemented
225#6481C23148yescomplemented
226#6481C23124yescomplemented
227D7×Q16C23148yescomplemented
228#6479C23148yescomplemented
229#6478C23124yescomplemented
230#6478C23124yescomplemented
231#6477C23124yescomplemented
232#6477C23124yescomplemented
233D7×SD16C23148yescomplemented
234#6474C2318yescomplemented
235#6474C23124yescomplemented
236#6472C23124yescomplemented
237#6471C23124yescomplemented
238#6470C23124yescomplemented
239D7×M16C23124yescomplemented
240C2×Dic28C2313yes—
241#6467C23124yescomplemented
242C2×D56C2313yes—
243C2×#1132C2313yes—
244C2×#1132C2316yes—
245C2×#1132C2311yescharacteristic
246C2×#1132C23124yescomplemented
247#6464C23124yescomplemented
248C2×#1131C2311yescharacteristic
249C2×#1131C2313yes—
250C2×#1131C2313yes—
251C2×#1131C2313yes—
252C2×#1131C23124yescomplemented
253C2×C8×D7C2316yes—
254C2×#585—71no—
255C22×2−1+4—71no—
256#3586—732no—
257C2×#578—71no—
258C2×#578—73no—
259C2×#578—73no—
260C2×#578D711yescharacteristic, complemented
261C2×#577—71no—
262C2×#577—73no—
263C2×#577—73no—
264C2×#577—71no—
265C2×#575—73no—
266C2×#575—73no—
267C22×#137—73no—
268C22×#137—73no—
269C2×#568—71no—
270C23×D7—23no—
271C23×D7—21no—
272C23×D7—23no—
273C23×D7C2×D413yes—
274C7×#41—224no—
275C7×#41—224no—
276C7×#41—26no—
277C7×#41—26no—
278C7×#41C2×D414yes—
279C7×#41C24112yes—
280C7×#41C24112yes—
281C7×#41C2414yes—
282C2×C7×Q8—28no—
283C2×C7×Q8—28no—
284C2×C7×Q8—23no—
285C2×C7×Q8—26no—
286C2×C7×Q8—23no—
287C2×C7×Q8—26no—
288C2×C7×Q8C2×D411yescharacteristic
289C2×C7×Q8C2413yes—
290C2×C7×Q8C2413yes—
291C2×C7×Q8C24112yes—
292C2×C7×Q8C24112yes—
293C2×C7×D4—23no—
294C2×C7×D4—23no—
295C2×C7×D4C2×D413yes—
296C2×C7×D4C2411yescharacteristic
297C2×C7×D4C2411yescharacteristic
298C22×C4×C7—23no—
299C22×C4×C7—23no—
300C22×C4×C7—23no—
301C22×C4×C7—23no—
302C22×C4×C7C2413yes—
303C2×C22⋊D7—23no—
304C2×C22⋊D7—23no—
305C2×C22⋊D7—21no—
306C2×C22⋊D7—23no—
307C2×C22⋊D7—23no—
308C2×C22⋊D7—21no—
309C2×C22⋊D7C2×D416yes—
310C22×Dic7—23no—
311C22×Dic7—23no—
312C22×Dic7—21no—
313C22×Dic7C2×D413yes—
314#1161—28no—
315#1161—224no—
316#1161—224no—
317#1161—224no—
318#1161—26no—
319#1161—224no—
320#1161—212no—
321#1161—26no—
322#1161C2×D418yes—
323#1161C24112yes—
324#1161C24112yes—
325#1161C24124yes—
326Q8×D7—28no—
327Q8×D7—26no—
328Q8×D7—224no—
329Q8×D7—212no—
330Q8×D7—224no—
331Q8×D7—26no—
332Q8×D7—224no—
333Q8×D7—224no—
334Q8×D7C2×D418yes—
335Q8×D7C24124yes—
336Q8×D7C24112yes—
337Q8×D7C24112yes—
338#1159—224no—
339#1159—248no—
340#1159—224no—
341#1159—224no—
342#1159—22no—
343#1159—26no—
344#1159C2×D4124yes—
345#1159C2414yes—
346#1159C24112yes—
347D4×D7—224no—
348D4×D7—224no—
349D4×D7—224no—
350D4×D7—248no—
351D4×D7—22no—
352D4×D7—26no—
353D4×D7C2×D4124yes—
354D4×D7C24112yes—
355D4×D7C2414yes—
356#1157—26no—
357#1157—26no—
358#1157—248no—
359#1157—248no—
360#1157—224no—
361#1157—224no—
362#1157—224no—
363#1157—224no—
364#1157C2×D4112yes—
365#1157C24112yes—
366#1157C24112yes—
367#1157C24112yes—
368C2×D28—23no—
369C2×D28—26no—
370C2×D28—224no—
371C2×D28—23no—
372C2×D28—23no—
373C2×D28—26no—
374C2×D28—224no—
375C2×D28C2×D413yes—
376C2×D28C2413yes—
377C2×D28C2411yescharacteristic
378C2×D28C24112yes—
379C2×C4×D7—23no—
380C2×C4×D7—23no—
381C2×C4×D7—26no—
382C2×C4×D7—224no—
383C2×C4×D7—23no—
384C2×C4×D7—23no—
385C2×C4×D7—23no—
386C2×C4×D7—26no—
387C2×C4×D7—23no—
388C2×C4×D7—224no—
389C2×C4×D7—224no—
390C2×C4×D7—224no—
391C2×C4×D7C2×D413yes—
392C2×C4×D7C2×D413yes—
393C2×C4×D7C2×D4112yes—
394C2×C4×D7C2413yes—
395C2×C4×D7C2411yescharacteristic
396C2×C4×D7C24112yes—
397C2×Dic14—23no—
398C2×Dic14—26no—
399C2×Dic14—26no—
400C2×Dic14—23no—
401C2×Dic14—224no—
402C2×Dic14—23no—
403C2×Dic14—224no—
404C2×Dic14C2×D413yes—
405C2×Dic14C2413yes—
406C2×Dic14C2411yescharacteristic
407C2×Dic14C24112yes—
408C7×Q16C24124yes—
409C7×Q16C24112yes—
410C7×SD16C24112yes—
411C7×SD16C24112yes—
412C7×D8C2414yes—
413C7×M16C24112yes—
414C2×C7×C8C2413yes—
415C2×C7×C8C2411yescharacteristic
416C2×C7×C8C24112yes—
417#1144C24112yes—
418#1144C24112yes—
419#1144C24124yes—
420#1143C24124yes—
421#1143C24112yes—
422#1143C24112yes—
423#1142C24112yes—
424#1142C2414yes—
425#1141C2414yes—
426#1141C24112yes—
427#1136C24112yes—
428C2×C7⋊C8C2413yes—
429C2×C7⋊C8C2411yescharacteristic
430C2×C7⋊C8C24112yes—
431Dic28C24112yes—
432D56C24112yes—
433#1132C24112yes—
434#1132C24124yes—
435#1132C2414yes—
436#1131C2414yes—
437#1131C24112yes—
438#1131C24112yes—
439#1131C24112yes—
440C8×D7C24124yes—
441#585—716no—
442#585—148no—
443C2×2−1+4—716no—
444C2×2−1+4—73no—
445C2×2−1+4—71no—
446C2×2−1+4—73no—
447C2×2−1+4—73no—
448C2×2−1+4—141no—
449C2×2−1+4—141no—
450C2×2−1+4—143no—
451C2×2−1+4—148no—
452C2×2−1+4C2×D711yescharacteristic, complemented
453C2×2−1+4C2×D711yescharacteristic, complemented
454C2×H(5,𝔽2)—73no—
455C2×H(5,𝔽2)—71no—
456C2×H(5,𝔽2)—143no—
457C22×#41—71no—
458C22×#41—73no—
459C22×#41—73no—
460C22×#41—73no—
461C22×#41—143no—
462C22×#41—141no—
463C22×#41—143no—
464C23×Q8—73no—
465C23×Q8—141no—
466#578—716no—
467#578—748no—
468#578—748no—
469#578C2×D7116yescomplemented
470#577—716no—
471#577—748no—
472#577—748no—
473#577—716no—
474#575—748no—
475#575—748no—
476C2×#137—73no—
477C2×#137—73no—
478C2×#137—73no—
479C2×#137—748no—
480C2×#137—76no—
481C2×#137—73no—
482C2×#137—76no—
483C2×#137—76no—
484C2×#137—73no—
485C2×#137—748no—
486C2×#137—73no—
487C2×#137—73no—
488C2×#137—73no—
489C2×#137C2×D713yescomplemented
490C2×#137C2×D713yescomplemented
491C2×AGL(1,ℤ/8)—73no—
492C2×AGL(1,ℤ/8)—73no—
493C2×AGL(1,ℤ/8)—73no—
494C2×AGL(1,ℤ/8)—71no—
495C2×AGL(1,ℤ/8)—73no—
496C2×AGL(1,ℤ/8)—73no—
497C2×#135—73no—
498C2×#135—73no—
499C2×#135—76no—
500C2×#135—76no—
501C2×#135—73no—
502C2×#135C2×D713yescomplemented
503C22×Q16—73no—
504C22×Q16—76no—
505C22×Q16C2×D713yescomplemented
506C22×SD16—73no—
507C22×SD16—76no—
508C22×SD16—73no—
509#568—716no—
510C2×#131—71no—
511C2×#131—73no—
512C2×#131—73no—
513C2×#131C2×D711yescharacteristic, complemented
514C22×M16—73no—
515C22×M16—73no—
516C23×C7—21no—
517C23×C7—21no—
518C23×C7C22×D413yes—
519C22×D7—21no—
520C22×D7—23no—
521C22×D7—212no—
522C22×D7—24no—
523C22×D7—212no—
524C22×D7—46no—
525C22×D7—44no—
526C22×D7—86no—
527C22×D7—86no—
528C22×D7C22×D411yescharacteristic
529C22×D7C22×D413yes—
530C22×D7C22×D4112yes—
531C7×Q8—23no—
532C7×Q8—212no—
533C7×Q8—23no—
534C7×Q8—212no—
535C7×Q8C22×D414yes—
536C7×Q8C2516yes—
537C7×Q8C2516yes—
538C7×D4—212no—
539C7×D4—212no—
540C7×D4—21no—
541C7×D4—21no—
542C7×D4C22×D4112yes—
543C7×D4C2512yes—
544C7×D4C2512yes—
545C2×C4×C7—23no—
546C2×C4×C7—212no—
547C2×C4×C7—23no—
548C2×C4×C7—212no—
549C2×C4×C7—212no—
550C2×C4×C7—212no—
551C2×C4×C7C22×D413yes—
552C2×C4×C7C22×D416yes—
553C2×C4×C7C2511yescharacteristic
554C2×C4×C7C2516yes—
555C22⋊D7—212no—
556C22⋊D7—212no—
557C22⋊D7—24no—
558C22⋊D7—212no—
559C22⋊D7—212no—
560C22⋊D7—24no—
561C22⋊D7C22×D4124yes—
562C2×Dic7—23no—
563C2×Dic7—21no—
564C2×Dic7—212no—
565C2×Dic7—212no—
566C2×Dic7—24no—
567C2×Dic7C22×D413yes—
568C2×Dic7C22×D411yescharacteristic
569C2×Dic7C22×D4112yes—
570D28—212no—
571D28—224no—
572D28—212no—
573D28—23no—
574D28—212no—
575D28—21no—
576D28C22×D4112yes—
577D28C2516yes—
578D28C2512yes—
579C4×D7—212no—
580C4×D7—212no—
581C4×D7—224no—
582C4×D7—212no—
583C4×D7—212no—
584C4×D7—212no—
585C4×D7—224no—
586C4×D7—212no—
587C4×D7C22×D4112yes—
588C4×D7C22×D4112yes—
589C4×D7C22×D412yes—
590C4×D7C22×D416yes—
591C4×D7C2516yes—
592C4×D7C2512yes—
593Dic14—23no—
594Dic14—212no—
595Dic14—21no—
596Dic14—224no—
597Dic14—212no—
598Dic14—212no—
599Dic14C22×D4112yes—
600Dic14C2516yes—
601Dic14C2512yes—
602C7×C8C2516yes—
603C7×C8C2512yes—
604C7⋊C8C2516yes—
605C7⋊C8C2512yes—
6062−1+4—24no—
6072−1+4—24no—
6082−1+4—724no—
6092−1+4—78no—
6102−1+4—724no—
6112−1+4—724no—
6122−1+4—1416no—
6132−1+4—1416no—
6142−1+4—1412no—
6152−1+4—1412no—
6162−1+4—1448no—
6172−1+4—1412no—
6182−1+4—144no—
6192−1+4C22×D718yescomplemented
6202−1+4C22×D718yescomplemented
621H(5,𝔽2)—724no—
622H(5,𝔽2)—78no—
623H(5,𝔽2)—1448no—
624H(5,𝔽2)—1412no—
625H(5,𝔽2)—144no—
626C2×#41—23no—
627C2×#41—23no—
628C2×#41—78no—
629C2×#41—78no—
630C2×#41—71no—
631C2×#41—73no—
632C2×#41—73no—
633C2×#41—724no—
634C2×#41—724no—
635C2×#41—73no—
636C2×#41—76no—
637C2×#41—73no—
638C2×#41—724no—
639C2×#41—73no—
640C2×#41—71no—
641C2×#41—73no—
642C2×#41—73no—
643C2×#41—143no—
644C2×#41—143no—
645C2×#41—146no—
646C2×#41—146no—
647C2×#41—143no—
648C2×#41—143no—
649C2×#41—143no—
650C2×#41—143no—
651C2×#41—143no—
652C2×#41—143no—
653C2×#41—1412no—
654C2×#41—1412no—
655C2×#41—1412no—
656C2×#41—146no—
657C2×#41—143no—
658C2×#41—143no—
659C2×#41—1448no—
660C2×#41—1416no—
661C2×#41—1448no—
662C2×#41—141no—
663C2×#41—143no—
664C2×#41C22×D713yes—
665C2×#41C22×D713yes—
666C2×#41C22×D711yescharacteristic
667C22×Q8—21no—
668C22×Q8—21no—
669C22×Q8—71no—
670C22×Q8—76no—
671C22×Q8—73no—
672C22×Q8—73no—
673C22×Q8—724no—
674C22×Q8—73no—
675C22×Q8—143no—
676C22×Q8—143no—
677C22×Q8—143no—
678C22×Q8—143no—
679C22×Q8—1412no—
680C22×Q8—1416no—
681C22×Q8—143no—
682C22×Q8—143no—
683C22×Q8—141no—
684C22×Q8C22×D713yes—
685C22×Q8C22×D713yes—
686C22×D4—73no—
687C22×D4—73no—
688C22×D4—71no—
689C22×D4—73no—
690C22×D4—143no—
691C22×D4—143no—
692C22×D4—146no—
693C22×D4—143no—
694C22×D4—143no—
695C22×D4—143no—
696C23×C4—73no—
697C23×C4—143no—
698C23×C4—143no—
699C23×C4—143no—
700C23×C4—143no—
701#137—724no—
702#137—724no—
703#137—724no—
704#137—748no—
705#137—724no—
706#137—748no—
707#137—748no—
708#137—724no—
709#137—724no—
710#137—724no—
711#137—724no—
712#137C22×D7124yescomplemented
713#137C22×D7124yescomplemented
714AGL(1,ℤ/8)—724no—
715AGL(1,ℤ/8)—724no—
716AGL(1,ℤ/8)—724no—
717AGL(1,ℤ/8)—78no—
718AGL(1,ℤ/8)—724no—
719AGL(1,ℤ/8)—724no—
720#135—724no—
721#135—724no—
722#135—748no—
723#135—748no—
724#135—724no—
725#135C22×D7124yescomplemented
726C2×Q16—73no—
727C2×Q16—76no—
728C2×Q16—73no—
729C2×Q16—724no—
730C2×Q16—748no—
731C2×Q16—73no—
732C2×Q16C22×D716yes—
733C2×Q16C22×D713yes—
734C2×Q16C22×D7124yescomplemented
735C2×SD16—73no—
736C2×SD16—76no—
737C2×SD16—724no—
738C2×SD16—73no—
739C2×SD16—73no—
740C2×SD16—71no—
741C2×SD16—748no—
742C2×SD16—76no—
743C2×SD16—73no—
744C2×SD16—724no—
745C2×SD16—71no—
746C2×SD16C22×D713yes—
747C2×SD16C22×D713yes—
748C2×D8—71no—
749C2×D8—73no—
750C2×D8—73no—
751C2×D8C22×D711yescharacteristic
752#131—78no—
753#131—724no—
754#131—724no—
755#131C22×D718yescomplemented
756C2×M16—73no—
757C2×M16—724no—
758C2×M16—73no—
759C2×M16—71no—
760C2×M16—73no—
761C2×M16—73no—
762C2×M16—724no—
763C2×M16C22×D713yes—
764C22×C8—73no—
765C22×C8—76no—
766C22×C8C22×D713yes—
767C22×C7—26no—
768C22×C7—22no—
769C22×C7—22no—
770C22×C7—42no—
771C22×C7—42no—
772C22×C7C23×D416yes—
773C22×C7C23×D411yescharacteristic
774C2×D7—22no—
775C2×D7—26no—
776C2×D7—22no—
777C2×D7—26no—
778C2×D7—412no—
779C2×D7—48no—
780C2×D7—42no—
781C2×D7—46no—
782C2×D7—812no—
783C2×D7—812no—
784C2×D7C23×D412yes—
785C2×D7C23×D416yes—
786C4×C7—26no—
787C4×C7—26no—
788C4×C7C23×D411yescharacteristic
789C4×C7C23×D416yes—
790C4×C7C2611yescharacteristic
791Dic7—26no—
792Dic7—22no—
793Dic7C23×D416yes—
794Dic7C23×D412yes—
795C24—73no—
796C24—141no—
797C24—143no—
798C24—143no—
799#41—224no—
800#41—224no—
801#41—26no—
802#41—26no—
803#41—78no—
804#41—724no—
805#41—712no—
806#41—712no—
807#41—712no—
808#41—724no—
809#41—712no—
810#41—712no—
811#41—74no—
812#41—712no—
813#41—712no—
814#41—1424no—
815#41—1424no—
816#41—1448no—
817#41—1448no—
818#41—1424no—
819#41—1424no—
820#41—1424no—
821#41—142no—
822#41—1424no—
823#41—146no—
824#41—146no—
825#41—1424no—
826#41—1424no—
827#41—1412no—
828#41—146no—
829#41—1448no—
830#41—1424no—
831#41—1424no—
832#41—148no—
833#41—1424no—
834#41—146no—
835#41—146no—
836#41D4×D714yes—
837#41C23×D7112yes—
838#41C23×D7112yes—
839#41C23×D714yes—
840C2×Q8—28no—
841C2×Q8—28no—
842C2×Q8—23no—
843C2×Q8—23no—
844C2×Q8—26no—
845C2×Q8—26no—
846C2×Q8—78no—
847C2×Q8—73no—
848C2×Q8—724no—
849C2×Q8—712no—
850C2×Q8—712no—
851C2×Q8—73no—
852C2×Q8—71no—
853C2×Q8—712no—
854C2×Q8—143no—
855C2×Q8—146no—
856C2×Q8—143no—
857C2×Q8—1424no—
858C2×Q8—1424no—
859C2×Q8—146no—
860C2×Q8—1424no—
861C2×Q8—1424no—
862C2×Q8—1412no—
863C2×Q8—146no—
864C2×Q8—1424no—
865C2×Q8—1424no—
866C2×Q8—148no—
867C2×Q8—143no—
868C2×Q8—146no—
869C2×Q8D4×D711yescharacteristic
870C2×Q8C23×D713yes—
871C2×Q8C23×D7112yes—
872C2×Q8C23×D713yes—
873C2×Q8C23×D7112yes—
874C2×D4—23no—
875C2×D4—23no—
876C2×D4—76no—
877C2×D4—724no—
878C2×D4—712no—
879C2×D4—74no—
880C2×D4—73no—
881C2×D4—71no—
882C2×D4—73no—
883C2×D4—712no—
884C2×D4—1424no—
885C2×D4—143no—
886C2×D4—146no—
887C2×D4—143no—
888C2×D4—1424no—
889C2×D4—142no—
890C2×D4—146no—
891C2×D4—143no—
892C2×D4—141no—
893C2×D4—1448no—
894C2×D4—1424no—
895C2×D4—1424no—
896C2×D4—141no—
897C2×D4—143no—
898C2×D4—143no—
899C2×D4—143no—
900C2×D4—1424no—
901C2×D4—143no—
902C2×D4—146no—
903C2×D4D4×D713yes—
904C2×D4C23×D711yescharacteristic
905C2×D4C23×D711yescharacteristic
906C22×C4—23no—
907C22×C4—23no—
908C22×C4—23no—
909C22×C4—23no—
910C22×C4—73no—
911C22×C4—73no—
912C22×C4—73no—
913C22×C4—712no—
914C22×C4—73no—
915C22×C4—71no—
916C22×C4—712no—
917C22×C4—143no—
918C22×C4—146no—
919C22×C4—143no—
920C22×C4—1424no—
921C22×C4—1424no—
922C22×C4—1424no—
923C22×C4—143no—
924C22×C4—143no—
925C22×C4—1424no—
926C22×C4—146no—
927C22×C4—141no—
928C22×C4—143no—
929C22×C4—143no—
930C22×C4—143no—
931C22×C4—143no—
932C22×C4C23×D713yes—
933Q16—712no—
934Q16—724no—
935Q16—712no—
936Q16—712no—
937Q16C23×D7124yes—
938Q16C23×D7112yes—
939SD16—724no—
940SD16—712no—
941SD16—712no—
942SD16—712no—
943SD16—74no—
944SD16—724no—
945SD16—712no—
946SD16—74no—
947SD16C23×D7112yes—
948SD16C23×D7112yes—
949D8—74no—
950D8—712no—
951D8—712no—
952D8C23×D714yes—
953M16—712no—
954M16—712no—
955M16—74no—
956M16—712no—
957M16—712no—
958M16C23×D7112yes—
959C2×C8—73no—
960C2×C8—71no—
961C2×C8—712no—
962C2×C8—724no—
963C2×C8C23×D713yes—
964C2×C8C23×D711yescharacteristic
965C2×C8C23×D7112yes—
966C2×C7—26no—
967C2×C7—42no—
968C2×C7—42no—
969C2×C7#358612yescomplemented
970C2×C7C24×D411yescharacteristic
971D7—22no—
972D7—26no—
973D7—42no—
974D7—46no—
975C23—21no—
976C23—21no—
977C23—71no—
978C23—73no—
979C23—712no—
980C23—144no—
981C23—1412no—
982C23—141no—
983C23—143no—
984C23—1412no—
985C23—286no—
986C23—284no—
987C23—566no—
988C23—566no—
989C23C2×D4×D713yes—
990Q8—212no—
991Q8—23no—
992Q8—212no—
993Q8—23no—
994Q8—712no—
995Q8—76no—
996Q8—72no—
997Q8—1412no—
998Q8—1424no—
999Q8—1412no—
1000Q8—1412no—
1001Q8—143no—
1002Q8—141no—
1003Q8C2×D4×D714yes—
1004Q8C24×D716yes—
1005Q8C24×D716yes—
1006D4—212no—
1007D4—212no—
1008D4—21no—
1009D4—21no—
1010D4—724no—
1011D4—72no—
1012D4—76no—
1013D4—712no—
1014D4—1412no—
1015D4—1424no—
1016D4—1412no—
1017D4—1412no—
1018D4—144no—
1019D4—144no—
1020D4—1412no—
1021D4—1412no—
1022D4—1412no—
1023D4—1412no—
1024D4—143no—
1025D4—141no—
1026D4C2×D4×D7112yes—
1027D4C24×D712yes—
1028D4C24×D712yes—
1029C2×C4—212no—
1030C2×C4—212no—
1031C2×C4—23no—
1032C2×C4—23no—
1033C2×C4—212no—
1034C2×C4—212no—
1035C2×C4—712no—
1036C2×C4—71no—
1037C2×C4—73no—
1038C2×C4—76no—
1039C2×C4—72no—
1040C2×C4—72no—
1041C2×C4—712no—
1042C2×C4—712no—
1043C2×C4—76no—
1044C2×C4—1412no—
1045C2×C4—1424no—
1046C2×C4—1412no—
1047C2×C4—1412no—
1048C2×C4—1412no—
1049C2×C4—1424no—
1050C2×C4—144no—
1051C2×C4—1412no—
1052C2×C4—1412no—
1053C2×C4—141no—
1054C2×C4—143no—
1055C2×C4—1412no—
1056C2×C4—1412no—
1057C2×C4C2×D4×D716yes—
1058C2×C4C2×D4×D713yes—
1059C2×C4C24×D716yes—
1060C2×C4C24×D711yescharacteristic
1061C8—76no—
1062C8—72no—
1063C8C24×D716yes—
1064C8C24×D712yes—
1065C7C2×#358611yescharacteristic, complemented, Sylow
1066C22—26no—
1067C22—22no—
1068C22—22no—
1069C22—42no—
1070C22—42no—
1071C22—72no—
1072C22—76no—
1073C22—142no—
1074C22—146no—
1075C22—142no—
1076C22—146no—
1077C22—2812no—
1078C22—288no—
1079C22—282no—
1080C22—286no—
1081C22—5612no—
1082C22—5612no—
1083C22C22×D4×D716yes—
1084C22C22×D4×D711yescharacteristic
1085C4—26no—
1086C4—26no—
1087C4—72no—
1088C4—76no—
1089C4—142no—
1090C4—146no—
1091C4C22×D4×D716yes—
1092C4C22×D4×D711yescharacteristic
1093C4C25×D711yescharacteristic
1094C2—26no—
1095C2—42no—
1096C2—42no—
1097C2—142no—
1098C2—146no—
1099C2—282no—
1100C2—286no—
1101C2#1174427912yesdirect product factor
1102C2C23×D4×D711yescharacteristic
subgroupG/H
centerC22C22×D4×D7
commutator, cosocleC4×C7C26
FrattiniC4C25×D7
FittingC2×C7×#578C2
socleC22×C7C23×D4
hypercenterC2×#578D7
hypocenterC7C2×#3586
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×D7×2−1+4C2semidirect
2. C2×#90620C2semidirect
3. C2×C7×#578C2semidirect
4. C2×#90529C2semidirect
5. C2×#90528C2semidirect
6. #11744279C2direct (N × H)
7. C2×#90470C2semidirect
8. C2×#90469C2semidirect
9. C2×#90468C2semidirect
10. C2×D7×#137C2semidirect
11. C2×#90461C2semidirect
12. C2×#90459C2semidirect
13. C2×#90457C2semidirect
14. C22×#6481C2semidirect
15. C2×#90442C2semidirect
16. C2×#90441C2semidirect
17. C2×C7×2−1+4C22semidirect
18. C2×C7×2−1+4C22semidirect
20. #90620C22semidirect
22. D7×2−1+4C22semidirect
24. C2×#6554C22semidirect
25. C2×#6554C22semidirect
27. C2×#6553C22semidirect
28. C2×#6553C22semidirect
33. C2×D7×#41C22semidirect
36. C2×#6551C22semidirect
37. C2×#6551C22semidirect
41. C22×Q8×D7C22semidirect
42. C7×#578C22semidirect
43. C2×C7×#137C22semidirect
44. C2×C7×#137C22semidirect
45. C2×C7×#135C22semidirect
46. C22×C7×Q16C22semidirect
47. C2×C7×#131C22semidirect
48. #90529C22semidirect
49. #90528C22semidirect
50. C2×#6514C22semidirect
51. C2×#6513C22semidirect
52. C2×#6513C22semidirect
53. C2×#6512C22semidirect
54. C2×#6511C22semidirect
55. C22×#1144C22semidirect
56. C2×#6505C22semidirect
57. C2×#6505C22semidirect
58. C22×#1143C22semidirect
59. #90470C22semidirect
60. #90469C22semidirect
61. #90468C22semidirect
62. D7×#137C22semidirect
63. #90461C22semidirect
64. #90459C22semidirect
65. #90457C22semidirect
66. C2×#6482C22semidirect
67. C2×#6481C22semidirect
68. C2×#6481C22semidirect
69. C2×#6481C22semidirect
70. C2×#6481C22semidirect
71. C2×#6481C22semidirect
72. C2×#6481C22semidirect
73. C2×D7×Q16C22semidirect
74. C2×#6479C22semidirect
75. C2×#6478C22semidirect
76. C2×#6478C22semidirect
77. C2×#6477C22semidirect
78. C2×#6477C22semidirect
79. C2×D7×SD16C22semidirect
80. C2×#6474C22semidirect
81. C2×#6474C22semidirect
82. #90442C22semidirect
83. #90441C22semidirect
84. C2×#6472C22semidirect
85. C2×#6471C22semidirect
86. C2×#6470C22semidirect
87. C2×D7×M16C22semidirect
88. C2×#6467C22semidirect
89. C22×#1132C22semidirect
90. C2×#6464C22semidirect
91. C22×#1131C22semidirect
95. C7×2−1+4C23semidirect
96. C7×2−1+4C23semidirect
109. #6554C23semidirect
110. #6554C23semidirect
114. #6553C23semidirect
115. #6553C23semidirect
123. D7×#41C23semidirect
128. #6551C23semidirect
129. #6551C23semidirect
153. C2×Q8×D7C23semidirect
188. C7×#137C23semidirect
189. C7×#137C23semidirect
190. C7×#135C23semidirect
193. C2×C7×Q16C23semidirect
197. C7×#131C23semidirect
200. #6514C23semidirect
201. #6513C23semidirect
202. #6513C23semidirect
203. #6512C23semidirect
204. #6511C23semidirect
208. C2×#1144C23semidirect
209. #6505C23semidirect
210. #6505C23semidirect
214. C2×#1143C23semidirect
221. #6482C23semidirect
222. #6481C23semidirect
223. #6481C23semidirect
224. #6481C23semidirect
225. #6481C23semidirect
226. #6481C23semidirect
227. D7×Q16C23semidirect
228. #6479C23semidirect
229. #6478C23semidirect
230. #6478C23semidirect
231. #6477C23semidirect
232. #6477C23semidirect
233. D7×SD16C23semidirect
234. #6474C23semidirect
235. #6474C23semidirect
236. #6472C23semidirect
237. #6471C23semidirect
238. #6470C23semidirect
239. D7×M16C23semidirect
241. #6467C23semidirect
246. C2×#1132C23semidirect
247. #6464C23semidirect
252. C2×#1131C23semidirect
260. C2×#578D7semidirect
452. C2×2−1+4C2×D7semidirect
453. C2×2−1+4C2×D7semidirect
469. #578C2×D7semidirect
489. C2×#137C2×D7semidirect
490. C2×#137C2×D7semidirect
502. C2×#135C2×D7semidirect
505. C22×Q16C2×D7semidirect
513. C2×#131C2×D7semidirect
619. 2−1+4C22×D7semidirect
620. 2−1+4C22×D7semidirect
712. #137C22×D7semidirect
713. #137C22×D7semidirect
725. #135C22×D7semidirect
734. C2×Q16C22×D7semidirect
755. #131C22×D7semidirect
969. C2×C7#3586semidirect
1065. C7C2×#3586semidirect
1101. C2#11744279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×2−1+42
C2×#906202
C2×C7×#5782
C2×#905292
C2×#905282
#117442792
C2×#904702
C2×#904692
C2×#904682
C2×D7×#1372
C2×#904612
C2×#904592
C2×#904572
C22×#64812
C2×#904422
C2×#904412
C2×#35867